Low-complexity equalization method in high-speed mobile environment

Abstract

The invention belongs to a wireless communication technology, and particularly relates to a low-complexity equalization method in a high-speed mobile environment, which is applied to a receiving end of an orthogonal time sequence multiplexing system, and comprises the following steps: at the receiving end, firstly, acquiring a preliminary rough estimation value of a transmission time domain signal based on a minimum mean square error criterion; then, a steepest descent method is used for optimizing the initial estimation value, and a suboptimal solution of the signal is obtained; in order to further improve the equalization effect, weighting processing is introduced into a Gaussian-Seid algorithm, the stability and convergence of the algorithm are improved through weight adjustment, the suboptimal solution is input into an iteration updating process until a preset convergence condition is met, and an equalized signal is output. According to the method disclosed by the invention, on the premise of keeping low algorithm complexity, the bit error rate performance is improved, the convergence efficiency of the algorithm is accelerated, and an efficient and reliable signal equalization solution is provided for a high-speed wireless communication system.

Description

Technical Field

[0001] The invention belongs to wireless communication technology, and in particular relates to a low-complexity equalization method in a high-speed mobile environment. Background Art

[0002] With the rapid development of high-speed railways in recent years and the widespread popularity of autonomous driving and vehicle networking technologies, the demand for voice calls and data traffic from high-speed mobile terminals is increasing. Therefore, how to improve the quality of mobile communication services in high-speed scenarios has received widespread attention.

[0003] There are two main problems in the wireless communication system of high-speed terminals: the first is fast time-varying fading. The multipath effect will cause the signal to selectively fade in frequency, resulting in a time-dispersive channel, while the Doppler effect will cause time-selective fading, resulting in channel frequency dispersion. In addition, the constant change in the terminal's moving speed increases the uncertainty of the two types of fading and the change in the channel gain coefficient, so the establishment and estimation of the channel model becomes more difficult; the second is Doppler frequency shift. When the electromagnetic wave reaches the moving terminal, it will produce Doppler frequency deviation, resulting in a mismatch in the synchronization frequency between the receiving end and the transmitting end. The frequency deviation will break the orthogonal relationship between the subcarriers, increasing the difficulty of the receiver to process the signal, thereby reducing the performance of the communication system.

[0004] The key idea of ​​OTSM modulation is to modulate information symbols in the delay-sequence domain, where the sequence is defined as the number of zero crossings per unit time interval. OTSM performs an inverse Walsh-Hadamard transform (IWHT) along the sequence domain to convert the information symbols in the delay-sequence domain into the delay-time domain, and finally transmits and receives signals in the time domain. It has the characteristics of strong anti-Doppler effect capability and strong adaptability to time-varying channels, and can effectively cope with the frequency offset and expansion caused by the Doppler effect and the channel characteristics of high-speed time-varying in high-speed mobile environments.

[0005] Equalization algorithms are mainly used in wireless communication systems to compensate and correct various distortions and interferences introduced during channel transmission, thereby restoring the integrity and quality of the original signal. This is crucial to improving the performance and stability of wireless communication systems. However, the existing equalization methods have a huge amount of calculations, and how to reduce the complexity while ensuring bit error performance has become a problem that needs to be solved. Summary of the invention

[0006] In order to reduce the complexity of the signal equalization process, the present invention proposes a low-complexity equalization method in a high-speed mobile environment. The method is applied to the receiving end of an orthogonal time multiplexing system. A preliminary rough estimate of the transmission time domain signal is obtained at the receiving end based on the minimum mean square error criterion, and then the initial estimate is optimized using the steepest descent method to obtain a suboptimal solution for the signal; weighted processing is introduced into the Gauss-Seidel algorithm, and the stability and convergence of the algorithm are improved by weight adjustment. The suboptimal solution is input into an iterative update process until the preset convergence condition is met, and the equalized signal is output.

[0007] Further, solving the second best solution according to the estimated value based on the steepest descent algorithm includes the following steps:

[0008]

[0009] in, is the suboptimal solution of the nth block time domain sample calculated based on the steepest descent algorithm; is the initial rough estimate of the time domain sample of the nth block obtained based on the minimum mean square error method; μ is the reduction coefficient; Indicates based on The reconstructed signal and the time domain output signal Z of the nth block n The residual between n represents the matched filter matrix of the nth block.

