High-order qam massive mimo signal detection method based on nested variational chain

Abstract

The application discloses a high-order QAM massive MIMO signal detection method based on a nested variational chain, and comprises the following steps: receiving a signal to be detected; and performing signal detection on the signal to be detected by using a GTA-EC algorithm to obtain a signal detection result; wherein the GTA-EC algorithm is an improved EP algorithm, in which the GTA algorithm and the EP algorithm are fused based on a nested variational chain to obtain an approximate distribution of a maximum a posteriori probability based on the fused KL divergence; and the maximum a posteriori probability is a probability of obtaining an original estimated signal under the condition that the received signal and the channel gain are known. The application can achieve a low bit error rate and low computational complexity under the conditions of a large number of transceiving antennas and high-order QAM modulation.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of communication, and particularly relates to a high-order QAM (Quadrature Amplitude Modulation) massive MIMO (Multiple Input Multiple Output) signal detection method based on nested variational chain. BACKGROUND

[0002] MIMO technology has been widely used in practical applications, and therefore a high-performance and low-complexity detection method is needed. When a high-order constellation is used, the detection problem becomes very serious. A variety of methods have been proposed to solve this problem.

[0003] The optimal detection algorithm includes the ML (Maximum Likelihood) detection algorithm in the hard decision algorithm and the MAP (Maximum A Posteriori) detection algorithm in the soft decision algorithm. The essence of the ML detection algorithm is to obtain the optimal detection effect by means of traversal. The BER (Bit Error Rate) detection effect of the ML detection algorithm has always been the evaluation standard and optimization target of the optimal BER detection effect of the detection algorithm in MIMO systems up to Massive MIMO systems. However, the computational complexity of the ML detection algorithm increases exponentially with the increase of the number of transmit antennas, and it is difficult to obtain the optimal BER detection effect within a limited polynomial complexity time. Therefore, the ML detection algorithm or the MAP detection algorithm cannot be directly applied to the actual detection of the massive MIMO system.

[0004] The suboptimal detection algorithm can be divided into linear detection algorithm and nonlinear detection algorithm according to the implementation. First, the linear detection algorithm includes MF (Matched Filtering), ZF (Zero Forcing) and MMSE (Minimum Mean Square Error) detection algorithm, etc. The computational complexity of the linear detection algorithm increases in a polynomial form with the increase of the number of transmit antennas, which is much lower than the exponential computational complexity of the optimal detection algorithm such as the ML algorithm. The ZF algorithm and the MMSE algorithm need to calculate the inverse matrix of the channel gain matrix, which increases the computational complexity in the case of a large number of antennas. The BER detection effect is relatively poor, and it is not directly applicable in the Massive MIMO system and needs to be improved and optimized.

[0005] Non-linear detection algorithms have better detection performance than linear detection algorithms. Interference cancellation-based detection algorithms, such as successive interference cancellation (SIC) and parallel interference cancellation (PIC) detection algorithms, have a polynomial computational complexity of similar order to linear detection algorithms, but the BER detection effect obtained by the algorithms is still far from the optimal ML detection algorithm. Based on the ML criterion, the sphere decoding (SD) detection algorithm appears, which is a detection method that obtains an accurate ML solution and is usually faster than brute-force enumeration. Although the search space is reduced, there is still the problem of more points to be tested due to the large radius, which causes algorithm complexity. SD and its variants are inefficient in large dimensions at low SNR, and therefore are not suitable for large-scale MIMO systems.

[0006] MAP-based detection algorithms are mainly message passing algorithms (MPA), which expand algorithm research according to the Bayesian inference method. In a large-scale system, it is difficult to obtain an accurate value due to the complexity of posterior probability calculation, and such an algorithm updates and transmits information through iteration, and approximately calculates or approximates the true value. Common message passing algorithms include belief propagation algorithm (BP), message passing algorithm using channel hardening (CHEMP), approximate message passing algorithm (AMP), and expectation propagation algorithm.

[0007] The expectation propagation (EP) algorithm is an approximate posterior distribution matrix matching algorithm in the Bayesian inference related message passing algorithm, which introduces a Gaussian distribution prior by replacing the true prior belonging to a discrete finite set, and can be updated in iteration. It is not only superior to the above detection methods, but also has lower complexity (its complexity is several times that of the maximum mean square error algorithm MMSE), and shows strong robustness to antenna configuration. Based on these advantages, various extensions, generalizations and modifications of EP have been proposed, and scenarios considering imperfect channel state information and related MIMO channels are considered.

[0008] The expectation propagation algorithm is an approximate Bayesian inference method for solving the probability distribution of random variables. Because the poor calculation of many integrands in the Bayesian model increases the difficulty of calculating the marginal distribution of the posterior distribution. Discrete random variables show exponential growth in complexity, making probability inference difficult, so finding its approximate solution is the key to solving this problem. The approximate probability distribution is determined by minimizing the KL divergence from the true posterior probability density function, and then the true value of the posterior probability distribution is approximated by continuously iterating a certain factor. The simulation results of applying the expectation algorithm to large-scale MIMO system signal detection all prove that when the model and parameters are consistent, it can realize fast and accurate inference of probability compared with other inference algorithms. The low complexity, high precision and strong robustness of EP algorithm to antenna and modulation structure have attracted the attention of more researchers, and then related optimization algorithms have been developed based on this algorithm. EP algorithm has a key disadvantage. The explicit matrix inversion in each iteration brings O(LM 3 ) complexity (L represents the number of iterations, and M represents the number of transmit antennas). As the system size increases, this will result in heavy computational burden, thus hindering its effective implementation in practice. SUMMARY

[0009] In order to solve the above problems existing in the prior art, the application provides a large-scale MIMO signal detection method based on nested variational chain high-order QAM.

