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Article

MIMO Signal Detection Based on IM-LSTMNet Model

1
College of Electrical and Electronic Information, Xihua University, Chengdu 610039, China
2
Department of Physics, Fribourg University, 1700 Fribourg, Switzerland
*
Author to whom correspondence should be addressed.
Electronics 2024, 13(16), 3153; https://doi.org/10.3390/electronics13163153
Submission received: 16 July 2024 / Revised: 8 August 2024 / Accepted: 8 August 2024 / Published: 9 August 2024

Abstract

:
Signal detection is crucial in multi-input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) systems, yet classical detection methods often struggle with nonlinear issues in wireless channels. To handle this challenge, we propose a novel signal detection method for MIMO-OFDM system based on the fractional Fourier transform (FrFT), leveraging the robust time series processing capabilities of long short-term memory (LSTM) networks. Our innovative approach, termed IM-LSTMNet, integrates LSTM with convolutional neural networks (CNNs) and incorporates a Squeeze and Excitation Network to emphasize critical information, enhancing neural network performance. The proposed IM-LSTMNet is applied to the FrFT-based MIMO-OFDM system to improve signal detection performance. We compare the detection results of IM-LSTMNet with zero forcing (ZF), minimum mean square error (MMSE), simple LSTM neural network, and CNN–LSTM network by evaluating the bit error rate. Experimental results demonstrate that IM-LSTMNet outperforms ZF, MMSE, LSTM, and other methods, significantly enhancing system signal detection performance. This work offers a promising advancement in MIMO-OFDM signal detection, presenting a deep learning-based solution that effectively improves the system signal detection performance.

