Asymptotic approximation method for spectral efficiency of cell-free massive MIMO systems

Abstract

The application discloses a method for approximating spectral efficiency of a cell-free massive MIMO system, and belongs to the technical field of wireless communication. The method comprises the following steps: constructing a quantization system model; grouping all user equipment, the groups being continuously detected, and simultaneously detecting user equipment in the same group; constructing a grouping signal detection algorithm; detecting a received signal matrix by using a ZF-GSIC algorithm to obtain a transmission signal estimation value of the user equipment; simulation results show that, in the case of less grouping, the system can achieve high spectral efficiency and high energy efficiency close to ZF-SIC detection, and the calculation complexity is greatly reduced, so that the hardware cost and energy consumption can be greatly reduced. In addition, the application derives an approximating expression of the spectral efficiency of the system, and simulation results verify the accuracy of the approximating expression of the spectral efficiency of the system, and the obtained asymptotic result can be used for fast system performance analysis.

Description

TECHNICAL FIELD

[0001] The present application relates to an asymptotic approximation method for the spectral efficiency of a cell-free massive MIMO system, and belongs to the technical field of wireless communication. BACKGROUND

[0002] Cell-free massive multiple-input multiple-output (MIMO) systems have become one of the most promising key technologies in future beyond 5G (B5G) and 6th generation (6G) networks. In a cell-free massive MIMO system, the system is based on distributed massive MIMO and breaks the division of cell boundaries, i.e. a large number of access points (APs) and user equipment (UEs) are distributed in a wide area, different APs are connected to a central processing unit (CPU) through a backhaul link, and under the same time-frequency resources, the CPU provides services to all users according to the instructions. Since the cell-free massive MIMO system greatly reduces the distance between users and APs, it has strong spatial macro-diversity gain and the ability to resist path loss, and can greatly improve the service quality of edge users. However, the cell-free massive MIMO system usually needs to deploy a large number of APs, and when the AP is configured with a full-precision analog-to-digital converter (ADC) for quantization processing, it will inevitably bring high hardware cost and huge energy consumption. In order to solve this problem, it is undoubtedly a more direct solution to configure a low-precision ADC at the AP for quantization processing. Therefore, the research on the cell-free massive MIMO system with low-resolution ADC is of great theoretical value and practical significance.

[0003] In the modeling of ADC quantization distortion, there are two main models recognized by the academic community, namely the Bussgang decomposition theorem and the additive quantization noise model (AQNM). Since the former is more cumbersome when measuring multi-bit quantization distortion, researchers usually only use it to model 1-bit ADC quantization, and the latter is more operable and can be used to analyze the impact of any bit quantization.

[0004] The existing spectral efficiency (SE) analysis of a cell-free massive MIMO system mainly focuses on linear signal detection algorithms, and there are few studies on nonlinear signal detection algorithms. Nonlinear successive interference cancellation (SIC) detection can not only improve SE, but also improve energy efficiency (EE). However, SIC detection leads to higher computational complexity than linear detection. In addition, a cell-free massive MIMO system needs to deploy a large number of APs and users, and the system is relatively complex, so it is relatively complex to directly analyze the spectral efficiency of the system. Some researchers have studied the asymptotic approximation of the spectral efficiency of the system in a cellular network, but there are few studies on the asymptotic approximation of the spectral efficiency of a cell-free massive MIMO system. The present application performs asymptotic approximation analysis on the spectral efficiency of a cell-free system, and the asymptotic results obtained can be used for fast system performance analysis. SUMMARY

[0005] In order to solve the problem that the existing cell-free massive MIMO system is relatively complex and it is difficult to directly analyze the spectral efficiency of the system, the present application provides an asymptotic approximation method for the spectral efficiency of a cell-free massive MIMO system, and the technical solution is as follows:

[0006] The asymptotic approximation method for the spectral efficiency of a cell-free massive MIMO system of the present application is shown in the following system model:

[0007]

[0008] The system model includes L access points (APs) and K user equipment (UEs), each AP is configured with N antennas, and each UE is configured with one antenna;

