CN104683074A

CN104683074A - Compressive Sensing Based Finite Feedback Method for Massive MIMO Systems

Info

Publication number: CN104683074A
Application number: CN201510111378.3A
Authority: CN
Inventors: 景小荣; 刘利; 张祖凡; 陈前斌
Original assignee: Chongqing University of Post and Telecommunications
Current assignee: Chongqing University of Post and Telecommunications
Priority date: 2015-03-13
Filing date: 2015-03-13
Publication date: 2015-06-03
Anticipated expiration: 2035-03-13
Also published as: CN104683074B

Abstract

The invention discloses a large-scale MIMO system limiting feedback method based on compressive sensing. In a large-scale MIMO limiting feedback system, an Nh*Nv-dimensional uniform planar array (UPA) is adopted at a base station, and a linear array is adopted at a user terminal. The large-scale MIMO system limiting feedback method comprises the following steps: firstly, seeking a sparse base matched with a large-scale MIMO horizontal-dimensional channel and a vertical-dimensional channel by using a compressive sensing (CS) theory, thereby furthermore obtaining a two-dimensional united sparse base matched with a large-scale MIMO channel according to a Kronecker product; secondly, projecting an observation matrix irrelevant to the sparse base to a low-dimensional space, thereby obtaining an observation signal, quantifying the signal, and feeding the quantified signal back to the base station; finally, reconstructing channel state information at the base station by using an orthogonal matching pursuit (OMP) algorithm. The utility model provides a simple and efficient implementation method for the large-scale MIMO limiting feedback system.

Description

Compressive Sensing Based Finite Feedback Method for Massive MIMO Systems

技术领域technical field

本发明涉及5G移动通信技术领域，具体给出了一种基于压缩感知的大规模MIMO系统有限反馈方法。The invention relates to the technical field of 5G mobile communication, and specifically provides a method for limited feedback of a massive MIMO system based on compressed sensing.

背景技术Background technique

随着通信数据量的急剧增长，对频谱利用率和能效的提高成为目前无线通信发展的关键。众所周知，MIMO(Massive-Multiple Input Multiple Output，Massive MIMO，大规模多输入多输出)技术能够提高链路传输可靠性和获得较高的系统容量，因此成为4G无线通信系统的关键技术。MIMO系统的容量随着天线数目的增加而增加，因此大规模MIMO在基站端配置了数目庞大的天线，从而获得更好的空间复用及空间分集效果，并且能够更有效的消除用户间的干扰。从能量效率的角度来看，大规模MIMO形成的波束较窄，能够使发射功率更集中于特定的用户，从而能够利用较小的发射功率获得较高的接收端信噪比。因为大规模MIMO具有低能耗和高性能的优点，所以受到了业界的广泛关注和成为5G的关键研究技术。由于大规模MIMO在基站端配置的天线数增加，从而传统的基于码本的有限反馈方法并不适用于大规模MIMO系统，因此需要设计有效的反馈算法来降低大规模MIMO系统的反馈开销。With the rapid increase of the amount of communication data, the improvement of spectrum utilization and energy efficiency has become the key to the development of wireless communication. As we all know, MIMO (Massive-Multiple Input Multiple Output, Massive MIMO, large-scale multiple input multiple output) technology can improve link transmission reliability and obtain higher system capacity, so it has become the key technology of 4G wireless communication system. The capacity of the MIMO system increases with the increase of the number of antennas. Therefore, massive MIMO configures a large number of antennas at the base station to obtain better spatial multiplexing and spatial diversity effects, and can more effectively eliminate interference between users. . From the perspective of energy efficiency, the beam formed by massive MIMO is narrower, which can make the transmission power more concentrated on a specific user, so that a higher signal-to-noise ratio at the receiving end can be obtained with a smaller transmission power. Because massive MIMO has the advantages of low energy consumption and high performance, it has received extensive attention from the industry and has become a key research technology for 5G. Due to the increase in the number of antennas configured at the base station for massive MIMO, traditional codebook-based limited feedback methods are not suitable for massive MIMO systems. Therefore, effective feedback algorithms need to be designed to reduce the feedback overhead of massive MIMO systems.

