阅读说明：本技术 一种毫米波大规模mimo系统中的混合预编码设计方法 (Hybrid precoding design method in millimeter wave large-scale MIMO system ) 是由 李正权 李树梅 袁月 马可 李君� 陆波 丁文杰 于 2021-08-06 设计创作，主要内容包括：本发明公开了一种毫米波大规模MIMO系统中的混合预编码设计方法,为了解决毫米波大规模MIMO系统的预编码设计过程中,对于非凸约束的优化问题的求解方式导致系统频谱效率低、计算复杂度高的问题,本发明提供的混合预编码设计方法采用波瓣分解信道模型,设计毫米波大规模MIMO系统中的混合预编码,在保证计算复杂度的同时,能够提高系统频谱效率。根据本发明的方法在系统建模时采用波瓣分解信道,将含有非凸约束的优化问题进行转化,并充分利用模拟预编码矩阵和数字预编码矩阵之间的相关性,并根据数字预编码矩阵的隐含稀疏结构,求出每个波瓣内每个数据流的自有支撑集与共有支撑集,据此联合设计混合预编码,以提高系统的频谱效率。(The invention discloses a hybrid precoding design method in a millimeter wave large-scale MIMO system, which aims to solve the problems of low system spectrum efficiency and high calculation complexity caused by a solving mode of a non-convex constrained optimization problem in the precoding design process of the millimeter wave large-scale MIMO system. According to the method, a lobe decomposition channel is adopted during system modeling, optimization problems containing non-convex constraints are converted, correlation between an analog precoding matrix and a digital precoding matrix is fully utilized, an own support set and a common support set of each data stream in each lobe are solved according to a hidden sparse structure of the digital precoding matrix, and accordingly mixed precoding is jointly designed to improve the spectral efficiency of the system.)

1. A hybrid precoding design method in a millimeter wave large-scale MIMO system is characterized in that the millimeter wave large-scale MIMO system comprises N_sAfter the transmitting end carries out digital pre-coding processing on the transmitting signal s of each data stream through the digital pre-coding module, the transmitting signal s is transmitted to the receiving endThe analog pre-coding module is composed of a radio frequency chain, a phase shifter and a radio frequency adder, and after analog pre-coding processing is carried out by the analog pre-coding module, the data stream is mapped to N_tTransmitting the data to a noisy lobe decomposition channel for data transmission on a root transmitting antenna, and transmitting the data to a receiving end through N_rThe root receiving antenna receives data, and the data are processed by the analog combining module and the digital combining module in sequence to obtain a receiving signal y, so that multi-path data transmission comprising a plurality of data streams is realized; the method comprises the following steps:

the method comprises the following steps: in order to maximize the spectral efficiency of a system, the design of a digital pre-coding module, an analog merging module and a digital merging module is optimized, and the optimization problem containing non-convex constraint in the design process of mixed pre-coding comprising an analog pre-coding matrix, a digital pre-coding matrix, an analog merger matrix and a digital merger matrix is converted into the problem of solving the minimum Euclidean distance;

step two: because of the independence among the lobes, the lobe channel is decomposed into L independent lobe sub-channels, the problem of solving the minimum Euclidean distance in the step one is simplified into a mixed precoding design aiming at each lobe sub-channel, and an analog precoding matrix and a digital precoding matrix are respectively designed aiming at each lobe sub-channel;

step three: solving analog precoding matrix corresponding to each lobe subchannelAnd a digital precoding matrixSelecting antenna array response A for each lobe subchannel_tlAs a precoding reference matrix F_resConstructing an analog precoding codebook according to the hardware limitation of a phase shifter in the analog precoding module; and at each analog precoding codebookSearching the position of the best code word to obtain an analog pre-coding matrixSelf-supported set Ψ_l；

Step four: solving the analog precoding matrix corresponding to each lobe subchannel in the third stepSelf-supported set Ψ_lIntroducing a joint sparse method, using an analog precoding matrix and a digital precoding matrixCorrelation between the two, and according to the implicit sparse structure of the digital pre-coding matrix, calculating a pre-coding reference matrix F_resIn-analog precoding codebookProjection of (2) onto (F)_resThe positions of the code words with strong projection are obtained, thereby obtaining a common support set among the analog pre-coding matrixes of different data streamsAnalog precoding matrix corresponding to each data streamSelf-supported set Ψ_lpFromAnd Ψ_lpForm Ψ_l；

Step five: according to the analog precoding matrix corresponding to each lobe subchannelSelf-supported set Ψ_lOptimizing the column vector distribution of the simulation pre-coding matrix to obtain the simulation pre-coding matrixObtaining the matrix of the analog combiner by the same methodAccordingly, Ψ_lEmbodies the correlation between the analog pre-coding matrix and the digital pre-coding matrix, so equivalent sub-channels are obtainedPerforming singular value decomposition to obtainA digital precoding matrix can be obtainedThe row vectors of the digital pre-coding matrix and the column vectors of the analog pre-coding matrix are in one-to-one correspondence, and the joint optimization of hybrid pre-coding is realized;

step six: repeating the first step to the fifth step, designing an own support set of the simulation precoding matrix corresponding to each lobe subchannel, and obtaining a simulation precoding matrix F_RFIs self-supporting set Ψ ═ Ψ { Ψ ═ Ψ₁，Ψ₂，...，Ψ_L}; simulating a precoding matrixThe same can obtain the matrix of the analog combinerAccordingly, the digital precoding matrix isThe digital combiner matrix is

2. The hybrid precoding design method of claim 1, wherein in step one of the method,

under the lobe decomposition channel model, the received signal y is:

taking the gaussian signal as the transmission signal s, the spectral efficiency of the system is:

in the formula (I), the compound is shown in the specification,is a noise covariance matrix;is transmitting a signal vector and satisfiesF_RFTo representDimension simulation precoding matrix, F_BBTo representDimension digital precoding matrix, W_RFTo representAnalog combiner matrix of dimensions, W_BBTo representNumber merger matrix of dimensions, F ═ F_RFF_BBFor the hybrid precoding matrix, the total transmission power is satisfiedW＝W_RFW_BBRepresenting a combiner matrix;for channel noise vector, σ²Is the power of the noise or noise,for the channel matrix, ρ represents the average received power; with the goal of maximizing the spectral efficiency of the system, the formula for hybrid precoding design is as follows:

wherein Ω is an analog precoding codebook with constant modulus constraint and satisfies

3. The hybrid precoding design method of claim 2, wherein in step one of the method,

in order to simplify the design, the formula (3) is converted into the problem of solving the euclidean distance minimum as shown in the formula (4), and the optimal code word is searched in the analog precoding codebook Ω to form an analog precoding matrix:

in the formula, F^optIs an optimal precoding reference matrix, which can be decomposed by singular value of channel matrix H^HTo obtain i.e. F_opt＝V(：，1：N_s)。

4. The hybrid precoding design method of claim 1, wherein the second step further comprises:

respectively designing an analog precoding matrix and a digital precoding matrix aiming at the L lobe sub-channels:

in the formula (I), the compound is shown in the specification,for the optimal precoding reference matrix corresponding to the l-th lobe subchannel,andrespectively corresponding to the l sub-channel, an analog pre-coding matrix and a digital pre-coding matrix, omega_lRepresents the ith analog precoding subcodebook, andassuming power averaging distribution, G_lIs the sum of the powers of all transmission paths in the first lobe.

