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

Abstract

The invention discloses a NOMA multi-user detection algorithm with a mixed greedy and taboo search strategy, which improves the problem that the connection capability of 5G mobile communication users needs to be enhanced in the prior art. The invention contains the following specific steps: (1) input the parameters necessary for the operation of the algorithm; (2) convert the multi-user detection problem into the target optimization problem P1; (3) use the local optimal solution as the initial solution of the tabu search algorithm

(4) Use the tabu search strategy to solve the combinatorial optimization problem P1; (5) In the judgment of the termination condition, take the satisfied solution x _best as the termination condition of the iteration, and judge whether the iteration reaches the set termination condition, and if so, output the search result. The global optimal solution x _best of the combinatorial optimization problem P1 is obtained, and the multi-channel user information to be recovered in the signal detection process is obtained, otherwise, return to step (4). This technology greatly reduces the number of iterations, shortens the processing delay, and is suitable for scenarios that are sensitive to delays.

Description

A NOMA Multi-User Detection Algorithm Based on Hybrid Greedy and Tabu Search Strategies

technical field

The present invention relates to the technical field of wireless communication, in particular to a NOMA multi-user detection algorithm combining greedy and taboo search strategies.

Background technique

With the commercialization of the fifth generation (5th Generation, 5G) mobile communication system, a large number of mobile devices are connected to the system, which leads to discussions on how to improve the spectral efficiency. Non-Orthogonal Multiple Access (NOMA) access scheme usually actively introduces interference at the transmitting end, superimposes multiple signals on the same physical resource block in a non-orthogonal manner, and then sends it out, and the receiving end uses The advanced multi-user detection technology recovers various signals from the superimposed signals and realizes demodulation. Compared with orthogonal multiple access, it has obvious technical advantages in improving spectral efficiency and enhancing user connection capability, which is a further development of mobile communication. One of the key technologies of the system.

However, the inherent multiple access interference of NOMA system hinders the signal detection process at the receiving end, which is equivalent to using complex receiver design in exchange for the improvement of spectral efficiency. Therefore, a key point of NOMA technology implementation is the design of high-performance and low-complexity signal detection algorithms. In the technical report TR 38.812 entitled "Study on non-orthogonal multiple access (NOMA) for NR", 3GPP divides uplink non-orthogonal multiple access technologies into three categories: symbol-level linear extension, bit-level interleaving/scrambling code superposition and multidimensional sparse expansion. Among them, the symbol-level linear extension type non-orthogonal multiple access technology, represented by Multi-User Shared Access (MUSA), uses a short non-orthogonal spreading code, and the receiving end uses a relatively simple hardware Interference cancellation. End users/devices can independently select non-orthogonal spreading codes at any time, which can better support contention-free scheduling scenarios. Therefore, such non-orthogonal multiple access technologies have received extensive attention.

For symbol-level linear extension NOMA-like systems, the optimal detection algorithm is Maximum Likelihood (ML) detection. The ML algorithm minimizes the Euclidean distance between the received signal vector and the product of all possible transmitted signal vectors and the equivalent channel, which is essentially an exhaustive search algorithm. Its complexity increases sharply with the increase of the modulation order and the number of users, and the complexity is extremely high, which cannot be used in engineering practice.

Yuan Z et al. in IEEE 83rd Vehicular Technology Conference (VTC Spring). IEEE, 2016: 1-5 in the article "Multi-User Shared Access for Internet of Things" proposed a serial interference cancellation based on minimum mean square error (MMSE) -SIC) algorithm for multi-user detection technology. However, the SIC algorithm suffers from an error propagation problem that degrades the multi-user detection performance. Additionally, this accumulation is more common in NOMA systems due to the imprecision of the initial linear solution. In order to deal with this error propagation phenomenon, the article "Performance Analysis of MUSA with Different Spreading Codes Using OrderedSIC Methods" by Eid E M et al. in the 12th International Conference on Computer Engineering and Systems (ICCES).IEEE, 2017:101-106 proposed SIC detection method based on signal-to-interference-noise ratio ranking to reduce errors in the detection process. However, the MMSE-SIC algorithm can only detect one user at a time, and the interference is eliminated one by one in a serial manner, which has high algorithm complexity and long processing delay.

The vigorous development of artificial intelligence provides new ideas for optimizing wireless communication systems. The article "An Enhanced Tabu Search based Receiver for Full-spreading NOMA Systems" by Jung I et al. in IEEEAccess, 2019, 7:159899-159917 utilizes meta-heuristic algorithms in the field of artificial intelligence, and considers the multi-user detection problem of NOMA systems as a combination To solve the optimization problem, use the tabu search algorithm to find its approximate optimal solution, and finally obtain a good detection performance that is close to the best. However, the disadvantage of the algorithm is that the number of iterations is large and the detection complexity is high.

SUMMARY OF THE INVENTION

The invention improves the problem that the connection capability of 5G mobile communication users needs to be enhanced in the prior art, and provides a NOMA multi-user detection algorithm that can be used for the mixed greedy and taboo search strategies of the symbol-level linear expansion type non-orthogonal multiple access system. .

借助贪婪算法的思想，对随机产生的算法初始解进行修正，得到一个局部最优解，将局部最优解作为禁忌搜索算法的起始解

The technical solution of the present invention is to provide a NOMA multi-user detection algorithm with a mixed greedy and tabu search strategy with the following steps: including the following specific steps: step (1), input parameters necessary for the operation of the algorithm; step (2) , convert the multi-user detection problem into a combinatorial optimization problem P1; step (3), in the process of generating the initial solution of the greedy strategy-assisted algorithm, an initial solution is randomly generated

With the help of the idea of greedy algorithm, the initial solution of the algorithm generated randomly is modified to obtain a local optimal solution, and the local optimal solution is used as the initial solution of the tabu search algorithm.

