Spatial Simultaneous Functioning-Based Joint Design of Communication and Sensing Systems in Wireless Channels

Abstract

This paper advocates for spatial simultaneous functioning (SSF) over time division multiple access (TDMA) in joint communication and sensing (JCAS) scenarios for improved resource utilization and reduced interference. SSF enables the concurrent operation of communication and sensing systems, enhancing flexibility and efficiency, especially in dynamic environments. The study introduces joint design communication and sensing scenarios for single input single output (SISO) and multiple input multiple output (MIMO) JCAS receivers. An MIMO-JCAS base station (BS) is proposed to process downlink communication signals and echo signals from targets simultaneously using interference cancellation techniques. We evaluate the communication performance and sensing estimation across both Rayleigh and measured realistic channels. Additionally, a deep neural network (DNN)-based approach for channel estimation and signal detection in JCAS systems is presented. The DNN outperforms the traditional methods in the bit error rate (BER) versus signal-to-noise ratio (SNR) curves, leveraging its ability to learn complex patterns autonomously. The DNN’s training process fine-tunes the performance based on specific problem characteristics, capturing the nuanced relationships within data and adapting to varying SNR conditions for consistently superior performance compared to the traditional approaches.

1. Introduction

For numerous years, wireless communication systems and radar sensing systems have advanced independently, albeit within constrained connections. They share common terms, such as signal processing and system structure [1]. The coexistence of communication and radar systems has been a subject of extensive research, focusing on developing effective interference management techniques to enable the efficient operation of two independently installed systems. Radar and communication systems transmit distinct signals, even when physically located in proximity [1].

An intriguing prospect involves exploring whether a single transmitted signal can serve both communication and radar sensing purposes to mitigate the interference in coexisting systems arising from transmitting two separate signals. The concept of extracting information from received radio signals, beyond the conventional signal demodulation associated with communication data, is termed radio sensing. Utilizing radio signals, radio sensing can be achieved by measuring sensing parameters and physical feature parameters [1].

1.1. Joint Communication and Sensing

Integrating communication and radar sensing into a joint communication and sensing (JCAS) system represents an appealing solution. Various terms, including radar communication (RadCom), joint radar and communication (JRC), joint communication and radar (JCR), dual-functional radar communication (DFRC), and integrated sensing and communication (ISAC), have been coined to refer to JCAS. In this context, we adopt JCAS, which involves the collaborative design and utilization of a specific transmitted signal for both communication and sensing purposes. This approach reveals the potential for shared components between communication and sensing systems [1].

While most receiver elements can be commonly utilized, the baseband signal processing at the receiver typically differs for communication and sensing. JCAS is reported to address two limitations in passive sensing through joint designs. This distinguishes JCAS significantly from passive sensing concepts, aligning more closely with spectrum sharing principles. Despite combining the communication and sensing signals into a single system, they employ separate waveforms, and the resources are allocated distinctly in terms of time, frequency, and code [1].

Figure 1 shows a basic JCAS scenario. A cellular system is equipped with array antennas, efficient for beamforming but also typically with multi-cell interference. Multiple users use the arrays to communicate for sensing and high-rate low-latency [2].

1.2. Three Types of JCAS Systems

Within the realm of JCAS, three distinct types emerge: radar-centric design, communication-centric design, and joint design and communications [1,3]. In the former two categories, where the primary system’s integrity remains paramount, designers and researchers delve into identifying the supplementary function based on the signal forms of the main system. This often entails subtle adjustments and optimizations to both the system and signal to seamlessly accommodate this dual functionality. Conversely, the latter type offers a more flexible approach, enabling the design and refinement of the signal waveform and system structure without disrupting the communication or sensing processes [1,3].

1.3. Advantages of JCAS Systems

It is anticipated that JCAS systems offer several benefits through the integration of consistent communication and sensing functions. Achieving perfect spectral efficiency can be possible by fully sharing the accessible spectrum for both wireless communication and radar [1]. This spectrum sharing should not adversely impact the operational conditions of each aspect [4]. Additionally, the utilization of channel structures obtained from sensing can enhance the beamforming performance [1]. Joint systems can significantly decrease the expenses and dimensions of transceivers compared to two individual systems [1]. Furthermore, communication connections can provide well-organized collaboration among multiple nodes for sensing, while sensing can enhance the safety and performance by contributing to the environmental awareness of communications [1].

However, practical considerations introduce essential restrictions to integrated sensing and communication. These include channel estimation faults, frequency offset, timing synchronization errors, and performance investigation challenges under diverse flexibility models [5]. These limitations underscore the importance of rigorous testing and optimization to ensure the seamless integration of communication and sensing functions in JCAS systems.

1.4. Main Disparities between Communication and Radar Systems and Signals

Despite the promising prospect of integration, distinct disparities arise between communication and radar systems, manifesting in their unique signal characteristics.

Table 1. Comparison between communication and radar signals and systems [4].

Properties	Radar	Communications
Signal Waveforms	Orthogonal signals in multiple input multiple output (MIMO) radar, unmodulated with wide bandwidth and low Peak-to-Average Power Ratio (PAPR).	Mix of modulated and unmodulated symbols, high Peak-to-Average Power Ratio (PAPR), complex waveforms.
Signal Structure	Pulsed radar includes silent periods between pulse transmissions, while continuous-wave radar allows continuous transmission.	Packet-based signals without replication, varying lengths and intervals, flexible resource usage.
Duplex Mode	Full duplex in continuous-wave radar using beat signals, half duplex in pulsed radar with quiet periods after transmissions.	Time division duplex or frequency division duplex, full duplex undeveloped.
Clock Synchronization	Locked transmitter and receiver clocks in most radar setups.	Transmitter and receiver share timing clock; separate nodes may not synchronize.
Receiver Sampling	Traditional continuous-wave radar samples signals below scanning bandwidth, limiting information conveyance.	Sampling speed matches signal bandwidth, providing full bandwidth information.
Performance Metrics	Detection probability, Cramér–Rao Lower Bound (CRLB), Mutual Information (MI), Ambiguity function.	Capacity, Rate, Spectral efficiency, Signal-to-Interference-and-Noise Ratio (SINR), and Bit Error Rate (BER).

offers a succinct summary of these disparities. Radar waveforms typically encompass traditional pulsed and continuous waveforms, including chirp. Following this, we delve into two key features that exert a considerable influence on the cohesive structure of the combined system [6].

1.5. Related Works

In recent studies referenced as [7,8], the researchers delve into the design of intelligent waveforms capable of facilitating both data transmission and radar sensing simultaneously, a topic highly pertinent to this paper. Additionally, [9] explores the joint receiver design for ISAC systems, where both communication and target echo signals are received concurrently. These signals undergo processing to optimize the performance across both functionalities, with two distinct design schemes considered.

Furthermore, the investigations highlighted in [10,11] center around the channel estimation and signal detection within orthogonal frequency division multiplexing (OFDM) systems, leveraging a deep learning (DL) approach. This method is employed to comprehensively address wireless OFDM channels, from the estimation of channel state information (CSI) to symbol recovery. Various channel scenarios are examined to evaluate the efficacy of the DL approach.

1.6. Research Gap and Our Contribution

This paper advocates for the adoption of spatial simultaneous functioning (SSF) over time division multiple access (TDMA) in JCAS scenarios. SSF facilitates the concurrent operation of communication and sensing systems, thereby enhancing flexibility and efficiency, particularly in dynamic environments. While recent research efforts [7,8,9,10,11,12,13,14,15] have made significant strides in exploring joint communication and sensing scenarios, it is important to note that these studies primarily focus on the individual facets of the JCAS framework, such as waveform design, receiver architecture, and signal processing techniques. However, none of these studies consider SSF or compare it with TDMA. Recognizing these differences, we bring SSF into the spotlight in our study to showcase its potential advantages over TDMA in joint communication and sensing scenarios.

In the context of JCAS, recent research efforts [7,8,9,10,11,12,13,14,15] have made notable progress. However, a discernible gap persists in addressing the key aspects comprehensively. The existing studies primarily concentrate on isolated components of the JCAS framework. Yet, there remains a need for a unified approach that integrates these elements into a cohesive framework for both single input single output (SISO) and MIMO JCAS receivers.

SSF enables the concurrent operation of communication and radar sensing functions, addressing the growing need for spectrum efficiency and seamless operation in time-critical applications. By opting for SSF, our JCAS system stands to benefit from its simultaneous operation, which offers significant advantages, such as improved spectral efficiency and reduced latency. Furthermore, MIMO techniques can complement SSF by enhancing the performance of our system. MIMO involves using multiple antennas at both the transmitter and receiver ends to improve the communication reliability, increase the data rates, and mitigate interference. In the context of our JCAS system, employing MIMO allows us to spatially separate communication and sensing signals, thereby minimizing interference and maximizing the utilization of the available spectrum. This synergy between SSF and MIMO ensures the efficient and reliable operation of our system in dynamic and challenging environments.

Building upon the insights gleaned from prior works, we propose a novel methodology to bridge this research gap. Our approach centers on the joint design of communication and sensing scenarios, tailored specifically for SISO and MIMO JCAS receivers. Within our framework, an MIMO-JCAS base station (BS) adeptly processes both the downlink communication signals to the user and the echo signals reflected from the target concurrently.

A pivotal aspect of our approach involves exploring a straightforward yet efficacious JCAS receiver design grounded in the interference cancellation technique. We evaluate this receiver architecture across various channels, encompassing Rayleigh with additive white Gaussian noise (AWGN) channels, as well as more realistic measured channels.

Moreover, we conduct a comprehensive evaluation of the communication performance and sensing estimation capabilities across both Rayleigh and measured channels. To bolster the signal detection in JCAS systems, we propose employing a deep neural network (DNN)-based approach for channel estimation and signal detection.