近几年来信号处理和通信领域出现了一种新的理论—压缩感知，为研究信道的压缩反馈提供了新的思路，该理论指出：只要信号是可压缩的或在某个变换域是稀疏的，那么就可以用一个与变换基不相关的观测矩阵将变换所得高维信号投影到一个低维空间上，然后通过求解一个优化问题就可以从这些少量的投影中以高概率重构出原信号，可以证明这样的投影包含了重构信号的足够信息。In recent years, a new theory-compressed sensing has emerged in the field of signal processing and communication, which provides a new idea for the study of channel compression feedback. The theory points out that as long as the signal is compressible or sparse in a certain transform domain , then you can use an observation matrix unrelated to the transformation base to project the transformed high-dimensional signal onto a low-dimensional space, and then by solving an optimization problem, you can reconstruct the original signal from these small projections with high probability , it can be shown that such a projection contains enough information to reconstruct the signal.

信号的稀疏表示是压缩感知理论应用的基础和前提，只有合理的选择了稀疏基，才能使信号的稀疏系数个数尽可能少，从而保证信号的恢复精度。常用的卡洛南-洛伊(Karhunen-Loeve Transform,KLT)变换是一个在统计意义下具有最小均方意义的变换，具有最优的去相关性和非常好的压缩效率，但是缺乏快速算法，且变换矩阵随信号而异，不同信号需计算不同的变换矩阵，因此计算复杂度较大。FFT具有高效的算法，所以FFT除了在理论上十分重要外，在实现各种数字信号处理算法中还起到核心作用。DCT具有很强的“能量集中”特性：大多数的声音和图像信号的能量都集中在离散余弦变换后的低频部分，而且当信号具有接近马尔科夫过程的统计特性时，DCT的去相关性接近于K-L变换。在大规模MIMO系统中，基于压缩感知的有限反馈技术，目前学术届和产业界均处于初步研究阶段。由于大规模MIMO基站天线数过多，并采用UPA，因此基于压缩感知的有限反馈技术研究不仅需要考虑如何找到适合的稀疏基，还需要有效降低反馈开销。The sparse representation of the signal is the basis and premise of the application of compressed sensing theory. Only when the sparse basis is reasonably selected can the number of sparse coefficients of the signal be reduced as much as possible, thereby ensuring the accuracy of signal recovery. The commonly used Karhunen-Loeve Transform (KLT) transform is a transformation with the least mean square significance in the statistical sense, which has optimal decorrelation and very good compression efficiency, but lacks a fast algorithm. Moreover, the transformation matrix varies with the signal, and different transformation matrices need to be calculated for different signals, so the calculation complexity is relatively large. FFT has an efficient algorithm, so FFT is not only very important in theory, but also plays a central role in realizing various digital signal processing algorithms. DCT has a strong "energy concentration" characteristic: most of the energy of sound and image signals is concentrated in the low-frequency part after the discrete cosine transform, and when the signal has statistical properties close to the Markov process, the decorrelation of DCT Close to K-L transformation. In the massive MIMO system, the limited feedback technology based on compressed sensing is currently in the preliminary research stage in both academic and industrial circles. Due to the large number of antennas in massive MIMO base stations and the use of UPA, the research on limited feedback technology based on compressed sensing not only needs to consider how to find a suitable sparse basis, but also needs to effectively reduce the feedback overhead.

发明内容Contents of the invention

针对以上现有技术的不足，本发明的目的在于提供一种基于压缩感知的大规模MIMO系统有限反馈方法，该方法不仅能找到适合于大规模MIMO系统的二维联合稀疏基，还能在基站端恢复出信道信息，同时降低反馈开销。In view of the deficiencies in the prior art above, the purpose of the present invention is to provide a limited feedback method for massive MIMO systems based on compressed sensing, which can not only find a two-dimensional joint sparse basis suitable for massive MIMO systems, but also The terminal recovers the channel information while reducing the feedback overhead.

本发明的技术方案如下：Technical scheme of the present invention is as follows:

一种基于压缩感知的大规模MIMO系统有限反馈方法，其包括以下步骤：A limited feedback method for massive MIMO systems based on compressed sensing, comprising the following steps:

步骤101、基站端为配置有N_h×N_v维的UPA，其中N_h为UPA的水平维发射天线数，N_v为UPA的垂直维发射天线数；用户端配置为单天线，信道可表示为其中h_h表示水平维信道信息，h_v表示垂直维信道信息。Step 101, the base station is configured with a UPA with N _h × N _v dimensions, where N _h is the number of transmitting antennas in the horizontal dimension of the UPA, and N _v is the number of transmitting antennas in the vertical dimension of the UPA; the user terminal is configured as a single antenna, and the channel can be represented by for Among them, h _h represents the channel information of the horizontal dimension, and h _v represents the channel information of the vertical dimension.