[0010] The technical problems to be solved by the application are solved by the following technical solutions:

[0011] A large-scale MIMO signal detection method based on nested variational chain high-order QAM, comprising:

[0012] Receiving a signal to be detected; the signal to be detected is a high-order QAM large-scale MIMO signal;

[0013] According to the signal to be detected, a GTA-EC algorithm is used for signal detection to obtain a signal detection result;

[0014] The GTA-EC algorithm is an improved EP algorithm, and the improvement is that the KL divergence of the GTA algorithm and the EP algorithm is fused based on the nested variational chain, so as to obtain the approximate distribution of the maximum posterior probability based on the fused KL divergence. The maximum posterior probability is the probability of obtaining the original estimated signal under the condition that the received signal and the channel gain are known.

[0015] In one embodiment, the way of fusing the KL divergence of the GTA algorithm and the EP algorithm based on the nested variational chain comprises:

[0016]

[0017] in, The left side represents the maximum a posteriori probability distribution of the original estimated signal, and Q(x) represents the first distribution approximating the maximum a posteriori probability distribution obtained according to the KL divergence of the EP algorithm. represents a second distribution approximating the maximum a posteriori probability distribution obtained by embedding the first distribution into the KL divergence of the GTA algorithm; x represents the signal transmitted by the transmitter, y represents the signal to be detected received by the receiver, and H represents the channel gain.

[0018] In one embodiment, obtaining a signal detection result by using a GTA-EC algorithm according to the signal to be detected includes:

[0019] Initialization step: Initialize parameters based on the signal to be detected and initialize the message value;

[0020] Factor Substitution Step: Define the First Distribution is the maximum a posteriori probability distribution Approximate distribution of ; define distribution and distribution As a response to Q GTA-EC (x) is replaced by a factor, and the moment of r(x) is derived. and the moment of q(x)

[0021] in, Indicates that the mean is y:Hx and the variance is Gaussian distribution; is the noise variance, I is the identity matrix; x i is the i-th symbol of x, and N is the number of symbols contained in x; is the cardinality of the QAM constellation set; γ q and Λ q They are respectively distributed The mean and variance of γ; r and Λ r They are respectively The mean and variance of s(x) are γ s , the variance is Λ s ,satisfy The superscript T indicates the matrix transpose;

[0022] Inner approximation step: constructing a maximum Gaussian spanning tree based on the initial covariance matrix to establish the relationship between the tree structure and the symbol; wherein, the initial covariance matrix is ​​based on μ r ,Σ r 、μ q and Σ q Constructed;

[0023] Symbol detection step: Get the mean γ of the first distribution r(x) by achieving consistency between the distribution q(x) and the distribution s(x) s and variance Λ s , and obtain the second distribution g(x) with additional true prior based on the established maximum Gaussian spanning tree and the derived moment; update the message based on the second distribution g(x) and perform message passing, and obtain Q by achieving consistency between g(x) and s(x) GTA-EC (x) mean and variance;

[0024] in,

[0025] Indicates f q The Gaussian tree approximation of (x) has the following conditional distribution:

[0026]

[0027] p' i|pa(i) (x i ) is the distribution of the i-th symbol in g(x); is μ r The i-th element on the diagonal of Σ r The i-th element on the diagonal of μ pa(i) represents x in the q(x) distribution i The expectation of the parent node, x pa(i) Indicates that q(x) corresponds to x i The parent node, Σ i,pa(i) Represents x i and the i-th element of the covariance matrix of its parent node, Σ pa(i),pa(i) Represents x i The covariance matrix of the parent node, Σ r The i-th element on the diagonal of ;

[0028] Factor update step: Update and Thus, update q new (x) until the maximum number of iterations is reached; where, and The update formula is β represents the preset damping factor, q new (x) is the updated result of q(x);

[0029] Output step: According to the latest q new The first moment of (x) is used to obtain a hard output.

[0030] The GTA-EC algorithm provided by the embodiment of the application combines the KL divergence of the GTA algorithm and the EP algorithm in a nested manner to form an approximate chain, so that a new distribution can be obtained, which can realize satisfactory detection performance of a large-scale MIMO system at low complexity, and the bit error rate performance is better than that of the original EP algorithm, and the complexity is reduced.

[0031] The application will be further described in detail below with reference to the drawings and the application. BRIEF DESCRIPTION OF DRAWINGS

[0032] Figure 1 is a flowchart of a GTA-EC algorithm based on a nested variational chain high-order QAM large-scale MIMO signal detection method provided by the embodiment of the application;

[0033] Figure 2 The GTA-EC algorithm of the embodiment of the application and the existing algorithm are compared in terms of bit error rate SER when the number of transmission and reception antennas is 16 and the constellation is 16-QAM.

