CN112202481A

CN112202481A - Compressed sensing channel estimation algorithm based on adaptive sensing matrix and implementation device

Info

Publication number: CN112202481A
Application number: CN202010590481.1A
Authority: CN
Inventors: 王亚峰; 肖宇
Original assignee: Beijing University of Posts and Telecommunications
Current assignee: Beijing University of Posts and Telecommunications
Priority date: 2020-06-24
Filing date: 2020-06-24
Publication date: 2021-01-08

Abstract

The invention discloses a compressed sensing channel estimation algorithm and a compressed sensing channel estimation device based on a self-adaptive sensing matrix in a millimeter wave large-scale MIMO system, which are used for solving the channel estimation problem caused by the under-dimension characteristic of a hybrid beam forming framework in the large-scale MIMO system. The algorithm adopts a compressed sensing algorithm to carry out channel estimation according to the sparsity of a millimeter wave channel; meanwhile, a perception matrix is constructed in a self-adaptive manner according to the received pilot frequency signal, so that the channel reconstruction probability under a low signal-to-noise ratio is effectively improved, and the normalized minimum mean square error of a reconstructed channel is reduced.

Description

Compressed sensing channel estimation algorithm based on adaptive sensing matrix and implementation device

Technical Field

The invention relates to the technical field of wireless communication, in particular to an under-dimension channel estimation algorithm for hybrid beam forming in a millimeter wave large-scale MIMO system.

Background

Due to the abundant spectrum resources, the millimeter wave communication technology is widely researched in the 5G mobile network. Although transferring data to the millimeter wave band may increase channel capacity, this is not without sacrifice. For the frequency band of millimeter waves, air is a highly absorbing medium, so that the path loss generated by the air is very serious, and the coverage range of the base station is limited. In order to overcome the disadvantages of millimeter wave communication and fully utilize the gain caused by multiple antennas, digital beam forming technology is widely studied. However, with the widespread application of massive MIMO, the sharp increase of hardware cost due to the increase of the number of antennas has become a major bottleneck. Therefore, the industry has adopted analog beamforming to reduce hardware cost, and has evolved into hybrid beamforming.

The biggest problem brought to the traditional channel estimation by the introduction of the hybrid beamforming technology is the channel information loss. That is, since the number of rf links in the hybrid beamforming architecture is much smaller than the number of large-scale antennas, the dimensionality of the received signals has been reduced from the number of antennas to the number of rf links. This condition may be referred to as signal undersensity. In order to solve the problem of under-dimension channel estimation of a hybrid beamforming architecture, a compressed sensing channel estimation algorithm based on an adaptive sensing matrix is provided.

Disclosure of Invention

The invention provides a compressed sensing channel estimation algorithm based on a self-adaptive sensing matrix in a millimeter wave large-scale MIMO system, which adaptively constructs the sensing matrix according to a received pilot signal in the implementation process, thereby effectively improving the channel reconstruction probability under a low signal-to-noise ratio and reducing the normalized minimum mean square error of a reconstructed channel.

The specific implementation process of the invention is as follows:

step 1: system model

Considering a single-user uplink scenario, the pilot signal transmitted by a user to a base station can be represented as

Wherein X_LIs the length of the signal transmitted by each antenna, the uplink base station received signal can be expressed as

Wherein U is_HBFAnd W_HBFRespectively an analog precoding matrix and a receiving matrix. They can be obtained by SVD decomposition of the channel or other methods. Z is additive white gaussian noise with a mean of zero and a variance of 1. Because the received signal is processed by the analog beamforming matrix, the channel state information contained in the received signal is subjected to a certain dimensionality reduction loss (from N)_RDown to N_RF). H is a millimeter wave sparse channel, which can be expressed as (2):

where L is the number of multipaths of the multipath channel,

is the complex gain of the channel and is,

and

respectively, an arrival angle steering vector and an departure angle steering vector.

