CN109361441B - Design method of finite feedback codebook for MU-MISO system based on channel statistics - Google Patents

Abstract

The invention discloses a method for designing a limited feedback codebook of an MU-MISO system based on channel statistical information, which comprises the following steps: step 1, analyzing traversal channel capacity at high and low signal-to-noise ratios under the condition of known complete channel state information and known statistical information of a transmitting terminal; step 2, respectively representing the capacity loss of the ergodic channel under two conditions by adopting a channel statistical information classification method; and 3, combining the method for inserting the feature matrix with the channel statistical information to realize the design of the code book. The codebook design method can reduce the influence of the ill-conditioned channel on the system traversal channel capacity and obviously improve the system traversal channel capacity.

Description

Design method of finite feedback codebook for MU-MISO system based on channel statistics

technical field

The invention relates to a method for designing a limited feedback codebook for a multi-user multiple-input single-output (MU-MISO) system based on channel statistical information.

Background technique

In a multi-input single-output (MISO) closed-loop system, the receiver can feed back the channel state information to the transmitter, and the transmitter obtains diversity and array gain through finite feedback precoding technology ([1]Love D J , Heath R W, Lau V K N, et al. An overview of limited feedback inwireless communication systems [J]. IEEE Journal on Selected Areas in Communications, 2008, 26(8): 1341-1365). Multi-Users MISO (MU-MISO) limited feedback technology under IID Rayleigh fading channel has been well studied ([2] Ko K, JungS, Lee J. Hybrid MU-MISO Scheduling with Limited Feedback Using HierarchicalCodebooks.IEEE Transactions on Communications,2012,60(4):1101-1113.[3]DuplicyJ,Badic B,Balraj R,et al.MU-MIMO in LTE Systems[J].Eurasip Journal onWireless Communications&Networking, 2011,2011(1):496763.[4]Ozbek B,Ruyet DL.Feedback strategies for wireless communication[J].2013,2(3583):452-4). Limited feedback techniques under spatially and temporally correlated channels are still the focus of research.

Studies have shown that when the MU-MISO channel has spatial correlation, the fading correlation reduces the system performance of the channel ([5] Shen W, Dai L, Zhang Y, et al. On the Performance of Channel Statistics-Based Codebook for Massive MIMO Channel Feedback[J].IEEE Transactions on VehicularTechnology,2017,8(66):7553-7557.). Existing feedback strategies are divided into codebook-based rotation and codebook-based scaling ([6] Choi J, Clerckx B, Lee N, et al. A New Design of Polar-Cap Differential Codebook for Temporally/Spatially Correlated MISO Channels [J] .IEEE Transactions on Wireless Communications,2012,11(2):703-711.[7]Sun Y,Zhang J,Zhang P,et al.Practical differential quantization for spatially and temporally correlated massive MISO channels[C]//IEEE,International Symposiumon Personal, Indoor, and Mobile Radio Communication. IEEE, 2015: 486-491) two types of algorithms, both of which do not consider the ill-conditioned channel caused by correlation. The feedback algorithm based on codebook scaling has better system performance than the feedback algorithm based on codebook rotation, but the design complexity of the codebook is relatively high, and the operation steps are relatively cumbersome. Although the performance of the feedback algorithm based on codebook rotation is suboptimal, the design method is extremely simple. Due to the existence of channel correlation, the channel is usually ill-conditioned, and the influence of the condition number of the ill-conditioned channel matrix on the capacity of the ergodic channel is inevitable. Among all channels with equal total power gain, the channel with condition number 1 has the largest ergodic channel capacity, but as the condition number increases, the ill-conditioned degree of the channel is also greater, and the ergodic channel capacity decreases accordingly ([8] Raghavan V , Hanly S V, Veeravalli V V.StatisticalBeamforming on the Grassmann Manifold for the Two-User Broadcast Channel[J].IEEE Transactions on Information Theory,2011,59(10):6464-6489.[9]Choi J,LoveD J. Bounds on Eigenvalues of a Spatial Correlation Matrix[J]. IEEE Communications Letters, 2014, 18(8):1391-1394).

