Progressive approximation method for spectrum efficiency of non-cellular large-scale MIMO system

Abstract

The invention discloses an asymptotic approximation method for spectrum efficiency of a non-cellular large-scale MIMO system, and belongs to the technical field of wireless communication. The method comprises the following steps: constructing a quantization system model; grouping all the user equipments, the groups being continuously detected, and simultaneously detecting the user equipments within the same group; constructing a grouped signal detection algorithm; detecting the received signal matrix by using a ZF-GSIC algorithm to obtain a sending signal estimated value of the user equipment; simulation results show that the system can reach high spectrum efficiency and high energy efficiency close to those of ZF-SIC detection under the condition of fewer groups, and the calculation complexity is greatly reduced, so that the hardware cost and the energy consumption can be greatly reduced. Besides, an asymptotic approximation expression of the system spectrum efficiency is deduced, the accuracy of the asymptotic approximation expression of the system spectrum efficiency is verified through a simulation result, and the obtained asymptotic result can be used for rapid system performance analysis.

Description

Technical Field

[0001] The invention relates to an asymptotic approximation method for spectrum efficiency of a non-cellular large-scale MIMO system, and belongs to the technical field of wireless communications. Background Art

[0002] The non-cellular massive multiple-input multiple-output (MIMO) system has become one of the most promising key technologies in the future B5G (Beyond 5G) and sixth generation (6G) networks. In the non-cellular massive MIMO system, the system is based on distributed massive MIMO and breaks the division of cell boundaries. That is, in a wide area, a large number of access points (APs) and user equipment (UEs) are distributed at the same time. Different APs are connected to the central processing unit (CPU) through backhaul links and provide services to all users under the same time and frequency resources according to the instructions of the CPU. Since the non-cellular massive MIMO system greatly reduces the distance between users and APs, it has a strong spatial macro-diversity gain and the ability to resist path loss, and can greatly improve the service quality of edge users. However, non-cellular massive MIMO systems usually require the deployment of a large number of APs. When the AP is equipped with a full-precision analog-to-digital converter (ADC) for quantization processing, it is bound to bring high hardware costs and huge energy consumption. In order to deal with this problem, configuring a low-precision ADC at the AP for quantization processing is undoubtedly a more direct solution. Therefore, the research on non-cellular massive MIMO systems equipped with low-resolution ADC is of great theoretical value and practical significance.

[0003] Regarding the modeling of ADC quantization distortion, there are two main models recognized by the academic community, namely Bussgang decomposition theorem and 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, while the latter can be used to analyze the impact of arbitrary bit quantization due to its strong operability.

[0004] The existing spectral efficiency (SE) analysis of non-cellular massive MIMO systems mainly focuses on linear signal detection algorithms, while there is less research on non-linear 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, non-cellular massive MIMO systems need to deploy a large number of APs and users, and the system is relatively complex. If the spectral efficiency of the system is directly analyzed, it will have certain complexity. In cellular networks, some researchers have studied the asymptotic approximation of the spectral efficiency of the system, but there are few studies on the asymptotic approximation of the spectral efficiency of non-cellular massive MIMO systems. The present invention performs an asymptotic approximation analysis on the spectral efficiency of the non-cellular system, and the asymptotic results obtained can be used for fast system performance analysis. Summary of the invention

[0005] In order to solve the problem that the existing non-cellular massive MIMO system is relatively complex and it is difficult to directly analyze the system spectrum efficiency, the present invention provides an asymptotic approximation method for the spectrum efficiency of the non-cellular massive MIMO system. The technical solution is as follows:

[0006] The asymptotic approximation method for the spectrum efficiency of the non-cellular massive MIMO system of the present invention, the system model is expressed as:

[0007]

[0008] The system model includes L access points AP and K user equipment UE, each AP is configured with N antennas, and each UE is configured with 1 antenna;

[0009] Among them, y l represents the signal received at the lth access point AP-1, x i represents the information symbol sent by the i-th user equipment UE-i, h il represents the channel vector between UE-i and AP-1, n l represents the additive white Gaussian noise on AP-1;

[0010] The method comprises:

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

[0012] Step 2: Divide all user equipment UEs into U groups evenly, each group consists of The groups are composed of user equipments UE, where 1≤U≤K, and these groups are detected continuously, and user equipments UE in the same group are detected simultaneously;