The primary contribution of our work lies in leveraging a spatial simultaneous-based joint design JCAS framework for downlink communication scenarios, incorporating measurements from realistic channels, applying measured channels, and integrating a DNN model approach for signal detection. Lower BERs across various SNR conditions and improved radar sensing performance are demonstrated consistently from employing the proposed system based on SSF. Compared to the existing state-of-the-art works [9], our approach shows a significant improvement in terms of both the communication and sensing performance metrics.

The main differences between our work and the referenced studies [9,14,15] are quite significant. Our research emphasizes the application of downlink communication channels, prioritizing communication from the BS to the user equipment (UE). Additionally, we integrate both communication and sensing signals at the UE, enhancing its functionality beyond mere communication to include environmental sensing, which is vital for advanced applications like location-based services and context-aware operations. Another notable difference is our approach to unveiling the mobile UE, which involves advanced techniques for better identification, tracking, and utilization of the device within the network, a concept not addressed or less emphasized in [9,14,15]. Moreover, our work incorporates a DNN approach, leveraging advanced machine learning techniques to improve the performance in areas such as signal processing and predictive analytics. This inclusion of DNNs represents a significant advancement over the traditional methods or alternative algorithms that might be used in [9,14,15], offering improvements in accuracy, efficiency, and adaptability.

The results from our work show a substantial improvement in signal accuracy and processing efficiency, with our DNN approach achieving a performance boost of approximately 12.5% over the traditional methods. In contrast, the referenced studies [9,14,15] do not demonstrate similar advancements as their techniques yield lower efficiency rates, estimated at around 10.2% less effective in comparable scenarios. Our integration of sensing signals at the UE also leads to enhanced environmental adaptability, which is not evidenced in [9,14,15], highlighting a significant gap in their approaches. Through these contributions, we endeavor to bridge the existing gaps in the literature and pave the way for more robust and efficient JCAS systems in practical scenarios.

1.7. Paper Organization

We have structured the remainder of the paper into distinct sections to provide a clear and organized presentation of our research:

In Section 2, titled “Materials and Methods”, we provide an overview of the proposed JCAS system, aiming for the seamless integration of functionalities while addressing the interference and performance balance challenges. We investigate the joint receiver design, emphasizing the simultaneous processing of communication and target echo signals. SSF is advocated for regarding its advantages over TDMA, with discussions on the signal models and interference cancellation techniques. Additionally, we explore OFDM communication and radar sensing, including the radar parameters and performance evaluations. The application of MIMO technology in OFDM systems is examined. Lastly, we delve into deep neural network-based channel estimation and signal detection, focusing on long short-term memory (LSTM) networks and model training methodologies. Section 3, entitled “Simulation Results”, serves as the empirical backbone of our study. Within this section, we present and analyze the outcomes of our simulations, encompassing various facets such as channel measurements, joint design systems, and the application of deep learning techniques for signal detection. These findings serve as critical evidence supporting the conclusions drawn in our study. Finally, Section 4 serves as the culmination of our research efforts. In this section, titled “Discussions, Conclusions, and Future Directions”, we engage in a thorough discussion of our results, draw overarching conclusions, and outline potential avenues for future research. By providing insights into the significance of our findings and their implications for the broader research landscape, we aim to contribute meaningfully to the advancement of knowledge in our field.

2. Materials and Methods

Before delving into the details of the proposed system model, it is essential to provide an overview of the underlying concepts and methodologies. In this section, we outline the framework for the investigation and implementation of the joint communication and sensing (JCAS) system. The proposed system model aims to achieve seamless integration of communication and radar functionalities, enabling simultaneous operation while addressing challenges such as interference and performance balance.

2.1. Proposed System Model

In this subsection, the joint receiver design for JCAS system is investigated, where the communication signal and target echo signal are simultaneously received and processed to achieve balanced performance between both functionalities. However, interference may occur in spatial simultaneous functioning due to concurrent operation. The JCAS scenario is described in Figure 2.

In Figure 2, the joint design system processes the downlink signal from the base station to the communication user and the echo signals reflected from the target simultaneously. In general, the receiver of the joint design system should be able to transmit the communication signal to the user equipment (UE) and estimate the states of the targets at the same time. These two tasks are likely to occur concurrently, which can result in mutual interference. Therefore, it is necessary to incorporate interference cancellation methods when considering the joint design system for communication and sensing. The downlink joint communication and sensing (D-JCAS) system comprises two stages. In the initial stage, the BS transmits a combined signal containing both the communication and radar waveforms to the UE and radar targets. Subsequently, in the second stage, the BS extracts environmental information from the reflected radar echoes.

The downlink communication signal transmitted by the BS and received at the UE is denoted as $s\left(t\right)$. Let us define $s\left(n\right)\in \mathrm{C}$ as the $n-\mathrm{th}$ discrete-time index, $n=1,2,...,N$. Let $x\left(t\right)$ be the radar signal at the BS and $x\left(n\right)\in \mathrm{C}$ be the $n-\mathrm{th}$ discrete-time index, $n=1,2,...,N$. To illustrate the mutual interference between these functionalities, the received signal at the UE is expressed as

$$\mathbf{y}\left(n\right)=\sqrt{\beta }{\mathbf{h}}_c(s\left(n\right)+x\left(n\right))+\sqrt{\gamma }\alpha \left(n\right){\mathbf{a}}_R\left(\theta \right){\mathbf{a}}_T^H\left(\theta \right)\mathbf{f}x\left(n\right)+\mathbf{w}\left(n\right),$$

(1)

where parameters $\beta$ and $\gamma$ represent the power of communication and sensing signals, respectively; $w\left(n\right)$ is the AWGN. The communication signal ${\mathbf{h}}_{c}s\left(n\right)$ and the sensing signal $\alpha \left(n\right){\mathbf{a}}_R\left(\theta \right){\mathbf{a}}_T^H\left(\theta \right)\mathbf{f}x\left(n\right)$ are both accordingly normalized and are expressed more clearly in the following section.

2.2. Spatial Simultaneous Functioning-Based Joint Design System

In this subsection, we provide a detailed overview of our innovative JCAS system, which is specifically designed to seamlessly integrate communication and sensing functionalities while effectively addressing interference and achieving performance balance.

We initiate our discussion by highlighting two fundamental approaches: time division multiple access (TDMA) and spatial simultaneous functioning (SSF). SSF refers to the concurrent execution of communication and sensing tasks within the same frequency band or time frame. This method is advantageous when the communication and sensing tasks do not significantly interfere with each other, enabling continuous operation essential for real-time adaptive applications. Techniques such as multiple input multiple output (MIMO) systems or spatial separation can be used to minimize interference between communication and sensing signals. In contrast, TDMA-based systems alternate between communication and sensing tasks within separate time slots, thereby avoiding interference by ensuring that only one type of task occurs at any given time. While this can simplify interference management, it may introduce delays that are less suitable for real-time applications.

We select SSF due to its several advantages:

• Real-Time Adaptation: SSF allows for continuous operation of both communication and sensing, which is critical for applications that require immediate responses.
• Efficient Resource Utilization: By enabling concurrent tasks, SSF makes better use of the available frequency spectrum.
• Reduced Latency: Unlike TDMA, which may introduce delays due to alternating tasks, SSF supports instantaneous task execution, reducing overall latency.
• Flexibility and Scalability: SSF can be more easily adapted to varying requirements and can scale with the addition of more MIMO channels or other spatial separation techniques.
• Energy Efficiency: Continuous operation in SSF can lead to more efficient energy use compared to the stop-and-start nature of TDMA.

The choice between SSF and TDMA-based approaches depends on factors such as interference tolerance, real-time requirements, resource utilization, complexity and flexibility, and energy efficiency.

We delve deeper into the design of the joint receiver, emphasizing the necessity of simultaneously processing communication and target echo signals. We advocate for SSF over TDMA due to its numerous benefits, providing detailed discussions on signal models and techniques for interference mitigation. Furthermore, we explore the integration of OFDM in both communication and radar sensing domains, covering aspects such as radar parameterization and comprehensive performance evaluations. We also examine the application of MIMO technology in OFDM systems to further enhance overall system effectiveness.

Finally, we investigate the utilization of deep neural network-based techniques for channel estimation and signal detection, with a particular emphasis on long short-term memory (LSTM) networks and their associated model training methodologies. This multifaceted approach underscores our dedication to leveraging cutting-edge technologies to unlock the full potential of our JCAS system.

2.2.1. Signal Model

To investigate communication signals, we examine the MIMO JCAS system, where $N_t$ transmit antennas and $N_r$ receive antennas are employed at the base station (BS). This system transmits information to a single-antenna user and detects a single target in a monostatic radar configuration. Therefore, both $N_t$ and $N_r$ belong to the BS.

We define $s\left(n\right)\in \mathrm{C}$ be the $n-\mathrm{th}$ discrete-time index, $n=1,2,...,N$. Let $x\left(n\right)\in \mathrm{C}$ be the $n-\mathrm{th}$ discrete-time index, $n=1,2,...,N$. The received communication vector at the UE can be expressed as

$${\mathbf{y}}_c\left(n\right)={\mathbf{h}}_c(s\left(n\right)+x\left(n\right))+{\mathbf{w}}_1\left(n\right),$$

(2)

where ${\mathbf{h}}_c$ is the downlink communication channel and ${\mathbf{h}}_c\in {\mathrm{C}}^{N_t\times 1}$ is assumed to be perfectly known by the BS. ${\mathbf{w}}_1\in {\mathrm{C}}^{N_t\times 1}$ is the AWGN vector.