5. The hybrid precoding design method of claim 4, wherein the third step further comprises:

to avoid high complexity matrix operations, an antenna array response A is selected_tAs a precoding reference matrix; the channel matrix H can be abbreviated as:

in order for the transmitting end antenna array to respond,responding to the receiving end antenna array; the multiplexing gain of each data transmission path is:

for each lobe subchannel, the antenna array response corresponds to L sub-antenna array responses, with a transmit side a_t＝[A_t1，A_t2，...，A_tL]The receiving end is A_r＝[A_r1，A_r2，...，A_rL]，A_rlAnd A_tlDenotes the L-th antenna array response, where L1, 2.

6. The hybrid precoding design method of claim 5, wherein in step three of the method,

constructing an analog pre-coding codebook according to the hardware limit of a phase shifter in the analog pre-coding module; assume an analog precoding codebook size of N_θ＝2^bAnd b represents that the phase resolution of the phase shifter is b-bit, the analog precoding codebook is as follows:

in the formula (I), the compound is shown in the specification,

representing a quantization azimuth of an ith codeword in the analog precoding codebook; the analog precoding codebook may be divided into L sub-codebooks corresponding to the L lobe subchannels

7. The hybrid precoding design method of claim 6, wherein in step three of the method,

setting the code word constituting the analog precoding matrixThe position is the self-supported set Ψ of the analog precoding matrix due to the analog precoding matrix of each lobe subchannelDigital precoding matrixAre independent of each other, and for each lobe corresponding to the simulated precoding matrix, there is a corresponding set of self-supporting Ψs_lWherein L is 1, 2.. L; different analog precoding matricesDoes not have the same support set and satisfies psi ═ psi₁，Ψ₂，...，Ψ_L}; because paths among different lobes are mutually independent, when a simulation precoding matrix is designed, the search of all codebooks is converted into the search of a plurality of subcodebooks, and the problem of target solution is as follows:

in the formula (I), the compound is shown in the specification,an L-th analog precoding codebook, wherein L is 1, 2.. L; the reference precoding matrix is an antenna array response, A_tlRepresenting the transmit antenna array response for the l-th lobe subchannel.

8. The hybrid precoding design method of claim 1, wherein the fourth step further comprises:

self-supporting set Ψ of analog precoding matrices for different data streams_lpThere is a common supporting set betweenAnd satisfyThe first lobe simulates the self-supporting set of the precoding matrix asWhereinTo representTo Ψ_lpA difference set of;

because the digital precoding matrix has a hidden sparse structure, the projection sizes of column vectors of the precoding reference matrix on different code words are different, and the analog precoding matrix for the p data stream of the ith lobeDesigning, wherein a plurality of strong projection conditions of a precoding reference matrix column vector are considered; to simplify the design, consider eachDesigned to have the same number of projectionsIs an integer; if a common support set exists among the simulation precoding matrixes of different data streamsSearchingA code word, whereinThe expression is rounded down so that the column vectors of at least two pre-coding reference matrices have a strong projection on the selected code words, the positions of the code words are set as the analog pre-coding matrixCommon supporting set ofSimulating precoding matrix for designing p-th data streamSearchingThe position of each code word and the common support setForm aSelf-supported set Ψ_lp(ii) a Thus, formula (10) is converted to:

whereinRepresenting the self-supporting set Ψ_lpThe cardinality of (a), i.e., the number of elements in the set;

in order to solve the problems, a hybrid pre-coding optimization algorithm based on joint sparsity is adopted; because each lobe mixing precoding design is independent and the method is the same, only the first lobe mixing precoding matrix design is introduced: firstly, designing a common supporting setPrecoding reference matrix F_resAntenna array response A for the l lobe_tlAnd calculating a correlation matrix of the reference matrix and the codebook:

searchingA code word such that a reference matrix F is precoded_resThe column vectors have a strong projection on the selected codeword, and if the selected codeword can be used as a common support, the condition is satisfied:

making a precoding reference matrix F_resExcept for j₀There are still other column vectors in the ith column vector in addition to the individual column vector₀Having a strong projection on each codeword, then the ith₀The individual code words being common supports, the code word position i being recorded₀Updating common supporting setSelf-supporting set Ψ of p-th data stream analog precoding matrix_lp(ii) a To design forSelecting a single antenna array response column vector A_tl(p) as a reference matrix F_resCalculating a correlation matrix R, similar to the common support set_cSearch forForming an analog precoding matrix from the individual codewords and updating Ψ_lpSimulation with the first lobeSelf-supporting set Ψ of coding matrices_l。

9. The hybrid precoding design method of claim 1, wherein the analog precoding codebook in the fourth step is constructed by using a uniform quantization mode and a non-uniform quantization mode.

10. Hybrid precoding design method according to one of claims 1 to 9, characterized in that the analog precoding matrix F obtained according to said method_RFDigital precoding matrix F_BBAnalog combiner matrix W_RFDigital combiner matrix W_BBThe frequency spectrum efficiency and the error rate performance of the millimeter wave large-scale MIMO system are improved.

Technical Field

The invention relates to a hybrid precoding design method in a millimeter wave large-scale MIMO system, and belongs to the technical field of wireless communication.

Background

With the explosive increase of wireless data volume, millimeter wave large-scale MIMO systems are receiving more and more attention, and have the significant advantages of high data transmission rate and high reliability as one of the key technologies of the fifth-generation mobile communication technology. In a traditional MIMO system, a sending end eliminates part or all interference among data streams in advance through a digital pre-coding technology, so that the spatial distribution characteristic of a sending signal is matched with a channel condition, and better spectrum efficiency and error rate performance are obtained. However, for a large-scale MIMO system, the scale of the antenna array is greatly increased, and if a conventional all-digital precoding technology is adopted, a large number of Radio Frequency (RF) links are required, which increases the hardware design difficulty and design cost. Researchers apply the analog precoding technology to a large-scale MIMO system, only a small number of RF links are needed, and hardware cost and power consumption are low. However, this application has a certain loss of spectral efficiency performance and weak anti-interference capability, so researchers have proposed a hybrid precoding structure combining a low-dimensional digital precoding technique and a high-dimensional analog precoding technique, which can fully utilize the gain brought by a large-scale antenna array while reducing the RF link.

