阅读说明：本技术 一种时间反演多址系统的多用户检测算法 (Multi-user detection algorithm of time reversal multiple access system ) 是由 梁静雯 朱江 于 2019-11-25 设计创作，主要内容包括：本发明公开了一种时间反演多址系统的多用户检测算法,检测器首先确定出译码矩阵G,然后从译码矩阵G中提取出包含主对角线的三对角线稀疏矩阵P,然后将三对角线稀疏矩阵P分成两个二对角线稀疏矩阵；然后分别求出两个二对角线稀疏矩阵的逆,利用两个二对角线稀疏矩阵的逆的乘积求出三对角线稀疏矩阵P的逆,最后,通过取译码矩阵G的Neumann级数展开项中的前L项来近似求取译码矩阵G的逆矩阵G<Sup>-1</Sup>,根据求得的逆矩阵G<Sup>-1</Sup>估计出发射机原始发送的发送信号,然后将该信号发送给基站,结果表明,通过该算法进行多用户检测时,基站就可以直接得到滤除了噪声信号的发送信号,并且在误码率和信道容量方面具有明显的性能优势,并且具有较低的复杂度。(The invention discloses a multi-user detection algorithm of a time reversal multiple access system.A detector firstly determines a decoding matrix G, then extracts a three-diagonal sparse matrix P containing main diagonal from the decoding matrix G, and then divides the three-diagonal sparse matrix P into two-diagonal sparse matrices; then, respectively solving the inverses of the two diagonal sparse matrixes, solving the inverse of the three-diagonal sparse matrix P by utilizing the product of the inverses of the two diagonal sparse matrixes, and finally, approximately solving the inverse matrix G of the decoding matrix G by taking the first L items in the Neumann series expansion items of the decoding matrix G ‑1 Based on the obtained inverse matrix G ‑1 The method estimates the original transmission signal sent by the transmitter, and then sends the signal to the base station, and the result shows that when the algorithm is used for multi-user detection, the base station can directly obtain the transmission signal with the noise signal filtered, and the method has obvious performance advantages in the aspects of bit error rate and channel capacity and has lower complexity.)

1. A multi-user detection algorithm for a time-reversal multiple access system, comprising:

s1: the detector determines a decoding matrix G for decoding the received signal according to a pre-stored channel gain matrix and a pre-stored noise signal matrix after receiving the transmission signal sent by the transmitter, wherein G is H^HH + R, H denotes the channel gain matrix, H^HA conjugate transpose matrix representing a channel gain matrix H, R representing a noise signal matrix;

s2: keeping elements in three diagonals including a main diagonal in the decoding matrix G unchanged, and setting the elements at the rest positions in the matrix G to be 0 to obtain a three-diagonal sparse matrix P after sparse processing;

s3; splitting a three-diagonal sparse matrix P into two-diagonal sparse matrices, respectively performing inversion operation on the two-diagonal sparse matrices, and solving the inverse of the three-diagonal sparse matrix P by using the product of the inverses of the two-diagonal sparse matrices, wherein the three-diagonal sparse matrix P is equal to the product of the two-diagonal sparse matrices;

s4: the detector approximates the inverse matrix G of the decoding matrix G by taking the first L terms of the Neumann series expansion terms of the decoding matrix G^-1According to the formula

s5: the detector sends the estimated transmission signal to the base station as the transmission signal originally sent by the transmitter.

2. The multi-user detection algorithm for time-reversal multiple access system of claim 1, wherein W ≧ N, W denotes the number of antennas configured on the base station side, and N denotes the number of single-antenna users.

3. The multi-user detection algorithm for time-reversal multiple access systems of claim 1, wherein L-2.

4. The multi-user detection algorithm for time-reversal multiple access systems of claim 3, wherein the inverse G of the G is decoded when L is 2^-1The following formula is used to solve:

and K represents a hollow matrix obtained by extracting the three-diagonal sparse matrix P from the decoding matrix G.

