SCWOMP Recovery Algorithm for 5G MIMO Communication Symbol Detection

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Introduction
With the rapid development of modern technology, 5G technology has once again become a research hotspot in the feld of communication. With the continuous increase in various communication services, the demand for the wireless transmission rate and symbol detection shows a continuous increase. However, under the condition of very developed science and technology at this stage, the network is an important means to realize human-computer interaction [1,2]. How to improve the network rate, make the network system capacity and transmission rate more excellent, and reduce unnecessary computation are a few problems to solve [3]. In order to solve the above problems, this study analyses the sparsity of MIMO systems and proposes a segmented backtracking weakly selective orthogonal matching and tracking algorithm (SCWOMP) in combination with a compression-aware matching and tracking algorithm, which is applied to 5G network systems. In communication, a simulation analysis of sampling points and sparsity is carried out for various Baran algorithms in order to provide people with a good experience [4,5]. Te MIMO technology involved in the research is developing rapidly, and the SCWOMP algorithm is a recovery algorithm with fewer iterations and a better recovery rate, which is suitable for unsupervised learning programs such as communication system networks. Te simulation data and models generated during the experiment can produce good data. Te two are combined with each other, and the comparison between the original waveform and the recovered waveform is used to verify the superiority of the algorithm performance. Tis has innovative signifcance for China's current communication technology and data costs and can promote the development and progress of science and technology.

Related Works
With the expansion of the layers and felds involved in 5G technology, new MIMO technology has gradually entered people's feld of vision, and more and more scholars have begun to study the combination of the compressive sensing reconstruction algorithm and SWOMP. In order to estimate and grasp the state of all targets, Zhang et al. proposed an adaptive Kalman information fltering algorithm. When the communication network is observed, the sensor network is variable, and the collective can be observed, it can be proved that the system matrix of the target is invariant. Te effectiveness of the algorithm is proved in simulation experiments [6]. Qu and Li proposed a distributed algorithm to cope with the accuracy of communication networks in an iterative process. Te algorithm can efectively utilize the smoothness of the function and quickly converge to the optimal solution at a certain speed, which means that the algorithm has a linear convergence speed. Tese two speeds are in line with the convergence speed of CGD. Te algorithm includes a gradient estimation scheme that enables a fast and accurate implementation of the average gradient using past historical information [7]. In order to provide strong infrastructure and services, Shen and Chen proposed a load-balancing method (RIAL) using resource intensity awareness. For each diferent heavy-load physical machine (PM), the algorithm will reasonably allocate resources according to diferent PM usage intensity and dynamics. Te practice can greatly reduce the time and cost. Algorithmically, tuning virtual machines (VMs) to reduce bandwidth costs has superior performance compared to other algorithms [8]. Li and Zhao conducted research on adaptive multiagent systems and found a nonlinear switching multiagent system with regard to the nonstrict feedback form and input saturation. Te process is represented by the Gaussian error function and the unsaturated model. Te algorithm is used to approximate some unknown encapsulated functions, and the inverse process is used to build a public function. On this basis, an adaptive consensus protocol is also proposed to make the tracking error converge to a minimum under arbitrary switching [9]. Saleem et al. proposed a speech enhancement algorithm capable of supervised sub-single-phase channel speech enhancement for the problem of speech enhancement. Te speed-up algorithm is based on a strong deep neural network (DNN) and a weaker Wiener flter as the DNN layer in the process. In the initial stage, the network learns speech features from the input noisy speech signal and extracts clean and noisy signals. Te results show that the proposed algorithm is excellent in both speech quality and intelligibility [10].