[0013] Step 3: Construct the group SIC signal detection algorithm GSIC. The GSIC signal detection algorithm is expressed as:

[0014]

[0015] in, represents the estimated value of the transmitted signal of the kth user equipment UE, v k is the receiving combination vector of the kth user equipment UE, α represents the distortion coefficient, Represents y l The quantized signal, represents the group number of the kth user equipment UE, h i Denotes the channel vector h il A collection of;

[0016] Step 4: Use the ZF-GSIC detection algorithm to detect the received signal matrix y q Perform detection to obtain the estimated value of the transmitted signal of the kth user equipment UE

[0017] Step 5: Make an asymptotic approximation to the spectrum efficiency expression of the system;

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

[0019]

[0020] Among them, in τ c The channel remains unchanged in the coherent time-frequency block of symbols. Each time-frequency block is realized independently and randomly. Assuming τ p The symbol is used for uplink training, τ c -τ p Used for uplink data transmission. It represents the signal to interference plus noise ratio SINR at the kth user equipment UE:

[0021]

[0022] Among them, p k represents the transmission power of the kth user equipment UE, Σ is a block diagonal matrix, and for The inverse matrix of represents the aggregate channel estimate of the kth UE.

[0023] Optionally, the step 4 uses the ZF-GSIC detection algorithm to detect the received signal matrix y q Perform detection to obtain the estimated value of the transmitted signal The process includes:

[0024] The received combination vector of the kth user equipment UE It is expressed as:

[0025]

[0026] in Indicates the uth k The combination vector of all UEs in the group is expressed as:

[0027]

[0028] in, represents the estimated value of the channel matrix, Representation Matrix The nth column of .

[0029] The receiving combination vector of the kth user equipment UE Substitute into the GSIC signal detection algorithm to obtain the signal estimation value of the kth user equipment UE

[0030] Optionally, in step 5:

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

[0032]

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

[0034]

[0035] Optionally, the step 4 uses the ZF-GSIC algorithm to perform signal detection. When U=K, G=1, u k = k, at this time, the receiving combination vector of the kth user equipment UE for:

[0036]

[0037] When U=1, G=K, u k =1, at this time, the receiving combination vector of the kth user equipment UE for:

[0038]

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

[0040]

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

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

[0043] Optionally, the channel vector between UE-i and AP-1 is a spatially correlated Rayleigh fading channel.

[0044] Optionally, the step 5 estimates the signal Rewrite it as:

[0045]

[0046] Where n represents the additive Gaussian white noise set of L access points AP, represents the aggregate channel estimation error of the kth UE.

[0047] The present invention provides a spectrum efficiency approximation device for a non-cellular massive MIMO system, comprising a memory and a processor;

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

[0049] The processor is configured to implement the spectrum efficiency approximation method as described in any one of the above items when executing the computer program.

[0050] The present invention provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the spectrum efficiency approximation method as described in any one of the above items is implemented.

[0051] The beneficial effects of the present invention are:

[0052] The present invention proposes a group ZF-SIC (ZF Group SIC, ZF-GSIC) signal detection method, which uses the ZF-GSIC signal detection method to obtain the estimated value of the transmitted signal of each user equipment UE from the received signal matrix, and at the same time, a zero forcing (ZF) signal detection method and a nonlinear ZF-SIC signal detection method can be used as four special cases of the ZF-GSIC signal detection method of the present invention under specific conditions. In addition, the present invention derives an asymptotic approximation expression of the system spectrum efficiency.

[0053] Simulation results show that the signal detection of non-cellular massive MIMO systems using the ZF-GSIC signal detection method proposed in the present invention can maintain high spectral efficiency and energy efficiency on the basis of effectively reducing signal processing complexity, processing delay and implementation cost. When using a low-precision ADC and a small number of groups, the spectral efficiency and energy efficiency of the ZF-GSIC signal detection method proposed in the present invention are very close to those of traditional ZF-SIC detection, but the computational complexity can be greatly reduced.