在邻域空间

内进行局部搜索，根据选优准则确定当前最佳移动(k_opt,n_opt,m_opt)，并根据禁忌表T_move进行禁忌和移动操作，更新本次迭代后的各个参数；Step (4), using the tabu search strategy to solve the combinatorial optimization problem P1, including generating the neighborhood of the current solution vector x through the neighborhood function

in the neighborhood space

Perform a local search inside, determine the current best move (k _opt , n _opt , m _opt ) according to the selection criteria, and perform taboo and move operations according to the taboo table T _move , and update each parameter after this iteration;

Step (5), in the termination condition determination, take the satisfied solution x _best as the iteration termination condition, and judge whether the iteration reaches the set termination condition, if so, output the searched global optimal solution x _best of the combinatorial optimization problem P1, Multi-channel user information to be recovered in the acquired signal detection process, otherwise return to step (4).

Preferably, the step (1) contains the following steps:

Step (1.1), using ideal channel estimation to obtain the received signal y, the equivalent channel gain matrix G, and the noise power σ ² , the received signal can be expressed by the following formula:

表示元素点乘运算符，y＝[y₁,…,y_l,…,y_L]^T是L×1维度的接收符号向量，

表示结合了信道增益和扩频序列的等效信道增益矩阵，n～CN(0,σ²I_L)是复高斯白噪声；symbol

represents the element-wise dot product operator, y=[y ₁ ,…,y _l ,…,y _L ] ^T is the received symbol vector of dimension L×1,

represents the equivalent channel gain matrix combining channel gain and spreading sequence, n～CN(0,σ ² I _L ) is complex white Gaussian noise;

Step (1.2), input the number of users K, the modulation order M, set the number of symbol neighborhoods N, and the taboo step size P.

Preferably, in the step (2), the signal detection problem in which the NOMA system receiver recovers multiple user information from the superimposed signal y is modeled as a process of finding the minimum value of a combinatorial optimization problem P1. The metric function is used as the objective function of this combinatorial optimization problem P1:

为一个解

通过一个邻域函数

生成的集合，

包含于S，S是整个解空间，对于所有K个用户，如果存在一个解向量x_best满足Ω(x_best)≤Ω(x)，则解向量x_best就是一个全局最优解。where the neighborhood

for a solution

through a neighborhood function

generated collection,

Contained in S, S is the entire solution space. For all K users, if there is a solution vector x _best satisfying Ω(x _best )≤Ω(x), then the solution vector x _best is a global optimal solution.

借助贪婪算法的思想，对随机产生的算法初始解进行修正，得到一个局部最优解，再将这一局部最优解作为禁忌搜索算法的起始解

其步骤如下：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

With the help of the idea of greedy algorithm, the initial solution of the algorithm generated randomly is modified to obtain a local optimal solution, and then this local optimal solution is used as the initial solution of the tabu search algorithm.

The steps are as follows:

Step (3.1), find ( ^GH y) and the real part of the upper triangular elements of the matrix ^GH G, let V=|Re[( ^GH y)]| and W=|Re( ^GH G)|, It can be seen that V is a K × 1-dimensional column vector, and W is a K × K-dimensional square matrix whose lower triangular part is 0;

个元素的序列X；Step (3.2), sort the elements of the upper triangular part of V and W in descending order to form a

a sequence X of elements;

Step (3.3), initialization, take the randomly generated initial solution as the initial value of this optimization algorithm

进行修正：对降序排列后得到的序列X的第一个元素进行判断，如果X₁＝|V_i|，则产生M个矢量，通过换

中的x_i分别为可能的M种取值，得到对应的似然函数值，选出使似然函数取得最大值的x_i，作为

如果X₁＝|W_ij|，则产生M²组矢量，通过换

中的x_i和x_j为可能的M²种取值组合，求出对应的似然函数值，同样选出使似然函数取得最大值的x_i和x_j替换

中的x_i和x_j从而得到

Step (3.4), for random initial value

Correction: Judging the first element of the sequence X obtained after sorting in descending order, if X ₁ =|V _i |, then generate M vectors, by changing

The x _i in the are respectively the possible M values, the corresponding likelihood function value is obtained, and the x _i that makes the likelihood function get the maximum value is selected as

If X ₁ =|W _ij |, then generate M ² sets of vectors, by changing

The x _i and x _j in the M are the possible M ² value combinations, and the corresponding likelihood function value is obtained. Similarly, the x _i and x _j that make the likelihood function achieve the maximum value are selected to replace

x _i and x _j in so that we get

作为TS-MUD算法的初始解，进行迭代。Step (3.5), the corrected initial solution

As the initial solution of the TS-MUD algorithm, an iteration is performed.

作为初始解，利用禁忌搜索策略对组合优化问题P1进行求解，其步骤如下：Preferably, the step (4) starts with

As the initial solution, use the tabu search strategy to solve the combinatorial optimization problem P1. The steps are as follows:

Step (4.1), the generation of the current solution vector neighborhood structure:

是M-PSK星座点的集合，将与当前符号x_k相邻的欧氏距离最近的N个星座点作为当前符号的符号邻域，记为

对于当前输入的包含K个用户的解向量x，对应生成KN个向量邻域，用一个邻域函数

表征这种映射关系，则将解向量x通过邻域函数

后，生成的所有向量邻域组成的候选解集

表示为如下矩阵形式：The candidate solution set with the closest Euclidean distance from the current solution vector is defined as a neighborhood by the current solution vector. First, for each symbol in the current solution vector x

is the set of M-PSK constellation points, and the N constellation points with the nearest Euclidean distance adjacent to the current symbol x _k are used as the symbol neighborhood of the current symbol, denoted as

For the current input solution vector x containing K users, correspondingly generate KN vector neighborhoods, using a neighborhood function

To characterize this mapping relationship, the solution vector x is passed through the neighborhood function

After, the candidate solution set composed of all the generated vector neighborhoods

It is represented in the following matrix form:

Step (4.2), determination of the best move:

在每次迭代中，根据组合优化问题P1中目标函数的极小化准则对属于邻域

的所有列向量η_i进行求值，选取最佳邻域解向量，即局部最优解x_opt成为下一次迭代的起始解，这一操作定义为“移动”，假设算法此次选择了第k个用户的符号q_m的第n个符号邻域所在的列向量η_(k-1)N+n作为下一次迭代初始解，就将此次迭代的最佳移动方向记为(k_opt,n_opt,m_opt)，在每次迭代中，TS算法只在集合Move的元素中取值并选择下一步；在第t次迭代中，我们确定最佳移动操作(k_opt,n_opt,m_opt)的准则是，使目标函数值最小的向量邻域

对应的移动(k,n,m)，即Tabu search is to generate a set of candidate solutions consisting of vector neighborhoods in all search spaces S from an initial solution x

In each iteration, according to the minimization criterion of the objective function in the combinatorial optimization problem P1, the pair belongs to the neighborhood

All column vectors η _i are evaluated, and the best neighborhood solution vector is selected, that is, the local optimal solution x _opt becomes the starting solution of the next iteration. This operation is defined as "moving", assuming the algorithm selects the first solution this time The column vector η _(k-1)N+n where the nth symbol neighborhood of the symbol q _m of k users is located is taken as the initial solution of the next iteration, and the optimal moving direction of this iteration is 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 chooses the next step; in the t-th iteration, we determine the optimal move operation (k _opt ,n _opt ,m _opt ) is the vector neighborhood that minimizes the value of the objective function

The corresponding movement (k,n,m), namely

Step (4.3), selection of amnesty mechanism and taboo mechanism:

作出更新，并且算法直接进入步骤(4.4.1)，否则转到步骤(4.3.1)，判断是否触发禁忌机制；Make a judgment on the candidate solution function value selected according to the optimal movement (k _opt , n _opt , m _opt ), if the following formula is satisfied, the current optimal solution vector is determined according to the amnesty mechanism

Make an update, and the algorithm goes directly to step (4.4.1), otherwise go to step (4.3.1) to determine whether the taboo mechanism is triggered;

The taboo mechanism is implemented by establishing a taboo table T _move . The taboo table T _move is an N×KM matrix (M is the modulation order), which contains all possible moving paths. The elements in T _move indicate that the moving path is prohibited. The number of iterations, also known as the taboo step, is denoted as P, the value of P can be obtained by simulation, and the taboo table T _move is written as:

If the optimal move operation selected in this iteration is (k _opt ,n _opt ,m _opt ), then the (n _opt ,(k _opt -1)M+m _opt )th item of the taboo table T _move follows step (4.4. 1) The rule update parameters;

Step (4.3.1), check the taboo table:

Compare the taboo table T _move , check whether the moving path (k _opt , n _opt , m _opt ) has been performed in the most recent P iterations, if the following conditions are met, the moving path has not been performed in the most recent P iterations, and it is not prohibited it, and the algorithm goes to step (4.4.2):

T _move (n _opt ,(k _opt -1)M+m _opt )==0

Otherwise, delete this duplicate move path (k _opt , n _opt , m _opt ) from the move set Move by the following operation, and return to step (4.2), where the operator \ represents removing an element from the set, if all Move paths are prohibited, resulting in Move is empty, then go to step (4.3.2)

Move ^(t) = Move ^(t) \(k _opt ,n _opt ,m _opt )

Step (4.3.2), accept the inferior solution and jump out of the local optimal trap:

If the move set Move is empty, select the minimum number of forbidden iterations from the vector neighborhood as the best move for this iteration (k _opt , n _opt , m _opt ), the specific operation is shown in the following formula, and go to step ( 4.4.1);

[n _opt ,(k _opt -1)M+m _opt ]=find(T _move ==min(min(T _move )))

Step (4.4), parameter update:

According to the selection of the best moving path (k _opt , n _opt , m _opt ) in step (4.3), firstly update the initial solution x ^(t+1) and tabu table T _move of the next iteration uniformly:

T _move =max(T _move -1,0)

Then go to the corresponding steps (4.4.1) and (4.4.2) according to the algorithm flow, and update other parameters in two different ways;

被更新：Step (4.4.1), the current optimal solution vector

Updated:

算法判断得出当前移动路径(k_opt,n_opt,m_opt)是一个可选方向，此外，根据特赦准则，即使该移动路径在最近的迭代中被禁止了，也就是说T_move(n_opt,(k_opt-1)M+m_opt)≠0，但是为了避免错过全局最优解，仍然会将其作为最佳移动路径(k_opt,n_opt,m_opt)，并将其禁忌量置为0，参数按以下方式更新：Update the optimal solution vector at the start of the next iteration

The algorithm judges that the current moving path (k _opt , n _opt , m _opt ) is an optional direction. In addition, according to the amnesty criterion, even if the moving path is prohibited in the most recent iteration, that is, T _move (n _opt ) ,(k _opt -1)M+m _opt )≠0, but in order to avoid missing the global optimal solution, it will still be taken as the best moving path (k _opt ,n _opt ,m _opt ), and its taboo is set to is 0, the parameters are updated as follows:

T _move (n _opt ,(k _opt -1)M+m _opt )=0

不能被更新：Step (4.4.2), the current optimal solution vector

cannot be updated:

At this time, the inferior solution is accepted, and the selected moving path (k _opt , n _opt , m _opt ) is set as taboo, access is prohibited in the subsequent P iterations, and a different direction is explored instead, and the tabu table is updated: T _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: taking obtaining a satisfactory solution x _best as the termination condition of the iteration, judging whether the iteration reaches the set termination condition, and if so, outputting the searched result of the combinatorial optimization problem P1 The global optimal solution x _best is the multi-channel user information to be recovered during the signal detection process, otherwise, return to step 4;

Compared with the prior art, the NOMA multi-user detection algorithm of the mixed greedy and tabu search strategies of the present invention has the following advantages:

1. The initial solution is generated by the greedy algorithm, which avoids the need to perform matrix inversion of the MMSE weight matrix in the existing method, and the complexity is lower, and by setting the iteration termination conditions reasonably, the number of iterations is greatly reduced, and the processing delay is shortened. It is suitable for scenarios that are sensitive to delay;

2. In the process of multi-user signal detection, the strategies of greedy algorithm and tabu search algorithm are combined, which has good global optimization ability and convergence characteristics, and the detection performance is close to the best detection performance, which is more suitable for transmission reliability requirements. High-performance, low-complexity signal detection of NOMA system can be realized in high scenarios, which promotes the better application of NOMA technology to 5G and next-generation mobile communication networks.