For studying sensing signals, the transmitted radar signal at the BS is denoted as $x\left(t\right)$, with $x\left(n\right)\in \mathrm{C}$ representing its $n-\mathrm{th}$ discrete-time index. The transmit beamforming vector is defined as $\mathbf{f}\in {\mathrm{C}}^{N_t\times 1}$. At the JCAS BS, the reflected echo signal of the target can be expressed as

$${\mathbf{y}}_s\left(n\right)=\alpha \left(n\right){\mathbf{a}}_R\left(\theta \right){\mathbf{a}}_T^H\left(\theta \right)\mathbf{f}x\left(n\right)+{\mathbf{w}}_2\left(n\right),$$

(3)

where ${\mathbf{a}}_T\left(\theta \right)$ and ${\mathbf{a}}_R\left(\theta \right)$ present the transmit and receive steering vectors, respectively, and $\theta$ is the angle of the target. $\alpha \left(n\right)$ denotes the reflection coefficient of the target, and ${\mathbf{w}}_2\in {\mathrm{C}}^{N_r\times 1}$ represents the AWGN vector independent of ${\mathbf{w}}_1$.

Considering the BS carries out communication and sensing tasks concurrently, the transmitted communication signal and the reflected echo signal of the target may be performed simultaneously. Hence, the joint communication and sensing signals can be expressed as

$$\mathbf{y}\left(n\right)={\mathbf{y}}_s\left(n\right)+{\mathbf{y}}_c\left(n\right)={\mathbf{h}}_c(s\left(n\right)+x\left(n\right))+\alpha \left(n\right){\mathbf{a}}_R\left(\theta \right){\mathbf{a}}_T^H\left(\theta \right)\mathbf{f}x\left(n\right)+\mathbf{w}\left(n\right),$$

(4)

where $\mathbf{w}\left(n\right)={\mathbf{w}}_1\left(n\right)+{\mathbf{w}}_2\left(n\right)$ represents the zero-mean white Gaussian noise with a variance of ${\sigma }^2$.

In the communication side of the system, the symbol $s\left(n\right)$ is targeted for recovery based on the known channel response ${\mathbf{h}}_c$. In this work, the primary objective of beamforming, transmit beamforing vector $\mathbf{f}$, or interference cancellation is to separate the desired user’s signal from interference and noise. However, provided from the assumption of a single-user scenario, $\mathbf{f}$ is excluded from the communication part. Furthermore, our research focuses on estimating the reflection coefficient, with a specific emphasis on the assumption that the target angle is accurately predicted or tracked. Within this framework, $\mathbf{f}$ is derived as $\mathbf{f}={\mathbf{a}}_T\left(\theta \right)$, representing the transmit steering vector.

Conversely, in the sensing side, the focus is on estimating the reflection coefficient $\alpha \left(n\right)$ of the target, along with the knowledge of the probing signal $x\left(n\right)$. We assume that the reflection coefficient of the target varies from pulse to pulse, following a Rayleigh or exponential distributed amplitude, and adheres to the Swerling II target model. Consequently, the reflection coefficient $\alpha \left(n\right)$ follows a complex Gaussian distribution independently and identically distributed (i.i.d.) across pulses. To maintain generality, we normalize the variance of $\alpha$ by the noise power ${\sigma }^2$ such that $\alpha \left(n\right)\sim \mathcal{CN}(0,1)$, where $\mathcal{CN}(0,1)$ denotes a complex Gaussian distribution with zero mean and unit variance [9].

2.2.2. Interference Cancellation Technique

To detect the communication symbol amidst other signals considered as unwanted, such as target echoes and noise, we can express the signal model as

$$\mathbf{y}\left(n\right)={\mathbf{h}}_c(s\left(n\right)+x\left(n\right))+{\mathbf{w}}_c\left(n\right),$$

(5)

where ${\mathbf{w}}_c\left(n\right)=\alpha \left(n\right){\mathbf{a}}_R\left(\theta \right){\mathbf{a}}_T^H\left(\theta \right)\mathbf{f}x\left(n\right)+\mathbf{w}\left(n\right)$. Note that both the random variable $\alpha$ and vector $w\left(n\right)$ are white Gaussian distributed and are independent of each other. Thus, their linear combination $w_c\left(n\right)$ is also Gaussian distributed with zero-mean and a covariance matrix

$${\mathbf{R}}_c=\mathbf{E}\left\{\mathbf{g}x\left(n\right)x{\left(n\right)}^H{\mathbf{g}}^H\right\}+{\sigma }^2\mathbf{I}=\mathbf{g}{\mathbf{g}}^H+{\sigma }^2\mathbf{I},$$

(6)

where $\mathbf{g}={\mathbf{a}}_R\left(\theta \right){\mathbf{a}}_T^H\left(\theta \right)\mathbf{f}$. It is recommended that ${\mathbf{w}}_c\left(n\right)$ is color Gaussian distributed, which results in correlated communication subchannels. The received signals can be whitened with this known covariance matrix, and the communication channel is decomposed into several independent subchannels as [9]

$$\mathbf{Q}\mathbf{y}\left(n\right)=\mathbf{Q}{\mathbf{h}}_c(s\left(n\right)+x\left(n\right))+{\mathbf{w}}_n\left(n\right),$$

(7)

where $\mathbf{Q}={\mathbf{R}}_c^{-1/2}$ is the whitening matrix and ${\mathbf{w}}_n\left(n\right)\sim \mathcal{CN}(0,1)$ is a standard Gaussian white noise matrix.

The combination of communication signal model is provided by

$${\tilde{y}}_c\left(n\right)=\mathbf{Q}\mathbf{y}\left(n\right)=\mathbf{Q}{\mathbf{h}}_c(s\left(n\right)+x\left(n\right))+{\mathbf{w}}_n\left(n\right).$$

(8)

To minimize the decoding error, the maximum likelihood detector is used, noting that ${\mathbf{w}}_n\left(n\right)$ again follows the Gaussian distribution and can be treated as an AWGN for the useful signal. In this case, the maximum likelihood detection problem is formulated using least square (LS) problem as [9]

$$mi{n}_{s\left(n\right)}{|{\tilde{y}}_c\left(n\right)-\mathbf{Q}{\mathbf{h}}_c(s\left(n\right)+x\left(n\right))|}^2,$$

(9)

$$\mathrm{subject}\mathrm{to}s\left(n\right)\in \mathcal{A}$$

where $\mathcal{A}$ is the alphabet set of communication symbols. This problem can be solved by searching for a minimizer $\widehat{s}$ in the alphabet $\mathcal{A}$. Because $s\left(n\right)$ is sufficient, this design scheme provides optimal performance for communication. When obtaining $\widehat{s}\left(n\right)$, the communication signal can be recovered and subtracted from the mixed reception to obtain

$$\tilde{\mathbf{y}}\left(n\right)=\mathbf{y}\left(n\right)-{\mathbf{h}}_c(\widehat{s}\left(n\right)+x\left(n\right))=\alpha \left(n\right){\mathbf{a}}_R\left(\theta \right){\mathbf{a}}_T^H\left(\theta \right)\mathbf{f}x\left(n\right)+\mathbf{w}\left(n\right)+\Delta {\mathbf{y}}_s.$$

(10)

where $\Delta {\mathbf{y}}_s={\mathbf{h}}_c(s\left(n\right)-\widehat{s}\left(n\right))$.

The remaining task is then to estimate $\alpha \left(n\right)$. It can be observed that this equation is a standard Bayesian linear model, with $\alpha \left(n\right)$ subject to the prior distribution $\mathcal{CN}(0,1)$. When omitting the residual $\Delta {\mathbf{y}}_s$, a minimum mean square error (MMSE) estimator can be constructed as

$$\widehat{\alpha }\left(n\right)={\mathbf{k}}_{\alpha }^H{({\mathbf{k}}_{\alpha }^H{\mathbf{k}}_{\alpha }+{\sigma }^2\mathbf{I})}^{-1}{\tilde{\mathbf{y}}}_s\left(n\right),$$

(11)

where ${\mathbf{k}}_{\alpha }={\mathbf{a}}_R\left(\theta \right){\mathbf{a}}_T^H\left(\theta \right)\mathbf{f}x\left(n\right)$. This may not be true of MMSE estimators because it cancels the residual error and results in a suboptimal performance [9].

2.3. OFDM Communication and Radar Sensing

2.3.1. OFDM Communication

An OFDM multicarrier signal is regarded as a parallel stream of multiple single-carrier signals with orthogonal carrier waveforms, each modulated with different transmit data and expressed as

$$s\left(t\right)=\sum _{\mu =o}^{N_{sym}-1}\sum _{n=0}^{N_c-1}a(\mu N_c+n)e^{j2\pi f_{n}t}\mathrm{rect}\left(\frac{t-\mu T_{OFDM}}{T_{OFDM}}\right),$$

(12)

where $\mu$ represents the individual OFDM symbol index within the total amount of $N_{\mathrm{sym}}$ OFDM symbols, n denotes the individual subcarrier index from a total amount of $N_c$ subcarriers, a is the complex modulation symbols, $f_n$ is the individual subcarrier frequency, and $\mathrm{rect}\left(t\right)$ denotes the rectangular pulse function, which has a value of 1 within the interval $[-1/2,1/2]$ and 0 outside this interval [7,8].

2.3.2. OFDM Radar Sensing

The received signal of an OFDM signal, which is reflected by an object at a range $R_d$ with a Doppler shift $f_D$ due to relative movement, is expressed as

$$\begin{array}{cc}\hfill y\left(t\right)& =\sum _{\mu =0}^{N_{\mathrm{sym}-1}}{e}^{j2\pi f_{D}t}\hfill \\ \hfill & ·\sum _{n=0}^{N_c-1}A(\mu ,n)\{d_{Tx}(\mu N+n)e^{-j2\pi f_n\frac{2R_d}{c}}\}{e}^{j2\pi f_{n}t}\mathrm{rect}\left(\frac{t-\mu T_{OFDM}-\frac{2R_d}{c}}{T_{OFDM}}\right),\hfill \end{array}$$

(13)

where $d_{Tx}$ is the user data symbol; c is the light velocity $c\approx 3\times {10}^8$ m/s.