[0009] wherein y l represents the signal received at the lth access point (AP-l), x i represents the information symbol sent by the ith user equipment (UE-i), h il represents the channel vector between UE-i and AP-l, n l represents the additive white Gaussian noise on AP-l;

[0010] The method comprises:

[0011] Step 1: constructing a quantization system model for the system model to be detected according to a linear additive quantization noise model (AQNM);

[0012] Step 2: dividing all user equipment (UEs) into U groups on average, each group has user equipments UEs, where 1≤U≤K, the groups are detected successively, and the user equipments UEs within the same group are detected simultaneously;

[0013] Step 3: constructing a group-wise successive interference cancellation (GSIC) signal detection algorithm, denoted as GSIC, the GSIC signal detection algorithm is expressed as:

[0014]

[0015] wherein, denotes the transmission signal estimation value of the kth user equipment UE, v k is the reception combination vector of the kth user equipment UE, and a denotes a distortion coefficient, denotes the quantized signal of y l , denotes the group number of the kth user equipment UE, h i denotes the set of channel vectors h il .

[0016] Step 4: detecting the received signal matrix y q using a ZF-GSIC detection algorithm to obtain the transmission signal estimation value of the kth user equipment UE

[0017] Step 5: performing an asymptotic approximation on the spectral efficiency expression of the system;

[0018] The spectral efficiency at the kth user equipment UE is expressed as:

[0019]

[0020] wherein, in a coherent time-frequency block of τ c symbols, the channel remains unchanged. Each time-frequency block is implemented independently and randomly. It is assumed that τ p symbols are used for uplink training, τ c -τ p symbols are used for uplink data transmission. denotes the signal-to-interference-and-noise ratio (SINR) at the kth user equipment UE:

[0021]

[0022] wherein, p k denotes the transmission power of the kth user equipment UE, ∑ is a block diagonal matrix, and is the inverse matrix of , denotes the collective channel estimation of the kth UE.

[0023] Optionally, the step 4 utilizes a ZF-GSIC detection algorithm to detect the received signal matrix yq performing detection to obtain the transmit signal estimate The process comprises:

[0024] The receive combining vector of the kth user equipment UE is denoted as:

[0025]

[0026] wherein denotes the combining vector of all UEs in the u k th group, denoted as:

[0027]

[0028] wherein, denotes the estimate of the channel matrix, denotes the n th column of the matrix

[0029] The receive combining vector of the kth user equipment UE is substituted into the GSIC signal detection algorithm to obtain the signal estimate of the kth user equipment UE

[0030] Optionally, in the step 5:

[0031] For ZF-SIC detection, U=K, u k =k, the SINR of the kth user is denoted as:

[0032]

[0033] For ZF detection, U=1, u k =1, the SINR of the kth user is denoted as:

[0034]

[0035] Optionally, the step 4 utilizes ZF-GSIC algorithm for signal detection, when U=K, G=1, u k =k, at this time, the receive combining vector of the kth user equipment UE is:

[0036]

[0037] When U=1, G=K, u k =1, at this time, the receive combining vector of the kth user equipment UE is:

[0038]

[0039] Optional, additive Gaussian quantization distortion The covariance matrix of the additive Gaussian quantization distortion is represented as:

[0040]

[0041] wherein, is a semi-positive definite covariance matrix describing the spatial correlation of the channel, p i denotes the transmit power of the i-th user equipment UE, σ 2 denotes the variance of the additive Gaussian white noise n l diag(·) is used to extract the diagonal elements and create a diagonal matrix, I N is an N×N identity matrix.

[0042] Optional, after the step 2 grouping, the u-th group is composed of UEs with serial numbers k=G(u-1)+1,…,Gu, and the group number of the k-th user equipment UE is

[0043] Optional, the channel vector between UE-i and AP-l is a spatially correlated Rayleigh fading channel.

[0044] Optional, the step 5 rewrites the estimated signal into:

[0045]

[0046] wherein, n represents a set of additive Gaussian white noises of L access points APs, denotes the set channel estimation error of the k-th UE.

[0047] The present application provides a kind of spectral efficiency approximation device of cell-free massive MIMO system, including memory and processor;

[0048] The memory is used to store computer program;

[0049] The processor is used to when executing the computer program, the spectral efficiency approximation method as described in any one of the above is realized.