[0054] The present invention solves the problem that the non-cellular massive MIMO system is relatively complex and difficult to directly analyze the system spectrum efficiency by performing asymptotic approximation analysis on the spectrum efficiency of the non-cellular massive MIMO system. The simulation results verify the accuracy of the asymptotic approximation expression of the system spectrum efficiency derived by the present invention, and the obtained asymptotic results can be used for rapid system performance analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0056] FIG1( a ) is a cumulative distribution function diagram of the total spectrum efficiency of the signal detection method for a non-cellular massive MIMO system based on the ZF-GSIC algorithm of the present invention under ideal and non-ideal CSI conditions when L=100 and N=1.

[0057] FIG1( b ) is a cumulative distribution function diagram of the total spectrum efficiency of the signal detection method for a non-cellular massive MIMO system based on the ZF-GSIC algorithm of the present invention under ideal and non-ideal CSI conditions when L=50 and N=2.

[0058] FIG2( a ) shows the average spectral efficiency results of three different detection algorithms under non-ideal CSI when U=2, and also provides the average spectral efficiency of an ideal ADC as a reference.

[0059] FIG2( b ) shows the average spectral efficiency results of three different detection algorithms under non-ideal CSI when U=5, and also provides the average spectral efficiency of an ideal ADC as a reference.

[0060] Figure 3(a) is a graph showing the average spectrum efficiency of each UE in the non-cellular massive MIMO system signal detection method based on the ZF-GSIC algorithm of the present invention as a function of the number of APs when U = 2 under ideal and non-ideal CSI conditions. The simulation results compare the spectrum efficiency approximation with the exact result obtained by the Monte Carlo simulation method.

[0061] Figure 3(b) is a graph showing the average spectrum efficiency of each UE in the non-cellular massive MIMO system signal detection method based on the ZF-GSIC algorithm of the present invention as a function of the number of APs when U = 5 under ideal and non-ideal CSI conditions. The simulation results compare the spectrum efficiency approximation with the exact result obtained by the Monte Carlo simulation method.

[0062] Figure 4 The figure is a curve diagram showing the variation of the average spectrum efficiency of each UE with the number of antennas of each AP in the non-cellular massive MIMO system signal detection method based on the ZF-GSIC algorithm of the present invention when U=2 and when U=5 under ideal and non-ideal CSI conditions. The simulation results compare the approximate value of the spectrum efficiency with the exact result obtained by the Monte Carlo simulation method.

[0063] FIG5(a) is a graph showing the energy efficiency corresponding to different detection algorithms when U=2 and the number of quantization bits.

[0064] FIG5( b ) is a graph showing the energy efficiency corresponding to different detection algorithms when U=5 and the number of quantization bits. DETAILED DESCRIPTION

[0065] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0066] Embodiment 1:

[0067] This embodiment provides an asymptotic approximation method for spectrum efficiency of a non-cellular massive MIMO system. The system model is expressed as follows:

[0068]

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

[0070] Among them, y lrepresents the signal received at the lth access point AP-1, x i represents the information symbol sent by the i-th user equipment UE-i, h il represents the channel vector between UE-i and AP-1, n l represents the additive white Gaussian noise on AP-1;

[0071] The method of this embodiment includes:

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

[0073] Step 2: Divide all user equipment UEs into U groups evenly, each group consists of The groups are composed of user equipments UE, where 1≤U≤K, and these groups are detected continuously, and user equipments UE in the same group are detected simultaneously;

[0074] Step 3: Construct the group SIC signal detection algorithm GSIC. The GSIC signal detection algorithm is expressed as:

[0075]

[0076] in, represents the estimated value of the transmitted signal of the kth user equipment UE, v k is the receiving combination vector of the kth user equipment UE, α represents the distortion coefficient, Represents y l The quantized signal, represents the group number of the kth user equipment UE, h i Denotes the channel vector h il A collection of;

[0077] Step 4: Use the ZF-GSIC detection algorithm to detect the received signal matrix y q Perform detection to obtain the estimated value of the transmitted signal of the kth user equipment UE

[0078] Step 5: Make an asymptotic approximation to the spectral efficiency expression of the system.

[0079] Embodiment 2:

[0080] This embodiment provides an asymptotic approximation method for spectrum efficiency of a non-cellular massive MIMO system, and the system model applicable to the method is:

[0081]

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

[0083] This embodiment considers a non-cellular massive MIMO system in a spatially correlated Rayleigh fading channel, with L geographically distributed APs and K UEs, each AP is configured with N antennas, and each UE is configured with one antenna. It is assumed that the time division duplex (TDD) protocol is used. In τ c The channel remains unchanged in the coherent time-frequency block of symbols. Each time-frequency block is realized independently and randomly. Assuming τ p The symbol is used for uplink training, τ c -τ p Used for uplink data transmission.

