CN114339828A - Design method of non-orthogonal time reversal uplink multiple access system - Google Patents

Design method of non-orthogonal time reversal uplink multiple access system Download PDF

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CN114339828A
CN114339828A CN202111483487.XA CN202111483487A CN114339828A CN 114339828 A CN114339828 A CN 114339828A CN 202111483487 A CN202111483487 A CN 202111483487A CN 114339828 A CN114339828 A CN 114339828A
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雷维嘉
李丽
张钥
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Chongqing University of Post and Telecommunications
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Abstract

The invention discloses a design method of a non-orthogonal time reversal uplink multiple access system, which divides users into several groups according to the correlation and gain of channels, wherein the users in each group have higher channel correlation, and the correlation of the users among the groups is lower. The base station adopts different time reversal receiving processing filters aiming at each user group to filter the received signals to realize the multiple access of a plurality of groups of users, and the users in the group realize the multiple access by distributing different signal powers. And jointly optimizing the transmission power of each user and a receiving filter aiming at each group of users by taking the system and the rate maximization as targets. The invention provides an iterative algorithm to solve the impulse response of the receiving filter of each user group signal and the power distribution of each user. Compared with the conventional time reversal multiple access scheme, the scheme provided by the invention has higher system and rate.

Description

Design method of non-orthogonal time reversal uplink multiple access system
Technical Field
The invention relates to the field of information communication, in particular to a design method for constructing a non-orthogonal time reversal uplink multiple access system and carrying out joint optimization design on the transmitting power of a user symbol and the impulse response of a time reversal receiving filter.
Background
Although the conventional multiple access technology can multiplex radio resources in time domain, frequency domain or code domain, with the rapid development of mobile communication technology and the exponential increase of the number of terminals, the spectrum resources are increasingly scarce, and it is increasingly difficult to provide reliable radio access for the devices which are increased in area. Time Reversal (TR) is a special spatial division technique that has been widely used in wireless communication systems in recent years. The TR transmission technique is a technique for realizing energy focusing of signals in time and space domains by utilizing multipath effects in wireless channels, and the TR system transmission is generally divided into two steps: firstly, a receiving end sends a Channel detection pulse signal to a sending end, the sending end estimates to obtain the pulse Response (CIR) of a multipath Channel according to the received pulse signal, and then the sending end carries out time reversal and conjugate operation on the CIR to be used as a tap coefficient of a TR filter; and finally, the transmission signal is filtered by a TR filter and then is transmitted to a channel. Early studies on TR transmission were primarily directed to underwater acoustic communications, and in recent years, wireless communications have also received attention [ Rouseff D, Jackson D R, Fox W L J, et al. Underwater adaptive communication by-phase communication: the order and experimental resources [ J ]. IEEE Journal of scientific Engineering,2001,26(4):821-831 ]. The document Derode A, Tourin A, Rosny J D, et al, labeling adaptation to communication with time-reversal antenna [ J ]. Physical Review Letters,2003,90(1):014301 ] shows that in a wireless communication system, since TR can fully utilize the multi-path effect in the wireless channel, when there is multiple scattering in the propagation medium, the transmission is error-free, but in a uniform medium, the error rate is large. Document [ HAN Feng, YANG Yuhuan, WANG beibeibei, et al, Time-Reversal Division Multiple Access [ J ]. IEEE Transactions on Communications,2012,60(7):1953-1965 ] discusses a wideband multi-user downlink system based on the Time-Reversal Division Multiple Access (TRDMA) concept, which uses the uniqueness of multipath propagation of each user channel to separate signals of different users using multipath channel coefficients as user-specific signatures to achieve multi-user transmission. And the advantages of the TRDMA scheme compared with the Rake receiver and the influence of the user space correlation on the TRDMA are researched, and research results show that the performance of the TRDMA scheme is superior to that of the Rake receiver scheme, and the performance of the TRDMA system is reduced along with the increase of the user space correlation. TR transmission can reduce Inter-symbol Interference (ISI), but can still cause large Interference to signal reception in a wideband system or with large delay spread. ISI may be mitigated by increasing the transmit symbol interval by up-sampling the transmit signal without employing receive equalization. The document LEI Weiji, YAO Li, Performance analysis of time reversal communication systems [ J ]. IEEE Communications Letters,2019,23(4):680 and 683 ] deduces the probability density function and the cumulative distribution function of the signal-to-noise ratio of a receiving end in a TR communication system under a Rayleigh fading channel, and further analyzes the traversal capacity, the outage probability and the bit error rate when binary phase shift keying is used of the system, and the analysis result shows that the ISI is reduced along with the increase of an up-sampling factor. A multi-user Uplink structure based on TRDMA is introduced in a document [ Feng H, Liu K.A Multiuser TRDMA Uplink System with 2D Parallel Interference registration [ J ]. IEEE Transactions on Communications,2014,62(3):1011 and 1022 ], and a two-dimensional Parallel Interference elimination scheme is proposed on the basis, so that the error rate performance under the condition of high signal-to-noise ratio is obviously improved by eliminating the intersymbol Interference and the intersymbol Interference.
