CN113572500B - NOMA multi-user detection algorithm of hybrid greedy and tabu search strategy - Google Patents

NOMA multi-user detection algorithm of hybrid greedy and tabu search strategy Download PDF

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CN113572500B
CN113572500B CN202110711019.7A CN202110711019A CN113572500B CN 113572500 B CN113572500 B CN 113572500B CN 202110711019 A CN202110711019 A CN 202110711019A CN 113572500 B CN113572500 B CN 113572500B
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李靖
王文丹
李慧芳
葛建华
张赛
闫伟平
武思同
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Xidian University
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Abstract

The invention discloses a NOMA multi-user detection algorithm of a hybrid greedy and tabu search strategy, which solves the problem that the connection capability of 5G mobile communication users in the prior art needs to be enhanced. The invention comprises the following steps: (1) inputting parameters necessary for algorithm operation; (2) converting the multi-user detection problem into a target optimization problem P1; (3) taking the local optimal solution as the initial solution of the tabu search algorithm
Figure DDA0003133757210000011
(4) Solving the combined optimization problem P1 by using a tabu search strategy; (5) in the determination of the termination condition, to obtain a satisfactory solution x best Judging whether the iteration reaches the set termination condition or not for the iteration termination condition, and if so, outputting the searched global optimal solution x of the combined optimization problem P1 best And (4) obtaining the multi-channel user information to be recovered in the signal detection process, and returning to the step (4) if not. The technology greatly reduces the iteration times, shortens the processing time delay and is suitable for scenes sensitive to the time delay.

Description

NOMA multi-user detection algorithm of hybrid greedy and tabu search strategy
Technical Field
The invention relates to the technical field of wireless communication, in particular to a NOMA multi-user detection algorithm of a hybrid greedy and tabu search strategy.
Background
With the commercialization of the fifth Generation (5G) mobile communication system, mass mobile devices are accessing the system, leading to a discussion on how to improve spectral efficiency. A Non-Orthogonal Multiple Access (NOMA) Access scheme is to actively introduce interference at a transmitting end, superimpose Multiple signals on the same physical resource block in a Non-Orthogonal manner, and then transmit the signals, and a receiving end uses an advanced multi-user detection technology to recover each signal from the superimposed signals to realize demodulation.
However, the multiple access interference inherent in the NOMA system brings obstruction to the signal detection process at the receiving end, which is equivalent to using a complicated receiver design to obtain an improvement of the spectrum efficiency. One key point in the implementation of NOMA technology is therefore the design of high-performance, low-complexity signal detection algorithms. The 3GPP classifies uplink non-orthogonal multiple access (NOMA) for NR) in a technical report TR 38.812 entitled "Study on non-orthogonal multiple access (NOMA) for NR" into three categories: linear expansion at the symbol level, interleaving/scrambling code superposition at the bit level, and multidimensional sparse expansion. The symbol-level linear spreading non-orthogonal multiple Access (MUSA) technique is represented by Multi-User Shared Access (MUSA), and uses a shorter non-orthogonal spreading code, and a receiving end uses relatively simple hard interference cancellation. The terminal user/equipment can independently select the non-orthogonal spreading code at any time and can better support the competitive scheduling-free scene, so the non-orthogonal multiple access technology is widely concerned.
For the symbol-level linear extension-like NOMA system, the best detection algorithm is Maximum Likelihood (ML) detection. The ML algorithm minimizes the euclidean distances between the received signal vector and the products of all possible transmitted signal vectors and equivalent channels, and is essentially an exhaustive search algorithm. The complexity of the system rises sharply along with the increase of modulation orders and the number of users, and the system is extremely high in complexity and cannot be used for engineering practice.
The article "Multi-User Shared Access for Internet of Things" by Yuan Z et al in IEEE 83rd temporal Technology Conference (VTC Spring). IEEE,2016:1-5 proposes a Multi-User detection technique based on the minimum mean square error successive interference cancellation (MMSE-SIC) algorithm. However, the SIC algorithm has an error propagation problem, which degrades the multi-user detection performance. In addition, this accumulation is more common in NOMA systems due to the inaccuracy of the initial linear solution. In order to cope with the error propagation phenomenon, an article "Performance Analysis of MUSA with Different Spreading Codes Using Ordered SIC Methods" of Eid E M et al in 12th International Conference on Computer Engineering and Systems (ICCES). IEEE,2017: 101-. However, the MMSE-SIC algorithm can only detect one user at a time, and adopts a serial manner to perform interference cancellation one by one, so that the algorithm complexity is high and the processing delay is long.
The explosive development of artificial intelligence provides a new idea for optimizing wireless communication systems. An article "An Enhanced Tabu Search based Receiver for Full-decoding NOMA Systems" of Jung I and the like in IEEE Access,2019,7:159899-159917 utilizes a metaheuristic algorithm in the field of artificial intelligence, treats a multi-user detection problem of the NOMA system as a combined optimization problem, and utilizes a Tabu Search algorithm to solve An approximately optimal solution, thereby finally obtaining the optimal detection performance. However, the algorithm has the disadvantages of more iteration times and higher detection complexity.
Disclosure of Invention
The invention improves the problem that the connection capability of a 5G mobile communication user needs to be enhanced in the prior art, and provides a NOMA multi-user detection algorithm for a hybrid greedy and tabu search strategy, which can be used for a symbol-level linear expansion type non-orthogonal multiple access system.