[0084] The channel is modeled as a spatially correlated Rayleigh fading distribution, so the channel vector h between UE-k and AP-l is kl It is expressed as:

[0085]

[0086] in is the semi-positive definite covariance matrix describing the spatial correlation of the channel; the average channel gain from an antenna at the lth AP to the kth UE is given by the normalized trace β kl =tr(R kl ) / N, which is the large-scale fading coefficient that describes geometric path loss and shadow fading.

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

[0088]

[0089] In this embodiment, L APs receive the received data signal {y l :l=1,...,L} is sent to the CPU, which is responsible for detecting the data signal. That is, the AP acts as a relay and forwards its received signal to the CPU for processing. More precisely, each AP sends the received pilot signal and the received uplink data signal to the CPU, and the CPU performs channel estimation, reception combination and data detection. The received signal available on the CPU is represented as:

[0090]

[0091] Formula (4) can be expressed in a more concise form:

[0092]

[0093] Assumptions is the distribution of the aggregate channels, where the block diagonal spatial correlation matrix is ​​given by In addition, Defined as the channel matrix.

[0094] Since in actual situations, the channel state information (CSI) is usually obtained during the training phase. In the present invention, the minimum mean-square error (MMSE) method is used to estimate the channel. Since the centralized non-cellular massive MIMO system is considered, the CPU can use the channel statistics obtained at the AP and the received pilot signal to calculate all MMSE channel estimates. These estimates can be calculated individually without losing optimality. Then, the aggregate channel estimate can be obtained at the CPU, and the aggregate channel estimate for the kth UE can be expressed as:

[0095]

[0096] The aggregate channel estimation error of the kth UE can be expressed as In addition, the definition As an estimate of the channel matrix H.

[0097] The method comprises:

[0098] Step 1: Construct a quantization system model of a low-precision ADC based on a linear additive quantization noise model (AQNM).

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

[0100]

[0101] in, represents the received signal vector at AP-1; is the information symbol (i.e., the transmitted signal) sent by the i-th UE, and its transmission power is p i ;h il is the channel vector between UE-i and AP-1;

[0102] is the additive Gaussian white noise on the lth AP, and its variance is σ 2 ; represents the quantized signal, α is the distortion coefficient, which depends on the number of quantized bits b; is with y l Uncorrelated additive Gaussian quantization distortion, The covariance matrix of is expressed as:

[0103]

[0104] The symbol diag(·) is used to extract the diagonal elements and create a diagonal matrix, I N is the N×N identity matrix.

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

[0106] The u-th group consists of UEs with sequence numbers k=G(u-1)+1,…,Gu. Therefore, the group number of the k-th UE is For example, consider a network of K=40 UEs, divided equally into U=10 groups. The number of UEs in 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 in the same group are detected simultaneously.

[0107] Step 3: Construct a group SIC (GSIC) signal detection algorithm based on the idea of ​​SIC detection;

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

[0109]

[0110] in represents the estimated value of the transmitted signal of the kth UE, v k is the received combination vector of the kth UE, and the superscript H indicates that the conjugate transpose is obtained.

[0111] Step 4: Use the ZF-GSIC detection algorithm to detect the received signal y q The transmitted signal of each user can be recovered.

[0112] Among them, the ZF-GSIC detection algorithm is used to detect the received signal y q The process of recovering the sent signal of each user is as follows:

[0113] Using formula (10) and the ZF-GSIC algorithm for signal detection, the receiving combination vector of the kth UE is It is expressed as:

[0114]

[0115] in Indicates the uth k The combination vector of all UEs in the group is expressed as:

[0116]

[0117] In particular, for the ZF-SIC detector, U = K, G = 1, u k = k, at this time, the receiving combination vector of the kth UE for:

[0118]

[0119] For the ZF detector, U = 1, G = K, u k =1, at this time, the receiving combination vector of the kth UE for:

[0120]

[0121] Finally, the received combination vector of the kth UE is Substituting into the GSIC signal detection algorithm of formula (9), the estimated value of the transmitted signal of the kth UE can be obtained.