步骤102、设计H的水平维稀疏基Ψ_h和垂直维稀疏基Ψ_v，其中Ψ_h采用离散余弦变换(discrete cosine transform,DCT)稀疏基，Ψ_v采用快速傅里叶变换(Fast Fourier Transform,FFT)稀疏基，再经过Kronecker积定理得到二维联合稀疏基 $Ψ = Ψ_{h} &CircleTimes; Ψ_{v} .$ Step 102, designing the horizontal-dimensional sparse basis Ψ _h and the vertical-dimensional sparse basis Ψ _v of H, wherein Ψ _h adopts a discrete cosine transform (discrete cosine transform, DCT) sparse basis, and Ψ _v adopts a Fast Fourier Transform (FFT, FFT) sparse basis, and then get the two-dimensional joint sparse basis through the Kronecker product theorem $Ψ = Ψ_{h} &CircleTimes; Ψ_{v} .$

步骤103、生成随机高斯观测矩阵Φ∈R^L×N，其中元素都服从0均值，方差为的独立正态分布，其中N＝N_h×Nv，L表示观测值，并且L＜N。Step 103. Generate a random Gaussian observation matrix Φ∈RL ^×N , in which the elements all obey the zero mean and the variance is Independent normal distribution of , where N=N _h ×Nv, L represents the observed value, and L<N.

步骤104、通过观测矩阵Φ把信道H投影到低维空间，得到L×N维的观测信号y。Step 104: Project the channel H into a low-dimensional space through the observation matrix Φ to obtain an L×N-dimensional observation signal y.

步骤105、基站端根据观测信号y、观测矩阵Φ和二维联合稀疏基Ψ，采用OMP算法正确的恢复出信道信息 Step 105: The base station uses the OMP algorithm to correctly recover the channel information according to the observed signal y, the observed matrix Φ, and the two-dimensional joint sparse basis Ψ

进一步的，步骤102中水平维信道稀疏表示如下：.h_h＝Ψ_hh₁.，其中h₁表示经过正交稀疏基变换后的信号，DCT稀疏基Ψ_h的具体公式如下：Further, in step 102, the horizontal dimension channel sparse representation is as follows: .h _h =Ψ _h h ₁ ., where h ₁ represents the signal after orthogonal sparse basis transformation, and the specific formula of DCT sparse basis Ψ _h is as follows:

$F f ((u u,, v v)) = = \frac{22}{{N N}_{h h}} C C ((u u)) C C ((v v)) [[{Σ Σ}_{i i = = 00}^{{N N}_{h h} - - 11} {Σ Σ}_{j j = = 00}^{{N N}_{h h} - - 11} f f ((i i,, j j)) cos cos \frac{((22 i i + + 11)) uπ uπ}{22 {N N}_{h h}} cos cos \frac{((22 i i + + 11)) vπ vπ}{22 {N N}_{h h}}]]$

反变换IDCT公式为：The inverse transformation IDCT formula is:

$F f ((i i,, j j)) = = \frac{22}{{N N}_{h h}} C C ((u u)) C C ((v v)) [[{Σ Σ}_{u u = = 00}^{{N N}_{h h} - - 11} {Σ Σ}_{v v = = 00}^{{N N}_{h h} - - 11} F f ((u u,, v v)) cos cos \frac{((22 i i + + 11)) uπ uπ}{22 {N N}_{h h}} cos cos \frac{((22 i i + + 11)) vπ vπ}{22 {N N}_{h h}}]]$

其中N_h为UPA的水平维发射天线数，i,j是空间坐标，i,j＝0,1,...N_h-1；u,v是DCT空间坐标，u,v＝0,1,...N_h-1。可变系数C(i)＝1(i＝1,2,3...N_h-1)。Among them, N _h is the number of transmitting antennas in the horizontal dimension of UPA, i, j are space coordinates, i, j=0,1,...N _h -1; u, v are DCT space coordinates, u, v=0,1 ,... N _h -1. variable coefficient C(i)=1 (i=1, 2, 3 . . . N _h −1).