1. Introduction

In the field of modern communication, multiple-input multiple-output (MIMO) technology is a significant technological innovation. MIMO technology improves the data transmission speed and reliability of wireless communication system by using multiple antennas to transmit and receive signals. The principle of MIMO technology is based on spatial diversity and channel diversity. Spatial diversity refers to the simultaneous transmission of signals through multiple antennas over different transmission paths, thus increasing the reliability of the signal [1]. Channel diversity means that the signal is received through multiple antennas in different channel environments, reducing the transmission error of the signal.
The multiple antennas in the MIMO system can be divided into transmitting antennas and receiving antennas, and the system structure diagram is in Figure 1. MIMO systems can divide data into n data streams, which are sent simultaneously at the transmitter through different antennas. At the receiver, the MIMO system can receive and decode these signals through n antennas. Due to the existence of separate channels between antennas, MIMO systems can transmit multiple signal streams simultaneously, which increases the data transfer rate and system capacity.
The benefits of MIMO technology include increased data transmission rates, increased system capacity, improved signal reliability, strong anti-interference capabilities, and increased coverage [2]. Massive MIMO has higher system capacity and faster transmission rates on the basis of MIMO systems, and can also be beamforming [3]. However, the Massive MIMO system is generally an antenna array, which is complex. Its antenna size and power consumption are large. Massive MIMO systems cannot operate in certain scenarios where resources are limited or hardware requirements are low, such as signal processing on Radio Frequency Identification systems. Compared with Massive MIMO, the MIMO system is simpler and less complex, which means that it can be better applied to resource-limited scenarios [4]. These make MIMO technology widely used in modern wireless communication systems and bring great impetus to the development of the wireless communication field. This paper focuses on the research of MIMO systems.
Because of the complicated radio communication environment, the signal from the transmitter is influenced by noise and other factors, making it extremely difficult to recover the signal. For the accurate recovery of transmission signals and the improvement of communication quality, it is imperative to detect the signal appropriately.
Multiple input multiple output orthogonal frequency division multiplexing (MIMO-OFDM) is one of the most popular technologies in 4G, 5G New Radio, and so on. MIMO techniques provide extra freedom in space and enhance channel capacity by spatial multiplexing. In order to achieve MIMO capacity gain, it is crucial to recover the plurality of transmitted data streams from multiple receiving antennas [5].
For MIMO-OFDM systems, the multi-antenna structure can improve the signal attenuation problem and increase the signal transmission rate. However, the signal received by a receiving antenna is often an alias of the signals transmitted by different transmitting antennas, and the channel gain and noise of different signals make the signal detection process of the receiver more complicated. Therefore, the signal detection problem has always been a hot research direction in MIMO systems.
Min Ma proposed a signal detection of the genetic algorithm for the massive MIMO physical layer spatial optical communication systems [6]. Additionally, a signal detection technique utilizing a genetic algorithm has been developed specifically for MIMO-OFDM systems. Yang Wang proposed an integrated MIMO-OFDM-IM system joint signal processing scheme based on sparse reconstruction [7]. An enhanced sequential Monte Carlo signal detection approach is presented to achieve efficient detection of communication signals. Addressing the limitations of the path elimination QR decomposition algorithm, Jae-Hyun Ro et al. proposed a signal detection method with high energy efficiency and low complexity that is based on adaptive QR with near-optimal error performance in a MIMO-OFDM system [8].
In recent years, with artificial intelligence (AI) rapidly developing, intelligent signal processing has attracted more and more attention. Deep learning (DL), a subset of AI, enhanced computers’ intelligence. DL has proven effectiveness in achieving this goal. A host of deep learning methods have been applied to signal detection [9,10,11].
Long short-term memory (LSTM) networks, a type of deep learning network, were proposed in 1997 to solve the long-term dependence problem in recurrent neural networks (RNN) [12]. Additionally, LSTM networks can catch nonlinear features in time series data more broadly. Because of the influence of pilot and cyclic prefix (CP) length, it can effectively deal with the problems of gradient disappearance, gradient explosion, and low estimation accuracy of traditional orthogonal frequency division multiplexing (OFDM) systems. Additionally, an LSTM network can easily handle the problem of long sequence dependence. An LSTM network can be applied to a MIMO-OFDM system for signal detection. Convolutional neural networks (CNNs) are some of the most representative and important network structures in deep learning. Compared with other deep learning methods, CNNs can extract features and gain important information better. Therefore, scholars have combined CNNs and LSTM to extract spatio-temporal features from input data more efficiently. Attention mechanisms can be utilized to emphasize important points across diverse information sources. The combination of attention mechanism and convolutional neural network–long short-term memory (CNN–LSTM) has been proven to be applicable to OFDM system for enhancing signal detection performance.
To enhance the signal detection capability of OFDM systems, Sun et al. proposed a signal detection method of an OFDM system based on an improved LSTM neural network [13]. They took an improved Chameleon Swarm algorithm to enhance LSTM’s initial hyperparameters, trained the CLCSA–LSTM model, and used the trained CLCSA–LSTM network model to detect signals in the OFDM system. Hassan proposed a receiver that uses LSTM to take low spectrum in OFDM wireless systems over Rayleigh fading channels [14]. Prior to online deployment and data retrieval, the proposed LSTM estimator uses offline training to collect channel state information from the sending and receiving part. Swaymprabha has proposed a new architecture, StressNet, which is a combination of two-dimensional CNN and LSTM networks, and applies them to detect stress states in electrical EEG signals [15]. Bibekananda proposes a deep convolutional long short-term memory (ConvNet–LSTM) auxiliary receiver for detecting signals in downlink NOMA systems [16]. The proposed technique implicitly estimates the channel state information and directly recovers the transmitted symbol. Zhang proposed an underwater acoustic (UWA) OFDM receiver based on deep learning and expertise [17]. The receiver combines deep learning with classic expertise in block-based signal processing in UWA OFDM to enhance both system performance and interpretability. It designs a skip connection CNN and cascaded attention mechanism-enhanced Bidirectional LSTM (BiLSTM) networks for joint channel estimation and signal detection.
Signal detection is very significant in MIMO-OFDM systems, but some classical detection methods do not deal well with nonlinear problems in wireless channels, such as the nonlinear distortion of wireless channels. The network layers in the neural network model, such as ReLU layer and sigmoid layer, can better handle nonlinear data. The neural network can deal with nonlinear distortion better and improve the signal detection performance of the MIMO system. At present, the research on signal detection in a MIMO-OFDM system using neural networks such as LSTM is very scarce. Therefore, this paper proposes a new neural network model, IM-LSTMNet, which combines an LSTM neural network and CNN neural network, and joins Squeeze-and-Excitation Network on this basis. IM-LSTMNet performs end-to-end signal detection, which improves the signal detection performance of the MIMO-OFDM system.
The main contributions in this paper are as follows:
(i)
We construct a MIMO-OFDM system that uses FrFT to replace the original fast Fourier transform (FFT) in OFDM modulation. This increases the flexibility of the MIMO-OFDM system, allowing it to have more direction choices when carrying out OFDM modulation;
(ii)
We developed an IM-LSTMNet framework and trained it using FrFT-based MIMO-OFDM signal data;
(iii)
The trained IM-LSTMNet model is applied to the online detection terminal to detect the signal of the FrFT-based MIMO-OFDM system. It is compared with other DL-based methods such as LSTM and CNN–LSTM, as well as traditional zero forcing (ZF) methods and minimum mean square error (MMSE) methods, to compare their bit error rate (BER) performance in the MIMO-OFDM system.
A summary of the paper’s structure is provided in this paragraph. The first section explains the background of MIMO-OFDM signal detection and LSTM neural network research, some work of other scholars, and the content of this paper. The second part describes the MIMO-OFDM system model, in which the OFDM system is the fractional Fourier transform-orthogonal frequency division multiplexing (FrFT-OFDM) system. The IM-LSTMNet framework is constructed and the structure and function of each part are described. This part also explains how to use neural network to detect the signal in the MIMO-OFDM system. The third part describes the data preprocessing and offline training of this experiment, and uses the trained IM-LSTMNet model to detect the signal in the MIMO-OFDM system under different conditions. The fourth part draws the conclusion of the paper and expounds this research’s development in the future.