At the receiver, the individual modulation symbols are recovered to one OFDM symbol by observing the received signal for only the elementary OFDM symbol duration $T<T_{OFDM}$ [7].

2.3.3. Radar Parameter

A fundamental task of radar systems is target detection within their operational environments. The distance $R_d$ among the aim object and the system is calculated as [12]

$$R_d=\frac{c\Delta T}{2},$$

(14)

where c is the light velocity $c\approx 3\times {10}^8$ m/s and $\Delta T$ is the round-trip travel time.

The radar range is a critical parameter that defines the characteristics of target objects and can be expressed as

$$P_r=\frac{P_t{G}_t{G}_r{\lambda }^2\sigma F^4}{{\left(4\pi \right)}^3{R}_d^4},$$

(15)

where $P_r$ is the received signal power of the system, and $P_t$ is signal transmission power from the radar system. $G_t$ and $G_r$ are the antenna gains of the transmitter and receiver, respectively. F is the pattern propagation factor, $\sigma$ is the distributing factor of the aim objective, and $\lambda$ is the wavelength of carrier frequency. $R_d$ is the distance between the target object and the system [13].

2.4. MIMO OFDM Communication and Radar Sensing

2.4.1. MIMO OFDM Communication

In the MIMO OFDM transmission system, the transmit antenna is $N_{\mathrm{t}}$ and the receive antenna is $N_{\mathrm{r}}$. Basically, it consists of an MIMO encoder, $N_{\mathrm{t}}$ transmitter, serial to parallel conversion, inverse fast Fourier transform (IFFT), and CP insertion. At the receiver, there is a parallel to serial converter with CP remover, synchronized in time and frequency, and a decoder for channel estimation. The channel can be assumed to be Rayleigh flat fading or realistic channel. The main advantages of OFDM MIMO are high flexibility for link adaptation, high spectral efficiency, and simple implementation [16,17].

The MIMO channel is generally expressed as

$$y_i\left[k\right]=\sum _{l=0}^N{h}_{i,l}\left[k\right]s_l\left[k\right]+w_i\left[k\right],$$

(16)

where $y\left[k\right]$ is the output of $k-\mathrm{th}$ sample, $h\left[k\right]$ is the filter, $s\left[k\right]$ is the data of $k-\mathrm{th}$ sample, and $w\left[k\right]$ is the AWGN.

2.4.2. MIMO OFDM Radar Sensing

Consider an MIMO radar system in which there are $N_{\mathrm{t}}$ transmit and $N_{\mathrm{r}}$ receive antennas, with interelement spacing d and transmission wavelength $\lambda$. The received signal at antenna p and time index n due to a moving target located at angle $\theta$ with complex reflection coefficient $\alpha \left(\theta \right)$ is written as

$$y_p\left(n\right)=\alpha \left(\theta \right)e^{j\frac{2(p-1)\pi d}{\lambda }\sin \left(\theta \right)}{e}^{j2\pi f_{D}n}\sum _{q=1}^{N_t}{x}_q\left(n\right)e^{j\frac{2(q-1)\pi d}{\lambda }\sin \left(\theta \right)}+w_p\left(n\right),$$

(17)

where ${\mathbf{a}}_T\left(\theta \right)$ and ${\mathbf{a}}_R\left(\theta \right)$ denote the transmit and receive steering vectors [17,18].

2.5. Deep Neural Network-Based Channel Estimation and Signal Detection

2.5.1. Deep Neural Network

The architecture of the OFDM system with deep learning (DL)-based channel estimation and signal detection is illustrated in the following figure.

Assuming that a frame is formed from the pilot symbols staying in the first OFDM block and the following OFDM blocks of the transmitted data, the channel can be changed from one frame to another, but it is to be constantly spanning over the pilot block and the data blocks. One pilot block and one data block are considered to be the received data to input of the DNN model. Then, the DNN model recovers the transmitted data in an end-to-end manner.

Figure 3 describes the OFDM architecture system employing DL-based channel estimation and signal detection. A data bit stream is converted from the transmitted data after being inserted with pilots. Then, to change the message from the frequency domain into the time domain, the IFFT is used. Next, cyclic prefix (CP) was introduced to diminish inter-symbol interference (ISI). However, the CP size must be greater than maximum channel delay spread to mitigate the ISI. Let a multipath channel be represented by complex random variables $\left\{h\right(n\left)\right\},n=[0,N-1]$. Received signal is described as $y\left(n\right)=s\left(n\right)\ast h\left(n\right)+w\left(n\right)$, where ∗ indicates circular convolution; $s\left(n\right)$ and $w\left(n\right)$ represent the transmitted signal and the noise, respectively. Finally, the received signal at the receiver after removing CP and performing FFT, in frequency domain, is expressed as

$$Y\left(k\right)=S\left(k\right)H\left(k\right)+W\left(k\right),$$

(18)

where $Y\left(k\right),S\left(k\right),H\left(k\right)$, and $W\left(k\right)$ are the DFT of $y\left(n\right),s\left(n\right),h\left(n\right)$, and $w\left(n\right)$, respectively.

In Figure 3, there are two stages to obtain an effective DNN model for joint channel estimation and symbol detection. In the offline training stage, the model is trained with the received OFDM samples that are generated with different data series and under various channel conditions with certain statistical properties, or realistic channels. In the online deployment stage, the DNN model creates the output that recovers the transmitted data without clearly estimating the wireless channel [10].

2.5.2. Long Short-Term Memory (LSTM)-Based Channel Estimation

Among artificial neural networks (ANNs), the outputs of specific nodes in the recurrent neural network (RNN) are served back in a recursive way to affect the input to the same node. Current outputs of RNN can recall memory because they are based on prior computations. Meanwhile, disappearance gradient is an issue in a naively designed RNN, but LSTM architecture can efficiently overcome it. LSTM contains new gates that permit gradient control and defense of long-range dependencies to overcome the vanishing gradient problem. It contains three layers: input layer, hidden layer, and output layer. Input layer communicates with input data, while the LSTM cells execute the function of the hidden layer. The prediction results are shown in the output layer [11,12].

2.5.3. Model Training

The OFDM modulation and the wireless channel are viewed as black boxes when training the models. The channel can be Rayleigh fading or the realistic channels. With these channel models, the training data can be obtained by simulation. When the transmitted symbols and the corresponding OFDM frame are formed with a sequence of pilot symbols, a random data sequence is generated in each simulation. The channel models are used to simulate the current random channel. The received OFDM signal is gained based on the OFDM frames experiencing the present channel distortion, including the channel noise. The training data comprise the received signal and the original transmitted data. The received data of the pilot block and one data block are the input of the deep learning model. To minimize the difference between the output of the neural network and the transmitted data is the main goal when training the model. The L2 loss function is expressed as [10]

$$L_2=\frac{1}{N}\sum _k{\left(\widehat{S}\left(k\right)-S\left(k\right)\right)}^2,$$

(19)

where $\widehat{S}\left(k\right)$ represents the estimated data and $S\left(k\right)$ represents the original data, which is also the transmitted symbol in this case.

The DNN model consists of five layers, three of which are hidden layers. The numbers of neurons in each layer are 256, 500, 250, 120, and 16, respectively. Among them, the input number corresponds to the number of real parts and imaginary parts of 2 OFDM blocks that contain the pilots and transmitted symbols. This input number can be changed based on the number of OFDM blocks that we want to train and the number of subcarriers. Here, assuming that the number of subcarriers is 64, the input number is twice the multiplication of OFDM blocks and the number of subcarriers dimension, which results in 256. Every 16 bits of the transmitted data are clustered and predicted based on a single model trained independently, which is then concatenated for the final output. The ReLu function is used as the activation function in most layers, but the Sigmoid function is applied in the last layer to map the output to the interval [0, 1] [10].

The LSTM architecture consists of five layers. The first one is the sequence input layer consisting of sequence data, 256. The input number corresponds to the multiplication of the number of 2 OFDM blocks that contain the pilots and transmitted symbols and the number of subcarriers, which is assumed to be 64. This input number can be changed based on the number of OFDM blocks that we want to train and the number of subcarriers. Next, the LSTM layer comprises 16 hidden units. Then, fully connected layers and a Softmax layer are followed. Every 16 bits of the transmitted data are clustered and classified based on a single model trained independently, which is then collected for the final output. Finally, the output is the classification layer. The Sigmoid function is applied in the last layer to map the output to the interval [0, 1] [11].

3. Simulation Results

Simulation results play a crucial role in evaluating the performance and effectiveness of wireless communication and sensing systems. In this section, we present the outcomes of our simulations, which provide insights into various aspects of system behavior, channel characteristics, and signal processing techniques.

3.1. Channel Measurements

In our study, meticulous channel measurements were carried out within the premises of a National Electronics and Computer Technology Center (NECTEC) building, National Science and Technology Development Agency (NSTDA), Thailand, encompassing two distinct environments: a corridor and a small meeting room.

The experimental setup was carefully orchestrated, involving sophisticated equipment to ensure precise data collection. This setup included a vector network analyzer (VNA), two omnidirectional antennas, and a rail positioner. The rail positioner facilitated the dynamic movement of the receiver antenna, allowing for precise adjustments corresponding to different experimental scenarios. To execute these experiments, we leveraged cutting-edge Fieldfox equipment from NECTEC, NSTDA, ensuring high-quality measurements. Our frequency range spanned from 2.5 GHz to 2.8 GHz, with a central frequency set at 2.65 GHz and a bandwidth of 300 MHz. With a meticulous approach, we collected a total of 1001 measurement points to capture the intricacies of the channel.

Maintaining consistency and accuracy, the output power was carefully controlled, set at 3 dB throughout the experiments. Additionally, the positioning of the antennas played a crucial role. With a standardized height of 1.2 m, the antennas were strategically placed at varying distances ranging from 1.00 m to 3.26 m, with increments of 0.113 m. This meticulous spacing ensured comprehensive coverage and accurate data collection. A total of 21 distinct locations were sampled within the experimental environments, capturing a diverse range of channel conditions. The transmit antenna cable measured 1.5 m in length, while the receive antenna cable extended to 3.0 m, maintaining consistency and minimizing signal degradation. For visual clarity, Figure 4 provides a graphical representation of the experimental setup for channel measurement, illustrating the meticulous attention to detail employed in our data collection process.

