CN105791185B - Low rank channel method of estimation based on half threshold value of singular value under extensive MIMO scene - Google Patents

Abstract

The invention discloses a low-rank channel estimation method based on a singular value half-threshold in a large-scale MIMO scene, which includes the following steps: 1) In a TDD large-scale MIMO system on an uplink, a base station is equipped with N uniform line arrays. antenna, the receiving end is M single-antenna users, and the users transmit pilot signals to the base station The base station receives the pilot signal Y, where the channel vector from user m to the base station is 2) The base station estimates the uplink channel through the received pilot signal Y, and then constructs the rank minimization problem; 3) Introduces the penalty factor λ in the rank minimization problem established in step 2); 4) Uses the half-threshold singularity The value iterative algorithm solves the rank minimization problem after introducing the penalty factor λ, obtains the channel matrix H corresponding to the optimal rank, and completes the low-rank channel estimation based on the singular value half-threshold in the massive MIMO scenario. The present invention can realize low-rank channel estimation, and the complexity of solution is low, and the robustness of the system is good.

Description

Low-rank channel estimation method based on singular value half-threshold in massive MIMO scenarios

technical field

The invention belongs to the field of antenna selection of a wireless communication system, and relates to a low-rank channel estimation method based on a singular value half-threshold in a large-scale MIMO scene.

Background technique

In a massive MIMO wireless communication system, considering that the base station is configured with a uniform line array, according to the scattering environment, the channel vectors of different users at the receiving end have the same steering vector, which makes the channels between users have a stable correlation. Furthermore, since the dimension of the steering vector is much smaller than the number of base station antennas and the number of users, this leads to low-rank characteristics of the channel in the massive MIMO scenario.

Among the existing schemes, the most common scheme is to relax the non-convex low-rank constraints to the nuclear norm constraints, and further transform the optimization problem into a semi-positive definite programming (SDP) problem for solution. Although these schemes can avoid solving non-convex problems directly, there are still many deficiencies in these schemes. On the one hand, the nuclear norm is not the optimal approximation of low-rank constraints, and the robustness of the solution and the accuracy of rank estimation need to be further improved; on the other hand, the complexity of directly solving the SDP problem in practice is too high.

To sum up, for the low-rank channel estimation problem in large-scale systems, it is necessary to design a scheme with high rank estimation accuracy and reasonable complexity.

Contents of the invention

The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art, and provide a low-rank channel estimation method based on a singular value half-threshold in a massive MIMO scenario. The method can estimate a low-rank channel, and the complexity of the solution is low. The robustness of the system is better.

In order to achieve the above object, the low-rank channel estimation method based on the singular value half-threshold in the massive MIMO scenario of the present invention includes the following steps:

1) In the TDD massive MIMO system under the uplink, the base station is equipped with N antennas arranged in a uniform line array, and the receiving end is M single-antenna users, and the users transmit pilot signals to the base station The base station receives the pilot signal Y, where the channel vector from user m to the base station is

2) The base station estimates the uplink channel through the received pilot signal Y, and then constructs the rank minimization problem;

3) Introduce the penalty factor λ in the rank minimization problem established in step 2);

4) Use the half-threshold singular value iterative algorithm to solve the rank minimization problem after introducing the penalty factor λ, and obtain the channel matrix H corresponding to the optimal rank, and complete the low-rank channel estimation based on the singular value half-threshold in massive MIMO scenarios.

The pilot signal Y observed by the base station is:

Y=XH+N (1)

in, is the channel from the user to the base station, N is the additive white Gaussian noise of the user m∈{1,...,M}, and

Channel vector from user m to base station for:

Among them, P is the number of resolvable physical paths, g _m,p is the angular spread of path p, θ _p is the departure angle of path p, and a(θ _p ) is the steering vector.

The expression of steering vector a(θ _p ) is:

The rank minimization problem constructed in step 2) is:

s.t.Y=XH+N

Wherein, rank(H) is the rank of the channel matrix H.

The relaxation of the low-rank estimation problem constructed in step 2) is:

s.t.Y=XH+N.

Then introduce the penalty factor λ into formula (5), then the low-rank estimation problem is transformed into:

The present invention has the following beneficial effects:

In the specific operation of the low-rank channel estimation method based on the singular value half-threshold in the massive MIMO scenario described in the present invention, the base station estimates the uplink channel through the received pilot signal Y, and constructs a rank minimization problem, and then The rank minimum problem is transformed by introducing a penalty factor, and then the converted rank minimum problem is solved by the half-threshold singular value iterative algorithm to obtain the channel matrix H corresponding to the optimal rank. It should be noted that the present invention uses the half-threshold singular value The iterative algorithm solves the minimum rank problem, thus effectively reducing the complexity of the solution and making the system more robust.

Description of drawings

Fig. 1 is the structural diagram of massive MIMO system described in the present invention;

Fig. 2 is the distribution diagram of the real part of the channel coefficient modulus of the present invention and the real part of the real channel coefficient modulus when SNR=25dB in the simulation experiment;

Fig. 3 is the distribution diagram of the imaginary part of the channel coefficient modulus of the present invention and the imaginary part of the real channel coefficient modulus when SNR=25dB in the simulation experiment;

Fig. 4 is a comparison diagram of MSE performance between the present invention and other channel estimation algorithms.

