CN105978674B - The pilot frequency optimization method of extensive mimo channel estimation under compressed sensing based FDD - Google Patents

Abstract

The invention discloses a kind of pilot frequency optimization methods of mimo channel extensive under compressed sensing based FDD estimation, and channel can be modeled as Y=HX+N in extensive mimo system first, whereinFor channel matrix,For pilot matrix,For receipt signal matrix,For interchannel noise, M is transmitting antenna number, and T is number of pilots；Then it converts channel matrix toWhereinThe variation of channel matrix is represented,The variation of pilot matrix is represented,Represent the variation that receiving end receives signal；Finally acquire optimal pilot matrix.Due toIt is a sparse vector, channel estimation problems can be modeled as compressed sensing Problems of Reconstruction: ||*||₁1- norm is represented, | | * | |₂Represent 2- norm, 0 < ε < 1.It can ensure that the MIMO Downlink channel estimation of compressed sensing based FDD can reduce the mean square error of channel estimation significantly, improve the performance of channel estimation.

Description

Pilot optimization method for massive MIMO channel estimation under FDD based on compressed sensing

technical field

The present invention relates to the technical field of pilot frequency assisted channel estimation and pilot frequency design of communication systems, and in particular, to a pilot frequency optimization method for massive MIMO channel estimation under FDD based on compressed sensing.

Background technique

In modern wireless communication, the degree of freedom of massive MIMO systems under FDD (Frequency Division Duplexing) increases, and the diversity and multiplexing gains brought by multiple antennas can significantly improve spectral efficiency and energy efficiency. In order for the base station to obtain the spatial multiplexing gain and the array gain, the base station transmitter or the user receiver needs to know channel state information (CSI, channel state information), which needs to be obtained through channel estimation. In a massive MIMO system in TDD mode, the base station can obtain channel uplink CSI, and channel reciprocity makes downlink channel estimation relatively easy. One of the challenges of massive MIMO systems in FDD mode is that the number of pilots increases linearly with the number of transmit antennas, resulting in huge pilot overhead, reducing the efficiency of the communication system, and it is not easy to accurately estimate downlink CSI. Since FDD is more efficient for delay-sensitive systems and most cellular networks currently use FDD, it is necessary to study more efficient channel estimation under FDD.

The large number of transmit antennas at the base station causes limited local scattering. As the number of transmit antennas increases, the channel exhibits a sparse nature. Using the implicit sparse property of the channel to estimate the channel can reduce the number of pilots, thereby improving the effectiveness of the system.

Compressed sensing is widely used in signal and image processing. Compressed sensing is based on sparse the target signal and select the appropriate measurement matrix, sampling and compressing the sparse signal at the same time, only need to transmit a small amount of data, the receiver will restore the signal according to the corresponding recovery matrix. Compressed sensing theory has shown excellent performance in channel estimation. In massive MIMO systems, compressed sensing reconstruction algorithms can be used for channel estimation, thereby reducing the number of pilots.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide a pilot frequency optimization method for massive MIMO channel estimation under FDD based on compressed sensing, aiming at the defects involved in the background technology, so that the obtained optimal pilot frequency matrix makes the channel estimation The MSE is significantly reduced, improving the performance of channel estimation.

The present invention adopts the following technical solutions for solving the above-mentioned technical problems:

Pilot optimization method for massive MIMO channel estimation under FDD based on compressed sensing, the FDD massive MIMO channel is a flat fading channel, the base station has M transmit antennas, the number of antennas for each user in the cell is 1, and the base station transmits length is the pilot training sequence of T, and the pilot optimization method includes the following steps:

Step 1), establish a channel model Y=HX+N;

in is the channel matrix, is the pilot matrix, is the received signal matrix, is the channel additive Gaussian noise, represents a complex vector space;

Step 2), let Make the channel model correspond to the compressed sensing model, and obtain the channel model corresponding to the compressed sensing model

in, is a unitary matrix, is the angle domain channel matrix, P is the signal-to-noise ratio of the pilot symbols, (*) ^H represents the conjugate transpose of the matrix or vector; PT is the signal-to-noise ratio of the transmission of T pilot symbols; the superscript ω is the angular frequency The symbol is used to illustrate that H ^ω is the representation of the channel matrix H in the angle domain; represents the transformed form of the channel matrix, represents the transformed form of the pilot matrix, Represents the transformed form of the signal received by the receiver;