5. The multi-user detection algorithm for time-reversal multiple access systems of any of claims 1-4, wherein the three-diagonal sparse matrix P is split into two diagonal sparse matrices by Thomas algorithm in step S3.

6. The multi-user detection algorithm for time-reversal multiple access systems of claim 5, wherein two of the diagonal sparse matrices are Z and X, respectively, wherein P-Z-X,

the values of the elements in the two diagonal sparse matrices Z and X are found according to the following formula:

e₁＝a₁，d_n＝c_n/e_n-1，e_n＝a_n-d_n/b_n-1，n＝2,3…N。

Technical Field

The invention relates to the technical field of wireless communication, in particular to a multi-user detection algorithm of a time reversal multiple access system.

Background

With the development of internet, more and more wireless devices need to access to a wireless network, and the traditional multiple access technology is difficult to meet the increasing user requirements. Time Reversal Multiple Access (TRDMA) is considered to be a space Division Multiple Access technique that is advantageous for constructing low-complexity, high-utilization green communications because of its good space-Time focusing characteristics.

The TRDMA technique distinguishes users according to independence between channel impulse responses. However, in actual communications, the channels are not everywhere independent of each other. Correlation between channels can lead to interference between users and also to a loss of channel capacity. It is therefore necessary to eliminate inter-user interference.

The interference cancellation algorithm of the TRDMA system may refer to a detection algorithm in a CDMA (Code Division Multiple Access) system. Classical linear detection algorithms include ZF (Zero Forcing) algorithm and MMSE (Minimum Mean Square Error) algorithm. The MMSE detection algorithm is proved to be capable of obtaining an approximately optimal detection effect when the ratio of the transmit-receive antennas is large, however, the MMSE detection algorithm is required to perform inversion calculation on a large-scale matrix, the complexity is high, and the MMSE detection algorithm is not suitable for being applied in practice. Therefore, how to reduce the complexity of the detection algorithm on the premise of ensuring the optimal detection effect becomes a technical problem to be solved urgently at present.

Disclosure of Invention

In order to solve the technical problems, the invention provides a multi-user detection and calculation method of a time reversal multiple access system, which adopts the technical scheme that:

a multi-user detection algorithm for a time-reversal multiple access system, comprising:

s1: the detector determines a decoding matrix G for decoding the received signal according to a pre-stored channel gain matrix and a pre-stored noise signal matrix after receiving the transmission signal sent by the transmitter, wherein G is H^HH + R, H denotes the channel gain matrix, H^HA conjugate transpose matrix representing a channel gain matrix H, R representing a noise signal matrix;

s2: keeping elements in three diagonals including a main diagonal in the decoding matrix G unchanged, and setting the elements at the rest positions in the matrix G to be 0 to obtain a three-diagonal sparse matrix P after sparse processing;

s3; splitting a three-diagonal sparse matrix P into two-diagonal sparse matrices, respectively performing inversion operation on the two-diagonal sparse matrices, and solving the inverse of the three-diagonal sparse matrix P by using the product of the inverses of the two-diagonal sparse matrices, wherein the three-diagonal sparse matrix P is equal to the product of the two-diagonal sparse matrices;

s4: the detector approximates the inverse matrix G of the decoding matrix G by taking the first L terms of the Neumann series expansion terms of the decoding matrix G^-1According to the formula

A transmit signal of a transmitter is estimated, wherein,

P^-1representing the inverse of the three-diagonal sparse matrix P, Y represents the received signal matrix,a sending signal matrix of the sender obtained by the estimation of the detector is shown, and L is a preset summation stage number;

s5: the detector sends the estimated transmission signal to the base station as the transmission signal originally sent by the transmitter.

Further, W is larger than or equal to N, W represents the number of antennas configured on the base station side, and N represents the number of single-antenna users.

Further, L ═ 2.

Further, when L is 2, decoding the inverse matrix G of the matrix G^-1The following formula is used to solve:

and K represents a hollow matrix obtained by extracting the three-diagonal sparse matrix P from the decoding matrix G.