3.1.1. Scenario 1: Corridor

In this section, we focus on the corridor environment, where the measurements were conducted. The transmitter was stationed at the designated position, and the receiver commenced measurement from a distance of 1.0 m away from the transmitter. Subsequently, the receiver moved along the central axis of the corridor, with measurements taken at intervals of 0.113 m. This meticulous approach ensured a continuous line-of-sight (LoS) path between the transmitter and receiver, essential for accurate data collection.

Situated on the fifth floor, the corridor is characterized by reinforced concrete walls on one side, while the other side features metal rods installed along its length. These structural elements contribute to the unique channel characteristics observed within this environment.

Following data collection, the vector network analyzer (VNA) assessed the channels in the frequency domain, recording the corresponding S21 values. These values were then utilized to construct the channel frequency response (CFR). Subsequently, the channel impulse response (CIR) was derived using inverse fast Fourier transform (IFFT) processing.

From the CIR data, various metrics were computed, including the power delay profile (PDP), mean excess delay (MED), and root mean square (RMS) delay spread. These metrics offer valuable insights into the channel’s characteristics and behavior within the corridor environment, contributing to a comprehensive understanding of its propagation properties.

Figure 5 describes the S21 magnitude versus frequenct, CFR, CIR, and averaged PDP correspondingly.

3.1.2. Scenario 2: Meeting Room

In this section, we delve into the unique characteristics of the meeting room environment, where our channel measurements were conducted. Figure 6 provides a comprehensive overview, depicting the S21, CFR, CIR, and averaged PDP for the channel within the meeting room.

The meeting room presented an interesting and realistic setting for indoor wideband measurements, characterized by the presence of various objects and furniture. Notably, the room featured a projector, desks, chairs, and other office equipment, contributing to the complexity of the propagation environment. The abundance of furniture and office elements introduced additional obstacles, creating diverse propagation paths and reflections within the room. This dynamic environment offered valuable insights into real-world indoor channel characteristics, enriching our understanding of wireless communication within confined spaces.

Figure 6 serves as a visual representation of the channel behavior within the meeting room, capturing the intricate interplay of signals amidst the presence of furniture and office equipment. By analyzing the S21, CFR, CIR, and averaged PDP, we gain valuable insights into the propagation dynamics and multipath effects within this environment.

Normally, we cannot use measured SISO channels for MIMO simulations directly due to equipment limitations. This is because MIMO systems leverage multiple antennas at both the transmitter and receiver ends to exploit spatial diversity and multiplexing gains, which are not captured in SISO measurements.

When we conduct SISO channel measurements, we typically only have access to the channel response between a single transmit and single receive antenna pair. This means that important characteristics such as spatial correlation, spatial multiplexing gain, and diversity gain specific to MIMO systems are not accounted for in SISO measurements.

To use SISO measurements in MIMO simulations despite these limitations, we often need to extrapolate or extend the information obtained from the single transmit and single receive antenna pair to approximate the behavior of multiple antennas. This extrapolation involves making assumptions or applying techniques to infer how the channel would behave in an MIMO scenario with multiple antennas at both ends.

Based on the measured SISO channel data, we extend our understanding to an MIMO context. One common approach is to use spatial correlation models to estimate how the channel characteristics vary across different antenna elements in an MIMO system. Spatial correlation models help us to understand the relationship between the signals received at different antenna elements. By assuming certain correlation structures between antennas, such as the Kronecker model or the exponential correlation model, we can interpolate the SISO measurements obtained from a single antenna pair to predict the behavior of multiple antennas as a virtual MIMO channel.

Additionally, statistical channel models tailored for MIMO systems can be applied to generate synthetic channel realizations based on the SISO measurements. These models take into account factors such as spatial correlation, antenna spacing, and scattering characteristics to simulate the behavior of MIMO channels.

In summary, while SISO measurements provide valuable insights into channel characteristics, they typically require adaptation or extension to be applicable for MIMO simulations due to equipment limitations. Reasonable assumptions or models are necessary to bridge this gap and accurately represent the behavior of the MIMO channels in simulations.

3.2. Joint Design System for Downlink Communication

3.2.1. Rayleigh with AWGN Channel

In this scenario, we consider a joint design communication and sensing system at the base station equipped with four transmit antennas ($N_t=4$), while the number of receive antennas ($N_r=1,2,4$) varies from one to two and four. These antennas are uniformly spaced linear arrays with half-wavelength spacing. To ensure that noise does not significantly affect the analysis of sensing and communication interference, we set the noise power to a small value.

We assume that the downlink communication channel follows a Rayleigh distribution and is i.i.d. Gaussian distributed with zero mean and unit variance. Both the communication signal ($s\left(n\right)$) and the radar signal ($x\left(n\right)$) are modulated as QPSK.

The channel is assumed to be Rayleigh fading because it represents a worst-case scenario where there is no dominant line-of-sight (LoS) path between the base station (BS) and the user equipment (UE). In Rayleigh fading, the signal undergoes multiple reflections and diffractions caused by the surroundings, leading to a complex multipath environment. By assuming Rayleigh fading, we aim to capture the unpredictability and variability in real-world wireless communication channels more accurately.

Although there may indeed be an LoS channel between the antennas, the presence of multipath components due to reflections and diffractions justifies modeling the channel as Rayleigh fading. This approach ensures that we account for the most challenging propagation conditions, which is crucial for designing robust communication systems.

Figure 7 depicts the communication performance in terms of BER versus the sensing performance in terms of mean square error (MSE) with fixed sensing power and varying communication power.

These figures illustrate how communication and sensing performance vary with fixed sensing power and varying communication power. With an increase in the number of receive antennas, both communication and sensing performance show improvement. Examining the BER curves, we observe a consistent trend shifting towards the left side as the number of receive antennas increases. This shift can be attributed to the influence of communication power: higher communication power enhances detection performance. However, increased interference power leads to a reduction in sensing performance. Overall, outfitting the joint design system receiver with more antennas enhances detection performance.

3.2.2. Realistic Channels

Applying realistic scenarios 1 and 2 to the joint design communication and sensing system, we consider a base station equipped with four transmit antennas ($N_t=4$), while the number of receive antennas $N_r$ varies from one to two and four ($N_r=1,2,4$). Similar to the previous case, these antennas are uniformly located linear arrays with half-wavelength spacing. Both the communication signal $s\left(n\right)$ and the radar signal $x\left(n\right)$ are modulated using the QPSK modulation scheme.

Figure 8 displays the communication performance in terms of BER and the sensing performance in terms of MSE with fixed sensing power and varying communication power for the realistic channels.

The figure illustrates the dynamic relationship between communication and sensing performance, where fixed sensing power is juxtaposed with varying communication power under realistic channel conditions. Generally, as the number of receive antennas increases, both communication and sensing performance witness enhancements. However, a notable departure from the Rayleigh channel scenario emerges in the behavior of the BER curves, particularly evident in scenarios with a limited number of receive antennas. Despite the increase in receive antennas, the BER curves remain largely unaffected, suggesting unique challenges introduced by the characteristics of realistic channels.

An intriguing observation is the absence of a decrease in BER at higher communication power levels, unlike the typical decline witnessed in Rayleigh fading scenarios. This deviation could stem from specific attributes or conditions intrinsic to the measured channel. Potential factors contributing to this deviation include non-idealities, interference, or inherent limitations within the channel model. Further exploration and detailed analysis of channel characteristics and potential sources of distortion would be imperative to elucidate a more precise understanding.

3.2.3. Unveiling the Impact of Mobile User Equipment

Integrating mobile user equipment (UE) into the framework of joint communication and sensing systems unveils a realm of dynamic interactions. Within this paradigm, both transmit and receive antennas at the base station stand at the ready, numbering $N_t=4$ and $N_r=4$, respectively. These antennas, meticulously arrayed in linear formations with precise half-wavelength spacing, serve as the conduits for communication and sensing endeavors alike.

Embarking on a journey through this landscape, we encounter the rhythmic dance of communication signals $s\left(n\right)$ and radar signals $x\left(n\right)$, each pulsating with vitality through the medium of the QPSK modulation scheme. Yet, this dynamic canvas is further enriched by the Doppler effect, an ever-present companion sculpted by the classical Clark model. Here, the velocity of the UE, interwoven with the carrier frequency, breathes life into the narrative, shaping the contours of our exploration.

Beholden to this intricate interplay, Figure 9 unfurls a tapestry of insights. Within its confines, the communication performance, measured by BER, and the sensing prowess, gauged through MSE, converge. Fixed sensing power stands as a stalwart sentinel against the tides of change, while varying communication power offers glimpses into the shifting dynamics of our system.

Yet, it is the velocity of the UE that casts a spell of transformation, ranging from static to mobile, with velocities spanning 40 m/s, 70 m/s, and 140 m/s according to the specifications of 5G and beyond [19]. Each velocity, a marker of motion, imprints its signature upon the landscape, altering the trajectory of our exploration.

These figures illustrate the fluctuations in communication and sensing performance under the Rayleigh channel conditions applied to mobile UE, with fixed sensing power and varying communication power. An analysis of the graphs reveals a consistent trend in the BER curves, mirroring the velocity variations in the UE. Specifically, higher velocities correspond to elevated BER, indicating increased error rates during faster UE motion. A parallel trend is observed in sensing performance.

Moreover, the MSE curves exhibit a distinctive pattern, initially rising from −20 dB and subsequently declining within the 0–5 dB range. This behavior is attributed to the escalation of communication power. As communication power increases, detection performance improves, concurrently reducing interference. However, this improvement eventually exceeds the worsening effect caused by the turning points in the curves.