Non-Orthogonal Multiple Access (NOMA) technology is considered to be a promising Multiple Access technology that can meet the requirements of low delay, high reliability, large-scale connection and high throughput [ YANG Kai, YANG Nan, YE Neng, et al. NOMA, roughly divided into power domain and coding domain, according to the difference of distinguishing user resource domain [ Rabe F A, Davaslioglu K, Gitlin R.the optimal received power levels of uplink non-orthogonal multiple access (NOMA) signals [ C ]//2017IEEE 18th Wireless and Microwave Technology Conference (WAMICON) ]. IEEE,2017 ]. For the downlink NOMA link, in order to implement multi-user detection, a successive interference cancellation receiver needs to be equipped at the user terminal, however, the power consumption and the processing capability of the user terminal are both limited, and thus the implementation difficulty of the scheme is increased. In the uplink, multi-user detection is only needed to be realized at the base station, and the realizability is stronger. The document Zuo H, Tao X.Power allocation optimization for uplink non-orthogonal multiple access systems [ C ]/20179 th International Conference on Wireless Communication and Signal Processing (WCSP).2017 ] studies the problem of maximizing the total throughput in a group within a specific user group in an uplink NOMA system consisting of a base station and a plurality of users under the constraint of the total transmission power in the group and the minimum rate requirement of the users, and derives a closed solution of optimal power allocation in the NOMA group by using the conditions of Karush-Kuhn-Tucker (KKT). And on the basis of ensuring that the rate of other users except the high-channel-gain user reaches the requirement of the minimum data rate, the residual power is completely distributed to the high-channel-gain user. The literature [ Zhang J, Zhu L, Xiao Z, et al, optical and sub-optical uplink NOMA: joint user grouping, decoding order, and power control [ J ]. IEEE Wireless Communications Letters,2020,9(2): 254-. This problem is a combined integer programming problem due to the discreteness and coupling of decoding order with user packets. The literature first derives a closed form optimal solution for its decoding order and power control for any fine group of users. A globally optimal solution to the problem can then be obtained by exhaustive search of the user-grouped variables. In order to achieve a balance between computational complexity and performance, the literature also proposes a sub-optimal user grouping algorithm of linear complexity.
Disclosure of Invention
The invention aims to provide a design of a non-orthogonal time reversal uplink multiple access system under the scene of larger user channel correlation so as to increase the system and the speed. The scheme divides users into several groups according to the correlation and gain of channels, wherein the users in each group have higher channel correlation, and the users between the groups have lower correlation. The base station adopts different time reversal receiving processing filters aiming at each user group to filter the received signals to realize the multiple access of a plurality of groups of users, and the users in the group realize the multiple access by distributing different signal powers. And jointly optimizing the transmission power of each user and a receiving filter aiming at each group of users to realize maximization of a system and a rate.
In order to achieve the purpose, the invention adopts the following technical scheme: firstly, grouping according to the correlation and gain difference of the channels of the users, for the grouping containing two users in the group, the users in the group adopt the same time reversal receiving filter to process at the base station side, the individual grouped users adopt the special time reversal receiving filter to extract information and inhibit interference, an optimization problem which aims at maximizing the system and the speed is further constructed, and then an iterative algorithm is provided to solve the impulse response of the receiving filter of the signals of each user group and the power distribution of each user.
The method comprises the following specific steps:
(1) constructing a communication system model: on the basis of a conventional uplink time reversal multiple access system, users are grouped, the number of users in each group is one or two, the same group of users adopts the same time reversal receiving filter to filter received signals, and the group containing a plurality of users is provided with a continuous interference elimination detector behind the time reversal receiving filter;
(2) constructing an optimized mathematical model for the transmit power of the users and the receive filters for each group of users with a goal of system and rate maximization;
(3) converting the optimization problem into two sub-problems of optimization of impulse response of a receiving filter and power distribution of each user;
(4) obtaining the impulse response of each group of time reversal receiving filters by a method of searching for the eigenvector corresponding to the maximum generalized eigenvalue of the matrix beam corresponding to the generalized Rayleigh quotient;
(5) obtaining the transmitting power of each user symbol by using an iterative lower bound approximation method and a multiplier method;
(6) and solving the impulse response of each group of receiving filters and the power distribution of each user by using an iterative algorithm.
Further, in step (1), the grouped users including multiple users in the group extract information and suppress interference through the same time reversal receiving filter at the receiving end, and the individual grouped users extract information and suppress interference through a user-specific time reversal receiving filter. The time reversal receiving filter is designed according to the channel condition of the user with smaller path loss in the group.
Further, grouping users specifically includes: the number of system users is K, (1) calculating the correlation coefficient between every two channels of all users, comparing the correlation coefficient with a preset threshold value, and putting the user combination with the channel correlation coefficient larger than the threshold value into a grouping candidate set; (2) selecting a combination with the largest channel gain difference from the grouping candidate set as a grouping for receiving processing by adopting the same time reversal receiving filter at a receiving end, and deleting all combinations containing the two users in the candidate set from the set; (3) repeating the process until the grouping candidate set is empty or the number of user groups reaches K/2; (4) users that do not enter the candidate packet set are individually grouped and processed with their particular time reversed receive filter.
Further, the multiplier method in the step (5) is specifically as follows: the extended Lagrangian function of the standard convex optimization problem after the lower bound expression and variable substitution is used as
Figure BDA0003396423020000031
Wherein, mu, lambdakMore than or equal to 0(K is 1,2, …, K) is an augmented Lagrange multiplier, delta>0 is a penalty factor. Then the unconstrained sub-problem of the optimization problem can be represented as
Figure BDA0003396423020000041
To be provided with
Figure BDA0003396423020000042
Solving for the initial point
Figure BDA0003396423020000043
Get the minimum point
Figure BDA0003396423020000044
The superscript "n-1" here denotes the result obtained after the (n-1) th iteration
Figure BDA0003396423020000045
The updated formula of the augmented Lagrange multiplier is
Figure BDA0003396423020000046
Figure BDA0003396423020000047
The iteration termination criterion is
Figure BDA0003396423020000048
Where epsilon represents a small positive number.
The specific steps of solving by the multiplier method are as follows: power of each user signal at the first iteration
Figure BDA0003396423020000049
Initial log2(PmaxK) where PmaxThe total transmission power of a base station end is represented, and K represents the number of users; initializing an augmented Lagrange multiplier and a penalty factor; to be provided with
Figure BDA00033964230200000410
Solving unconstrained subproblems for initial points
Figure BDA00033964230200000411
Get the minimum point
Figure BDA00033964230200000412
Judge this moment
Figure BDA00033964230200000413
Whether the result is true or not; if not, updating the augmented Lagrange multiplier and penalty factor to obtain the result in the current turn
Figure BDA00033964230200000414
And carrying out the next round of solution for the initial point, otherwise, ending the iteration.