[0010] Furthermore, the process of iteratively updating the suboptimal solution as the initial input based on the weighted Gauss-Seidel algorithm includes:

[0011]

[0012] in, is the estimated value of the nth block time domain sample obtained based on the i-1th iteration of the weighted Gaussian algorithm, i is an integer greater than or equal to 2; w is the weight in the weighted Gaussian algorithm, D n represents the matrix composed of the diagonal elements of the matched filter matrix, L n is a matrix consisting of strictly lower triangular elements of the matched filter matrix, is the matrix L n The conjugate matrix of n represents the time domain output signal of the nth block; Based on The reconstructed signal and Z n The residual between .

[0013] Furthermore, the iteration matrix T in the Gauss-Seidel algorithm n , b n Respectively expressed as:

[0014]

[0015] b n =(D n +L n ) -1 ·Z n

[0016] Among them, D n represents the matrix composed of the diagonal elements of the matched filter matrix, L n is a matrix consisting of strictly lower triangular elements of the matched filter matrix, is the matrix L n The conjugate matrix of .

[0017] Furthermore, the weight in the weighted Gaussian algorithm is initially set to 1 and then updated in each iteration. The weight in the weighted Gaussian algorithm in the k+1th iteration is expressed as:

[0018]

[0019] Among them, w k+1 、w k They represent the weights of the k+1th and kth iterations in the weighted Gauss-Seidel algorithm, respectively. (k) 、residual (k-1) They represent the residuals of the k+1th and kth iterations in the weighted Gauss-Seidel algorithm respectively; ||·|| means finding the norm.

[0020] Furthermore, the residual of the kth iteration in the weighted Gauss-Seidel algorithm is (k) It is expressed as:

[0021]

[0022] Among them, R n represents the matched filter matrix of the nth block; Represents the estimate of the nth block obtained by the kth iteration of the weighted Gauss-Seidel algorithm.

[0023] The steepest descent-weighted Gauss-Seidel equalization algorithm based on OTSM proposed in the present invention not only improves the bit error performance, but also accelerates the convergence speed, making the equalization processing more efficient. This method effectively reduces the complexity of the equalization processing while ensuring the communication performance, and provides an efficient and reliable solution for high-speed wireless communication systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 A schematic diagram of a transceiver model of a low-complexity equalization method in a high-speed mobile environment of the present invention;

[0025] Figure 2 A simulation diagram comparing the bit error performance of the present invention with that of other equalizers in the prior art;

[0026] Figure 3 It is a schematic diagram comparing the number of iterations of the present invention and other equalizers in the prior art. DETAILED DESCRIPTION

[0027] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0028] The present invention proposes a low-complexity equalization method in a high-speed mobile environment. The method is applied to the receiving end of an orthogonal time multiplexing system. At the receiving end, a preliminary rough estimate of a transmission time domain signal is obtained based on a minimum mean square error criterion, and then the initial estimate is optimized using a steepest descent method to obtain a suboptimal solution for the signal. Weighted processing is introduced into a Gauss-Seidel algorithm, and the stability and convergence of the algorithm are improved by weight adjustment. The suboptimal solution is input into an iterative update process until a preset convergence condition is met, and a signal that has completed equalization is output.

[0029] In high-speed scenarios, wireless communication systems often face significant challenges brought by fast time-varying fading and Doppler shift. These factors cause the channel characteristics to change rapidly, thereby increasing the difficulty of signal demodulation and data transmission. In order to solve these problems, the present invention proposes a steepest descent-weighted Gauss-Seider equalization algorithm (SD-WGS) based on orthogonal time series modulation (OTSM) for equalizing the estimated symbols. In this embodiment, the following steps are specifically included:

[0030] First, this algorithm uses the steepest descent method to optimize the initial estimate. The steepest descent method is an iterative optimization technique that gradually adjusts the estimate along the negative gradient direction to quickly approach the global optimal solution. Through this process, a better initial solution can be obtained.

[0031] Then, this better solution is used as the initial iteration value and input into the weighted Gaussian iterative equalizer for further processing. The weighted Gaussian iterative equalizer gradually corrects the estimated symbols through weighted processing and Gaussian iterative method, further improving the accuracy and performance of equalization.