Step 3), initialize the total number of iterations Iter _opt , the current number of iterations q=1, and the pilot matrix at the first iteration The elements of the matrix satisfy the normal distribution, i.e. x _{i, j} is the pilot matrix Elements;

Step 4), find the current Gram matrix is the current pilot matrix;

Step 5), calculate the reduced Gram matrix according to the preset reduction coefficient γ

Among them, i, j=1, 2...M, g _ij are the elements of the matrix G _q , is a matrix Elements;

Step 6), use singular value decomposition to Reduce the rank, keep the largest top T singular values, and obtain a matrix based on the top T singular values

Step 7), by Square root decomposition yields Z _q , let Get the pilot matrix at the next iteration;

Step 8), add 1 to the current iteration number q;

Step 9), repeat step 4) to step 8), until the current number of iterations q is equal to the total number of iterations Iter _opt ;

Step 10), input the optimized matrix

As a further optimization solution of the pilot frequency optimization method for massive MIMO channel estimation under compressed sensing based on FDD of the present invention, the preset reduction coefficient γ is 0.95.

As a further optimization solution of the pilot frequency optimization method for massive MIMO channel estimation under compressed sensing based on FDD of the present invention, the total number of iterations Iter _opt is 800 times.

Compared with the prior art, the present invention adopts the above technical scheme, and has the following technical effects:

In the channel estimation based on compressed sensing in the FDD massive MIMO system, compared with using the randomly generated non-optimized pilot matrix, the optimal pilot matrix obtained by the present invention can significantly reduce the mean square error of channel estimation. , MSE). Improve the performance of channel estimation.

Description of drawings

Fig. 1 is the influence of optimization and non-optimization of pilot matrix of different pilot numbers on reconstruction performance;

Figure 2 shows the effects of optimization and non-optimization of pilot matrix on reconstruction performance for different numbers of transmit antennas.

Detailed ways

Below in conjunction with accompanying drawing, the technical scheme of the present invention is described in further detail:

The present invention includes two main technical problems, one is to convert the channel estimation problem into a compressed sensing problem, so that the pilot sequence optimization problem is modeled as a measurement matrix optimization problem in compressed sensing; the other is to propose a pilot frequency optimization algorithm to solve The measurement matrix is optimized to obtain the optimal pilot matrix. The embodiments of the two parts are introduced separately below, and the beneficial effects of the pilot frequency allocation method on improving the performance of channel estimation based on compressed sensing are illustrated by simulation.

(1) Acquisition of pilot optimization criteria

Consider a massive MIMO system in FDD mode, the channel is a flat fading channel, the base station has M uniform transmit antennas spaced by half wavelengths, and each user in the cell has only one antenna. The base station transmits a pilot training sequence of length T. Denote the pilot signal of the i-th time slot as Then the signal _yi received on the receiving antenna is:

y _i =Hx _i +n _i , i=1,2,...,T (1)

channel matrix quasi-static channel, is additive Gaussian noise. remember Have:

Y=HX+N (2)

The signal-to-noise ratio of each pilot time slot is denoted as P, and the total signal-to-noise ratio of the T pilot time slots is tr(X ^H X)=PT.

In actual use, the virtual angular domain representation can make the nonlinear channel model parameters approximately linear, and the virtual representation of the channel is processed to facilitate analysis and estimation. The virtual representation of a non-selective MIMO channel is:

is a unitary matrix, and M is the number of transmitting antennas. is the angle-domain channel matrix. Due to the local scattering effect of the base station, H ^ω is sparse.

Convert equation (2) into a compressed sensing model. Will

and Substituting into formula (2), we get:

Equation (6) corresponds to the noisy compressed sensing model (7):

y=Ds+N (7)

where s of T×1 is the sparse signal, To restore the matrix, is additive Gaussian noise. The sparse signal s solution problem can be transformed into:

ε is a positive constant close to zero.

Can get: pilot matrix Corresponding to the measurement matrix D, is the sparse signal, corresponding to s. From this, the channel parameters are estimated The problem can be transformed into the problem of sparse signal reconstruction in compressed sensing theory. At the same time, the optimization problem of pilot sequence can also be transformed into a measurement matrix optimization problem of compressed sensing.

In order to solve the compressed sensing problem, if the recovery matrix D satisfies the Mutual Incoherence Property (MIP), then the sparse signal can be accurately reconstructed with a high probability. Therefore, compressive sensing problem solving and measurement matrix optimization problems can be based on MIP.

for a recovery matrix Its cross-correlation value is defined as the maximum normalized absolute value of the inner product between the two different columns, i.e.