Description of drawings

1 is a block diagram of a symbol-level linear extension class non-orthogonal multiple access system model used in the present invention;

Fig. 2 is the flow chart of the present invention;

Fig. 3 is the concrete algorithm flow chart of the present invention;

FIG. 4 is a simulation comparison diagram of the detection performance of the present invention and the traditional NOMA system multi-user detection method.

Detailed ways

The NOMA multi-user detection algorithm of the hybrid greedy and taboo search strategy of the present invention will be further described below in conjunction with the accompanying drawings and specific embodiments: In this embodiment, in order to achieve the above purpose, the technical solutions include the following:

(1) Input the parameters necessary for the operation of the algorithm: the received signal y, the equivalent channel gain matrix G, the noise power σ ² , the number of users K, the modulation order M, the number of symbol neighborhoods N, and the taboo step size P;

(2) The signal detection problem in which the receiver of the NOMA system recovers the information of multiple users from the superimposed signal y is modeled as a process of finding the extremum of a combinatorial optimization problem P1, and the metric function of ML detection is used as the combinatorial optimization problem P1 The objective function of , solves the minimum value of P1:

为一个解

通过一个邻域函数

生成的集合，

包含于S，S是整个解空间。where the neighborhood

for a solution

through a neighborhood function

generated collection,

Contained in S, where S is the entire solution space.

借助贪婪算法的思想，对随机产生的算法初始解进行修正，得到一个局部最优解，再将这一局部最优解作为禁忌搜索算法的起始解

(3) The greedy strategy assists the generation of the initial solution of the algorithm. Randomly generate an initial solution

With the help of the idea of greedy algorithm, the initial solution of the algorithm generated randomly is modified to obtain a local optimal solution, and then this local optimal solution is used as the initial solution of the tabu search algorithm.

在邻域空间

内进行局部搜索，根据选优准则确定当前最佳移动(k_opt,n_opt,m_opt)，并根据禁忌表T_move进行禁忌和移动操作，更新本次迭代后的各个参数；(4) Use the tabu search strategy to solve the combinatorial optimization problem P1, including generating the neighborhood of the current solution vector x through the neighborhood function

in the neighborhood space

Perform a local search inside, determine the current best move (k _opt , n _opt , m _opt ) according to the selection criteria, and perform taboo and move operations according to the taboo table T _move , and update each parameter after this iteration;

(5) Take the satisfied solution x _best as the iteration termination condition, and judge whether the iteration reaches the set termination condition. If so, output the searched global optimal solution x _best of the combinatorial optimization problem P1, and the acquired signal needs to be recovered during the detection process. multi-channel user information, otherwise, return 4);

The specific embodiments and effects of the present invention will be further described below with reference to the accompanying drawings. Referring to FIG. 1 , the symbol-level linear extension type non-orthogonal multiple access system applied in the present invention is composed of K single-antenna users and a single-antenna base station. It is assumed that K non-orthogonal users share the same time-frequency resource. At the transmitting end, the data bits d _k and d _k of the kth user are firstly channel-coded by an encoder with a code rate of R to generate the encoded bits _ck =[ _ck (1),...,c _k (τ )], where τ is the length of the coded _{bits ck} , which is then modulated by a modulator, such as an M-QAM modulator, where M is the size of the quadrature amplitude modulation (QAM) constellation, to generate modulated symbols

是调制符号的星座点集合，调制阶数为

x _k = [x _k (1),...,x _k (τ/log2(M))], where for any user k, we have

is the set of constellation points of modulation symbols, and the modulation order is

For the convenience of description, assuming that each user k contains only one modulation symbol, the modulated symbol vector x is denoted as x=[x ₁ , . . . , x _K ] ^T . Further, extend it with an extension sequence of length L _sk =[s _1,k ,...,s _l,k ,...,s _L,k ] ^T to obtain an expanded symbol t _k =s _k ·x _k = [t _1,k ,...,t _l,k ,...,t _L,k ] ^T and transmit it, it is defined that when K>L is satisfied, the system is in an overload state.

Referring to Figure 2 and Figure 3, the present invention is based on the multi-user detection algorithm of the mixed greedy and tabu search strategies of the symbol-level linear extension class non-orthogonal multiple access system of Figure 1, and the implementation steps are as follows:

(1) Input the parameters necessary for the operation of the algorithm;

(1.1) Using ideal channel estimation, obtain the received signal y, the equivalent channel gain matrix G, and the noise power σ ² . The received signal can be expressed by the following formula:

表示元素点乘运算符，y＝[y₁,…,y_l,…,y_L]^T是L×1维度的接收符号向量，

表示结合了信道增益和扩频序列的等效信道增益矩阵，n～CN(0,σ²I_L)是复高斯白噪声；Among them, the symbol

represents the element-wise dot product operator, y=[y ₁ ,…,y _l ,…,y _L ] ^T is the received symbol vector of dimension L×1,

represents the equivalent channel gain matrix combining channel gain and spreading sequence, n～CN(0,σ ² I _L ) is complex white Gaussian noise;

(1.2) Input the number of users K, the modulation order M, set the number of symbol neighborhoods N, and the taboo step size P;

(2) The signal detection problem in which the receiver of the NOMA system recovers the information of multiple users from the superimposed signal y is modeled as a process of finding the minimum value of a combinatorial optimization problem, and the metric function of ML detection is used as the combinatorial optimization problem P1 The objective function of :

为一个解

通过一个邻域函数

生成的集合，

包含于S，S是整个解空间。where the neighborhood

for a solution

through a neighborhood function

generated collection,

Contained in S, where S is the entire solution space.