The technical scheme of the invention is to provide a NOMA multi-user detection algorithm of a mixed greedy and taboo search strategy, which comprises the following steps: comprises the following steps: step (1), inputting parameters necessary for algorithm operation; step (2), converting the multi-user detection problem into a combined optimization problem P1; and (3) randomly generating one greedy strategy auxiliary algorithm initial solution in the generation processInitial solution
Figure GDA0003695271180000021
Correcting the algorithm initial solution generated randomly by means of the thought of a greedy algorithm to obtain a local optimal solution, and taking the local optimal solution as the initial solution of a tabu search algorithm
Figure GDA0003695271180000022
Step (4), solving the combined optimization problem P1 by using a tabu search strategy, wherein the method comprises the step of generating a neighborhood of a current solution vector x through a neighborhood function
Figure GDA0003695271180000023
In the neighborhood space
Figure GDA0003695271180000024
Local search is performed to determine the current best movement (k) according to the preference criteria opt ,n opt ,m opt ) According to a tabu table T move Carrying out tabu and moving operations, and updating each parameter after the iteration;
step (5), in the judgment of termination condition, obtaining satisfactory solution x best Judging whether the iteration reaches the set termination condition or not for the iteration termination condition, and if so, outputting the searched global optimal solution x of the combined optimization problem P1 best And (5) obtaining multi-channel user information to be recovered in the signal detection process, and otherwise, returning to the step (4).
Preferably, the step (1) comprises the steps of:
step (1.1), adopting ideal channel estimation to obtain received signal y, equivalent channel gain matrix G and noise power sigma 2 The received signal can be expressed by the following formula:
Figure GDA0003695271180000025
(symbol)
Figure GDA00036952711800000212
denotes the element dot product operator, y ═ y 1 ,…,y l ,…,y L ] T Is a received symbol vector of dimension L x 1,
Figure GDA0003695271180000026
represents an equivalent channel gain matrix combining channel gain and spreading sequence, n-CN (0, sigma) 2 I L ) Is complex gaussian white noise;
and (1.2) inputting the number K of users and the modulation order M, and setting the number N of symbol neighborhoods and the taboo step length P.
Preferably, in the step (2), the signal detection problem that the NOMA system receiving end recovers the multiple user information from the superposed signal y is modeled as a minimum process of a combinatorial optimization problem P1, and a metric function of ML detection is used as an objective function of the combinatorial optimization problem P1:
Figure GDA0003695271180000027
where the neighborhood is
Figure GDA0003695271180000028
Is a solution
Figure GDA0003695271180000029
By a neighborhood function
Figure GDA00036952711800000210
The set of the generated data is then generated,
Figure GDA00036952711800000211
contained in S, which is the entire solution space, if there is one solution vector x for all K users best Satisfy omega (x) best ) Less than or equal to omega (x), then solving vector x best Is a globally optimal solution.
Preferably, in the step (3), the multi-user detection problem is converted into a combinatorial optimization problem P1, and an initial solution is randomly generated
Figure GDA0003695271180000031
Correcting the algorithm initial solution generated randomly by means of the thought of a greedy algorithm to obtain a local optimal solution, and taking the local optimal solution as the initial solution of a tabu search algorithm
Figure GDA0003695271180000032
The method comprises the following steps:
step (3.1) of obtaining (G) H y) and matrix G H The real part of the element of the triangle on G, let V ═ Re [ (G) H y)]| and W ═ Re (G) H G) L, it can be known that V is a K × 1-dimensional column vector, and W is a K × K-dimensional square matrix with lower triangular parts all being 0;
step (3.2), sorting the elements of the triangular parts on V and W in a descending order to form a container
Figure GDA0003695271180000033
A sequence X of elements;
step (3.3), initialization is carried out, and the initial solution generated randomly is used as the initial value of the optimization algorithm
Figure GDA0003695271180000034
Step (3.4), to the random initial value
Figure GDA0003695271180000035
And (5) correcting: judging the first element of the sequence X obtained after descending order arrangement, if X is 1 ＝|V i If, then M vectors are generated, by exchange
Figure GDA0003695271180000036
X in (2) i Obtaining the corresponding likelihood function values for the possible M values, and selecting x which makes the likelihood function obtain the maximum value i As a
Figure GDA0003695271180000037
If X is 1 ＝|W ij If l, then M is generated 2 Group vectors, by permutation
Figure GDA0003695271180000038
X in (2) i And x j To possible M 2 Selecting a value combination to obtain the corresponding likelihood function value, and selecting x for making the likelihood function maximum i And x j Replacement of
Figure GDA0003695271180000039
X in (2) i And x j Thereby obtaining
Figure GDA00036952711800000310
Step (3.5), the corrected initial solution is processed
Figure GDA00036952711800000311
As an initial solution to the TS-MUD algorithm, an iteration is performed.
Preferably, the step (4) is performed by
Figure GDA00036952711800000312
As an initial solution, the combined optimization problem P1 is solved by using a tabu search strategy, which includes the following steps:
step (4.1), generating a current solution vector neighborhood structure:
defining the candidate solution set nearest to the Euclidean distance of the current solution vector as a neighborhood by the current solution vector, firstly aiming at each symbol in the current solution vector x
Figure GDA00036952711800000313
Figure GDA00036952711800000314
Is a set of M-PSK constellation points to be associated with a current symbol x k The N constellation points with the nearest Euclidean distance are taken as the symbol neighborhood of the current symbol and are recorded as
Figure GDA00036952711800000315
Inclusion of current inputThe solution vector x of K users correspondingly generates KN vector neighborhoods, and a neighborhood function is used
Figure GDA00036952711800000316
Characterizing the mapping relationship, the solution vector x is passed through the neighborhood function
Figure GDA00036952711800000317
Then, generating a candidate solution set composed of all vector neighborhoods
Figure GDA00036952711800000318
Expressed in matrix form as follows:
Figure GDA00036952711800000319
Figure GDA0003695271180000041
step (4.2), determination of optimal movement:
the tabu search is to generate a set of candidate solutions composed of vector neighborhoods in all search spaces S from an initial solution x
Figure GDA0003695271180000042
In each iteration, the pair of the objective functions belonging to the neighborhood belongs to the minimization criterion of the objective function in the combinatorial optimization problem P1
Figure GDA0003695271180000043
All column vectors η of i Evaluating, and selecting the best neighborhood solution vector, i.e. local optimal solution x opt Becomes the starting solution for the next iteration, this operation is defined as "move", assuming the algorithm has selected the symbol q for the kth user this time m The column vector η of the nth symbol neighborhood (k-1)N+n As the initial solution of the next iteration, the optimal moving direction of the iteration is recorded as (k) opt ,n opt ,m opt ) In each iteration, the TS algorithm is only inCollecting values in elements of Move and selecting the next step; in the t-th iteration, we determine the best move operation (k) opt ,n opt ,m opt ) Is the vector neighborhood that minimizes the value of the objective function
Figure GDA0003695271180000044
Corresponding shift (k, n, m), i.e.