Because of the high frequency and short wavelength of the millimeter wave, the millimeter wave will generate serious loss due to the influence of environmental factors in the transmission process, and the scattering of the millimeter wave is limited, so line-of-sight transmission is the main transmission mode, and the channel characteristics are specifically expressed as the sparsity of the channel. Meanwhile, based on the constant modulus constraint and the discrete characteristic of a codeword in a simulated precoding codebook, researchers convert a mixed precoding design problem into an optimization problem containing non-convex constraint in order to maximize the system spectral efficiency, and adopt an Orthogonal Matching Pursuit (OMP) to reconstruct sparse signals to design a mixed precoding matrix, but the OMP algorithm needs Singular Value Decomposition (SVD) and inversion operation of a high-dimensional matrix, which leads to obviously increased computational complexity. Some scholars improve the spectrum efficiency and the error rate performance of the system by designing a precoding codebook, improving an RF connection structure, optimizing an iterative algorithm and the like, but balance among the spectrum efficiency, the error rate performance and the calculation complexity of the system is difficult to realize.

In addition, most of the existing hybrid precoding technologies are based on a time cluster channel model, and the angle sparse characteristic of a millimeter wave communication transmission path is ignored. Research shows that the Angle of Arrival (AOA) and the Angle of Departure (AOD) of the millimeter wave transmission path have the characteristic of lobe decomposition, and the channel can be decomposed into a plurality of orthogonal lobe sub-channels, thereby avoiding SVD of high-dimensional matrix, but the method sacrifices partial system performance. Therefore, if a hybrid precoding design in a millimeter wave massive MIMO system needs to be performed based on a lobe decomposition channel model, the system spectrum efficiency and the bit error rate performance also need to be improved.

Disclosure of Invention

The invention provides a hybrid precoding design method in a millimeter wave large-scale MIMO system, aiming at solving the problems of low system spectrum efficiency and error rate performance and high calculation complexity caused by a solving mode of a non-convex constraint optimization problem in the precoding design process of the millimeter wave large-scale MIMO system. The method of the invention adopts a lobe decomposition channel model to design mixed precoding in a millimeter wave large-scale MIMO system, and improves the system spectrum efficiency and the error rate performance while ensuring the calculation complexity.

The hybrid precoding design method according to the present invention is in millimetersIn a wave massive MIMO system, comprising N_sAfter the transmitting end carries out digital pre-coding processing on the transmitting signal s of each data stream through the digital pre-coding module, the transmitting signal s is transmitted to the receiving endThe analog pre-coding module is composed of a radio frequency chain, a phase shifter and a radio frequency adder, and after analog pre-coding processing is carried out by the analog pre-coding module, the data stream is mapped to N_tTransmitting the data to a noisy lobe decomposition channel for data transmission on a root transmitting antenna, and transmitting the data to a receiving end through N_rThe receiving antenna receives data, and the data are processed by the analog combining module and the digital combining module in sequence to obtain a receiving signal y, so that multi-path data stream transmission is realized.

However, the analog precoding module only adjusts the deflection phase of each phase shifter to realize analog precoding, so the analog precoding matrix has a constant modulus constraint condition, and in addition, due to the limitation of the phase shifter hardware design, the phase resolution of the phase shifters is often constant, and the number of code words in the analog precoding codebook is constant and has a discrete characteristic, so that the mixed precoding design problem including the digital precoding design and the analog precoding design is an optimization problem including non-convex constraint based on the above characteristics of the analog precoding codebook.

According to the method, a lobe decomposition channel is adopted during system modeling, optimization problems containing non-convex constraints are converted, correlation between an analog pre-coding matrix and a digital pre-coding matrix is fully utilized, an own support set and a common support set of each data stream in each lobe are solved according to an implicit sparse structure of the digital pre-coding matrix, and accordingly mixed pre-coding is jointly designed, so that the spectral efficiency and the error rate performance of a system are improved.

In order to solve the technical problems, the invention provides the following technical scheme:

a hybrid precoding optimization design method in a millimeter wave large-scale MIMO system, wherein the millimeter wave large-scale MIMO system comprises N_sThe transmitting signal s of each data stream is pre-coded digitally at the transmitting endAfter the code module carries out digital pre-coding processing, the code module transmits the data to the code moduleThe analog pre-coding module is composed of a radio frequency chain, a phase shifter and a radio frequency adder, and after analog pre-coding processing is carried out by the analog pre-coding module, the data stream is mapped to N_tTransmitting the data to a noisy lobe decomposition channel for data transmission on a root transmitting antenna, and transmitting the data to a receiving end through N_rThe root receiving antenna receives data, and the data are processed by the analog combining module and the digital combining module in sequence to obtain a receiving signal y, so that multi-path data transmission comprising a plurality of data streams is realized; in the millimeter wave large-scale MIMO system, N is assumed at the transmitting end_tThe number of the transmitting antennas is the same as,a radio frequency chain, a receiving end has N_rThe antenna is received at the root of the antenna,a radio frequency chain, the number of transmission data streams is N_s. In order to ensure multiplexing gain and realize multi-path data stream communication, the number of radio frequency chains at the transmitting end and the receiving end respectively satisfiesIs transmitting a signal vector and satisfiesIn the formula (I), the compound is shown in the specification,is a noise covariance matrix;is transmitting a signal vector and satisfiesF_RFTo representDimension simulation precoding matrix, F_BBTo representDimension digital precoding matrix, W_RFTo representAnalog combiner matrix of dimensions, W_BBTo representNumber merger matrix of dimensions, F ═ F_RFF_BBFor the hybrid precoding matrix, the total transmission power is satisfiedW＝W_RFW_BBRepresenting a combiner matrix;for channel noise vector, σ²Is the power of the noise or noise,for the channel matrix, ρ represents the average received power; the method comprises the following steps:

the method comprises the following steps: in order to maximize the spectral efficiency of a system, the design of a digital pre-coding module, an analog merging module and a digital merging module is optimized, and the optimization problem containing non-convex constraint in the design process of mixed pre-coding comprising an analog pre-coding matrix, a digital pre-coding matrix, an analog merger matrix and a digital merger matrix is converted into the problem of solving the minimum Euclidean distance;

under the lobe decomposition channel model, the received signal is y,

taking the gaussian signal as the transmission signal s, the system spectrum efficiency is:

in the formulaIs a noise covariance matrix. With the goal of maximizing spectral efficiency, the formula for hybrid precoding design is as follows:

wherein omega is an analog precoding codebook with constant modulus constraint and satisfies