同理，垂直维信道稀疏表示如下：h_v＝Ψ_vh₂，其中h₂表示经过正交稀疏基变换后的信号，FFT稀疏基Ψ_v的具体公式如下：Similarly, the sparse representation of the vertical dimension channel is as follows: h _v =Ψ _v h ₂ , where h ₂ represents the signal after the orthogonal sparse basis transformation, and the specific formula of the FFT sparse basis Ψ _v is as follows:

$X x ((m m)) = = {X x}_{11} ((m m)) + + {W W}_{{N N}_{v v}}^{m m} {X x}_{11} ((m m)),, m m = = 0,1 0,1,, . . . . . . \frac{{N N}_{v v}}{22} - - 11$

$X x ((m m + + \frac{{N N}_{v v}}{22})) = = {X x}_{11} ((m m)) - - {W W}_{{N N}_{v v}}^{m m} {X x}_{11} ((m m)),, m m = = 0,1 0,1,, . . . . . . \frac{{N N}_{v v}}{22} - - 11$

其中N_v为基站端均匀面阵的垂直维发射天线数，where N _v is the number of vertical-dimensional transmitting antennas of the uniform planar array at the base station,

$X_{1} (m) = Σ_{r = 0}^{\frac{N_{v}}{2} - 1} x (2 r) W_{\frac{N_{v}}{2}}^{rm}, X_{2} (m) = Σ_{r = 0}^{\frac{N_{v}}{2} - 1} x (2 r + 1) W_{\frac{N_{v}}{2}}^{rm}$ 以及 $W_{N_{v}}^{m} = e^{- j \frac{2 π}{N_{v}} m} .$ $x_{1} (m) = Σ_{r = 0}^{\frac{N_{v}}{2} - 1} x (2 r) W_{\frac{N_{v}}{2}}^{rm}, x_{2} (m) = Σ_{r = 0}^{\frac{N_{v}}{2} - 1} x (2 r + 1) W_{\frac{N_{v}}{2}}^{rm}$ as well as $W_{N_{v}}^{m} = e^{- j \frac{2 π}{N_{v}} m} .$

根据Kronecker积定理： $(A &CircleTimes; B) (C &CircleTimes; D) = AC &CircleTimes; BD,$ 并把水平维信道和垂直维信道的稀疏表示代入大规模MIMO信道模型中，进而得到二维联合稀疏基Ψ，具体表示如下：According to the Kronecker product theorem: $(A &CircleTimes; B) (C &CircleTimes; D.) = AC &CircleTimes; BD,$ And substitute the sparse representation of the horizontal channel and the vertical channel into the massive MIMO channel model, and then obtain the two-dimensional joint sparse basis Ψ, which is expressed as follows:

$H h = = {h h}_{h h} &CircleTimes; &CircleTimes; {h h}_{v v} = = {Ψ Ψ}_{h h} {h h}_{11} &CircleTimes; &CircleTimes; {Ψ Ψ}_{v v} {h h}_{22} = = (({Ψ Ψ}_{h h} &CircleTimes; &CircleTimes; {Ψ Ψ}_{v v})) (({h h}_{11} &CircleTimes; &CircleTimes; {h h}_{22})) = = Ψh Ψh$

其中H表示N×1的大规模MIMO信道信息，h_h表示N_h×1的大规模MIMO水平维信道信息，h_v表示N_v×1的大规模MIMO垂直维信道信息，Ψ_h表示N_h×N_h的DCT稀疏基，Ψ_h表示N_h×N_h的FFT稀疏基，Ψ表示N×N二维联合稀疏基，h₁,h₂,h表示经过正交稀疏基变换后的信号。where H represents N×1 massive MIMO channel information, h _h represents N _h ×1 massive MIMO horizontal dimension channel information, h _v represents N _v ×1 massive MIMO vertical dimension channel information, Ψ _h represents N _h ×N _h DCT sparse basis, Ψ _h represents N _h ×N _h FFT sparse basis, Ψ represents N×N two-dimensional joint sparse basis, h ₁ , h ₂ , h represent the signal after orthogonal sparse basis transformation.