Further, the step (6) of solving the impulse responses of the groups of receiving filters and the power allocation of each user by using an iterative algorithm includes the following steps: in the first iteration, firstly, the signal-to-interference-and-noise ratio under the condition of user equal power distribution is used
Figure BDA00033964230200000415
Calculating alpha(0)And beta(0)Substituting the vector into a standard convex optimization problem for variable substitution and solving a power distribution vector
Figure BDA00033964230200000416
By using
Figure BDA00033964230200000417
Updating the signal to interference plus noise ratio gamma of the user(t)Comparing the SINR vector obtained by the iteration with the SINR vector obtained by the last iteration, judging whether the iteration converges, if not, updating alpha and beta according to the current SINR vector, and performing the next iteration, otherwise, ending the iteration.
Compared with the prior relevant research, the invention has the following beneficial technical effects: (1) related documents about TRDMA system research, such as [ HAN Yi, CHEN Yan, WANG beibeibeibei, et al, time-reverse major multi effect: a single-anti-antenna "major MIMO" solution [ J ]. IEEE Transactions on Communications,2016,64(8):3382 and 3394 ], are retrieved at present, and most of the documents are based on the assumption that the user channel is uncorrelated to perform system performance analysis, power optimal allocation and optimal design of a reception filter. However, for the wireless channel, when the distance between users is close or the environmental scatterers are less, the correlation between user channels is higher, and the high user correlation can cause the interference between users in the TRDMA system to increase, which limits the performance of the TRDMA system, so the invention has more practicability considering the scenario of high user channel correlation. (2) The invention can improve the system performance under the condition of ensuring the same user access scale as the TRDMA system, and simulation experiments show that the system and the speed of the invention are obviously superior to the conventional time reversal multiple access scheme. (3) The present invention maximizes the system and rate by jointly optimizing the user signal transmit power and receive filter vector. Aiming at the problem that an optimal solution is difficult to find, an iterative algorithm for alternately optimizing the transmitting power and the receiving filter vector is provided until convergence is achieved.
Drawings
FIG. 1 is a communication system model of the present invention;
FIG. 2 is a diagram of system and rate as a function of transmit power for various scenarios;
FIG. 3 influence of sampling factors on system and rate;
FIG. 4 the effect of the number of multipaths and the number of users on the system and rate;
figure 5 receives the effect on the system and rate when filters are designed for different users within a group.
Detailed Description
Considering the transmission system model as shown in fig. 1, there are K users in the system, and the base station and each user are equipped with a single antenna. The channel is a frequency selective fading channel, and the impulse response of the channel from user K (K ═ 1,2, …, K) to the base station is denoted as hk[m]And m represents the mth time. For convenience of description, the present invention assumes that the length of the channel impulse response of all users is L, i.e., when m is<0 or m is greater than or equal to L, hk[m]0. Representing the channel impulse response in vector form, i.e. hk＝[hk[0],hk[1],…,hk[L-1]]THere, superscript is givenT denotes the transpose of a vector or matrix. The K users are divided into M groups, and the number of users in each group is 1 or 2. Assuming that the number of users in each of the first N groups is 2, and the number of users in each of the remaining K-2N groups is 1, M is K-N. For a group of 2 users, two users are called a near user (a user with smaller loss, or called a strong user) and a far user (a user with larger loss, or called a weak user) according to path loss, respectively, without loss of generality, the serial number of the near user is an odd number, and the serial number of the far user is an even number. The symbol sequence of the message transmitted by K users to the base station is recorded as { x1,x2,...,xK}. The symbol sequence is up-sampled before transmission over the antennas, increasing the sample rate and thereby mitigating inter-symbol interference. The up-sampling factor D is the ratio of the sampling rate and the symbol baud rate. The upsampled sequence of symbols for user k is
Figure BDA0003396423020000051
The superimposed signal received at the base station side can be represented as
Figure BDA0003396423020000052
Wherein the symbols
Figure BDA0003396423020000053
Representing a discrete convolution, pkFor the power of the user k signal, n [ m ]]Is the channel noise, with mean 0 and variance σ2White gaussian noise sequence.
At the base station, the received signal is first passed through a user-specific receive filter to extract information and suppress interference. The impulse response of the receive filter is also represented in vector form, gk＝[gk[0],gk[1],…,gk[L-1]]T. The signals passing through the receiving filter are down-sampled (namely samples with integer times of the serial number of D are extracted as the sample values of symbols) to obtain the signals of the i (1 is more than or equal to i is less than or equal to M) th group of users
Figure BDA0003396423020000061
Wherein the content of the first and second substances,
Figure BDA0003396423020000062
is a variance of σ2White noise of (2). Where L denotes the number of paths.
For a packet containing two users in a group, a far user needs to detect a symbol sent to a near user by using a Successive Interference Cancellation (SIC) technique, reconstruct a received symbol according to channel information, and cancel Intra-group Interference (ICI) in a received signal. Thus, the received signals of the near and far users in the ith (1 ≦ i ≦ N) group may be represented as
Figure BDA0003396423020000063
In the above equation, the first part on the right of the middle sign is the desired received signal, the second part is ISI, the third part is ICI, the fourth part is Multi Cluster Interference (MCI), and the fifth part is noise.
Figure BDA0003396423020000064
In the above equation, the first part to the right of the equal sign is the desired received signal, the second part is ISI, the third part is MCI, and the fourth part is noise. For the last M-N groups with only one user in the group, i.e. N < i ≦ M, the received signal of the user is
Figure BDA0003396423020000065
Note the book
Figure BDA0003396423020000066
Toeplitz matrix of dimensions and first column
Figure BDA0003396423020000067
The other columns being shifts of the first column, i.e.