Figure GDA0003695271180000045
Step (4.3), selecting a privileged mechanism and a taboo mechanism:
according to the optimal movement (k) opt ,n opt ,m opt ) The selected candidate solution function value is judged, and if the following formula is satisfied, the current optimal solution vector is determined according to the privilege mechanism
Figure GDA0003695271180000046
Updating is carried out, the algorithm directly enters the step (4.4.1), otherwise, the step (4.3.1) is carried out, and whether a taboo mechanism is triggered or not is judged;
Figure GDA0003695271180000047
by establishing a tabu table T move To realize the tabu mechanism, tabu table T move Is an N x KM matrix (M is modulation order) containing all possible mobile paths, T move The element in (1) represents the number of forbidden iterations of the moving path, also called the taboo step length, and is marked as P, the value of P can be obtained by simulation, and a taboo table T move Writing into:
Figure GDA0003695271180000048
if the best shift operation selected in this iteration is (k) opt ,n opt ,m opt ) Otherwise, it is forbidden to show T move (n) th opt ,(k opt -1)M+m opt ) The item updates the parameters according to the rule of step (4.4.1);
step (4.3.1), checking a tabu table:
contraindication list T move Checking the movement path (k) opt ,n opt ,m opt ) Whether it has been done in the last P iterations, if the following condition is met, then the movement path has not been executed in the last P iterations, it is not disabled, and the algorithm goes to step (4.4.2):
T move (n opt ,(k opt -1)M+m opt )＝＝0
otherwise, this duplicate movement path (k) is deleted from the movement set Move by the following operation opt ,n opt ,m opt ) And returning to step (4.2), wherein the operator \ represents the deletion of the element from the set, if all movement paths are forbidden, resulting in Move being null, then going to step (4.3.2)
Move (t) ＝Move (t) \(k opt ,n opt ,m opt )
And (4.3.2) receiving the inferior solution, and jumping out the local optimal trap:
if the motion set Move is empty, selecting the motion with the minimum forbidden iteration number from the vector neighborhood as the optimal motion (k) of the current iteration opt ,n opt ,m opt ) The specific operation is shown in the following formula, and the process goes to the step (4.4.1);
[n opt ,(k opt -1)M+m opt ]＝find(T move ＝＝min(min(T move )))
and (4.4) updating parameters:
according to the optimal moving path (k) in the step (4.3) opt ,n opt ,m opt ) First, uniformly updating the initial solution x of the next iteration (t+1) And tabu watch T move ：
Figure GDA0003695271180000051
T move ＝max(T move -1,0)
Then, the corresponding steps (4.4.1) and (4.4.2) are carried out according to the algorithm flow, and other parameters are updated in two different ways;
step (4.4.1), current optimal solution vector
Figure GDA0003695271180000052
Is updated:
updating the optimal solution vector at the beginning of the next iteration
Figure GDA0003695271180000053
The algorithm judges and obtains the current moving path (k) opt ,n opt ,m opt ) Is an optional direction and, furthermore, according to a privilege criterion, even if the movement path was disabled in the last iteration, that is to say T move (n opt ,(k opt -1)M+m opt ) Not equal to 0, but still as the best moving path (k) in order to avoid missing the global optimal solution opt ,n opt ,m opt ) And setting the taboo quantity to be 0, and updating the parameters in the following way:
Figure GDA0003695271180000054
T move (n opt ,(k opt -1)M+m opt )＝0
step (4.4.2), current optimal solution vector
Figure GDA0003695271180000055
Cannot be updated:
at this time, the inferior solution is accepted, and the moving path (k) to be selected opt ,n opt ,m opt ) Setting the table as a tabu, forbidding access in the subsequent P iterations, searching a direction different from the tabu, and updating a tabu table: t is move (n opt ,(k opt -1)M+m opt )＝P。
Preferably, the step of determining the termination condition in the step (5) is as follows: to be provided withObtain a satisfactory solution x best Judging whether the iteration reaches the set termination condition or not for the iteration termination condition, and if so, outputting the searched global optimal solution x of the combined optimization problem P1 best Obtaining multi-channel user information to be recovered in the signal detection process, and returning to the step 4 if not;
compared with the prior art, the NOMA multi-user detection algorithm of the hybrid greedy and tabu search strategy has the following advantages:
the method has the advantages that the initial solution is generated through a greedy algorithm, the operation that matrix inversion needs to be carried out on an MMSE weight matrix in the existing method is avoided, the complexity is lower, the iteration times are greatly reduced through reasonably setting an iteration termination condition, the processing time delay is shortened, and the method is suitable for scenes sensitive to the time delay;
in the multi-user signal detection process, strategies of a greedy algorithm and a tabu search algorithm are combined, the method has good global optimization capability and convergence characteristics, the detection performance approaches to the optimal detection performance, the method is more suitable for scenes with high transmission reliability requirements, the signal detection of the NOMA system is realized with high performance and low complexity, and the NOMA technology is promoted to be better applied to the next generation of 5G mobile communication networks.