In order to simplify the design, the formula (3) is converted into the problem of solving the euclidean distance minimum as shown in the formula (4), and the optimal code word is searched in the analog precoding codebook Ω to form an analog precoding matrix:

in the formula, F^optIs an optimal precoding reference matrix, and can be decomposed by singular values of a channel matrix, H ═ U ∑ V^HTo obtain i.e. F_opt＝V(：，1：N_s)。

Step two: according to mutual independence among the lobes, the lobe channel is decomposed into a plurality of independent lobe sub-channels, the problem (4) in the first step can be converted into a mixed precoding design problem based on the independent lobe sub-channels, and an analog precoding matrix and a digital precoding matrix are respectively designed;

respectively designing an analog precoding matrix and a digital precoding matrix aiming at the L lobe sub-channels:

in the formulaFor the optimal precoding reference matrix corresponding to the l-th lobe subchannel,andrespectively corresponding to the l sub-channel, an analog pre-coding matrix and a digital pre-coding matrix, omega_lRepresents the ith analog precoding subcodebook, andthe invention assumes power averaging distribution, G_lIs the sum of the powers of all transmission paths in the first lobe.

Step three: solving analog precoding matrix corresponding to each lobe subchannelAnd a digital precoding matrixSelecting antenna array response A for each lobe subchannel_tlAs a precoding reference matrix F_resConstructing an analog precoding codebook according to the hardware limitation of a phase shifter in the analog precoding module; at each analog precoding codebookSearching the position of the best code word to form an analog precoding matrixSelf-supported set Ψ_l。

More than two single antennas working at the same frequency are arranged according to a certain space to form an antenna array; and mapping the transmission signals to the transmission antenna after precoding to form antenna array response. To avoid high complexity matrix operations, an antenna array response A is selected_tAs a precoding reference matrix F_res. The channel matrix H can be abbreviated as:

in order for the transmitting end antenna array to respond,and responding by the antenna array at the receiving end. The multiplexing gain of each data transmission path is

For each lobe subchannel, the antenna array response corresponds to L sub-antenna array responses, with a transmit side a_t＝[A_t1，A_t2，...，A_tL]The receiving end is A_r＝[A_r1，A_r2，...，A_rL]，A_rlAnd A_tlDenotes the L-th antenna array response, where L1, 2.

And constructing an analog precoding codebook according to the hardware limit of a phase shifter in the analog precoding module. Assume an analog precoding codebook size of N_θ＝2^bAnd b represents that the phase resolution of the phase shifter is b-bit, the analog precoding codebook is as follows:

in the formula (I), the compound is shown in the specification,

representing the quantization azimuth of the ith codeword in the analog precoding codebook. The analog precoding codebook may be divided into L sub-codebooks corresponding to the L lobe subchannels

Setting the position of the code word forming the analog precoding matrix to be the self-supporting set psi of the analog precoding matrix, because of the analog precoding matrix of each lobe subchannelDigital precoding matrixAre independent of each other, and for each lobe corresponding to the simulated precoding matrix, there is a corresponding set of self-supporting Ψs_lDifferent analog precoding matricesThere is no identical support set between the self-supporting sets, i.e. the common support set isAnd satisfies Ψ ═ Ψ { Ψ₁，Ψ₂，...，Ψ_L}. Because paths among different lobes are independent, when a simulation precoding matrix is designed, the search of all codebooks is converted into the search of a plurality of subcodebooks, namely a precoding reference matrix F is searched_resIn-analog precoding codebookThe largest codeword is up-projected. The target solution problem is:

in the formula (I), the compound is shown in the specification,is the L-th analog precoding codebook, where L is 1, 2. The reference precoding matrix is an antenna array response, A_tlRepresenting the transmit antenna array response for the l-th lobe subchannel.

Step four: simulating a precoding matrix for solving the corresponding problem of each lobe subchannel in the step threeSelf-supported set Ψ_lA joint sparse method is introduced, the correlation between the analog pre-coding matrix and the digital pre-coding matrix is utilized, and a pre-coding reference matrix F is calculated according to the implicit sparse structure of the digital pre-coding matrix_resIn-analog precoding codebookThe size of the projection is recorded, and the position of the code word with strong projection is recorded, so that a common support set among different data stream simulation pre-coding matrixes is obtainedAnalog precoding matrix corresponding to each data streamSelf-supported set Ψ_lpThe two constitute psi corresponding to each lobe subchannel_l。

Forming an analog precoding matrix F_RFIs located in the analog precoding matrix F_RFDue to the analog precoding of each lobe subchannelMatrix arrayDigital precoding matrixAre independent of each other. Similarly, for each lobe, a corresponding analog precoding matrix is usedAll have corresponding self-supporting sets psi_lWherein L is 1, 2. Different analog precoding matricesThere is no identical support set between the self-supporting sets, i.e. the common support set isAnd satisfies Ψ ═ Ψ { Ψ₁，Ψ₂，...，Ψ_L}. Analog precoding matrix for each data streamWith its own supporting set of Ψ_lpEach data stream simulating a precoding matrixThere is a common supporting set betweenSatisfy the requirement ofThe first lobe simulates a precoding matrixSelf-supporting set ofAnd (3) actual solving: in a lobe, each data stream is sharedCorresponding psi of each data stream_lpThe two constitute psi for each lobe pair_lFinally, psi corresponding to all lobes is obtained. Correspondingly, the analog precoding matrix of each data stream is solved firstAnalog precoding matrix for each lobe subchannelThereby obtaining a complete analog precoding matrix F_RF。

Because the digital precoding matrix has a hidden sparse structure, the projection sizes of column vectors of the precoding reference matrix on different code words are different, and the analog precoding matrix for the p data stream of the ith lobeDesign, consider that there are multiple strong projection cases for the precoded reference matrix column vector. To simplify the design, consider eachDesigned to have the same number of projectionsAre integers. If a common support set exists among the simulation precoding matrixes of different data streamsSearchingA code word, whereinThe expression is rounded down so that the column vectors of at least two pre-coding reference matrices have a strong projection on the selected code words, the positions of the code words are set as the analog pre-coding matrixCommon supporting set ofSimulating precoding matrix for designing p-th data streamSearchingThe position of each code word and the common support setForm aSelf-supported set Ψ_lp. Thus, the formula (10) is converted into,

whereinRepresenting the set Ψ_lpThe cardinality of (c), i.e., the number of elements in the set.