Further, the three-diagonal sparse matrix P is split into two diagonal sparse matrices by the Thomas algorithm in step S3.

Further, the two diagonal sparse matrices are Z and X, respectively, wherein P ═ Z · X,

g_ijrepresenting the elements in the ith row and jth column of the decoding matrix G,

the values of the elements in the two diagonal sparse matrices Z and X are found according to the following formula:

e₁＝a₁，d_n＝c_n/e_n-1，e_n＝a_n-d_n/b_n-1，n＝2,3…N。

according to the multi-user detection algorithm of the time reversal multiple access system, a detector firstly determines a decoding matrix G, then extracts a three-diagonal sparse matrix P containing main diagonal lines from the decoding matrix G, and then divides the three-diagonal sparse matrix P into two-diagonal sparse matrices; then, respectively solving the inverses of the two diagonal sparse matrixes, solving the inverse of the three-diagonal sparse matrix P by utilizing the product of the inverses of the two diagonal sparse matrixes, and finally, approximately solving the inverse matrix G of the decoding matrix G by taking the first L items in the Neumann series expansion items of the decoding matrix G^-1Based on the obtained inverse matrix G^-1The method estimates the transmission signal originally sent by the transmitter, and then sends the signal to the base station, and the result shows that when the algorithm is used for multi-user detection, the base station can directly obtain the transmission signal with the noise signal filtered, and the method has obvious performance advantages in the aspects of bit error rate and channel capacity and has lower complexity.

Drawings

The invention will be further described with reference to the accompanying drawings and examples, in which:

FIG. 1 is a schematic flow diagram of a multi-user detection algorithm for a time-reversal multiple access system;

FIG. 2 is a schematic diagram of a time-reversed MIMO channel model;

FIG. 3 is a schematic diagram of the variation of bit error rate with signal-to-noise ratio during the experiment;

fig. 4 is a diagram illustrating the variation of channel capacity with signal-to-noise ratio during the experiment.

Detailed Description

In order to make the technical problems, technical solutions and advantages of the present invention more apparent, the following detailed description is given with reference to the accompanying drawings and specific embodiments, it being understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention.

In order to solve the problem that the operation process is complex when the multi-user detection is performed based on the existing minimum mean square error algorithm, the embodiment provides a multi-user detection algorithm of a time reversal multiple access system, as shown in fig. 1, which includes the following steps:

s1: the detector determines a decoding matrix G for decoding the received signal according to a pre-stored channel gain matrix and a pre-stored noise signal matrix after receiving the signal sent by the transmitter, wherein G is H^HH + R, H denotes the channel gain matrix, H^HThe conjugate transpose of the channel gain matrix H is represented and R represents the noise signal matrix.

In this embodiment, W is equal to or greater than N, W represents the number of antennas arranged on the base station side, and N represents the number of single-antenna users. The following description will be specifically made.

Referring to fig. 2, the time-reversed MIMO channel model includes three parts: base station end, user end, TDNS (Three-dimensional Decomposition New Series, Noiman Series of Three diagonal matrix Decomposition) detector. The TRM array in fig. 2 collects the signals and performs time reversal and retransmission. W antennas are configured at the base station end, N single antennas are configured at the user end, and W is larger than or equal to N. The transmission is subject to multipath rayleigh fading. s ═ s₁,s₂,…,s_N]^TN x 1 dimensional data transmitted simultaneously for all users, H ═ H₁,h₂,…h_N]Representing the channel gain matrix, h_i＝[h_1i,h_2i,…,h_Wi]^TIs the channel gain vector from the ith user to the base station, where i is 1,2 … N. It should be noted that the detector in this embodiment may receive the channel state information and the noise information transmitted by the base station in advance, so as toThe Information is stored in advance, and the base station may acquire Channel State Information (CSI) by using the prior art, thereby obtaining a Channel gain matrix from the CSI and sending the Channel gain matrix to the detector for storage²I_NWherein, I_NRepresenting the identity matrix, σ²Representing the variance of the noise signal.

