Intelligent Transmission Control Scheme for 5G mmWave Networks Employing Hybrid Beamforming

Abstract

Hybrid beamforming plays a critical role in evaluating wireless communication technology, particularly for millimeter-wave (mmWave) multiple-input multiple-out (MIMO) communication. Several hybrid beamforming systems are investigated for millimeter-wave multiple-input multiple-output (MIMO) communication. The deployment of huge grant-free transmission in the millimeter-wave (mmWave) band is required due to the growing demands for spectrum resources in upcoming enormous machine-type communication applications. Ultra-high data speed, reduced latency, and improved connection are all promised by the development of 5G mmWave networks. Yet, due to severe route loss and directional communication requirements, there are substantial obstacles to transmission reliability and energy efficiency. To address this limitation in this research we present an intelligent transmission control scheme tailored to 5G mmWave networks. Transport control protocol (TCP) performance over mmWave links can be enhanced for network protocols by utilizing the mmWave scalable (mmS)-TCP. To ensure that users have the stronger average power, we suggest a novel method called row compression two-stage learning-based accurate multi-path processing network with received signal strength indicator-based association strategy (RCTS-AMP-RSSI-AS) for an estimate of both the direct and indirect channels. To change user scenarios and maintain effective communication constantly, we utilize the innovative method known as multi-user scenario-based MATD3 (Mu-MATD3). To improve performance, we introduce the novel method of “digital and analog beam training with long-short term memory (DAH-BT-LSTM)”. Finally, as optimizing network performance requires bottleneck-aware congestion reduction, the low-latency congestion control schemes (LLCCS) are proposed. The overall proposed method improves the performance of 5G mmWave networks.

1. Introduction

The demand for high-capacity, low-latency communication has led to the development of 5G mmWave networks. Despite their potential, mmWave communications suffer from significant path loss, limited coverage, and increased susceptibility to interference. With growing needs for high-capacity digital services like video streaming, cloud storage, and real-time industrial automation, mmWave communication stands as a key driver for future wireless networks [1,2]. However, the deployment of 5G mmWave networks is constrained by compelling challenges, such as high path loss, critical signal attenuation, and directional communication limitations, which affect transmission reliability and energy efficiency [3,4]. To overcome these issues, hybrid beamforming (HB) emerges as a potential solution, leveraging the benefits of both analog and digital beamforming to enhance spectral efficiency while minimizing power consumption [5,6]. With HB, base stations (BS) and user equipment (UE) can optimize transmission strategies to achieve maximum data throughput while reducing power consumption [7]. Further, intelligent reflecting surfaces (IRS) have also been investigated as a substitute for enormous MIMO systems, offering better signal propagation by dynamically changing reflection angles [8].

Despite these developments, transmission control optimization in 5G mmWave networks is still a pressing research issue. Legacy TCP is challenged by varying mmWave channel conditions, leading to higher latency and lower link utilization [9]. Several approaches have been suggested to improve network reliability, such as deep reinforcement learning for adaptive beamforming [10], congestion-aware transmission schemes [11], and multi-user hybrid beamforming techniques [12]. Nevertheless, current methods do not effectively handle interference, congestion, and real-time adaptability, hence bounding their performance in dynamic network conditions [13,14,15].

An intelligent transmission control scheme for 5G mmWave Networks is presented in this paper to address these problems. In contrast to stacked intelligent metasurface (SIM) techniques [16], which need cascaded reconfigurable layers, our system integrates machine learning, IRS-assisted NLOS connections, and hybrid beamforming (HB) to achieve similar performance with less complicated hardware. This suggested plan incorporates the following:

• Addresses the limitations of classic TCP in mmWave dynamic scenarios by proposing a new mmS-TCP protocol and low latency congestion control schemes to enhance throughput and minimize latency in 5G mmWave networks.
• The row compression two-stage learning-based accurate multipath process network with received signal strength indicator-based association strategy (RCTS-AMP-RSSI-AS) is proposed to reduce training costs and improve the accuracy of both direct and cascaded channel estimates in IRS-assisted mmWave systems.
• Combines digital and analog hybrid beam training with long short-term memory (DAH-BT-LSTM with Mu-MATD3), which optimizes beamforming, enhances spectrum efficiency and interference management, and deals with multi-usr situations.

The proposed framework’s performance is evaluated using simulation experiments in a 5G mmWave network environment simulated with NS-3.35 and Python 3.9.6. The evaluation metrics include throughput, end-to-end delay, packet loss rate, beamforming accuracy, and SNR. The remainder of this paper is structured as follows: Section 2 presents a literature review of related works. Section 3 details the system model. Section 4 introduces the proposed methodology. Section 5 discusses the experimental setup and performance evaluation, followed by the conclusion and future research directions in Section 6.

2. Literature Survey

The authors of [16] examined three 5G technology concepts, implementations, contrasts, and debates, while taking beamforming and precoding techniques into account. However, when a lot of antennas and radio frequencies (RFs) are employed, these technologies become more sophisticated. In addition, the pilot contamination issue, which could restrict the number of scheduled users and reduce the effectiveness of the channel estimation, needs to be addressed by an additional study that takes practical implementation into account.

The authors of [17] proposed a unique handover mechanism that ensures the quality of service (QoS) of each of the user equipment (UE) and optimizes both the total system delay and throughput. In particular, optimization theory and the reinforcement learning (RL) algorithm are integrated into the suggested handover system known as O-MAPPO. Determining handover trigger conditions involves an RL technique called multi-agent proximal policy optimization (MAPPO). Moreover, they use a Handover (HO) penalty technique to increase system efficiency by preventing needless HO and lowering the HO rate.

The authors of [18] provided dependable wireless communications and examined an anti-jamming HB design in millimeter-wave (mmWave) massive MIMO systems. Unlike the conventional systems designed under the presumption of perfect jamming and channel state information (CSI), we investigate two HBF topologies, including partial connections. Furthermore, they have shown that the LNAPS-based HBF system is free from small communication channel flaws, implying feasible protection against jamming assaults.

The authors of [19] suggested a UAV relay-assisted multi-BS mm-wave massive MIMO system with HB architecture, which prevents abrupt link disconnections brought on by high path loss and LoS obstruction in the mm-wave frequency band. This system enables the use of UAV relay-based architecture in serving various ground BS-user pairs. In upcoming work, they will solve the computational complexity issue and investigate possible UAV relaying systems considering channel estimates.

The authors of [20] proposed intelligent DAPS (I-DAPS) HO, a unique learning-based DAPS HO technology that avoids abrupt radio link failure (RLF) while maintaining a high data rate The proposed I-DAPS HO uses a Double Deep Q-network (DDQN) deep reinforcement learning (DRL) framework to generate blockage predictions based on historical signal data, therefore enabling RLFs to be actively avoided. In scenario A, the recommended I-DAPS HO completes HO before the RLF; hence, I-DAPS HO experiences a 0 ms MIT and achieves an average throughput gain of 247.29 Mbps and 589.81 Mbps.

The authors of [21] proposed many handover (HO) solutions that can provide a near-zero mobility interruption time (MIT) to ensure smooth real-time connectivity for 5G applications. However, we look into how to apply selection schemes by utilizing the results of two different DNNs.

The authors of [22] created an algorithm known as alternating optimization (AO). They tackled the resource distribution challenge by maintaining the hybrid beamforming and RIS phase shifts, and the phase shifts, analog beamforming, and transmit beamforming were designed, respectively, using an alternating manifold optimization (AMO)-based approach and a sequential convex approximation (SCA)-based method, given the power allocation matrix. However, because the RIS is realized passively, obtaining the CSI is challenging. Therefore, in subsequent research, we create a reliable transmission scheme in a RIS-assisted mmWave system by fusing the suggested algorithm with the MMSE approach.

The authors of [23] downlinked a millimeter wave (mmWave) multi-user massive MIMO system and proposed an HB design framework for interference cancellation (IC). Depending on the provided architecture, three HB methods 34re developed employing successive interference cancellation (SIC) to resolve intra- and inter-user interference. Specifically, the previous approach uses interference SIC to remove interference within a user and zero-forcing (ZF) to remove interference between users. The development of efficient IC-assisted HB research for wide mmWave channels and partially connected topology, which may become increasingly prevalent in future applications, is one possible extension of the current study.

The authors of [24] proposed a novel mmWave technique to address obstruction concerns with the support of an intelligent reflecting surface (IRS). By maximizing the communication capabilities of the equipment, the IRS’s active beamforming, and the many users’ detectors of the base station concurrently, the method lowers the power required by the users in a multi-user mmWave system, thus achieving latency standards.

The authors of [25] used neural networks (NNs) to solve the channel estimation issue in full-duplex mmWave MIMO systems. In the method, user equipment (UE) and transmit antennas at the base station (BS) share pilot resources to lower pilot overhead in full-duplex systems and bring it down to a level equivalent to that of half-duplex systems. The channel from the downlink UEs to the receive antenna (RX) arrays is mapped to the channel from the TX arrays to the downlink UEs using a neural network (NN) to solve this.

The authors of [26] introduced a reconstruction and recovery network-based innovative method for channel estimation in high mobility scenarios. To rebuild channel pictures using the fast super-resolution convolution neural network (FSRCNN). Next, to lower channel noise and increase channel estimate accuracy, the denoising convolutional neural network (DnCNN) was used.

The authors of [27] provided a successful frequency-selective channel estimate technique based on the training channel model in an urban traffic setting. Given the sparsity of the subcarrier multi-channels and the sparsity of the realistic mmWave MIMO channel, they considered the channel estimation issue as the sparse channel recovery and provided a multipath simultaneous matching tracking estimation approach. A certain correlation between the practical channels’ noise is believed to exist, and this correlation affects the choice of the best atomic support set throughout the channel recovery procedure.

The authors of [28] used quantum computing technology to build an enhanced quantum singular value (IQSV)-based channel estimation strategy for large multiple-input multiple-output (MIMO) millimeter-wave (mmWave) systems. Ultimately, the revised quantum state data extraction method reported in this work is able to effectively extract the amplitude, phase, and symbol information of the output quantum state data.

Table 1. Overview of the literature survey.

References	Method	Advantages	Limitations
[16]	Precoding/beamforming survey	A thorough classification of 5G methods	Pilot pollution lacks practical remedies
[17]	Reinforcement learning (RL) algorithm and optimization theory	Improves throughput and QoS	High computational cost for real-time decisions
[18]	Anti-jamming hybrid beamforming	Robust to imperfect CSI	Limited single-user environment
[19]	Unmanned aerial vehicle-relayed mmWave MIMO	Removes LoS obstructions	High complexity in channel estimation
[20]	I-dual active protocol stack (DAPS) handover (HO)	Uses proactive handover to avoid RLF	Needs a lot of previous signal data
[21]	Multiple active protocol stack, handover	Minimal disruption to the movement	Dual DNNs are needed, which raises overhead
[22]	Alternating optimization-based RIS optimization	Joint IRS/beamforming design	Assumes stable reflection angles and passive RIS
[23]	Hybrid analog and digital BeamForming	Eliminates interference between and within users	Only functions with HBF designs that are completely linked
[24]	Intelligent reflecting surface-assisted mmWave NOMA	Enhances the energy efficiency	Limited to static users
[25]	Neural network-based full-duplex CE	Reduces full-duplex pilot overhead	TX-RX antenna separation is necessary (hardware limitation)
[26]	Fast super-resolution convolutional neural network, denoising convolutional neural network channel estimation	Manages situations involving excessive mobility	Computationally demanding (processing images)
[27]	Sparse recovery CE	Dependable in situations with several paths	Assumptions that are sensitive to noise correlation
[28]	Quantum-based channel estimation	Low overhead	Need quantum hardware

shows the general summary of the literary review.

The authors of [29] examined the channel estimates for RIS-assisted millimeter-wave communications. By assuming that homogeneous arrays provide “the array manifolds of the base station antennas and the RIS”, an efficient two-stage channel estimate strategy was proposed that depended on array signal processing techniques. Then, some practical issues are examined, including complexity, faulty RIS hardware, and channel path counting.

• More pilot symbols are required when there are direct channels, as they only consider indirect channel estimation. The proposed approach for channel parameter estimation has a small training overhead suitable in both cases with and without direct channels.

The authors of [30] proposed deep reinforcement learning (DRL)-based network partitioning techniques. Furthermore, they created a novel hybrid analogy beam-steering digital beamforming model that simultaneously maximizes the instantaneous sum rate of all UEs within each sub-network and zero-forces interference amongst different cell-free sub-networks to mitigate interference between them. The HB model is implemented using a special coupled DRL-convex optimization method.

• Changing the CSI has a big effect on the variance and convergence rate of DRL methods, such as the SARSA algorithm.