Wei and Liao studied the design of the transmitted waves of a MIMO radar system using a DAC. In order to solve the optimization problem composed of the constrained fractional quadratic problem, the sparse semidefnite relaxation method is used to transform the problem into monthly reduced convex semidefnite programming (SDP). It is also proposed to utilize a customized interior point algorithm to solve small-scale SDP problems. Te desired sequence of bit transmit waveforms is also appropriately synthesized by a Gaussian randomization problem. Te results show that the method has good performance [11]. Baek et al. proposed a simple method for applying deep learning neural network algorithms to traditional multiple-input multiple-output (MIMO) communication systems. In the process, the signal detection of the single-tap MIMO channel with the basic DNN structure is used, and the convolutional neural network and the recurrent neural network are proposed for the reason of the multipath fading channel in the system. It is proved by experiments that the proposed two structures can efectively transmit the correct system signal [12]. Zhou et al. investigated the ability of active beamforming to reduce user equipment (UE) positioning errors in MIMO systems. Tis research is quite challenging, and to address this challenge, a novel sequential localization and beamforming (SLAB) scheme is proposed. In the process, the long-term UE position and the instantaneous channel state are combined, and continuous optimization is carried out according to the obtained estimated value. Simulation experiments show that the proposed scheme outperforms the existing baselines [13]. Mehrabi et al. proposed a decision-directed (DD) channel estimation (CE) algorithm for multiple-input multiple-output (MIMO) systems in the vehicle environment of a high-speed moving vehicle. During the process, the Doppler rate in the vehicle communication system is very variable, requiring a large number of pilots and preambles to intervene. Simulation results show that, compared with other existing algorithms, the proposed DL-based DD-CE algorithm can have a lower propagation error and better grasp of Doppler frequency [14]. Zhong and Chongjun proposed a piecewise OMP (POMP) method for modern 5G application problems. Tis algorithm can well preserve the piecewise sparse structure of the piecewise signal. Based on the advantages of the OMP algorithm, the POMP algorithm also has the roles of CoSaMP and OMMP in piecewise sparse recovery, which can more accurately approximate the error attenuation and use better sufcient conditions and better recovery success rates. Te proposed algorithm performs better repair of segmented sparse signals according to the segmental structure of the communication signal and is more stable and efective than other algorithms [15].
In summary, in the current new intelligent era, the network communication and technology is developing rapidly, how to detect the communication symbols, improve the system capacity and reduce the energy consumption has also attracted extensive attention from researchers. Among them, the MIMO system technology has been known for a long time, but the SCWOMP algorithm is improved by combining compressive sensing reconstruction and MIMO, and the proposed algorithm is improved to build a model and improve performance. It is urgent to provide new directions and ideas for the research of communication technology systems through this research.

Improved Algorithm Design of the SWOMP Algorithm in Symbol Detection of the Communication Technology System
3.1. Analysis of the MIMO Technology System and the Compression Sensing Recovery Algorithm. Multiple-input multiple-output (MIMO) system technology communication is a wireless communication system that uses multiple antennas in common between the transmitter and receiver. But based on various considerations, generalized spatial modulation (GSM) is usually regarded as a part of the MIMO system [16,17]. GSM is a special MIMO system where the transmitting unit is larger than the transmitting unit derived from the spatial modulation multiple-input multiple-output (SM-MIMO) system of a single RF spatial modulation MIMO system. Tis system retains the basic transmission characteristics of SM-MIMO and is not limited to a single active antenna. Unlike spatial multiplexing, the main diference between spatial modulation systems and spatial multiplexing is that information bit blocks are mapped into two information carrying units: spatial constellation symbols and signal constellation symbols. When sending, only one or a few antennas are activated, which reduces the number of links and provides the possibility of reducing hardware costs for the receiving end, giving it more development advantages. Te transmission signal of the GSM system is shown in equation (1). At the same time, if the information of the perfect channel has been obtained, the corresponding system's reception model is expressed in the following equation: In equation (1), y represents N r × 1 the sequence vector. N τ represents the number of input signal antennas in the MIMO system, S represents the set of constellation symbols, x represents N r × 1 a vector of numbers, where sparsity is N A , that is, x ∈ S N T ×1 , H and C both represent matrices, the channel matrix of H ∈ C N T ×N R and N T × N R represent the order of spatial diversity, n represents white Gaussian noise, ρ represents the signal-to-noise ratio, and E x � N T i�1 ‖x i ‖ 2 2 /N T is the average value of the energy contained in the transmitted symbols. Tis is a 5G communication system built through spatial modulation technology, which is no longer limited to traditional amplitude modulation and phase modulation, but extends the modulation content from the numerical feld to 3D spatial characteristics. In a physical sense, it is understood that the serial number of the transmitting antenna is used as one of the mapping relationships for information transmission. Tis