2. Methods

This section explains the framework for detecting signals from an FrFT-based MIMO-OFDM system. Figure 2 describes the flow diagram for offline training and online signal detection of the FrFT-based MIMO-OFDM system by our proposed IM-LSTMNet model.
Figure 2 clearly illustrates that we construct a MIMO-OFDM system and replace the Fourier transform in OFDM modulation with FrFT to increase the flexibility of the system. Then, the IM-LSTMNet network model is trained using MIMO-OFDM signals based on FrFT. The IM-LSTMNet model combines the traditional CNN with the LSTM neural network, and then adds the Squeeze-and-Excitation Network to the attention mechanism module. Finally, at the online testing, the proposed IM-LSTMNet model is used to detect the signal of the FrFT-based MIMO-OFDM system. The superiority of the proposed model in the process of signal detection is verified.

2.1. MIMO-OFDM Signal Detection Model Based on FrFT

OFDM technology has some defects, such as frequency bias sensitivity and uniform waveform parameters of the full frequency band, which cannot fully support the various scenarios in future communication, e.g., new multi-carrier technology—OFDM based on fractional Fourier transform [18]. The processes of modulation and demodulation are completed by fractional Fourier transform. In the FrFT-OFDM system, the subcarriers’ frequency changes linearly with time and is no longer a fixed value. Therefore, the optimal transformation order can be selected to ensure that the system has the best performance in the corresponding fractional domain and to improve the ability of the system to resist time-selective fading. In this sense, the traditional OFDM system is a special case of FrFT-OFDM when the order is 1, and it is an extended form of OFDM technology.
The structure block diagram of the MIMO-OFDM system based on FRFT is shown in Figure 3. It can be seen that the modules and functions of the system are almost the same as those of the traditional MIMO-OFDM system IFrFT and that FrFT replaces the IFFT and FFT function blocks in the OFDM system. Subcarrier modulation and demodulation are accomplished in different ways. The FrFT-OFDM system increases the flexibility of the system and ensures the BER performance by adding the supplementary parameter of order p.
Figure 3 clearly illustrates that, in the MIMO-OFDM system model based on FrFT, the input data symbol stream is first divided into sub-symbol streams by string/parallel transformation, and the encoded data are modulated by the QPSK modulator. The QPSK-modulated signal realizes inverse fractional Fourier transform orthogonal frequency division multiplexing (IFrFT-OFDM) modulation processing in the IFrFT circuit, and completes the conversion of frequency domain data into time domain data. This process is
s i ( m ) = k = 0 N 1 S i ( k ) F α ( m , k ) , 0 m < N 1
where S i ( k ) is the QPSK-modulated signal and F α ( m , k ) is the IFrFT transform. The FrFT is given by
F α ( m , n ) = A α e x p [ j c o t α 2 ( m 2 t 2 + n 2 u 2 ) j 2 π n m N ]
where A α = ( s i n α j c o s α ) / N . t and u are sampling intervals in the time domain and the fractional Fourier domain, respectively, which satisfy t · u = 2 π s i n α / N .
CP is added to each FrFT-OFDM symbol to reduce the effect of channel delay expansion. These processed FrFT-OFDM signal streams are transmitted parallelly to each other, and each signal stream is transmitted according to a specified transmitting antenna.
The signal passes through the channel, and the received signal can be represented as
y N r × 1 = H N r × N t x N t × 1 + n N r × 1
where y = [ y 1 , y 2 , , y N r ] represents the received signal; x = [ x 1 , x 2 , , x N r ] represents the sending signal vector; H represents the channel matrix; and n = n 1 , n 2 , . . . , n N r is the Gaussian white noise vector at the receiver.
As shown in Figure 3, the receiver performs a signal processing opposite to the transmitter, first receiving signals through the N i root receiving antenna at the receiver; these signals are demodulated by FrFT, and then the CP is removed. At this step, the time domain data are transformed into frequency domain data, and then the data are restored in the frequency domain according to the channel matrix.
The IFrFT/FrFT, the addition and removal of CP, the string/parallel transformation, and the parallel/string transformation of the signal are all carried out in each separate transmission and reception module. The space-time coding and spatial multiplexing technology of MIMO can also be applied to each subcarrier of OFDM. To sum up, in the MIMO-OFDM system, increasing diversity and multiplexing in the frequency domain bring greater system gain and system capacity.