In order to solve the problems, the invention provides a combined sparse mixed precoding optimization algorithm based on a lobe decomposition channel. Since each lobe mixing precoding design is independent and the method is the same, only the first lobe mixing precoding matrix design is introduced below. Firstly, designing a common supporting setPrecoding reference matrix F_resAntenna array response A for the l lobe_tlCalculating a correlation matrix of the reference matrix and the codebook,

searchingA code word such that a reference matrix F is precoded_resThe column vectors have a strong projection on the selected codeword, and if the selected codeword can be used as a common support, the condition needs to be satisfied,

making a precoding reference matrix F_resExcept for j₀There are still other column vectors in the ith column vector in addition to the individual column vector₀Having a strong projection on each codeword, then the ith₀The individual code words being common supports, the code word position i being recorded₀Updating common supporting setSelf-supporting set Ψ of p-th data stream analog precoding matrix_lp. To design forSelecting a single antenna array response column vector A_tl(p) as a reference matrix F_resCalculating a correlation matrix R, similar to the common support set_cSearch forForming an analog precoding matrix from the individual codewords and updating Ψ_lpModeling the self-supporting set Ψ of the precoding matrix with the l-th lobe_l。

Step five: modeling the own branch of the precoding matrix according to each lobeProp set Ψ_lOptimizing the column vector distribution of the simulation pre-coding matrix to obtain the simulation pre-coding matrixObtaining the matrix of the analog combiner by the same methodAccordingly, Ψ_lEmbodies the correlation between the analog pre-coding matrix and the digital pre-coding matrix, so equivalent sub-channels are obtainedPerforming singular value decomposition to obtainThat is, a digital precoding matrix can be obtainedThe row vectors of the digital pre-coding matrix and the column vectors of the analog pre-coding matrix are in one-to-one correspondence to realize the joint optimization of the hybrid pre-coding, and the digital combiner matrix is obtained in the same way

Step six: repeating the first step to the fifth step, designing an own support set of the simulation precoding matrix corresponding to each lobe subchannel to obtain a simulation precoding matrix F_RFIs self-supporting set Ψ ═ Ψ { Ψ ═ Ψ₁，Ψ₂，...，Ψ_L}. The analog precoding matrix isSimilarly, the combiner matrix is simulatedCorresponding digital precoding matrix isThe digital combiner matrix is

The method also comprises the steps of constructing an analog precoding codebook by adopting a uniform quantization and non-uniform quantization mode, and drawing the change condition of the communication performance index along with the signal-to-noise ratio by utilizing MATLAB simulation. The communication performance index of the millimeter wave large-scale MIMO system is the frequency spectrum efficiency.

The simulation pre-coding matrix F obtained according to the pre-coding design method of the invention_RFDigital precoding matrix F_BBAnalog combiner matrix W_RFDigital combiner matrix W_BBThe frequency spectrum efficiency of the millimeter wave large-scale MIMO system can be improved. Moreover, the invention also provides the application of the hybrid precoding designed by the method in the technical field of wireless communication.

The invention has the beneficial effects that:

according to the hybrid precoding design method, based on the lobe decomposition channel, the hybrid precoding optimization design is carried out by introducing the joint sparse method, the original hybrid precoding design problem is converted into the hybrid precoding design problem corresponding to a plurality of lobes and a plurality of data streams, the complexity of the precoding design process is simplified, the precoding design is optimized, and better system performance can be obtained in a large-scale MIMO system.

The hybrid precoding design method also reduces the requirement of the system on an analog precoding codebook, is more suitable for a practical large-scale MIMO system, fully utilizes the correlation between analog precoding and digital precoding, obtains the self-supporting set and the shared supporting set of each lobe and each data stream corresponding to the analog precoding matrix according to the implicit sparse structure of the digital precoding matrix, realizes the joint optimization of the analog precoding and the digital precoding, and improves the spectrum efficiency and the error rate performance of the system on the premise of ensuring the calculation complexity of the system.

Drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.

FIG. 1 is a schematic diagram of a hybrid precoding structure in a millimeter wave massive MIMO system according to the present invention;

fig. 2 shows that in a 32 × 16, 128 × 32MIMO system with a lobe splitting channel, a millimeter wave frequency of 28GHz, and a bandwidth of 100MHz, the number of lobes L is 2, the number of paths in the lobes P is 2, and a radio frequency chain at a transmitting end is used as a transmit endReceiving end radio frequency chainData stream N_sUnder the condition that the phase resolution b of the phase shifter is 6, comparing the optimal pre-coding, an orthogonal matching pursuit algorithm (UQ-OMP) based on a uniform quantization codebook, a lobe decomposition algorithm (UQ-SLD) based on the uniform quantization codebook, a lobe decomposition algorithm (NUQ-SLD) based on a non-uniform quantization codebook and a schematic diagram of the change condition of the spectrum efficiency of the technical method of the invention along with the signal-to-noise ratio;

fig. 3(a) is a graph comparing the spectral efficiency variation of each algorithm when using non-uniform quantization codebooks under different phase resolutions of phase shifters, where b is 3, 4, and 5; fig. 3(b) is a graph comparing the spectral efficiency variation of each algorithm when uniform quantization and non-uniform quantization codebooks are used, wherein uniform quantization b is 6 and non-uniform quantization b is 4; the system is a 32 × 16MIMO system, the number of lobes L is 2, the number of paths in the lobes P is 2, and a radio frequency chain at a transmitting endReceiving end radio frequency chainData stream N_s＝LP；

Fig. 4(a) is a comparison of the spectral efficiency variation of each algorithm when the present invention adopts a uniform quantization codebook in the case of different numbers of paths in lobes, where b is 6; fig. 4(b) is a comparison of the spectral efficiency variation of each algorithm when the number of paths in lobes is different and a non-uniform quantization codebook is used, where b is 4; in the 32 × 16MIMO system, the number of lobes L is 2, the number of paths in the lobes P is 2, and the transmitting-end radio frequency chainReceiving end radio frequency chainData stream N_s＝LP；