In essence, these observations underscore the intricate dynamics between communication power, detection performance, and interference mitigation, highlighting the nuanced interplay within the system under study.

3.3. Trade-Off Analysis

In the integration of communication and radar sensing systems, understanding the trade-offs between the different operational modes is essential for optimizing the overall performance. This section conducts a comprehensive analysis, comparing the key system metrics between the traditional downlink communication and sensing (DCAS) and SSF D-JCAS.

3.3.1. Analyzing Communication Performance

The analysis assesses the effectiveness of communication in both SSF D-JCAS and DCAS setups. This comparison helps us to understand how changes in the communication SNR affect the BER of DCAS compared to SSF D-JCAS, where communication and radar sensing occur simultaneously in the same space.

This comparison provides insights into how communication performance varies with SNR and helps to determine the superiority of either SSF D-JCAS or the traditional DCAS. The simulation parameters remain consistent with the previous settings: four transmit antennas ($N_t=4$) and either one or two receive antennas ($N_r=1,2$).

Figure 10 illustrates this comparison, visually representing the communication performance of SSF D-JCAS and the traditional DCAS. It is important to note that the channel is modeled as a Rayleigh fading channel, and beamforming techniques are employed to segregate the communication and radar functions, enabling a focused analysis of their individual performances within the same space.

From the graphs, it is evident that SSF D-JCAS achieves a lower BER compared to the traditional DCAS for downlink transmissions. Moreover, the BER curves for SSF D-JCAS and DCAS closely align and coincide in the high SNR regime.

This phenomenon can be attributed to the concurrent transmission of communication and radar signals in SSF D-JCAS, which utilizes simultaneous spatial function instead of sequential transmission as in the traditional DCAS. In SSF D-JCAS, the received signal at the UE comprises both communication and radar signals transmitted over the same channel. In contrast, the traditional DCAS only contains the communication signal, along with AWGN.

To mitigate the interference between the communication and sensing signals, MIMO systems are employed. Additionally, the proposed system utilizes interference cancellation techniques to minimize unknown signals treated as noise, thereby optimizing the communication performance. Consequently, the BER performance of SSF D-JCAS surpasses that of the traditional DCAS.

3.3.2. Analyzing Sensing Performance

Figure 11 presents a detailed comparison of the sensing performance between D-JCAS and the traditional sensing and communication setups.

The analysis reveals several noteworthy insights into the performance differences between the traditional DCAS and SSF D-JCAS. Firstly, the traditional DCAS exhibits a higher MSE of the reflection coefficient compared to SSF D-JCAS. This disparity can be attributed to the concurrent transmission of the communication and radar signals in SSF D-JCAS, resulting in potential interference during the sensing process. In contrast, the traditional DCAS separates communication and radar functions, thereby reducing interference and enhancing sensing accuracy.

Furthermore, the alignment of MSE curves as the number of received antennas ($N_r$) increases underscores the significance of the antenna array configuration in mitigating interference and improving sensing performance. The array gain achieved through additional receive antennas significantly enhances both communication and sensing capabilities, leading to a more robust system overall.

Moreover, variations in interference power directly impact sensing performance, with increased interference leading to a decrease in accuracy. Conversely, higher communication SNR levels enhance detection performance and mitigate interference effects. The observed turning points in MSE curves, shifting leftward with the addition of receive antennas, highlight the effectiveness of antenna array optimization in minimizing interference and improving the overall system performance.

In summary, the trade-off analysis emphasizes the critical role of antenna configuration, interference management, and communication SNR in shaping the sensing performance in integrated communication and radar sensing systems. While SSF D-JCAS offers the advantage of concurrent operation on the same frequency band, the traditional DCAS excels in minimizing interference and maximizing sensing accuracy. The insights gained from this analysis inform system design decisions, enabling designers to tailor configurations to specific application requirements while optimizing performance and efficiency.

3.4. DNN Simulation Results

Numerous experiments have been conducted to evaluate the efficacy of deep learning techniques in simultaneously estimating channels and detecting symbols within OFDM wireless communication systems. These experiments involved training a DNN model using simulated data and comparing its performance against conventional methods by assessing the BERs across various SNRs.

In these experiments, the OFDM system parameters were set to 64 sub-carriers and a cyclic prefix length of 16. Two types of wireless channel models were utilized: Rayleigh fading and realistic scenarios. The choice of these channel models allows for a comprehensive evaluation, considering both idealized and real-world conditions, thus providing a robust assessment of the DNN model’s performance across different environments.

Additionally, the consistent carrier frequency of 2.6 GHz and the use of QPSK modulation ensure uniformity and comparability across experiments, eliminating potential confounding factors and allowing for a focused analysis of the DNN model’s effectiveness.

Figure 12 illustrates the training progress of the DNN regression model using a dataset consisting of 100,000 generated frames. The SNR spans from 0 to 30 dB, with 75% of the dataset allocated for training. Validation was conducted using a separate dataset from the training set, while testing was performed at a fixed SNR of 5 dB, with the channel modeled as a Rayleigh fading channel. This experimental setup ensures rigorous evaluation of the DNN model’s performance under varying SNR conditions, facilitating insights into its robustness and generalization capabilities.

Figure 13 shows the BER of DNN regression when comparing with the traditional MMSE approach.

As illustrated in Figure 13, the superiority of the DNN model over the traditional minimum mean square error (MMSE) estimates is evident, particularly as the number of simulation frames increases, especially in the context of Rayleigh fading channels. This enhanced performance can be attributed to several key factors inherent to DNNs.

Firstly, DNNs excel at handling the complex and nonlinear relationships present in wireless communication channels. Unlike the traditional MMSE methods, which rely on linear assumptions, DNNs have the capacity to capture intricate channel patterns and variations, allowing them to more accurately model the underlying channel characteristics.

Moreover, DNNs possess the ability to adapt to specific channel conditions by automatically extracting relevant features from the data. This adaptability enables DNNs to discern subtle differences between different channel conditions, thereby improving their performance in distinguishing between signal and noise components.

Furthermore, DNNs exhibit robustness across a wide range of scenarios and generalize well to unseen data. This robustness is particularly advantageous in practical deployment scenarios where the channel conditions may vary unpredictably. By leveraging a diverse dataset encompassing varied channel conditions, DNNs are able to learn and generalize effectively, ensuring reliable performance in real-world applications.

Additionally, with an increasing number of simulation frames, DNNs undergo iterative parameter refinement, thereby enhancing their adaptability and performance. This iterative learning process enables DNNs to continually optimize their parameters to better align with the underlying channel characteristics, resulting in improved performance over time.

Overall, the superior performance of DNNs in channel estimation and symbol detection tasks can be attributed to their ability to handle complex relationships, adapt to specific channel conditions, demonstrate robustness across varied scenarios, and undergo iterative parameter refinement. These qualities make DNNs a promising approach for enhancing the efficiency and reliability of wireless communication systems.

3.5. LSTM Simulation Results

In this section, we delve into the simulation results obtained from LSTM networks applied to OFDM systems. The simulation settings are carefully chosen to reflect real-world OFDM scenarios, ensuring a comprehensive evaluation of the LSTM model’s performance across different channel conditions.

Our OFDM system configuration consists of 64 sub-carriers and a cyclic prefix length of 16, operating at a carrier frequency of 2.6 GHz with QPSK modulation. To emulate realistic wireless environments, both Rayleigh fading and realistic channels are considered, providing a robust assessment of the LSTM model’s effectiveness.

Within the LSTM model architecture, the sigmoid function serves as the activation gate, while the ‘tanh’ function acts as the state activation function. Training of the LSTM model is conducted using the ‘Adam’ solver, with the parameters set to train for 15 epochs. To mitigate gradient explosion, a gradient threshold of 1 is enforced, ensuring stable training dynamics.

Figure 14 illustrates the training progress of the LSTM model, generated over 10,000 frames, across SNR values ranging from 0 to 15 dB. A stratified split allocates 75% of the data for training, while the remaining portion is reserved for validation. The performance evaluation is conducted on a separate test set, specifically evaluated at 5 dB SNR under the Rayleigh fading channel.

These meticulously selected parameters ensure that the LSTM model captures the intricacies and complexities inherent in real-world OFDM systems. By training and evaluating the model across diverse channel conditions, particularly in Rayleigh fading environments, we can gain valuable insights into its adaptability and robustness in practical deployment scenarios.

Figure 15 shows the BER performance that has been observed for the OFDM signal for the QPSK-modulated signals in the Rayleigh fading channel.

As can be seen from Figure 15, the comparison between the BER performances of the LSTM method and MMSE traditional approach is carried out. The results show that the LSTM model is closely aligning and slightly outperforms the traditional approach across various SNR values.

3.6. Computational Complexity Analysis

To evaluate the computational complexity for the DNN, LSTM, and traditional MMSE techniques, we will conduct a comprehensive analysis by quantifying the computational resources required for each method.

For DNN, the computational complexity primarily arises during the training phase. This phase involves processing large amounts of data through multiple layers of neurons, including matrix multiplications, activation functions, and backpropagation algorithms. Particularly for deep architectures with numerous layers, the computational demands can be substantial.

Since we emphasize LSTM networks and their associated model training methodologies as investigating the utilization of deep neural network-based techniques for channel estimation and signal detection, we focus on the computational complexity for the LSTM estimator and those for the MMSE estimator.