The authors of [31] intended to assess the performance of an adaptive beamforming technique. Here, beamforming is accomplished under the guidance of a predefined set of configurations that, by appropriately producing highly directional beams on demand, can manage a spectrum of traffic conditions. Concurrent with this, a machine learning (ML) beamforming method is also investigated. This technique uses the k-nearest neighbors (k-NN) approximation and is trained to provide suitable beamforming configurations based on the spatial distribution of throughput demand.

• In this instance, thorough beamforming designs that would possibly permit the admission of additional users in the orientation are excluded.

The authors of [32], because of the super-resolution technology, suggested a low overhead analog beam selection strategy based on deep learning. To put it in practical terms, beam quality estimation based on partial beam observations was carried out by deep neural networks. Our proposed technique covers all directions of arriving signals with little overhead by means of codebooks with different beam widths. The deconvolution scenario, on the other hand, requires more time to train the parameters, which causes a rather slower training rate every epoch.

The authors of [33] proposed an analog deep neural network (ADNN) structure, which can be applied to conventional RF components. This structure is integrated into an extended hybrid analog–digital deep neural network (HDNN). MIMO systems make implementation easier.

• Nevertheless, a bottlenecking impact in the information flow from the digital DNN to the ADNN and vice versa may affect the HDNN, depending on the particular task.

The authors of [34] simulated and studied the uplink in a two-hop 5G new radio cooperative system using relay nodes (RNs) in millimeter bands. They examined two uplink mmWave MIMO decode-and-forward (DF) relaying methods under the assumption that the uplink channel is fully understood and that the uplink channel is estimated using the least squares (LS) algorithm.

• Here, using the new ratio for transmission achieves the lower throughput.

To improve the performance of 5G mmWave networks, several new schemes are proposed herein along with the use of the terms RCTS-AMP-RSSI-AS for channel estimation, Mu-MATD3 for user scenarios, DAH-BT-LSTM for beam training, and LLCCS for congestion control. These schemes tackle the issues of path loss and directional communication to achieve improved data speed, latency, and connectivity.

3. System Model

The proposed intelligent transmission control scheme is designed for a 5G mmWave network environment characterized by hybrid analog–digital beaming, multiple-user nodes, and an intelligent reflecting surface (IRS) for non-line-of-sight (NLOS) conditions. The mmWave base station is provided with a hybrid analog–digital beamforming mechanism, and the user devices are equipped with adaptive antenna arrays for directional transmission.

• Network components

Base station (BS): We used a 4-element hybrid beamforming antenna array, which was tasked with pointing signals at multiple users. User node (UN): All users were fitted with a 100-element antenna array, which can facilitate adaptive beamforming to provide robust communication links. When direct transmission is disrupted, IRSs backscatter the BS signals toward consumers.

3.1. Comparative Study of Methodologies Based on Metasurface

The IRS-assisted method (Equations (13)–(15)) employs a single-layer reconfigurable surface alongside hybrid analog–digital precoding, whereas stacked intelligent metasurfaces (SIM) [35] utilize multi-layer phase-shift configurations to enhance beamforming gain. This design decision results in reduced calibration overhead; SIM requires the simultaneous optimization of stacked layers, whereas RCTS-AMP-RSSI-AS optimizes the IRS coefficients (Section 4.2). Energy consumption: Power usage diminishes with a reduction in active components. Implementation cost: In densely populated metropolitan settings, SIM hardware is overly complex [36], but our HB-IRS integration is compatible with the existing 5G infrastructure.

3.2. Communication Links

The transmission involves two types of links, direct line-of-sight (LOS) and indirect sight (NLOS) links.

• Direct link: LOS connection between BS and UN.
• Indirect link: NLOS condition, where signals reflect off the IRS before reaching the user.

The mobile millimeter-wave (mmWave) bands have unique propagation and scattering behavior, which are characterized by high path loss, sparse multipath propagation, and a variety of blockages; thus, the mmWave channel can be modeled using the Saleh–Valenzuela model, which can model both the large-scale fading (path loss and shadowing) and the small-scale fading, such as the multipath components with different angles of arrival/angles of departure. The signal received by the user $k$ can be modeled as follows:

$$y_k=H_{BU}W+H_{IRS}\Theta H_{BI}W+n_k$$

(1)

where $H_{BU}$ represents the BS-to-user channel matrix, $H_{IRS}$ and $H_{BI}$ are the IRS-to-user and BS-to-IRS channel matrices, $W$ is the hybrid beamforming matrix at the BS, $\Theta$ represents the IRS reflection coefficient, $x$ is the transmitted signal coefficient, and $n_k$ is the additive noise.

• Environmental Description:

Channel model: The mmWave channel is described as a mixture of large-scale fading (path loss, shadowing) and small-scale fading (multipath components). The Saleh–Valenzuela model is utilized to represent the channel as follows:

$$H={\sum }_{l-1}^L{\alpha }_l{a}_r\left({\theta }_{r,l}\right)a_t^H\left({\theta }_{t,l}\right)$$

(2)

where $L$ is the number of multipath components, ${\alpha }_l$ denotes the complex path gain of the $l^{th}$ path, ${\theta }_{r,l} \mathrm{a}\mathrm{n}\mathrm{d} {\theta }_{t,l}$ are the angles of arrival and departure, and $a_r$ and $a_t$ are the array response vectors at the receiver and transmitter.

3.3. Interference and Noise Considerations

The interference is simulated as zero-mean additive white Gaussian noise (AWGN) with variance ${\sigma }^2$. Interference in the mmWave band is low because of very directional beams; yet, inter-user interference (IUI) is taken into account in a multi-user environment. The signal-to-interference-plus-noise Ratio (SINR) at user $k$ is shown as follows:

$${SINR}_k={\displaystyle \frac{{\left|h_k{w}_k\right|}^2}{\sum _{j\ne k}{\left|h_k{w}_j\right|}^2+{\sigma }^2}}$$

(3)

where $h_k$ and $w_k$ are the channel vector and beamforming weight for user k.

Mobility model: User mobility is simulated through the Gauss–Markov mobility model, updating the direction and velocity of users at every time step to make movement realistic in dynamic environments.

• Mathematical Formulations

Beamforming optimization model: To maximize the data rate with minimal power consumption, the problem of beamforming optimization can be defined as follows:

$$\underset{w,\mathsf{\Theta }}{\max }{\sum }_{k-1}^K{log}_2(1+{SINR}_k)$$

(4)

Subject to the following:

$${‖W‖}^2\le P_{max,} \mathsf{\Theta }=diag(e^{j{\varphi }_1},\dots ..e^{j{\varphi }_N})$$

(5)

where $P_{max,}$ is the maximum transmit power, and $\mathsf{\Theta }$ consists of IRS phase shift coefficients.

• Congestion Control Mechanism

The mmS-TCP congestion window (cwnd) adaptation follows the following equation:

$${cwnd}_{t+1}={cwnd}_t+\alpha ·{\displaystyle \frac{{RTT}_{min}}{{RTT}_t}}$$

(6)

where $\alpha$ is the learning rate for congestion control, and ${RTT}_{min}$ and ${RTT}_t$ are the minimum and current round-trip times.

4. Proposed Work

The main goal and scope of this research are to channel estimation accuracy, beamforming efficiency, training speed, and overall network throughput. The overall architecture of the proposed method is illustrated in Figure 1. Here, the proposed methodology is detailed and discussed below:

• Network protocol;
• Channel estimation;
• Beamforming;
• Train the beamforming;
• Bottleneck-aware congestion mitigation.

4.1. Network Protocol

For network protocols, TCP performance over mmWave links can be enhanced by utilizing the mmS-TCP. Because of the extremely fluctuating mmWave channel’s low link utilization, the current TCP is unable to offer enough throughput. The design aim of 5G cannot be realized since throughput may improve but “Round-Trip Time (RTT)” will also increase depending on the mmWave base station queue management approach used. Therefore, to meet the 5G design target of a rapid delivery rate and extremely low latency simultaneously, the current TCP congestion control technique was adjusted to enhance link consumption, and the AQM approach has been added to lower end-to-end delay. The S-TCP approach to traffic window increase or decrease was first adjusted to improve TCP flow stability while preserving high throughput. Moreover, mmWave base stations were equipped with the CoDel queue management technique to avoid buffer bloat and reduce end-to-end latency.

4.1.1. Scalable TCP for 5G MmWave Networks

S-TCP offers excellent performance and expandability. Previously, in high “Bandwidth-delay product (BDP)” networks, NewReno TCP decreased cwnd by half after each packet loss, resulting in a notable decrease in link utilization. S-TCP enhances link utilization by accelerating the growth of cwnd compared to NewReno TCP. Similar to NewReno TCP, the cwnd increase and decrease process in S-TCP is determined by packet loss and acknowledgments. For each ACK received, the following is true:

$$cwnd\leftarrow cwnd+0.01$$

(7)

For each packet loss, the following is true:

$$cwnd\leftarrow cwnd-[0.125-cwnd]$$

(8)

Equation (8) S-TCP manages reduction in the congestion window (cwnd) due to packet loss. S-TCP, unlike other classical TCP congestion control approaches like NewReno TCP that normally drop the cwnd to half of the current value at the first loss detection, reduces cwnd gradually by a factor of 0.125 in every packet loss incidence (except retransmission timeout). This method avoids unnecessary cwnd reduction, which would otherwise cause long recovery time in high-speed networks. With the use of a smaller reduction factor, S-TCP guarantees a quicker recovery process, thus minimizing the overall time taken for TCP to achieve its original transmission rate. For instance, for a 10 Gbps connection, this adaptive reduction process enables TCP to recover in about 15 s as opposed to the traditional 4 h recovery period. This method enhances the stability of S-TCP with high throughput and fairness in mmWave networks.

4.1.2. Enhanced mmWave Scalable TCP Protocol

Modifications were implemented to the Cwnd growth and reduction procedures in S-TCP to enhance stability and ensure high throughput in mmWave networks. The enhancement of the raise or lower approaches augments S-TCP’s equity and stability in the mmWave network without compromising its throughput.

Mathematical Analysis of cwnd Growth in mmS-TCP

TCP’s congestion window (cwnd) regulates how many packets may be sent before an acknowledgment. Traditional TCP congestion control methods, such as NewReno, halve cwnd when packet loss is detected, causing underutilization in low-latency, high-bandwidth mmWave networks.

We suggest the following modified cwnd update rule:

After seeing an ACK, cwnd boosts as follows:

$$Cwnd-cwnd+1/b$$

where $b$ is incremented up to a threshold (e.g., 125).

When packet loss is detected (apart from retransmission timeouts), cwnd decreases as follows:

$$Cwnd-cwnd-0.125\times cwnd$$

Instead of the traditional halving.

The modified additive increase guarantees quicker recovery without being too aggressive in high-speed networks. The $b$ parameter controls the growth rate dynamically so that there is gradual adaptation according to network conditions. In comparison to NewReno, which increases linearly (one segment per RTT), the proposed technique guarantees a higher throughput with improved stability in dynamic mmWave scenarios.

The conventional TCP congestion control cuts cwnd by 50%, which, in high-speed networks can be too aggressive and results in excessive underutilization over the long term. The suggested 0.125× reduction makes smoother adaptation possible and prevents sudden drops in throughput, allowing faster recovery and improved multi-user fairness. This mechanism is consistent with delay-based congestion control mechanisms and provides enhanced TCP fairness in multi-flow environments.

Cwnd Raise the Mechanism of mm-Scalable TCP

MmS-TCP can enhance TCP fairness by altering the cwnd increase mechanism. Upon receiving 100 ACKs, S-TCP increments the cwnd size by 1 packet. Receiving 100 ACKs when sending one packet consistently results in a quicker delivery rate compared to NewReno. On the other hand, a sudden rise in S-TCP could harm other TCP flows with different congestion controls. To reduce the aggressiveness of S-TCP and avoid a drop in quantity, we modified the growth rate of continuous cwnd as follows for whenever an ACK is established:

$$cwnd\leftarrow 1/b$$

(9)

where b is increased by 1 each time and ACK is received until it reaches 125. Whenever an ACK is established, the S-TCP value rises by 1/100; when 100 ACKs are established, the cwnd rises by one container. The growth rate and level of aggressiveness of S-TCP are dictated by the value of b of Equation (7). When the value of b is low, S-TCP will rise quickly, whereas when b is high, the cwnd will increase at a slower pace.

cwnd Reduction Mechanism of mm-Scalable TCP

The mmS-TCP cwnd reduction feature is designed to prevent high packet losses during the start of a connection and to improve network reliability. In all instances of packet loss, excluding “Retransmission time-out (RTO)”, S-TCP reduces cwnd by 0.125, as illustrated in Equation (8). In the initial phase, the congestion window (cwnd) may exceed the connection’s capacity due to the bottleneck buffer size; a decrement of 0.125 in cwnd could lead to additional retransmission timeouts (RTO) and initiate a recurrence of the delayed start phase.