Figure BDA0003396423020000071
Equivalent channel matrix H for user kkIs (2L)D-1) x L dimension Toeplitz matrix, defined as
Figure BDA0003396423020000072
Wherein e isx,yThe y column of the x dimension identity matrix is shown, and x and y correspond to the two subscripts of e in the formula. H of the equivalent matrixkIs effectively a matrix
Figure BDA0003396423020000073
R x D line of (1), i.e. HkIs formed by
Figure BDA0003396423020000074
Is formed by an integer multiple of rows of D. By using
Figure BDA0003396423020000075
Represents the equivalent channel matrix HkTransposed of the m-th line of (1). User k equivalent channel matrix HkL toDLine of
Figure BDA0003396423020000076
Is the transpose of the time reversal of the user k-channel impulse response, i.e.
Figure BDA0003396423020000077
The received signal of the user can be represented in vector form as
Figure BDA0003396423020000078
Figure BDA0003396423020000079
Figure BDA0003396423020000081
The near user in the ith (i is more than or equal to 1 and less than or equal to N) group processes the symbol sent to the far user as Noise, directly detects the received Signal, and the received Signal to Interference plus Noise Ratio (SINR) is
Figure BDA0003396423020000082
Wherein the subscripts 2i-1 and 2i herein denote the near and far users within the group, respectively;
Figure BDA0003396423020000083
Figure BDA0003396423020000084
here, the superscript "H" denotes a conjugate transpose operation of a vector or matrix, and the superscript "denotes a conjugate operation. The numerator term of the above equation is the power of the useful signal, the denominator 1 st term is the ISI power, the 2 nd term is the ICI power, the 3 rd term is the power of the MCI, and the 4 th term is the channel noise power. The received SINR of the far user is
Figure BDA0003396423020000085
The denominator of the above equation has term 1 as ISI power, term 2 as MCI power, and term 3 as channel noise power. For the last M-N groups with only one user in the group, namely N < i ≦ M, the received SINR of the user is
Figure BDA0003396423020000086
The achievable transmission rate for user K (K ═ 1,2, …, K) is
Figure BDA0003396423020000087
Where B is the channel bandwidth. Gamma raykRepresenting the signal to interference plus noise ratio.
The specific steps of the user grouping algorithm are as follows: (1) calculating the correlation coefficient between every two channels of all users, comparing the correlation coefficient with a preset threshold value, and putting the user combination with the channel correlation coefficient larger than the threshold value into a grouping candidate set; (2) selecting a combination with the largest channel gain difference from the grouping candidate set as a grouping for receiving processing by adopting the same time reversal receiving filter at a receiving end, and deleting all combinations containing the two users in the candidate set from the set; (3) repeating the process until the grouping candidate set is empty or the number of user groups reaches K/2; (4) users that do not enter the candidate packet set are individually grouped and processed with their particular time reversed receive filter.
After the user grouping is determined, the transmission power of each user signal and the channel impulse response of the time reversal receiving filter are optimized jointly under the constraint of ensuring the minimum transmission rate, the total transmission power and the time reversal receiving filter power gain normalization of each user, and the system and the rate are maximized. The optimization problem can be expressed as
P1:
Figure BDA0003396423020000091
s.t.C1:
Figure BDA0003396423020000092
C2:Rk≥Rk,min,k＝1,2,…,K
C3:
Figure BDA0003396423020000093
Constraint C1Indicating that the power gain of the time-reversed receive filter is 1. Constraint C2Determining a lower bound for user rate, wherein Rk,minRepresenting the minimum rate requirement for user k. Constraint C3Determining the total transmission power of the system, i.e. the sum of all user powers should be the total transmission power Pmax。
The P1 problem is a non-convex optimization problem that is difficult to solve. Therefore, the invention decomposes the original optimization problem into two sub-problems to solve:
(1) transmission power p at each userkOptimizing the receive filter vector g for each group, given the knowledgeiMaximizing system and rate, i.e.
P2:
Figure BDA0003396423020000094
s.t.C1
(2) Receive filter vector g in each groupiOptimizing the transmission power p of each user in a known mannerkMaximizing system and rate, i.e.
P3:
Figure BDA0003396423020000095
s.t.C2,C3
Considering the achievable rate R of a userkIs about gammakSo the P2 problem is equivalent to
P4:
Figure BDA0003396423020000096
s.t.C1
The SINR of the near users in the ith (i is more than or equal to 1 and less than or equal to N) group can be rewritten as
Figure BDA0003396423020000097
Here, I denotes an identity matrix of L × L dimensions. Sigma2Representing the noise power.
It can be seen that γ2i－1Is a matrix bundle
Figure BDA0003396423020000101
The maximum value of the generalized Rayleigh quotient is the maximum generalized eigenvalue of the matrix beam, and the normalized generalized eigenvector corresponding to the maximum generalized eigenvalue is the receiving filter vector gi. Similarly, γ can be obtained from the SINR formula of the far user2iMaximum value of (2) is a matrix bundle
Figure BDA0003396423020000102
The normalized eigenvector corresponding to the maximum eigenvalue is the receiving filter vector gi。
SINR of individual group users can be rewritten as
Figure BDA0003396423020000103
Can know gammaN+iMaximum value of (2) is a matrix bundle
Figure BDA0003396423020000104
The normalized eigenvector corresponding to the maximum eigenvalue is the receiving filter vector gi. In order to maximize the sum of the rates of two users in a group, the receive filter vector of the present invention is designed to maximize the SINR of strong users, and individual group users are designed directly to maximize their SINR.