进一步的，步骤103中的随机高斯矩阵Φ具有一个重要的性质：对于一个L×N的随机高斯矩阵Φ，当L≥cK log(N/K)时ΦΨ在很大概率下具有RIP性质：Further, the random Gaussian matrix Φ in step 103 has an important property: for a L×N random Gaussian matrix Φ, when L≥cK log(N/K), ΦΨ has the RIP property with a high probability:

$((11 - - δ δ)) {| | | | h h | | | |}_{22}^{22} \leq \leq {| | | | Φh Φh | | | |}_{22}^{22} \leq \leq ((11 + + δ δ)) {| | | | h h | | | |}_{22}^{22},,$

其中δ∈(0,1)，c表示一个很小的常数，K表示信道的稀疏度，N表示信道的长度，且N＝N_h×N_v。Where δ∈(0,1), c represents a small constant, K represents the sparsity of the channel, N represents the length of the channel, and N=N _h ×N _v .

进一步的，步骤104中观测信号可表示成如下形式：Further, the observed signal in step 104 can be expressed in the following form:

y＝ΦH＝ΦΨhy=ΦH=ΦΨh

其中Φ表示L×N的随机高斯矩阵，H表示N×1的大规模MIMO信道信息，Ψ表示N×N二维联合稀疏基，h表示经过二维联合稀疏基变换后的信号。Among them, Φ represents the L×N random Gaussian matrix, H represents the N×1 massive MIMO channel information, Ψ represents the N×N two-dimensional joint sparse basis, and h represents the signal transformed by the two-dimensional joint sparse basis.

进一步的，步骤105中恢复出的信道和大规模MIMO信道H之间的归一化均方误差(Mean Squared Error,MSE)，可通过下式求得：Further, the channel recovered in step 105 The normalized mean square error (Mean Squared Error, MSE) between the massive MIMO channel H can be obtained by the following formula:

$θ θ = = \frac{{| | | | H h - - \overset{~ ~}{H h} | | | |}_{22}^{22}}{{| | | | H h | | | |}_{22}^{22}}$

本发明考虑了大规模MIMO天线数过多的特点，提出基于压缩感知的有限反馈方法，首先，利用CS理论寻找与大规模MIMO信道相匹配的二维联合稀疏基，然后，利用观测矩阵将稀疏信道从高维到低维进行线性投影，最后，在基站端，通过OMP算法恢复反馈的信道状态信息。本发明提出的基于压缩感知的大规模MIMO系统有限反馈方法，相比于传统的MIMO有限反馈技术，不仅更加的匹配大规模MIMO信道，而且可以有效的降低反馈开销和计算复杂度，因而，该发明为大规模MIMO有限反馈提供了一种简单而高效的实现方案。The present invention considers the characteristics of too many massive MIMO antennas, and proposes a limited feedback method based on compressed sensing. First, it uses CS theory to find a two-dimensional joint sparse basis that matches the massive MIMO channel, and then uses the observation matrix to convert the sparse The channel is linearly projected from high-dimensional to low-dimensional, and finally, at the base station, the feedback channel state information is recovered through the OMP algorithm. Compared with the traditional MIMO limited feedback technology, the limited feedback method of massive MIMO system based on compressed sensing proposed by the present invention not only matches the massive MIMO channel better, but also can effectively reduce feedback overhead and computational complexity. Therefore, the method The invention provides a simple and efficient implementation scheme for massive MIMO limited feedback.

附图说明Description of drawings

图1为本发明提出的基于压缩感知的大规模MIMO系统有限反馈方法的系统框图；Fig. 1 is the system block diagram of the limited feedback method of massive MIMO system based on compressed sensing proposed by the present invention;

图2为基站采用垂直极化天线的均匀面阵示意图；FIG. 2 is a schematic diagram of a uniform area array using a vertically polarized antenna in a base station;

图3为压缩感知基本操作流程图；Figure 3 is a flowchart of the basic operation of compressed sensing;

图4为本发明基于压缩感知的有限反馈流程图。Fig. 4 is a flowchart of limited feedback based on compressed sensing in the present invention.