[0034] Figure 3 The GTA-EC algorithm of the embodiment of the application and the existing algorithm are compared in terms of bit error rate SER when the number of transmission and reception antennas is 16 and the constellation is 64-QAM.

[0035] Figure 4 The GTA-EC algorithm of the embodiment of the application and the existing algorithm are compared in terms of bit error rate SER when the number of transmission and reception antennas is 32 and the constellation is 16-QAM.

[0036] Figure 5 The GTA-EC algorithm of the embodiment of the application and the existing algorithm are compared in terms of bit error rate SER when the number of transmission and reception antennas is 32 and the constellation is 64-QAM.

[0037] Figure 6 The GTA-EC algorithm of the embodiment of the application and the existing algorithm are compared in terms of bit error rate SER when the number of transmission and reception antennas is 64 and the constellation is 16-QAM.

[0038] Figure 7 The GTA-EC algorithm of the embodiment of the application and the existing algorithm are compared in terms of bit error rate SER when the number of transmission and reception antennas is 64 and the constellation is 64-QAM. DETAILED DESCRIPTION

[0039] The application will be further described in detail below with reference to the drawings and the application.

[0040] As Figure 1As shown, it is assumed that each transmitter selects an arbitrary symbol from a set of Quadrature Amplitude Modulation (QAM) constellations where denotes the complex domain, and the cardinality of the constellation set is The transmitted symbols can be represented as a vector where the average energy of each QAM symbol is defined as After propagating through the wireless channel, the received signal At the base station can be represented as:

[0041]

[0042] where, represents an Additive White Gaussian Noise (AWGN) with zero mean and variance is defined as the matrix obtained by superimposing the channel coefficients where hi is the Rayleigh flat-fading channel coefficient of the ith symbol. It is assumed that perfect Channel State Information (CSI) is known at the base station. By considering the real and imaginary parts separately, the above channel model is usually re-expressed in the real domain. By defining and as the operations that take the real and imaginary parts of a variable or matrix, one can define:

[0043]

[0044]

[0045] where denotes the real domain.

[0046] The equivalent model in the real domain is then given by:

[0047] y = Hx + n.

[0048] The real domain model described above can be written in the following form:

[0049]

[0050] where the variance of each element of n is equal to The symbols in x belong to a set of Pulse Amplitude Modulation (PAM) constellations containing the real and imaginary parts of the A-QAM alphabet, whose cardinality is The average energy of the PAM symbols is The Signal-to-Noise Ratio (SNR) of the MIMO system is defined as:

[0051] ​

[0052] First assume that the transmitted symbols are uniformly distributed, denoted as where is an indicator function that constrains the value of denotes the QAM modulation constellation set. Then the posterior distribution p(x|y) is:

[0053]

[0054] Since the posterior distribution p(x|y) in the inference is difficult to obtain in MIMO detection, in order to construct an approximate distribution that belongs to the exponential family and is easy to handle, the non-Gaussian part in equation (1) can be replaced by an exponential probability density function (PDF) as follows:

[0055]

[0056] The similarity between q(x) and p(x|y) is assumed by matching the first and second moments of the two distributions, which is called the moment matching condition. However, it is infeasible to obtain γ and Λ due to the intractability of p(x|y). To overcome this problem, the sequential EP algorithm considers a posterior probability function of the form where the ith marginal distribution p(x i ) is constructed by replacing the ith Gaussian factor of the ith marginal of equation (2) with the non-Gaussian factor in equation (1) as follows:

[0057]

[0058] q(x i ) is the ith marginal of q(x), whose cavity distribution can be expressed as:

[0059]

[0060] Equation (3) can be inferred since it only contains one non-exponential factor. To this end, instead of considering the joint distribution, the moment matching between the marginal q(x i ) and for each i is considered, so that each pair of (γi, Λi) can be computed iteratively and in parallel. Obviously, the recursive update of (γ i , Λ i ) is equivalent to updating the mean vector μ and the covariance matrix Σ of the Gaussian function q(x). As the iteration process proceeds, the approximation accuracy gradually increases. The initial solution γ i = 0 and Λ i = E s -1 ​where Es represents the average symbol energy.

[0061] The sequential EP algorithm for MIMO detection is described as follows. First, the mean μ and variance Σ of q(x) are expressed as:

[0062]

[0063]

[0064] For the ith edge, in the lth iteration of input (γ (l-1) , Λ (l-1) ), the update procedure of EP is:

[0065] 1) Update the mean Σ (l) and variance μ (l) in the joint PDF q (l) (x) with Equations (5) and (6). The superscript (1) denotes the 1st iteration.

[0066] 2) Update the mean and variance of the edge p (l) i (l) (x (l) i ), where the mean μ ii i is equal to the ith element of μ (l) and the variance is represented by the ith diagonal element of Σ i .

[0067] 3) Calculate the mean t (l) i and variance h 2(l) i of the cavity edge distribution p (l+1) i (x i i ).