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a limited feedback codebook design method for MU-MISO system based on channel statistics, which can reduce the impact of ill-conditioned channels on system ergodic channel capacity, and can significantly improve system ergodic channel capacity.

In order to achieve the above-mentioned purpose, the solution of the present invention is:

A method for designing a limited feedback codebook for a MU-MISO system based on channel statistical information, comprising the following steps:

Step 1, analyze the traversal channel capacity at high and low signal-to-noise ratios when the transmitting end knows the complete channel state information and the transmitting end knows the statistical information;

Step 2, using the method of channel statistical information classification to respectively represent the traversal channel capacity loss in two cases;

In step 3, the method of inserting the feature matrix is combined with the channel statistical information to realize the design of the codebook.

The above MU-MISO system is configured with M transmitting antennas, the number of users is K, each user is configured with one receiving antenna, and the received signal of the i-th user is:

为加性复高斯白噪声；发射信号

f_i为M×1预编码矢量；s_i为数据符号且E[|s_i|²]＝1。Among them, ρ is the signal-to-noise ratio; _hi is the M×1 channel matrix; x is the transmitted signal;

is additive white Gaussian noise; the transmitted signal

f _i is an M×1 precoding vector; s _i is a data symbol and E[|s _i | ² ]=1.

In the above step 1, when the transmitter knows the complete channel state information, the channel capacity R _perf of the system satisfies the following conditions:

为h₁与h₂之间的弦距离：Among them, ρ is the signal-to-noise ratio; _hi is the channel matrix of M×1, M is the number of transmitting antennas, and M=2;

is the chord distance between _h1 and h2 _:

Meanwhile, the ergodic channel capacity E[R _perf ] of the system is:

Λ_i＝diag([λ₁(R_i),λ₂(R_i)])；λ₁(R_i)与λ₂(R_i)分别为半正定矩阵R_i∈C^M×M的第1个与第2个特征值且λ₁(R_i)≥…≥λ_M(R_i)。in,

Λ _i =diag([λ ₁ (R _i ),λ ₂ (R _i )]); λ ₁ ( ^R _i ) and λ ₂ (R _{i )} are the first and the second eigenvalue and λ ₁ (R _i )≥…≥λ _M (R _i ).

In the above step 1, when the transmitter knows the statistical information, the traversal channel capacity of the system in the case of low signal-to-noise ratio is:

Among them, R _i is the spatial emission correlation matrix;

Z＝[z₁,z₂]；η₁≥η₂≥0；高信噪比时遍历信道容量为definition

Z=[z ₁ ,z ₂ ]; η ₁ ≥η ₂ ≥0; when the signal-to-noise ratio is high, the ergodic channel capacity is

in,

In the above step 2, when the transmitter knows the complete channel state information, two conditions in the channel are defined:

C ₂ : U _i =U _j P,j≠i

Among them, R _i is the spatial emission correlation matrix; the condition number of R _i χ _i =χ(R _i )=λ ₁ (R _i )/λ ₂ (R _i ) is an index to measure the ill-conditioned degree of the channel matrix; M is the The number of transmitting antennas, and M=2; P is a 2×2 permutation matrix;

If the channel does not satisfy the condition C _1,i but satisfies the condition C ₂ , the performance loss of traversing the channel capacity is

If the channel satisfies the condition C _1,i but not the condition C ₂ , the performance loss of traversing the channel capacity is

In the above step 2, when the transmitter knows the statistical information, two conditions in the channel are defined:

C ₂ : U _i =U _j P,j≠i

Among them, R _i is the spatial emission correlation matrix; the condition number of R _i χ _i =χ(R _i )=λ ₁ (R _i )/λ ₂ (R _i ) is an index to measure the ill-conditioned degree of the channel matrix; M is the The number of transmitting antennas, and M=2; P is a 2×2 permutation matrix;

If the channel does not satisfy the condition C _1,i but satisfies the condition C ₂ , the performance loss of traversing the channel capacity is

If the channel satisfies the condition C _1,i but not the condition C ₂ , the performance loss of traversing the channel capacity is