[0050] The present application provides a kind of computer readable storage medium, the storage medium is stored with computer program, when the computer program is executed by processor, the spectral efficiency approximation method as described in any one of the above is realized.

[0051] The present application has the beneficial effects that:

[0052] The application provides a ZF-GSIC signal detection method, which is used for obtaining the sending signal estimation value of each user equipment (UE) from a receiving signal matrix, and meanwhile, the zero forcing (ZF) signal detection method and the nonlinear ZF-SIC signal detection method can be used as four special cases of the ZF-GSIC signal detection method under certain conditions. In addition, the application derives an asymptotic approximation expression of the system spectral efficiency.

[0053] Simulation results show that the ZF-GSIC signal detection method can effectively reduce the signal processing complexity, processing delay and implementation cost, and maintain high spectral efficiency and energy efficiency. In the case of using low-precision ADC and small number of groups, the spectral efficiency and energy efficiency of the ZF-GSIC signal detection method are very close to those of the traditional ZF-SIC detection, but the calculation complexity can be greatly reduced.

[0054] The application solves the problem that the large-scale MIMO system is relatively complex and difficult to directly analyze the system spectral efficiency by performing asymptotic approximation analysis on the spectral efficiency of the large-scale MIMO system. Simulation results verify the accuracy of the asymptotic approximation expression of the system spectral efficiency derived by the application, and the asymptotic result can be used for fast system performance analysis. BRIEF DESCRIPTION OF DRAWINGS

[0055] In order to more clearly illustrate the technical solutions in the embodiments of the application, the drawings needed in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the application, and other drawings can be obtained by those skilled in the art without creative labor.

[0056] Figure 1a For when L=100, N=1, in the ideal and non-ideal CSI cases, the cumulative distribution function graph of the total spectral efficiency of the large-scale MIMO system signal detection method based on the ZF-GSIC algorithm.

[0057] Figure 1b For when L=50, N=2, in the ideal and non-ideal CSI cases, the cumulative distribution function graph of the total spectral efficiency of the large-scale MIMO system signal detection method based on the ZF-GSIC algorithm.

[0058] Figure 2aThe results of average spectral efficiency of three different detection algorithms under non-ideal CSI when U=2, and the average spectral efficiency of ideal ADC is also provided as a reference.

[0059] Figure 2b The results of average spectral efficiency of three different detection algorithms under non-ideal CSI when U=5, and the average spectral efficiency of ideal ADC is also provided as a reference.

[0060] Figure 3a The curve of average spectral efficiency per UE of the signal detection method of the non-cellular massive MIMO system based on the ZF-GSIC algorithm of the application with the number of APs when U=2 under ideal and non-ideal CSI is shown in the figure. The simulation results compare the approximate value of spectral efficiency with the accurate result obtained by the Monte Carlo simulation method.

[0061] Figure 3b The curve of average spectral efficiency per UE of the signal detection method of the non-cellular massive MIMO system based on the ZF-GSIC algorithm of the application with the number of APs when U=5 under ideal and non-ideal CSI is shown in the figure. The simulation results compare the approximate value of spectral efficiency with the accurate result obtained by the Monte Carlo simulation method.

[0062] Figure 4 The curve of average spectral efficiency per UE of the signal detection method of the non-cellular massive MIMO system based on the ZF-GSIC algorithm of the application with the number of antennas of each AP when U=2 and when U=5 under ideal and non-ideal CSI is shown in the figure. The simulation results compare the approximate value of spectral efficiency with the accurate result obtained by the Monte Carlo simulation method.

[0063] Figure 5a The curve of energy efficiency corresponding to different detection algorithms with different quantization bits when U=2 is shown in the figure.

[0064] Figure 5b The curve of energy efficiency corresponding to different detection algorithms with different quantization bits when U=5 is shown in the figure. DETAILED DESCRIPTION

[0065] In order to make the purpose, technical scheme and advantages of the application clearer, the embodiments of the application will be further described in detail below with reference to the drawings.