[0068]

[0069]

[0070]

[0071] 4) Calculate the mean and variance of the edge probability distribution p i (x

[0072] i ) in Equation (3). 5) Update the parameter pair (γ i (l+1) , Λ i (l+1) so that the mean and variance of the following distribution match

[0073]

[0074]

[0075]

[0076] Finally, to improve the robustness of the algorithm, the parameter updates in (9) and (10) (i.e., the low-pass filter) are smoothed by a convex combination with the former values, i.e.,

[0077] γ i (l+1) = βγ i (l+1) + (1 - β)γ i (l) (11)

[0078] Λ i (l+1) = βΛ i (l+1) + (1 - β)Λ i (l) (12)

[0079] After convergence or reaching a pre-set maximum number of iterations L, the average value μ is used to independently hard-decode each transmitted symbol xi:

[0080]

[0081] From the above description, it can be observed that the computational complexity of the EP algorithm is mainly the updates of μ and Σ, especially the update of Σ in (5), which involves the matrix inversion. The complexity of this inversion is O(N 3 ), which will become an unbearable computational burden for large-scale MIMO systems.

[0082] To achieve low-complexity MIMO detection, a popular approach is to approximate the true posterior with another distribution that is easier to infer, and the KL divergence is often used to obtain the desired distribution. Let Q(x) be defined as the distribution used to approximate the true posterior, the minimization of the KL divergence can be expressed as:

[0083]

[0084] or

[0085]

[0086] It is well known that the KL divergence with asymmetry is not a true distance measure, and it is generally believed that and Contradictory. That is, when choosing one approximation method, the other method is naturally abandoned. For example, the GTA algorithm adopts the former way, while the EP algorithm adopts the latter way. Here, Gaussian tree approximation (GTA) and expectation propagation (EP) are two typical methods of realizing signal detection based on variational approximation, which are suitable for detection of high-order constellations. Both algorithms try to approximate the true likelihood function under the constraint of a discrete finite set by a new distribution by minimizing the Kullback-Leibler (KL) divergence, that is:

[0087]

[0088]

[0089] where, is the true distribution (actually ), Q'(x) is the approximate distribution, Q GTA (x) and Q EP (x) are the derived distributions of GTA and EP, respectively, by minimizing their corresponding KL divergences. The two divergences are usually considered to be contradictory to each other, that is, any one divergence is mutually exclusive with the other divergence. That is, since the KL divergence is not a real distance measure, the GTA and EP algorithms choose to optimize the KL divergence in two opposite ways, respectively.

[0090] Therefore, in order to solve the problem of poor bit error rate performance and high computational complexity in the prior art, an embodiment of the present application provides a high-order QAM large-scale MIMO signal detection method based on nested variational chain, which can achieve good bit error rate performance and low computational complexity under large-scale transceiver antenna number and high-order QAM modulation.

[0091] As shown in Figure 1 , the high-order QAM large-scale MIMO signal detection method based on nested variational chain provided by the embodiment of the present application comprises the following steps:

[0092] S10: receiving a to-be-detected signal, the to-be-detected signal being a high-order QAM large-scale MIMO signal.

[0093] It can be understood that the to-be-detected signal is a signal received by a receiver, which is a signal transmitted by a transmitter x propagating through a channel to reach the receiver, and the to-be-detected signal is represented by y.

[0094] S20: according to the to-be-detected signal, performing signal detection by using a GTA-EC algorithm to obtain a signal detection result; the GTA-EC algorithm is an improved EP algorithm, and the improvement is that the GTA algorithm and the EP algorithm are combined based on a nested variational chain to form a KL divergence, and an approximate distribution of a maximum a posteriori probability is obtained based on the formed KL divergence, the maximum a posteriori probability being a probability of obtaining an original estimated signal under a condition that a received signal and a channel gain are known.

[0095] In the embodiment of the application, a nested variational chain is proposed to combine the KL divergences of the GTA algorithm and the EP algorithm to form an improved EP algorithm, which is named as the GTA-EC algorithm. The expected variational distribution is embedded into another optimization of Q(x), as shown below:

[0096]

[0097]

[0098] The above processing actually forms a variational chain with a nested structure, which can be expressed as:

[0099]

[0100] wherein, The left side represents a maximum a posteriori probability distribution of an original estimated signal, Q(x) represents a first distribution approximating to the maximum a posteriori probability distribution obtained according to a KL divergence of the EP algorithm, Q'(x) represents a second distribution approximating to the maximum a posteriori probability distribution obtained by embedding the first distribution into a KL divergence of the GTA algorithm; x represents a signal transmitted by a transmitter, y represents a to-be-detected signal received by a receiver, and H represents a channel gain. The expression of the variational chain shows that Q(x) should be obtained according to the minimization of Q'(x) first, and then can be obtained.

[0101] According to the above technical route, the application first derives a nested variational chain to expand the variational inference paradigm. The basic idea is that the KL divergences of the GTA algorithm and the EP algorithm are not completely exclusive, and can be combined in a nested manner to form an approximate chain. The following describes the variational inference paradigm as follows:

[0102] First, a general statistical model should be defined as follows:

[0103]

[0104] wherein, ​​are functions belonging to the exponential family, i = 1,..., I i (x) is a non-negative factor. Typically, in performing inference is difficult and even reaches a complexity level that is prohibitive, which makes the variational inference based approach provide another tractable distribution Q(x). The nested variational chain consists of four steps, namely factor substitution, inner approximation, sign detection, and factor update. For factor substitution, the optimization of the KL divergence should be implemented first, i.e. The EP framework can be employed. The EP algorithm assumes a distribution belonging to the exponential family.