In the above step 3, when the signal-to-noise ratio is low, the optimal codeword wi _,opt =u ₁ (R _i ) of each user is obtained by solving the eigenvector equation R _i w _i =γ _i w _i , i=1,2 , i=1,2, u ₁ (·) is the main unit normalized eigenvector of the matrix; when the signal-to-noise ratio is high, by solving the vector equation R _i w _i =γ _i R _j w _i , i≠j, i= 1, 2 Obtain the optimal codeword of each user, at this time, the optimal codeword of each user is represented by the generalized eigenvector group

Using the method of inserting the feature matrix to solve the design problem of the optimal code word when the signal-to-noise ratio is high and low

R _i w _interp,i =(R _i +α _i (ρ)I)w _interp,i →w _interp,i =u ₁ ((R _i +α _i (ρ)- ¹ I)R _i )

Therefore, the codebook is designed as

为单用户时的码书。where α _i (ρ) is a function of R ₁ , R ₂ and ρ;

The codebook when it is a single user.

In above-mentioned step 3, adopt following code word selection criterion:

In step a, it is assumed that each user only guarantees that the mapping value of the precoding vector on its channel is the largest, namely:

为一个与信道矢量h_j无关而与空间发射相关矩阵R_j有关的常量；in,

is a constant which is independent of the channel vector h _j and related to the spatial emission correlation matrix R _j ;

作为第i个用户的候选预编码矢量，S_i的估计值

I_i的估计值为step b,

As the candidate precoding vector of the ith user, the estimated value of S _i

The estimated value of I _i is

的最大化，即Step c, the optimal codeword selection criterion is the estimated value of SINR _i

maximization of

After adopting the above scheme, the present invention starts from the shortcomings of the codebook-based rotation feedback algorithm and the ill-conditioned channel matrix, uses the method of channel statistical information classification to calculate the loss of traversal channel capacity when the signal-to-noise ratio is high and low, and then inserts the feature matrix. The codeword is designed by combining the method with channel statistics. Simulation experiments show that, compared with the existing methods, the present invention significantly improves the traversal channel capacity of the system for channels with different ill-conditioned degrees.

Description of drawings

Fig. 1 is a graph showing the variation of ΔR with χ ₁ and χ ₂ ;

Figure 2 is a schematic diagram of the comparison of traversal channel capacity in four different scenarios;

FIG. 3 is a schematic diagram of the traversal channel capacity when B=1, 2, 3, and 4;

Figure 4 is a schematic diagram of the traversal channel capacity of each user.

Detailed ways

The technical solutions and beneficial effects of the present invention will be described in detail below with reference to the accompanying drawings.

1. System Model

The multi-user MISO limited feedback system is configured with M transmitting antennas, the number of users is K, and each user is configured with one receiving antenna. The received signal of the i-th user is:

为加性复高斯白噪声。发射信号

f_i为M×1预编码矢量；s_i为数据符号且E[|s_i|²]＝1。Among them, ρ is the signal-to-noise ratio; _hi is the M×1 channel matrix; x is the transmitted signal;

is additive complex Gaussian white noise. transmit a signal

f _i is an M×1 precoding vector; s _i is a data symbol and E[|s _i | ² ]=1.

中选择出最优码字；如使得接收信噪比最大化的最优码字选取准则为：In the limited feedback method based on the codebook, the receiver estimates h _i through the channel, and based on some optimization criteria

The optimal codeword is selected from among them; for example, the optimal codeword selection criterion to maximize the received signal-to-noise ratio is:

The receiving end uses B feedback bits to index the 2 ^B codewords, and feeds back the index value of the optimal codeword c _i,opt to the transmitting end through a low-speed feedback channel, and the transmitting end uses this index value to find the corresponding code in the codebook. codeword, and use this codeword as the precoding vector ^[10-11] .

In the space transmission related multi-user MISO system studied by the present invention, the channel matrix of the i-th user is:

为独立同分布的矢量。本实施例中假设K＝M。Among them, R _i is the spatial emission correlation matrix;

is an independent and identically distributed vector. In this embodiment, it is assumed that K=M.