[0066] Embodiment one:

[0067] The embodiment provides an asymptotic approximation method for spectral efficiency of a non-cellular massive MIMO system, and the system model is represented as:

[0068]

[0069] The system model comprises L access points AP and K user equipments UE, each AP is configured with N antennas, and each UE is configured with 1 antenna;

[0070] wherein y l represents a signal received at the lth access point AP-l, x i represents an information symbol sent by the ith user equipment UE-i, h il represents a channel vector between UE-i and AP-l, n l represents an additive white Gaussian noise on AP-l;

[0071] The method of the embodiment comprises:

[0072] Step 1: constructing a quantization system model for the system model to be detected according to a linear additive quantization noise model AQNM;

[0073] Step 2: dividing all user equipments UE into U groups averagely, each group consisting of user equipments UE, wherein 1≤U≤K, the groups are detected continuously, and the user equipments UE in the same group are detected simultaneously;

[0074] Step 3: constructing a grouping SIC signal detection algorithm GSIC, the GSIC signal detection algorithm is represented as:

[0075]

[0076] wherein, represents a sending signal estimation value of the kth user equipment UE, v k is a receiving combination vector of the kth user equipment UE, and α represents a distortion coefficient, represents a quantization signal of y l , represents a group number of the kth user equipment UE, h i represents a set of channel vectors h il ;

[0077] Step 4: detecting the receiving signal matrix y q using a ZF-GSIC detection algorithm to obtain the sending signal estimation value

[0078] Step 5: performing an asymptotic approximation on a spectral efficiency expression of the system.

[0079] Embodiment two:

[0080] This embodiment provides an asymptotic approximation method for the spectral efficiency of a cellular-free massive MIMO system. The system model to which this method is applicable is:

[0081]

[0082] In the above formula This represents the signal received at the l-th AP (AP-1), where The information symbol (i.e., the transmitted signal) transmitted for the i-th UE (UE-i) has a transmission power of p. i h il It is the channel vector between UE-i and AP-l; The additive white Gaussian noise over AP-l has a variance of σ. 2 ; This represents a complex Gaussian distribution.

[0083] This embodiment considers a cellular-free massive MIMO system under a spatially correlated Rayleigh fading channel, with L geographically distributed access points (APs) and K user units (UEs). Each AP is equipped with N antennas, and each UE is equipped with one antenna. It is assumed that a time division duplex (TDD) protocol is used. At τ... c Within the coherent time-frequency blocks of the symbols, the channel remains unchanged. Each time-frequency block is implemented independently and randomly. Assume τ p The symbol τ is used for uplink training. c -τ p Used for uplink data transmission.

[0084] If the channel is modeled as a spatially correlated Rayleigh fading distribution, then the channel vector h between UE-k and AP-l... kl Represented as:

[0085]

[0086] in It is the positive semidefinite covariance matrix describing the spatial correlation of the channel; the average channel gain from one antenna at the l-th AP to the k-th UE is given by the normalized trace β. kl =tr(R) kl The factor ) / N is determined by the large-scale fading coefficient that describes geometric path loss and shadow fading.

[0087] After quantization using the AQNM method, the quantized signal is obtained.

[0088]

[0089] In this embodiment, L APs receive the data signal {y} lThe data signals are sent to the CPU by the APs, which act as relays and forward the signals they receive to the CPU for processing. More precisely, each AP sends the received pilot signals and the received uplink data signals to the CPU, which performs channel estimation, receive combining and data detection. The received signals available at the CPU are denoted as:

[0090]

[0091] Equation (4) can be expressed in a more compact form:

[0092]

[0093] Assume is the distribution of the aggregate channel, where the block-diagonal spatial correlation matrix is given by Moreover, define as the channel matrix.

[0094] Since in a real scenario, the Channel State Information (CSI) is usually obtained in a training phase. In this invention, the Minimum Mean-Square Error (MMSE) method is used to estimate the channel. Since the centralized processing is considered for the cell-free massive MIMO system, the CPU can use the channel statistics obtained at the APs and the received pilot signals to compute all MMSE channel estimates These estimates can be computed individually without loss of optimality. Then, the aggregate channel estimates at the CPU can be obtained, and the aggregate channel estimate for the kth UE can be denoted as:

[0095]

[0096] The aggregate channel estimation error for the kth UE can be denoted as Moreover, define as the estimate of the channel matrix H.