[0105]

[0106] where, instead of t i (x) (i = 1,..., I) as a correction factor, belonging to the exponential family. It should be noted that the EP framework replaces each non-negative factor t i (x) with another However, the distribution remains constant during this optimization process, which can be further exploited. Based on this idea, another variational distribution can be embedded inside as an inner approximation to obtain the final distribution The optimization in (12) can be performed as follows for Q(x):

[0107]

[0108] The approximation is usually denoted as When G j (x) (j = 1,..., J) is defined as a non-joint group, it is a commonly used mean field approximation. When G j (x) overlap with each other, a structured approximation can also be employed. For sign detection, the marginal distribution of each factor can be shown as in (3-46), and the final distribution can be represented as (3-47):

[0109]

[0110]

[0111] where, is defined as a new distribution for sign detection by appending a true factor p i (x) can be obtained by exploiting the true distribution t i (x) as φ(x) represents the sufficient statistics of the exponential family. A new factor can be updated by satisfying the power matching condition q i(x) can be expressed as formula (3-48), so that the distribution Q(x) can be updated iteratively:

[0112]

[0113] Therefore, the pseudo code of the nested variation chain detection algorithm is as follows:

[0114] Nested Variational Chain Detection Algorithm

[0115]

[0116]

[0117] It should be noted that, for some purpose, any step in the above nested variational chain algorithm can be skipped, such as factor replacement, internal approximation or factor update, thus forming a special case of nested variational chain.

[0118] Under the guidance of the nested variational chain detection algorithm provided in the embodiment of the present invention, the GTA-EC algorithm obtained by fusing the KL divergence of the GTA algorithm and the EP algorithm in the embodiment of the present invention is as follows:

[0119] (1) Initialization step: Initialize parameters based on the signal to be detected and initialize the message value;

[0120] (2) Factor substitution step: defining the first distribution is the maximum a posteriori probability distribution Approximate distribution of ; define distribution and distribution As a response to Q GTA-EC (x) is replaced by a factor, and the moment of r(x) is derived. and the moment of q(x)

[0121] in, Indicates that the mean is y:Hx and the variance is Gaussian distribution; is the noise variance, I is the identity matrix; x i is the i-th symbol of x, and N is the number of symbols contained in x; is the cardinality of the QAM constellation set; γ q and Λ q They are respectively distributed The mean and variance of γ; r and Λ r They are respectively distributed The mean and variance of s(x) are γ s , the variance is Λ s ,satisfy T denotes matrix transpose;

[0122] (3) Inner approximation step: constructing a maximum Gaussian spanning tree according to the initial covariance matrix to establish the relationship between the structure and the symbol of the tree; wherein the initial covariance matrix is constructed according to μ r , Σ r , μ q and Σ q ;

[0123] (4) Symbol detection step: obtaining the mean γ s and variance Λ s of the first distribution r(x) by realizing the consistency of the distribution q(x) and the distribution s(x), and obtaining the second distribution g(x) of the additional true prior according to the maximum Gaussian spanning tree established and the matrix derived; updating the message based on the second distribution g(x) and performing message passing, and obtaining the mean and variance of Q GTA-EC (x) by realizing the consistency of g(x) and s(x);

[0124] wherein,

[0125] denotes the Gaussian tree approximation of f q (x), and the conditional distribution is:

[0126]

[0127] p' i|pa(i) (x i ) is the distribution of the i th symbol in g(x); is the i th element on the diagonal of μ r , is the i th element on the diagonal of Σ r , μ pa(i) denotes the expectation of the parent node of x i in the q(x) distribution, x pa(i) denotes the parent node of x i corresponding to q(x), Σ i,pa(i) denotes the i th element of the covariance matrix of x i and its parent node, Σ pa(i),pa(i) denotes the covariance matrix of the parent node of x i , is the i th element on the diagonal of Σ r ;

[0128] (5) Factor update step: updating and so as to update q new (x) until the maximum iteration number is reached; wherein, and The update formula for q(x) is β represents a preset damping factor, q new (x) is an update result of q(x);

[0129] (6) An output step: obtaining a hard output according to a first moment of the latest q new (x);

[0130] It can be understood that the process of the GTA-EC algorithm is the process of signal detection by using the GTA-EC algorithm in step S20. The GTA-EC algorithm will be described in more detail below.

[0131] Specifically, given First, the likelihood function with a discrete prior is started as formula (3-59), which can be divided into two parts. Wherein

[0132]

[0133] Then, the new distribution q(x) can be defined as formula (3-60), and the moment can be represented as formula (3-61):

[0134]

[0135]

[0136] Note that (γ q ,Λ q ) acts as the prior of all symbols to be updated, and the definition of q(x) actually acts as a factor replacement. In order to achieve moment consistency, another distribution s(x) is defined as:

[0137]

[0138] Where the moment matching between s(x) and q(x) should be achieved to obtain (γ s ,Λ s ). Assuming another distribution is (3-63):

[0139]

[0140] The moment of r(x) is derived as:

[0141]

[0142] It can be observed that the distribution actually acts as the marginal distribution of the symbol by subtracting the replacement prior (γ q ,Λ q ) of the symbol.