The W × 1-dimensional received signal Y received at the base station may be represented as Y ═ H · s + n.

Wherein H ∈ C^W×NFor a multipath Rayleigh fading channel, the channel gain obeys a mean value of 0 and a variance of

Cyclic Symmetric Complex Gaussian (CSCG) random variable of (c), T_SIs the system sampling period, σ_TFor the channel rms delay spread, where l is the number of taps. n is the mean 0 and the variance σ²The W × 1 dimensional Additive White Gaussian Noise (AWGN) matrix of (1) satisfies n ~ (0, σ ~ -²I_W) Wherein, I_WIs an identity matrix.

S2: keeping the elements in the three diagonals including the main diagonal in the decoding matrix G unchanged, and setting the elements at the rest positions in the matrix G to be 0 to obtain a three-diagonal sparse matrix P after sparse processing.

The three diagonal sparse matrix P is:

g_ijwhich represents the elements in the ith row and jth column of the decoding matrix G.

S3; and splitting the three-diagonal sparse matrix P into two-diagonal sparse matrices, respectively performing inversion operation on the two-diagonal sparse matrices, and solving the inverse of the three-diagonal sparse matrix P by using the product of the inverses of the two-diagonal sparse matrices, wherein the three-diagonal sparse matrix P is equal to the product of the two-diagonal sparse matrices.

In step S3 of the present embodiment, the three-diagonal sparse matrix P may be split into two diagonal sparse matrices by a Thomas (Thomas) algorithm. Assuming that the two split diagonal sparse matrices are Z and X, respectively, then P ═ Z · X,

wherein the content of the first and second substances,

the values of the elements in the two diagonal sparse matrices Z and X can be found according to the following formula:

e₁＝a₁，d_n＝c_n/e_n-1，e_n＝a_n-d_n/b_n-1，n＝2,3…N。

s4: the receiver approximates the inverse matrix G of the decoding matrix G by taking the first L terms of the Neumann series expansion terms of the decoding matrix G^-1According to the formula

A transmit signal of a transmitter is estimated, wherein,

P^-1representing the inverse of the three-diagonal sparse matrix P, Y represents the received signal matrix,

and L is a preset summation stage number.

S5: the detector sends the estimated transmission signal to the base station as the transmission signal originally sent by the transmitter.

In step S5, the detector will estimate the signal

As a transmission signal originally transmitted by the transmitter, and transmits the signal to the base station.

The multi-user detection in the embodiment is to receive the signal with the noise signal vectorEstimating a transmitting end vector by calculating a number Y through a formulaEstimating a vector

The formula of (1) is:

that is, to obtain

The G matrix needs to be inverted, and the complexity of the inversion operation increases exponentially as W and N increase, so that the inversion needs to be simplified and the complexity needs to be reduced.

The G matrix is expanded by a Neumann (noelman) series:

wherein P is an invertible matrix and satisfies:

approximating G by taking the first L term of the above equation^-1：

From the above description of step S3, it can be found that:

to obtain P^-1It is necessary to separately find X^-1And Z^-1. First, an equivalent transformation is performed on X.

Matrix for two diagonals

In this embodiment, if N is an odd number, each entry in the last column has an opposite sign, and the diagonal matrix B^-1Comprises the following steps:

from B^-1By deriving X from the derivative law^-1And Z^-1。

From X^-1，Z^-1To obtain P^-1Is composed of

P^-1＝X^-1·Z^-1

Due to P^-1Each element of the matrix is too large, each element of P is replaced by a symbol, and the value of each element is described in detail.

Wherein, in P^-1In line 1, there is a general rule except for column 1 and column N elements. Thus, column 1 and column N elements are listed individually, with the remaining columns being represented by general formulas. The values in row 1 and column 1 are:

1 row N column:

line 2, with the exception of columns 1,2 and the last column, is generally used, so that column 1, column 2 and the last column of line 2 are listed separately and the remaining columns are expressed as a general formula. There is also a rule between the last column of the general formulas in each row, and the starting value of i is the current row number.