The cross-correlation value μ{D} reflects the maximum similarity between the two columns of the measurement matrix. Another representation form of the cross-correlation value is as follows: Gram matrix G=D ^H D, D is the form after column normalization. The off-diagonal elements g _i,j of G are the inner products appearing in formula (9), and the cross-correlation coefficient is the maximum value of the off-diagonal elements. The cross-correlation value represents the maximum correlation between matrix elements, and it has been shown in the literature that the smaller the cross-correlation value, the smaller the reconstruction error. Therefore, the reduction of the cross-correlation value directly affects the reconstruction performance of the compressive sensing recovery algorithm.

(2) Pilot Matrix Optimization Algorithm

Pilot matrix by reducing μ _t of Gram matrix G Optimization. The core idea of optimization is to select an appropriate optimization threshold t to reduce the element |g _ij | of G, that is, to optimize for |g _ij | greater than the value of t, t∈[0,1]. The reduced equation becomes:

γ is the attenuation factor, which is 0.95. get the reduced matrix is a matrix Elements. because The rank of G may be greater than the number of rows of the pilot matrix. In order to decompose the square root of the pilot matrix to obtain an optimized pilot matrix, it is necessary to use Singular Value Decomposition (SVD) to reduce the rank of G to T. The specific process of rank reduction is as follows: In the qth iteration, use SVD to Reducing the rank to keep the first T singular values, we get

U _T and V _M are unitary matrices of T×T and M×M, respectively, and the diagonal of Σ is singular value, and is represented by Square root decomposition yields Z _q , let The above process of reduction and rank reduction needs to be iterated many times to reduce the cross-correlation coefficient to a relatively stable value. At the end of the iteration we get the optimized matrix Finally, the final optimized pilot matrix X _opt is obtained according to formula (5). The specific process of pilot optimization is shown in Algorithm 1:

Algorithm 1: Optimization Algorithm for Pilot Matrix

Input: Pilot Matrix It is a randomly generated Gaussian matrix, matrix elements satisfy the independent identical distribution. Each row represents the number of T pilot sequences sent by each antenna of the base station.

Step 1), ask for According to formula (5), it can be obtained from X

Step 2), optimize get The number of initialization iterations q=1, set Iter _opt = 800 iterations in total.

Step 2.1), find the Gram matrix G _q : by obtain;

Step 2.2), ask for Obtain the reduced Gram matrix according to equation (10)

Step 2.3), find Z _q : use SVD to Reduce the rank, keep the largest top T singular values to obtain the matrix and by Square root decomposition yields Z _q ,

Step 2.4), judge: if q reaches Iter _opt times, jump out of the loop and get the optimized matrix Otherwise, set q=q+1, and skip to step 2.1).

Step 3), the optimized pilot matrix output.

In the next section, we will demonstrate by simulation that the pilot matrix obtained by Algorithm 1 will enable FDD massive MIMO downlink based on Orthogonal Matching Pursuit (OMP) compared to the unoptimized pilot matrix. The channel estimation obtains a smaller mean square error, so that the system obtains a higher channel estimation performance.

(3) Simulation results

Based on the simulation needs, the virtual angular domain channel matrix H ^ω used in the simulation adopts the Spatial Channel Model SCM (Spatial Channel Model SCM) of 3GPP and is generated based on the urban micro-cellular scene. The pilot length is T, the number of base station transmit antennas is M, and the signal sparsity is K. In the simulation, the pilot sequence is sent in a time-division manner. The channel matrix ^Hω is sparse, let the sparsity K be 6. As shown in Equation (2), the base station transmits the signal Y to the user, and according to Equation (4), the signal is converted into a form that conforms to the compressed sensing model. Since the pilot frequency X is known at the receiving end, it can be converted into For equation (6), we restore the channel matrix according to the compressed sensing reconstruction algorithm OMP After conversion, the channel matrix H is obtained, and the channel estimation is completed. We adopt normalized MSE to measure the performance of sparse signal recovery. MSE is defined as:

in represents a sparse signal The kth element in , Represents the reconstruction The kth element in . We carry out simulation analysis from two aspects: the number of different pilots and the number of different transmitting antennas.