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FIG. 1 is a block diagram of a symbol-level linear expansion class non-orthogonal multiple access system model used by the present invention;
FIG. 2 is a block flow diagram of the present invention;
FIG. 3 is a flow chart of a specific algorithm of the present invention;
fig. 4 is a comparison graph of the present invention and the detection performance simulation of the conventional NOMA system multi-user detection method.
Detailed Description
The NOMA multi-user detection algorithm of the hybrid greedy and tabu search strategy of the present invention is further described with reference to the accompanying drawings and the following detailed description: in order to achieve the above object, the technical solution in this embodiment includes the following:
(1) parameters necessary for the algorithm to operate are input: received signal y, equivalent channel gain matrix G, noise power σ 2 User number K, modulation order M, symbolNumber of number neighborhood N, taboo step length P;
(2) the signal detection problem of multiple user information recovered from the superposed signal y by the receiving end of the NOMA system is modeled as a process of solving an extreme value by a combined optimization problem P1, and a metric function of ML detection is taken as an objective function of the combined optimization problem P1 to solve a minimum value of P1:
Figure GDA0003695271180000061
where the neighborhood is
Figure GDA0003695271180000062
Is a solution
Figure GDA0003695271180000063
By a neighborhood function
Figure GDA0003695271180000064
The set of the generated data is then generated,
Figure GDA0003695271180000065
contained in S, which is the entire solution space.
(3) A greedy strategy assists in the generation of the initial solution of the algorithm. Randomly generating an initial solution
Figure GDA0003695271180000066
Correcting the algorithm initial solution generated randomly by means of the thought of a greedy algorithm to obtain a local optimal solution, and taking the local optimal solution as the initial solution of a tabu search algorithm
Figure GDA0003695271180000067
(4) Solving the combinatorial optimization problem P1 using a tabu search strategy, including neighborhood generation of a current solution vector x by a neighborhood function
Figure GDA0003695271180000068
In the neighborhood space
Figure GDA0003695271180000069
Local search is performed to determine the current best movement (k) according to the preference criteria opt ,n opt ,m opt ) And according to the taboo table T move Carrying out tabu and moving operations, and updating each parameter after the iteration;
(5) to obtain a satisfactory solution x best Judging whether the iteration reaches the set termination condition for the iteration termination condition, and if so, outputting the searched global optimal solution x of the combined optimization problem P1 best Obtaining multi-channel user information to be recovered in the signal detection process, and if not, returning to step 4);
the following further describes embodiments and effects of the present invention with reference to the drawings. Referring to fig. 1, the symbol-level linear expansion type non-orthogonal multiple access system applied in the present invention is composed of K single-antenna users and a single-antenna base station. Assume that K non-orthogonal users share the same time-frequency resource. At the transmitting end, the data bit d of the k-th user k ，d k Firstly, the encoder with the code rate of R carries out channel coding to generate coded bits c k ＝[c k (1),…,c k (τ)]Where τ is the coded bit c k After c k Modulating via a modulator, e.g. using an M-QAM modulator, where M is the size of a Quadrature Amplitude Modulation (QAM) constellation, to generate modulated symbols
x k ＝[x k (1),…,x k (τ/log2(M))]Wherein for any user k, there is
Figure GDA0003695271180000071
Figure GDA0003695271180000072
Is a set of constellation points of modulation symbols of modulation order
Figure GDA0003695271180000073
Assuming for ease of description that each user k contains only one modulation symbol, thenThe modulated symbol vector x is recorded as x ═ x 1 ,…,x K ] T . Further, with a spreading sequence s of length L k ＝[s 1,k ,…,s l,k ,…,s L,k ] T It is extended to obtain the extended symbol t k ＝s k ·x k ＝[t 1,k ,…,t l,k ,…,t L,k ] T And transmitting, and when the definition meets K & gt L, the system is in an overload state.
Referring to fig. 2 and 3, the multi-user detection algorithm of the mixed greedy and tabu search strategy of the symbol-level linear expansion type non-orthogonal multiple access system of fig. 1 according to the present invention is implemented as follows:
(1) inputting parameters necessary for the operation of the algorithm;
(1.1) adopting ideal channel estimation to obtain a received signal y, an equivalent channel gain matrix G and noise power sigma 2 The received signal can be expressed by the following formula:
Figure GDA0003695271180000074
wherein, the symbol
Figure GDA00036952711800000711
Denotes the element dot product operator, y ═ y 1 ,…,y l ,…,y L ] T Is a received symbol vector of dimension L x 1,
Figure GDA0003695271180000075
represents an equivalent channel gain matrix combining channel gain and spreading sequence, n-CN (0, sigma) 2 I L ) Is complex white gaussian noise;
(1.2) inputting the number K of users and the modulation order M, and setting the number N of symbol neighborhoods and the taboo step length P;
(2) the signal detection problem of a plurality of user information recovered from the superposed signal y by the receiving end of the NOMA system is modeled as a process of solving a minimum value of a combined optimization problem, and a metric function of ML detection is taken as an objective function of the combined optimization problem P1:
Figure GDA0003695271180000076
where the neighborhood is
Figure GDA0003695271180000077
Is a solution
Figure GDA0003695271180000078
By a neighborhood function
Figure GDA0003695271180000079
The set of the generated data is then generated,
Figure GDA00036952711800000710
contained in S, which is the entire solution space.
For all K users, if there is one solution vector x best Satisfy the requirements of
Ω(x best )≤Ω(x)
Then solve for vector x best Is a globally optimal solution.
