CN109361441B - MU-MISO system limited feedback codebook design method based on channel statistical information - 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

MU-MISO system limited feedback codebook design method based on channel statistical information

Technical Field

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

Background

In a multiple-input Single-output (MISO) closed-loop system, a receiving end can feed back channel state information to a transmitting end, and the transmitting end obtains a set of scores and an array gain ([1] Love D J, Heath R W, Lau V K N, et al.an overview of limited feedback in wireless communication systems [ J ]. IEEE Journal on Selected Areas in Communications,2008,26(8): 1341-. Multi-user multiple input single output (MU-MISO) Limited Feedback technology under independent identically distributed Runlie fading channels has been well studied ([2] Ko K, Jung S, Lee J.hybrid MU-MISO Scheduling with Limited Feedback Using high efficiency codes. IEEE Transactions on Communications,2012,60(4): 1101-. Limited feedback techniques in both spatially and temporally correlated channels are still the focus of research.

Studies have shown that fading correlation degrades the system Performance of MU-MISO channels when they have spatial correlation ([5] Shen W, Dai L, Zhang Y, et al. on the Performance of Channel Statistics-Based code book for Massive MIMO Channel Feedback [ J ]. IEEE Transactions on Vehicular Technology,2017,8(66):7553- & 7557.). Existing feedback strategies are classified into Codebook rotation-based and Codebook scaling-based algorithms ([6] Choi J, ClerckX B, Lee N, et al. A New Design of Polar-Cap Differential Codebook for temporal/spatial Correlated MISO Channels [ J ]. IEEE Transactions on Wireless communication, 2012,11(2): 703. 711. 7. Sun Y, Zhang J, Zhang P, et al. practical Differential quantization for spectral and temporal Correlated Channels [ C ]// IEEE, International Signal, Indono, and particle communication, 491, class 486), which result in no correlation of the above mentioned algorithms. The feedback algorithm based on codebook scaling has better system performance than the feedback algorithm based on codebook rotation, but the codebook design complexity is higher and the operation steps are more complicated. 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 usually exhibits ill-conditioned state, and the condition number of the ill-conditioned channel matrix has unavoidable influence on the capacity of the traversed channel. In all channels with equal total power gain, the traversal Channel capacity is the largest for a Channel with condition number 1, but as the condition number increases, the larger the ill-conditioned degree of the Channel, the smaller the traversal Channel capacity decreases ([8] Raghavan V, Handy S V, dimensional V.Stationality Beamforming on the Grassmann-modified for the Two-User broadband Channel [ J ]. IEEE Transactions on Information Theory,2011,59(10): 6464-.

Disclosure of Invention

The invention aims to provide a method for designing a limited feedback codebook of an MU-MISO system based on channel statistical information, which can reduce the influence of a pathological channel on the capacity of a system traversal channel and can obviously improve the capacity of the system traversal channel.

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

a method for designing a limited feedback codebook of an MU-MISO system based on channel statistical information 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 MU-MISO system is configured with M transmitting antennas, the number of users is K, each user is configured with a receiving antenna, and the received signal of the ith user is:

wherein rho is the signal-to-noise ratio; h is_iA channel matrix of mx 1; x is a transmission signal;

additive complex white gaussian noise; transmitting signal

f_iIs an Mx 1 pre-coding vector; s_iIs a data symbol and E [ | s_i|²]＝1。

In step 1, the channel capacity R of the system is obtained when the transmitting end knows the complete channel state information_perfThe conditions are satisfied as follows:

wherein rho is the signal-to-noise ratio; h is_iThe channel matrix is M multiplied by 1, M is the number of transmitting antennas, and M is 2;

is h₁And h₂Chord distance between:

at the same time, the system traverses the channel capacity ER_perf]Comprises the following steps:

wherein,

Λ_i＝diag([λ₁(R_i),λ₂(R_i)])；λ₁(R_i) And λ₂(R_i) Are respectively a semi-positive definite matrix R_i∈ C ^M×M1 and 2 characteristic values of₁(R_i)≥…≥λ_M(R_i)。

In the step 1, the traversal channel capacity of the system under the condition of known statistical information and low signal-to-noise ratio at the transmitting end is

Wherein R is_iTransmitting a correlation matrix for the space;

definition of

Z＝[z₁,z₂]；η₁≥η₂Not less than 0; traversing channel capacity at high signal-to-noise ratio of

Wherein,

in step 2, under the condition that the transmitting end knows the complete channel state information, two conditions in the channel are defined:

C₂:U_i＝U_jP,j≠i

wherein R is_iTransmitting a correlation matrix for the space; r_iCondition number of_i＝χ(R_i)＝λ₁(R_i)/λ₂(R_i) Is an index for measuring the ill-conditioned degree of the channel matrix; m is the number of transmitting antennas, and M is 2; p is a permutation matrix of 2 x 2;

if the channel does not satisfy condition C_1,iTo satisfy the condition C₂Performance loss across channel capacity is

If the channel satisfies condition C_1,iAnd does not satisfy the condition C₂Performance loss across channel capacity is

In step 2, under the condition that the transmitting end knows the statistical information, two conditions in the channel are defined:

C₂:U_i＝U_jP,j≠i

wherein R is_iTransmitting a correlation matrix for the space; r_iCondition number of_i＝χ(R_i)＝λ₁(R_i)/λ₂(R_i) Is an index for measuring the ill-conditioned degree of the channel matrix; m is the number of transmitting antennas, and M is 2; p is a permutation matrix of 2 x 2;

if the channel does not satisfy condition C_1,iTo satisfy the condition C₂Performance loss across channel capacity is

If the channel satisfies condition C_1,iAnd does not satisfy the condition C₂Performance loss across channel capacity is

In the step 3, the characteristic vector equation R is solved when the signal-to-noise ratio is low_iw_i＝γ_iw_iI-1, 2 obtains the optimal codeword w for each user_i,opt＝u₁(R_i)，i＝1,2，u₁(. to) is the principal unit normalized feature vector of the matrix; by solving the vector equation R at high signal-to-noise ratio_iw_i＝γ_iR_jw_iI ≠ j, i ≠ 1,2 obtains the optimal code word of each user, and the optimal code word of each user is represented by the generalized feature vector group at the moment

Method for solving design problem of optimal code word in high and low signal-to-noise ratio by inserting characteristic matrix

R_iw_interp,i＝(R_i+α_i(ρ)I)w_interp,i→w_interp,i＝u₁((R_i+α_i(ρ)-¹I)R_i)

Therefore, the code book is designed as

Wherein alpha is_i(p) is R₁、R₂A function of ρ;

the code book is a code book of a single user.

In the step 3, the following codeword selection criteria are adopted:

step a, assuming that each user only guarantees that the mapping value of the precoding vector on the channel is maximum, namely:

wherein,

is a channel vector h_jIndependent of spatial emission correlation matrix R_jA related constant;

in the step b, the step (c),

as candidate precoding vectors for the ith user, S_iIs estimated value of

I_iIs estimated as

Step c, the optimal code word selection criterion is SINR_iEstimated value

To a maximum of, i.e.

After the scheme is adopted, the invention starts from the defects existing in the codebook rotation feedback algorithm and the ill-conditioned channel matrix, calculates the loss of the traversal channel capacity when the signal-to-noise ratio is high and low by utilizing a channel statistical information classification method, and then combines a method for inserting the characteristic matrix with the channel statistical information to design the code words. Simulation experiments show that: compared with the prior art, the method obviously improves the system traversal channel capacity for channels with different pathological degrees.

Drawings

FIG. 1 is Δ R vs. χ₁、χ₂A variation graph;

FIG. 2 is a comparison diagram of the traversal channel capacity in 4 different scenarios;

fig. 3 is a diagram of the traversal channel capacity when B is 1,2,3, 4;

fig. 4 is a graphical representation of the traversal channel capacity for each user.

Detailed Description

The technical solution and the advantages of the present invention will be described in detail with reference to the accompanying drawings.

1. System model

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

wherein rho is the signal-to-noise ratio; h is_iA channel matrix of mx 1; x is a transmission signal;

is additive complex white gaussian noise. Transmitting signal

f_iIs an Mx 1 pre-coding vector; s_iIs a data symbol and E [ | s_i|²]＝1。

In the limited feedback method based on code book, the receiving end estimates h through the channel_iAnd based on some optimization criterion in code book

Selecting the optimal code word; the optimal codeword selection criterion for maximizing the received signal-to-noise ratio is:

the receiving end uses B feedback bits to convert 2^BIndexing individual code words and optimizing the code words c_i,optThe index value is fed back to the transmitting terminal through a low-speed feedback channel, the transmitting terminal finds the corresponding code word in the code book through the index value, and the code word is taken as a precoding vector^[10-11]。

The channel matrix of the ith user of the space transmission related multi-user MISO system researched by the invention is as follows:

wherein R is_iTransmitting a correlation matrix for the space;

are independent and equally distributed vectors. In this embodiment, K ═ M is assumed.