Multiple instances of a slow start phase may result in numerous packet losses during the initial stages of a TCP connection, impacting other flows that utilize the same connection. Although S-TCP’s repeated slow-start phases resulted in numerous duplicated ACKs, mmS-TCP managed to greatly decrease the occurrence of duplicated ACKs during the initial connection, ultimately leading to enhanced network stability and a slight increase in throughput.

With improved network stability and throughput, we have therefore obtained good results with the mmS-Transport Control Protocol. To proceed, we process this network protocol using channel estimation.

4.2. Accurate Channel Estimation for mmWave Systems

For IRS-assisted mmWave systems, this study suggests a “two-stage LAMP network with row compression (RCTS-LAMP)” to address the combined estimation problem of direct and cascaded channels. Specifically, by utilizing the deep unfolding technique, the suggested RCTS-LAMP is a model-driven neural network that combines the benefits of “deep learning (DL)” and “compressive sensing (CS)”. In this way, we can recover the direct and cascaded channels with CS under low training overhead, and the joint optimization of DL and DL may greatly enhance the estimation performance. We employ an innovative technique termed row compression two-stage learning-based accurate multi-path processing network with “received signal strength indicator association strategy” (RCTS-AMP) to estimate the channel in both direct and indirect pathways. They propose a correlation based on the intensity of the received signal indication to ensure that clients obtain the optimal average energy.

The technique takes into account the differences “between LOS and non-LOS mmWave” broadcasts that use the “received signal strength indicator-based association strategy (RSSI-AS)”. For channel estimation, we used the novel method called row compression two-stage learning-based accurate multi-path processing network with “received signal strength indicator-based association strategy” (RCTS-AMP- RSSI-AS)”, prior to exploring the particulars of the proposed RCTS-LAMP. This section briefly analyzes the LAMP network developed to address the sparse data issue in signal recovery.

Table 2. Notations of symbols.

Symbol	Definition	Symbol	Definition
$H$	Channel matrix in mmWave communication	$RSSI$	Received signal strength indicator
$A$	Measurement matrix used in LAMP network	$P_{signal}$	Received signal power
$\lambda$	Soft-thresholding parameter	$P_{noise}$	Noise power in mmWave communication
$b$	Congestion window growth rate (cwnd)	$T_{delay}$	End-to-end delay (ms)
${\mathsf{\theta }}_{A_{0}A}$	Angle of arrival	$\mathrm{L}\mathrm{A}\mathrm{M}\mathrm{P}$	Learned approximate message passing network
${\mathsf{\theta }}_{A_{0}D}$	Angle of departure	$RTT$	Round trip time
$MSE$	Mean squared error	$PL$	Packet loss percentage
$SNR$	Signal-to-noise Ratio	$T_{throughput}$	Throughput (Mbps)
$N_u$	Number of users	$LSTM$	Long short-term memory network
$cwnd$	Congestion window size (TCP)	$LLCCS$	Low-latency congestion control scheme
$DAH-BT$	Digital and analog hybrid beam training

delineates the notations of symbols.

4.2.1. Sparse Signal Recovery Using LAMP Network

The TRICE framework, in contrast to its counterpart, requires AMP as an iterative thresholding algorithm that directly restores the sparse angular channel by estimating the true spatial frequencies with the soft-thresholding function. Therefore, we can reconstruct every trajectory of the linked channel by utilizing grid points that are near the actual spatial frequencies. While the AMP algorithm works well for sparse recovery in general, its channel estimation performance is constrained by using identical linear transform matrices and shrinkage parameters throughout all iterations. To enhance AMP’s efficiency for the issue of cascaded channel estimation, it is possible to unfold the AMP algorithm iterations into trainable layers using deep unfolding, as follows:

$${\tilde{H}}_{e,k}^d=\mathcal{T}({\tilde{H}}_{e,l-1}^d+X_l{Y}_{l-1});{\displaystyle \frac{{\alpha }_l}{\sqrt{AH}}}\Vert Y_{l-1}\Vert$$

(10)

$$Y_l=Z-Q_l{\tilde{H}}_{e,k}^d+{\displaystyle \frac{1}{AH}}{\Vert {\tilde{H}}_{e,k}^d\Vert }_0{Y}_{l-1}$$

(11)

where ${\tilde{H}}_{e,k}^d$ and $Y_l$, the calculated angles, are, respectively, the series of communication channels and the remaining interference set as the initial values ${\tilde{H}}_{e,k}^d=0 \mathrm{a}\mathrm{n}\mathrm{d} Y_0=Y.$ $X_l$ is the consistent CS literature notation. The function $\mathcal{T}$, known as a soft-thresholding operator, has additional features that offer noise reduction functionality as well as enhancing clarity ${\tilde{H}}_{e,k}^d$, taking into account the lack of density. The definition of the function pertaining to the soft-thresholding approach is shown as follows:

$$[{\mathcal{T}(X; \lambda )]}_k=\left(X_k-\lambda {\displaystyle \frac{X_k}{\left|X_k\right|}}\right) I(\left|X_k>\lambda \right|)$$

(12)

At index negative lambda, the absolute value is represented by a larger than symbol, which may reduce the elements of the set to zero if their amplitude is lower than the function that acts as an indicator.

Additionally, the term ${\displaystyle \frac{1}{AH}} {\Vert {\tilde{H}}_{e,k}^d\Vert }_0{Y}_{l-1}$ is introduced for the calculation of $Y_l$ to accelerate convergence. To boost the cascaded channel approximation demonstration, we can optimize ${\{Q_l, X_l,{\alpha }_l\}}_{l=1}^L$ as the tuneable parameters of the LAMP network through DL, where the linear transform matrices ${\{ Q_l\}}_{l=1}^L \mathrm{a}\mathrm{n}\mathrm{d} {\left\{X_l\right\}}_{l=1}^L$, respectively, replace the measurement matrix $A$ and the matched filter $A^H$ in the original AMP, and ${\{ {\alpha }_l\}}_{l=1}^L$ denotes the shrinkage parameters for the soft-thresholding function. Lastly, the cascaded channel is improved by altering the valued angular cascaded channel ${\tilde{H}}_{e,L}^d$ into the time domain channel via the following:

$$H_{e,L}^d=(A_S^{\ast }⨁A_B){\tilde{H}}_{e,L}^d$$

(13)

Nevertheless, the LAMP system solves the combined recovery issue to directly restore the cascaded channel.

$$Z=vec\left(Y\right)\approx \left({\Theta }^T\otimes Q^H\right)vec\left(A_B\widetilde{H_c}{A}_S^H\right)+n=\left({\Theta }^T\otimes Q^H\right)\left(A_S^{\ast }\otimes A_B\right){\tilde{H}}_e+n=A{\tilde{H}}_e+n$$

(14)

Somewhere, ${\widetilde{ H}}_e=vec \widetilde{{(H}_c}) \in C^{K_b{K}_s\times 1}$, $n=vec \left(N\right)\in C^{AT\times 1}, \mathrm{a}\mathrm{n}\mathrm{d} A=\left({\Theta }^T\otimes Q^H\right) \left(A_S^{\ast }\otimes A_B\right)$. The angular cascaded channel ${ \tilde{H}}_e$ is recovered directly in the joint CS method using the 3D measurement matrix A made up of $K_b{K}_s$ atoms. Each particle characterizes an AoA at the BS and a pair of active and advancement AoDs at the IRS. The computational difficulty of the LAMP network is $O(LT {AK}_b{BK}_s$), and even with lower grid resolutions, the computational cost is too high for practical systems. To solve this problem, our suggestion is a “two-phase LAMP network that incorporates row compression (RCTS-LAMP)” for sequential channel estimation. This will raid an improved trade-off between estimation enactment and computational intricacy.

Enhanced Two-Stage LAMP Network with Row Compression

Instead of the joint CS method, which directly retrieves $\widetilde{H_c}$ utilizing a single LAMP network and the 3D measurement matrix $A$, the proposed “two-stage LAMP (TS-LAMP)” network sequentially retrieves $\widetilde{H_c}$ with two LAMP networks. Therefore, the TS-LAMP network can take advantage of this approach by utilizing an efficient LAMP network, and it can benefit from reduced complexity by breaking down the process of channel recovery. Furthermore, it also utilizes the angular cascade’s sparsity in rows. In channel $\widetilde{H_c}$, a row compression (COMP) mechanism is introduced to detect the row support $\widehat{\Omega }$. Hence, the suggested RTCS-LAMP network is capable of further decreasing the computational burden streamlining by just recovering the rows of matrix $\widetilde{H_c}$ that are on the row back $\widehat{\Omega }$. The LAMP network utilizes the structure that resides in the overall measurement matrix $Y$, as follows:

$$Y\approx B_1 \widetilde{H_c} B_2^T+N$$

(15)

where $B_1=Q^H{A}_B ϵ C^{{A\times K}_b} \mathrm{a}\mathrm{n}\mathrm{d}$ $B_2={\theta }^T{A}_S^{\ast }ϵ{ C}^{{T\times K}_s}$ are the matching extent conditions for $\widetilde{H_c}$ at the BS and IRS. According to the row organization of $\widetilde{H_c}$, the suggested TS-LAMP is designed for the network to break down the series channel estimation into two parts, as outlined in Algorithm 1, to develop a more simplified estimation of the mmWave cascaded channel.

Step 1: Several rows should be parceled off with a LAMP network to recover a row-sparse matrix. During this stage, only the most significant rows are selected, and this stage compresses the channel.

Step 2: Once the row support is computed in step 1, a second LAMP network will estimate the angular cascaded channel using only the support of the compressed row. The output is now the full cascaded channel estimate after transforming from angular domain back into time domain.

The benefit appears to be in cutting the computational time down whilst maintaining a good level of accuracy by taking something challenging and breaking it down into two less challenging transformations. One should begin by laying the foundation and setting the groundwork to address the row-sparse matrix recovery issue, as follows:

$$Y=B_1{H}_{row}+N$$

(16)

where $H_{row}=\widetilde{H_c}{B}_2^T$ is an $L_G$ row-sparse matrix since is $\widetilde{H_c}$ has $L_G$ non-zero rows. Note that the recovery of $H_{row}$ is an MMV problem, where each column of $H_{row}$ results in a “single measurement vector (SMV)”. Since all the vectors in $Y$ result from the common measure matrix $A_1$, we can address MMV concerning Equation (16) using only one LAMP network with concurrent processing. While the measurement matrix $A$ is in use by using the collaborative CS approach, we can create the initial LAMP system to recover the columns from the equivalent measure matrix $A_1$ of Originate by running all the SMV simultaneously through parallel computation. In $Y$, the rows of $H_{row}$ can be concurrently recreated within the original LAMP network. The result from the initial network is referred to as $H_{row}$; it represents the approximate value of $H_{row}$. In the next step, the angular cascaded channel $\widetilde{H_c}$ is extracted from the $L_G$ row-sparse matrix $H_{row}$, addressing a different MMV issue.

Algorithm 1: Two-stage LAMP (TS-LAMP) Network.

Input: Overall matrix Y for measurements 1: Step 1: Give back the calculated row-sparse matrix ${H_{row}}^e$ line from Y with the A1-generated LAMP network. 2: Step 2: Bring back the approximate angular cascaded channel $\widetilde{H_c}$ calculated by ${H_{row}}^e$ using the LAMP network built from A1. 3: Step 3: $H_c^e=A_B{\tilde{H}}_c^e{A}_S^H$ 4: Provide the predicted combined channel $H_c^e$

The two-stage learned approximate message passing (TS-LAMP) network is a sophisticated channel estimation technique that aims to increase accuracy while minimizing computational overhead in mmWave communication systems. The conventional cascaded channel estimation techniques tend to have excessive overhead stemming from the mmWave channels’ multi-dimensional characteristics, thus causing real-time processing difficulty. To mitigate this, the TS-LAMP network splits the estimation process into two separate steps. The algorithm uses, during the initial step, a Learned Approximate Message Passing (LAMP) network to approximate the row-sparse channel matrix structure and estimate key channel parameters via a soft-thresholding operator to remove noise while retaining salient channel parameters. This leaves only the most important rows of the channel structure that contribute predominantly to the overall structure of the channel, omitting unnecessary calculations. When the row-sparse matrix is produced, it then goes through row compression, and non-essential information is dropped to maximize efficiency. In stage two, there is another LAMP network, which conducts more precise channel estimation but only for the compressed rows determined in stage one, such that accuracy can be maximized without too much computational load. In contrast to traditional methods that try to estimate the whole channel matrix at one time, the two-stage method focuses on important components first, which leads to reduced training overhead, improved convergence, and better estimation accuracy. This method is especially helpful in intelligent reflecting surface (IRS)-aided mmWave networks, where both direct and indirect channels need to be estimated efficiently. Through the utilization of deep learning optimizations, the TS-LAMP network learns optimal thresholding and row selection parameters dynamically, continuing to improve its performance with multiple iterations of training. This approach significantly improves channel clarity, reduces latency, and promotes spectral efficiency, making it an efficient option for next-generation wireless communication systems.