2. Traversal channel capacity analysis

If the interference between users is regarded as noise, the traversal channel capacity of the i-th user is:

M＝2时，分发射端已知完整信道状态信息和发射端已知统计信息两种情况对遍历信道容量进行分析，并引入了以发射相关矩阵为信道状态信息分类的方法。2.1完整信道状态信息Among them, SINR _i is the signal-to-interference-noise ratio. Ergodic Channel Capacity of Multi-User MISO Systems

When M=2, the ergodic channel capacity is analyzed in two cases, the complete channel state information is known by the transmitter and the statistical information is known by the transmitter, and a method of classifying the channel state information by the transmit correlation matrix is introduced. 2.1 Complete channel state information

When the complete channel state information of all users is known at the transmitter, the minimum mean square error precoding can minimize the performance loss at high signal-to-noise ratios. At this time, the channel capacity R _perf of the system satisfies the following conditions:

为h₁与h₂之间的弦距离：in,

is the chord distance between _h1 and h2 _:

Meanwhile, the ergodic channel capacity E[R _perf ] of the system is:

Λ_i＝diag([λ₁(R_i),λ₂(R_i)])；λ₁(R_i)与λ₂(R_i)为半正定矩阵R_i∈C^M×M的第1个与第2个特征值且λ₁(R_i)≥…≥λ_M(R_i)。in,

Λ _i = _diag ([λ ₁ ( ^R _i ),λ _{2 (} R _{i )} ] _{) ;} with the second eigenvalue and λ ₁ (R _i )≥…≥λ _M (R _i ).

2.2 Statistics

When the base station only knows the spatial transmission correlation matrix of each user, the multipath gain of linear precoding will be completely lost. At this time, the ergodic channel capacity of the system in the case of low SNR ([8] Raghavan V, Hanly S V, Veeravalli V V. Statistical Beamforming on the Grassmann Manifold for the Two-UserBroadcast Channel [J]. IEEE Transactions on Information Theory, 2011 ,59(10):6464-6489.) is

Z＝[z₁,z₂]；η1≥η2≥0；高信噪比时遍历信道容量为definition

Z=[z ₁ ,z ₂ ]; η1≥η2≥0; when the signal-to-noise ratio is high, the ergodic channel capacity is

η1、η2分别为对角矩阵diag([η₁,η₂])中的主对角线上的元素；Z为使矩阵R对角化的矩阵；z₁、z₂是Z中的元素。in,

η1 and η2 are respectively elements on the main diagonal in the diagonal matrix diag([η ₁ , η ₂ ]); Z is a matrix that diagonalizes the matrix R; z ₁ and z ₂ are elements in Z.

2.3 Classification of channel statistics

定义为Channel statistics when M=2

defined as

限制着每个用户的病态程度。通过确定信道统计信息分类可以获得系统的遍历信道容量E[R_perf]与R_stat的最大值。Wherein, R _i is full rank; the condition number of R _i is χ _i =χ(R _i )=λ ₁ (R _i )/λ ₂ (R _i ), which is an index to measure the ill-conditioned degree of the channel matrix;

Limits how sick each user is. The maximum value of the ergodic channel capacity E[R _perf ] and R _stat of the system can be obtained by determining the classification of the channel statistics.

Define two conditions in the channel:

C ₂ : U _i =U _j P,j≠i (15)

中第i个用户的最坏病态信道；条件C₂对应于两个用户主特征模式的正交性。低信噪比时，式(8)中R_perf,low的值在

的任意信道中均不变；当信道满足条件C_1,i时式(11)中R_stat,low取得最大值。高信噪比时，当信道同时满足条件C_1,i与条件C₂时式(9)中

与式(12)中R_stat,high取得最大值。Among them, U _i is a transformation matrix that makes R _i a diagonal matrix Λ _i ; U _j is a transformation matrix that makes R _j a diagonal matrix Λ _j ; P is a 2×2 permutation matrix. Condition C _1,i corresponds to

The worst ill-conditioned channel of the i-th user in ; the condition C ₂ corresponds to the orthogonality of the main eigenmodes of the two users. When the signal-to-noise ratio is low, the value of R _perf,low in equation (8) is

It remains unchanged in any channel of ; when the channel satisfies the condition C _1,i , R _stat,low in equation (11) gets the maximum value. When the signal-to-noise ratio is high, when the channel satisfies the condition C _{1, i} and condition C ₂ at the same time, in Equation (9)

and R _stat,high in formula (12) to obtain the maximum value.