2.2. MIMO-OFDM Signal Detection Model Based on FrFT

In order to carry out signal detection in the FrFT-based MIMO-OFDM system, we built an IM-LSTMNet model, as shown in Figure 4. The IM-LSTMNet model proposed in this paper combines the traditional neural network CNN and LSTM, and adds the Squeeze-and-Excitation Network on the basis of this to improve the model’s capability of capturing vital information.
As shown in Figure 4, the signal is sent to the CNN module and the Squeeze-and-Excitation Network as inputs. The two outputs are taken as inputs for the point-by-point attention layer. The information obtained through the point-by-point attention layer is entered into the LSTM module for processing.

2.2.1. Convolutional Neural Network Module

Convolutional neural networks (CNNs) are advantageous for dealing with high-dimensional unstructured data such as images, where many classical CNNs were originally used for image classification. The CNN’s advantage is the sparse interaction feature, which provides storage requirements and statistical efficiency by setting the size of the convolution kernel to be smaller than the size of the input. The second advantage stems from the concept of parameter sharing in CNN, where the convolution kernel is applied to the entire input to create a feature map. In addition, convolution and pooling operations allow the CNN to process the input data to the desired output size. Finally, CNNs can catch high-level representational features by themselves for mining intrinsic information.
A CNN can capture temporal and spatial dependencies from raw data, automatically learning and extracting features closely related to MIMO-OFDM signal detection. The convolutional neural network module in the IM-LSTMNet model is shown in Figure 5. We select two convolutional layers with convolutional kernel [1×1], step size [1×1], channel number 32, and channel number 64. Since the ReLU activation function has no complicated mathematical operations, the calculation cost is small and the convergence is faster. The ReLU activation function is selected for connection in the convolutional neural network module.

2.2.2. Squeeze-and-Excitation Network

The attention mechanism can filter out irrelevant information and highlight key information to improve neural network performance. In this study, an attention mechanism module is designed based on the Squeeze-and-Excitation Network proposed by JieHu et al. to clearly model the interdependencies between channels and adaptively recalibrate the channel intelligent feature response [19].
The extrusion excitation block is a unit of calculation that can construct any given transformation F t r : X U . To enhanse the network’s sensitivity for the information features, the filter response is recalibrated in two steps: squeeze and excitation. Squeeze is the process of global information embedding. The purpose of the excitation is adaptive recalibration. To take advantage of the information aggregated during the squeeze operation, a second operation follows it with the goal of fully capturing the channel-related dependencies. In order to achieve this, two requirements must be meet in the function. Firstly, it must be flexible. In particular, it must be able to learn nonlinear interactions between channels. Secondly, it has to learn the non-exclusive relationship because it wants to ensure that multiple channels are able to be emphasized rather than one-hot activation.
The Squeeze-and-Excitation Network in our proposed IM-LSTMNet model is shown in Figure 6. The global spatial information is compressed into the channel descriptor, which is achieved by generating channel statistics through the global average pool. The extrusion process uses a linear rectification function (ReLU function); in order to limit the model complexity, the gating mechanism is parameterized by forming a bottleneck of two fully connected layers around the nonlinearity, and the final output is transformed by re-scaling the output using the sigmoid function.

2.2.3. Long Short-Term Memory Module

LSTM is a kind of long short-term memory network and a special recurrent neural network. Its structure is shown in Figure 7. Compared with traditional RNN, LSTM is more suitable for processing and predicting important events with long intervals in time series. In this paper, an LSTM neural network with a parameter value of 64 is used to capture the relationship between MIMO-OFDM signal sequences and detect signals.
As shown in Figure 7, LSTM can effectively solve the long sequence problem by introducing the concepts of memory cells, input gates, output gates, and forgetting gates [20]. The control of these gates can effectively capture important long-term dependencies in the sequence and can solve the gradient problem.
The memory cell is responsible for preserving important information. By manipulating the three gates and linear operation, it determines which information should be forgotten and discarded and which information should be retained or unchanged, so as to generate the cell state C t at the current moment and then output to the next moment, as well as to update the memory. The forgetting gate’s object is the cell state C t 1 , whose function is to commmand the information in the cell state for selective forgetting. It resolves which parts need to be discarded and which need to be retained. The object of the input gate is also the cell state, and the role is to decide what new information to store in the cell state, that is, what new memories the cell state selectively adds. Construct an input gate i t that decides what information is added to the cell state as a new memory. Construct candidate cell states C ˜ t , determine which memories are useful, and retain information as new memories to add to the new cell states. The role of the output gate is to determine the final output, which is h t . o t is obtained using the sigmoid function, which determines which part of the cell state needs to be output. The new cell state is processed by the tanh function, which changes the output value to [−1, 1] and is dotted with o t to control which part needs to be output.