2. Ergodic channel capacity analysis

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

wherein, the SINR_iIs the signal to interference plus noise ratio. Ergodic channel capacity for multi-user MISO systems

When M is 2, the traversal channel capacity is analyzed under two conditions of the known complete channel state information of the transmitting terminal and the known statistical information of the transmitting terminal, and a method for classifying the channel state information by using a transmitting correlation matrix is introduced. 2.1 complete channel State information

When the transmitting end knows the complete channel state information of all users, the performance loss at high signal-to-noise ratio can be reduced to the minimum by adopting the minimum mean square error precoding. Channel capacity R of the system at this time_perfThe conditions are satisfied as follows:

wherein,

is h₁And h₂Chord distance between:

at the same time, the system traverses the channel capacity ER_perf]Comprises the following steps:

wherein,

Λ_i＝diag([λ₁(R_i),λ₂(R_i)])；λ₁(R_i) And λ₂(R_i) For a semi-positive definite matrix R_i∈C^M×M1 and 2 characteristic values of₁(R_i)≥…≥λ_M(R_i)。

2.2 statistical information

When only the spatial transmit correlation matrix of each user is known at the base station side, the multipath gain of the linear precoding will be completely lost. At this time, the traversal Channel capacity ([8] Raghavan V, Handy S V, Veeravalli V. statistical Beamforming on the Grassmann modified for the Two-User Broadcast Channel [ J ]. IEEE Transactions on Information Theory,2011,59(10):6464-

Definition of

Z＝[z₁,z₂](ii) a Eta 1 is more than or equal to eta 2 and more than or equal to 0; traversing channel capacity at high signal-to-noise ratio of

Wherein,

eta 1 and eta 2 are diagonal matrices diag ([ eta ] respectively₁,η₂]) Elements on the main diagonal of (1); z is a matrix that diagonalizes the matrix R; z is a radical of₁、z₂Is an element in Z.

2.3 channel statistics Classification

Channel statistics when M is 2

Is defined as

Wherein R is_iIs full rank; r_iCondition number of_i＝χ(R_i)＝λ₁(R_i)/λ₂(R_i) Is an index for measuring the ill-conditioned degree of the channel matrix;

limiting the degree of morbidity for each user. The ergodic channel capacity E [ R ] of the system can be obtained by determining the channel statistical information classification_perf]And R_statIs measured.

Two conditions in the channel are defined:

C₂:U_i＝U_jP,j≠i (15)

wherein, U_iIs that R is_iIs a diagonal matrix Λ_iThe transformation matrix of (2); u shape_jIs that R is_jIs a diagonal matrix Λ_jThe transformation matrix of (2); p is a 2 × 2 permutation matrix. Condition C_1,iCorrespond to

The worst ill-conditioned channel of the ith user; condition C₂Corresponding to the orthogonality of the two user dominant eigenmodes. R in formula (8) at low SNR_perf,lowHas a value of

Is unchanged in any channel of (a); when the channel satisfies condition C_1,iR in formula (11)_stat,lowThe maximum value is taken. At high signal-to-noise ratioWhen the channels simultaneously satisfy the condition C_1,iAnd condition C₂In the hour formula (9)

And R in the formula (12)_stat,highThe maximum value is taken.

When the transmitting end knows the complete channel state information, if the channel does not satisfy the condition C_1iTo satisfy the condition C₂Namely, it is

The performance penalty of traversing the channel capacity is

When the transmitting end knows the complete channel state information, if the channel satisfies the condition C_1,iAnd does not satisfy the condition C₂Performance loss across channel capacity is

When the transmitting end knows the statistical channel state information, if the channel does not satisfy the condition C_1,iTo satisfy the condition C₂Namely, it is

The performance penalty of traversing the channel capacity is

When the transmitting end knows the statistical channel state information, if the channel satisfies the condition C_1,iAnd does not satisfy the condition C₂Performance loss across channel capacity is

The following can be obtained by comparing the expressions (16) and (17), and the expressions (18) and (19): when the condition C is satisfied₂When the performance loss across the channel capacity is smaller, condition C₂To obtain

R_stat,highThe maximum value of (a) has a greater influence. When U is turned_i＝U_jI ≠ j, i ≠ 1,2

Get

Following x%₁，χ₂The curve of the change is shown in fig. 1.

It is evident from FIG. 1 that: when x₁＝χ₂When the two users are independently and simultaneously distributed, the maximum value of the delta R is obtained; the value of ar is still large when there is one and only one user among them is approximately independent of the same distribution.