For all K users, if there exists a solution vector x _best satisfying

Ω(x _best )≤Ω(x)

Then the solution vector x _best is a global optimal solution.

借助贪婪算法的思想，对随机产生的算法初始解进行修正，得到一个局部最优解，再将这一局部最优解作为禁忌搜索算法的起始解

(3) The greedy strategy assists the generation of the initial solution of the algorithm. Randomly generate an initial solution

With the help of the idea of greedy algorithm, the initial solution of the algorithm generated randomly is modified to obtain a local optimal solution, and then this local optimal solution is used as the initial solution of the tabu search algorithm.

(3.1) Find the real part of (G ^H y) and the elements of the upper triangle of the matrix G ^H G, let V=|Re[( ^GH y)]| and W=|Re( ^GH G)|, we can know that V is a K×1-dimensional column vector, and W is a K×K-dimensional square matrix whose lower triangular part is 0;

个元素的序列X；(3.2) Sort the elements of the upper triangular part of V and W in descending order to form a

a sequence X of elements;

(3.3) Initialization, take the randomly generated initial solution as the initial value of this optimization algorithm

进行修正：对降序排列后得到的序列X的第一个元素进行判断，如果X₁＝|V_i|，则产生M个矢量，通过换

中的x_i分别为可能的M种取值，得到对应的似然函数值，选出使似然函数取得最大值的x_i，作为

如果X₁＝|W_ij|，则产生M²组矢量，通过换

中的x_i和x_j为可能的M²种取值组合，求出对应的似然函数值，同样选出使似然函数取得最大值的x_i和x_j替换

中的x_i和x_j从而得到

(3.4) For random initial values

Correction: Judging the first element of the sequence X obtained after sorting in descending order, if X ₁ =|V _i |, then generate M vectors, by changing

The x _i in the are respectively the possible M values, the corresponding likelihood function value is obtained, and the x _i that makes the likelihood function get the maximum value is selected as

If X ₁ =|W _ij |, then generate M ² sets of vectors, by changing

The x _i and x _j in the M are the possible M ² value combinations, and the corresponding likelihood function value is obtained. Similarly, the x _i and x _j that make the likelihood function achieve the maximum value are selected to replace

x _i and x _j in so that we get

作为TS-MUD算法的初始解，进行迭代。(3.5) Put the corrected initial solution

As the initial solution of the TS-MUD algorithm, an iteration is performed.

作为初始解，利用禁忌搜索策略对组合优化问题P1进行求解；(4) with

As the initial solution, use the tabu search strategy to solve the combinatorial optimization problem P1;

(4.1) Generation of the current solution vector neighborhood structure:

是M-PSK星座点的集合，将与当前符号x_k相邻的欧氏距离最近的N个星座点作为当前符号的符号邻域，记为

那么对于当前输入的包含K个用户的解向量x，可以对应生成KN个向量邻域，我们用一个邻域函数

表征这种映射关系，则可以将解向量x通过邻域函数

后，生成的所有向量邻域组成的候选解集

表示为如下矩阵形式：The candidate solution set with the closest Euclidean distance to the current solution vector is defined as a neighborhood by the current solution vector. First for each symbol in the current solution vector x

is the set of M-PSK constellation points, and the N constellation points with the nearest Euclidean distance adjacent to the current symbol x _k are used as the symbol neighborhood of the current symbol, denoted as

Then for the current input solution vector x containing K users, KN vector neighborhoods can be generated correspondingly, we use a neighborhood function

To characterize this mapping relationship, the solution vector x can be passed through the neighborhood function

After, the candidate solution set composed of all the generated vector neighborhoods

It is represented in the following matrix form:

(4.2) Determination of the best move:

在每次迭代中，根据组合优化问题P1中目标函数的极小化准则对属于邻域

的所有列向量η_i进行求值，选取最佳邻域解向量，即局部最优解x_opt成为下一次迭代的起始解，这一操作定义为“移动”。假设算法此次选择了第k个用户的符号q_m的第n个符号邻域所在的列向量η_(k-1)N+n作为下一次迭代初始解，就可以将此次迭代的最佳移动方向记为(k_opt,n_opt,m_opt)。在每次迭代中，TS算法只在集合Move的元素中取值并选择下一步。在第t次迭代中，确定最佳移动操作(k_opt,n_opt,m_opt)的准则是，使目标函数值最小的向量邻域

对应的移动(k,n,m)，即Tabu search is to generate a set of candidate solutions consisting of vector neighborhoods in all search spaces S from an initial solution x

In each iteration, according to the minimization criterion of the objective function in the combinatorial optimization problem P1, the pair belongs to the neighborhood

All column vectors η _i of are evaluated, and the best neighborhood solution vector is selected, that is, the local optimal solution x _opt becomes the starting solution of the next iteration, and this operation is defined as "moving". Assuming that the algorithm selects the column vector η _(k-1)N+n where the n-th symbol neighborhood of the k-th user's symbol q _m is located this time as the initial solution for the next iteration, the optimal solution for this iteration can be The moving direction is denoted as (k _opt ,n _opt ,m _opt ). In each iteration, the TS algorithm simply takes values in the elements of the set Move and chooses the next step. In the t-th iteration, the criterion for determining the optimal move operation (k _opt , n _opt , m _opt ) is the vector neighborhood that minimizes the value of the objective function

The corresponding movement (k,n,m), namely

(4.3) Selection of amnesty mechanism and taboo mechanism:

作出更新，并且算法直接进入步骤(4.4.1)，否则转到步骤(4.3.1)，判断是否触发禁忌机制。Make a judgment on the candidate solution function value selected according to the optimal movement (k _opt , n _opt , m _opt ), if the following formula can be satisfied, the current optimal solution vector is determined according to the amnesty mechanism

An update is made, and the algorithm goes directly to step (4.4.1), otherwise it goes to step (4.3.1) to determine whether the taboo mechanism is triggered.