[0143] The next step involves inner approximation. Since the full factorization of r(x) neglects the correlation between the signs, the detection can be performed with the Gaussian approximation tree according to the mean μ r , Σ r , μ q and Σ q . This is because the Gaussian approximation tree can capture the correlation between the signs instead of treating them independently. In this case, the new Gaussian tree-based distribution g(x) instead of r(x) can be defined as:

[0144]

[0145] where, is the new distribution by appending the true prior, while the conditional distribution can be expressed as:

[0146]

[0147] where, and are taken from the diagonal of μ r and Σ r , respectively; while μ i and Σ i,i (i = 1,..., N) are taken from the diagonal of μ q and Σ q , respectively. Based on g(x), the messages passed on the Gaussian tree can be exactly the same as the GTA-EC in (3-64)-(3-66). To achieve consistency, the distribution s(x) can be again utilized to achieve the moment matching condition between g(x) and s(x), thus obtaining γ s and Λ s , and the prior moments can finally be updated as:

[0148]

[0149] The beneficial effects of the embodiments of the present application are described below by simulation experiments. In the simulation, the detection performance of the MIMO system is evaluated according to the symbol error rate (SER) and the complexity. In the simulation process, 5000 channel matrices are used for implementation, and each implementation is used to send a message. As a comparison, several existing algorithms such as MMSE, GTA, GTA-SIC and EP algorithms are compared and evaluated. The case of α = N / M = 1 when N = M = 16, N = M = 32, N = M = 64 is mainly considered, and high-order constellations 16-QAM and 64-QAM are also considered. The factor β of the EP and GTA-EC algorithms is set to 0.2. The iteration number of the EP and GTA-EC algorithms is set to 2, 4 and 6, respectively, because the iteration of 6 times can approach convergence.

[0150] Complexity analysis:

[0151] The computation of GTA-EC is mainly divided into three parts. The first one involves the factor substitution step, which requires the computation of the second and first order moments listed in (3-61) derived from (3-63), which is the same as the MMSE method or the EP algorithm. It is well known that its complexity in one iteration can be expressed as O(N 3 ) when N = M. The second part is the construction of the tree graph for the inner approximation, which only needs to be initialized at the beginning of the iteration. The construction is based on the Prim algorithm, whose complexity is O(N 2 ). The last one is the computation of the message passing and factor update. For each iteration, the main complexity lies in the computation of the "downward" and "upward" messages in (3-64) and (3-65), each of which requires a maximum likelihood detection on the conditional distribution of the PAM constellation with cardinality .

[0152] Since there are N - 1 conditional distributions in the tree graph, the complexity can be expressed as Therefore, by defining the number of iterations to be performed, the total complexity can be expressed as O((N iter + 1)N 3 + N 2 + N iter NA) ~ O((N iter + 1)N 3 ), since N 3 >> NA is usually satisfied in large-scale MIMO systems. This shows that the complexity of GTA-EC is approximately Niter times that of the MMSE method or the GTA algorithm, i.e., O(N3). As a comparison, the complexity of the EP algorithm can be expressed as which shows that the complexity of the GTA-EC algorithm is roughly the same. The less the number of iterations an algorithm needs to perform, the lower its complexity is. The complexity of the existing algorithms is listed in Table 1.

[0153] Table 1

[0154]

[0155]

[0156] Performance evaluation and analysis:

[0157] Figure 2 and Figure 3 show the SER comparison of the GTA-EC algorithm with the existing algorithms. In which, the number of antennas deployed at the transmitter and receiver in the system is N = M = 16, Figure 1 the constellation is 16-QAM, Figure 2 the constellation is 64-QAM.

[0158] From Figure 2 it can be seen that the EP performance with 2 iterations is better than MMSE and Gaussian approximation of belief propagation algorithm GTA, and is comparable to GTA-SIC() performance. With the increase of the number of iterations, better performance can be obtained. For GTA-EC, it can be observed that GTA-EC with 2 iterations is significantly better than EP, and GTA-EC with 4 iterations is better than EP with 6 iterations. GTA-EC can achieve better performance when 6 iterations are performed. GTA-EC shows better diversity gain than EP in the high signal-to-noise ratio condition. In Figure 3 , when 64-QAM is used, the performance of GTA-SIC (Gaussian tree approximation algorithm with serial interference cancellation) after 2 iterations is better than EP, but still better than EP with 4 or 6 iterations. In this scenario, it can be found that GTA-EC has a significant performance advantage over EP, and GTA-EC with 2 iterations is better than EP with 4 and 6 iterations in the high signal-to-noise ratio condition. GTA-EC can also achieve better diversity gain in the high signal-to-noise ratio condition.

[0159] Figure 4 and Figure 5 The SER comparison of GTA-EC algorithm with existing algorithms is shown. In the comparison, the number of antennas deployed at the transmitter and receiver is N = M = 32, Figure 4 the constellation is 16-QAM, Figure 5 the constellation is 64-QAM.

[0160] In Figure 4 , when 16-QAM is used, it can be found that GTA-EC with 2 iterations is better than EP with 4 iterations, and GTA-EC with 4 iterations is better than EP with 6 iterations. GTA-EC converges when 4 iterations are performed in this scenario. In Figure 5 , when 64QAM is used, the same conclusion is that GTA-EP with 2 iterations and GTA-EP with 4 iterations are better than EP with 4 iterations and EP with 6 iterations, respectively. It is obvious that GTA-EC shows better diversity gain in the high signal-to-noise ratio condition.