3. Design of code book

To obtain R_statAt maximum, by solving the eigenvector equation R at low signal-to-noise ratio_iw_i＝γ_iw_iWherein R is_iFor spatial transmit correlation matrix, w_iIs a code word, also called R_iThe feature vector of (2); gamma ray_iIs R_iA characteristic value of (d); obtaining the optimal code word w of each user when i is 1 and 2_i,opt＝u₁(R_i)，i＝1,2，u₁(. cndot.) is the principal unit normalized feature vector of the matrix. By solving the vector equation R at high signal-to-noise ratio_iw_i＝γ_iR_jw_iI ≠ j, i ≠ 1,2 obtains the optimal code word of each user, and the optimal code word of each user can be represented by the generalized eigenvector group at this time

The method for inserting the feature matrix can simultaneously solve the design problem of the optimal code word in high and low signal-to-noise ratios

R_iw_interp,i＝(R_i+α_i(ρ)I)w_interp,i→w_interp,i＝u₁((R_i+α_i(ρ)^-1I)R_i) (21)

Therefore, the code book is designed as

Wherein alpha is_i(p) is R₁、R₂A function of ρ;

the code book is a code book of a single user. As discussed in section 2, to maximize the capacity of the system's ergodic channel, α is_i(p) reduced to α_i＝χ_i(method1) and alpha_i＝1/χ_i(method 2) two protocols. method1 and method2 compromise locality and expansibility of codewords in the codebook, and improve robustness of the codebook.

4. Criterion for selecting code word

The signal-to-interference-and-noise ratio of the ith user is

Wherein S_iIs the signal power; i is_iIs the noise power;

is h_iThe channel direction vector of (a). R_sumAnd SINR_iProportional, SINR_iWhen maximum value is obtained R_sumThe maximum value is also obtained. The received signal-to-noise ratio maximization criterion in the formula (2) is such that SINR_iThe numerator has the largest value, neglecting the SINR_iImportance of denominator value minimization. SINR, especially in interference limited situations_iThe median denominator value is the mostMiniaturization is as important as maximizing molecular value. A new optimal codeword selection criterion is proposed:

step 1: assuming that each user only guarantees maximum mapping value of the precoding vector on its channel:

wherein,

is a channel vector h_jIndependent of spatial emission correlation matrix R_jThe channel statistics information classification method can be adopted at the receiving end due to the related constants.

Step 2:

as candidate precoding vectors for the ith user, S_iIs estimated value of

I_iIs estimated as

Equation (25) can be viewed as the precoding vector for the ith user

To (c) is performed.

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

And step 3: the optimal code word selection criterion is SINR_iEstimated value

To a maximum of, i.e.

5. Performance analysis

When the number of users is 2, the channel is divided into three cases of Good-conditioning, Bad-conditioning and word-conditioning according to the different channel states, and the condition numbers of the channel statistical information corresponding to the three cases are

(1)

(2)

(3)

Take tau₁＝3，τ₂The codebook presented herein was performance simulated in four different scenarios:

(1) scene 1: R₁＝Σ_G1，R₂＝Σ_G2

(2) Scenario 2: R₁＝Σ_G2，R₂＝Σ_W1

(3) Scenario 3: R₁＝Σ_B2，R₂＝Σ_W2

(4) Scenario 4: R₁＝Σ_B1，R₂＝Σ_B2

Wherein, sigma_G1And sigma_G2The space emission correlation matrix under Good-conditioning is adopted; sigma_B1And sigma_B2A spatial emission correlation matrix under Bad-conditioning; sigma_W1And sigma_W2Is the spatial transmit correlation matrix under Worse-conditioning.

Fig. 2 is a graph showing a comparison of the simulation of the system traversal channel capacity when the feedback bit number B is 3 in 4 scenarios. In the figure, Grass and RVQ represent codebooks in document [5] designed based on a Grassmannian codebook and a Random Vector Quantization (RVQ) codebook, respectively. The pathological degrees of the scene 1, the scene 2, the scene 3 and the scene 4 are gradually deepened, the correlation of the pathological matrix limits the performance of the system along with the deepening of the pathological degrees, and the traversal channel capacity of each codebook is reduced; the two codebook designs, method1 and method2, have significantly better performance than the Grass codebook and the RVQ codebook.

When the number of users is more than 2, the design of the code book is as follows:

wherein, the same holds for alpha_i＝χ_i(method 1)，α_i＝1/χ_i(method 2). The optimal codeword selection criterion is consistent with that when the number of users is 2. Fig. 3 shows simulation of the ergodic channel capacity corresponding to different feedback bit numbers of method1 and method2 in scenario 1, where the ergodic channel capacity of the two schemes increases as the number of feedback bits of the system increases. Fig. 4(a) and (b) show the channel capacity per user when the number of users in scene 1 and scene 2 is 4, respectively. Comparing fig. 4(a) and fig. 2(a), and fig. 4(b) and fig. 2(b), respectively, the following results are obtained: when the number of users increases, the two codebook design algorithms provided by the invention have more stable system performance and are not easily influenced by the correlation of fading channels.