2.2.4. MIMO-OFDM Signal Detection Based on the IM-LSTMNet Model

The signal detection in the MIMO-OFDM system using IM-LSTMNet is different from existing MIMO-OFDM receivers that first explicitly estimate channel state information (CSI) and then use the estimated CSI to detect or recover transmitted symbols. The method based on IM-LSTMNet implicitly estimates the CSI and immediately recovers the transmitted symbols. Figure 8 shows the signal detection framework of the MIMO-OFDM system by a neural network [21].
In Figure 8, in order to obtain a valid IM-LSTMNet for signal detection, there are two stages. In the offline training stage, MIMO signals are preprocessed by ZF detection using MIMO-OFDM signal samples. The preprocessed signal is trained to IM-LSTMNet so that it can learn channel state features better. In the online signal detection, the offline trained IM-LSTMNet is put into the MIMO-OFDM system model for signal detection. In each simulation, the data at the receiver are used as a neural network input to generate an output that recovers the transmitted data without explicitly estimating the wireless channel. The process is as follows: the MIMO signal is first modulated by QPSK and then transformed by IFrFT. CP is inserted into the signal, and the newly generated signal is sent through a Gaussian channel with noise after the parallel-to-serial transformation. After the conversion of serial to parallel and CP removal, the received signal can be obtained. The received signal in the frequency domain can be obtained after passing through the FrFT. The received signal is preprocessed by ZF detection, which is used as input to pass through the offline trained neural network model, thus recovering the transmitted signal end-to-end and obtaining the signal.

3. Experiments and Results of Signal Detection

3.1. Data Preprocessing and Training of Signal Detection

Before the formal signal detection, it is necessary to preprocess the signal data and train the model offline. In this section, the preprocessing of signal data and the training of IM-LSTMNet model are mainly introduced.

3.1.1. Data Preprocessing

In this paper, the input data of the IM-LSTMNet model are the output signal of the MIMO-OFDM system. Given that the signal is modulated using QPSK and IFrFT, the final output is complex. At present, the input data of the neural network are mostly real numbers, not complex numbers. Therefore, in the whole research work, direct processing of complex numbers is avoided and complex data are converted to real data. The input data follows the equation
( Y ) ( Y ) = ( H ) ( H ) ( H ) ( H ) ( X ) ( X ) + ( N ) ( N )
where R e ( ) ˙ and I m ( ) ˙ represent, respectively, the real and imaginary parts. After merging, the data dimension has changed, the received signal is Y 2 N r × τ , the transmitted signal is X 2 N t × τ , the channel matrix is H 2 N r × 2 N t , and the Gaussian white noise is N 2 N r × τ [22].

3.1.2. Offline Training

In the offline training stage, MIMO signals are pre-detected by ZF detection using MIMO-OFDM signal samples based on FrFT. After ZF pre-detection, the signal is preprocessed by Formula (4). The preprocessed data are used as the input of the neural network model to train the model so that it can learn the channel state features better. The parameters used in training the IM-LSTMNet model are shown in Table 1.
When the IM-LSTMNet model is trained under different signal noise ratio (SNR) values, the accuracy and loss of IM-LSTMNET model are different, which will affect the BER of online signal detection. In order to maximize the performance improvement of the IM-LSTMNet model on MIMO-OFDM signal detection based on FrFT, we discuss the accuracy and loss of the IM-LSTMNet model under different SNR values, as shown in Table 2.
As can be seen from Table 2, when the training SNR is 10 dB, the model accuracy is higher and the loss is lower. When the training SNR is less than 10 dB, the model accuracy is lower and the loss is higher. Training SNR greater than 10 dB is prone to overfitting.
The IM-LSTMNet model training diagram and loss diagram when the training SNR is 10 dB are shown in Figure 9 and Figure 10.
As can be seen in Figure 9, the accuracy rate reached 99.66% in the first round of training, the accuracy range of small batches before the fifth round fluctuated greatly, and the tenth round basically converged to 99.66%.
As can be seen from Figure 10, in the first round of training, the loss dropped below 0.5, the loss range of small batches before the fifth round fluctuated greatly, and the tenth round basically converged to 0.0605.
When the training SNR is 10 dB, the model accuracy is higher, the loss is smaller, and the model performance is better. Therefore, in the subsequent signal detection process, the training model with SNR = 10 dB is used for simulation.