遍历信道容量的性能损失为When the transmitter knows the complete channel state information, if the channel does not meet the condition C _1i but meets the condition C ₂ , that is,

The performance penalty for traversing the channel capacity is

When the transmitter knows the complete channel state information, if the channel satisfies the condition C _1,i but does not satisfy the condition C ₂ , the performance loss of traversing the channel capacity is:

遍历信道容量的性能损失为When the transmitting end knows the statistical channel state information, if the channel does not meet the condition C _1,i but meets the condition C ₂ , that is,

The performance penalty for traversing the channel capacity is

When the transmitter knows the statistical channel state information, if the channel satisfies the condition C _1,i but does not satisfy the condition C ₂ , the performance loss of traversing the channel capacity is

R_stat,high的最大值影响更大。当U_i＝U_j,i≠j,i＝1,2时

取

随着χ₁，χ₂变化的曲线如图1所示。Comparing Equation (16) with Equation (17), Equation (18) and Equation (19) respectively, we can get: when the condition C ₂ is satisfied, the performance loss of the traversal channel capacity is smaller, then the condition C ₂ can obtain

The maximum value of R _stat,high has a greater impact. When U _i =U _j , i≠j, i=1,2

Pick

The curve of the variation of χ ₂ with χ ₁ is shown in FIG. 1 .

Figure 1 shows that ΔR takes the maximum value when χ ₁ =χ ₂ =1, that is, both users are IID; when there is one and only one user is approximately IID, the value of ΔR is still relatively large.

3. Codebook Design

In order to obtain the maximum value of R _stat , when the signal-to-noise ratio is low, the eigenvector equation R _i w _i =γ _i w _i is solved, where R _i is the spatial emission correlation matrix, and w _i is the codeword, also called R eigenvector of _i ; γ _i is the eigenvalue of Ri; _i =1,2 to obtain the optimal codeword for each user wi _,opt =u ₁ (R _i ), i=1,2, u ₁ (· ) is the normalized eigenvector of the principal unit of the matrix. When the signal-to-noise ratio is high, the optimal codeword for each user is obtained by solving the vector equation R _i w _i =γ _i R _j w _i , i≠j, i=1, 2. At this time, the optimal codeword for each user It can be represented by a generalized eigenvector group

The method of inserting the feature matrix can simultaneously solve the design problem of the optimal codeword when the signal-to-noise ratio is high and low

R _i w _interp,i =(R _i +α _i (ρ)I)w _interp,i →w _interp,i =u ₁ ((R _i +α _i (ρ) ^-1 I)R _i ) (21)

Therefore, the codebook is designed as

为单用户时的码书。根据第2小节的讨论，为达到系统遍历信道容量的最大值，将α_i(ρ)简化为α_i＝χ_i(method1)与α_i＝1/χ_i(method 2)两种方案。method 1与method 2将码书中码字的局部性与扩展性进行了折中，提高了码书的稳健性。where α _i (ρ) is a function of R ₁ , R ₂ and ρ;

The codebook when it is a single user. According to the discussion in Section 2, in order to achieve the maximum ergodic channel capacity of the system, α _i (ρ) is simplified into two schemes: α _i =χ _i (method1) and α _i =1/χ _i (method 2). Method 1 and method 2 compromise the locality and scalability of codewords in the codebook, and improve the robustness of the codebook.

4. Code word selection criteria

The signal-to-interference-noise ratio of the i-th user is

为h_i的信道方向矢量。R_sum与SINR_i成正比，SINR_i取得最大值时R_sum亦取得最大值。式(2)中的接收信噪比最大化准则使得SINR_i分子的值最大，忽略了SINR_i分母值最小化的重要性。特别是在干扰受限的情况下，SINR_i中分母值最小化与分子值最大化同样重要。本文提出了一种新的最优码字选取准则：Wherein S _i is the signal power; I _i is the noise power;

is the channel direction vector of _hi . R _sum is proportional to SINR _i , and when SINR _i is at its maximum value, R _sum is also at its maximum value. The receiving signal-to-noise ratio maximization criterion in formula (2) makes the value of the numerator of SINR _i the largest, ignoring the importance of minimizing the value of the denominator of SINR _i . Especially in the case of limited interference, minimizing the denominator value in SINR _i is as important as maximizing the numerator value. This paper proposes a new optimal codeword selection criterion:

Step 1: Assume that each user only guarantees that the mapping value of the precoding vector on its channel is the largest, namely:

为一个与信道矢量h_j无关而与空间发射相关矩阵R_j有关的常量，故可在接收端采用信道统计信息分类的方法。in,

It is a constant which is independent of the channel vector h _j but related to the spatial transmission correlation matrix R _j , so the method of channel statistics classification can be adopted at the receiving end.

作为第i个用户的候选预编码矢量，S_i的估计值

I_i的估计值为Step 2:

As the candidate precoding vector of the ith user, the estimated value of S _i

The estimated value of I _i is

上的映射。

也可看作第i个用户对第j个用户信道干扰的估计。Equation (25) can be regarded as the precoding vector of the i-th user in

on the mapping.

It can also be regarded as the estimation of the channel interference of the jth user by the ith user.

的最大化，即Step 3: The optimal codeword selection criterion is the estimated value of SINR _i

maximization of

5. Performance Analysis

When the number of users is 2, according to the different channel states, the channels are divided into three cases: Good-conditioning, Bad-conditioning, and Worse-conditioning. The corresponding channel statistics condition numbers are:

(1)

(2)

(3)

Take τ ₁ =3, τ ₂ =12, and perform performance simulation on the codebook proposed in this paper in four different scenarios:

(1) Scenario 1: R ₁ =Σ _G1 , R ₂ =Σ _G2

(2) Scenario 2: R ₁ =Σ _G2 , R ₂ =Σ _W1

(3) Scenario 3: R ₁ =Σ _B2 , R ₂ =Σ _W2

(4) Scenario 4: R ₁ =Σ _B1 , R ₂ =Σ _B2

Among them, Σ _G1 and Σ _G2 are the spatial emission correlation matrices under Good-conditioning; Σ _B1 and Σ _B2 are the spatial emission correlation matrices under Bad-conditioning; Σ _W1 and Σ _W2 are the spatial emission correlation matrices under Worse-conditioning.

FIG. 2 shows a simulation comparison diagram of the system traversal channel capacity when the number of feedback bits B=3 in four scenarios. In the figure, Grass and RVQ respectively represent the codebooks in the literature [5] designed with Grassmannian codebooks and random vector quantization (Random Vector Quantization, RVQ) codebooks as the base codebooks. Scenario 1, Scenario 2, Scenario 3, Scenario 4 are ill-conditioned gradually. With the deepening of ill-conditioning, the correlation of ill-conditioned matrices limits the performance of the system, and the traversal channel capacity of each codebook decreases; while method1 and method2 The performance of the two codebook designs is obviously superior to that of the Grass codebook and the RVQ codebook.

When the number of users is greater than 2, the codebook is designed as:

Wherein, similarly α _i =χ _i (method 1), α _i =1/χ _i (method 2). The optimal codeword selection criterion is the same as when the number of users is 2. Figure 3 shows the simulation of the ergodic channel capacity corresponding to different feedback bit numbers of method 1 and method 2 in scenario 1. As the number of system feedback bits increases, the ergodic channel capacity of the two schemes also increases. Figures 4(a) and (b) show the traversal channel capacity of each user when the number of users is 4 in scenario 1 and scenario 2, respectively. Compare and analyze Fig. 4(a) and Fig. 2(a), Fig. 4(b) and Fig. 2(b) respectively, it is concluded that: when the number of users increases, the two codebook design algorithm systems proposed by the present invention The performance is relatively robust and is not easily affected by fading channel correlation.

The above embodiments are only to illustrate the technical idea of the present invention, and cannot limit the protection scope of the present invention. Any modification made on the basis of the technical solution according to the technical idea proposed by the present invention falls within the protection scope of the present invention. Inside.