enriches the transmission methods of information, but overall, due to the small number of receiving antennas for users and the large number of antennas for BS, signal detection in the system is essentially a challenging large-scale underdetermined problem. Te mode of the transmission signal is sparse. In order to better detect symbols in MIMO systems, the research proposes to combine compression sensing with improved recovery algorithms. Compressed sensing can efectively reduce the sampling process and unify the sparsity and sampling process into a sensing process. In the process, s is the length of the discrete signal set as N and the element is expressed as x[N]; then, the specifc expression is shown in the following equation: (2) In equation (2), x represents the sequence vector of the weighting coefcient, s and x have the same efect, but s is expressed in the space-time domain, and x is expressed in the Ψ domain. We reexpress y through integration, as shown in the following equation: In equation (3), Θ � ΦΨ is an M × N matrix. Compressed sensing Φ is fxed and does not depend on the signal s. Te model is summarized in Figure 1. Figure 1 shows that there are three overall important processes: the sparseness of the nonsparse signal, the design of the sensing matrix, and the reconstruction algorithm of the signal. Te SCWOMP algorithm is reconstructed and improved by using compressed sensing. If the number of nonzero items is smaller than the dimension of the vector, the vector is called a sparse vector. To examine the measure of sparsity, the s norm of the ‖s‖ 0 vector is used here l 0 , which is defned as the following equation: In equation (4), when (s 1 + s 2 � 2), if s � [s 1 , s 2 ] sparse, at least one of them needs to be s x equal to 0; that is to say, by calling the sparse constraint, the number of solutions that can be solved is from infnity to two: Since the norm counts the number of nonzero entries in the majority vector, the function is facilitated by sparsity, so the problem of fnding the most redundant input vector among the measured vectors can be expressed as the following equation: In equation (5), ‖.‖ 0 means to fnd the zero norm, that is, the number of nonzero items. Te equation is optimized according to the existing literature, see the following equation: In equation (6), ‖.‖ 1 represents the sum of the absolute values of the nonzero components.

3.2.
Steps and Models of Improving the SWOMP Algorithm for the Communication Technology System. Using the abovementioned model, it can be found that the transformation and recovery of compressed sensing are a problem of seeking an optimal solution. On this basis, the improved algorithm SCWOMP is reconstructed. First, the principle of the improved algorithm is mastered. Te piecewise approximation method has evolved from the earliest sparse adaptation. Entering the next stage, this step size is unchanged. Te set step size is estimated until the iteration produces a residual greater than or equal to the residual of the previous iteration, as shown in the following equation: In equation (7), r represents the residual value, k represents the number of iterations, and ‖·‖ 2 represents the sum of nonzero items. When equation (7) is satisfed, it means that the current step size will not reduce the margin any more, and there will even be an error in the estimator due to the relationship between the step sizes. Ten, the approximate step size needs to be updated, see the following equation: In equation (8), stage represents the step size before updating and stage ′ represents the updated step size. Different strategic ideas are used to increase complexity by switching the selection criteria when certain conditions are met, as shown in the following equation: In equation (9), α ∈ (0, 1), T represents the large step size, and h represents the number of step size iterations. Tere is the literature to prove that the α � 0.5 recovery probability is the best, so the frst weak selection of the study directly selects coefcient 0.5. Another criterion is the principle of selecting the largest correlation column in the later stage of the iteration, that is, the precise iteration with small step size. Both stages retain the fast recovery characteristics of the SWOMP algorithm and avoid overestimation when iterating to the actual ground truth. Tis completes the frst atomic column selection of each iteration of the improved algorithm. Ten, a second flter is added to prune candidate sets containing staggered columns with weak threshold selection, specifcally not being able to backtrack every iteration. If there is no support set that can contain all the correct atoms, then Λ T ∈ Λ t the relationship between them is shown in the following equation: In equation (10), Λ T represents the correct candidate set, Λ t represents the candidate set of the tth iteration, and ϕ represents the empty set. Equation (11) is explained for the superposition vector of the estimated signal ε: During the process, the appearance of the noise vector interferes with the size of the original value, and the calculation will also be interfered during backtracking. Terefore, in order to ensure the efect of backtracking, the number of atomic columns in the support set needs to be limited, and sparsity begins to be reduced. We make the set value greater than or equal to sparsity and backtrack when the condition is met. Te selection of the second weak threshold is specifcally expressed as the following equation: In equation (12), ∀i � J represents the set of serial numbers in the g sensing matrix selected for the frst time in the process, Φ represents the coefcient, and the numerical range is in (0, 0.5]. Even if the backtracking process is added in the calculation process, the redundant and unnecessary number of iterations can be removed by secondary selection, and the signal can be recovered quickly by increasing recovery probability. Te fowchart of the improved algorithm (SCWOMP) is shown in Figure 2.