The taboo mechanism is implemented by establishing a taboo table T _move . The taboo table T _move is an N×KM matrix (M is the modulation order), which contains all possible moving paths. The elements in T _move indicate that the moving path is prohibited. The number of iterations, also known as the taboo step, is denoted as P, and the value of P can be obtained by simulation. Therefore, the taboo table T _move can be written as:

If the optimal move operation selected in this iteration is (k _opt ,n _opt ,m _opt ), then the (n _opt ,(k _opt -1)M+m _opt )th item of the taboo table T _move follows step (4.4. 1) The rules update parameters.

(4.3.1) Check the taboo table:

Check whether the move path (k _opt , n _opt , m _opt ) has been performed in the most recent P iterations against the taboo table T _move . If the following conditions are met, the move path has not been executed in the last P iterations, it is not prohibited, and the algorithm goes to step (4.4.2):

T _move (n _opt ,(k _opt -1)M+m _opt )==0

Otherwise, delete this repeated move path (k _opt , n _opt , m _opt ) from the move set Move by the following operation, and return to step (4.2), where the operator \ represents removing an element from the set. If all move paths are forbidden, resulting in an empty Move, go to step (4.3.2)

Move ^(t) = Move ^(t) \(k _opt ,n _opt ,m _opt )

(4.3.2) Accept inferior solutions and jump out of the trap of local optimum:

If the move set Move is empty, select the minimum number of forbidden iterations from the vector neighborhood as the best move for this iteration (k _opt , n _opt , m _opt ), the specific operation is shown in the following formula, and go to step ( 4.4.1).

[n _opt ,(k _opt -1)M+m _opt ]=find(T _move ==min(min(T _move )))

Step (4.4) parameter update:

According to the selection of the best moving path (k _opt , n _opt , m _opt ) in step (4.3), firstly update the initial solution x ^(t+1) and tabu table T _move of the next iteration uniformly:

T _move =max(T _move -1,0)

Then go to the corresponding steps (4.4.1) and (4.4.2) according to the algorithm flow, and update other parameters in two different ways.

可以被更新：(4.4.1) Current optimal solution vector

can be updated:

算法判断得出当前移动路径(k_opt,n_opt,m_opt)是一个可选方向。此外，根据特赦准则，即使该移动路径在最近的迭代中被禁止了，也就是说T_move(n_opt,(k_opt-1)M+m_opt)≠0，但是为了避免错过全局最优解，仍然会将其作为最佳移动路径(k_opt,n_opt,m_opt)，并将其禁忌量置为0。参数按以下方式更新：Update the optimal solution vector at the start of the next iteration

The algorithm determines that the current moving path (k _opt , n _opt , m _opt ) is an optional direction. Furthermore, according to the amnesty criterion, even if the move path is forbidden in the most recent iteration, that is, T _move (n _opt ,(k _opt -1)M+m _opt )≠0, in order to avoid missing the global optimal solution , it will still be used as the optimal moving path (k _opt ,n _opt ,m _opt ), and its taboo is set to 0. Parameters are updated as follows:

T _move (n _opt ,(k _opt -1)M+m _opt )=0

不能被更新：(4.4.2) Current optimal solution vector

cannot be updated:

In this case, the inferior solution is accepted, and the chosen travel path (k _opt , n _opt , m _opt ) is made taboo, and access is prohibited for the subsequent P iterations, and a different direction is explored instead. Update the taboo table:

T _move (n _opt ,(k _opt -1)M+m _opt )=P

(5) Judgment of termination conditions. Taking the satisfied solution x _best as the iteration termination condition, judge whether the iteration reaches the set termination condition, if so, output the searched global optimal solution x _best of the combinatorial optimization problem P1, and obtain the multi-path to be restored in the process of signal detection. User information, otherwise, return 4);

就是欲求解的全局最优解x_best，算法将终止迭代，即Specifically, it is assumed that at the t-th iteration, the optimal solution after the algorithm updates the parameters

is the global optimal solution x _best to be solved, and the algorithm will terminate the iteration, that is,

表示为：The residual signal energy in the system at this time

Expressed as:

可进一步表示为Considering the noise factor, the energy of the residual signal

can be further expressed as

Since the system noise is Gaussian white noise with mean 0 and variance σ ² . Therefore, the above formula can be further expressed as

Among them, L is the length of the spreading sequence, then the iteration termination condition can be set as:

That is, when the energy of the residual signal is less than or equal to L times the noise power, a satisfactory solution is obtained, and the algorithm stops iterating.

Further, considering that in the case of low signal-to-noise ratio, the noise power is relatively large, the algorithm may only go through a small number of iterations, and the residual energy easily reaches the iteration termination condition, thus stopping the search, resulting in poor algorithm performance, so the parameter β _th is introduced as the minimum value. Iterative threshold is used to ensure sufficient iterative search, and it is combined with noise power to control the iterative termination condition. If the following formula is satisfied, the algorithm terminates the iteration. Otherwise, t=t+1, return to step 1. The value of the threshold β _th can be obtained through experiments.

This can not only ensure the search performance of the TS algorithm under low signal-to-noise ratio, but also avoid repeated search after the TS algorithm converges under high signal-to-noise ratio, which brings high computational complexity. So far, the signal detection is completed.