And

the azimuth angles of the two vectors, respectively, are typically at (0,2 π]It is administered orally and uniformly distributed. Assuming that the antenna is a uniformly distributed linear array (ULA), the steering vectors are generally expressed as follows

Where d ═ λ/2 is the antenna spacing and λ is the carrier wavelength. Channel H may further emphasize sparsity by sparse channel representation, with the conversion process shown below

Wherein, V_RAnd V_TIs a unitary Discrete Fourier Transform (DFT) matrix of respective size N_R×N_RAnd N_T×N_T. And H_VIs a virtual channel element matrix of size N_R×N_T。

Step 2: received signal adaptive processing

The effective received signal of equation (1) is the first term on the right hand side of the equation, i.e.

Using Kronecker product

By the nature of (1) vectoring the effective received signal to obtain

Wherein h is_SIs H_VComprises a virtual channel coefficient matrix H_VSparse information of (2). The vectorized received signal can thus be represented as

Due to the matrix

The finite equidistant nature of the compressed sensing is not satisfied, so that, by SVD decomposition of G, the received signal (6) can be rewritten to

vec(Y)＝UDV^Hh_S (7)

Equality two-sided left multiplication by U^HAnd

to counteract the UD on the right side of the equation, so that the orthogonal basis V is^HExposed to the outside. The perceptual matrix can be made to satisfy the finite equidistant property by constructing the matrix Φ.

And step 3: perceptual matrix design

To satisfy the finite equidistant criterion, a matrix Φ is designed such that the perceptual matrix Θ^HΘ ≈ I, where Θ ═ Φ V,

Θ^HΘ＝V^HΦ^HΦV≈I (8)

the left and right ends are respectively multiplied by a base matrix V^HAnd V, and to VV^HPerforming eigenvalue decomposition, i.e.

Can obtain the product

Let Γ equal to Φ U₂Wherein r ═ τ₁,…,τ_M]^T，τ＝[τ₁,…τ_N]^T. The problem translates into an optimization problem to solve Γ,

then, define

The optimized objective function (10) can be rewritten to

For matrix E_jPerforming eigenvalue decomposition, i.e.

Order to

τ_max,jIs E_jMaximum eigenvalue of, beta_max,jIs the eigenvector corresponding to the largest eigenvalue. Thus, formula

The maximum difference in the values of (a) and (b) can be eliminated. Then tau_j＝[τ_j,1,…,τ_j,N]^TCan be updated according to the following equation

Is most preferred

Can utilize

Thus obtaining the product. Further, a measurement matrix

And a perception matrix

Can be calculated from

And 4, step 4: compressed sensing channel estimation algorithm design

After constructing the adaptive sensing matrix according to the above description, the "l" of the compressed sensing₀Norm minimization' solving sparse channel, and a related expression of a compressed sensing algorithm can be written as

Wherein the content of the first and second substances,

by reconstructing (14) with a Compressive Sampling matching Pursuit algorithm (CoSaMP), a sparse vector h can be obtained_S. The actual estimated channel can thus be expressed as

Wherein the content of the first and second substances,

is a sparse vector h_SAnd removing the quantized result.

DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION

The following are the simulation parameters for the specific embodiment:

the simulation results are shown in fig. 2 and 3. As can be seen from fig. 2, the proposed algorithm improves over other algorithms in the performance of the NMSE. The low complexity Compressed Sensing (CS) algorithm performs the worst, which at low SNR is 15dB worse than the same algorithm. This is because the sparse channel coefficient matrix, AoA, AoD are estimated simultaneously for the low complexity CS algorithm. Estimation errors caused by noise are more likely to be superimposed over multiple estimates, with greater impact than other algorithms, especially in low SNR situations. The performance of the two-dimensional MUSIC algorithm and the conventional CS algorithm at low SNR is very close to that of the proposed algorithm, but the gap increases as the SNR increases.