To solve the power allocation problem P3, the present invention uses the lower bound relation α log2Q+β≤log2(1+ Q) to relax it. Wherein, alpha and beta are respectively
Figure BDA0003396423020000105
When Q is Q0When, underThe boundary relation equation is established. According to the lower bound, the achievable transmission rate of user k can be approximated as
Figure BDA0003396423020000106
Wherein the content of the first and second substances,
Figure BDA0003396423020000107
Figure BDA0003396423020000108
wherein the content of the first and second substances,
Figure BDA0003396423020000109
the SINR of the previous iteration for user k. The equivalent problem to the P3 problem can therefore be expressed as P5:
Figure BDA00033964230200001010
s.t.C3
Figure BDA00033964230200001011
in the above formula, when αkAnd betakThe P5 problem remains a non-convex problem when fixed. Order to
Figure BDA00033964230200001012
And substituting the formula to obtain a new variable
Figure BDA00033964230200001013
Is an optimization problem of
P6:
Figure BDA0003396423020000111
Figure BDA0003396423020000112
Figure BDA0003396423020000113
For the ith (1. ltoreq. i. ltoreq.N) group containing two users in the group, there are
Figure BDA0003396423020000114
Figure BDA0003396423020000115
For the ith (N < i ≦ M) group containing one user, there are
Figure BDA0003396423020000116
The P6 problem is a standard convex optimization problem with a unique optimal solution and can therefore be solved by a multiplier method. When in use
Figure BDA00033964230200001115
After known, can be obtained by
Figure BDA00033964230200001116
Back substitution to obtain { pkThe solution of.
The augmented Lagrangian function of the P6 problem is
Figure BDA0003396423020000117
Wherein, mu, lambdakMore than or equal to 0(K is 1,2, …, K) is an augmented Lagrange multiplier, delta>0 is a penalty factor. Its unconstrained subproblem can be expressed as
P7:
Figure BDA0003396423020000118
To be provided with
Figure BDA0003396423020000119
Solving the above-mentioned unconstrained problem for the initial point to obtain the minimum point
Figure BDA00033964230200001110
The superscript "n-1" here denotes the result obtained after the (n-1) th iteration
Figure BDA00033964230200001111
The updated formula of the augmented Lagrange multiplier is
Figure BDA00033964230200001112
Figure BDA00033964230200001113
The iteration termination criterion is
Figure BDA00033964230200001114
Where epsilon represents a small positive number.
The algorithm for solving the power allocation optimization sub-problem is shown as algorithm 1. The algorithm mainly comprises two parts, namely: outer iteration (updating α and β) and inner iteration (solving unconstrained subproblem P7), where t represents the number of outer iterations and n represents the number of inner iterations. When external iteration is carried out for the first time, the power is distributed according to users under the condition of equal power
Figure BDA0003396423020000121
Calculating alpha(0)And beta(0)(ii) a Power of each user signal at first internal iteration
Figure BDA0003396423020000122
(K-1, 2, …, K) is initially log2(PmaxK), and initializing an augmented lagrange multiplier and a penalty factor; to be provided with
Figure BDA0003396423020000123
Solving an unconstrained subproblem P7 for the initial point to obtain a minimum point
Figure BDA0003396423020000124
Judging whether the iteration termination criterion is satisfied at the moment; if not, updating the augmented Lagrange multiplier and penalty factor to obtain the result in the current turn
Figure BDA0003396423020000125
The solution of the next round is carried out for the initial point, otherwise
Figure BDA0003396423020000126
Updating SINR gamma of users(t)The SINR vector gamma obtained by the iteration is used(t)SINR vector gamma obtained from last iteration(t-1)And comparing to judge whether the iteration converges. If not, according to the current SINR vector gamma(t)Updating alpha and beta, performing the next round of external iteration, and
Figure BDA0003396423020000127
(obtained from the last internal iteration of the current round)
Figure BDA0003396423020000128
) As the initial point for the first time of the internal iteration, otherwise, the iteration is ended. In the algorithm 1, t represents the number of external iterations, and n represents the number of internal iterations; mu, lambdakMore than or equal to 0(K is 1,2, …, K) is an augmented Lagrange multiplier, delta>0 is a penalty factor; theta is a positive number with a value ranging from 0 to 1, eta is a positive number with a smaller value, and the theta and the eta are combined to determine the size of the next iteration penalty factor; epsilon1The positive number with a smaller value is used for judging whether the power obtained in the internal iteration process meets the termination criterion; to be provided with
Figure BDA0003396423020000129
As a condition for convergence of the external iteration, where ε2Is a positive number with a small value.
Algorithm 1 Power distribution iterative Algorithm
Initializing the external iteration time t as 0;
Figure BDA00033964230200001210
(k＝1,2,…,K)。
(1)t＝t+1。
(2) initializing the internal iteration number n to be 0; augmented Lagrange multiplier mu(0),λ(0)(ii) a Penalty factor delta(0)And the factor θ, η.
(3)n＝n+1。
(4) To be provided with
Figure BDA00033964230200001211
Solving unconstrained subproblems for initial points
Figure BDA00033964230200001212
Get the minimum point
Figure BDA00033964230200001213
(5) Judgment of beta(n)≤ε1Whether or not this is true. If yes, stopping internal iteration and outputting
Figure BDA00033964230200001214
As an approximate minimum for the unconstrained subproblem. To be provided with
Figure BDA00033964230200001215
Updating signal-to-interference-and-noise ratio of users
Figure BDA00033964230200001216
Judgment of
Figure BDA00033964230200001217
Whether or not this is true. If yes, turning to the step (8); if not, respectively based on
Figure BDA00033964230200001218
Figure BDA00033964230200001219
Update alpha and beta and order
Figure BDA00033964230200001220
Turning to the step (2); otherwise, go to step (6).
(6) Updating the augmented Lagrangian multiplier.
(7) If beta is(n)≥θβ(n-1)Let δ(n+1)＝ηδ(n)Turning to the step (3); else δ(n+1)＝δ(n)And (4) turning to the step (3).
(8) Outputting an optimization problem solution:
Figure BDA0003396423020000131
in summary, the detailed solution process of the P1 problem is shown in algorithm 2. Wherein j represents the number of iterations; epsilon3The method is a positive number with a smaller value and is used for judging whether the system and the rate increase of the previous and subsequent times in the iteration process is small enough.
