CN113572500A - 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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CN113572500A
CN113572500A CN202110711019.7A CN202110711019A CN113572500A CN 113572500 A CN113572500 A CN 113572500A CN 202110711019 A CN202110711019 A CN 202110711019A CN 113572500 A CN113572500 A CN 113572500A
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CN113572500B (en
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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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    • H—ELECTRICITY
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    • H04B1/71055—Joint detection techniques, e.g. linear detectors using minimum mean squared error [MMSE] detector
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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 xbestJudging 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 P1bestObtaining the multi-channel user information to be recovered in the signal detection process, or notReturning to the step (4). 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 (5th 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 of 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 tabu 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 target optimization problem P1; and (3) randomly generating an initial solution in the generation process of the greedy strategy auxiliary algorithm initial solution
Figure BDA0003133757190000021
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 BDA0003133757190000022
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 BDA0003133757190000023
In the neighborhood space
Figure BDA0003133757190000024
Local search is performed to determine the current best movement (k) according to the preference criteriaopt,nopt,mopt) According to a tabu table TmoveCarrying out tabu and moving operations, and updating each parameter after the iteration;
step (5), in the judgment of termination condition, obtaining satisfactory solution xbestJudging 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 P1bestTo obtain signals during the detection processAnd (4) recovering the multi-path user information, 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 sigma2The received signal can be expressed by the following formula:
Figure BDA00031337571900000212
＝Gx+n
(symbol)
Figure BDA00031337571900000211
denotes the element dot product operator, y ═ y1,…,yl,…,yL]TIs a received symbol vector of dimension L x 1,
Figure BDA0003133757190000025
represents an equivalent channel gain matrix combining channel gain and spreading sequence, n-CN (0, sigma)2IL) Is complex white gaussian 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), a signal detection problem that the NOMA system receiving end recovers a plurality of user information from the superimposed signal y is modeled as a process of minimizing a combinatorial optimization problem, and a metric function of ML detection is used as an objective function of the combinatorial optimization problem P1:
Figure BDA0003133757190000026
where the neighborhood is
Figure BDA0003133757190000027
Is a solution
Figure BDA0003133757190000028
By a neighborhood function
Figure BDA0003133757190000029
The set of the generated data is then generated,
Figure BDA00031337571900000210
contained in S, which is the entire solution space, if there is one solution vector x for all K usersbestSatisfy omega (x)best) Less than or equal to omega (x), then solving vector xbestIs a globally optimal solution.
Preferably, in the step (3), the multi-user detection problem is converted into the target optimization problem P1, and an initial solution is randomly generated
Figure BDA0003133757190000031
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 BDA0003133757190000032
The method comprises the following steps:
step (3.1) of obtaining (G)Hy) and matrix GHThe real part of the element of the triangle on G, let V ═ Re [ (G)Hy)]| and W ═ Re (G)HG) 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) of sequencing the elements of the triangular parts on V and W in descending order to form a group containing
Figure BDA0003133757190000033
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 BDA0003133757190000034
Step (3.4), to the random initial value
Figure BDA0003133757190000035
And (5) correcting: judging the first element of the sequence X obtained after descending order arrangement, if X is1＝|ViIf, then a vector is generated, by exchange
Figure BDA0003133757190000036
X in (2)iObtaining the corresponding likelihood function values for the possible M values, and selecting x which makes the likelihood function obtain the maximum valueiAs a
Figure BDA0003133757190000037
If X is1＝|WijIf l, then M is generated2Group vectors, by permutation
Figure BDA0003133757190000038
X in (2)iAnd xjTo possible M2Selecting a value combination to obtain the corresponding likelihood function value, and selecting x for making the likelihood function maximumiAnd xjReplacement of
Figure BDA0003133757190000039
X in (2)iAnd xjThereby obtaining
Figure BDA00031337571900000310
Step (3.5), the corrected initial solution is processed
Figure BDA00031337571900000311
As an initial solution to the TS-MUD algorithm, an iteration is performed.