Claims (2)

1. a MU-MISO system limited feedback codebook design method based on channel statistical information, is characterized in that: described MU-MISO system configures M transmitting antennas, and the number of users is K, and each user configures a receiving antenna, The received signal of the i-th user is:

Among them, ρ is the signal-to-noise ratio; _hi is the M×1 channel matrix; x is the transmitted signal;

is additive white Gaussian noise; the transmitted signal

f _i is an M×1 precoding vector; s _i is a data symbol and E[|s _i | ² ]=1; The design method includes the following steps: Step 1, analyze the traversal channel capacity at high and low signal-to-noise ratios when the transmitting end knows the complete channel state information and the transmitting end knows the statistical information; In the step 1, when the transmitter knows the complete channel state information, the channel capacity R _perf of the system is:

Among them, M=2; d _c (h ₁ , h ₂ ) is the chord distance between h ₁ and h ₂ :

Meanwhile, the ergodic channel capacity E[R _perf ] of the system is:

in,

Λ _i =diag([λ ₁ (R _i ),λ ₂ (R _i )]); λ _i (A) is the eigenvalue of a positive semi-definite matrix A∈C ^M×M and λ ₁ (A)≥…≥λ _M (A);

In the step 1, when the transmitting end knows the statistical information, the traversal channel capacity of the system in the case of low signal-to-noise ratio is:

Among them, R _i is the spatial emission correlation matrix; definition

Z=[z ₁ ,z ₂ ]; η ₁ ≥η ₂ ≥0; η ₁ and η ₂ are the elements on the main diagonal in the diagonal matrix diag([η ₁ ,η ₂ ]) respectively; Z is A matrix that diagonalizes the matrix R; z ₁ , z ₂ are elements in Z; the traversal channel capacity at high SNR is

in,

Step 2, using the method of channel statistical information classification to respectively represent the traversal channel capacity loss in two cases; In step 2, when the transmitter knows the complete channel state information, two conditions in the channel are defined:

C ₂ : U _i =U _j P,j≠i Wherein, the condition number of R _i is χ _i =χ(R _i )=λ ₁ (R _i )/λ ₂ (R _i ), which is an index to measure the ill-conditioned degree of the channel matrix; P is a 2×2 permutation matrix; If the channel does not satisfy the condition C _1,i but satisfies the condition C ₂ , the performance loss of traversing the channel capacity is

If the channel satisfies the condition C _1,i but not the condition C ₂ , the performance loss of traversing the channel capacity is

In the step 2, when the transmitter knows the statistical information, two conditions in the channel are defined:

C ₂ : U _i =U _j P,j≠i If the channel does not satisfy the condition C _1,i but satisfies the condition C ₂ , the performance loss of traversing the channel capacity is

If the channel satisfies the condition C _1,i but not the condition C ₂ , the performance loss of traversing the channel capacity is

Step 3, combining the method of inserting the feature matrix with the channel statistical information to realize the design of the codebook; In the step 3, when the signal-to-noise ratio is low _, the optimal codeword _{w i ,opt} =u _{1 (} R _i ), i=1,2, u ₁ (·) is the main unit normalized eigenvector of the matrix; when the signal-to-noise ratio is high, by solving the vector equation R _i w _i =γ _i R _j w _i , i≠j, i =1,2 to obtain the optimal codeword of each user, at this time, the optimal codeword of each user is represented by the generalized eigenvector group

Using the method of inserting the feature matrix to solve the design problem of the optimal code word when the signal-to-noise ratio is high and low R _i w _interp,i =(R _i +α _i (ρ)I)w _interp,i →w _interp,i =u ₁ ((R _i +α _i (ρ) ^-1 I)R _i ) Therefore, the codebook is designed as

where α _i (ρ) is a function of R ₁ , R ₂ and ρ;

The codebook when it is a single user. 2. the MU-MISO system limited feedback codebook design method based on channel statistical information as claimed in claim 1, is characterized in that: in described step 3, adopt following codeword selection criterion: In step a, it is assumed that each user only guarantees that the mapping value of the precoding vector on its channel is the largest, namely:

in,

is a constant which is independent of the channel vector h _j and related to the spatial emission correlation matrix R _j ; step b,

As the candidate precoding vector of the ith user, the estimated value of S _i

The estimated value of I _i is

Step c, the optimal codeword selection criterion is the estimated value of SINR _i

maximization of

Images