(3) A greedy strategy assists in the generation of the initial solution of the algorithm. Randomly generating an initial solution
Figure GDA0003695271180000081
Correcting the algorithm initial solution generated randomly by means of the thought of a greedy algorithm to obtain a local optimal solution, and taking the local optimal solution as the initial solution of a tabu search algorithm
Figure GDA0003695271180000082
(3.1) obtaining (G) H y) and matrix G H The real part of the element of the triangle on G, let V ═ Re [ (G) H y)]| and W ═ Re (G) H G) L, it can be known that V is a K × 1-dimensional column vector, and W is a K × K-dimensional square matrix with lower triangular parts all being 0;
(3.2) sorting the elements of the triangular parts of V and W in descending order to form a container
Figure GDA0003695271180000083
A sequence X of elements;
(3.3) initializing, and taking the randomly generated initial solution as the initial value of the optimization algorithm
Figure GDA0003695271180000084
(3.4) to the random initial value
Figure GDA0003695271180000085
And (5) correcting: judging the first element of the sequence X obtained after descending order arrangement, if X is 1 ＝|V i If, then M vectors are generated, by exchange
Figure GDA0003695271180000086
X in (2) i Obtaining the corresponding likelihood function values for the possible M values, and selecting x which makes the likelihood function obtain the maximum value i As a
Figure GDA0003695271180000087
If X is 1 ＝|W ij If l, then M is generated 2 Group vectors by permutation
Figure GDA0003695271180000088
X in (1) i And x j To possible M 2 Selecting a value combination to obtain the corresponding likelihood function value, and selecting x for making the likelihood function maximum i And x j Replacement of
Figure GDA0003695271180000089
X in (2) i And x j Thereby obtaining
Figure GDA00036952711800000810
(3.5) the corrected initial solution
Figure GDA00036952711800000811
As an initial solution to the TS-MUD algorithm, an iteration is performed.
(4) To be provided with
Figure GDA00036952711800000812
As an initial solution, solving the combined optimization problem P1 by using a tabu search strategy;
(4.1) generation of a current solution vector neighborhood structure:
and defining the candidate solution set closest to the Euclidean distance of the current solution vector as a neighborhood by the current solution vector. First for each symbol in the current solution vector x
Figure GDA00036952711800000813
Figure GDA00036952711800000814
Is a set of M-PSK constellation points to be associated with a current symbol x k The N constellation points with the nearest Euclidean distance are taken as the symbol neighborhood of the current symbol and are marked as
Figure GDA00036952711800000815
Then for the currently input solution vector x containing K users, KN vector neighborhoods can be correspondingly generated, and a neighborhood function is used
Figure GDA00036952711800000816
By characterizing the mapping relationship, the solution vector x can be passed through the neighborhood function
Figure GDA00036952711800000817
Then, generating a candidate solution set composed of all vector neighborhoods
Figure GDA00036952711800000818
Expressed in matrix form as follows:
Figure GDA00036952711800000819
Figure GDA0003695271180000091
(4.2) determination of optimal movement:
the tabu search is to generate a set of candidate solutions composed of vector neighborhoods in all search spaces S from an initial solution x
Figure GDA0003695271180000092
In each iteration, the pair of the objective functions belonging to the neighborhood belongs to the minimization criterion of the objective function in the combinatorial optimization problem P1
Figure GDA0003695271180000093
All column vectors η of i Evaluating, and selecting the best neighborhood solution vector, i.e. local optimal solution x opt Becomes the starting solution for the next iteration, and this operation is defined as "move". Suppose the algorithm selects the symbol q for the kth user this time m The column vector η of the nth symbol neighborhood (k-1)N+n As the initial solution of the next iteration, the optimal moving direction of the iteration can be recorded as (k) opt ,n opt ,m opt ). In each iteration, the TS algorithm only takes values in the elements of the set Move and selects the next step. In the t-th iteration, the optimal move operation (k) is determined opt ,n opt ,m opt ) Is the vector neighborhood that minimizes the value of the objective function
Figure GDA0003695271180000094
Corresponding shift (k, n, m), i.e.
Figure GDA0003695271180000095
(4.3) selection of the privileged mechanism and the taboo mechanism:
to according to the optimal movement (k) opt ,n opt ,m opt ) The selected candidate solution function value is judged, if the value can satisfy the following formula, the current optimal solution vector is processed according to the privilege mechanism
Figure GDA0003695271180000096
The update is made and the algorithm proceeds directly to step (4.4.1), otherwise to step (4.3.1) to determine if a contraindication mechanism is triggered.
Figure GDA0003695271180000097
By establishing a tabu table T move To realize the tabu mechanism, tabu table T move Is an N x KM matrix (M is the modulation order) containing all possible moving paths, T move The element in (b) represents the number of iterations for which the movement path is forbidden, also called the taboo step size, denoted as P, whose value can be obtained by simulation. Therefore, the tabu chart T move Can be written as:
Figure GDA0003695271180000098
if the best shift operation selected in this iteration is (k) opt ,n opt ,m opt ) Otherwise, the table T is forbidden move (n) th opt ,(k opt -1)M+m opt ) The item updates the parameters according to the rules of step (4.4.1).
(4.3.1) checking tabu table:
contraindication list T move Checking the movement path (k) opt ,n opt ,m opt ) Whether it has been performed in the last P iterations. If the following condition is met, the movement path has not been executed in the last P iterations, it is not disabled, and the algorithm goes to step (4.4.2):
T move (n opt ,(k opt -1)M+m opt )＝＝0
otherwise, this duplicate movement path (k) is deleted from the movement set Move by the following operation opt ,n opt ,m opt ) And returning to the step (4.2), wherein the operator represents the deletion of the element from the set. If all movement paths are disabled, resulting in Move being nullGo to step (4.3.2)
Move (t) ＝Move (t) \(k opt ,n opt ,m opt )
(4.3.2) receiving a poor solution, and jumping out a local optimal trap:
if the motion set Move is null, selecting the motion with the minimum forbidden iteration number from the vector neighborhood as the optimal motion (k) of the current iteration opt ,n opt ,m opt ) The procedure is as shown below and goes to step (4.4.1).