3.2. The Result of the Signal Detection

In this part, we simulate the MIMO-OFDM system with dimension 2 × 2 under different FrFT orders, different subcarrier numbers, with or without CP, and different channel responses. The BER results of MIMO-OFDM signal detection based on the IM-LSTMNet model trained by the MIMO-OFDM signal based on FrFT are presented. In addition, the proposed IM-LSTMNet is compared with the traditional ZF detection, MMSE detection, CNN–LSTM neural network detection, and LSTM neural network detection.

3.2.1. The Influence of a Different Order of FrFT

The introduction of FrFT in the MIMO-OFDM system can extend the Fourier transform to different orders, increase the flexibility of the system, and reduce the BER. In the simulation of this section, MIMO-OFDM signal detection based on FrFT is carried out in different orders. Figure 11 shows the comparison between the IM-LSTMNet signal detection method proposed by us and the traditional algorithm and two other neural network methods when the FrFT order is 1, that is, the traditional Fourier transform.
As can be seen from Figure 11, when the FrFT order is 1, the IM-LSTMNet neural network detection is superior to the traditional algorithm, and it is also superior to the LSTM and CNN–LSTM detection algorithms. In particular, when SNR > 10 dB, the detection performance of ZF and MMSE can no longer be improved with an increase in SNR. The detection performance of the three neural network methods can also decrease with an increase in SNR.
Figure 12 and Figure 13 describe the performance comparison between our proposed IM-LSTMNet method, the traditional ZF algorithm, and the MMSE algorithm, as well as the performance comparison between the IM-LSTMNet method and the simple LSTM and CNN–LSTM methods under FrFT order p of 1.4, 1.6, and 1.8.
As shown in Figure 12, when the order p is 1.4 and 1.8, the detection performance of ZF and MMSE (i.e., traditional methods) can no longer be improved with an increase in SNR when SNR > 10 dB. When the order p is 1.6, the performance of the traditional method can still improve with an increase in SNR. The detection performance of the IM-LSTMNet method can be improved with an increase in SNR with the three orders, and the performance is obviously better than that of ZF and MMSE, i.e., the two traditional algorithms. Therefore, the MIMO-OFDM system performance with order 1.6 is significantly better than that of the MIMO-OFDM system with order 1.4 and 1.8.
As shown in Figure 13, with an order of 1.6, the signal detection performance of the three neural network methods for the MIMO-OFDM system is significantly better than that of the two cases with the orders of 1.4 and 1.8. At the same time, the detection performance of IM-LSTMNet is obviously better than that of LSTM and CNN–LSTM.
In summary, replacing DFT with FrFT in the MIMO-OFDM system not only increases system flexibility, but also brings better performance to the system. In particular, when the FrFT order p is 1.6, the MIMO-OFDM system’s BER is the lowest and the system performance is the best. Meanwhile, the IM-LSTMNet detection algorithm proposed by us has better performance than the traditional MIMO signal detection algorithm and other neural network signal detection algorithms such as LSTM under different order conditions.

3.2.2. The Effect of the Subcarriers’ Number

In the MIMO-OFDM system, the subcarriers’ number will affect the system performance. In the experimental simulation in this section, the FrFT order is set to 1.6 and the CP to 16, and the influence of 64, 32, and 16 subcarriers on the signal detection performance of the FrFT-based MIMO-OFDM system is discussed. Figure 14 and Figure 15, respectively, describe the performance comparison between our proposed IM-LSTMNet method and the traditional ZF algorithm and MMSE algorithm and the performance comparison between the IM-LSTMNet method and the simple LSTM and CNN–LSTM methods when the number of subcarriers is 64, 32, and 16.
As shown in Figure 14, when the number of subcarriers K is 64, the improved algorithm proposed by us has a lower bit error rate than the traditional algorithm, and the signal detection performance of the FrFT-based MIMO-OFDM system is better. When the subcarriers’ number K is 16, the improved algorithm and the traditional algorithm have higher BER and worse signal detection performance.
As shown in Figure 15, when the subcarriers’ number K is 64, the improved algorithm proposed by us and the simpler CNN–LSTM and LSTM neural network algorithms have lower BER, and the FrFT-based MIMO-OFDM system has better signal detection performance. When the subcarriers’ number K is 16, the improved algorithm, CNN–LSTM, and LSTM neural network algorithms have higher BER, and the system signal detection performance is worse.
Compared with the results obtained in Figure 14 and Figure 15, when the subcarrier number is 64, 32, and 16, the IM-LSTMNet’s BER is lower than that of the traditional methods and the other two neural network algorithms, and the signal detection performance is better than that of the traditional methods and the other two neural network algorithms.
In conclusion, the larger the subcarrier number K, the smaller the BER of MIMO-OFDM signal detection based on FrFT and the better the system performance. The smaller the subcarrier number K, the greater the BER of MIMO-OFDM signal detection based on FrFT and the worse the system performance.