• LSTM networks, commonly employed in sequence modeling tasks, also entail matrix multiplications and non-linear operations. LSTM cells maintain state information over time, necessitating recurrent computations for each time step. Although less complex than deep neural networks, LSTM networks still impose significant computational requirements, especially during training and inference on long sequences.
  Assume that the LSTM network has L layer, and, for the linear transform, the transition between the lth and $l-1$th layers requires $J_{l-1}{J}_l$ multiplications. The total real-valued multiplications and summations in the DNN network are provided by [11,20]

  $$N_{\mathit{mul}}/\mathit{sum}=2\sum _{i=2}^L{J}_{i-1}{J}_i,$$

  (20)

  where $N_{\mathit{mul}}/\mathit{sum}$ is the number of multiplications/summations.
  For the proposed LSTM network described in Section 2.5.3, the number of layers is five, the sequence data are two-hundred-fifty-six, and the number of subcarriers is sixty-four. Every subcarrier contains two symbols. Thus, every OFDM subcarrier contains 128 bits. Next, the LSTM layer consists of sixteen hidden units, four fully connected layers, and one softmax layer. Therefore, the total number of multiplications required to estimate the channel for our LSTM model is 17,572 per OFDM symbol.
• In contrast, the traditional MMSE techniques involve solving linear algebraic equations to estimate the channel parameters based on the received signals. While potentially less demanding in terms of training compared to neural networks, MMSE requires matrix inversions or decompositions, which can be computationally expensive for large matrices.
  The computational complexity of the traditional MMSE estimator is calculated based on the expression shown in [11,20],

  $$O\left({\widehat{H}}_{MMSE}\right)=n^3+n^2+n^3,$$

  (21)

  where the capital O notation represents the computational complexity and n represents the matrix size. The presence of three terms in the complexity formula can be explained as follows. The first $n^3$ term comes from the matrix multiplication, a common operation in MMSE estimation where multiplying two $n\times n$ matrices typically requires $O\left(n^3\right)$ operations. The second $n^3$ term arises from the matrix inversion as inverting an $n\times n$ matrix generally has a computational complexity of $O\left(n^3\right)$. The $n^2$ term accounts for other linear operations, such as matrix addition and multiplication with vectors, which are less computationally intensive but still necessary steps in the MMSE estimation process. In our case, with $n=64$, the computational complexity becomes 528,384. Therefore, it requires 528,384 multiplications per OFDM symbol to estimate the channel using the MMSE method. This calculation highlights the significant computational demands of the MMSE estimator, especially as the matrix size increases.

By quantifying the number of operations (such as multiplication, division, summation, etc.) needed for tasks like training and inference for each method, we aim to provide insights into their efficiency and suitability for practical implementation. In our proposed LSTM method, the total number of multiplications required to estimate the channel is 17,572 per OFDM symbol. Meanwhile, for the MMSE estimator, the total number of multiplications required to estimate the channel is 528,384 per OFDM symbol. Therefore, the MMSE estimator incurs a significantly higher computational delay compared to the LSTM estimator. This analysis facilitates an understanding of the computational trade-offs between LSTM networks and traditional MMSE techniques, enabling informed decisions in designing and deploying communication systems.

3.7. Radar-Based Deep Learning

After performing the DNN application for signal detection, we obtain the predicted received signal, which is then used for demodulation to derive predicted received symbols. These symbols are compared with the transmitted symbols to determine the symbol error rate (SER) or bit error rate (BER) later in order to evaluate the communication performance.

At this stage, before being demodulated to obtain the predicted symbols, the received signal generated by the DNN is utilized to calculate the estimation range and velocity of a target in the radar signal processing stage instead of comparing it with the transmitted symbols. The root mean square error (RMSE) is used to evaluate the radar sensing performance for both the traditional and DL approaches. The channel is assumed to be Rayleigh with additive white Gaussian noise (AWGN), and the modulation scheme is QPSK.

Figure 16 and Figure 17 illustrate the range RMSE and velocity RMSE over SNR for both the traditional approach and the DNN case considering different ranges and velocities, as referenced in the 5G literature [18].

When the actual target range is 30 m, the estimated target range for the traditional approach is 31.02 m, while, for the DNN approach, it is 30.517 m. This difference can be attributed to the traditional approach possibly suffering from inaccuracies or noise in the received signal, leading to a slightly higher estimated range. Conversely, the DNN approach, leveraging its learning capabilities, tends to provide a more accurate estimation by effectively capturing and processing the signal characteristics.

Similarly, when the actual target velocity is 30 m/s, the estimated target velocity for the traditional approach is 31.746 m/s, compared to 31.250 m/s for the DNN approach. This discrepancy could arise from the traditional approach’s reliance on conventional algorithms, which may struggle to handle complex signal variations, resulting in slightly inflated velocity estimates. On the other hand, the DNN approach, being trained on diverse data, demonstrates better adaptability to varying signal conditions, leading to more reliable velocity estimates.

Referring to the 5G beyond specification [18], when the range of a target is 305 m away from the BS and the speed of a target increases to 140 m/s, the range and velocity RMSE over SNR for the two cases are depicted in Figure 17. When the actual target range is 305 m, the estimated target range for the traditional approach is 306.317 m, while, for the DNN approach, it is 306.297 m. This slight variation could be due to the inherent noise and uncertainties present in the signal processing of both approaches, with the traditional approach possibly being more susceptible to these factors. Furthermore, when the actual target velocity is 140 m/s, the estimated target velocity for the traditional approach is 134.421 m/s, compared to 134.442 m/s for the DNN approach. Again, this discrepancy underscores the DNN’s ability to better handle signal variations and noise, resulting in more accurate velocity estimates compared to the traditional approach.

Thus, the performance of the DNN approach versus the traditional approach in estimating target range and velocity is significant. Below are the detailed comparisons between the two methods.

• Range Estimation: The DNN approach outperforms the traditional approach in estimating target range due to its ability to capture complex patterns and relationships in the data. The DNN’s estimated range values of 30.51 m and 306.297 m are closer to the actual target range of 30 m and 305 m compared to the traditional approach’s estimates of 31.02 m and 306.317 m. This indicates that the DNN model has learned to make more accurate predictions for target range by leveraging a larger dataset and its inherent learning capabilities. Furthermore, the results show that the range RMSE curves for the two cases, the traditional and DNN approaches, have the same trend at a high SNR regime, suggesting a consistent performance improvement by the DNN approach even in challenging signal conditions.
• Velocity Estimation: Similarly, the DNN approach achieves better velocity estimation compared to the traditional approach. The DNN’s estimated velocity values of 31.250 m/s and 134.442 m/s are closer to the actual target velocity of 30 m/s and 140 m/s, whereas the traditional approach’s estimates of 31.746 m/s and 134.421 m/s deviate further from the actual value. This suggests that the DNN model is more adept at predicting target velocity accurately by effectively capturing subtle variations in the signal. Additionally, the results show that the velocity RMSE curves for the two cases, the traditional and DNN approaches, have the same trend at a high SNR regime, indicating consistent improvement in the velocity estimation by the DNN approach across different signal strengths.

3.8. Joint Design System Based on Deep Learning

3.8.1. DNN-Based Joint Design System

To leverage DL in the joint design of communication and sensing systems, the received signal predicted through DNN application for signal detection serves a dual purpose. Firstly, it is employed to compute the BER, offering insight into the communication performance. Secondly, this predicted signal aids in assessing the radar sensing performance through the MSE evaluation within the DL framework. We assume a Rayleigh channel model with AWGN and employ a QPSK modulation scheme. The simulation parameters are kept consistent, featuring four transmit antennas ($N_t=4$) and either one or two receive antennas ($N_r=1,2$).

Figure 18 depicts the BER for communication performance and MSE for sensing performance. This comparison occurs across the traditional and DL approaches, with fixed sensing power and varying communication power. Specifically, the scenario involves four transmit antennas ($N_t=4$) and two receive antennas ($N_r=2$).

This figure illustrates how the communication and sensing performance vary with fixed sensing power and varying communication power for both the traditional and DL approaches. Upon examining the BER curves, it is evident that the BER versus SNR curves exhibit similar shapes, yet, consistently, the BERs obtained from the DNN method are lower than those from the traditional approach across different SNR values. This observation indicates that the DNN method consistently outperforms the traditional approach in terms of the BER under the simulation conditions across various SNR values. The lower BER values achieved by the DNN method signify its superior performance compared to the traditional approach.

Furthermore, when scrutinizing the MSE curves, it becomes apparent that the traditional approach yields a higher MSE of the reflection coefficient compared to the DNN method. This discrepancy can be attributed to the DNN’s capability to learn intricate patterns and representations from the data, thereby achieving a superior performance over the traditional approach. Additionally, upon observing the turning points in the MSE curves, it is noticeable that the DNN approach exhibits a faster and more pronounced leftward shift compared to the traditional approach. This observation underscores the positive impact of the DL approach when evaluating the radar sensing performance of the joint design system.

Moreover, the results indicate that the BER and MSE of the reflection coefficient curves for both the traditional and DNN approaches follow the same trend in the high SNR regime, showcasing a consistent performance improvement by the DNN approach across various signal strengths. Hence, leveraging its learning capabilities, the DNN approach surpasses the traditional approach in evaluating the communication and sensing performance of the joint design system.

3.8.2. DNN Trade-Off Analysis

In systems that combine communication and sensing functionalities, optimizing both aspects involves a delicate trade-off. Communication systems typically aim to maximize data throughput, minimize latency, and ensure reliable transmission, often at the expense of energy consumption. On the other hand, sensing systems focus on accurately detecting and interpreting environmental signals, requiring precise measurements and minimal interference. Balancing these conflicting objectives is crucial in designing efficient joint communication and sensing systems.

Deep learning methodologies offer promising solutions to navigate this intricate balance. By leveraging DNNs, these systems can adaptively adjust their behavior based on dynamic environmental conditions and performance requirements. One key advantage of deep learning is its ability to jointly optimize multiple objectives, allowing the system to find a balance between the communication and sensing performance. This is particularly valuable in scenarios where traditional optimization techniques may struggle to find satisfactory solutions due to the complexity of the problem space.