The following step involves obtaining the angular cascaded channel $\widetilde{H_c}$ from the $L_G$ row-sparse matrix ${H_{row}}^e$, solving a different MMV problem:

$${{{(H}_{row}}^e)}^T=A_2{\tilde{J}}_c^T+X$$

(17)

where $X$ represents the leftover noise resulting from the estimation mistake in the initial LAMP network in every column of the matrix ${\tilde{H}}_c^T$. The outcome is a sparse matrix vector in the ${{{(H}_{row}}^e)}^T$ space from the shared measurement matrix $A_2$; the rows of this matrix can be reconstructed by a different LAMP network. Just like in the initial phase, we build the second LAMP network using the corresponding measure matrix $A_2$ to simultaneously retrieve the rows of $\widetilde{H_c}$. In the end, the predictable cascaded network ${\tilde{H}}_c^e$ is obtained by converting the angular network to the time domain using the dictionary matrices $A_B$ and $A_S$, following Step 3 in Algorithm 1. The TS-LAMP network proposed eliminates the costly 3D measurement matrix from the joint CS method by breaking down the estimation process. In addition, deep learning can be used to optimize both LAMP networks for improved performance.

Nevertheless, because the TS-LAMP network successfully restores all ${AK}_b, {BK}_s$ components of the angular cascaded channel $\widetilde{H_c}$ in the second phase, there is still a high computational complexity when using high grid resolutions ${AK}_b \mathrm{a}\mathrm{n}\mathrm{d} {BK}_s$. Luckily, because of the sparse structure of the angular cascaded channel $\widetilde{H_c}$, the extra LAMP network provides redundancy in rows. In order to reduce computational complexity in the second phase, we can achieve a condensed version of the estimated row-sparse matrix by focusing on the rows of the evaluated row-sparse matrix with higher norms.

Algorithm 2 outlines the structure of the RCTS-LAMP network and is an efficient channel estimation algorithm aimed at improving accuracy and lowering computational complexity in mmWave systems, especially in IRS-assisted networks. An adaptive thresholding approach and row compressing are used to improve TS-LAMP. Row norm filtering and soft-thresholding are used to remove noise/weak rows. We propose a method that takes weights from cascaded channel learning and uses them with transfer learning to improve direct channel estimation. This is critical because they are adaptive in the mmWave paths (direct and indirect, or IRS), greatly reduce training time, and improve spectral efficiency. Unlike traditional methods that estimate the whole channel matrix simultaneously, RCTS-LAMP adopts a two-stage process with row compression to achieve efficient computation. In the first stage, a LAMP network estimates the initial row-sparse matrix through soft thresholding to eliminate noise and extract meaningful channel components. A row compression (COMP) process is then used to eliminate low-power rows, keeping only useful data for subsequent processing. In the second phase, another LAMP network further refines the channel estimation, using only the compressed row support to reduce redundancy and enhance accuracy. This selective strategy minimizes the computational load while preserving high estimation accuracy. Through the utilization of deep learning-based parameter optimization, RCTS-LAMP adaptively adjusts thresholding and compression techniques, with a substantial enhancement in training efficiency, spectral purity, and processing speed. This makes it an excellent candidate for low-latency, high-accuracy mmWave communication systems where accurate channel state information (CSI) is essential to ensure network performance, which incorporates a row compression mechanism to generate the row support $\widehat{\Omega }$ for the estimated row-sparse matrix ${H_{row}}^e$. The row support $\widehat{\Omega }$ is employed to filter out the valuable rows of ${H_{row}}^e$ and then is input into the second LAMP network as ${H_{row}}^e$ $\left(\widehat{\Omega }, :\right)$, the power level of a single row ${H_{row}}^e$ $(i, :)$ in the matrix.

Algorithm 2: LAMP network with compression in rows in two stages (RCTS-LAMP network).

Input: Overall matrix Y for measurements 1: Step 1: Give back the predicted row-sparse matrix ${H_{row}}^e$ by applying the LAMP network created using A1 to Y 2: Row Compression (COMP): ${H_{row}}^e$ row support $\widehat{\mathsf{\Omega }}$ is returned. 3: Step 2: Give back the expected angular cascaded channel ${{\tilde{H}}_c}^e$ on the support $\widehat{\mathsf{\Omega }}$ from ${H_{row}}^e\left(\widehat{\mathsf{\Omega }}, :\right)$ with the LAMP network created from A2. 4: Step 3: $A_B \left(:,\widehat{\mathsf{\Omega }}\right){{\tilde{H}}_c}^e(\widehat{\mathsf{\Omega }},:)A_S^H$ 5: Cascaded channel ${{\tilde{H}}_c}^e$ Approximation is given.

The size will be significant if the spatial frequency matches. The bandwidth of that particular line is near the actual spatial frequency ${\phi }_G^{L_G}$. To efficiently indicate power, we utilize the $l_2$-norm of a row $\Vert {H_{row}}^e(i,:)\Vert$. Due to Herow being a $L_G$ row-sparse matrix; the $l_2$-norm distribution is skewed to the right, with the majority of rows having small $l_2$-norms and only a few rows having large $l_2$-norms, creating a long right tail in the distribution. Additionally, because the small norms primarily come from the residual noise in the rows, the average of the norms will be near the level of noise, particularly at higher grid resolution $K_b$. Thus, utilizing the average value as the fluctuating threshold will lead to the exclusion of rows with norms lower than or near the noise level. Given that the excluded rows may introduce noise that could affect the cascaded channel’s information, we can safely ignore them in the second stage without sacrificing performance. This situation is shown as follows:

$$\widehat{\Omega }=\left\{i:\Vert {H_{row}}^e(i,:)\Vert >{\sum }_{H=1}^{K_b}\hspace{1em}\Vert {H_{row}}^e(H,:)\Vert /K_b\right\}$$

(18)

where ${\sum }_{j=1}^{{ K}_b}\hspace{1em}\Vert {H_{row}}^e(H,:)\Vert /K_b$ denotes the changing threshold calculated by averaging all the $l_2$ norms. Consequently, only ${{\tilde{H}}_c}^e \left(\widehat{\Omega }, :\right)$ is restored in the second LAMP network, disregarding the remaining $K_b$ − $\widehat{|\Omega }|$ rows of ${{\tilde{H}}_c}^e$ to reduce computation and suppress noise. In the end, Algorithm 2’s Step 4 regains the time domain channel ${{\tilde{H}}_c}^e$ from the angular domain using dictionary matrices $A_B\left(\widehat{\Omega }, :\right)$, and ${ A}_S$.

4.2.2. Row-Compressed Two-Stage LAMP (RCTS-LAMP) for Channel Estimation

Before delving into the proposed RCTS-LAMP network, we provide a quick indication of the LAMP network for sparse signal recovery. AMP, an iterative thresholding approach, recovers the sparse angular channel directly using the soft-thresholding function, in contrast to the TRICE framework, which requires the calculation of the true three-dimensional occurrences. We are able to recreate each cascaded channel path when the grid points are close to the real spatial frequencies. The AMP method works well for general sparse recovery situations, but its channel estimation performance is limited because the shrinkage parameters and linear transform matrices stay fixed during the rounds. By deeply unfolding the AMP algorithm’s iterations into trainable layers, we can improve AMP’s performance and adapt it to the cascaded channel estimation problem.

While the primary focus of the RCTS-LAMP network is arranged, the complex task of estimating cascaded channels with the direct channel blocked can be expanded to include the simultaneous estimation of both series of channels without changing the network structure. This approach tackles the joint estimation of direct and cascaded channels for IRS-assisted mmWave systems. It applies a two-stage LAMP network that incorporates row compression to save computational complexity with high estimation accuracy. An LAMP network estimates the row-sparse channel matrix in the first stage, discarding noise and choosing significant channel elements. The second stage deals with accurate channel estimation using compressed rows. This method balances estimation precision and computational complexity very well, particularly for mmWave communication systems. The equation for this situation is shown as follows:

$$X_c\approx B_1 \widetilde{H_c}+m_0$$

(19)

where the angular direct channel $\widetilde{H_c}$ is evaluated using the matrix $B_1=W^H{B}_d \in C^{Q\times K_B}$, just like in the row-sparse matrix $H_{row}$. As a result, using the equivalent measure matrix A1, we may build an LAMP network to accurately estimate the angle of the straight channel $\widetilde{H_c}$. The transmitted channel estimate can be resolved using the RCTS-LAMP network once the direct channel has been estimated, considering the primary channel $e_d$ estimation error. The added memory and training expense caused by the supplementary LAMP structure for straightforward channel estimation, however, might make the networks less feasible for use in real-world IRS-assisted systems of communication.

The added memory and training expense caused by the supplementary LAMP networks for straightforward channel calculation, however, might make the networks less feasible for use in real-world IRS-assisted communication systems. The development process and storage requirements for an entirely novel LAMP network may be challenging and redundant, even though two separate LAMP networks for the estimate of $H_{row}$ and $\widetilde{H_c}$ may improve visualization strength and produce higher estimation performance. Given that the row-sparse matrix $H_{row}$ and the direction of the straight channel $\widetilde{H_c}$ are both determined by the same equivalent matrix $B_1$, our suggestion is to estimate $H_{row}$ and $\widetilde{H_c}$ using the first LAMP network in the RCTS-LAMP network.

Thus, the knowledge gained from estimating $H_{row}$ can be used for estimating $\widetilde{H_c}$. To enhance the functionality of the initial LAMP network and improve the RCTS-LAMP network with consideration to the estimation error $e_d$, we suggest a three-step training approach for the RCTS-LAMP network.

It is important to remember that the three-step training process applies to the RCTS-LAMP-MMV network as well, as the LAMP-MMV network will transform into the LAMP network if there is only one measurement vector. Therefore, we can utilize the LAMP-MMV for purposes of calculating both $H_{row}$ and $\widetilde{H_c}$. Yet, for clarity, we provide details on the training process in three stages for the network of RCTS-LAMP. During the initial phase of the training process, we address the issue of cascaded channel estimation when the direct channel is obstructed or accurately determined. To retrieve the cascaded channel $H_e$ the RCTS-LAMP network takes the total received signal Y as input and generates the predicted cascaded channel $H_e^d$ using two LAMP networks.

Before fine-tuning the tuneable parameters of the two LAMP networks, $W_1={\{Q_{l,2},X_{l,2},{\alpha }_{i,2},\}}_{l=1}^L \mathrm{a}\mathrm{n}\mathrm{d} W_2={\{Q_{l,2},X_{l,2},{\alpha }_{i,2}\}}_{l=1}^L$, we initialize $W_1$ and $W_2$ as $Q_{l,1}=X_{l,1}^H=A_1, {Q_{l,2}=X}_{l,2}^H=A_2 \mathrm{a}\mathrm{n}\mathrm{d} {\alpha }_{i,1}={\alpha }_{i,2}=constant$ as the original AMP procedure, which provides an efficient starting point guaranteed by performance. The normalized mean square error (NMSE) loss of $H_e$, which is defined as follows, can then be minimized by optimizing the tuneable parameters $W_1$ and $W_2$ through end-to-end training:

$$L_{CC}={\displaystyle \frac{1}{u_{CC}}}{\sum }_{u=1}^{u_{CC}}\hspace{1em}\left\{{\displaystyle \frac{{\Vert H_C^{\left(u\right)}-H_C^{e,\left(u\right)}\Vert }^2}{{\Vert H_C^{\left(u\right)}\Vert }^2}}\right\}$$

(20)

where $H_C^{\left(u\right)}$ represents the predicted cascaded channel for every instance u. Following the initial training phase, the RCTS-LAMP network can be used to expect the cascaded channel in cases where the direct channel is obstructed or has already been accurately estimated. This situation is comparable to the overall system, excluding the estimation error of the direct channel, and we view it as a preliminary stage for the overall system with both direct and cascaded channels present.

The two LAMP networks are only appropriate for cascaded channel estimation because, despite the first LAMP network’s ability to reconstruct a row-sparse signal ${H_{row}}^e$ from the measurement of $A_1$, the loss function in the first stage is the NMSE loss of the $H_e$. We use transfer learning for cascaded channel estimation to enable the first LAMP network to be capable of the direct estimation of the channels. Therefore, the sparse $\widetilde{H_c}$ might be recovered using the knowledge obtained from the extraction from the row-sparse signal ${H_{row}}^e$.