The effect of the present invention can be further illustrated by the following simulation:

1. Simulation conditions

The simulation uses the MUSA system, which consists of 6 single-antenna users and a single-antenna base station. The system overload rate is 150%. QPSK modulation is used. The elements of the spreading sequence are selected from {1, i, -1, -i}. The frequency length L=4, after a flat Rayleigh fading channel, the receiving end adopts the ideal channel estimation, and the taboo step size is set to P=15.

2. Simulation content

The present invention and three existing signal detection methods are used for bit error rate simulation, and the results are shown in Figure 4. The abscissa of Fig. 4 is the signal-to-noise ratio, and the ordinate is the bit error rate of the system. in:

The ML curve is the maximum likelihood detection performance, which represents the optimal detection performance of the system obtained by an exhaustive search in an ideal case.

The MMSE-SIC curve refers to the detection performance of the existing minimum mean square error serial interference cancellation algorithm, and its detection performance is affected by the error propagation effect, which is far from the optimal detection performance.

The Enhanced-TS curve refers to the detection performance of the existing enhanced tabu search algorithm, proposed by Jung I et al., and obtained a good performance approaching ML detection.

The GA-TS curve refers to the detection performance of the algorithm proposed in the present invention.

Comparing the bit error rate performance of the present invention and the traditional multi-user detection algorithm, it can be found that the present invention shows better detection performance than the traditional MMSE-SIC algorithm, and is close to the detection performance of the Enhanced-TS algorithm, both approaching the ideal condition. extreme performance.

The computational complexity of the four detection algorithms is analyzed below. In order to facilitate comparison, this paper uses the number of floating point operations (FLOPs) to reflect the complexity of each algorithm, a complex multiplication (division) method and a complex addition (subtraction) ) method corresponds to 6 floating-point operations and 2 floating-point operations, respectively.

Table 1. Complexity analysis of multi-user detection algorithm in MUSA system

Different from the ML receiver, the complexity of the GA-TS multi-user detection algorithm proposed in the present invention does not increase exponentially with the increase of the number of users or the modulation order, and the complexity is acceptable, and it can be seen that at the same iteration Under the number of times, the complexity of the Enhanced-TS algorithm is obviously higher than that of the proposed GA-TS algorithm due to the inversion of the weight matrix.

To sum up, the detection performance of the present invention is close to the performance of 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 mixed greed and taboo search strategy, is characterized in that: contain following concrete steps: Step (1), input the parameters necessary for the operation of the algorithm; Step (2), convert the multi-user detection problem into a combinatorial optimization problem P1; the signal detection problem in which the NOMA system receiver recovers multiple user information from the superimposed signal y is modeled as a combinatorial optimization problem P1 to find the minimum value The process of taking the metric function of ML detection as the objective function of the combinatorial optimization problem P1:

where the neighborhood

for a solution

through a neighborhood function

generated collection,

Contained in S, S is the entire solution space. For all K users, if there is a solution vector x _best that satisfies Ω(x _best )≤Ω(x), then the solution vector x _best is a global optimal solution; Step (3), in the process of generating the initial solution of the greedy strategy-assisted algorithm, an initial solution is randomly generated.

With the help of the idea of greedy algorithm, the initial solution of the algorithm generated randomly is modified to obtain a local optimal solution, and the local optimal solution is used as the initial solution of the tabu search algorithm.

Step (4), using the tabu search strategy to solve the combinatorial optimization problem P1, including generating the neighborhood of the current solution vector x through the neighborhood function

in the neighborhood space

Perform a local search inside, determine the current best move (k _opt , n _opt , m _opt ) according to the selection criteria, and perform taboo and move operations according to the taboo table T _move , and update each parameter after this iteration; Step (5), in the termination condition determination, take the satisfied solution x _best as the iteration termination condition, and judge whether the iteration reaches the set termination condition, if so, output the searched global optimal solution x _best of the combinatorial optimization problem P1, That is, the multi-channel user information to be recovered in the signal detection process is obtained, otherwise, return to step (4). 2. the NOMA multi-user detection algorithm of hybrid greedy and taboo search strategy according to claim 1, is characterized in that: described step (1) contains following steps: Step (1.1), using ideal channel estimation to obtain the received signal y, the equivalent channel gain matrix G, and the noise power σ ² , the received signal can be expressed by the following formula:

=Gx+n symbol

represents the element-wise dot product operator, y=[y ₁ ,…,y _l ,…,y _L ] ^T is the received symbol vector of dimension L×1,

represents the equivalent channel gain matrix combining channel gain and spreading sequence, n～CN(0,σ ² I _L ) is complex white Gaussian noise; Step (1.2), input the number of users K, the modulation order M, set the number of symbol neighborhoods N, and the taboo step size P. 3. the NOMA multi-user detection algorithm of hybrid greedy and taboo search strategy according to claim 1, is characterized in that: in described step (3), multi-user detection problem is converted into combinatorial optimization problem P1, an initial solution is randomly generated

With the help of the idea of greedy algorithm, the initial solution of the algorithm generated randomly is modified to obtain a local optimal solution, and then this local optimal solution is used as the initial solution of the tabu search algorithm.

The steps are as follows: Step (3.1), find ( ^GH y) and the real part of the upper triangular elements of the matrix ^GH G, let V=|Re[( ^GH y)]| and W=|Re( ^GH G)|, It can be seen that V is a K × 1-dimensional column vector, and W is a K × K-dimensional square matrix whose lower triangular part is 0; Step (3.2), sort the elements of the upper triangular part of V and W in descending order to form a

a sequence X of elements; Step (3.3), initialization, take the randomly generated initial solution as the initial value of this optimization algorithm

Step (3.4), for random initial value

Correction: Judging the first element of the sequence X obtained after sorting in descending order, if X ₁ =|V _i |, then generate M vectors, by changing

The x _i in the are respectively the possible M values, the corresponding likelihood function value is obtained, and the x _i that makes the likelihood function get the maximum value is selected as