Te SCWOMP algorithm fow steps in Figure 2 are as follows: at the beginning, we input the number of sampling points, set the sensing matrix and the sparsity range, then carry out diferent planning of the standard, and start the calculation; after completion, we select the calculation of the second standard and take the maximum value corresponding to the footmark, which is stored in support Jining for sequence update. Te least squares solution is solved in turn. If it meets the requirements of the equation, we go to the next step; if not, we return to step 2. We update the calculated residuals, analyze the value, and judge whether the result meets the conditions. If so, we output the fnal output θ t . If not, we then judge whether it meets the criteria and conditions of the transformation selection. Te fnal process ends [18][19][20]. During the operation of the SCWOMP algorithm, although a backtracking process has been added, which involves an additional least squares estimation step per iteration compared to OMP and SWOMP algorithms, secondary selection through appropriate thresholds can reduce the number of iterations and enable faster signal recovery. Terefore, in the case of little change in operation time, the recovery probability can be improved. In the comparison experiment of the algorithm, if the error and complexity are required to be calculated, the complexity In equation (13), K represents the number of iterations, m represents the number of matrix rows used for observation, s represents the sparsity, and l represents the calculation bit accuracy. Te SCWOMP algorithm is applied in a MIMO system, starting from a basic model, where the target signal is transmitted through a linear channel with additive white Gaussian noise (AWGN). Te input-output relationship of the model is shown in the following equation: In equation (14), y represents the vector of the received signal, H represents the system matrix, satisfying H ∈ C m×n , s represents the expected signal vector, and v represents the noise vector, obeying v ∼ N(0, σ 2 I). In actual cases, it is more likely that the expected signal is not sparse, so cardinality can be selected ψ i to represent the signal as a linear combination of cardinality. Using a suitable fundamental matrix Ψ � [ψ 1 · · · ψ n ], the input vector can be expressed as s � n i�1 x i ψ i � Ψ x , and the input-output relationship evolves into the following equation: In equation (14), x is the representation in the Ψ domain s. In the process, the original nonsparse vector can be s replaced with a sparse vector by properly selecting the cardinality domain x. Tis method of replacement does not change the model of the system. Combined with the algorithm equation mentioned above, the improved GSM-MIMO symbol detection algorithm uses the mechanism of the SCWOMP algorithm to detect the active antenna position set in network communication and combines with the MMSE algorithm to improve a more suitable system detection algorithm. As described in the literature, since the steps of the OMP algorithm keep these error sequences, the detection performance is low, so on the basis of the aforementioned equation, equation (12) is rewritten in the MIMO system modulation communication system, see the following equation: In equation (16), S represents the modulation constellation set. Ten, we use MMSE to detect the reserved and closest antenna that satisfes the spatial symbol as the spatial symbol detection value. Te specifc fowchart is shown in Figure 3.

Performance Comparison of Diferent Compression Aware
Reconstruction Recovery Algorithms. In order to demonstrate the performance superiority of the algorithm proposed by the research institute, the StOMP algorithm, OMP algorithm, and SP algorithm were selected to compare their performance with the SCWOMP algorithm constructed by the research institute at diferent sampling points [21][22][23]. Experiments were performed using the Gaussian sparse signal, set signal length N � 256, and tested once at 5s intervals. Te measurement matrix of the experiment is an M × N Gaussian random matrix, and the iterations are performed 1000 times. We calculate the reconstruction probability if the reconstruction error is less than 1 × 10 −6 , and it means that reconstruction is successful. Te simulation results are shown in Figure 4. It can be found in Figure 4 that, with a gradual increase in the number of sampling points, the recovery probabilities of various algorithms begin to increase at diferent rates.