[0122] Step 5: Make an asymptotic approximation to the spectral efficiency expression of the system.

[0123] First, the estimated signal Rewrite it as In order to facilitate subsequent derivation, it is further abbreviated as:

[0124]

[0125] in, represents the channel estimation error, defined as in,

[0126]

[0127] The spectrum efficiency at the kth user equipment UE is expressed as:

[0128]

[0129] Among them, in τ c The channel remains unchanged in the coherent time-frequency block of symbols. Each time-frequency block is realized independently and randomly. Assuming τ p The symbol is used for uplink training, τ c -τ pUsed for uplink data transmission. Expressing expectation.

[0130] in is the signal to interference plus noise ratio SINR at the kth user equipment UE, expressed as:

[0131]

[0132] Among them, p k represents the transmission power of the kth UE.

[0133] in because In space it is not white, so by using a filter To whiten it, we get:

[0134]

[0135] where Σ is a block diagonal matrix represented as:

[0136]

[0137] Among them, Σ l represents the lth block in the diagonal matrix Σ.

[0138] Each term in formula (18) represents the variance of channel noise, the quantization distortion covariance matrix and the variance of channel estimation error. The ZF-GSIC detection vector can be further expressed as:

[0139]

[0140] in, represents the inverse matrix of Σ,

[0141] The received combination vector of the kth UE is Therefore, we can get:

[0142]

[0143] Then, the SINR of the kth user is expressed as:

[0144]

[0145] in Furthermore, formula (21) can be approximated as:

[0146]

[0147] Furthermore, the final approximate expression can be obtained as:

[0148]

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

[0150]

[0151] For ZF detection, U=1,u k =1, formula (23) can be expressed as:

[0152]

[0153] In order to make the purpose, technical solution and advantages of the present invention clearer, some classic detection algorithms are used to compare with the present invention to show the superiority of the signal detection method based on the ZF-GSIC algorithm of the present invention in improving system performance. In addition, the asymptotic approximation expression of the spectrum efficiency of the present invention is compared with the real spectrum efficiency.

[0154] The detection algorithms used for simulation are respectively based on the ZF detection algorithm, the ZF-SIC detection algorithm and the signal detection method based on the ZF-GSIC algorithm of the present invention, and the approximate expression and true expression of the system spectrum efficiency under ZF-GSIC detection are simulated and analyzed.

[0155] Among them, the ZF detection algorithm is a classic linear detection algorithm, and the ZF-SIC detection algorithm is a classic nonlinear detection algorithm; the signal detection method based on the ZF-GSIC algorithm of the present invention can achieve system SE and EE performance close to that of the SIC detection algorithm at low complexity through fewer groups. In addition, the simulation results verify the accuracy of the approximate expression of the spectral efficiency derived by the present invention, and the obtained asymptotic results can be used for rapid performance analysis.

[0156] The experimental results are shown in the simulation curve in the accompanying drawings. It can be seen from the simulation curve that the spectrum efficiency of the system detected by the ZF-GSIC of the present invention can be improved as the number of groups increases, and when there are fewer groups, such as in 5 groups, the system can achieve a spectrum efficiency and energy efficiency that are very close to that when SIC detection is used. In addition, the system of the ideal ADC and the system of ADC quantization are compared through simulation experiments. The results show that when the number of quantization bits is 5 or 6, the spectrum efficiency and energy efficiency of the system can reach the optimal situation. This shows that under tolerable performance loss, a 5-bit ADC can be used to replace the ideal ADC, thereby significantly reducing hardware costs and energy consumption. In addition, the simulation results compare the approximate value of the spectrum efficiency with the exact result obtained by the Monte Carlo simulation method. The results show that the approximate result has a high accuracy, which verifies the analysis results of the present invention.

[0157] As shown in Figure 1(a) and Figure 1(b), the SIC detection method significantly improves the performance of the system. In addition, the performance of the spectral efficiency of the ZF-SIC detection significantly exceeds that of the linear ZF detection. The performance of the system spectral efficiency of the proposed ZF-GSIC detection with lower latency is between that of ZF and ZF-SIC. The performance difference between ideal CSI and non-ideal CSI originates from the channel estimation error, resulting in higher spectral efficiency under ideal CSI. Figure 1(a) and Figure 1(b) show the cases when the number of APs and their antennas are L=100, N=1 and L=50, N=2 respectively. Figure 1(b) considers the same setting, but with fewer APs equipped with multiple antennas. It can be seen from the figure that the overall trend of Figure 1(b) is the same as that of Figure 1(a), but the SE of Figure 1(b) is lost compared to Figure 1(a) due to the reduction of macro-diversity, that is, the increase in the average distance from UE to AP.