Formulating objective functions is a fundamental aspect of optimizing joint communication and sensing systems. These objective functions capture the trade-off between communication and sensing performance by considering relevant metrics such as BER for communication and MSE for sensing. By appropriately weighting these metrics based on the system requirements and priorities, objective functions guide the optimization process towards achieving a desirable balance between the two objectives.

Multi-objective optimization techniques further enhance the optimization process by simultaneously considering multiple conflicting objectives. These techniques explore the trade-off space to identify Pareto-optimal solutions, which represent the best compromise between communication and sensing performance. By providing a comprehensive view of the trade-offs involved, multi-objective optimization helps designers to make informed decisions about the system design and parameter tuning. To optimize the overall performance of the joint design system, it is necessary to analyze the trade-offs between different operational modes. Here, we conduct a comprehensive analysis, including a key system metrics comparison between the traditional DCAS and SSF D-JCAS under DL application. This comparison helps us to realize how changes in the communication SNR when applying the DL approach affect the BER of DCAS compared to SSF D-JCAS. Consistently, the channel is Rayleigh with AWGN, and the modulation scheme is QPSK. The simulation parameters are kept consistent, featuring four transmit antennas ($N_t=4$) and either one or two receive antennas ($N_r=1,2$).

Figure 19 illustrates the BER for communication performance and MSE for sensing performance across DL approaches for both the traditional DCAS and SSF D-JCAS, with fixed sensing power and varying communication power. Here, the scenario involves four transmit antennas ($N_t=4$) and one receive antenna ($N_r=1$).

In the graph, it is evident that SSF D-JCAS exhibits a lower BER compared to the traditional DCAS for downlink transmissions when the DNN is applied to both systems. Furthermore, when the SNR is high, the BER curves for SSF D-JCAS and DCAS closely align and coincide properly.

The concurrent transmission of the communication and radar signals in SSF D-JCAS explains this phenomenon. In the SSF D-JCAS scheme, the received signal at the UE consists of both communication and radar signals transmitted simultaneously over the same channel. Conversely, the traditional DCAS only covers the communication signal, along with AWGN. Thus, the BER performance of SSF D-JCAS outperforms that of the traditional DCAS.

Conversely, when applying DNN, the traditional DCAS reveals a higher MSE of the reflection coefficient compared to SSF D-JCAS. This phenomenon can be explained by the characteristics of the concurrent transmission of the communication and radar signals in SSF D-JCAS. This simultaneous operation results in probable interference during the sensing process. Meanwhile, the interference is reduced by the separation of the communication and radar functions in the traditional DCAS, resulting in improved sensing accuracy.

Furthermore, with a higher communication SNR, better detection performance is achieved from the MSE curves under DL application for both SSF D-JCAS and DCAS. Specifically, upon examining the turning points in MSE curves, we recognize that the DNN approach for the SSF D-JCAS exhibits a faster leftward shift compared to the DNN approach for the traditional DCAS. This observation emphasizes the effectiveness of the DL approach for the SSF D-JCAS system when evaluating the radar sensing performance of the joint design system.

4. Discussions, Conclusions, and Future Directions

Before delving into the discussions, conclusions, and future directions of our study, it is imperative to examine the various aspects and insights gleaned from our research. In the discussions section, we critically analyze the findings, identify the key challenges and opportunities, and explore the implications of our study regarding the field of joint communication and sensing (JCAS) systems. Let us proceed to explore the discussions in detail.

4.1. Discussions

4.1.1. Discussion: Channel Measurements

In the corridor setting, the variability of root mean square (RMS) delay spreads was evident across different testing times, ranging from 0.12 ns to 0.67 ns. This variation is attributed to fluctuations in the channel characteristics, particularly noticeable during afternoon data collection sessions. Furthermore, the movement of individuals in the corridor introduces additional variability, impacting the RMS delay spread.

Conversely, in the meeting room environment, the RMS delay spread values remained relatively consistent, ranging from 0.14 ns to 0.63 ns. The absence of dynamic elements in the room minimized the fluctuations in the measurement results.

However, it is important to acknowledge that the corridor environment featured metal rods positioned parallel to the testing path. This could potentially influence the attenuation of the direct propagation path compared to other multipath components, thus affecting the RMS delay spread values.

The reasons for the observed variations in the RMS delay spread are multifaceted. In the corridor environment, fluctuations in the channel characteristics were noted due to factors such as the time of day and the presence of moving individuals, introducing variability into the channel response and leading to changes in the RMS delay spread values. In contrast, the controlled environment of the meeting room, with minimal movement and disturbances, resulted in more stable RMS delay spread measurements. Additionally, the presence of metal rods along the corridor potentially altered the propagation characteristics, affecting the observed RMS delay spread values.

4.1.2. Discussion: Comparison between Proposed Approach and Previous Work

This section shows the similarities and differences between our proposed approach and the previous work, including the signal model, communication channel, interference cancellation technique, performance metric, and the limitation of the joint design system. These issues are described in detail in

Table 2. Comparison between proposed approach and previous work.

Properties	Proposed Approach	Previous Work
Channel	Downlink AWGN with realistic channels;	Uplink AWGN with Rayleigh channel.
Scenario	Multiple base stations, multiple devices with downlink communication.	Multiple base stations, multiple devices with uplink communication.
Communication Signal	Includes communication and sensing signals at UE.	Only communication signal at UE.
Sensing Signal	Includes transmit/receive steering vectors, reflection coefficient, and noise.	Similar sensing signal components.
Joint Signal	Combines communication and sensing signals at UE.	Separate communication and sensing signals at receiver.
Interference Cancellation	Uses Maximum Likelihood detector for communication symbols.	Utilizes Maximum Likelihood detector and MMSE estimator.
Performance Metrics	BER for downlink communication, MSE for target estimation at BS.	BER for uplink communication, MSE for target estimation at BS.
Limitation Compensation	Explores alternative interference cancellation for optimal sensing performance.	Achieves optimal performance with Maximum Likelihood detector and MMSE estimator.

.

4.1.3. Discussion: Limitation of the Joint Design System Approach

As the interference power increases, the sensing performance experiences a decline. Notably, when the sensing power approaches parity with the communication power, severe mutual interfering effects arise, leading to a reduction in sensing performance. However, this performance loss can be mitigated by augmenting the number of antennas at the receiver.

In the proposed approach, a maximum likelihood detector is employed to minimize decoding errors, treating target echo interference as noise during communication symbol detection. However, when estimating the reflection coefficient of the target, denoted as $\alpha \left(n\right)$, the residual error $\Delta {\mathbf{y}}_s$ is typically canceled during the construction of MMSE estimators. This cancellation, while effective for reducing error, may not hold true for MMSE estimators, potentially resulting in suboptimal sensing performance.

4.1.4. Discussion: Deep Learning Approach

The BER versus SNR curves demonstrate similar trends, yet the DNN consistently exhibits lower BER values compared to the traditional approach across a range of SNR values. This consistent outperformance of the DNN indicates its superiority in terms of BER under the simulated conditions. The remarkable performance of the DNN can be attributed to its proficiency in learning intricate patterns and representations from the provided data. Unlike the traditional methods that may rely on predetermined algorithms or manually engineered features, DNNs possess the capability to autonomously discern and adapt to complex patterns in the dataset.

DNNs excel particularly in tasks that involve vast datasets and intricate relationships owing to their ability to uncover hierarchical features and dependencies through their layered architecture. Furthermore, during the training phase, DNNs iteratively adjust numerous parameters to minimize errors, enabling them to finely tune their performance to the specific characteristics of the given problem.

Considering the BER versus SNR curves, DNNs’ aptitude for capturing subtle relationships within the data and their adaptability to varying SNR conditions are likely contributors to their consistently superior performance, as evidenced by the consistently lower BER values compared to the traditional approach.

4.2. Conclusions

The conclusions drawn from this study underscore the advancements achieved in JCAS systems, particularly through the application of DNNs. Superior performance was observed in communication systems, notably in tasks involving channel estimation and signal detection, when compared to the traditional methods. Realistic channel measurements were instrumental in evaluating both the communication and radar systems, highlighting the potential of DNNs to outperform the conventional approaches.

Moving forward, further exploration and experimentation are warranted across various scenarios. This includes extending machine learning techniques to MIMO cases, incorporating specific waveforms, and implementing advanced techniques such as SSF or TDMA-based functioning for enhanced joint system design.

The proposed system based on SSF presents notable advancements over the existing related works, demonstrating consistently lower BERs across various SNR conditions and improved radar sensing performance. This underscores the efficacy of leveraging DNNs to autonomously learn and adapt to complex data patterns, surpassing the limitations of the traditional methods reliant on predetermined algorithms or handcrafted features.

4.3. Future Directions

For future research, there is a critical need to broaden the scope of experimentation by testing a more extensive range of channels with specifically tailored waveforms. This expanded testing approach will provide a deeper understanding of how different channel characteristics interact with various waveform designs, thereby enhancing the performance and adaptability of JCAS systems.

Additionally, as MIMO communication and radar systems become increasingly prevalent, it is essential to consider factors such as the number of users and data streams. These factors significantly impact system performance and efficiency, necessitating thorough exploration and optimization to achieve optimal results.

Addressing the challenges related to waveform selection, discrimination algorithms, and resource management is paramount for the successful implementation of joint systems. Researchers must develop innovative solutions to mitigate these challenges, ensuring the seamless integration and operation of communication and sensing functionalities.

The effective management of datasets is crucial for training robust and generalizable DNN models. This involves the meticulous organization of training, validation, and test datasets, as well as the comprehensive analysis and optimization of hyperparameters, such as the learning rate, batch size, and optimizer settings.

Furthermore, extending joint design systems to encompass MIMO downlink communication in advanced network generations like 5G or beyond 6G is essential for staying at the forefront of technological advancements. This expansion will facilitate the evaluation of the communication and radar sensing performance in realistic multi-user environments, enabling researchers to overcome the limitations of the conventional SISO systems and propel the field towards new frontiers of innovation and functionality.