Fig. 5(a) is a comparison of the bit error rate variation of each algorithm when the uniform quantization codebook is used in the case of different numbers of paths in lobes, where b is 6; fig. 5(b) is a comparison of the bit error rate variation of each algorithm when the number of paths in lobes is different and a non-uniform quantization codebook is used, where b is 4; in the 32 × 16MIMO system, the number of lobes L is 2, the number of paths in the lobes P is 2, and the transmitting-end radio frequency chain is configured to transmit data in the uplinkReceiving end radio frequency chainData stream N_sThe phase resolution b of the phase shifter is 6 for LP.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

The first embodiment is as follows:

this embodiment provides a method for designing hybrid precoding in a millimeter wave massive MIMO system, which combines the schematic diagram of the hybrid precoding structure shown in fig. 1In the millimeter wave massive MIMO system, N is included_sAfter the transmitting end carries out digital pre-coding processing on the transmitting signal s of each data stream through a digital pre-coder, the transmitting signal s is transmitted to the receiving endThe analog precoder composed of the RF chain, the phase shifter and the RF adder is used for mapping the data stream to N after analog precoding processing is carried out by the analog precoder_tTransmitting the data to a noisy lobe decomposition channel for data transmission on a root transmitting antenna, and transmitting the data to a receiving end through N_rAnd the receiving antenna receives data and processes the data through the analog combiner and the digital combiner in sequence to obtain a receiving signal y, so that multi-path data transmission comprising a plurality of data streams is realized.

Assuming that N is arranged at a transmitting end in the millimeter wave massive MIMO system_tThe number of the transmitting antennas is the same as,a radio frequency chain, a receiving end has N_rThe antenna is received at the root of the antenna,a radio frequency chain, the number of transmission data streams is N_s. In order to ensure multiplexing gain and realize data stream communication of multiple channels, the number of radio frequency chains at the transmitting end and the receiving end respectively satisfiesIs transmitting a signal vector and satisfiesIn the formula (I), the compound is shown in the specification,is a noise covariance matrix;is transmitting a signal vector and satisfiesF_RFTo representDimension simulation precoding matrix, F_BBTo representDimension digital precoding matrix, W_RFTo representAnalog combiner matrix of dimensions, W_BBTo representNumber merger matrix of dimensions, F ═ F_RFF_BBFor the hybrid precoding matrix, the total transmission power is satisfiedW＝W_RFW_BBRepresenting a combiner matrix;for channel noise vector, σ²Is the power of the noise or noise,for the channel matrix, ρ represents the average received power.

According to this embodiment, and as shown in fig. 1, the hybrid precoding design method includes the following specific steps:

the method comprises the following steps: in order to maximize the spectral efficiency of a system, the design of a digital precoder, an analog combiner and a digital combiner is optimized, and the optimization problem containing non-convex constraint in the design process of mixed precoding comprising an analog precoding matrix, a digital precoding matrix, an analog combiner matrix and a digital combiner matrix is converted into the problem of solving the minimum Euclidean distance;

under the lobe decomposition channel model, the received signal is y,

taking the gaussian signal as the transmission signal s, the system spectrum efficiency is:

in the formula (I), the compound is shown in the specification,is a noise covariance matrix. With the goal of maximizing spectral efficiency, the formula for hybrid precoding design is as follows:

wherein omega is an analog precoding codebook with constant modulus constraint and satisfies

In order to simplify the design, the formula (3) is converted into the problem of solving the euclidean distance minimum as shown in the formula (4), and the optimal code word is searched in the analog precoding codebook Ω to form an analog precoding matrix:

in the formula, F^optIs an optimal precoding reference matrix, and can be decomposed by singular values of a channel matrix, H ═ U ∑ V^HTo obtain i.e. F_opt＝V(:，1：N_s)。

Step two: according to mutual independence among the lobes, the lobe channel is decomposed into a plurality of independent lobe sub-channels, the problem (4) in the first step can be converted into a mixed precoding design problem based on the independent lobe sub-channels, and an analog precoding matrix and a digital precoding matrix are respectively designed;

respectively designing an analog precoding matrix and a digital precoding matrix aiming at the L lobe sub-channels:

in the formula (I), the compound is shown in the specification,for the optimal precoding reference matrix corresponding to the l-th lobe subchannel,andrespectively corresponding to the l sub-channel, an analog pre-coding matrix and a digital pre-coding matrix, omega_lRepresents the ith analog precoding subcodebook, andthe invention assumes power averaging distribution, G_lIs the sum of the powers of all transmission paths in the first lobe.

Step three: solving analog precoding matrix corresponding to each lobe subchannelAnd a digital precoding matrixSelecting antenna array response A for each lobe subchannel_tlAs a precoding reference matrix F_resAnd constructing an analog precoding codebook according to the hardware limitation of a phase shifter in the analog precoding module. At each sub-codebookSearching the position of the best code word to form an analog precoding matrixSelf-supported set Ψ_l。

To avoid high complexity matrix operations, an antenna array response A is selected_tAs a precoding reference matrix. The channel matrix H can be abbreviated as:

in order for the transmitting end antenna array to respond,and responding by the antenna array at the receiving end. Each path has a multiplexing gain of

For each lobe subchannel, the antenna array response corresponds to L sub-antenna array responses, with a transmit side a_t＝[A_t1，A_t2，...，A_tL]The receiving end is A_r＝[A_r1，A_r2，...，A_rL]，A_rlAnd A_tlDenotes the L-th antenna array response, where L1, 2.

And constructing an analog precoding codebook according to the hardware limit of a phase shifter in the analog precoding module. Assume an analog precoding codebook size of N_θ＝2^bAnd b represents that the phase resolution of the phase shifter is b-bit, the analog precoding codebook is as follows:

in the formula (I), the compound is shown in the specification,

representing the quantization azimuth of the ith codeword in the analog precoding codebook. The analog precoding codebook may be divided into L sub-codebooks

Setting the position of the code word forming the analog precoding matrix to be the self-supporting set psi of the analog precoding matrix, because of the analog precoding matrix of each lobe subchannelDigital precoding matrixAre independent of each other, and for each lobe corresponding to the simulated precoding matrix, there is a corresponding set of self-supporting Ψs_lWherein L is 1, 2. Different analog precoding matricesThere is no identical support set between the self-supporting sets, i.e. the common support set isAnd satisfies Ψ ═ Ψ { Ψ₁，Ψ₂，...，Ψ_L}. Because paths among different lobes are independent, when a simulation precoding matrix is designed, the search of all codebooks is converted into the search of a plurality of subcodebooks, namely a precoding reference matrix A is searched_tlIn-analog precoding codebookThe largest codeword is up-projected. The target solution problem is:

in the formula (I), the compound is shown in the specification,is the L-th analog precoding codebook, where L is 1, 2. The reference precoding matrix is an antenna array response, A_tlRepresenting the transmit antenna array response for the l-th lobe subchannel.