Preferably, the step (4) is performed by
Figure BDA00031337571900000312
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:
from the current solution vectorDefining the candidate solution set closest to the Euclidean distance of the current solution vector as a neighborhood, firstly, for each symbol in the current solution vector x
Figure BDA00031337571900000313
(k＝1,2,…,K)，
Figure BDA00031337571900000314
Is a set of M-PSK constellation points to be associated with a current symbol xkThe N constellation points with the nearest Euclidean distance are taken as the symbol neighborhood of the current symbol and are marked as nearxkFor the currently input solution vector x containing K users, KN vector neighborhoods are correspondingly generated, and a neighborhood function is used
Figure BDA00031337571900000315
Characterizing the mapping relationship, the solution vector x is passed through the neighborhood function
Figure BDA00031337571900000316
Then, generating a candidate solution set composed of all vector neighborhoods
Figure BDA00031337571900000317
Expressed in matrix form as follows:
Figure BDA00031337571900000318
Figure BDA0003133757190000041
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 BDA0003133757190000042
In each iteration, the pairs belonging to the neighborhood belong to the minimization criterion of the objective function in the question P1
Figure BDA0003133757190000043
All column vectors η ofiEvaluating, and selecting the best neighborhood solution vector, i.e. local optimal solution xoptBecomes 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 timemThe column vector η of the nth symbol neighborhood(k-1)N+nAs the initial solution of the next iteration, the optimal moving direction of the iteration is recorded as (k)opt,nopt,mopt) 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, we determine the best move operation (k)opt,nopt,mopt) Is the vector neighborhood that minimizes the value of the objective function
Figure BDA0003133757190000044
Corresponding shift (k, n, m), i.e.
Figure BDA0003133757190000045
Step (4.3), selecting a privileged mechanism and a taboo mechanism:
according to the optimal movement (k)opt,nopt,mopt) 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 BDA0003133757190000046
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 BDA0003133757190000047
by establishing a tabu table TmoveTo realize the tabu mechanism, tabu table TmoveIs an NxKM matrix (M is the modulation order)) Including all possible movement paths, TmoveThe 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 TmoveWriting into:
Figure BDA0003133757190000048
if the best shift operation selected in this iteration is (k)opt,nopt,mopt) Otherwise, it is forbidden to show Tmove(n) thopt,(kopt-1)M+mopt) The item updates the parameters according to the rule of step (4.4.1);
step (4.3.1), checking a contraindication table:
contraindication list TmoveChecking the movement path (k)opt,nopt,mopt) 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):
Tmove(nopt,(kopt-1)M+mopt)＝＝0
otherwise, this duplicate movement path (k) is deleted from the movement set Move by the following operationopt,nopt,mopt) 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)\(kopt,nopt,mopt)
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 iterationopt,nopt,mopt) The specific operation is shown in the following formula, and the process goes to the step (4.4.1);
[nopt,(kopt-1)M+mopt]＝find(Tmove＝＝min(min(Tmove)))
and (4.4) updating parameters:
according to the optimal moving path (k) in the step (4.3)opt,nopt,mopt) First, uniformly updating the initial solution x of the next iteration(t+1)And tabu watch Tmove：
Figure BDA0003133757190000051
Tmove＝max(Tmove-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 BDA0003133757190000052
Is updated:
updating the optimal solution vector at the beginning of the next iteration
Figure BDA0003133757190000053
The algorithm judges to obtain the current moving path (k)opt,nopt,mopt) 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 Tmove(nopt,(kopt-1)M+mopt) Not equal to 0, but still as the best moving path (k) in order to avoid missing the global optimal solutionopt,nopt,mopt) And the taboo amount is set to 0, and the parameters are updated according to the following modes:
Figure BDA0003133757190000054
Tmove(nopt,(kopt-1)M+mopt)＝0
step (4.4.2), currently the most important oneOptimal solution vector
Figure BDA0003133757190000055
Cannot be updated:
at this time, the inferior solution is accepted, and the moving path (k) to be selectedopt,nopt,mopt) 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 ismove(nopt,(kopt-1)M+mopt)＝P。
Preferably, the step of determining the termination condition in step (5) is as follows: to obtain a satisfactory solution xbestJudging 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 P1bestObtaining 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 σ2The number K of users, the modulation order M, 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 an extreme 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 to solve the minimum value of P1:
Figure BDA0003133757190000061
where the neighborhood is
Figure BDA0003133757190000062
Is a solution
Figure BDA0003133757190000063
By a neighborhood function
Figure BDA0003133757190000064
The set of the generated data is then generated,
Figure BDA0003133757190000065
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 BDA0003133757190000066
For random generation by means of greedy algorithmCorrecting the initial solution of the algorithm to obtain a local optimal solution, and using the local optimal solution as the initial solution of the tabu search algorithm
Figure BDA0003133757190000067
(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 BDA0003133757190000068
In the neighborhood space
Figure BDA0003133757190000069
Local search is performed to determine the current best movement (k) according to the preference criteriaopt,nopt,mopt) According to a tabu table TmoveCarrying out tabu and moving operations, and updating each parameter after the iteration;
(5) to obtain a satisfactory solution xbestJudging 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 P1bestObtaining multi-channel user information to be recovered in the signal detection process, and returning to step 4) if not;
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 userk，dkFirstly, an encoder with a code rate of R carries out channel coding to generate coded bits ck＝[ck(1),…,ck(τ)]Where τ is the coded bit ckAfter ckModulating via a modulator, e.g. using an M-QAM modulator, where M is the size of a Quadrature Amplitude Modulation (QAM) constellation, to generate a modulated symbol xk＝[xk(1),…,xk(τ/log2(M))]Wherein for any user k, there is
Figure BDA0003133757190000071
(k＝1,2,…,K)，
Figure BDA0003133757190000072
Is a set of constellation points of modulation symbols of modulation order
Figure BDA0003133757190000073
For convenience of description, assuming that each user k only contains one modulation symbol, the modulation symbol vector x is denoted as x ═ x1,...,xK]T. Further, with a spreading sequence s of length Lk＝[s1,k,…,sl,k,…,sL,k]TIt is extended to obtain the extended symbol tk＝sk·xk＝[t1,k,…,tl,k,…,tL,k]TAnd transmitting, and when K is larger than L, the system is in 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 algorithm operation;
(1.1) adopting ideal channel estimation to obtain a received signal y, an equivalent channel gain matrix G and noise power sigma2The received signal can be expressed by the following formula:
Figure BDA00031337571900000710
＝Gx+n
wherein, the symbol
Figure BDA00031337571900000711
Denotes the element dot product operator, y ═ y1,…,yl,…,yL]TIs a received symbol vector of dimension L x 1,
Figure BDA0003133757190000074
represents an equivalent channel gain matrix combining channel gain and spreading sequence, n-CN (0, sigma)2IL) 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 BDA0003133757190000075
where the neighborhood is
Figure BDA0003133757190000076
Is a solution
Figure BDA0003133757190000077
By a neighborhood function
Figure BDA0003133757190000078
The set of the generated data is then generated,
Figure BDA0003133757190000079
contained in S, which is the entire solution space.
For all K users, if there is one solution vector xbestSatisfy the requirement of
Ω(xbest)≤Ω(x)
Then solve for vector xbestIs 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 BDA0003133757190000081
Initial solution to a randomly generated algorithm with the aid of the idea of a greedy algorithmCorrecting to obtain a local optimal solution, and using the local optimal solution as an initial solution of a tabu search algorithm
Figure BDA0003133757190000082
(3.1) obtaining (G)Hy) and matrix GHThe real part of the element of the triangle on G, let V ═ Re [ (G)Hy)]| and W ═ Re (G)HG) 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 BDA0003133757190000083
A sequence X of elements;
(3.3) initializing, and taking the randomly generated initial solution as the initial value of the optimization algorithm
Figure BDA0003133757190000084
(3.4) to the random initial value
Figure BDA0003133757190000085
And (5) correcting: judging the first element of the sequence X obtained after descending order arrangement, if X is1＝|ViIf, then a vector is generated, by exchange
Figure BDA0003133757190000086
X in (2)iObtaining the corresponding likelihood function values for the possible M values, and selecting x which makes the likelihood function obtain the maximum valueiAs a
Figure BDA0003133757190000087
If X is1＝|WijIf l, then M is generated2Group vectors, by permutation
Figure BDA0003133757190000088
X in (2)iAnd xjTo possible M2Seed value groupCombining to obtain corresponding likelihood function value, and selecting x for making likelihood function maximumiAnd xjReplacement of
Figure BDA0003133757190000089
X in (2)iAnd xjThereby obtaining
Figure BDA00031337571900000810
(3.5) the corrected initial solution
Figure BDA00031337571900000811
As an initial solution to the TS-MUD algorithm, an iteration is performed.