具体实施方式Detailed ways

在大规模MIMO有限反馈方案中，通过观测矩阵把稀疏信道投影到低维空间，并把得到的观测信号反馈给基站，基站利用OMP算法重建反馈的信道状态信息，这样，可以降低计算复杂度和反馈开销。In the massive MIMO limited feedback scheme, the sparse channel is projected into a low-dimensional space through the observation matrix, and the obtained observation signal is fed back to the base station, and the base station uses the OMP algorithm to reconstruct the feedback channel state information, thus reducing the computational complexity and Feedback overhead.

如图1所示，图1为本发明提出的基于压缩感知的大规模MIMO系统有限反馈的系统框图。在基站端配置N_h×N_v维的UPA，其中N_h为UPA的水平维发射天线数，N_v为UPA的垂直维发射天线数，接收端配置单天线的M个用户，用户端进行信道估计得到3D信道矩阵H，并且H可表示为其中h_h表示水平维信道信息，h_v表示垂直维信道信息。As shown in FIG. 1 , FIG. 1 is a system block diagram of the limited feedback of the massive MIMO system based on compressed sensing proposed by the present invention. Configure N _h × N _v dimensional UPA at the base station, where N _h is the number of UPA transmit antennas in the horizontal dimension, N _v is the number of UPA transmit antennas in the vertical dimension, and the receiving end is configured with M users with a single antenna. The 3D channel matrix H is estimated, and H can be expressed as Among them, h _h represents the channel information of the horizontal dimension, and h _v represents the channel information of the vertical dimension.

图2为本发明提出的均匀面阵模型，考虑到天线物理尺寸的限制，如图所示该模型采用UPA结构。Fig. 2 is the uniform area array model proposed by the present invention. Considering the limitation of the physical size of the antenna, the model adopts the UPA structure as shown in the figure.

图3为压缩感知基本操作流程图。如图所示，压缩感知理论主要包括三部分，首先，信号的稀疏表示，然后，设计观测矩阵，要在降低维数的同时保证原始信号的信息损失最小，最后，设计信号恢复算法，利用观测值无失真地恢复出原始信号。Figure 3 is a flowchart of the basic operation of compressed sensing. As shown in the figure, the compressed sensing theory mainly includes three parts. First, the sparse representation of the signal. Then, design the observation matrix to minimize the information loss of the original signal while reducing the dimension. Finally, design the signal recovery algorithm, using the observation value to restore the original signal without distortion.

图4为本发明提出基于压缩感知的有限反馈流程图。Fig. 4 is a flow chart of the limited feedback based on compressed sensing proposed by the present invention.

步骤41：基站端配置N_h×N_v维垂直极化天线的UPA，其中N_h为UPA的水平维发射天线数，N_v为UPA的垂直维发射天线数，接收端配置单天线的M个用户。Step 41: The base station configures a UPA with N _h × N _v vertically polarized antennas, where N _h is the number of UPA transmit antennas in the horizontal dimension, N _v is the number of UPA transmit antennas in the vertical dimension, and the receiver is configured with M single antennas user.

步骤42：对水平维信道进行DCT变换，即：Step 42: Perform DCT transformation on the horizontal dimension channel, namely:

h_h＝Ψ_hh₁ h _h = Ψ _h h ₁

其中h₁表示经过正交稀疏基变换后的信号，DCT稀疏基Ψ_h的具体公式如下：where h ₁ represents the signal after orthogonal sparse basis transformation, and the specific formula of DCT sparse basis Ψ _h is as follows:

反变换IDCT公式为：The inverse transformation IDCT formula is:

其中N_h为均匀面阵UPA的水平维发射天线数，i,j是空间坐标，i,j＝0,1,...N_h-1；u,v是DCT空间坐标，u,v＝0,1,...N_h-1。可变系数C(i)＝1(i＝1,2,3...N_h-1)_。 Among them, N _h is the number of horizontal dimension transmitting antennas of uniform area array UPA, i, j are space coordinates, i, j=0,1,...N _h -1; u, v are DCT space coordinates, u, v= 0,1,... N _h -1. variable coefficient C(i)=1 (i=1, 2, 3 . . . N _h −1 ) _.