The angular direct channel ${{\tilde{H}}_c}^e$ is displayed, which is converted to the estimated direct channel $H_e^d$ in the time domain $H_e^d=A_B {{\tilde{H}}_c}^e$. The data used for training purposes $D_{DC}={{\left\{(Z_e^{\left(u\right)},H_e^d)\right\}}_{u=1}}^{u_{DC}}$ can be generated with $u_{DC}$ realizations. We use transfer learning to fine-tune the parameter $W_1$ based on the parameters learned from stage 1 to minimize the NMSE loss of $H_e$, which is defined as follows:

$$L_{DC}={\displaystyle \frac{1}{u_{DC}}}{\sum }_{u=1}^{u_{DC}}\hspace{1em}\left\{{\displaystyle \frac{{\Vert H_d^{\left(u\right)}-H_d^{e,\left(u\right)}\Vert }^2}{{\Vert H_d^{\left(u\right)}\Vert }^2}}\right\}$$

(21)

where the predicted direct channel for each realization $u$ is indicated by the symbol $H_d^{e,\left(u\right)}$. Following the subsequent training phase, the initial LAMP network may recover $H_e$ high-definition data. We consider the entire system to include direct and indirect connections. The initial and subsequent LAMP networks can reconstruct the sparse signals obtained from matrices $A_1$ and $A_2$, respectively, because the RCTS-LAMP network has progressively acquired the ability to estimate the cascaded and direct channels in the first two training phases, shown as follows:

$$L_{JO}={\displaystyle \frac{1}{u_{JO}}}{\sum }_{u=1}^{u_{JO}}\hspace{1em}\left\{{\displaystyle \frac{{\Vert H_d^{\left(u\right)}-H_d^{e,\left(u\right)}\Vert }^2}{{\Vert H_d^{\left(u\right)}\Vert }^2}}+{\displaystyle \frac{{\Vert H_C^{\left(u\right)}-H_C^{e,\left(u\right)}\Vert }^2}{{\Vert H_C^{\left(u\right)}\Vert }^2}}\right\}$$

(22)

where two pairs of input and output for each of the two estimated tasks are included for each instance of u. To simultaneously optimize both of the adjustable parameters $W_1$ and $W_2$ of the LAMP networks, we consider the combined NMSE loss for $H_e$ and $H_e$, which has the following definition.

$H_d^{e,\left(u\right)}$ and $H_C^{e,\left(u\right)}$ represent the direct calculation, and the parameters $W_1$ and $W_2$ enhance the ability of the two LAMP networks to recover $H_e$ despite the impact of estimation errors caused by estimating hd with the first LAMP network. The primary goal of the three-stage training approach is to enhance the versatility of the initial LAMP network by utilizing a common adjustable parameter $W_1={\{Q_{l,1},X_{l,1},{\alpha }_{i,1},\}}_{l=1}^L$; it can also be effectively implemented with the extra adjustable parameter $W_d$ for the first LAMP network in direct channel estimation methods. This means that we should take into account the adjustable parameter $W_d$ in the direct channel estimation for the training procedures in stages 2 and 3. During stage 2, $W_d$ is set using the parameter $W_1$ obtained in stage 1 and is improved through transfer learning. During stage 3, $W_d$ is optimized together with $W_1$ and $W_2$, considering the joint NMSE loss $L_{JO}$ in Equation (22).

Including the modifiable parameter $W_d$ could enhance the representational capacity of the initial LAMP network and could potentially enhance the precision of both direct and cascaded predictions. Extra channel memory overhead may impede deployment in real-world systems.

Table 3. Various weight-sharing approaches.

Method	Parameter	Memory Overhead	Capability
All shared	$W_1={\{Q_{l,1},X_{l,1},{\alpha }_{i,1}\}}_{l=1}^L$	Low	Low
None shared	$W_1={\{Q_{l,1},X_{l,1},{\alpha }_{i,1}\}}_{l=1}^L$ $W_1={\{Q_{l,d},X_{l,d},{\alpha }_{i,d}\}}_{l=1}^L$	High	High
Separate $\alpha$	$W_1={\{Q_{l,1},X_{l,1},{\alpha }_{i,1}\}}_{l=1}^L$ $W_d={\left\{{\alpha }_{i,d}\right\}}_{l=1}^L$	Low	Medium

displays a study of various weight-sharing approaches that target improving the balance between estimation accuracy and memory usage. Both ends of the spectrum are exemplified by the strategies of complete sharing and complete non-sharing. The original RCTS-LAMP network can facilitate direct and cascaded channel estimations by implementing the all-shared technique. Additionally, a separate LAMP network will be created using the non-shared method for direct channel estimation.

We also take into account the idea of splitting $\alpha$, noting that the shrinkage parameters ${\alpha }_i$ and the linear transformation matrices $(Q_l \mathrm{a}\mathrm{n}\mathrm{d} X_l)$ play different roles in the LAMP network. Although utilizing the individual $\alpha$ may result in minimal memory usage, it can provide customized shrinkage parameters by considering the power of each signal when reconstructing $H_{row}$ and $\widetilde{H_c}$. Nonetheless, by utilizing the identical matrix $A_1$ to measure both $\widetilde{H_c}$ and $H_{row}$, along with their analogous signal patterns, the recovery of $H_{row}$ and $\widetilde{H_c}$ can be achieved using the same transform matrices $(Q_l \mathrm{a}\mathrm{n}\mathrm{d} X_l)$, resulting in no decrease in performance. Therefore, the approach of the distinct $\alpha$ is better for the retrieval of $H_{row}$ and $\widetilde{H_c}$, as it can enhance the estimation results without significant memory usage.

4.2.3. RSSI-Based Association Strategy for Channel Selection

When the TBU link experiences “non-line-of-sight (NLOS)” propagation, IRSs are used to improve the performance of blocked users by offering “line-of-sight (LOS)” transmission and reflection gain [37]. In this scenario, we use a criterion based on RSSI for association, where the user is connected to the IRS with the highest long-term average received power. Ideally, the IRS can manipulate the reflection angle of the incoming signal to adjust the orientation of the intended user. Yet, in reality, the IRS needs complete channel state information to achieve this outcome, making it a challenging task. Hence, we investigate a scenario in which IRSs are limited in adjusting the reflection angle and are only able to offer a set reflection direction. Additionally, we assume that the main lobe beam’s reflection direction from each IRS is randomly and uniformly distributed, while the BS can align its beam direction towards the serving IRS. According to the prior conversation, the serving IRS must make sure that the combination of reflection gain and path loss for the RU link is at its highest possible value [35]. This situation is shown in the following equation:

$$Y_{q_0}=agrmax H_{q_0}{\Vert Y_q-Y_0\Vert }^{-\alpha A}$$

(23)

where $H_{q_0}$ represents the gain of the reflection array from $Y_q$ to $Y_0$ in a specific reflection beam direction, and $\alpha$ is the path loss exponent. The SINR of the typical user at the position $Y_0$ with an IRS at $Y_{q_0}$ is provided in the following scenario:

$${SINR}_2={\displaystyle \frac{\mu H_{Bm} H_{q_0}{l}_q\left(Y_{q_0}{Y}_0\right)G_{qU}}{N_{0}W+{\sum }_{Y_B\in {\Phi }_{B\backslash Y_{q_0}}}\hspace{1em}\mu G_B\left({\phi }_b\right)l_B(Y_q,Y_0)G_{BU}}}$$

(24)

where ${SINR}_2$ represents the signal-to-interference-plus-noise ratio for the typical user position $Y_0$ with IRS assistance, $\mu$ denotes the transmit power or power scaling factor, $H_{Bm}$ is the channel gain among the base station and the mobile station, $H_{q_0}$ represents the reflection gained from the ISR at $Y_{q_0}$ to the user at $Y_0$ in a specific beam direction, $l_q\left(Y_{q_0}{Y}_0\right)$ denotes the path loss among the IRS at $Y_{q_0}$ to the user at $Y_0$, $G_{qU}$ is the beamforming gain at the user from the IRS, $N_0$ denotes noise power spectral density, $W$ denotes bandwidth, ${\Phi }_{B\backslash Y_{q_0}}$ are the set of interfering base stations excluding the serving IRS at $Y_{q_0},$ $G_B\left({\phi }_b\right)$ represents the beamforming gain at the interfering BS for angle ${\phi }_b$, $l_B(Y_q,Y_0)$ represents the path loss among the interfering BS at $Y_q$ and the user at $Y_0$, and $G_{BU}$ denotes the beamforming gain at the user from the interfering BS. The SINR of the typical user at position k in an IRS-assisted mmWave network is given by Equation (24). It accounts for the revised signal strength, interference, and noise, providing a comprehensive view of network performance. The equation allows us to consider the influence of the position of the IRS and the reflection angles on the network performance and coverage.

SINR represents the ratio of the desired signal’s power to the combined interference and noise power, assessing signal quality. The integration of the reflection gain from the IRS to the user in a specific beam direction accounts for the effectiveness of the IRS in enhancing the signal. Factors in the user’s position, the IRS’s placement, and the reflection angles reflect a realistic evaluation of the network performance. The noise component and interference are modeled considering the typical high-density user scenarios in 5G mmWave networks.

Unlike traditional approaches that focus solely on the closest IRS for user association, Equation 18 evaluates the overall network geometry and channel conditions. This approach acknowledges the practical limitations of IRSs, such as restricted reflection angle adjustments and incomplete channel state information. It emphasizes the importance of optimized IRS deployment to maximize signal quality and reduce interference.

Overall, this formulation offers a more accurate and holistic view of network performance in IRS-assisted mmWave systems, facilitating effective resource allocation and communication strategies.

This assumption is not suitable for distributed systems. IRS-equipped mmWave mobile networks are favored due to their disregard for the variability in signal attenuation experienced by the user being served, which are typically implemented through LOS/NLOS mmWave communication. An example would be that an IRS that is near an NLOS connection might offer lower signal quality compared to an additional IRS with an LOS connection, albeit closeness typically leads to an increased likelihood of experiencing LOS. Furthermore, the predetermined reflection angles of IRSs also contribute to the variability in the reflection gain received by the user, a factor that cannot be explained by simply considering the closest proximity. Our goal is to assess the downlink performance of distributed mmWave networks with IRS implementation. Our main focus is on the downlink coverage probability, represented by $P\left(T\right)$, which is the likelihood that the average user encounters an SINR above the threshold $T$, shown as follows:

$$P\left(T\right)=P[SINR>T]$$

(25)

By observing Equations (23) and (24), it is evident that varying SINRs exist for various user connection statuses. To obtain them or to have them determine coverage probability, it is essential to gather statistical data on the signal power and interference power of the desired signal in various connection scenarios. These abilities are closely connected to the distance distributions and the line-of-sight/non-line-of-sight propagation condition. As a consequence, we have obtained precise findings for channel estimation through optimization. We proceed to process this channel estimation using hybrid beamforming.

4.3. Hybrid Beamforming for Multi-User mmWave Networks

After channel estimation, hybrid beamforming (HB) is a fundamental technology in mmWave networks that integrates analog and digital beamforming to enhance spectral efficiency at a lower hardware cost. This paper introduces an optimized HB model that incorporates adaptive beam training, machine learning-based optimization, and multi-user scheduling to promote network performance and alleviate interference. The proposed HB method involves two main stages. First, analog beamforming optimization is carried out with a greedy beam search algorithm, which repeatedly chooses phase configurations for phase shifters to achieve maximum signal strength with minimum interference. This guarantees effective signal transmission to multiple users. Then, digital beamforming is invoked using a zero-forcing precoder to further optimize signal transmission and suppress inter-user interference. To enhance beamforming choices, a multi-agent deep reinforcement learning (MADRL) system is integrated, in which the multi-agent twin delayed deep deterministic policy gradient (MATD3) algorithm learns to change beamforming methods based on real-time network states like signal power and interference levels.

For an improved beam, the digital and analog hybrid beam training with a long short-term memory (DAH-BT-LSTM) network is adopted. This system learns over time from previous beam training experience and minimizes excessive beam search so that it adapts adjustments when in a changing network environment. By combining machine learning and reinforcement learning methodologies, the devised HB approach optimizes beam alignment, reduces training overhead, enhances performance, and saves interference. The overall strategy guarantees stable and efficient communication in 5G mmWave networks, and it is thus apt for high-density user environments.

4.3.1. Multi-User Beamforming Strategies for mmWave Networks

Millimeter-wave (mmWave) systems can support many antennas based on half-wavelengths in a small size. Consistently, high-gain beamformers are recommended to offset their significant path loss. HB consists of a direct arrangement of antenna elements. In the RF domain, phase modulators are typically employed in conjunction with digital beamforming for millimeter-wave communications. The hybrid transmits and receives beamforming, which was optimized iteratively using the “minimum mean-square-error” criterion. Analog beamformers are optimized using nonlinear manifold optimization techniques. The authors have created multiple methods for constructing analog beamformers to advance multi-user uplink mmWave communication. Recently, various HB algorithms have been presented for multi-user downstream mmWave communications. They suggest hybrid beamforming algorithms that are based on “zero-forcing (ZF)”. Assuming the number of users equals the number of RF chains, the resulting ZF beamforming problem might not be well-posed. To produce an established difficulty, the number of users was reduced to the number of transmitting antennas. Hybrid beamforming based on “regularized zero-forcing (RZF)” was examined; channel statistics were used to define the analog and baseband beamformer design, and equal-power-constructed RZF beamforming was used to decide the beamforming technique.