(4) To be provided with
Figure BDA00031337571900000812
As an initial solution, solving the combined optimization problem P1 by using a tabu search strategy;
(4.1) generating 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 BDA00031337571900000813
(k＝1,2,…,K)，
Figure BDA00031337571900000814
Is a set of M-PSK constellation points to be associated with a current symbol xkThe N constellation points with the nearest Euclidean distance are taken as the symbol neighborhood of the current symbol and are recorded as
Figure BDA00031337571900000815
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 BDA00031337571900000816
By characterizing this mapping relationship, the solution can be solvedVector x passes through the neighborhood function
Figure BDA00031337571900000817
Then, generating a candidate solution set composed of all vector neighborhoods
Figure BDA00031337571900000818
Expressed in matrix form as follows:
Figure BDA00031337571900000819
Figure BDA0003133757190000091
(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 BDA0003133757190000092
In each iteration, the pairs belonging to the neighborhood belong to the minimization criterion of the objective function in the question P1
Figure BDA0003133757190000093
All column vectors η ofiEvaluating, and selecting the best neighborhood solution vector, i.e. local optimal solution xoptBecomes 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 timemThe column vector η of the nth symbol neighborhood(k-1)N+nAs the initial solution of the next iteration, the optimal moving direction of the iteration can be recorded as (k)opt,nopt,mopt). 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 determinedopt,nopt,mopt) Is the vector neighborhood that minimizes the value of the objective function
Figure BDA0003133757190000094
Corresponding shift (k, n, m), i.e.
Figure BDA0003133757190000095
(4.3) selection of the privileged mechanism and the taboo mechanism:
according to the optimal movement (k)opt,nopt,mopt) 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 BDA0003133757190000096
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 BDA0003133757190000097
By establishing a tabu table TmoveTo realize the tabu mechanism, tabu table TmoveIs an N x KM matrix (M is the modulation order) containing all possible moving paths, TmoveThe 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 TmoveCan be written as:
Figure BDA0003133757190000098
if the best shift operation selected in this iteration is (k)opt,nopt,mopt) Otherwise, it is forbidden to show Tmove(n) thopt,(kopt-1)M+mopt) The item updates the parameters according to the rules of step (4.4.1).
(4.3.1) check contraindications table:
contraindication list TmoveChecking the movement path (k)opt,nopt,mopt) 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):
Tmove(nopt,(kopt-1)M+mopt)＝＝0
otherwise, this duplicate movement path (k) is deleted from the movement set Move by the following operationopt,nopt,mopt) 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 empty, go to step (4.3.2)
Move(t)＝Move(t)\(kopt,nopt,mopt)
(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 iterationopt,nopt,mopt) The procedure is as shown below and goes to step (4.4.1).
[nopt,(kopt-1)M+mopt]＝find(Tmove＝＝min(min(Tmove)))
And (4.4) updating parameters:
according to the optimal moving path (k) in the step (4.3)opt,nopt,mopt) First, uniformly updating the initial solution x of the next iteration(t+1)And tabu watch Tmove：
Figure BDA0003133757190000101
Tmove＝max(Tmove-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 BDA0003133757190000102
Can be updated:
updating the optimal solution vector at the beginning of the next iteration
Figure BDA0003133757190000103
The algorithm judges to obtain the current moving path (k)opt,nopt,mopt) 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 Tmove(nopt,(kopt-1)M+mopt) Not equal to 0, but still as the best moving path (k) in order to avoid missing the global optimal solutionopt,nopt,mopt) And the contraindication amount is set to 0. The parameters are updated as follows:
Figure BDA0003133757190000104
Tmove(nopt,(kopt-1)M+mopt)＝0
(4.4.2) current optimal solution vector
Figure BDA0003133757190000105
Cannot be updated:
in this case, a poor solution is accepted, and a moving path (k) to be selectedopt,nopt,mopt) The access is prohibited in the subsequent P iterations, and the direction different from the access is searched. Updating a taboo table:
Tmove(nopt,(kopt-1)M+mopt)＝P
(5) and (5) judging the termination condition. To obtain a satisfactory solution xbestJudging 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 P1bestObtaining 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 BDA0003133757190000111
Is the global optimal solution x to be solvedbestThe algorithm will terminate the iteration, i.e.
Figure BDA0003133757190000112
The residual signal energy in the system at the moment
Figure BDA0003133757190000113
Expressed as:
Figure BDA0003133757190000114
considering noise factor, the energy of the residual signal
Figure BDA0003133757190000115
Can be further expressed as
Figure BDA0003133757190000116
The system noise is 0 in mean and sigma in variance2White gaussian noise. Thus, the above formula can be further represented as
Figure BDA0003133757190000117
Where L is the length of the spreading sequence, the iteration termination condition may be set as:
Figure BDA0003133757190000118
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 iterations, the residual energy easily reaches the iteration termination condition, and therefore, the search is stopped, the performance of the algorithm is poor, and therefore, a parameter beta is introducedthAnd 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 betathThe value of (b) can be obtained by experiments.