3.2.3. The Effect of the Cyclic Prefix

As previously mentioned, CP is necessary to change the linear convolution of a physical channel to a circular convolution and to mitigate ISI. Its transmission consumes time and energy, and less CP contributes to better system performance. In this experiment, we study the effect of CP on system performance based on an FrFT order of 1.6 and subcarrier number of 64.
Figure 16 and Figure 17, respectively, describe the performance comparison between our proposed IM-LSTMNet method and the traditional ZF algorithm and MMSE algorithm and the performance comparison between the IM-LSTMNet method and the simple LSTM and CNN–LSTM methods with or without CP.
As shown in Figure 16, without CP, the improved algorithm proposed by us has a lower bit error rate than the traditional algorithm, and the signal detection performance of the FrFT-based MIMO-OFDM system is better.
As shown in Figure 17, without CP, the improved algorithm proposed by us has a lower bit error rate than simpler CNN–LSTM and LSTM neural network algorithms, and better signal detection performance of FrFT-based MIMO-OFDM system. This result shows that the proposed IM-LSTMNet model could learn the wireless channel’s characteristics during the training.

3.2.4. Influence of Channel Matrix

In the experiments in the above section, offline training and online deployment use the same channel matrix. However, in practical applications, there may be a mismatch between these two processes—offline training and online deployment use different channel matrices. As a consequence, it is significant that the trained IM-LSTMNet is robust in this condition.
To prove the robustness of the proposed IM-LSTMNet network for the signal detection of the FrFT-based MIMO-OFDM system, the experiments in this section are carried out when the FrFT order is 1.6, the subcarrier number is 64, and the CP number is 16. In offline training and online signal detection, a different channel matrix H is selected to discuss the signal detection performance of the FrFT-based MIMO-OFDM system. The experimental results are shown in Figure 18.
As shown in Figure 18, when the offline training and the online detection adopt different values of H, the neural network still has a certain signal detection ability for the FrFT-based MIMO-OFDM system. The IM-LSTMNet network proposed by us has lower BER and more effective performance than the other two neural network detection algorithms when using different values of H. It can be concluded that the IM-LSTMNet network proposed in this paper is more robust than the FrFT-based MIMO-OFDM system.

3.2.5. IM-LSTMNet Detects MIMO-OFDM Signals under Optimal Conditions

When the FrFT order P is 1.6, subcarrier number is 64, CP value is 16, and the channel impulse response H is the same at the detection and the training, the IM-LSTMNet model has the best signal detection performance for the MIMO-OFDM system. Under this condition, the BER of MIMO-OFDM signal detection by IM-LSTMNet model under different SNRS is shown in Table 3.
As can be seen from Table 3, when SNR < 5 dB, the bit error rate of the IM-LSTMNet detection of MIMO-OFDM signals is large and decreases slowly, resulting in poor system performance. When SNR > 5 dB, IM-LSTMNet detects MIMO-OFDM signals with small bit error rate and rapid decline, resulting in improved system performance.
According to the above experiments, the signal detection performance of the IM-LSTMNet model introduced in this paper surpasses not only the traditional ZF and MMSE methods but also outperforms the LSTM and CNN–LSTM neural network approaches.

4. Conclusions

In this paper, we propose a novel framework, IM-LSTMNet, for detecting signals in an FrFT-based MIMO-OFDM system. The IM-LSTMNet network, combining CNN and LSTM neural networks with a Squeeze-and-Excitation Network in the attention mechanism module, was trained offline using simulation data from an FrFT-modified MIMO-OFDM system. This approach demonstrates the deep neural network’s ability to handle the complexities of wireless channels characterized by severe distortion and interference.
Our experimental results confirmed that IM-LSTMNet significantly enhances signal detection accuracy in an FrFT-based MIMO-OFDM system, outperforming traditional methods such as zero forcing (ZF), minimum mean square error (MMSE), simple LSTM, and CNN–LSTM networks. This demonstrates the deep learning model’s ability to remember and analyze complex wireless channel characteristics, proving its potential for practical applications.
For real-world deployment, it is critical that the IM-LSTMNet network exhibits robust generalization capabilities, ensuring effective performance even when online conditions differ from those during the training phase. The findings suggest substantial potential for improving the reliability and efficiency of 5G and other advanced wireless networks.
Future work will involve more rigorous analysis and comprehensive experiments to further validate our results. Additionally, we will extend the IM-LSTMNet approach to a larger-scale Massive MIMO-OFDM system, combined with Spatial Modulation and Joint Constellation by additive superposition, which could further enhance communication performance and meet the increasing demands of modern wireless networks [23]. This work presents a promising advancement in MIMO-OFDM signal detection by introducing a deep learning-based solution that effectively addresses the complexities of wireless channels.