If X ₁ =|W _ij |, then generate M ² sets of vectors, by changing

The x _i and x _j in the M are the possible M ² value combinations, and the corresponding likelihood function value is obtained. Similarly, the x _i and x _j that make the likelihood function achieve the maximum value are selected to replace

x _i and x _j in so that we get

Step (3.5), the corrected initial solution

As the initial solution of the TS-MUD algorithm, an iteration is performed. 4. the NOMA multi-user detection algorithm of mixed greedy and tabu search strategy according to claim 1, is characterized in that: described step (4) is with

As the initial solution, use the tabu search strategy to solve the combinatorial optimization problem P1. The steps are as follows: Step (4.1), the generation of the current solution vector neighborhood structure: The candidate solution set with the closest Euclidean distance from the current solution vector is defined as a neighborhood by the current solution vector. First, for each symbol in the current solution vector x

is the set of M-PSK constellation points, and the N constellation points with the nearest Euclidean distance adjacent to the current symbol x _k are used as the symbol neighborhood of the current symbol, denoted as

For the current input solution vector x containing K users, KN vector neighborhoods are generated correspondingly, and a neighborhood function is used.

To characterize this mapping relationship, the solution vector x is passed through the neighborhood function

After, the candidate solution set composed of all the generated vector neighborhoods

It is represented in the following matrix form:

Step (4.2), determination of the best move: Tabu search is to generate a set of candidate solutions consisting of vector neighborhoods in all search spaces S from an initial solution x

In each iteration, according to the minimization criterion of the objective function in the combinatorial optimization problem P1, the pair belongs to the neighborhood

All column vectors η _i are evaluated, and the best neighborhood solution vector is selected, that is, the local optimal solution x _opt becomes the starting solution of the next iteration. This operation is defined as "moving", assuming the algorithm selects the first solution this time The column vector η _(k-1)N+n where the nth symbol neighborhood of the symbol q _m of k users is located is taken as the initial solution of the next iteration, and the optimal moving direction of this iteration is 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, determine the optimal move operation (k _opt ,n _opt ,m _opt ) ) is the vector neighborhood that minimizes the value of the objective function

The corresponding movement (k,n,m), namely

Step (4.3), selection of amnesty mechanism and taboo mechanism: Make a judgment on the candidate solution function value selected according to the optimal movement (k _opt , n _opt , m _opt ), if the following formula is satisfied, the current optimal solution vector is determined according to the amnesty mechanism

Make an update, and the algorithm goes directly to step (4.4.1), otherwise go to step (4.3.1) to determine whether the taboo mechanism is triggered;

The taboo mechanism is implemented by establishing a taboo table T _move . The taboo table T _move is an N×KM matrix, M is the modulation order, and contains all possible moving paths. The elements in T _move represent the forbidden iterations of the moving path. The number of times, also known as the taboo step, is denoted as P, the value of P can be obtained by simulation, and the taboo table T _move is written as:

If the optimal move operation selected in this iteration is (k _opt ,n _opt ,m _opt ), then the (n _opt ,(k _opt -1)M+m _opt )th item of the taboo table T _move follows step (4.4. 1) The rule update parameters; Step (4.3.1), check the taboo table: Compare the taboo table T _move , check whether the moving path (k _opt , n _opt , m _opt ) has been performed in the most recent P iterations. If the following conditions are met, the moving path has not been performed in the most recent P iterations, and it is not prohibited it, and the algorithm goes to step (4.4.2): T _move (n _opt ,(k _opt -1)M+m _opt )==0 Otherwise, remove this duplicate move path (k _opt , n _opt , m _opt ) from the move set Move by the following operation, and return to step (4.2), where the operator \ represents removing an element from the set, if all The moving paths are all forbidden, resulting in the Move being empty, then go to step (4.3.2) Move ^(t) = Move ^(t) \(k _opt ,n _opt ,m _opt ) Step (4.3.2), accept the inferior solution and jump out of the local optimal trap: If the move set Move is empty, select the minimum number of forbidden iterations from the vector neighborhood as the best move (k _opt , n _opt , m _opt ) for this iteration, the specific operation is shown in the following formula, and go to step ( 4.4.1); [n _opt ,(k _opt -1)M+m _opt ]=find(T _move ==min(min(T _move ))) Step (4.4), parameter update: According to the selection of the best moving path (k _opt , n _opt , m _opt ) in step (4.3), firstly update the initial solution x ^(t+1) and tabu table T _move of the next iteration uniformly:

T _move =max(T _move -1,0) Then go to the corresponding steps (4.4.1) and (4.4.2) according to the algorithm flow, and update other parameters in two different ways; Step (4.4.1), the current optimal solution vector

Updated: Update the optimal solution vector at the start of the next iteration

The algorithm judges that the current moving path (k _opt ,n _opt ,m _opt ) is an optional direction. In addition, according to the amnesty criterion, even if the moving path is prohibited in the latest iteration, that is, T _move (n _opt ) ,(k _opt -1)M+m _opt )≠0, but in order to avoid missing the global optimal solution, it will still be taken as the best moving path (k _opt ,n _opt ,m _opt ), and its taboo is set to is 0, the parameters are updated as follows:

T _move (n _opt ,(k _opt -1)M+m _opt )=0 Step (4.4.2), the current optimal solution vector

cannot be updated: At this time, the inferior solution is accepted, and the selected moving path (k _opt , n _opt , m _opt ) is set as taboo, access is prohibited in the subsequent P iterations, and a different direction is explored instead, and the tabu table is updated: T _move (n _opt ,(k _opt -1)M+m _opt )=P. 5. the NOMA multi-user detection algorithm of hybrid greedy and taboo search strategy according to claim 1, is characterized in that: in described step (5), the step that termination condition is judged is as follows: be iterative termination condition to obtain satisfactory solution x _best , determine whether the iteration reaches the set termination condition, if so, output the searched global optimal solution x _best of the combinatorial optimization problem P1, that is, the multi-channel user information to be recovered in the signal detection process, otherwise, return to step (4 ) .

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