Row 2 and column 1:

row 2 column 2:

starting from 2 rows and 3 columns to 2 rows and N-1 columns, the following rule applies:

2 rows N columns are:

the regularity of the middle row is similar, the irregular number of columns in front of each row increases progressively row by row, and the initial value of the last column of elements i increases progressively with the number of rows. The intermediate row formulas have the following rule: containing b_iThe starting value of multiplication by i increases with the number of rows. The middle row is regularly omitted and the last row of elements is listed below.

The common rule of N rows, columns 1 to N columns is expressed by the following general formula.

Rule of N rows 1 columns to N columns:

finding P^-1Then, G is approximated by Neumann series^-1. Will P^-1Substituting Neumann series to obtain G of the front L term^-1Comprises the following steps:

k denotes an empty matrix after the three-diagonal sparse matrix P is extracted by the decoding matrix G, that is, K is G-P.

When L is 2, the formula is

In the above formula, the first and second carbon atoms are,

has a complexity of O (N)²)。

In order to verify the effectiveness of the method provided in this example, relevant experiments were performed based on the method.

FIG. 3 is a comparison graph of error rate when Neumann series takes different number of terms in the experimental process, FIG. 4 is a comparison graph of channel capacity when Neumann series takes different number of terms in the experimental process, the mean value of channel gain obedience in the experimental process is 0, and the variance is

The CSCG random variable adopts a 16-QAM modulation mode. Let the channel bandwidth B be 500MHz, and the sampling period T_SRoot mean square delay spread σ, 1/B200 ns_T100/B, time-reversal multipath number L_TR80. In the experimental process, the antenna configurations are respectively 32 × 8, 64 × 8 and 128 × 8, that is, the number of antennas on the user side is configured to be 8, and the number of antennas on the base station side is configured to be 32,64 and 128. The MMSE detection algorithm, the detection algorithm provided in this example, is compared in terms of BER performance when L is 2,3, and 4. MMSE is used as an exact inversion algorithm as a reference standard. From the figure canWhen W is 32 and 64, the BER of the detection algorithm provided in this embodiment is the lowest when L is 4, then L is 3 and again L is 2, but the BER is not very different in 3 cases. As the number of antennas increases, the result of the TDNS detection algorithm provided by the present embodiment is closer to the detection result of the MMSE detection algorithm. When W is 128, L is 2,3,4, BER substantially coincides with BER of MMSE, which means that when W is equal to or greater than N, the selection of L has little influence on BER, and when L is 2, the performance can approach the level of MMSE.

However, considering both BER and computational complexity, L is preferably 2, which can achieve better BER performance at lower complexity.

The invention provides a low-complexity detection algorithm based on tri-diagonal matrix decomposition aiming at the problem of high BER caused by inter-user interference in a TRDMA uplink system. By combining the above simulations and analyses, the following conclusions can be drawn: the performance of the TDNS detection algorithm is close to MMSE, and the complexity is O (N) from MMSE³) Reduction to O (N)²) (ii) a When the number of base station end antennas far exceeds the number of users, the BER of the TDNS detection algorithm when L is 2 can be reduced to the level of MMSE.

The above-mentioned serial numbers of the embodiments of the present invention are merely for description and do not represent the merits of the embodiments.

Through the above description of the embodiments, those skilled in the art will clearly understand that the above embodiment method can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware, but in many cases, the former is a better embodiment. Based on such understanding, the technical solution of the present invention may be substantially or partially embodied in the form of a software product stored in a storage medium (e.g., ROM/RAM, magnetic disk, optical disk), and including instructions for enabling a terminal (e.g., a mobile phone, a computer, a server, an air conditioner, or a network device) to execute the method according to the embodiments of the present invention.

While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.