Journal of Computer Networks and Communications
Among them, when the number of sampling points is 60, the CoSaMP algorithm has a relatively large increase in the recovery rate. Tis is because the number of backtracking times set in the backtracking process of the fxed number of atomic columns of the algorithm is less, so the recovery probability in the process will have a big improvement. Other algorithms also have error atomic columns, and the recovery probability also has the opportunity to improve. During the operation of the system, the recovery probability of the StOMP algorithm and SP algorithm shows a high degree of coincidence. When the number of sampling points is 90, the recovery probability of both algorithms tends to 1. Te recovery probability of the SCWOMP algorithm is the best. Many researchers choose to go back one step of the iterative result and adjust the step size when overestimating, so as to avoid overestimating the atomic column selection. When the number of sampling points is 80, the SCWOMP algorithm and the fxed steps are diferent but all reach the maximum recovery rate at this moment. When the number of sampling points is about 72, the recovery rate of SCWOMP is almost 1. Te rate is faster than that of other algorithms. Ten, the infuence of sparsity on the recovery rate of the algorithm is described, as shown in Figure 5. Figure 5 shows a performance comparison diagram of diferent sparsity under various compressed sensing recovery algorithms. It can be found that the recovery rates of all algorithms start to decrease at diferent rates as sparsity increases. Among them, the CoSaMP algorithm represented the fastest decline, and the recovery rate dropped to nearly 0 when sparsity was around 50. However, the recovery rate of the OMP algorithm, StOMP algorithm, and SP algorithm starts to decrease slowly with an increase in sparsity, and when sparsity reaches 60K, the reduction is close to 0. When the recovery probability of the StOMP algorithm and SP algorithm is 0, the corresponding sparsity values are 55 and 65, respectively.
When the SCWOMP algorithm has a fxed step size of 5, as sparsity increases, the slope corresponding to the recovery rate curve is larger than that of other algorithms, indicating that the rate of reduction in the recovery probability is slower than that of other algorithms. We conducted an experiment with diferent step sizes of the SCWOMP algorithm. In the experiment, we try to set a more appropriate threshold value and flter multiple atomic columns to reduce the number of iterations. It can be seen from the results that the same sparsity can achieve better than other algorithms' recovery rate.

Simulation Analysis of the Improved Compressed Sensing
Recovery Algorithm. Te experimental parameter settings are the same as in Figure 4. Te SCWOMP algorithm is used to compare the simulation with other algorithms under diferent coefcients, 1000 times, and the reconstruction probability is calculated. When the reconstruction error is less than 10 −6 , the reconstruction is successful. Te experimental simulation results are shown in Figure 6.
In Figure 6(a), the sparsity is set to 20. During the process, the infuence of the recovery probability is observed when the measurement value changes and the ordinate corresponds to the reconstructed power of the signal. It can be found that, in the process of increasing the number of sampling points, the recovery probability under all algorithms begins to increase, and the SCWOMP algorithm has a higher recovery probability than other algorithms. When the pruning coefcient g � 0.5 and the number of sampling points is 80, the reconstruction rate has a maximum value. Te recovery probability also increases with the pruning factor. M, when the other three algorithms reach the maximum reconstruction probability, is signifcantly larger than that of the SCWOMP algorithm. In Figure 6(b), the measurement value is set to 130. During the process, the infuence of the change of sparsity on the recovery   probability is observed and the ordinate corresponds to the reconstruction probability. With an increase in sparsity, the rate of reduction of the reconstruction probability of the SCWOMP algorithm is signifcantly lower than that of other algorithms, and when sparsity reaches 70, the reconstruction probability becomes 0, which indicates that the proposed algorithm has a wider range of reconfgurable range. Te simulation trial used two diferent sets of the original signals: (1) f � cos (2 π/ 256 t) + sin (2 π/128 t) and (2) f � 0.3cos (2 π × 0.625 t) + 0.6sin (2 π × 0.125 t); signal sparsity uses the discrete cosine transform (DCT) method. Te trim coefcient is set to 0.5. Using the proposed SCWOMP algorithm, the comparison between the recovered signal and the original signal waveform is plotted in Figure 7.