[0097] The method comprises:

[0098] Step 1: Construct the quantization system model of the low-precision ADC according to the linear additive quantization noise model (Additive Quantization Noise Model, AQNM).

[0099] The AQNM quantization system model is constructed by using the following equation (7):

[0100]

[0101] where represents the received signal vector at the AP-l; is the information symbol (i.e., the transmitted signal) sent by the i-th UE with transmit power p i ; h il is the channel vector between UE-i and AP-l;

[0102] is the additive white Gaussian noise on the l-th AP with variance σ 2 ; represents the quantized signal, and a is the distortion coefficient, which depends on the number of bits b of the quantization; is the additive Gaussian quantization distortion, which is uncorrelated with y l ; The covariance matrix of y k is given by:

[0103]

[0104] where the notation diag(·) is used to extract the diagonal elements and create a diagonal matrix, and I N is the N x N identity matrix.

[0105] Step 2: Divide all UEs evenly into U groups, each consisting of UEs, where 1 < U < K.

[0106] The u-th group consists of UEs with serial numbers k = G(u - 1) + 1,..., Gu. Thus, the group number of the k-th UE is For example, consider a network of K = 40 UEs, which are evenly divided into U = 10 groups. The number of UEs within each group is G = 4. The group number of UE-7 is u7= 2, and the second group contains UEs from UE-5 to UE-8. These groups are detected consecutively, and UEs within the same group are detected simultaneously.

[0107] Step 3: Construct a group-wise successive interference cancellation (GSIC) signal detection algorithm based on the idea of SIC detection;

[0108] The GSIC signal detection algorithm is constructed using the following equation (9):

[0109]

[0110] where represents the transmitted signal estimate of the k-th UE, v k is the received combining vector of the k-th UE, and the superscript H denotes the conjugate transpose.

[0111] Step 4: Use the ZF-GSIC detection algorithm to detect the transmitted signal from the received signal y qThe transmitted signal of each user is recovered from the received signal y

[0112] where the ZF-GSIC detection algorithm is used to recover the transmitted signal of each user from the received signal y q The process of recovering the transmitted signal of each user from the received signal y

[0113] The ZF-GSIC algorithm is used to perform signal detection with Equation (10), and the received combining vector of the kth UE is denoted as

[0114]

[0115] where denotes the combining vector of all UEs in the u k th group, and is denoted as

[0116]

[0117] In particular, for the ZF-SIC detector, U = K, G = 1, u k = k, at which time the received combining vector of the kth UE is

[0118]

[0119] For the ZF detector, U = 1, G = K, u k = 1, at which time the received combining vector of the kth UE is

[0120]

[0121] Finally, the received combining vector of the kth UE is substituted into the GSIC signal detection algorithm of Equation (9), and the transmitted signal estimate of the kth UE can be obtained.

[0122] Step 5: Perform asymptotic approximation on the spectral efficiency expression of the system.

[0123] First, rewrite the estimated signal as For subsequent derivation, further simplify it as

[0124]

[0125] where denotes the channel estimation error, which is defined as where k = diag(C k1 ,...,C kL ), ​​​​

[0126] The spectral efficiency at the kth user equipment (UE) is expressed as:

[0127]

[0128] Among them, in τ c Within the coherent time-frequency blocks of the symbols, the channel remains unchanged. Each time-frequency block is implemented independently and randomly. Assume τ p The symbol τ is used for uplink training. c -τ p Used for uplink data transmission. It indicates a desire for the expected value.

[0129] in The signal-to-interference-plus-noise ratio (SINR) at the k-th user equipment (UE) is expressed as:

[0130]

[0131] Where, p k This represents the transmit power of the k-th UE.

[0132] in because It's not white in space, so a filter is used. To whiten it, we get:

[0133]

[0134] Where Σ is a block diagonal matrix represented as:

[0135]

[0136] Where, Σ l This represents the l-th block in the diagonal matrix Σ.

[0137] Each term in Equation (18) represents the channel noise variance, the quantization distortion covariance matrix, and the variance of the channel estimation error, respectively. The ZF-GSIC detection vector can be further expressed as:

[0138]

[0139] in, Denotes the inverse matrix of Σ.