The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the protection scope of the present invention.

Claims (2)

1. A method for designing a limited feedback codebook of an MU-MISO system based on channel statistical information is characterized in that: the MU-MISO system is configured with M transmitting antennas, the number of users is K, each user is configured with a receiving antenna, and the received signal of the ith user is:

wherein rho is the signal-to-noise ratio; h is_iA channel matrix of mx 1; x is a transmission signal;

additive complex white gaussian noise; transmitting signal

f_iIs an Mx 1 pre-coding vector; s_iIs a data symbol and E [ | s_i|²]＝1；

The design method 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;

in step 1, the channel capacity R of the system is obtained when the transmitting end knows the complete channel state information_perfComprises the following steps:

wherein M ═ 2; d_c(h₁,h₂) Is h₁And h₂Chord distance between:

at the same time, the system traverses the channel capacity ER_perf]Comprises the following steps:

wherein,

Λ_i＝diag([λ₁(R_i),λ₂(R_i)])；λ_i(A) for a semi-positive definite matrix A ∈ C^M×MCharacteristic value of (A) and λ₁(A)≥…≥λ_M(A)；

In step 1, the traversal channel capacity of the system under the condition of known statistical information of the transmitting terminal and low signal-to-noise ratio is

Wherein R is_iTransmitting a correlation matrix for the space;

definition of

Z＝[z₁,z₂]；η₁≥η₂≥0；η₁、η₂Are respectively diagonal matrix diag ([ eta ]₁,η₂]) Elements on the main diagonal of (1); z is a matrix that diagonalizes the matrix R; z is a radical of₁、z₂Is an element in Z; traversing channel capacity at high signal-to-noise ratio of

Wherein,

step 2, respectively representing the capacity loss of the ergodic channel under two conditions by adopting a channel statistical information classification method;

in step 2, under the condition that the transmitting end knows the complete channel state information, two conditions in the channel are defined:

C₂:U_i＝U_jP,j≠i

wherein R is_iCondition number of_i＝χ(R_i)＝λ₁(R_i)/λ₂(R_i) Is an index for measuring the ill-conditioned degree of the channel matrix; p is a permutation matrix of 2 x 2;

if the channel does not satisfy condition C_1,iTo satisfy the condition C₂Performance loss across channel capacity is

If the channel satisfies condition C_1,iAnd does not satisfy the condition C₂Performance loss across channel capacity is

In step 2, under the condition that the transmitting end knows the statistical information, two conditions in the channel are defined:

C₂:U_i＝U_jP,j≠i

if the channel does not satisfy condition C_1,iTo satisfy the condition C₂Performance loss across channel capacity is

If the channel satisfies condition C_1,iAnd does not satisfy the condition C₂Performance loss across channel capacity is

Step 3, combining the method of inserting the characteristic matrix with the channel statistical information to realize the design of the code book;

in the step 3, the characteristic vector equation R is solved when the signal-to-noise ratio is low_iw_i＝γ_iw_iI-1, 2 obtains the optimal codeword w for each user_i,opt＝u₁(R_i)，i＝1,2，u₁(. to) is the principal unit normalized feature vector of the matrix; by solving the vector equation R at high signal-to-noise ratio_iw_i＝γ_iR_jw_iI ≠ j, i ≠ 1,2 obtains the optimal code word of each user, and the optimal code word of each user is represented by the generalized feature vector group at the moment

Method for solving design problem of optimal code word in high and low signal-to-noise ratio by inserting characteristic matrix

R_iw_interp,i＝(R_i+α_i(ρ)I)w_interp,i→w_interp,i＝u₁((R_i+α_i(ρ)^-1I)R_i)

Therefore, the code book is designed as

Wherein alpha is_i(p) is R₁、R₂A function of ρ;

the code book is a code book of a single user.

2. The method of claim 1, wherein the MU-MISO system finite feedback codebook design method based on channel statistics is characterized by: in step 3, the following codeword selection criteria are adopted:

step a, assuming that each user only guarantees that the mapping value of the precoding vector on the channel is maximum, namely:

wherein,

is a channel vector h_jIndependent of spatial emission correlation matrix R_jA related constant;

in the step b, the step (c),

as candidate precoding vectors for the ith user, S_iIs estimated value of

I_iIs estimated as

Step c, the optimal code word selection criterion is SINR_iEstimated value

To a maximum of, i.e.

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