Algorithm 2 iterative solution of the original optimization problem
Initializing the iteration number j to be 0; p is a radical of(0)＝PmaxK; system and rate
Figure BDA0003396423020000132
(1)j＝j+1。
(2) With p(j-1)Updating a receive filter vector g(j)And C in the P1 question is judged2If the constraint is established, if so, turning to the step (3), otherwise, making g(j)＝g(j-1)And (4) turning to the step (3).
(3) Computing P with Power Allocation Algorithm of Algorithm 1(j)。
(4) Judgment of
Figure BDA0003396423020000133
If yes, the step (5) is carried out, otherwise, the step (1) is carried out to continue iteration.
(5) Outputting an optimization problem solution: g(j)，p(j)。
The present invention will be described in further detail below with reference to the accompanying drawings. Unless otherwise specified, in the simulation, users are uniformly distributed in a circle with a minimum radius of 10m and a maximum radius of 50m centered on the transmitting end. The user channels have random correlation of correlation coefficients, when in simulation, the CIRs of half users are randomly generated according to the distribution characteristics of the channels, then the CIRs of other users respectively having correlation with the users are generated, and the correlation coefficients are uniformly distributed among [0.5,1 ]. The parameters in the simulation are set as follows: the user number K is 6; the path number L of the multipath channel is 20; the channel bandwidth B is 20 MHz; the channel is a rayleigh fading channel, and the channel fading includes large-scale fading and small-scale fading, that is, the coefficient of the channel impulse response is a complex gaussian random variable with the mean value of 0, and the variance is
Figure BDA0003396423020000134
In the above formula, σT＝1×10-6Root mean square delay of path, T s1/B is the sampling period. The large-scale fading coefficient of the user k channel is
Figure BDA0003396423020000135
c is 4 as path loss exponent, η0＝10-5For transmission loss at a reference distance, reference distance d0＝10m，dk(10m≤dkLess than or equal to 50m) is the distance between the base station and the user k; channel noise power σ2＝1×10-12W; the upsampling factor D is 4. Convergence factor ε1＝1×10﹣6，ε2＝1×10﹣6，ε3＝1×10﹣6。
Design of time inversions using ZF criterionWhen the receiving filter is switched, the impulse response coefficient vector of the ith group of receiving filters is
Figure BDA0003396423020000136
Here, the
Figure BDA0003396423020000137
Is that
Figure BDA0003396423020000138
The pseudo-inverse of (a) is,
Figure BDA0003396423020000139
is a channel matrix composed of strong users and individual user channel vectors,
Figure BDA00033964230200001310
is K (2L)D-1)×K(2LD-1) th of the dimensional identity matrixiColumn, li＝(i-1)(2LD-1)+LD，
Figure BDA0003396423020000141
To make the filter power gain a normalized factor of 1. When the MF rule is used to design the time reversal receiving filter, the impulse response of the i-th group of receiving filters is the time reversal and phase conjugation of the impulse response of the strong user channel in the group.
User minimum rate constraint R in the optimization problem in simulationk,minThe correlation coefficient threshold is ζ 0.75 for the minimum user rate when the TRDMA method without packet reception, the time reversal reception filter are designed according to the MF rule, and each user signal is transmitted with equal power. The data of each point in the graph given by the invention is 5 multiplied by 105Mean values of simulation results under the group channel samples.
FIG. 2 is a simulation result of system and rate variation with transmit power, wherein "conventional TRDMA" indicates a scheme in which users are not grouped, a receive filter is designed using a matched filtering criterion, and user signals are transmitted at equal power; the power optimization TRDMA is a scheme of performing optimized allocation on the transmission power of a user signal by adopting the algorithm 1 of the invention on the basis of the conventional TRDMA; the 'alternative optimization TRDMA' adopts the scheme of the invention under the condition of no grouping; "MF-NOMA" means that the receiving filter is designed by adopting a matched filtering criterion after users are grouped, and the signal power of the users is optimally distributed by adopting the algorithm 1 of the invention; the "ZF-NOMA" scheme is similar to the "MF-NOMA" except that the receive filter is designed using a zero forcing criterion; the 'alternative optimization TR-NOMA' is the scheme of the invention.
As can be seen from the observation of FIG. 2, the alternative optimization scheme provided by the present invention is obviously superior to other schemes, whether the TRDMA system or the TR-NOMA system. This is because the inventive scheme considers increasing the received power, reducing the ISI power and IUI power at the same time when designing the receive filter. Comparing the performance of the TR-NOMA system and the TRDMA system under the optimization scheme of the invention, the system sum rate of the TR-NOMA system is always higher than that of the TRDMA, and the sum rate of the TR-NOMA system increases faster with the increase of the transmission power. This is because the TR-NOMA system performs packet reception for users with high correlation, the receiving end uses the same time reversal receiving filter to extract information and suppress interference, the weak users use SIC technology to eliminate the interference of strong users in the group, and compared with the TRDMA scheme, the rate of the weak users in the group is greatly improved. The higher the transmission power, the more obvious the benefits of SIC are, and the higher the rate is increased. It can be seen from the observation of the graph that the performance of the receiving filter designed by the ZF criterion is significantly better than that designed by the MF criterion. This is because the MF criterion is only to maximize the received signal power of the user and does not take IUI and ISI into account, while the ZF criterion only takes interference cancellation into account when designing the receive filter, but the sum rate of using the ZF filter is lower in the low transmit power interval due to the non-considered signal power because the noise contribution is greater than the interference. As the transmit power increases, the interference power increases synchronously, and the receive filter in the form of MF will saturate quickly due to the larger interference power and the slower rate growth. While filters in the form of ZF have the advantage over MF due to lower interference power and the rate that can increase with increasing transmit power. Comparing the performance of the TRDMA scheme with and without the optimized transmit power allocation, it can be seen that the sum rate is significantly improved after the optimized power allocation.