[n opt ,(k opt -1)M+m opt ]＝find(T move ＝＝min(min(T move )))
And (4.4) updating parameters:
according to the optimal moving path (k) in the step (4.3) opt ,n opt ,m opt ) First, uniformly updating the initial solution x of the next iteration (t+1) And tabu watch T move ：
Figure GDA0003695271180000101
T move ＝max(T move -1,0)
The algorithm then goes to the corresponding steps (4.4.1) and (4.4.2) to update the other parameters in two different ways.
(4.4.1) current optimal solution vector
Figure GDA0003695271180000102
Can be updated:
updating the optimal solution vector at the beginning of the next iteration
Figure GDA0003695271180000103
The algorithm judges to obtain the current moving path (k) opt ,n opt ,m opt ) Is an optional direction. Furthermore, according to the privilege criterion, even if the movement path was disabled in the last iteration, that is to say T move (n opt ,(k opt -1)M+m opt ) Not equal to 0, but still as the best moving path (k) in order to avoid missing the global optimal solution opt ,n opt ,m opt ) And the contraindication amount is set to 0. The parameters are updated as follows:
Figure GDA0003695271180000104
T move (n opt ,(k opt -1)M+m opt )＝0
(4.4.2) current optimal solution vector
Figure GDA0003695271180000105
Cannot be updated:
in this case, a poor solution is accepted, and a moving path (k) to be selected opt ,n opt ,m opt ) The access is prohibited in the subsequent P iterations, and the direction different from the access is searched. Updating a taboo table:
T move (n opt ,(k opt -1)M+m opt )＝P
(5) and (5) judging the termination condition. To obtain a satisfactory solution x best Judging whether the iteration reaches the set termination condition or not for the iteration termination condition, and if so, outputting the searched global optimal solution x of the combined optimization problem P1 best Obtaining multi-channel user information to be recovered in the signal detection process, and returning to step 4) if not;
specifically, assume that the algorithm updates the optimal solution of the parameters at the time of the t-th iteration
Figure GDA0003695271180000111
Is the global optimal solution x to be solved best The algorithm will terminate the iteration, i.e.
Figure GDA0003695271180000112
The residual signal energy in the system at the moment
Figure GDA0003695271180000113
Expressed as:
Figure GDA0003695271180000114
considering noise factor, the energy of the residual signal
Figure GDA0003695271180000115
Can be further expressed as
Figure GDA0003695271180000116
The system noise is 0 in mean and sigma in variance 2 White gaussian noise. Thus, the above formula can be further represented as
Figure GDA0003695271180000117
Where L is the length of the spreading sequence, the iteration termination condition may be set as:
Figure GDA0003695271180000118
that is, when the energy of the residual signal is less than or equal to L times of the noise power, a satisfactory solution is obtained, and the algorithm stops iteration.
Further, considering that under the condition of low signal-to-noise ratio, the noise power is large, the algorithm may only pass a small amount of iteration, the residual energy is easy to reach the iteration termination condition, and therefore, the search is stopped, and the performance of the algorithm is poor, so that a parameter beta is introduced th And the minimum iteration time threshold is used for ensuring sufficient iteration search and controlling the iteration termination condition in combination with the noise power. The algorithm terminates the iteration if the following equation is satisfied. Otherwise, returning to the step 1 when t is t + 1. Threshold beta th The value of (b) can be obtained by experiments.
Figure GDA0003695271180000119
Therefore, the TS algorithm searching performance under low signal-to-noise ratio can be ensured, and the problem that the TS algorithm is repeatedly searched after being converged under high signal-to-noise ratio to bring over-high calculation complexity can be avoided. At this point, signal detection is completed.
The effects of the present invention can be further illustrated by the following simulations:
1. simulation conditions
The simulation uses the MUSA system, which is composed of 6 single-antenna users and a single-antenna base station, the overload rate of the system is 150%, QPSK modulation is adopted, spreading sequence elements are selected from {1, i, -1, -i }, the spreading length L is 4, after passing through a flat rayleigh fading channel, the receiving end adopts ideal channel estimation, and the taboo step length is set to be P15.
2. Emulated content
The results of bit error rate simulation using the present invention and three existing signal detection methods are shown in fig. 4. The abscissa of fig. 4 is the signal-to-noise ratio and the ordinate is the bit error rate of the system. Wherein:
the ML curve is the performance of maximum likelihood detection and represents the optimal detection performance of the system from an exhaustive search under ideal conditions.
The MMSE-SIC curve refers to the detection performance of the existing minimum mean square error successive interference cancellation algorithm, and the detection performance of the MMSE-SIC curve is influenced by an error propagation effect and is far away from the optimal detection performance.
The Enhanced-TS curve refers to the detection performance of the existing Enhanced tabu search algorithm, and is proposed by Jung I and the like, so that the good performance approaching ML detection is obtained.
The GA-TS curve refers to the detection performance of the algorithm provided by the invention.
Comparing the error rate performance of the invention with that of the traditional multi-user detection algorithm, the invention can be found to show better detection performance than that of the traditional MMSE-SIC algorithm, and the detection performance of the invention is close to that of the Enhanced-TS algorithm, and the detection performance of the invention is close to the limit performance under the ideal condition.
For convenience of comparison, the number of floating point operations (FLOP) is used herein to reflect the complexity of each algorithm, and a complex multiplication (division) method and a complex addition (subtraction) method respectively correspond to 6 floating point operations and 2 floating point operations.
TABLE 1 MUSA System multiuser detection algorithm complexity analysis
Figure GDA0003695271180000121
Different from the ML receiver, the complexity of the GA-TS multi-user detection algorithm provided by the invention can not exponentially increase along with the increase of the number of users or the modulation order, the complexity is acceptable, and meanwhile, under the same iteration times, the complexity is obviously higher than that of the GA-TS algorithm because the Enhanced-TS algorithm has the operation of weight matrix inversion,
in conclusion, the detection performance of the invention approaches the performance of the optimal detection of ML, and the complexity is far lower than that of ML detection.