[0161] Figure 6 and Figure 7 The SER (bit error rate) comparison of GTA-EP algorithm with existing algorithms is shown when the number of antennas deployed at the transmitter and receiver is N = M = 64. In the comparison, Figure 6 the constellation is 16-QAM, Figure 7 the constellation is 64-QAM.

[0162] In Figure 6In the case of 16-QAM, it can be found that the performance of GTA-EC with 2, 4, and 6 iterations is better than that of EP with 2, 4, and 6 iterations respectively. When 6 iterations are used, the performance of GTA-EC is not much improved, but under high SNR conditions, the diversity gain of GTA-EC is slightly better. Figure 7 In the example, when 64QAM is used, it can be observed that GTA-EC with 2, 4, and 6 iterations significantly outperforms EP with 2, 4, and 6 iterations, respectively. GTA-EC also exhibits better diversity gains.

[0163] based on Figures 2 to 6 , we can draw conclusions about the performance comparison of GTA-EC and existing algorithms. First, both EP and GTA-EC algorithms can significantly outperform existing algorithms such as MMSE, GTA, and GTA-SIC. In particular, GTA-EC outperforms these methods even with only two iterations, while EP, in contrast, requires four iterations to surpass them. Second, GTA-EC significantly outperforms EP in most cases when using 16-QAM or 64-QAM. When adopting higher-order constellations, such as moving from 16QAM to 64-QAM, the performance gain of GTA-EP is even greater, with even greater diversity gain observed in the 64-QAM scenario. This demonstrates that GTA-EP has superior performance, particularly for higher-order modulation. This performance improvement in GTA-EP primarily stems from its ability to exploit the interactions between symbols rather than treating them individually.

[0164] Finally, regarding complexity, GTA-EC with 2 and 4 iterations outperforms EP with 4 and 6 iterations, respectively. This indicates that the computational burden of GTA-EC is determined by the number of required iterations, resulting in lower complexity than EP. Simulation results suggest that GTA-EC requires 4 iterations, resulting in a complexity approximately four times that of the MMSE method, demonstrating its practicality as a massive MIMO signal detection method.

[0165] In summary, the high-order QAM large-scale MIMO signal detection method based on nested variational chains provided by the embodiment of the present invention combines the KL divergence divergence of the GTA algorithm and the EP algorithm in a nested manner to form an approximate chain, thereby obtaining a new distribution. This distribution can achieve satisfactory detection performance of large-scale MIMO systems with low complexity, and the bit error rate performance is better than the original EP algorithm, while reducing complexity.

[0166] The methods provided in the embodiments of the present invention can be applied to electronic devices. Specifically, the electronic devices can be base stations, desktop computers, portable computers, smart mobile terminals, and servers. This is not a limitation; any electronic device that can implement the present invention falls within the scope of protection of the present invention.

[0167] The embodiment of the present application also provides an electronic device, comprising a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory complete mutual communication through the communication bus, and the memory is used for storing a computer program.

[0168] The processor is used for executing the program stored in the memory, and the method steps of the high-order QAM massive MIMO signal detection method based on the nested variational chain are realized.

[0169] The communication bus mentioned in the electronic device can be a peripheral component interconnect (PCI) bus or an extended industry standard architecture (EISA) bus.

[0170] The communication interface is used for communication between the electronic device and other devices.

[0171] The memory can comprise a random access memory (RAM) and can also comprise a non-volatile memory (NVM), for example at least one disk memory. Optionally, the memory can also be at least one storage device located away from the aforementioned processor.

[0172] The processor mentioned above can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP) and the like; can also be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic device, a discrete gate or transistor logic device, a discrete hardware component.

[0173] The present application also provides a computer readable storage medium. The computer readable storage medium stores a computer program, and the computer program is executed by the processor to realize the method steps of the high-order QAM massive MIMO signal detection method based on the nested variational chain.

[0174] Optionally, the computer readable storage medium can be a non-volatile memory (NVM), for example, at least one disk memory.

[0175] Optionally, the computer readable storage medium can be a non-volatile memory (NVM), for example, at least one disk memory.

[0176] In yet another embodiment of the present application, a computer program product containing instructions which, when executed on a computer, cause the computer to carry out the method steps of the above-mentioned method for high-order QAM massive MIMO signal detection based on nested variational chain is also provided.

[0177] It should be noted that for the electronic device / storage medium / computer program product embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referred to the part of the method embodiments.

[0178] It should be noted that the terms "first", "second", and the like are used to distinguish similar objects, and do not necessarily have to be used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged under appropriate circumstances, so that the embodiments of the disclosure described herein can be implemented in an order other than those illustrated or described herein. The embodiments described in the following exemplary embodiments do not represent all the embodiments consistent with the present disclosure. Rather, they are merely examples of devices and methods consistent with some aspects of the present disclosure.

[0179] In the description of the present specification, the description of the terms "one embodiment", "some embodiments", "an example", "a specific example", or "some examples" and the like means that the specific features or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In the present specification, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in the present specification.