As can be seen from fig. 3, the proposed algorithm achieves an NMSE gain of nearly 30dB during the increase of the number of RF chains from 2 to 6. The traditional CS algorithm, the low complexity algorithm and the two-dimensional MUSIC algorithm are similar in overall change, and compared with the two provided compressed sensing algorithms, the two provided compressed sensing algorithms have about 15dB of gain. While the compressed sensing algorithm (red inverted triangular dotted line) based on the adaptive sensing matrix has a further gain than the general sensing matrix. In summary, the larger the number of RF chains, the better the final effect of the proposed channel estimation algorithm. Therefore, in practical applications, the number of RF chains should be increased as much as possible in combination with the complexity and overhead of hardware.

In conclusion, the simulation verifies that the method is successful and credible.

Drawings

FIG. 1 is a schematic diagram of a compressed sensing channel estimation device based on an adaptive sensing matrix;

FIG. 2 is a comparison graph of NMSE simulations of various channel estimation algorithms based on different SNRs;

fig. 3 is a comparison graph of NMSE simulations for various channel estimation algorithms based on different RF chain numbers.

Claims

1. A compressed sensing channel estimation algorithm based on a self-adaptive sensing matrix and a realization device are characterized in that firstly, the sensing matrix is self-adaptively constructed according to a received pilot signal; on the basis, a sparse channel matrix is reconstructed based on a compression sampling matching tracking algorithm, and an actual channel is recovered to the maximum extent.

2. The method of claim 1, wherein adaptively designing the base station received signal comprises:

for a single-user uplink scenario, the pilot signal transmitted by a user to the base station can be represented as

Wherein U is_HBFAnd W_HBFThe method comprises the steps that a simulation precoding matrix and a receiving matrix are respectively obtained by carrying out SVD (singular value decomposition) or other methods on a channel, and Z is additive white Gaussian noise with the mean value of zero and the variance of 1;

vectoring the active received signal, i.e.

Wherein h is_SIs H_VComprises a virtual channel coefficient matrix H_VSo that the vectorized received signal can be represented as

Due to the matrix

The finite equidistant nature of the compressed sensing is not satisfied, so that, by SVD decomposition of G, the received signal (3) can be rewritten to

vec(Y)＝UDV^Hh_S (4)

Equality two-sided left multiplication by U^HAnd

to counteract the UD on the right side of the equation, so that the orthogonal basis V is^HTo expose, the sensing matrix can be made to satisfy the finite equidistant property by constructing the matrix Φ.

3. Method according to claims 1 and 2, characterized in that, according to the finite equidistant criterion of compressed sensing, a matrix Φ is designed such that the sensing matrix Θ is^HΘ ≈ I, where Θ ═ Φ V,

Θ^HΘ＝V^HΦ^HΦV≈I (5)

Can obtain the product

Let Γ equal to Φ U₂After mathematical transformation, the problem is transformed into an optimization problem for solving gamma

Wherein Λ is defined by VV^HIs subjected to characteristic value decomposition to obtain V V^H＝UΛU^HTo obtain the optimum

Then, the design formula of the perception matrix is

4. A method as claimed in claims 1, 2 and 3, characterized in that after construction of the adaptive sensing matrix, the "l" according to the compressed sensing₀Norm minimization' solving sparse channels specifically comprises:

correlation expression of compressed sensing algorithm

Wherein the content of the first and second substances,

by reconstructing (9) with Compressive Sampling matching Pursuit (CoSaMP), a sparse vector h can be obtained_SThus, the actual estimated channel can be expressed as

Wherein the content of the first and second substances,

is a sparse vector h_SAnd removing the quantized result.

5. A compressed sensing channel estimation implementation apparatus with adaptive sensing matrix construction, comprising:

the vectorization module is used for vectorizing the input received signal;

the G matrix calculation module is used for adaptively calculating a G matrix according to the input signal;

a perception matrix construction module, which constructs an adaptive perception matrix according to the method of claims 1, 2 and 3;

a compressed sensing signal recovery module to reconstruct sparse channel vectors according to claim 4;

a de-directional quantization module for de-directionally quantizing the estimated sparse channel vector and then V_R,

Multiplying to obtain an estimated channel