[0140] The receive combination vector of the k-th UE Therefore, we can obtain:

[0141]

[0142] Then, the SINR of the kth user is expressed as:

[0143] where Further, the formula (21) can be approximated as:

[0144]

[0145] Further, the final approximate expression can be obtained as:

[0146]

[0147] For the ZF-SIC detection, U = K, u k = k, the formula (23) can be expressed as:

[0148]

[0149] For the ZF detection, U = 1, u k = 1, the formula (23) can be expressed as:

[0150]

[0151] In order to make the purposes, technical solutions and advantages of the present application more clear, some classical detection algorithms will be compared with the present application below, and the superiority of the signal detection method based on the ZF-GSIC algorithm of the present application in improving the system performance will be shown. In addition, the approximate expression of the spectral efficiency of the present application and the real spectral efficiency are compared.

[0152] The detection algorithms used for simulation are the signal detection methods based on the ZF detection algorithm, the ZF-SIC detection algorithm and the ZF-GSIC algorithm of the present application respectively, and the approximate expression and the real expression of the system spectral efficiency under the ZF-GSIC detection are simulated and analyzed.

[0153] Among them, the ZF detection algorithm is a classical linear detection algorithm, and the ZF-SIC detection algorithm is a classical nonlinear detection algorithm; the signal detection method based on the ZF-GSIC algorithm of the present application can realize low complexity while showing the system SE and EE performance close to the SIC detection algorithm through less grouping. In addition, the simulation results verify the accuracy of the approximate expression of the spectral efficiency derived by the present application, and the obtained asymptotic result can be used for fast performance analysis.

[0154] The simulation curves in the drawings show that the spectral efficiency of the system using the ZF-GSIC detection can be improved with the increase of the number of groups, and in the case of fewer groups, for example, in 5 groups, the system can achieve a spectral efficiency and energy efficiency very close to that of the SIC detection. In addition, the ideal ADC system and the ADC quantization system are compared through simulation experiments, and the results show that when the number of quantization bits is 5 or 6, the spectral efficiency and energy efficiency of the system can reach the optimal condition. This shows that under the tolerable performance loss, a 5-bit ADC can be used instead of an ideal ADC, thereby greatly reducing the hardware cost and energy consumption. In addition, the simulation results compare the approximate value of the spectral efficiency with the accurate result obtained by the Monte Carlo simulation method. The results show that the approximate result has high accuracy, verifying the analysis result of the application.

[0155] As shown in Figure 1a and Figure 1b , the SIC detection method significantly improves the performance of the system. In addition, the spectral efficiency performance of the ZF-SIC detection is significantly better than that of the linear ZF detection. The spectral efficiency performance of the proposed ZF-GSIC detection with lower delay is between that of the ZF and the ZF-SIC. The performance difference between the ideal CSI and the non-ideal CSI is due to the channel estimation error, thereby resulting in higher spectral efficiency under the ideal CSI. Figure 1a and Figure 1b show the case when the number of APs and the number of their antennas are L = 100, N = 1 and L = 50, N = 2, respectively. Figure 1b The same settings are considered, but the number of APs equipped with multiple antennas is less. As can be seen from the figure, Figure 1b has the same overall trend as Figure 1a , but due to the decrease in macro diversity, i.e. the increase in the average distance from the UE to the AP, the SE of Figure 1b is lost compared to Figure 1a .

[0156] As shown in Figure 2a and Figure 2b , the ZF-SIC detection produces the highest spectral efficiency, while the linear ZF detection produces the lowest spectral efficiency, and the ZF-GSIC detection proposed by the application is between the two. The results show that with the increase of the number of quantization bits, the average spectral efficiency approaches the case of ideal ADC. When the number of quantization bits is 6, the spectral efficiency converges to a fixed bound, which shows that the 6-bit ADC architecture can achieve a performance comparable to that of the ideal ADC. Figure 2a and Figure 2b are the cases when U = 2 and U = 5, respectively. As can be seen from the simulation results, when there are more groups, the system has higher spectral efficiency.