[0158] As shown in Figure 2(a) and Figure 2(b), the ZF-SIC detection produces the highest spectral efficiency, while the linear ZF detection produces the lowest spectral efficiency. The ZF-GSIC detection proposed in the present invention is between the two. The results show that as the number of quantization bits increases, the average spectral efficiency approaches that of an ideal ADC. When the number of quantization bits is 6, the spectral efficiency converges to a fixed bound, which indicates that a 6-bit ADC architecture can achieve performance comparable to that of an ideal ADC. Figure 2(a) and Figure 2(b) are the cases when U=2 and U=5, respectively. It can be seen from the simulation results that when there are more groups, the system has higher spectral efficiency.

[0159] As shown in Figure 3(a) and Figure 3(b), the approximate results of the spectrum efficiency have high accuracy, which verifies the analysis results of the present invention. In addition, as the number of APs increases, the average spectrum efficiency of each UE gradually increases, so the performance of the system can be improved by increasing the number of APs. Figure 3(a) and Figure 3(b) are the cases when U=2 and U=5, respectively. The results show that as the number of groups increases, the performance of the spectrum efficiency of the system is improved accordingly. Therefore, increasing the number of groups can improve the system performance, which further confirms the accuracy of the derived asymptotic approximation expression.

[0160] like Figure 4 As shown in the figure, as the number of antennas of each AP increases, the average spectrum efficiency of each UE gradually increases, so the performance of the system can be improved by increasing the number of AP antennas. In addition, the approximate result of the system spectrum efficiency is compared with the exact result, and the result verifies the accuracy of the asymptotic approximation expression introduced by the present invention. Similar to the result of FIG3 , the number of groups detected by ZF-GSIC is set to 5 groups. It can be found that when the number of antennas of the AP changes, as the number of groups increases, the performance of the spectrum efficiency of the system is improved accordingly. Therefore, increasing the number of groups can improve the system performance, which further confirms the accuracy of the derived asymptotic approximation expression.

[0161] As shown in Figures 5(a) and 5(b), for different detection algorithms, higher energy efficiency can be achieved at lower quantization bit numbers (such as b = 2 and 3). In addition, it can be seen that under different detectors, the energy efficiency increases with the increase of quantization bits, and then decreases due to severe quantization loss and increased 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 the energy efficiency of low-resolution ADC systems can be improved by properly selecting quantization bits. This insight shows that low-resolution ADC architectures have great potential for improvement regardless of the detector type. Figures 5(a) and 5(b) 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 that of the ZF-SIC receiver, and this result also confirms that higher system performance can be achieved by adopting a smaller number of groups. In addition, the larger the number of groups, the higher the energy efficiency, that is, in Figures 5(a) and 5(b), the energy efficiency at U = 5 is higher than that at U = 2. Through the simulation of energy efficiency performance, the effectiveness of the signal detection method based on the ZF-GSIC algorithm proposed in the present invention applied to the non-cellular system is further verified.

[0162] In summary, compared with linear detection, the SIC detection system has higher spectral efficiency and energy efficiency. On the basis of effectively reducing the signal processing complexity, processing delay and implementation cost, using a low-precision ADC, under a small number of groups, the spectral efficiency and energy efficiency of the system under the signal detection method based on the ZF-GSIC algorithm proposed in the present invention are very close to the traditional ZF-SIC detection. In addition, the simulation results verify the accuracy of the asymptotic approximation expression of the system spectral efficiency derived by the present invention, and the obtained asymptotic results can be used for rapid system performance analysis.

[0163] Some steps in the embodiments of the present invention may be implemented using software, and the corresponding software program may be stored in a readable storage medium, such as a CD or a hard disk.