1) We first study the effect of the optimized pilot matrix on the channel estimation performance under different pilot numbers. The number M of transmit antennas of the base station is selected as 200, and the number of pilot frequencies T is selected as 20, 30 and 40 respectively. The simulation results are shown in Figure 1. The results show that there are obvious differences in the reconstruction performance between optimized and unoptimized pilots under different pilot numbers. When the SNR is 25dB, when using 20 pilots and 30 pilots, using the optimized pilots can reduce the MSE by 1-2dB; when the SNR is larger, the MSE can be further reduced. It is worth noting that the channel estimation MSE using the optimized pilot matrix when the number of pilots is 30 is very close to the MSE using the unoptimized pilot matrix when the number of pilots is 40. That is, on the premise of the same reconstruction performance, using the optimized pilots can reduce the number of pilots, thereby improving the effectiveness of the system. In addition, it can be seen from the simulation curve that with the increase of the number of pilots, obviously this optimization effect will gradually weaken.

2) We study the improvement of channel estimation MSE by pilot matrix optimization when the number of base station transmit antennas is different. Considering that the number of pilots is 30, the number of base station transmit antennas is 100, 200 and 300, respectively. It can be seen from Fig. 2 that with the increase of the number of transmit antennas of the base station, the recovery performance of the channel matrix decreases. But in the case of three different numbers of transmit antennas, in the normal SNR greater than 15dB signal propagation environment, the optimization of the pilot matrix can achieve a good reconstruction effect. When the SNR is 25dB and the number of transmit antennas is three, using the optimized pilot matrix can reduce the MSE of channel estimation by about 1.5dB compared with the non-optimized pilot matrix. When the SNR is larger, this value will reach 4dB. It can also be seen from the simulation curve in Fig. 2 that when the number of base station transmit antennas is large, the MSE performance improved by optimizing the pilot band is greater.

It can be seen from the simulation that when the signal-to-noise ratio is high, that is, when the SNR is greater than 15dB, the use of the optimized pilot sequence can effectively reduce the MSE of channel estimation, regardless of whether the number of pilots or the base station transmit antenna changes.

It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art and, unless defined as herein, are not to be taken in an idealized or overly formal sense. explain.

The specific embodiments described above further describe the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above descriptions are only specific embodiments of the present invention, and are not intended to limit the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims (3)

1. A pilot frequency optimization method for FDD large-scale MIMO channel estimation based on compressed sensing is characterized in that the pilot frequency optimization method comprises the following steps:

step 1), establishing a channel model Y ═ HX + N;

wherein,in order to be a matrix of channels,in order to be a pilot matrix, the pilot matrix,in order to receive the matrix of signals,is the additive gaussian noise of the channel and,representing a complex vector space;

step 2), let Making the channel model correspond to the compressed sensing model to obtain the channel model corresponding to the compressed sensing model

Wherein,is a unitary matrix of the matrix,is an angle domain channel matrix, P is the signal-to-noise ratio of the pilot symbol, (+)^HRepresenting the conjugate transpose of a matrix or vector; PT is the signal-to-noise ratio of transmitting T pilot symbols; the symbol of angular frequency is denoted by the superscript omega, which is used to illustrate H^ωIs the representation of the channel matrix H in the angle domain;representing a transformed form of the channel matrix,represents a transformed form of the pilot matrix,representing a transformed version of the received signal at the receiving end;

step 3), initializing the total iteration times Iter_optThe current iteration number q is 1, and a pilot matrix in the first iteration The elements of the matrix satisfying a normal distribution, i.e.i＝1，2…T，j＝1，2…M，x_i，jIs a pilot matrixAn element of (1);

step 4), solving the current gram matrix Is a current pilot matrix;

step 5), calculating a reduced gram matrix according to a preset reduction coefficient gamma

Wherein i, j is 1, 2 … M, g_ijIs a matrix G_qThe elements are selected from the group consisting of,is a matrixAn element of (1);

step 6), using singular value decompositionReducing rank, reserving the first T maximum singular values, and obtaining matrix according to the first T singular values

Step 7) ofDecomposition of square root to obtain Z_qLet us orderObtaining a pilot matrix in the next iteration;

step 8), adding 1 to the current iteration times q;

step 9), repeatedly executing the steps 4) to 8) until the current iteration number q is equal to the total iteration number Iter_opt；

Step 10), inputting an optimized matrix

2. The pilot optimization method for massive MIMO channel estimation under FDD according to claim 1, wherein the predetermined reduction coefficient γ is 0.95.

3. The pilot optimization method for massive MIMO channel estimation under FDD based on compressed sensing of claim 1, wherein the total number of iterations Iter_optThe number of the treatment was 800 times.