Claims (5)

1. A NOMA multi-user detection algorithm of a hybrid greedy and tabu search strategy is characterized in that: comprises the following steps:
inputting parameters necessary for running an algorithm;
step (2), converting the multi-user detection problem into a combined optimization problem P1; the signal detection problem that a receiving end of the NOMA system recovers a plurality of user information from the superposed signal y is modeled as a process of solving a minimum value of a combined optimization problem P1, and a metric function of ML detection is taken as an objective function of the combined optimization problem P1:
Figure FDA0003695271170000011
where the neighborhood is
Figure FDA0003695271170000015
Is a solution
Figure FDA00036952711700000112
By a neighborhood function
Figure FDA0003695271170000017
The set of the generated data is then generated,
Figure FDA0003695271170000018
contained in S, which is the entire solution space, if there is one solution vector x for all K users best Satisfy omega (x) best ) Less than or equal to omega (x), then solving vector x best Is a global optimal solution;
and (3) randomly generating an initial solution in the generation process of the greedy strategy auxiliary algorithm initial solution
Figure FDA0003695271170000012
Correcting the algorithm initial solution generated randomly by means of the thought of a greedy algorithm to obtain a local optimal solution, and taking the local optimal solution as the initial solution of a tabu search algorithm
Figure FDA0003695271170000013
Step (4), solving the combined optimization problem P1 by using a tabu search strategy, wherein the method comprises the step of generating a neighborhood of a current solution vector x through a neighborhood function
Figure FDA0003695271170000019
In the neighborhood space
Figure FDA00036952711700000110
Local search is performed internally, and the current best movement (k) is determined according to the optimization criterion opt ,n opt ,m opt ) According to a tabu table T move Carrying out tabu and moving operations, and updating each parameter after the iteration;
step (5), in the judgment of the termination condition, obtainingSatisfactory solution x best Judging whether the iteration reaches the set termination condition or not for the iteration termination condition, and if so, outputting the searched global optimal solution x of the combined optimization problem P1 best And (4) obtaining the multi-channel user information to be recovered in the signal detection process, and otherwise, returning to the step (4).
2. The NOMA multi-user detection algorithm for a hybrid greedy and tabu search strategy of claim 1, wherein: the step (1) comprises the following steps:
step (1.1), adopting ideal channel estimation to obtain received signal y, equivalent channel gain matrix G and noise power sigma 2 The received signal can be expressed by the following formula:
Figure FDA00036952711700000113
＝Gx+n
(symbol)
Figure FDA00036952711700000114
denotes the element dot product operator, y ═ y 1 ,…,y l ,…,y L ] T Is a received symbol vector of dimension L x 1,
Figure FDA00036952711700000111
represents an equivalent channel gain matrix combining channel gain and spreading sequence, n-CN (0, sigma) 2 I L ) Is complex gaussian white noise;
and (1.2) inputting the number K of users and the modulation order M, and setting the number N of symbol neighborhoods and the taboo step length P.
3. The NOMA multi-user detection algorithm for a hybrid greedy and tabu search strategy of claim 1, wherein: in the step (3), the multi-user detection problem is converted into a combined optimization problem P1, and an initial solution is randomly generated
Figure FDA0003695271170000014
Correcting the algorithm initial solution generated randomly by means of the thought of a greedy algorithm to obtain a local optimal solution, and taking the local optimal solution as the initial solution of a tabu search algorithm
Figure FDA00036952711700000218
The method comprises the following steps:
step (3.1) of obtaining (G) H y) and matrix G H The real part of the element of the triangle on G, let V ═ Re [ (G) H y)]| and W ═ Re (G) H G) L, it can be known that V is a K × 1-dimensional column vector, and W is a K × K-dimensional square matrix with lower triangular parts all being 0;
step (3.2), sorting the elements of the triangular parts on V and W in a descending order to form a container
Figure FDA0003695271170000021
A sequence X of elements;
step (3.3), initialization is carried out, and the initial solution generated randomly is used as the initial value of the optimization algorithm
Figure FDA00036952711700000217
Step (3.4), to the random initial value
Figure FDA00036952711700000215
And (5) correcting: judging the first element of the sequence X obtained after descending order arrangement, if X is 1 ＝|V i If, then M vectors are generated, by exchange
Figure FDA00036952711700000216
X in (2) i Obtaining the corresponding likelihood function values for the possible M values, and selecting x which makes the likelihood function obtain the maximum value i As a
Figure FDA00036952711700000213
If X is 1 ＝|W ij If l, then M is generated 2 Group vectors, by permutation
Figure FDA00036952711700000214
X in (2) i And x j To possible M 2 Combining values of different kinds, finding out the corresponding likelihood function value, and selecting x for making the likelihood function maximum i And x j Replacement of
Figure FDA00036952711700000212
X in (2) i And x j Thereby obtaining
Figure FDA00036952711700000211
Step (3.5), the corrected initial solution is processed
Figure FDA00036952711700000210
As an initial solution to the TS-MUD algorithm, an iteration is performed.