[0164] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. An asymptotic approximation method for the spectrum efficiency of a non-cellular massive MIMO system. The system model is expressed as: The system model includes L access points AP and K user equipment UE, each AP is configured with N antennas, and each UE is configured with 1 antenna; in, y l represents the signal received at the lth access point AP-1, x i represents the information symbol sent by the i-th user equipment UE-i, h il represents the channel vector between UE-i and AP-1, n l represents the additive white Gaussian noise on AP-1; Characterized in that the method comprises: Step 1: construct a quantization system model for the system model to be detected according to a linear additive quantization noise model AQNM; Step 2: Divide all user equipment UEs into U groups evenly, each group consists of The groups are composed of user equipments UE, where 1≤U≤K, and these groups are detected continuously, and user equipments UE in the same group are detected simultaneously; Step 3: Construct the group SIC signal detection algorithm GSIC. The GSIC signal detection algorithm is expressed as: in, represents the estimated value of the transmitted signal of the kth user equipment UE, v k is the receiving combination vector of the kth user equipment UE, α represents the distortion coefficient, Represents y l The quantized signal, represents the group number of the kth user equipment UE, h i Denotes the channel vector h il A collection of; Step 4: Use the ZF-GSIC detection algorithm to detect the received signal matrix y q Perform detection to obtain the estimated value of the transmitted signal of the kth user equipment UE Step 5: Make an asymptotic approximation to the spectrum efficiency expression of the system; The spectrum efficiency at the kth user equipment UE is expressed as: In τ c In the coherent time-frequency block of the symbol, the channel remains unchanged, and each time-frequency block is realized independently and randomly; assuming τ p The symbol is used for uplink training, τ c -τ p Used for uplink data transmission; It represents the signal to interference plus noise ratio SINR at the kth user equipment UE: Among them, p k represents the transmission power of the kth user equipment UE, Σ is a block diagonal matrix, and for The inverse matrix of represents the aggregate channel estimate of the kth UE.

2. The method according to claim 1, characterized in that: The step 4 uses the ZF-GSIC detection algorithm to detect the received signal matrix y q Perform detection to obtain the estimated value of the transmitted signal The process includes: The received combination vector of the kth user equipment UE It is expressed as: in Indicates the uth k The combination vector of all UEs in the group is expressed as: in, represents the estimated value of the channel matrix, Representation Matrix The nth column of The receiving combination vector of the kth user equipment UE Substitute into the GSIC signal detection algorithm to obtain the signal estimation value of the kth user equipment UE 3. The method according to claim 2, characterized in that In step 5: For ZF-SIC detection, U = K,u k =k, the SINR of the kth user is expressed as: For ZF detection, U=1,u k =1, the SINR of the kth user is expressed as:

4. The method according to claim 2, characterized in that: Step 4 uses the ZF-GSIC algorithm to detect the signal. When U=K, G=1, u k = k, at this time, the receiving combination vector of the kth user equipment UE for: When U=1, G=K, u k =1, at this time, the receiving combination vector of the kth user equipment UE for:

5. The method according to claim 2, characterized in that: Additive Gaussian Quantization Distortion The covariance matrix of is expressed as: in, is the semi-positive definite covariance matrix describing the spatial correlation of the channel, p i represents the transmission power of the i-th user equipment UE, σ2 represents the additive white Gaussian noise n l The variance of , diag(·) is used to extract the diagonal elements and create a diagonal matrix, I N is the N×N identity matrix.

6. The method according to claim 2, characterized in that After the grouping in step 2, the uth group consists of UEs with sequence numbers k=G(u-1)+1,…,Gu, and the group number of the kth user equipment UE is 7. The method according to claim 2, characterized in that The channel vector between UE-i and AP-1 is a spatially correlated Rayleigh fading channel.

8. The method according to claim 2, characterized in that: The step 5 estimates the signal Rewrite it as: Where n represents the additive Gaussian white noise set of L access points AP, represents the aggregate channel estimation error of the kth UE.

9. An asymptotic approximation device for spectrum efficiency of a non-cellular massive MIMO system, characterized in that: including memory and processor; The memory is used to store computer programs; The processor is configured to implement the asymptotic approximation method for the spectrum efficiency of a non-cellular massive MIMO system as claimed in any one of claims 1 to 8 when executing the computer program.

10. A computer-readable storage medium, characterized in that: The storage medium stores a computer program, and when the computer program is executed by a processor, the asymptotic approximation method for the spectrum efficiency of a non-cellular massive MIMO system as described in any one of claims 1 to 8 is implemented.

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