Figure BDA0003133757190000119
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 the bit error rate simulation performed by 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, it can be found that the invention shows better detection performance than the traditional MMSE-SIC algorithm, and the detection performance is close to that of the Enhanced-TS algorithm, and both approach to the limit performance under the ideal condition.
In the following, the calculation complexity of the four detection algorithms is analyzed, for convenience of comparison, the number of floating point operations (FLOPs) is used herein to reflect the complexity of each algorithm, and one complex multiplication (division) method and one 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 BDA0003133757190000121
Different from the ML receiver, the complexity of the GA-TS multi-user detection algorithm provided by the invention can not grow exponentially 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 (6)

1. A NOMA multi-user detection algorithm of a hybrid greedy and tabu search strategy is characterized in that: comprises the following steps:
step (1), inputting parameters necessary for algorithm operation;
step (2), converting the multi-user detection problem into a target optimization problem P1;
and (3) randomly generating an initial solution in the generation process of the greedy strategy auxiliary algorithm initial solution
Figure FDA0003133757180000011
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 FDA0003133757180000012
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 FDA0003133757180000013
In the neighborhood space
Figure FDA0003133757180000014
Local search is performed to determine the current best movement (k) according to the preference criteriaopt,nopt,mopt) According to a tabu table TmoveCarrying out tabu and moving operations, and updating each parameter after the iteration;
step (5), in the judgment of termination condition, obtaining satisfactory solution xbestJudging 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 P1bestAnd (4) obtaining the multi-channel user information to be recovered in the signal detection process, and returning to the step (4) if not.
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 sigma2The received signal can be represented byThe expression:
Figure FDA0003133757180000015
(symbol)
Figure FDA0003133757180000016
denotes the element dot product operator, y ═ y1,…,yl,…,yL]TIs a received symbol vector of dimension L x 1,
Figure FDA0003133757180000017
represents an equivalent channel gain matrix combining channel gain and spreading sequence, n-CN (0, sigma)2IL) Is complex white gaussian 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 (2), a signal detection problem of a plurality of user information is recovered from the superposed signal y by the receiving end of the NOMA system, a process of solving a minimum value of a combined optimization problem is modeled, and a metric function of ML detection is used as an objective function of the combined optimization problem P1:
Figure FDA0003133757180000018
where the neighborhood is
Figure FDA0003133757180000019
Is a solution
Figure FDA00031337571800000110
By a neighborhood function
Figure FDA00031337571800000111
The set of the generated data is then generated,
Figure FDA00031337571800000112
contained in S, which is the entire solution space, if there is one solution vector x for all K usersbestSatisfy omega (x)best) Less than or equal to omega (x), then solving vector xbestIs a globally optimal solution.
4. 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 target optimization problem P1, and an initial solution is randomly generated
Figure FDA0003133757180000021
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 FDA0003133757180000022
The method comprises the following steps:
step (3.1) of obtaining (G)Hy) and matrix GHThe real part of the element of the triangle on G, let V ═ Re [ (G)Hy)]| and W ═ Re (G)HG) 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) of sequencing the elements of the triangular parts on V and W in descending order to form a group containing
Figure FDA0003133757180000023
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 FDA0003133757180000024
Step (3.4), to the random initial value
Figure FDA0003133757180000025
And (5) correcting: judging the first element of the sequence X obtained after descending order arrangement, if X is1＝|ViIf, then a vector is generated, by exchange
Figure FDA0003133757180000026
X in (2)iObtaining the corresponding likelihood function values for the possible M values, and selecting x which makes the likelihood function obtain the maximum valueiAs a
Figure FDA0003133757180000027
If X is1＝|WijIf l, then M is generated2Group vectors, by permutation
Figure FDA0003133757180000028
X in (2)iAnd xjTo possible M2Selecting a value combination to obtain the corresponding likelihood function value, and selecting x for making the likelihood function maximumiAnd xjReplacement of
Figure FDA0003133757180000029
X in (2)iAnd xjThereby obtaining
Figure FDA00031337571800000210
Step (3.5), the corrected initial solution is processed
Figure FDA00031337571800000211
As an initial solution to the TS-MUD algorithm, an iteration is performed.