Fig. 3 is a simulation result of the system and rate at different sampling factors D. Under the condition that the channel bandwidth is not changed, the symbol period is increased when the sampling factor D is increased, so that the symbol rate of the user is reduced while the reachable rate of the user is increased. It can be seen that in the low transmission power region, the smaller D, the higher the system and rate, but the lower the increase speed of the system and rate when the transmission power increases, namely: the smaller D, the more saturated the system and rate; and in a high transmission power region, the larger D, the higher the system and rate. This is because when the transmission power is small, the channel noise power accounts for a greater proportion of the denominator of SINR, and therefore when D is small, the system and rate are high because symbols are transmitted more frequently, although ISI and IUI are large. When the transmission power is increased, because ISI and IUI power are synchronously increased along with the signal power, the smaller the D is, the larger the ISI and IUI is, the slower the SINR is increased, and the faster the rate is, the saturation is reached; therefore, it is necessary to select an appropriate upsampling factor D according to the available transmit power, channel condition, etc. of the system.
Fig. 4 shows simulation results of the system and the speed when the number of users is different and the number of paths is different. When the path number L is 20, the corresponding bandwidth B is 20MHz, and when L is 12, the corresponding bandwidth B is 12MHz, and the root mean square delay of both paths is σT＝1×10-6. As can be seen from the figure, the sum rate when the number K of users is 6 is higher than the sum rate when K is 4, regardless of whether L is 20 or 12. This is because the IUI between users with low correlation can be better resolved by using the user channel impulse response as the user signature, and the IUI between them is relatively small, while the users with high channel correlation are processed by the same time reversal receive filter and then detect the signal by the SIC technique, so that the more the number of users, the more the number of packets containing two users in the group is, the higher the summation rate of the system is. It can also be seen from a review of fig. 4 that the system and rate is higher when the number of channel paths is greater. This is because when the number of paths increases, ISI and IUI power increases, but after processing by the TR receive filter, the ISI and IUI power increasesGreater diversity reception gain is achieved, the received signal power of the user increases, and the system and rate also increase.
Fig. 5 shows the comparison of the system and the rate when the reception filter is designed based on the channel of the strong user or the weak user in the group. As can be seen from the figure, the system and rate of the receiving filter designed for the channel of the strong user are better than those designed for the channel of the weak user, and the gap is more obvious as the transmission power increases. This is because when the time reversal receive filter is designed according to the channel condition of the strong user, the ICI suffered by the strong user is small, and because the weak user adopts the SIC technique to eliminate the interference of the strong user in the group, the rate of the strong user in the group is greatly increased compared to the scheme in which the receive filter is designed according to the channel condition of the weak user. If the receiving filter is designed according to the channel condition of the weak users, the rate of the weak users in the group can be increased, but the rate is improved lower because the channel gain of the weak users is lower, and the rate of the strong users is reduced greatly because the power of the received signals is reduced and the ICI interference is increased. The receiving filter is designed with a higher sum rate according to the channel of the strong user, and the ICI has a more significant effect and the rate is increased more as the transmission power increases.

Claims (10)

1. The design method of the non-orthogonal time reversal uplink multiple access system is characterized by comprising the following steps:
(1) constructing a communication system model: on the basis of a conventional uplink time reversal multiple access system, users are grouped, the number of users in each group is one or two, the same group of users adopts the same time reversal receiving filter to filter received signals, and the group containing a plurality of users is provided with a continuous interference elimination detector behind the time reversal receiving filter;
(2) constructing an optimized mathematical model for the transmit power of the users and the receive filters for each group of users with a goal of system and rate maximization;
(3) converting the optimization problem into two sub-problems of optimization of impulse response of a receiving filter and power distribution of each user;
(4) obtaining the impulse response of each group of time reversal receiving filters by a method of searching for the eigenvector corresponding to the maximum generalized eigenvalue of the matrix beam corresponding to the generalized Rayleigh quotient;
(5) obtaining the transmitting power of each user symbol by using an iterative lower bound approximation method and a multiplier method;
(6) and solving the impulse response of each group of receiving filters and the power distribution of each user by using an iterative algorithm.
2. The method of claim 1, wherein the method further comprises: and (1) extracting information and suppressing interference by using the same time reversal receiving filter at a receiving end for the grouped users containing a plurality of users in the group, and extracting information and suppressing interference by using a user-specific time reversal receiving filter for the single grouped users.
3. The method of claim 1, wherein the method further comprises: the mathematical model in the step (2) comprises modeling of user signal to interference plus noise ratio, user transmission rate and system and rate, and specifically comprises the following steps:
i is more than or equal to 1 and less than or equal to N, and the signal-to-interference-and-noise ratios of the near user and the far user in the group are respectively as follows:
Figure FDA0003396423010000011
Figure FDA0003396423010000012
where subscripts 2i-1 and 2i denote the near and far users within the group, respectively; pkThe transmit power for user k; giReceiving a filter tap coefficient vector form for the time reversal of the ith group of users; sigma2Is the noise power of the channel; note the bookHkIs a Toeplitz matrix of dimensions (2L-1) xL, i.e.
Figure FDA0003396423010000021
Where L is the number of multipaths, hk[n]Represents the channel impulse response of user k, for HkSampling to obtain equivalent channel matrix H of user kk(ii) a In the expression of I-th group user signal-to-interference-and-noise ratio
Figure FDA0003396423010000022
Figure FDA0003396423010000023
Figure FDA0003396423010000024
Represents HkL toDIn the row, the superscript H represents the conjugate transpose operation of the vector or matrix, and the superscript "+" represents the conjugate operation;
for a group with only one user in the group, i.e. N < i ≦ M, the received signal-to-interference-and-noise ratio of the user is:
Figure FDA0003396423010000025
user K (K ═ 1,2, …, K) has a transmission rate of
Figure FDA0003396423010000026
Wherein B represents the system bandwidth and D represents the upsampling factor;
system and rate of
Figure FDA0003396423010000027
Here, K represents the number of users.