步骤43：对垂直维信道进行正交稀疏基变换，得到稀疏信号h₂，即：Step 43: Perform orthogonal sparse basis transformation on the vertical dimension channel to obtain the sparse signal h ₂ , namely:

h_v＝Ψ_vh₂ h _v ＝Ψ _v h ₂

其中FFT稀疏基Ψ_v的具体公式如下：The specific formula of the FFT sparse basis Ψ _v is as follows:

其中in

步骤44：根据Kronecker积定理： $(A &CircleTimes; B) (C &CircleTimes; D) = AC &CircleTimes; BD,$ 并把水平维信道和垂直维信道的稀疏表示代入大规模MIMO信道模型中，进而得到二维联合稀疏基Ψ，具体表示如下：Step 44: According to the Kronecker product theorem: $(A &CircleTimes; B) (C &CircleTimes; D.) = AC &CircleTimes; BD,$ And substitute the sparse representation of the horizontal channel and the vertical channel into the massive MIMO channel model, and then obtain the two-dimensional joint sparse basis Ψ, which is expressed as follows:

步骤45：生成随机高斯矩阵Φ，且必须具有一个重要的性质：对于一个L×N的随机高斯矩阵Φ，对于一个L×N的随机高斯矩阵Φ，当L≥cK log(N/K)时ΦΨ在很大概率下具有RIP性质：Step 45: Generate a random Gaussian matrix Φ, which must have an important property: for an L×N random Gaussian matrix Φ, for a L×N random Gaussian matrix Φ, when L≥cK log(N/K) ΦΨ has the RIP property with high probability:

其中δ∈(0,1)，c表示一个很小的常数，K表示信道的稀疏度，N表示信道的长度，且N＝N_h×N_v，h表示经过二维联合稀疏基变换后的信号。Where δ∈(0,1), c represents a very small constant, K represents the sparsity of the channel, N represents the length of the channel, and N=N _h ×N _v , h represents the two-dimensional joint sparse basis transformation Signal.

步骤46：利用L×N维的观测矩阵Φ将信道从高维到低维进行线性投影，得到L×N维的观测信号y：Step 46: Use the L×N-dimensional observation matrix Φ to linearly project the channel from high-dimensional to low-dimensional, and obtain an L×N-dimensional observation signal y:

y＝ΦH＝ΦΨhy=ΦH=ΦΨh

步骤47：基站端根据观测信号y、观测矩阵Φ和二维联合稀疏基Ψ，采用OMP算法恢复出信道信息并通过下式求的归一化MSE：Step 47: The base station uses the OMP algorithm to restore the channel information according to the observed signal y, the observed matrix Φ, and the two-dimensional joint sparse basis Ψ And the normalized MSE obtained by the following formula:

$θ θ = = \frac{{| | | | H h - - \overset{~ ~}{H h} | | | |}_{22}^{22}}{{| | | | H h | | | |}_{22}^{22}} . .$

可见，本发明为大规模MIMO有限反馈系统提供了一种而简单而高效的实现方法。It can be seen that the present invention provides a simple and efficient implementation method for the massive MIMO limited feedback system.

Claims

1., based on an extensive mimo system limited feedback method for compressed sensing, it is characterized in that: comprise the following steps:

Step 101, base station end are for being configured with N _h× N _vthe UPA of dimension, wherein N _hfor the horizontal dimension number of transmit antennas of UPA, N _vfor the vertical dimension number of transmit antennas of UPA; User side is configured to single antenna, and channel can be expressed as wherein h _hrepresent horizontal dimension channel information, h _vrepresent vertical dimension channel information;

The sparse base Ψ of horizontal dimension of step 102, design H _hbase Ψ sparse in vertical dimension _v, wherein Ψ _hadopt discrete cosine transform (DCT) sparse base, Ψ _vadopt fast Fourier transform (FFT) sparse base, then amass theorem through Kronecker and obtain two-dimentional joint sparse base

Step 103, generation random Gaussian observing matrix Φ ∈ R ^{l × N}, wherein element all obeys 0 average, and variance is independent normal distribution, wherein N=N _h× N _v, L represents measured value, and L < N;

Step 104, by observing matrix Φ, channel H is projected to lower dimensional space, obtain the observation signal y of L × N dimension;

Step 105, base station end, according to observation signal y, observing matrix Φ and two-dimentional joint sparse base Ψ, adopt OMP algorithm to recover channel information

2. method according to claim 1, is characterized in that, in step 102, horizontal dimension channel rarefaction representation is as follows: h _h=Ψ _hh ₁, wherein h ₁represent the signal after orthogonal sparse base conversion, Ψ _hrepresent the sparse base of DCT;

Vertical dimension channel rarefaction representation is as follows: h _v=Ψ _vh ₂, wherein h ₂represent the signal after orthogonal sparse base conversion, Ψ _vrepresent the sparse base of FFT.