The impact of combining HB and “non-orthogonal multiple access (NOMA)” on the total data rate achievable when dealing with beam misalignment was investigated in a scenario where each “radio frequency (RF)” chain serves multiple users. Additionally, the issue of maximizing energy efficiency in both concerns has also been raised regarding the multi-user mmWave networks’ uplink and downlink. They first discussed the NOMA concept to match two users per RF chain. After that, they used a variation of the convex function programming approach to handle the interconnected optimization of power distribution.

For both single-cell and twin-cell applications, they provide a time-fraction oriented mmWave transmission method that enables an unparalleled max–min user rate to be achieved using an integrated beamforming. There are the following three noteworthy advancements in the present investigation:

• In the greatest common scenario where the user count is the highest, the paper demonstrates that the number of RF chains should not exceed a certain amount in a basic HB configuration, which corresponds to the RZF baseband beamforming being used by the analog beamforming to adapt to the channel’s stage efficient transmission quality. It can achieve performance close to the ideal fully digital ZF beamforming in terms of the channel maximum and minimum rates of users. The best fully digital ZF system uses beamforming that can also achieve the capacity of massive MIMO channels according to an important finding about a constrained quantity of RF chains that does not appreciably reduce the amount of mmWave channels, provided the total RF quantity is more than the number of user links.
• In cases where the number of users doubles, we design a time fraction based on the quantity of RF chains. HB is enabled by a mmWave scheme created to attain an unmatched maximum–minimum user rate.
• In the case of a twin-cell mmWave communication system experiencing an introduced time-sharing scheme to mitigate strong interference between cells, an mmWave-based system can achieve high performance and ensure that the highest possible user rating is achieved while maintaining a minimum user rate; with consideration for the number of workers, the cell value is less than or equivalent to double the RF value chains that are employed at the primary position.

We calculate the best power distribution to exploit the minimum rate of the employers. In conclusion, simple path-following algorithms with fast convergence are created to calculate the optimal power. The developed HB is demonstrated to be effective just like the ideal entirely digital beamformer in regard to the highest minimum user rating. We also introduce a novel time division concept hybrid enabled by mmWave transmission regime beamformers developed to excel in both single-cell and doubled; the same number of cells is still being used up to double the amount of RF chains. Current research focuses on developing hybrid beamformers that can maintain both the quality of service and physical layer security for users.

4.3.2. Multi-Agent Deep Reinforcement Learning for Beamforming Optimization

A cooperative “multi-agent deep reinforcement learning (MADRL)” procedure, named “multi-agent twin delayed deep deterministic policy gradient (MATD3)”, is created for “NAFD cell-free mmWave networks”. In situations where exact “channel state information (CSI)” is understood, MADRL algorithms are used. Numerical replications are conducted to confirm the effectiveness of the recommended channel estimation techniques and to assess the MATD3 technique’s progress. This section outlines the implementation of the MATD3 algorithm presented in this study, with a focus on treating users as performers in both uplink and downlink. It also covers the key components of the algorithm, such as the state information agents observe, their actions, and the rewards they receive. This technique builds on the MATD3 algorithm to dynamically adapt hybrid beamforming in multi-user systems. The method applies cooperative multi-agent deep reinforcement learning (MADRL), where each agent (downlink and uplink users) decides based on estimated channel state information (CSI) and interference. The strategy is to maximize communication performance regardless of user number fluctuations.

Actions are determined by the optimization for each agent issue with variables. In particular, the $jth$ transmission strength coefficient is involved in the uplink user′s activity, $P_{U,j}$, whereas the $kth$ downlink user’s action pertains to the strength coefficient ${\eta }_k$.

Each agent’s observed value is the same as its estimated CSI. The $jth$ uplink user agent specifically observes ${\widehat{g}}_{j,z}$, the projected corresponding CSI to all R-APs from all connection users, for all $j \mathrm{a}\mathrm{n}\mathrm{d} z$. It also captures interference data between uplink and downlink users, denoted as $t_{k,j}$ for all $k \mathrm{a}\mathrm{n}\mathrm{d} j$. As for the downlink user device, it records the estimated equivalent CSI from each T-AP to every downlink user, represented as ${\widehat{h}}_{km}$ for every $k \mathrm{a}\mathrm{n}\mathrm{d} m$, along with IUI information, denoted as $t_{k,j}$, for every $k \mathrm{a}\mathrm{n}\mathrm{d} j$.

Rewards are given when every agent interacts with their environment after ten minutes of training to receive their immediate reward. The reaction provided by $R_{D,k}^{LB}\left(t\right)$ and $R_{U,j}^{LB}\left(t\right)$ guides the agent in making the subsequent decision. We generate immediate reinforcement for two-way agents during the $th$ training step, as outlined in the following:

$$R_{D,k}^{LB}\left(t\right)={\omega }_D{R}_{D,k}^{LB}+\left(P_D-P_{D,m},-1,1\right),$$

(26)

$$R_{U,j}^{LB}\left(t\right)={\omega }_U{R}_{U,j}^{LB},$$

(27)

where the term following the first one in the mentioned equation suggests that, in case the power constraint is met, positive feedback is implemented; otherwise, the opposite applies, with β being the appropriate penalty factor determined through multiple simulations. Thus, the sum of the immediate rewards at time slot t is calculated as follows:

$$R\left(t\right)={\sum }_{k=1}^K\hspace{1em}{R}_{D,k}^{LB}\left(t\right)+{\sum }_{j=1}^J\hspace{1em}{R}_{U,j}^{LB}(t)$$

(28)

By analyzing the recreation outcomes, we confirm the efficiency of the suggested network estimate methods and the union of the MATD3 algorithm. This is further extended by the innovative method known as multi-user scenario-based MATD3 (Mu-MATD3), which adjusts the hybrid beamforming to constantly change user scenarios to maintain efficient communication regardless of changes in the user count. We have reached optimal spectral efficiency at a lower hardware cost process, and further, we use the process with the optimized beam training.

4.4. Optimized Beam Training for Adaptive mmWave Communication

The “digital and analog beam training with long short-term memory (DAH-BT-LSTM)” network is utilized to further improve performance. By examining the signals received from earlier training sessions, this technique improves the beam direction and makes it easier for the system to forecast and modify the beam direction. DAH-BT-LSTM lowers training expenses, increases noise resilience, and lessens the need for regular recalibration by utilizing both long-term and short-term signal patterns. To provide the greatest possible signal quality and performance, the beam is constantly aligned thanks to this ongoing adjustment and optimization process.

4.4.1. Digital and Analog Hybrid Beam Training (DAH-BT) Approach

We suggest a quick beam training approach by incorporating the suggested DA-hybrid design, which we dub the new beam training method DAH-BT. In this research, we consider the possibility of MS being devices like vehicles with large antenna arrays by assuming $N_t\gg L$ and $N_t\gg L^5$. Our approach is based on the sparse nature of the angular equivalent channel matrix $H_a$ and the direct correspondence between AoAs/AoDs and entries in $H_a$.

$S_d$ is described as the collection of predominant values in $H_a$, where $S_d=\{\left(i.k\right):\left|H_a\left(i,k\right)\right|>ϵ\}$ with the threshold $ϵ$ being suitably chosen. If the cardinality of the set $S_d$ is greater than or equal to $d=\left|S_d\right|\ll G_r{G}_t$ we say that $H_a$ is efficiently containing few non-zero elements. This study derived the formula for $H_a$ using a “uniform linear array (ULA)” positioned at both the “base station (BS)” and “mobile station (MS)”. It can be concluded that the $(i, k)$-th element of $H_a$ for a “uniform planar array (UPA)” located at both BS and MS is defined as follows:

$${ H}_a\left(i.k\right)\approx {\sum }_{t=1}^L\hspace{1em}{\alpha }_l{f}_{N_r^{az}}\left({\displaystyle \frac{m\left(i\right)}{N_r^{az}}}-{\theta }_l^{az}\right)f_{N_r^{el}}\left({\displaystyle \frac{n\left(i\right)}{N_r^{el}}}-{\theta }_l^{el}\right)\times {f\ast }_{N_r^{az}}\left({\displaystyle \frac{p\left(k\right)}{N_t^{az}}}-{\varnothing }_l^{az}\right){f\ast }_{N_r^{az}}\left({\displaystyle \frac{q\left(k\right)}{N_t^{el}}}-{\varnothing }_l^{el}\right)$$

(29)

where $m(i)\triangleq \lfloor {\displaystyle \frac{i}{G_r^{el}}}\rfloor +1n(i)\triangleq mod\{{\displaystyle \frac{i}{G_r^{el}}}\}p(k)\triangleq \lfloor {\displaystyle \frac{k}{G_r^{el}}}\rfloor$, $q\left(k\right)\triangleq mod\left\{{\displaystyle \frac{i}{G_r^{el}}}\right\}; f_{N_r^{az}}\left(.\right),f_{N_r^{el}}$ (·), $f_{N_t^{ez}}(.)$, and $f_{N_t^{el}}(.)$ are the Dirichlet kernels, according to the following outlined method of ordered arrangements:

$$f_N\left(\theta \right)={\displaystyle \frac{1}{N}}{\sum }_{i=1}^N\hspace{1em}{e}^{-j2\pi i\theta }.$$

(30)

$$f_N(\theta )={\displaystyle \frac{1}{N}}{e}^{-j\pi (N+1)\theta }{\displaystyle \frac{sin sin \left(N\pi \theta \right)}{sin sin \left(\pi \theta \right)}}$$

(31)

The sinc function’s property suggests that the dominating values in $H_a$ correspond to AoA/AoD pairs, showing that $H_a$ is effectively L-sparse with $L$ paths. As a result, we can locate the matching beams by using standard CS techniques to approximately recover $H_a$.

Algorithm 3 provides a summary of the beam training phase 1 procedure, which is optimized to effectively estimate the angles of arrival (AoA) in mmWave communication systems with reduced training overhead. In beam training, the angles of arrival (AoA) are estimated. The following actions should be taken: Broad beams are sent in all directions by BS. A basic Digital Beamforming (DBF) circuit is used by MS to receive. To extract dominant AoAs, orthogonal matching pursuit (OMP) should be used. The best AoAs should be saved for the following stage. This is beneficial because it narrows the search space in dynamic situations and lowers the overhead of beam training. This phase starts with the hybrid beamforming module sending signals in every direction from the base station (BS) and with the mobile station (MS) receiving them omnidirectionally with a low-cost digital beamforming (DBF) circuit. After gathering the received signals, the OMP algorithm is utilized to estimate the leading AoAs by extracting the highest signal components. This is conducted through iterative picking of the maximum-energy beam directions from the channel response matrix and the subsequent adaptation of the estimation process via an adaptive thresholding strategy. The selected top AoA values are stored for refinement in the subsequent stage of beam training. This phase-one OMP-based DAH-BT greatly minimizes the search space, improves precision, and optimizes beam alignment with low computational complexity, thus making it suitable for dynamic and high-mobility mmWave networks. DAH-BT-LSTM combines the long-term and short-term pattern analysis of signal patterns to maximize beam training to minimize noise and the necessity of recalibration. DAH-BT-LSTM employs a two-phase beam training technique with OMP for AoA and AoD estimation. LSTM modifies beam direction from previous and current beam training signals, which results in better accuracy and lowered overhead in training.

Algorithm 3: The Initial Stage of OMP-Based DAH-BT.