4. The method of claim 1, wherein the method further comprises: the optimization mathematical model in the step (2) maximizes the system and the rate by normalizing the minimum rate of each user, the total transmitting power of the user and the power gain of the time reversal receiving filter as constraint conditions, and the optimization problem is constructed as
Figure FDA0003396423010000028
s.t.C1:
Figure FDA0003396423010000029
C2:
Figure FDA00033964230100000210
C3:
Figure FDA00033964230100000211
Wherein P ismaxIndicates the total transmit power, R, of the subscriber terminalk,minRepresents the minimum rate requirement, R, for user kkIndicates the achievable transmission rate, g, of user kiA time reversed receive filter representing the ith group of users.
5. The method for designing a non-orthogonal time-reversal uplink multiple access system according to claim 1 or 4, wherein: converting the optimization problem into two sub-problems of optimization of the impulse response of the receiving filter and power distribution of each user, specifically comprising:
(1) transmission power p at each userkOptimizing the impulse response g of each set of time-reversed receive filters, given the known conditionsiMaximizing system and rate, i.e.
Figure FDA0003396423010000031
s.t.C1
(2) Inverting the impulse response g of the receive filter at each set of timesiOptimizing the transmission power p of each user in a known mannerkMaximizing system and rate, i.e.
Figure FDA0003396423010000032
s.t.C2,C3。
6. The method of claim 5, wherein the method further comprises: the step (4) of obtaining the impulse response of each group of time reversal receiving filters by using a method of finding the eigenvector corresponding to the maximum generalized eigenvalue of the matrix beam corresponding to the generalized rayleigh quotient specifically includes: in the objective function of the optimization sub-problem of the impulse response of the receive filter, RkIs about gammakSo the problem is equivalent to
Figure FDA0003396423010000033
s.t.C1
I is more than or equal to 1 and less than or equal to N, and the signal-to-interference-and-noise ratio of the near users in the group can be rewritten as follows:
Figure FDA0003396423010000034
it can be seen that γ2i－1Is a matrix bundle
Figure FDA0003396423010000035
The maximum value of the generalized Rayleigh quotient is the maximum generalized eigenvalue of the matrix beam, and the normalized generalized eigenvector corresponding to the maximum generalized eigenvalue is the receiving filter vector gi(ii) a Similarly, γ can be obtained from the SINR formula of the far user2iMaximum value of (2) is a matrix bundle
Figure FDA0003396423010000036
The normalized eigenvector corresponding to the maximum eigenvalue is the receiving filter vector gi；
For a group with only one user in the group, i.e. N < i ≦ M, the received SINR of the user is rewritten as:
Figure FDA0003396423010000037
can know gammaN+iMaximum value of (2) is a matrix bundle
Figure FDA0003396423010000041
The normalized eigenvector corresponding to the maximum eigenvalue is the receiving filter vector gi。
7. The method of claim 1 or 6, wherein the method further comprises: the lower bound approximation method in step (5) utilizes a lower bound relation alpha log2Q+β≤log2(1+ Q) performing relaxation transformation on the power distribution problem of each user, wherein alpha and beta are respectively as follows:
Figure FDA0003396423010000042
Figure FDA0003396423010000043
when Q is Q0When the lower bound relational expression is established, the equal sign of the lower bound relational expression is established; according to the lower bound, the achievable transmission rate of user k is approximately
Figure FDA0003396423010000044
Wherein the content of the first and second substances,
Figure FDA0003396423010000045
Figure FDA0003396423010000046
here, the
Figure FDA0003396423010000047
Is the signal to interference plus noise ratio of the previous iteration of user k.
8. The method of claim 7, wherein the method further comprises: the equivalence of the relaxed power allocation problem via the lower bound relation can be expressed as
Figure FDA0003396423010000048
s.t.C3
Figure FDA0003396423010000049
When alpha iskAnd betakWhile fixed, the above problem remains a non-convex problem; order to
Figure FDA00033964230100000410
And substituting the above formula to obtain a compoundNew variables
Figure FDA00033964230100000411
Is an optimization problem of
Figure FDA00033964230100000412
s.t
Figure FDA00033964230100000413
Figure FDA00033964230100000414
The optimization problem is a standard convex optimization problem, has a unique optimal solution, and can be solved by a multiplier method or a convex optimization tool box when
Figure FDA00033964230100000415
After known, can be obtained by
Figure FDA00033964230100000416
Back substitution to obtain { pkThe solution of.
9. The method of claim 1, wherein the method further comprises: the concrete steps of solving by the multiplier method in the step (5) are as follows: power of each user signal at the first iteration
Figure FDA0003396423010000051
Initial log2(PmaxK) where PmaxThe total transmission power of a base station end is represented, and K represents the number of users; initializing an augmented Lagrange multiplier and a penalty factor; to be provided with
Figure FDA0003396423010000052
Is an initialPoint solution unconstrained subproblems
Figure FDA0003396423010000053
Get the minimum point
Figure FDA0003396423010000054
Judging beta at this time(1)Whether the result is true or not; if not, updating the augmented Lagrange multiplier and penalty factor to obtain the result in the current turn
Figure FDA0003396423010000055
And carrying out the next round of solution for the initial point, otherwise, ending the iteration.
10. The method of claim 1, wherein the method further comprises: the step (6) of solving the impulse response of each group of receiving filters and the power allocation of each user by using an iterative algorithm comprises the following steps: in the first iteration, firstly, the signal-to-interference-and-noise ratio under the condition of user equal power distribution is used
Figure FDA0003396423010000056
Calculating alpha(0)And beta(0)Substituting the vector into a standard convex optimization problem for variable substitution and solving a power distribution vector
Figure FDA0003396423010000057
By using
Figure FDA0003396423010000058
Updating the signal to interference plus noise ratio gamma of the user(t)Comparing the SINR vector obtained by the iteration with the SINR vector obtained by the last iteration, judging whether the iteration converges, if not, updating alpha and beta according to the current SINR vector, and performing the next iteration, otherwise, ending the iteration.
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