[0032] Specifically, Figure 1 , in an orthogonal time multiplexing system, let x,y∈c NM×1is the information symbol sent and received, where M represents the number of rows of the transmission symbol matrix and N represents the number of columns of the transmission symbol matrix; the total frame length and total bandwidth of the transmitted OTSM signal frame are T f =NT and B=MΔf, where Δf=1 / T, T represents the time length of a single symbol, i.e., for any pulse shaping waveform, the signal is critically sampled.

[0033] At the transmitter, the information symbols are divided into vectors 1. The symbol vector is arranged into a delay sequence matrix as follows:

[0034] X=[x0,x1,...,x M-1 ] T

[0035] Finally max symbol vector, that is, m ≥ Ml max , x max is a zero vector, where l max is the discrete channel delay spread index. Figure 1 As shown, this zero padding (ZP) along the delay domain helps to avoid inter-block interference due to channel delay spread. Then, an N-point inverse WHT is applied to each of these symbol vectors (rows) to transform it to the delay time domain:

[0036]

[0037] Among them, W N represents the Walsh-Hadamard transformation matrix (consisting of binary values ​​(usually +1 and -1), and constructed recursively), Represents the information symbol vector after N-point inverse WHT processing.

[0038] matrix Contains delayed time samples that are vectorized column-wise to obtain time domain samples to be sent to the physical channel It is expressed as:

[0039]

[0040] The above transmitter operation can be expressed in simple matrix form as:

[0041]

[0042] Where P is the row-column interleaver matrix, I M Table M×M identity matrix, represents the Kronecker product. This permutation is called a complete shuffle in the literature and has the following properties:

[0043]

[0044] For a given square matrix A and B, the complete shuffle property in the above formula is achieved, so the transmitter operation can be simplified to:

[0045]

[0046] At the receiving end, the received time domain signal r(t) is processed by analog-to-digital conversion (ADC) to generate a time domain vector The received time domain samples r are folded into the matrix Y by column as follows

[0047]

[0048] The received delayed sequence information symbols are obtained by performing an N-point WHT on the rows of the received delay time matrix Y:

[0049]

[0050] The receiver operation can be rewritten in matrix form as:

[0051]

[0052] in

[0053] The time domain input and output relationship of the OTSM model is as follows:

[0054] r n =G n ·s n +w n ,n=0,...,N-1

[0055] Among them G n is the time domain channel matrix. In the GS low complexity detector, the GS iteration is performed in the matched filter channel matrix block After the matched filter operation, the matrix input-output relationship can be written as:

[0056]

[0057] in The GS method is used to iteratively find the least squares solution:

[0058]

[0059] Assume D n and L n Respectively represent the matched filter matrix R n A matrix with diagonal elements and strictly lower triangular elements. In each iteration, find The estimated GS iteration method is as follows:

[0060]

[0061] In order to further accelerate the convergence speed and detection accuracy of the GS algorithm, this paper proposes a low-complexity weighted Gaussian-Seidel (SD-WGS) scheme based on the steepest descent method on the basis of the traditional Gaussian-Seidel algorithm. The iterative process of the WGS algorithm is shown in the formula:

[0062]

[0063] In the weighted Gauss-Seidel algorithm, i is an integer greater than or equal to 2.

[0064] According to the method of steepest descent, Then we have:

[0065]

[0066] set up Thus, we can know

[0067] The weight in the weighted Gaussian algorithm is initially set to 1 and then updated in each iteration. The weight in the weighted Gaussian algorithm in the k+1th iteration is expressed as:

[0068]

[0069] Among them, w k+1 、w k They represent the weights of the k+1th and kth iterations in the weighted Gauss-Seidel algorithm, respectively. (k) 、residual (k-1) They represent the residuals of the k+1th and kth iterations in the weighted Gauss-Seidel algorithm, respectively. If the residual is gradually decreasing, w will increase, indicating an increase in the update step size. If the residual decreases slowly or becomes larger, w will decrease accordingly, thereby achieving adaptive weight iteration; ||·|| represents the norm.

[0070] The residual of the kth iteration in the weighted Gauss-Seidel algorithm (k) It is expressed as:

[0071]

[0072] Among them, R n represents the matched filter matrix of the nth block; Represents the estimate of the nth block obtained by the kth iteration of the weighted Gauss-Seidel algorithm.