[0157] As Figure 3a and Figure 3b shown, the approximate result of the spectral efficiency has a high accuracy, verifying the analysis result of the present application. In addition, with the increase of the number of APs, the average spectral efficiency of each UE gradually increases, so the performance of the system can be improved by increasing the number of APs. Figure 3a and Figure 3b are the cases when U = 2 and U = 5, respectively. The results show that with the increase of the number of groups, the performance of the spectral efficiency of the system has a corresponding improvement. Therefore, increasing the number of groups can improve the performance of the system, further verifying the accuracy of the derived asymptotic approximation expression.

[0158] As Figure 4 shown, with the increase of the number of antennas of each AP, the average spectral efficiency of each UE gradually increases, so the performance of the system can be improved by increasing the number of antennas of the AP. In addition, the approximate result of the spectral efficiency of the system is compared with the exact result, and the result verifies the accuracy of the asymptotic approximation expression derived by the present application. Similar to the results of Figure 3a and Figure 3b , by setting the number of groups of the ZF-GSIC detection to 5 groups, it can be found that when the number of antennas of the AP changes, with the increase of the number of groups, the performance of the spectral efficiency of the system has a corresponding improvement. Therefore, increasing the number of groups can improve the performance of the system, further verifying the accuracy of the derived asymptotic approximation expression.

[0159] As Figure 5a and Figure 5b shown, for different detection algorithms, at a lower number of quantization bits (such as b = 2 and 3), a higher energy efficiency can be achieved. In addition, it can be seen that under different detectors, the energy efficiency increases with the increase of the number of quantization bits, and then decreases due to the loss of severe quantization and the increase of total energy consumption. The energy efficiency of the ZF-SIC detector is the largest, the energy efficiency of the linear ZF detector is relatively small, and the energy efficiency of the ZF-GSIC detector is between the two. The simulation results show that by appropriately selecting the number of quantization bits, the energy efficiency of the low-resolution ADC system can be improved. This insight shows that the low-resolution ADC architecture has great potential for improvement regardless of the type of detector. Figure 5a and Figure 5b are the cases when the number of groups is U = 2 and 5, respectively. The value of the system energy efficiency of the ZF-GSIC receiver at U = 5 is closer to the case of the ZF-SIC receiver, and this result also verifies that a higher system performance can be achieved by using a smaller number of groups. In addition, the larger the number of groups, the higher the energy efficiency, that is, in Figure 5a and Figure 5bIn the middle, the energy efficiency at U=5 is higher than that at U=2. Through the simulation of the energy efficiency performance, the effectiveness of the signal detection method based on the ZF-GSIC algorithm proposed in the application applied to the cell-free system is further verified.

[0160] In summary, compared with the linear detection, the SIC detection system has higher spectrum efficiency and energy efficiency. On the basis of effectively reducing the signal processing complexity and processing delay and the implementation cost, using the low-precision ADC, the spectrum efficiency and energy efficiency of the system under the signal detection method based on the ZF-GSIC algorithm are very close to the traditional ZF-SIC detection under the condition of fewer groups. In addition, the simulation results verify the accuracy of the asymptotic approximation expression of the system spectrum efficiency derived in the application, and the asymptotic result obtained can be used for fast system performance analysis.

[0161] Part of the steps in the embodiments of the application can be realized by software, and the corresponding software program can be stored in a readable storage medium, such as an optical disc or a hard disk.

[0162] The above only describes the preferred embodiments of the application and is not intended to limit the application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the application shall be included in the protection scope of the application.