Step four: simulating a precoding matrix for solving the corresponding problem of each lobe in the third stepSelf-supported set Ψ_lA joint sparse method is introduced, the correlation between the analog pre-coding matrix and the digital pre-coding matrix is utilized, and a pre-coding reference matrix F is calculated according to the implicit sparse structure of the digital pre-coding matrix_resIn-analog precoding codebookThe size of the projection is recorded, and the position of the code word with strong projection is recorded, so that a common support set among different data stream simulation pre-coding matrixes is obtainedAnalog precoding matrix corresponding to each data streamSelf-supported set Ψ_lpThe two form Ψ_l。

Forming an analog precoding matrix F_RFIs located at the position of the analog precoding F_RFDue to the analog precoding matrix of each lobe subchannelDigital precoding matrixAre independent of each other. Similarly, for each lobe, a corresponding analog precoding matrix is usedAll have corresponding self-supporting sets psi_lDifferent analog precoding matricesThere is no identical support set between the self-supporting sets, i.e. the common support set isAnd satisfies Ψ ═ Ψ { Ψ₁，Ψ₂，...，Ψ_L}. Analog precoding matrix for each data streamWith its own supporting set of Ψ_lpEach data stream simulating a precoding matrixThere is a common supporting set betweenSatisfy the requirement ofThe first lobe simulates a precoding matrixSelf-supporting set ofWhereinTo representTo Ψ_lpThe difference set of (2). And (3) actual solving: in a lobe, each data stream is sharedCorresponding psi of each data stream_lpThe two constitute psi corresponding to each lobe_lFinally, psi corresponding to all lobes is obtained. Correspondingly, the analog precoding matrix of each data stream is solved firstAnalog precoding matrix for each lobe subchannelThereby obtaining a complete analog precoding matrix F_RF。

Because the digital precoding matrix has a hidden sparse structure, the projection sizes of column vectors of the precoding reference matrix on different code words are different, and the analog precoding matrix for the p data stream of the ith lobeDesign, consider that there are multiple strong projection cases for the precoded reference matrix column vector. To simplify the design, consider eachDesigned to have the same number of projectionsAre integers. If a common support set exists among the simulation precoding matrixes of different data streamsSearchingA code word, whereinThe expression is rounded down so that the column vectors of at least two pre-coding reference matrices have a strong projection on the selected code words, the positions of the code words are set as the analog pre-coding matrixCommon supporting set ofSimulating precoding matrix for designing p-th data streamSearchingThe position of each code word and the common support setForm aSelf-supported set Ψ_lp. Thus, the formula (10) is converted into,

whereinRepresenting the set Ψ_lpThe cardinality of (c), i.e., the number of elements in the set.

In order to solve the problems, the invention provides a combined sparse mixed precoding optimization algorithm based on a lobe decomposition channel. Due to each lobe being mixedThe combined precoding design is independent and the method is the same, and only the first lobe mixed precoding matrix design is introduced below. Firstly, designing a common supporting setPrecoding reference matrix F_resAntenna array response A for the l lobe_tlCalculating a correlation matrix of the reference matrix and the codebook,

searchingA code word such that a reference matrix F is precoded_resThe column vectors have a strong projection on the selected codeword, and if the selected codeword can be used as a common support, the condition needs to be satisfied,

making a precoding reference matrix F_resExcept for j₀There are still other column vectors in the ith column vector in addition to the individual column vector₀Having a strong projection on each codeword, then the ith₀The individual code words being common supports, the code word position i being recorded₀Updating common supporting setSelf-supporting set Ψ of p-th data stream analog precoding matrix_lp. To design forSelecting a single antenna array response column vector A_tl(p) as a reference matrix F_resCalculating a correlation matrix R, similar to the common support set_cSearch forForming an analog precoding matrix from the individual codewords and updating Ψ_lpModeling the self-supporting set Ψ of the precoding matrix with the l-th lobe_l。

Step five: modeling the self-supporting set Ψ of the precoding matrix according to each lobe_lOptimizing the column vector distribution of the simulation pre-coding matrix to obtain the simulation pre-coding matrixObtaining the matrix of the analog combiner by the same methodAccordingly, Ψ_lEmbodies the correlation between the analog pre-coding matrix and the digital pre-coding matrix, so equivalent sub-channels are obtainedPerforming singular value decomposition to obtainThat is, a digital precoding matrix can be obtainedThe row vectors of the digital pre-coding matrix and the column vectors of the analog pre-coding matrix are in one-to-one correspondence, the joint optimization of hybrid pre-coding is realized, and the digital combiner matrix is obtained in the same way

Step six: repeating the first step to the fifth step, designing an own support set of the simulation precoding matrix corresponding to each lobe subchannel to obtain a simulation precoding matrix F_RFIs self-supporting set Ψ ═ Ψ { Ψ ═ Ψ₁，Ψ₂，...，Ψ_L}. The analog precoding matrix isCorresponding digital precoding matrix isThe same can obtain the matrix of the analog combinerDigital combiner matrix

In order to make the purpose, technical scheme and advantages of the present invention clearer, some classical precoding algorithms are compared with the proposed algorithm to show the superiority of the joint sparse mixed precoding optimization design method in the aspects of computational complexity, spectral efficiency and error rate performance.

The precoding algorithms used for comparison are respectively an optimal precoding algorithm (OPT), a uniform quantization orthogonal matching algorithm (UQ-OMP), a non-uniform quantization orthogonal matching algorithm (NUQ-OMP), a uniform quantization spatial lobe decomposition algorithm (UQ-SLD) and a non-uniform quantization spatial lobe decomposition algorithm (NUQ-SLD).

The optimal precoding algorithm is a classic precoding algorithm, and shows better spectrum efficiency performance in a large-scale MIMO system. The UQ-OMP algorithm and the NUQ-OMP algorithm respectively adopt a uniform quantization mode and a non-uniform quantization mode to construct a simulation precoding codebook, the OMP algorithm is used for solving the sparse reconstruction problem, the UQ-SLD algorithm and the NUQ-SLD algorithm reconstruct the original problem into a mixed precoding design problem of a plurality of sub-channels by utilizing the sparsity of azimuth angles of paths in space lobes, and respectively adopt the uniform quantization mode and the non-uniform quantization mode to construct the simulation precoding codebook.