5. The NOMA multi-user detection algorithm for a hybrid greedy and tabu search strategy of claim 1, wherein: the step (4) is carried out
Figure FDA00031337571800000212
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 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 FDA00031337571800000213
(k＝1,2,…,K)，
Figure FDA00031337571800000214
Is a set of M-PSK constellation points to be associated with a current symbol xkThe N constellation points with the nearest Euclidean distance are taken as the symbol neighborhood of the current symbol and are recorded as
Figure FDA00031337571800000220
For the currently input solution vector x containing K users, KN vector neighborhoods are correspondingly generated, and a neighborhood function is used
Figure FDA00031337571800000215
Characterizing the mapping relationship, the solution vector x is passed through the neighborhood function
Figure FDA00031337571800000216
Then, generating a candidate solution set composed of all vector neighborhoods
Figure FDA00031337571800000217
Expressed in matrix form as follows:
Figure FDA00031337571800000218
Figure FDA00031337571800000219
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 FDA0003133757180000031
In each iteration, the pairs belonging to the neighborhood belong to the minimization criterion of the objective function in the question P1
Figure FDA0003133757180000032
All column vectors η ofiEvaluating, and selecting the best neighborhood solution vector, i.e. local optimal solution xoptBecomes 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 timemThe column vector η of the nth symbol neighborhood(k-1)N+nAs the initial solution of the next iteration, the optimal moving direction of the iteration is recorded as (k)opt,nopt,mopt) 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, we determine the best move operation (k)opt,nopt,mopt) Is the vector neighborhood that minimizes the value of the objective function
Figure FDA0003133757180000033
Corresponding shift (k, n, m), i.e.
Figure FDA0003133757180000034
Step (4.3), selecting a privileged mechanism and a taboo mechanism:
according to the optimal movement (k)opt,nopt,mopt) The selected candidate solution function value is judged, and if the following formula is satisfied, the current optimal solution is decoded according to the privilege mechanism(Vector)
Figure FDA0003133757180000035
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 FDA0003133757180000036
by establishing a tabu table TmoveTo realize the tabu mechanism, tabu table TmoveIs an N x KM matrix (M is the modulation order) containing all possible moving paths, TmoveThe 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 TmoveWriting into:
Figure FDA0003133757180000037
if the best shift operation selected in this iteration is (k)opt,nopt,mopt) Otherwise, it is forbidden to show Tmove(n) thopt,(kopt-1)M+mopt) The item updates the parameters according to the rule of step (4.4.1);
step (4.3.1), checking a contraindication table:
contraindication list TmoveChecking the movement path (k)opt,nopt,mopt) 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):
Tmove(nopt,(kopt-1)M+mopt)＝＝0
otherwise, this duplicate movement path (k) is deleted from the movement set Move by the following operationopt,nopt,mopt) And returning to the step (4.2), wherein the operator represents deleting from the setExcept for element, if all movement paths are disabled, resulting in Move being empty, go to step (4.3.2)
Move(t)＝Move(t)\(kopt,nopt,mopt)
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 iterationopt,nopt,mopt) The specific operation is shown in the following formula, and the process goes to the step (4.4.1);
[nopt,(kopt-1)M+mopt]＝find(Tmove＝＝min(min(Tmove)))
and (4.4) updating parameters:
according to the optimal moving path (k) in the step (4.3)opt,nopt,mopt) First, uniformly updating the initial solution x of the next iteration(t+1)And tabu watch Tmove：
Figure FDA0003133757180000041
Tmove＝max(Tmove-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 FDA0003133757180000042
Is updated:
updating the optimal solution vector at the beginning of the next iteration
Figure FDA0003133757180000043
The algorithm judges to obtain the current moving path (k)opt,nopt,mopt) Is an optional direction, and furthermore, according to the privilege criterion, even if the movement path is nearestIs forbidden in iteration, that is to say Tmove(nopt,(kopt-1)M+mopt) Not equal to 0, but still as the best moving path (k) in order to avoid missing the global optimal solutionopt,nopt,mopt) And the taboo amount is set to 0, and the parameters are updated according to the following modes:
Figure FDA0003133757180000044
Tmove(nopt,(kopt-1)M+mopt)＝0
step (4.4.2), current optimal solution vector
Figure FDA0003133757180000045
Cannot be updated:
at this time, the inferior solution is accepted, and the moving path (k) to be selectedopt,nopt,mopt) 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 ismove(nopt,(kopt-1)M+mopt)＝P。
6. 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 xbestJudging 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 P1bestAnd obtaining the multi-channel user information to be recovered in the signal detection process, and returning to the step 4 if not.
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