Step 1: The hybrid module transmits xDL in all directions through the BS. Step 2: This inexpensive DBF module provides the MS with omnidirectional reception of the signal ${\mathrm{r}=}_{\mathrm{A}\mathrm{D}\mathrm{C}}^{\mathrm{D}\mathrm{L}} \mathsf{\eta } \frac{\sqrt{{\mathrm{N}}_{\mathrm{t}}} }{\mathrm{G}\mathrm{t}} {\mathsf{\chi }}_{\mathrm{m}\mathrm{s}}{\underset{\_}{\mathrm{A}}}_{\mathrm{r}} {\mathrm{h}}_{\mathrm{v}}^{\mathrm{D}\mathrm{L}}+{\mathrm{n}}_{\mathrm{e}}^{\mathrm{D}\mathrm{L}}$. Step 3: Estimating the AoAs using OMP. Input: ${\mathrm{r}=}_{\mathrm{A}\mathrm{D}\mathrm{C}}^{\mathrm{D}\mathrm{L}}$, $\mathsf{\Phi }=\mathsf{\eta }\frac{\sqrt{{\mathrm{N}}_{\mathrm{t}}}}{{\mathrm{G}}_{\mathrm{t}}} {\mathsf{\chi }}_{\mathrm{m}\mathrm{s}} {\underset{\_}{\mathrm{A}}}_{\mathrm{r}}$ and stopping criterion Establishing over: ${\mathrm{r}}^0={\mathrm{r}=}_{\mathrm{A}\mathrm{D}\mathrm{C}}^{\mathrm{D}\mathrm{L}}, {\mathrm{x}}^0=0, {\mathsf{\Lambda }}^0=\mathrm{Ø},\mathrm{t}=0$ When they don’t converge, Match: ${\mathrm{V}}^{\mathrm{t}}={\mathsf{\Phi }}^{\mathrm{T}}{\mathrm{r}}^{\mathrm{t}}$ Identify: ${\mathsf{\Lambda }}^{\mathrm{t}+1}{=\mathsf{\Lambda }}^{\mathrm{t}} \bigcup \left\{{\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{m}\mathrm{a}\mathrm{x}}_{\mathrm{j}}\right|{\mathrm{u}}^{\mathrm{t}}\left(\mathrm{j}\right)\left|\right\}$ (where ut(j) is the j-th entry of ut(j) is the j-th entry of Vt). Update: ${\mathrm{X}}^{\mathrm{t}+1}=\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{m}\mathrm{i}\mathrm{n} {\Vert \mathrm{r}-\mathsf{\Phi }\mathrm{z}\Vert }_2$ $\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{Z}:\mathrm{s}\mathrm{u}\mathrm{p}\mathrm{p}\left(\mathrm{z}\right)\subseteq {\mathsf{\Lambda }}^{\mathrm{t}}$ $\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{\mathrm{r}}^{\mathrm{t}+1}=\mathrm{r}-\mathsf{\Phi } {\mathrm{X}}^{\mathrm{t}+1}$     t = t + 1 conclude While Results: ${\widehat{\mathrm{h}}}_{\mathrm{v}}^{\mathrm{D}\mathrm{L}} = {\mathrm{x}}^{\mathrm{t}}$ Step 4: Identify the greatest Lest values in ${\widehat{\mathrm{h}}}_{\mathrm{v}}^{\mathrm{D}\mathrm{L}}$, compute the matching angles by Equation (28), and note them in the designated SAoA.

In summary, Algorithm 4 summarizes the beam training phase 2 procedures and emphasizes the estimation of angles of departure (AoD) for beam alignment maximization in mmWave communication. Once the angles of departure (AoAs) have been determined, the AoDs should be estimated. Procedures: MS sends out directed beams. DBF is how BS obtains it. The strongest AoDs are found using OMP. Ideal transmit–receive beam pairs should be formed by combining with earlier AoAs. This is beneficial because it minimizes the computation required to finish the hybrid beamforming beam alignment procedure. Following the AoA estimations of the initial phase, the hybrid beamforming module now sends directional signals sequentially from the mobile station (MS), whereas the base station (BS) receives them omnidirectionally via a cost-effective digital beamforming (DBF) circuit. The OMP algorithm is then utilized to retrieve the most dominant AoD values by iteratively choosing the maximum-energy transmission angles. Estimated AoDs are stored in addition to the already established AoAs, and an optimized beam pair choice for increased transmission efficiency is created. This OMP-based DAH-BT in the second phase continues to reduce beam training overhead, improves beam alignment, and lessens interference; hence, it is optimized for high-speed and adaptive mmWave networks. We ultimately determine which beam pairs, transmission and being received, are documented in $S_{AoD}$ and $S_{AoD}$, respectively, following phases 1 and 2 of the DAH-BT.

Algorithm 4: OMP-based DAH-BT phase 2.

Step 1: The hybrid module sequentially sends $x_l^{UL}= {a\ast }_{Rx} ({\underset{\_}{\theta }}_{AoA}^{az},{\underset{\_}{\theta }}_{{AoA}_1}^{az})$, where l = 1, …, Lest, utilizing the MS. Step 2: The inexpensive DBF circuit provides the omnidirectional reception of the signal $r_{ADC}^{UL}=\eta (I\otimes {\chi }_{bs}{\underset{\_}{A}}_t^{\ast })h_v^{UL}+n_e^{UL}$ via the BS. Step 3: The OMP-based approximation of AoDs is comparable to Step 3 in Algorithm 3, where the output is $h_v^{UL}$ and the input is $r_{ADC}^{UL}$ and $\tilde{\Phi }=\eta (I\otimes {\chi }_{bs}{\underset{\_}{A}}_t^{\ast })$. Step 4: Transform $h_v^{UL}\in C^{G_t L_{est}\times 1}$ into ${\widehat{H}}_a\in C^{G_t L_{est}\times 1}$. The AoD of the l-th path is represented by the index of the greatest entry in the l-th column of $\widehat{H}$. Next, record AoDs in set SAoD.

4.4.2. LSTM

Utilizing a “long short-term memory (LSTM)” network allows for tracking employer motion and making adjustments to the beam direction by analyzing signals obtained from prior beam training sessions, resulting in enhanced noise immunity. Previous beam training data are leveraged to better align beams. The structure has convolutional layers that provide input from prior beam patterns. To predict the optimal beam direction, LSTM looks at time series patterns. In the end, the robotic arm uses the beam direction with the greatest forecast success. This is useful because it reduces retraining costs and improves the robustness to noise in mobile situations.

LSTM is chosen as the forecasting model because of its outstanding performance ability to learn sequences over time. In Figure 2A, the basic composition of LSTM is demonstrated. At each time slot t, the current input $x_t$ is coupled through the cell state and output from the earlier time slot $\{c_{t-1}, h_{t-1}\}$ and provided to LSTM. This allows LSTM to acquire knowledge from past inputs. The suggested model based on LSTM is shown in Figure 2B. After the $t-th$ wide beam training, the established indications are initially inputted to the preprocessing and convolution units to identify the initial features linked to $y_{w,t}$. Then, the LSTM component adjusts the precise beam angle by analyzing the signals from the current and previous beam training sessions. In the end, the output module gives predicted probabilities $\{{\widehat{p}}_1,t,{\widehat{p}}_2,t,\dots ,{\widehat{p}}_{N_{Tx}},t\}$, and the optimal beam is chosen based on the highest probability, represented by index ${\widehat{m}}_t^{\ast }$. The model is trained using cross-entropy loss, where every practice sample’s loss is equal to the mean of the UE’s wide beam estimates.

4.5. Bottleneck-Aware Congestion Control for Low-Latency Transmission

Optimizing network performance requires bottleneck-aware congestion reduction, particularly in settings where traffic might adversely affect data delivery. A “low-latency congestion control scheme (LLCCS)”, which concentrate on variables like bottleneck bandwidth and round-trip propagation time, are used to address this. An LLCCS dynamically shifts data rates adaptively in real-time according to network conditions such as bottleneck bandwidth and round-trip time. It works towards keeping low latency and high throughput with congestion avoidance before the occurrence of performance degradation. This approach plays a vital role in dealing with variable traffic in 5G mmWave networks. Through the evaluation of these characteristics, LLCCS can detect and handle network bottlenecks that result in latency and decreased throughput. By adjusting data transmission rates dynamically in response to actual network conditions, these schemes make sure that congestion is reduced before it causes a noticeable decline in performance.

Numerous congestion control algorithms with low latency have been suggested in research to address the issue of buffer bloat. BBR aims to minimize queueing delays by functioning within the “bandwidth-delay product (BDP)” of a route in the system. BBR restricts the number of packets transferred to a fixed number of the projected BDP and updates its estimates for the bottleneck bandwidth and minimum RTT of the network path frequently. TCP BBR’s initial implementation consists of four stages. During the initial stage, known as the startup phase, the goal is to promptly determine the bottleneck bandwidth by estimating it. Next, during the second phase known as the drain phase, the sending rate is decreased to empty the queue accumulated in the initial phase. BBR reaches a steady state where it alternates between conducting bandwidth probing and “round-trip time (RTT)” probing. BBR mainly focuses on bandwidth probing, typically sending data at the estimated bottleneck bandwidth rate, while occasionally exceeding this rate to find any extra capacity. In this stage, the CWND is adjusted to twice the calculated BDP. BBR continuously tracks the lowest RTT, and if 10 s pass without any changes to this value, it starts the RTT exploring phase. During the RTT exploring phase, BBR configures its CWND to four segments to clear the queue and ascertain the connection’s base RTT. BBR returns to the bandwidth exploring step after updating the minimal RTT estimation.

Version 2 of BBR brings about several alterations; however, it functions based on the same concept of calculating the BDP, focusing mainly on seeking additional bandwidth, and occasionally lowering its transmission speed to calculate the shortest RTT. L4S is a network service design that consists of the following two main parts, with a focus on low latency, low loss, and scalable throughput:

• TCP Prague traffic management: TCP Prague, much like DCTCP, relies on precise ECN feedback to regulate the rate of sending. Nevertheless, it contains various additions and modifications compared to DCTCP, which enhance its compatibility for Internet usage, especially when sharing links with loss-based congestion control flows.
• Dual-Q paired AQM: The L4S architecture uses a Dual-Q paired AQM to address disparity in loss-based traffic flow control and to maintain minimal queuing latency for flows that comply with ECN. To provide fairness and low latency for ECN-responsive flows, this queue differentiates between classic loss-based streams and ECN-responsive streams.

Through the use of comprehensive data on round-trip times and bottleneck bandwidth, LLCCS can make well-informed adjustments that minimize latency, avoid congestion, and maximize resource usage. This proactive strategy guarantees consistent and effective network performance even with fluctuating traffic volumes. We have enhanced the overall transmission control for 5G networks.

5. Experimental Results

This section outlines the experimental study conducted to evaluate the performance of the proposed 5G mmWave network technique. Furthermore, this section is separated into the following three subsections: research overview, comparative analysis, and simulation setup.

5.1. Experimental Setup for Performance Evaluation

To simulate the proposed research method, Ns-3.35 with Python–3.9.6 (64-bit) version was used. This tool is efficient and provides all specifications for the proposed technique.

Table 4. System specifications.

Software specifications	OS	Ubuntu 22.04
	Tool	Ns-3.35 with Python–3.9.6 (64-bit) version
Hardware specifications	RAM	4 GB
	Hard disk	500 GB
Parameter	Value/description
Base station(BS)	The 4-element hybrid beamforming antenna array
User node(UN)	100-element antenna array
IRS type	Single-layer IRS (not multi-layer SIM)
Channel model	Saleh–Valenzuela channel model
Mobility model	Gauss–Markov mobility model
Noise model	AWGN with variance ${\sigma }^2$
Modulation/PHY	Not mentioned explicitly
Beamforming strategy	DAH-BT-LSTM (uses long short-term memory), trained with Mu-MATD3 agent-based RL
Channel estimation method	RCTS-AMP-RSSI-AS (LAMP-based two-stage network with row compression)
Congestion control	Modified mms-TCP and low-lantency congestion control schemes (LLCCS)

indicates the system specifications.

5.2. Performance Comparison with Existing Methods

This section compares the proposed approach to many existing ones, such as the stacked intelligent metasurface-aided downlink multiuser transmission (SIM-ADMT) [38], FB-TCP (fuzzy based-transmission control protocol) [32], MP-TCP (multi-path-transmission control protocol) [33], Deep IA (deep learning initial access) [34], and UL-SCH (uplink shared channel) + PUSCH (physical uplink shared channel) [31], and it evaluates its efficacy using performance metrics such as “throughput (Mbps), round-trip times, end-to-end delays, packet loss, SNR, and beamforming accuracy”.

A theoretical comparison with BBR, CUBIC, and NewReno reveals the following:

BBR is bandwidth-probing centered but is not congestion-responsive. CUBIC is less aggressive in its recovery rate post-congestion incidents. The overly aggressive reduction of NewReno results in wasteful recovery on high-BDP networks. Our approach provides better link utilization with stability and is most suitable for use in mmWave networks.

5.2.1. Evaluating Throughput Performance

The throughput per user often drops when more users join the 5G mmWave network because of resources being shared. The system may regulate user density and enhance throughput for high-speed data transmission by employing efficient hybrid beamforming algorithms. Stacked metasurfaces are employed in SIM-ADMT [38] for multi-user beamforming; nevertheless, the overhead is greater (see to Section 3). The proposed method utilizing IRS-assisted HB achieves enhanced throughput.

Table 5. Numerical outcomes of throughput (Mbps).

No of User (x-Axis)		Throughput (MBPS)-(y-Axis)
	SIM-ADMT	FB-TCP	UL-SCH + PUSCH	Proposed
20	17	23	35	53
40	30	35	55	85
60	47	56	43	70
80	56	62	58	83
100	32	40	60	90

and Figure 3 suggest that the method provides 53 MBPS throughput with 20 users, which is much greater than 17 MBPS for SIM-ADMT, 23 MBPS for FB-TCP, and 35 MBPS for UL-SCH + PUSCH. The suggested system sustains a competitive throughput of 70 MBPS when the number of users rises to 60, whereas the other schemes fluctuate, with UL-SCH + PUSCH falling to 43 MBPS. The suggested system shows this by leading with 90 MBPS when we reach 100 users, while SIM-ADMT reduces to 32 MBP, and SFB-TCP drops to 40 MBPS. In general, the suggested plan continuously exhibits higher throughput, indicating that it can be handled with high user densities in 5G mmWave networks.