4. The NOMA multi-user detection algorithm for a hybrid greedy and tabu search strategy of claim 1, wherein: the step (4) is to
Figure FDA0003695271170000029
As an initial solution, the combined optimization problem P1 is solved by using a tabu search strategy, which includes the following steps:
step (4.1), generation of a current solution vector neighborhood structure:
defining the candidate solution set closest to the Euclidean distance of the current solution vector as a neighborhood by the current solution vector, firstly, for each symbol in the current solution vector x
Figure FDA0003695271170000026
Figure FDA00036952711700000219
Is a set of M-PSK constellation points to be associated with the current symbolNumber x k The N constellation points with the nearest Euclidean distance are taken as the symbol neighborhood of the current symbol and are marked as
Figure FDA00036952711700000220
For the current input solution vector x containing K users, KN vector neighborhoods are correspondingly generated, and a neighborhood function is used
Figure FDA0003695271170000025
Characterizing the mapping relationship, the solution vector x is passed through a neighborhood function
Figure FDA0003695271170000028
Then, generating a candidate solution set composed of all vector neighborhoods
Figure FDA0003695271170000024
Expressed in matrix form as follows:
Figure FDA0003695271170000022
Figure FDA0003695271170000023
step (4.2), determination of optimal movement:
tabu search is a process of generating a set of candidate solutions consisting of vector neighborhoods in all search spaces S from an initial solution x
Figure FDA0003695271170000037
In each iteration, the pair of the objective functions belonging to the neighborhood belongs to the minimization criterion of the objective function in the combinatorial optimization problem P1
Figure FDA0003695271170000036
All column vectors η of i Evaluating, and selecting the best neighborhood solution vector, i.e. local optimal solution x opt Becomes the starting solution for the next iteration, this operation is defined as "move", assuming the algorithm has selected the symbol q for the kth user this time m The column vector η of the nth symbol neighborhood (k-1)N+n As the initial solution of the next iteration, the optimal moving direction of the iteration is recorded as (k) opt ,n opt ,m opt ) In each iteration, the TS algorithm only takes values in elements of the Move set and selects the next step; in the t-th iteration, the optimal move operation (k) is determined opt ,n opt ,m opt ) Is the vector neighborhood that minimizes the value of the objective function
Figure FDA0003695271170000035
Corresponding shift (k, n, m), i.e.
Figure FDA0003695271170000031
Step (4.3), selecting a privileged mechanism and a taboo mechanism:
according to the optimal movement (k) opt ,n opt ,m opt ) The selected candidate solution function value is judged, and if the following formula is satisfied, the current optimal solution vector is determined according to the privilege mechanism
Figure FDA0003695271170000034
Updating is carried out, the algorithm directly enters the step (4.4.1), otherwise, the step (4.3.1) is carried out, and whether a taboo mechanism is triggered or not is judged;
Figure FDA0003695271170000032
by establishing a tabu table T move To realize the tabu mechanism, tabu table T move Is an N x KM matrix, M is a modulation order, and includes all possible moving paths, T move The element in (1) represents the number of forbidden iterations of the moving path, also called the taboo step length, and is denoted as P, and the value of P can be obtained by simulationTo, tabu watch T move Writing into:
Figure FDA0003695271170000033
if the best shift operation selected in this iteration is (k) opt ,n opt ,m opt ) Otherwise, the table T is forbidden move (n) th opt ,(k opt -1)M+m opt ) The item updates the parameters according to the rule of step (4.4.1);
step (4.3.1), checking a contraindication table:
contraindication list T move Checking the movement path (k) opt ,n opt ,m opt ) Whether it has been done in the last P iterations, the move path has not been executed in the last P iterations, it is not disabled, and the algorithm goes to step (4.4.2) if the following condition is met:
T move (n opt ,(k opt -1)M+m opt )＝＝0
otherwise, this duplicate movement path (k) is deleted from the movement set Move by the following operation opt ,n opt ,m opt ) And returning to step (4.2), wherein the operator \ represents the deletion of the element from the set, if all movement paths are forbidden, resulting in Move being null, then going to step (4.3.2)
Move (t) ＝Move (t) \(k opt ,n opt ,m opt )
And (4.3.2) receiving the inferior solution, and jumping out the local optimal trap:
if the motion set Move is null, selecting the motion with the minimum forbidden iteration number from the vector neighborhood as the optimal motion (k) of the current iteration opt ,n opt ,m opt ) The specific operation is shown in the following formula, and the process goes to the step (4.4.1);
[n opt ,(k opt -1)M+m opt ]＝find(T move ＝＝min(min(T move )))
and (4.4) updating parameters:
according to the stepsOptimal moving path (k) in step (4.3) opt ,n opt ,m opt ) First, uniformly updating the initial solution x of the next iteration (t+1) And tabu watch T move ：
Figure FDA0003695271170000041
T move ＝max(T move -1,0)
Then, the corresponding steps (4.4.1) and (4.4.2) are carried out according to the algorithm flow, and other parameters are updated in two different ways;
step (4.4.1), current optimal solution vector
Figure FDA0003695271170000045
Is updated:
updating the optimal solution vector at the beginning of the next iteration
Figure FDA0003695271170000044
The algorithm judges to obtain the current moving path (k) opt ,n opt ,m opt ) Is an optional direction, and furthermore, according to the privilege criterion, even if the movement path was disabled in the last iteration, that is to say T move (n opt ,(k opt -1)M+m opt ) Not equal to 0, but still as the best moving path (k) in order to avoid missing the global optimal solution opt ,n opt ,m opt ) And the taboo amount is set to 0, and the parameters are updated according to the following modes:
Figure FDA0003695271170000042
T move (n opt ,(k opt -1)M+m opt )＝0
step (4.4.2), current optimal solution vector
Figure FDA0003695271170000043
Cannot be updated:
at this time, the inferior solution is accepted, and the moving path (k) to be selected opt ,n opt ,m opt ) Setting the table as a tabu, forbidding access in the subsequent P iterations, searching a direction different from the tabu, and updating a tabu table: t is move (n opt ,(k opt -1)M+m opt )＝P。
5. The NOMA multi-user detection algorithm for a hybrid greedy and tabu search strategy of claim 1, wherein: the step of determining the termination condition in the step (5) is as follows: to obtain a satisfactory solution x best Judging whether the iteration reaches the set termination condition or not for the iteration termination condition, and if so, outputting the searched global optimal solution x of the combined optimization problem P1 best And (4) obtaining the multi-channel user information to be recovered in the signal detection process, and otherwise, returning to the step (4).
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