[0073] This embodiment also provides a pseudo code of a low-complexity equalization method in a high-speed mobile environment as shown in Table 1.

[0074] Table 1 Pseudo code of the method of the present invention

[0075]

[0076]

[0077] In order to verify the performance of the proposed method, this embodiment is simulated on Matlab 2021a. The simulation parameters are shown in Table 1:

[0078] Table 2 System simulation parameters

[0079]

[0080]

[0081] Speed ​​is 500 km / h, modulation is 4-QAM and BER=10 -4 When Figure 2 As shown in Figure 2, the error performance of the proposed method is improved by 1.75 dB. Figure 3 As shown, the average reduction is 1 time compared with the control method.

[0082] The simulation results show that the proposed method is less complex than the traditional equalization method based on Orthogonal Time-Frequency-Space (OTFS), and the bit error rates of the two methods are almost the same. Compared with the GS equalizer of OTSM, the bit error performance is improved and the complexity is slightly reduced.

[0083] In summary, the OTSM-based steepest descent-weighted Gauss-Seidel equalization algorithm proposed in the present invention effectively reduces the complexity of equalization processing while ensuring bit error performance, and provides an efficient and reliable solution for high-speed wireless communication systems.

[0084] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A low-complexity equalization method in a high-speed mobile environment, characterized in that: The method is applied to the receiving end of an orthogonal time multiplexing system. At the receiving end, a preliminary rough estimate of a transmission time domain signal is obtained based on a minimum mean square error criterion, and then the initial estimate is optimized using the steepest descent method to obtain a suboptimal solution of the signal. Weighted processing is introduced into the Gauss-Seidel algorithm, and the stability and convergence of the algorithm are improved by weight adjustment. The suboptimal solution is input into an iterative update process until a preset convergence condition is met, and a balanced signal is output.

2. The low-complexity equalization method in a high-speed mobile environment according to claim 1, characterized in that: Solving the second best solution based on the estimated value based on the steepest descent algorithm includes the following steps: in, is the suboptimal solution of the nth block time domain sample calculated based on the steepest descent algorithm; is the initial rough estimate of the time domain sample of the nth block obtained based on the minimum mean square error method; μ is the reduction coefficient; Indicates based on The reconstructed signal and the time domain output signal Z of the nth block n The residual between n represents the matched filter matrix of the nth block.

3. The low-complexity equalization method in a high-speed mobile environment according to claim 1, characterized in that: The process of iteratively updating the suboptimal solution as the initial input based on the weighted Gauss-Seidel algorithm includes: in, is the estimated value of the nth block time domain sample obtained based on the i-1th iteration of the weighted Gaussian algorithm, i is an integer greater than or equal to 2; w is the weight in the weighted Gaussian algorithm, D n represents the matrix composed of the diagonal elements of the matched filter matrix, L n is a matrix consisting of strictly lower triangular elements of the matched filter matrix, is the matrix L n The conjugate matrix of n represents the time domain output signal of the nth block; Based on The reconstructed signal and Z n The residual between .

4. The low-complexity equalization method in a high-speed mobile environment according to claim 3, characterized in that: Iteration matrix T in Gauss-Seidel algorithm n , b n Respectively expressed as: b n =(D n +L n ) -1 ·Z n Among them, D n represents the matrix composed of the diagonal elements of the matched filter matrix, L n is a matrix consisting of strictly lower triangular elements of the matched filter matrix, is the matrix L n The conjugate matrix of .

5. The low-complexity equalization method in a high-speed mobile environment according to claim 3, characterized in that: The weight in the weighted Gaussian algorithm is initially set to 1 and then updated in each iteration. The weight in the weighted Gaussian algorithm in the k+1th iteration is expressed as: Among them, w k+1 、w k They represent the weights of the k+1th and kth iterations in the weighted Gauss-Seidel algorithm, respectively. (k) 、residual (k-1) They represent the residuals of the k+1th and kth iterations in the weighted Gauss-Seidel algorithm respectively; ||·|| means finding the norm.

6. The low-complexity equalization method in a high-speed mobile environment according to claim 5, characterized in that: The residual of the kth iteration in the weighted Gauss-Seidel algorithm (k) It is expressed as: Among them, R n represents the matched filter matrix of the nth block; Represents the estimate of the nth block obtained by the kth iteration of the weighted Gauss-Seidel algorithm.

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