5.2.2. Analyzing Round-Trip Time in mmWave Networks

Round-trip times usually increase as the number of users increases because of increased network traffic. This can be reduced by improving beam management and cutting down on transmission delays with efficient control of the transfer approach.

The comparative analysis of round-trip time (ms) is represented in Figure 4 and

Table 6. Numerical results of round-trip time (ms).

Number of User (x-Axis)		Round-Trip Time (ms) (y-Axis)
	SIM-ADMT	FB-TCP	UL-SCH + PUSCH	Proposed
20	95	85	100	65
40	130	100	120	85
60	120	110	135	58
80	135	125	150	90
100	180	150	175	120

. From the below figure, it is clear that the proposed design has the lowest RTT of 65 (ms) starting with 20 users, which is faster than SIM-ADMT at 95 (ms), FB-TCP at 85 (ms), and UL-SCH + PUSCH at 100 (ms). As we move toward the middle of 60 users, the recommended plan performs even better, with an RTT of just 58 (ms). In contrast, the other two plans have higher latency, with UL-SCH + PUSCH reaching 135 (ms), SIM-ADMT achieving 120 (ms), and FB-TCP rising to 110 (ms). After 100 users have completed the test, the suggested technique maintains a fast RTT of 120 (ms), which is much faster than the 180 (ms) of SIM-ADMT, 150 (ms) of FB-TCP, and 175 (ms) of UL-SCH + PUSCH. Effectiveness in lowering round-trip time (RTT) is demonstrated by the proposed scheme’s ability to sustain steady state performance in high-density 5G mmWave network conditions, which makes it the ideal choice for accommodating effective communication.

5.2.3. Measuring End-to-End Delay for Data Transmission

End-to-end delays rise with an increase in users, which slows down data transfer across the network. In 5G mmWave networks, optimized hybrid beamforming can minimize this delay by increasing signal efficiency and decreasing traffic. SIM-ADMT, and MP-TCP function in the transport layer, while UL-SCH + PUSCH functions in the physical and MAC layers. From the perspective of end-to-end latency, they are not comparable because they are working at different tiers. Nevertheless, both methods have an impact on the network’s overall performance. MP-TCP maximizes multi-path data transmission, which impacts transport-layer performance, while UL-SCH + PUSCH impacts radio link transmission efficiency. Such protocols can therefore be present in the same network, and in maximizing them at once, 5G mmWave networks become more efficient all in all, considering latency.

Figure 5 and

Table 7. Numerical outcomes of end-to-end delay (ms).

No of User (x-Axis)		End-to-End Delay (ms)-(y-Axis)
	SIM-ADMT	MP-TCP	UL-SCH + PUSCH	Proposed
20	63	60	58	52.5
40	52	50	55	60.0
60	65	70	78	61.5
80	74	80	93	62.5
100	80	90	98	70.0

represent the suggested system that has the least delay, starting at 20 users, at 52.5 (ms), in contrast to UL-SCH + PUSCH at 58 (ms), MP-TCP at 60 (ms), and SIM-ADMT at 63 (ms). The suggested strategy keeps an acceptable latency of 61.5 (ms) at the halfway point of 60 users, whereas SIM-ADMT climbs to 65 (ms), MP-TCP climbs to 70 (ms), and UL-SCH + PUSCH increases to 78 (ms). The suggested scheme’s latency by the final measurement at 100 users is 70 (ms), which is higher than at lower user counts but still beats out SIM-ADMT at 80 (ms), MP-TCP at 90 (ms), and UL-SCH + PUSCH at 98 (ms). For high-density user scenarios in 5G mmWave networks, the suggested approach consistently provides improved end-to-end delay performance, proving its efficacy.

5.2.4. Packet Loss Analysis in High-Density Scenarios

Packet loss increases when more users connect to the network, which is generally caused by interference and signal collisions. A smart control method improves beamforming precision, decreasing packet loss and guaranteeing dependable data transmission.

The suggested methods found in

Table 8. Numerical outcomes of packet loss (%).

No of User (x-Axis)		Packet loss (%)-(y-Axis)
	SIM-ADMT	MP-TCP	UL-SCH + PUSCH	Proposed
20	25	30	28	45
40	58	60	55	35
60	44	50	39	25
80	68	70	62	30
100	85	80	70	50

and Figure 6 show a somewhat higher packet loss rate of 45% with 20 users, compared to 25% for SIM-ADMT, 30% for MP-TCP, and 28% for UL-SCH + PUSCH. For 40 users, the recommended strategy improves performance by 35%, but the loss rates for SIM-ADMT, MP-TCP, and UL-SCH + PUSCH rise to 58%, 60%, and 55%, respectively. Out of 60 users, the recommended plan has the lowest packet loss rate of 25%, which is higher than 44% of SIM-ADMT, 39% of UL-SCH + PUSCH, and 50% of MP-TCP. The loss rate of the suggested scheme increases to 50% with 100 users, whereas it is 85% for SIM-ADMT, 80% for FB-TCP + MP-TCP + Deep IA, and 70% for UL-SCH + PUSCH. Overall, the proposed scheme exhibits a lower packet loss, especially for moderate user counts, suggesting that it works well in dense 5G mmWave network scenarios.

5.2.5. Signal-to-Noise Ratio (SNR) Evaluation

Increasing user densities results in lower signal-to-noise ratios (SNR), which lower signal quality. Effective beam steering is ensured by an effectively implemented transmission management mechanism to maintain good SNR despite user expansion.

The comparative analysis of SNR (db) is represented in Figure 7 and

Table 9. Numerical outcomes of SNR (dB).

No of User (x-Axis)		SNR (dB)-(y-Axis)
	SIM-ADMT	FB-TCP	UL-SCH + PUSCH	Proposed
20	6.3	6.0	5.0	8.3
40	5.4	5.0	6.0	7.0
60	4.0	4.5	3.7	6.6
80	6.3	7.5	5.8	8.8
100	7.5	8.0	7.0	9.0

. When there are 20 users, the suggested approach performs better than FB-TCP + MP-TCP + Deep IA and UL-SCH + PUSCH, and SIM-ADMT with an SNR of 8.3 dB as opposed to 6.0 dB and 5.0 db, 6.3 db, respectively. The technique suggested maintains a high SNR of 7.0 dB with 40 users, while FB-TCP drops to 5.0 (db). After 60 users, the proposed system performs better again, with 6.6 dB, compared with 4.0 (db) for SIM-ADMT, 4.5 (db) for FB-TCP, and 3.7 (db) for UL-SCH + PUSCH. The proposed plan maintains its higher efficiency over SIM-ADMT at 6.3 (db), FB-TCP at 8.0 (db), and UL-SCH + PUSCH at 7.0 (db) at the end of the assessment with 100 users, achieving 9.0 (db). The recommended strategy generally yields higher SNR values, demonstrating better signal quality in high-density scenarios. The DAH-BT-LSTM model may overfit or underfit at this intermediate scale, and less-than-ideal beamforming and congestion control follow from the absence of training data for 60 users. This clarifies why, in the 60-user case, performance is poorer. Furthermore, with 60 users, there is higher inter-user interference, beam overlap, and pipeline congestion than with 40 users. More complete improvements, including RCTS-LAMP’s sparsity control, boost performance with 80 users. Furthermore, environmental non-stationarity and coordination problems impede multi-agent reinforcement learning methods, such as Mu-MATD3, at this intermediate scale, therefore compromising convergence and performance.

5.2.6. Beamforming Accuracy in Dynamic User Environments

Beamforming accuracy may decrease when more users join because of additional interference. However, even with an increasing number of users, the 5G mmWave framework’s superior control algorithms can retain high accuracy.

Beamforming accuracy in a millimeter-wave system is the accuracy with which a beamforming system aligns its broadcast or received beams toward the desired user directions. It tests the system’s capacity to lower interference, increase signal strength, and change with the channel conditions.

Beamforming accuracy metric: Accuracy is measured by the following normalization formula: $Beamforming accuracy\left(\%\right)=1-{\displaystyle \frac{‖{\mathfrak{H}}_{ideal}-{\mathfrak{H}}_{estimated}‖}{‖{\mathfrak{H}}_{ideal}‖}}$.

Figure 8 and

Table 10. Numerical outcomes of beamforming accuracy (%).

No of User (x-Axis)		Beamforming Accuracy (%) (y-Axis)
	SIM-ADMT	Deep IA	UL-SCH + PUSCH	Proposed
20	15	20	40	70
40	25	30	45	75
60	35	40	50	68
80	55	60	70	81
100	65	70	80	98

indicate the outcomes of beamforming accuracy, and the suggested technique outperforms SIM-ADMT at 15%, Deep IA at 20%, and UL-SCH + PUSCH at 40%, with a high accuracy of 70% at 20 users. The suggested method improves even more to 75%, as user numbers reach 40, whereas SIM-ADMT is at 25%, deep IA rises to 30%, and UL-SCH + PUSCH reaches 45%. The suggested system maintains a reasonable accuracy of 68% at 60 users, while SIM-ADMT achieves 35%, FB-TCP + MP-TCP + Deep IA achieves 40%, and UL-SCH + PUSCH achieves 50% of the accuracy. The suggested technique outperforms SIM-ADMT at 65%, Deep IA at 70%, and UL-SCH + PUSCH at 80%, with an amazing 98% accuracy by 100 users. With all things considered, the suggested approach continuously exhibits higher beamforming accuracy, proving its usefulness in handling situations with a large user density. Compared with the proposed and existing methods, the proposed methods have a greater efficiency.

5.3. Research Summary

Initially, we constructed the 5G network with a hundred user nodes, four base stations, and one server. Then, we implemented a multimedia messaging service (MMS) using mmS-TCP. Next, we estimated the channel using the RCTS-AMP. Next, we implemented digital beamforming using the “multi-user scenario-based MATD3 (Mu-MATD3)” method to improve communication performance. Next, we trained the beam using the DAH-BT-LSTM network. Next, we optimized the bottleneck-aware congestion mitigation using LLCCS. Finally, we plotted performance for the following metrics: number of users vs. throughput (MBPS), number of users vs. round-trip time (ms), number of users vs. end-to-delay (ms), number of users vs. packet loss (%), number of users vs. SNR (dB), and number of users vs. beamforming accuracy (%); these are illustrated in Figure 3, Figure 4, Figure 5, Figure 6, Figure 7 and Figure 8 and Table 5, Table 6, Table 7, Table 8, Table 9, Table 10 and

Table 11. Performance comparison of proposed vs. existing methods.

Metric			Proposed vs. Existing Methods
	FP-TCP	SIM-ADMT	UL-SCH + PUSCH	Deep IA	Proposed
Throughput (Mbps)	40	32	60	-	90
Round-trip time (ms)	150	180	175	-	120
Packet loss (%)	80	85	70	-	50
SNR (dB)	8.0	7.0	7.0	-	9.0
End-to-end delay (ms)	90	80	98	-	70
Beamforming accuracy (%)	-	65	80	70	98

.

6. Conclusions

In conclusion, the main concerns regarding time, beamforming efficiency, channel estimate accuracy, and overall network throughput are addressed by the suggested “intelligent transmission control scheme for 5G mmWave networks employing hybrid beamforming” technique. To fulfill the high needs of 5G mmWave networks, the method includes some novel techniques, such as utilizing CODel queue management to reduce latency and enhancing classic TCP performance with mmS-TCP. With less training overhead, the new “row compression two-stage learning-based accurate multi-path processing network (RCTS-AMP-RSSI-AS)” framework guarantees accurate channel estimations for both direct and cascaded channels, improving the performance of the system. For dynamic multi-user situations, beamforming maximizes technology performance and spatial accuracy by integrating digital and analog approaches with the Mu-MATD3. The refinement of the beamforming process is improved by the “digital and analog beam training with LSTM (DAH-BT-LSTM)” network, which boosts noise resilience, decreases training overhead, and guarantees the real-time optimization of beam alignment. Finally, “low latency congestion control schemes (LLCCS)” adapt data transmission rates in real-time to manage congestion effectively, guaranteeing both high throughput and low latency in fluctuating traffic conditions. The suggested approach guarantees reliable, high-performance communication with reduced latency and enhanced reliability in modern 5G mmWave networks by merging advanced techniques. Our results show that Mu-MATD3 and DAH-BT-LSTM deliver greater throughput (90 Mbps vs. 32 Mbps) and beamforming accuracy (98% vs. 65%) using real-world hardware, even if SIM offers theoretical benefits under ideal circumstances. Although SIM hybridization for terahertz bands may be investigated in future research, the existing system effectively satisfies 5G criteria.