Claims

1. An asymptotic approximation method for spectral efficiency of a cell-free massive MIMO system, a system model is represented as: wherein, H is a channel matrix, N is the number of antennas of each access point (AP), K is the number of user equipments (UEs), and N is the number of antennas of each UE. The system model comprises L APs and K UEs, each AP is configured with N antennas, and each UE is configured with 1 antenna; wherein y l represents a signal received at the lth access point, AP-l, x i represents an information symbol transmitted by the ith user equipment, UE-i, h il represents a channel vector between UE-i and AP-l, n l represents additive white Gaussian noise at AP-l; The method comprises: Step 1: constructing a quantized system model for the system to be detected according to a linear additive quantization noise model (AQNM); Step 2: All user equipments, UEs, are evenly divided into U groups, each group consisting of user equipments, UEs, where 1 ≤ U ≤ K, these groups are continuously detected, and the user equipments, UEs, within the same group are detected simultaneously; Step 3: constructing a group successive interference cancellation (SIC) signal detection algorithm (GSIC), the GSIC signal detection algorithm is represented as: wherein, denotes the transmit signal estimate of the kth user equipment UE, v k is the receive combining vector of the kth user equipment UE, a denotes a distortion coefficient, denotes the quantized signal of y l denotes the group number of the kth user equipment UE, h i denotes the set of channel vectors h il .​ Step 4: detecting the received signal matrix y using the ZF-GSIC detection algorithm q performing detection to obtain a transmission signal estimate of the kth user equipment UE Step 5: performing asymptotic approximation on the spectral efficiency expression of the system; The spectral efficiency at the kth UE is represented as: In τ c In the coherent time-frequency blocks of the symbols, the channel remains unchanged, and each time-frequency block is implemented independently and randomly; assuming τ p The symbol τ is used for uplink training. c -τ p Used for uplink data transmission; The signal-to-interference-plus-noise ratio (SINR) at the k-th user equipment (UE) is: Where, p k This represents the transmit power of the k-th user equipment (UE). Σ is a block diagonal matrix, and for The inverse matrix, p represents the ensemble channel estimate for the k-th UE. i σ represents the transmit power of the i-th user equipment (UE). 2 n represents additive white Gaussian noise l The variance, diag(·) is used to extract the diagonal elements and create a diagonal matrix, I N It is an N×N identity matrix. Indicates additive Gaussian quantization distortion The covariance matrix, Indicates the expectation. Indicates channel estimation error, superscript H This indicates the method to find the conjugate transpose.

2. The method of claim 1, wherein, The step 4 utilizes a ZF-GSIC detection algorithm to detect the received signal matrix y q to obtain the transmission signal estimate The process includes: A receive combining vector for a kth user equipment (UE) is represented as: wherein represents the u-th k combination vector of all UEs in the group, denoted as: wherein denotes an estimate of the channel matrix, denotes the nth column of the matrix H. combining the received signals of the kth user equipment UE substituting into the GSIC signal detection algorithm to obtain the signal estimate of the kth user equipment UE 3. The method of claim 2, wherein, In the step 5: For ZF-SIC detection, U = K, u k = k, the SINR of the kth user is denoted as: For ZF detection, U = 1, u k = 1, the SINR of the kth user is denoted as:

4. The method of claim 2, wherein, The step 4 utilizes the ZF-GSIC algorithm for signal detection, when U=K, G=1, u k =k, the received combining vector of the kth user equipment UE is: : When U = 1, G = K, u k = 1, the receive combining vector of the kth user equipment UE is: :

5. The method of claim 2, wherein, Additive Gaussian quantization distortion The covariance matrix of the additive Gaussian quantization distortion is given by: wherein is a semi-definite covariance matrix describing the channel spatial correlation.

6. The method of claim 2, wherein, After the step 2 grouping, the u-th group consists of UEs with sequence numbers k = G(u - 1) + 1,..., Gu, and the k-th user equipment UE has a group number 7. The method of claim 2, wherein, The channel vector between UE-i and AP-l is a spatially correlated Rayleigh fading channel.

8. The method of claim 2, wherein, The step 5 to estimate the signal is rewritten as: where n represents a set of additive white Gaussian noise of L access points APs, denotes the set channel estimation error of the kth UE.

9. An apparatus for asymptotic approximation of spectral efficiency of a cell-free massive MIMO system, the apparatus comprising: comprise a memory and a processor; The memory is configured to store a computer program; The processor is configured to implement the asymptotic approximation method for spectral efficiency of a cell-free massive MIMO system according to any one of claims 1 to 8 when executing the computer program.

10. A computer-readable storage medium, characterized in that, The storage medium has a computer program stored thereon, and the computer program, when executed by a processor, implements the asymptotic approximation method for spectral efficiency of a cell-free massive MIMO system according to any one of claims 1 to 8.

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