Fig. 2 shows that in a 32 × 16, 128 × 32MIMO system with a lobe splitting channel, a millimeter wave frequency of 28GHz, and a bandwidth of 100MHz, the number of lobes L is 2, the number of paths in the lobes P is 2, and a radio frequency chain at a transmitting end is used as a transmit endReceiving end radio frequency chainData stream N_sUnder the condition that the phase resolution b of the phase shifter is 6, comparing the optimal pre-coding, an orthogonal matching pursuit algorithm (UQ-OMP) based on a uniform quantization codebook, a lobe decomposition algorithm (UQ-SLD) based on the uniform quantization codebook, a lobe decomposition algorithm (NUQ-SLD) based on a non-uniform quantization codebook and a schematic diagram of the change condition of the spectrum efficiency of the technical method of the invention along with the signal-to-noise ratio;

fig. 3(a) is a graph comparing the spectral efficiency variation of each algorithm when using non-uniform quantization codebooks under different phase resolutions of phase shifters, where b is 3, 4, and 5; fig. 3(b) is a graph comparing the spectral efficiency variation of each algorithm when uniform quantization and non-uniform quantization codebooks are used, wherein uniform quantization b is 6 and non-uniform quantization b is 4; the system is a 32 × 16MIMO system, the number of lobes L is 2, the number of paths in the lobes P is 2, and a radio frequency chain at a transmitting endReceiving end radio frequency chainData stream N_s＝LP；

Fig. 4(a) is a comparison of the spectral efficiency variation of each algorithm when the present invention adopts a uniform quantization codebook in the case of different numbers of paths in lobes, where b is 6; fig. 4(b) is a comparison of the spectral efficiency variation of each algorithm when the number of paths in lobes is different and a non-uniform quantization codebook is used, where b is 4; in the 32 × 16MIMO system, the number of lobes L is 2, the number of paths in the lobes P is 2, and the transmitting-end radio frequency chainReceiving end radio frequency chainData stream N_s＝LP；

Fig. 5(a) is a comparison of the bit error rate variation of each algorithm when the uniform quantization codebook is used in the case of different numbers of paths in lobes, where b is 6; fig. 5(b) is a comparison of the bit error rate variation of each algorithm when the number of paths in lobes is different and a non-uniform quantization codebook is used, where b is 4; in the 32 × 16MIMO system, the number of lobes L is 2, the number of paths in the lobes P is 2, and the transmitting-end radio frequency chain is configured to transmit data in the uplinkReceiving end radio frequency chainData stream N_sThe phase resolution b of the phase shifter is 6 for LP.

As shown in fig. 2, the spectral efficiency of the above algorithm is improved with the increase of the signal-to-noise ratio. When N is present_t＝32、N_r＝16，

When the uniform quantization codebook is adopted, compared with the UQ-SLD algorithm, the spectral efficiency of the invention is improved by 0.68bps/Hz, when the non-uniform quantization codebook is adopted, compared with the NUQ-SLD algorithm, the spectral efficiency of the algorithm of the invention is improved by 0.44bps/Hz, and under the two conditions, the spectral efficiency of the algorithm respectively reaches 89.6 percent and 99 percent of that of the OPT algorithm. Likewise, when N is_t＝128、N_rWhen the value is 32 and the value b is 8, the frequency spectrum efficiency of the algorithm is obviously improved. Compared with the OMP algorithm, the algorithm has gap in spectrum efficiency performance, but the algorithm greatly reduces the calculation complexity, and the larger the number of the antennas is, the larger the reduction range of the calculation complexity is (see section 3.3). The algorithm and the SLD algorithm both select antenna array response as a reference matrix to avoid complex matrix operation and sacrifice the spectral efficiency performance of part of systems; compared with the SLD algorithm, under the condition of two quantization modes, the algorithm of the invention has reduced spectrum efficiency difference, which shows that the influence of the analog precoding codebook quantization mode on the system spectrum efficiency is reduced, thereby reducing the influence on a phase shifterPhase resolution requirements.

Fig. 3(a) shows that the algorithm spectrum efficiency changes under different phase resolutions of phase shifters when the non-uniform quantization codebook is used. As can be seen from the figure, as the phase resolution b of the phase shifter is increased, the spectral efficiency of several algorithms is improved, and the spectral efficiency gradually approaches to the OPT algorithm. Fig. 3(b) is a comparison graph of the spectral efficiency of the algorithm under the conditions of uniform quantization and non-uniform quantization. As can be seen from the figure, the spectral efficiency when the non-uniform quantization b is 4 is similar to that when the uniform quantization b is 6, because the quantization precision of the non-uniform quantization is higher than that of the uniform quantization (see section 3.1), and when the phase resolution of the phase shifter is the same, the algorithm has higher spectral efficiency when the non-uniform quantization is used compared with the uniform quantization. When in non-uniform quantizationThen the total angulation angleIs a uniform quantization of the total quantization angleTherefore, when the spectral efficiency is close, the non-uniform quantization is 2 bits less than the uniform quantization.

Fig. 4(a) and 4(b) are graphs comparing the changes of spectral efficiency in the case of different path numbers P, for uniform quantization and non-uniform quantization, respectively. As can be seen from the figure, regardless of whether a uniform quantization codebook or a non-uniform quantization codebook is used, the spectral efficiency of each algorithm is improved as the number of paths P increases, and the spectral efficiency when the non-uniform quantization b is 4 is close to that when the uniform quantization b is 6.

Fig. 5(a) and 5(b) show the bit error rate of each algorithm as a function of the signal-to-noise ratio when the quantization is uniform and non-uniform, respectively. As can be seen from the figure, when P is 1, the error rate of each algorithm is lower than that of P2, regardless of whether uniform quantization or non-uniform quantization is used. Since the smaller the number of paths P, the less interference between transmission paths within a lobe, the lower the system error rate. Under two quantification modes, the error rate performance of the algorithm is close to that of an OPT algorithm, and compared with an SLD algorithm, the error rate is 6 multiplied by 10^-2When the signal-to-noise ratio gain is increased by about 2dB under the condition that P is 1, the error rate difference with the OMP algorithm is reduced by 50%; when the error rate is 5 x 10^-1When P is 2, the snr gain is increased by about 3.7dB, and the snr loss from the OMP algorithm is only 0.3 dB.

As can be seen from the results of fig. 2 to fig. 5(b), the joint sparse hybrid precoding algorithm exhibits the advantages of higher spectral efficiency and bit error rate performance, and can still ensure the spectral efficiency and bit error rate performance of the large-scale MIMO system under the condition of lower phase shifter resolution.

Some steps in the embodiments of the present invention may be implemented by software, and the corresponding software program may be stored in a readable storage medium, such as an optical disc or a hard disk.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.