[0180] Although the present application is described herein in conjunction with various embodiments, other variations of the disclosed embodiments can be understood and implemented by those skilled in the art with reference to the drawings and the disclosure. In the description of the present application, the word "comprising" does not exclude other components or steps, "one" or "an" does not exclude a plurality, and "plurality" means two or more, unless otherwise explicitly specified. In addition, some measures are described in different embodiments, but this does not mean that these measures cannot be combined to produce good results.

[0181] Those skilled in the art will appreciate that embodiments of the present application can be readily used as a method, apparatus (device) or computer program product. Accordingly, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects all generally referred to herein as a "module" or "system". Furthermore, the present application can take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage devices, etc.) embodying computer readable program code thereon for use by or in connection with an instruction execution system. The user or

[0182] The present application is described in reference to the flowchart illustrations and / or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general purpose computer, special purpose computer, embedded processing system or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart illustrations and / or block diagrams block or blocks. Figure 1 one or more flowcharts and / or blocks Figure 1 means for carrying out the function specified by the flowchart

[0183] These computer program instructions can also be stored in a computer- readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the flowchart illustrations and / or block diagrams block or blocks. Figure 1 one or more flowcharts and / or blocks Figure 1 means for carrying out the function specified by the flowchart

[0184] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the flowchart illustrations and / or block diagrams block or blocks. Figure 1 one or more flowcharts and / or blocks Figure 1 means for carrying out the function specified by the flowchart

[0185] The above is further detailed description of the present application in combination with specific preferred embodiments, and cannot be deemed as limitation of the specific implementation of the present application to these descriptions. For those skilled in the art to which the present application belongs, without departing from the concept of the present application, a number of simple deductions or substitutions can be made, and all should be deemed as falling within the protection scope of the present application.

Claims

1. A method for high-order QAM massive MIMO signal detection based on nested variational chain, characterized in that, The method comprises the steps of: receiving a signal to be detected; the signal to be detected is a high-order QAM large-scale MIMO signal; performing signal detection on the signal to be detected by using a GTA-EC algorithm to obtain a signal detection result; wherein the GTA-EC algorithm is an improved EP algorithm, and the improvement is that the GTA algorithm and the EP algorithm are fused based on a nested variational chain to obtain an approximate distribution of a maximum a posteriori probability based on the fused KL divergence, the maximum a posteriori probability being a probability of obtaining an original estimated signal under the condition that the received signal and the channel gain are known; the way of fusing the GTA algorithm and the EP algorithm based on the nested variational chain includes: wherein, The left side represents the maximum a posteriori probability distribution of the original estimated signal, Q(x) represents a first distribution approximating the maximum a posteriori probability distribution obtained according to the KL divergence of the EP algorithm, The left side represents the maximum a posteriori probability distribution of the original estimated signal, Q(x) represents a first distribution approximating the maximum a posteriori probability distribution obtained according to the KL divergence of the EP algorithm, The right side represents a second distribution approximating the maximum a posteriori probability distribution obtained by embedding the first distribution into the KL divergence of the GTA algorithm; x represents the signal transmitted by the transmitter, y represents the signal to be detected received by the receiver, and H represents the channel gain.

2. The nested variational chain high-order QAM massive MIMO signal detection method according to claim 1, characterized in that, the GTA-EC algorithm is used to obtain the signal detection result according to the signal to be detected, which comprises: an initialization step of initializing parameters based on the signal to be detected and initializing a message value; Factor substitution step: define first distribution Posterior distribution Approximate distribution; define distribution And distribution As a factor substitution form of Q GTA-EC Moment of r(x) Moment of q(x) wherein denotes a Gaussian distribution with mean y:Hx and variance is the noise variance and I is the identity matrix; x i is the i-th symbol of x and N is the number of symbols contained in x; is the cardinality of the QAM constellation set; γ q and Λ q are the mean and variance of the distribution , respectively; γ r and Λ r are the mean and variance of the distribution , respectively; the mean of s(x) is γ s and the variance is Λ s , satisfying the superscript T denotes matrix transposition;​ The inner approximation step: constructing a maximum Gaussian spanning tree according to the initial covariance matrix to establish the relationship between the structure and the symbol of the tree; wherein the initial covariance matrix is constructed according to μ r , Σ r , μ q and Σ q ; Symbol detection step: Get the mean γ of the first distribution r(x) by achieving consistency between the distribution q(x) and the distribution s(x) s and variance Λ s , and obtain the second distribution g(x) with additional true prior based on the established maximum Gaussian spanning tree and the derived moment; update the message based on the second distribution g(x) and perform message passing, and obtain Q by achieving consistency between g(x) and s(x) GTA-EC (x) mean and variance; wherein represents a Gaussian tree approximation of f q (x) with conditional distributions p i| a ( i ) (x i ) is the distribution of the i-th symbol in g(x); is the i-th element on the diagonal of μ r , is the i-th element on the diagonal of Σ r , μ pa(i) denotes the expectation of the parent of x i in the q(x) distribution, x pa(i) denotes the parent of x i for q(x), Σ i,pa(i) denotes the i-th element of the covariance matrix of x i and its parent, Σ pa(i),pa(i) denotes the covariance matrix of the parent of x i , is the i-th element on the diagonal of Σ r ; Factor update step: update and Thus, update q new (x) until the maximum number of iterations is reached; wherein, and The update formula for q β represents a preset damping factor, q new (x) is the update result of q(x); Output step: The hard output is obtained from the first moment of (x) new (x).

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