3. method according to claim 2, is characterized in that, the sparse base Ψ of DCT _hconcrete formula as follows:

F (u, v) = \frac{2}{N_{h}} C (u) C (v) [Σ_{i = 0}^{N_{h} - 1} Σ_{j = 0}^{N_{h} - 1} f (i, j) \cos \frac{(2 i + 1) uπ}{{2 N}_{h}} \cos \frac{(2 i + 1) vπ}{{2 N}_{h}}]

Inverse transformation IDCT formula is:

F (i, j) = \frac{2}{N_{h}} C (u) C (v) [Σ_{u = 0}^{N_{h} - 1} Σ_{v = 0}^{N_{h} - 1} F (u, v) \cos \frac{(2 i + 1) uπ}{{2 N}_{h}} \cos \frac{(2 i + 1) vπ}{{2 N}_{h}}]

Wherein N _hfor the horizontal dimension number of transmit antennas of UPA, i, j are space coordinatess, i, j=0,1 ... N _h-1; U, v are DCT space coordinatess, u, v=0,1 ... N _h-1.Variable coefficient c (i)=1 (i=1,2,3...N _h-1).

4. method according to claim 2, is characterized in that, the sparse base Ψ of FFT _vconcrete formula as follows:

X (m) = X_{1} (m) + W_{N_{v}}^{m} X_{1} (m), m = 0,1, . . . \frac{N_{v}}{2} - 1

X (m + \frac{N_{v}}{2}) = X_{1} (m) - W_{N_{v}}^{m} X_{1} (m),, = 0,1, . . . \frac{N_{v}}{2} - 1

Wherein N _vfor the vertical dimension number of transmit antennas of base station end uniform surface battle array,

X_{1} (m) = Σ_{r = - 0}^{\frac{N_{v}}{2} - 1} x (2 r) W_{\frac{N_{v}}{2}}^{rm}, X_{2} (m) = Σ_{r = 0}^{\frac{N_{v}}{2} - 1} x (2 r + 1) W_{\frac{N_{v}}{2}}^{rm}

And

W_{N_{v}}^{m} = e^{- j \frac{2 π}{N_{v}} m} .

5. method according to claim 3, is characterized in that, amasss theorem according to Kronecker:

(A &CircleTimes; B) (C &CircleTimes; B) = AC &CircleTimes; BD,

Horizontal dimension and vertical dimension channel are brought into thus obtain two-dimentional joint sparse base Ψ, namely

H = h_{h} &CircleTimes; h_{v} = Ψ_{h} h_{1} &CircleTimes; Ψ_{v} h_{2} = (Ψ_{h} &CircleTimes; Ψ_{v}) (h_{1} &CircleTimes; h_{2}) = Ψh,

Wherein h represents the condition of sparse channel after two-dimentional joint sparse base conversion.

6. method according to claim 1, it is characterized in that, in step 103, condition of sparse channel is carried out linear projection by the observing matrix Φ utilizing L × N to tie up from higher-dimension to low-dimensional, the product of its observing matrix and sparse basis array must meet limited equidistant condition (RIP), thus to guarantee from observation signal reconstruction signal accurately, RIP condition is as follows:

(1 - δ) {| | h | |}_{2}^{2} \leq {| | φh | |}_{2}^{2} \leq (1 + δ) {| | h | |}_{2}^{2}

Wherein δ ∈ (0,1), h represent the condition of sparse channel after two-dimentional joint sparse base conversion.

7. method according to claim 1, is characterized in that, in step 104, observation signal can be expressed as following form:

y＝ΦH＝ΦΨh

Wherein Φ represents the random Gaussian matrix of L × N, and H represents the extensive mimo channel information of N × 1, and Ψ represents N × N two dimension joint sparse base, and h represents the signal after two-dimentional joint sparse base conversion.

8. method according to claim 1, is characterized in that, the channel recovered in step 105 and the normalized mean squared error (MSE) between extensive mimo channel H, try to achieve by following formula:

θ = \frac{{| | H - \tilde{H} | |}_{2}^{2}}{{| | H | |}_{2}^{2}} .