Author Contributions

Methodology, J.L.; Writing—original draft, Y.Y.; Writing—review & editing, X.H. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the Chun Hui plan project of the Ministry of Education, China (Grant No.z2011089), and Graduate Discipline Competition Project of Xihua University (Grant No.RC2400002114).

Data Availability Statement

Data are contained within the article.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. MIMO system structure diagram.
Figure 1. MIMO system structure diagram.
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Figure 2. Flow chart of the IM-LSTMNet model detecting the MIMO-OFDM signal based on FrFT.
Figure 2. Flow chart of the IM-LSTMNet model detecting the MIMO-OFDM signal based on FrFT.
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Figure 3. Block diagram of the FrFT-based MIMO-OFDM system.
Figure 3. Block diagram of the FrFT-based MIMO-OFDM system.
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Figure 4. IM-LSTMNet frame diagram.
Figure 4. IM-LSTMNet frame diagram.
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Figure 5. Convolutional neural network module diagram.
Figure 5. Convolutional neural network module diagram.
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Figure 6. Squeeze-and-Excitation Network.
Figure 6. Squeeze-and-Excitation Network.
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Figure 7. LSTM structure diagram.
Figure 7. LSTM structure diagram.
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Figure 8. Framework diagram for the detection of the MIMO-OFDM signal by a neural network.
Figure 8. Framework diagram for the detection of the MIMO-OFDM signal by a neural network.
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Figure 9. SNR = 10 dB; IM-LSTMNet model training diagram.
Figure 9. SNR = 10 dB; IM-LSTMNet model training diagram.
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Figure 10. SNR = 10 dB; IM-LSTMNet model loss diagram.
Figure 10. SNR = 10 dB; IM-LSTMNet model loss diagram.
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Figure 11. The MIMO-OFDM system’s BER with FrFT order of 1.
Figure 11. The MIMO-OFDM system’s BER with FrFT order of 1.
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Figure 12. The BER of IM-LSTMNet and traditional algorithms under different orders.
Figure 12. The BER of IM-LSTMNet and traditional algorithms under different orders.
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Figure 13. The BER of IM-LSTMNet and other neural network algorithms at different orders.
Figure 13. The BER of IM-LSTMNet and other neural network algorithms at different orders.
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Figure 14. The BER of IM-LSTMNet and the traditional algorithms under different subcarrier numbers.
Figure 14. The BER of IM-LSTMNet and the traditional algorithms under different subcarrier numbers.
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Figure 15. The BER of IM-LSTMNet and other neural network algorithms under different subcarrier numbers.
Figure 15. The BER of IM-LSTMNet and other neural network algorithms under different subcarrier numbers.
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Figure 16. The BER of IM-LSTMNet and the traditional algorithms with or without CP.
Figure 16. The BER of IM-LSTMNet and the traditional algorithms with or without CP.
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Figure 17. The BER of IM-LSTMNet and other neural network algorithms with or without CP.
Figure 17. The BER of IM-LSTMNet and other neural network algorithms with or without CP.
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Figure 18. The BER of the neural network algorithm under different values of H.
Figure 18. The BER of the neural network algorithm under different values of H.
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Table 1. Training neural network parameters.
Table 1. Training neural network parameters.
ParametersValue
Antenna number2×2
ChannelGaussian
Cyclic prefix16
Modulation systemQPSK
Subcarrier number64
FrFT order1
Signal noise ratio10 dB
Optimization algorithmAdam
Max epochs10
Mini batch size10
Learning rate0.001
Learning rate decline factor0.3
Simulation toolMATLAB (2022a) Deep learning toolbox
Table 2. Accuracy and loss of IM-LSTMNet model.
Table 2. Accuracy and loss of IM-LSTMNet model.
SNR4681012
Accuracy (%)95.6996.7598.1699.66100
Loss0.21490.17050.10950.06050.0315
Table 3. BER of MIMO-OFDM signal detection by IM-LSTMNet under optimal conditions.
Table 3. BER of MIMO-OFDM signal detection by IM-LSTMNet under optimal conditions.
SNR(dB)−10−505101520
BER0.640.5010.370.190.04780.002680.000005
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Huang, X.; Yuan, Y.; Li, J. MIMO Signal Detection Based on IM-LSTMNet Model. Electronics 2024, 13, 3153. https://doi.org/10.3390/electronics13163153

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Huang X, Yuan Y, Li J. MIMO Signal Detection Based on IM-LSTMNet Model. Electronics. 2024; 13(16):3153. https://doi.org/10.3390/electronics13163153

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Huang, Xiaoli, Yumiao Yuan, and Jingyu Li. 2024. "MIMO Signal Detection Based on IM-LSTMNet Model" Electronics 13, no. 16: 3153. https://doi.org/10.3390/electronics13163153

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