In Figure 7, the red curve represents the recovered waveform and the blue curve represents the original waveform. Observing the frequency domain, it can be found that the main components of the signal of the proposed algorithm are gradually recovered in the process. By comparing the red recovery waveform with the blue original waveform in two phases, the SCWOMP algorithm can repair the original signal within a certain error range. Trough the matching pursuit algorithm, it can be known that the difference in the overall calculation amount is mainly related to the diference in the number of iterations. Using a twoharmonic signal in the OMP algorithm, the CoSaMP algorithm and the improved algorithm SCWOMP algorithm are compared in the simulation of the number of iterations and the error margin, as shown in Figure 8.

Journal of Computer Networks and Communications
In Figure 8, it can be found that the proposed SCWOMP algorithm can reach the minimum error margin value faster than the OMP algorithm, avoiding unnecessary step size changes, but it can be closer to the performance of the OMP algorithm. When the OMP algorithm reaches almost the same error margin as the CoSaMP algorithm, 70 iterations are required; by using the improved algorithm proposed in the study, it can not only achieve excellent performance in a short time but also can perform fewer iterations than the OMP algorithm. Te improved algorithm in the fgure can achieve the efect of 100 iterations of the OMP algorithm when it performs about 10 iterations. Tis again proves that the improved algorithm has the excellent performance of the other two algorithms and can make the recovery performance signifcantly improved. Finally, in order to ensure that other advantages of compressed sensing have an impact on the bit error rate of the algorithm, frst, we contrast their complexity, as shown in Table 1.
It can be seen from Table 1 that the complexity of the proposed algorithm is quite consistent with the theory, and the complexity of the ML algorithm is the highest, the complexity of the OMP algorithm is the lowest, and the proposed algorithm is lower. Since the communication system will be afected by the surrounding environment and noise in the process of operation, the system analyzes the bit error rate of signal transmission in the process of the change in a signal-to-noise ratio of diferent algorithms, see Figure 9. Figure 9 shows the trend diagram of the bit error rate (BER) of the ML, ZF, MMSE, and OMP algorithms and the improved algorithm in the process of changing the signal-tonoise ratio. Te BER of the proposed algorithm is lower than that of the ZF algorithm, MMSE algorithm, and OMP algorithm in the process of change and can also be closer to the performance of the excellent ML algorithm. When the signal-to-noise ratio is 10 dB, there is a minimum bit error    Although all algorithms using compressive sensing reconstruction have foor efects, the proposed algorithm has signifcantly lower foor efects.

Conclusion
Te 5G era is about to enter, and modern society has never stopped exploring the advantages of MIMO technology. Te research proposes the SCWOMP algorithm. First, we compare the performance of diferent sampling points and sparsity under various compressed sensing recovery algorithms; then, we compare the recovery probability of the improved algorithm and other algorithms when the measured value and sparsity are diferent and the performance of the improved algorithm under diferent original waveforms. Te recovered waveforms are compared with the algorithm's error margin and performance changes. Te results show that the increase in sparsity reduces the reconstruction probability of the SCWOMP algorithm at a signifcantly lower rate than other algorithms. By setting the trim coefcient to 0.5, the original waveform in the frequency domain can be repaired within a certain error range through the operation of the algorithm. When calculating the error margin of the algorithm with diferent iteration times, the proposed algorithm can reach the value of the minimum error margin faster than the OMP algorithm and can avoid unnecessary step size changes. Te fnal result shows that the SCWOMP algorithm is performing. Te best performance can be achieved after about 10 iterations. Comparing the SNR with many algorithms, when the SNR reaches 10 dB, there is a minimum bit error rate, which is about 10 −3 , and the existing foor efect is the lowest. All of these prove that the overall performance of the proposed algorithm is optimal, which can be of great help to the communication system technology. However, there are very few studies on the combination of compressed sensing and segment backtracking at present. Te follow-up expansion of the research scope and the use of the advantages of the algorithm to extreme are still the direction that can be continued to be explored.

Data Availability
Te datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Conflicts of Interest
Te authors declare that there are no conficts of interest.