Detailed ways

The present invention is described in further detail below in conjunction with accompanying drawing:

With reference to Fig. 1, the low-rank channel estimation method based on the singular value half-threshold under the massive MIMO scene of the present invention comprises the following steps:

1) In the TDD massive MIMO system under the uplink, the base station is equipped with N antennas arranged in a uniform line array, and the receiving end is M single-antenna users, and the users transmit pilot signals to the base station The base station receives the pilot signal Y, where the channel vector from user m to the base station is in

The pilot signal Y observed by the base station is:

Y=XH+N (1)

in, is the channel from the user to the base station, N is the additive white Gaussian noise of the user m∈{1,...,M}, and

Channel vector from user m to base station for:

Among them, P is the number of resolvable physical paths, g _m,p is the angular expansion of path p, θ _p is the departure angle of path p, a(θ _p ) is the steering vector, and the expression of steering vector a(θ _p ) for:

2) The base station estimates the uplink channel through the received pilot signal Y, and then constructs the rank minimization problem, where

The rank minimization problem is:

s.t.Y=XH+N

Wherein, rank(H) is the rank of the channel matrix H.

3) Introduce the penalty factor λ in the rank minimization problem established in step 2), where

The relaxation of the low-rank estimation problem constructed in step 2) is:

s.t.Y=XH+N.

Then introduce the penalty factor λ into formula (5), then the low-rank estimation problem is transformed into:

4) Use the half-threshold singular value iterative algorithm to solve the rank minimization problem after introducing the penalty factor λ, and obtain the channel matrix H corresponding to the optimal rank, and complete the low-rank channel estimation based on the singular value half-threshold in massive MIMO scenarios.

In step 4), the specific operation of using the half-threshold singular value iterative algorithm to solve the rank minimization problem after introducing the penalty factor λ is as follows:

According to the threshold representation theory, the threshold iterative expression for low-rank estimation based on l _1/2 regularization is:

B ^(k+1) = H ^(k) + μX ^H (XH ^(k) -Y) (7)

Do Svd decomposition on B ^(k+1) , get

[UDV]＝Svd(B ^(k+1) ) (8)

Using the half-threshold operator, the iterative expression of the channel matrix H is obtained:

H ^(k+1) ＝U*diag(H _μ (σ))V ^H ] (9)

Among them, σ is the singular value of B ^(k+1) , H _μ (·) is the half-threshold operator, defined as:

H _μ (σ)＝[h _λ (σ ₁ ),h _λ (σ ₂ ),...,h _λ (σ _N )] ^T (10)

The update formula of the penalty factor is:

[σ(H _k )] _r is the singular value whose index is r when sorting the singular values of H _k in descending order, then

Perform the above steps iteratively, when the maximum number of iterations is reached or the error is less than a certain threshold, the output

simulation test

The simulation parameters are shown in Table 1, and the simulation results are shown in Fig. 2, Fig. 3 and Fig. 4. From Fig. 2, Fig. 3 and Fig. 4, it can be seen that the present invention has higher robustness to the prior art.

Table 1

Claims (1)

1. A low-rank channel estimation method based on singular value half-threshold under a massive MIMO scene, it is characterized in that, comprising the following steps: 1) In the TDD massive MIMO system under the uplink, the base station is equipped with N antennas arranged in a uniform line array, and the receiving end is M single-antenna users, and the users transmit pilot signals to the base station The base station receives the pilot signal Y, where the channel vector from user m to the base station is 2) The base station estimates the uplink channel through the received pilot signal Y, and then constructs the rank minimization problem; 3) Introduce the penalty factor λ in the rank minimization problem established in step 2); 4) Use the half-threshold singular value iterative algorithm to solve the rank minimization problem after introducing the penalty factor λ, and obtain the channel matrix H corresponding to the optimal rank, and complete the low-rank channel estimation based on the singular value half-threshold in the massive MIMO scenario; The pilot signal Y observed by the base station is: Y=XH+N (1) in, is the channel from the user to the base station, N is the additive white Gaussian noise of the user m∈{1,...,M}, and Channel vector from user m to base station for: Among them, P is the number of resolvable physical paths, g _m,p is the angular expansion of path p, θ _p is the departure angle of path p, and a(θ _p ) is the steering vector; The expression of steering vector a(θ _p ) is: The rank minimization problem constructed in step 2) is: s.t.Y=XH+N Wherein, rank (H) is the rank of channel matrix H; The relaxation of the low-rank estimation problem constructed in step 2) is: s.t.Y=XH+N Then introduce the penalty factor λ into formula (5), then the low-rank estimation problem is transformed into: In step 4), the specific operation of using the half-threshold singular value iterative algorithm to solve the rank minimization problem after introducing the penalty factor λ is as follows: According to the threshold representation theory, the threshold iterative expression for low-rank estimation based on l _1/2 regularization is: B ^(k+1) = H ^(k) + μX ^H (XH ^(k) -Y) (7) Do Svd decomposition on B ^(k+1) , get [UDV]＝Svd(B ^(k+1) ) (8) Using the half-threshold operator, the iterative expression of the channel matrix H is obtained: H ^(k+1) ＝U*diag(H _μ (σ))V ^H ] (9) Among them, σ is the singular value of B ^(k+1) , H _μ (·) is the half-threshold operator, defined as: H _μ (σ)＝[h _λ (σ ₁ ),h _λ (σ ₂ ),...,h _λ (σ _N )] ^T (10) The update formula of the penalty factor is: [σ(H _k )] _r is the singular value whose index is r when sorting the singular values of H _k in descending order, then Iteratively execute the above steps, when the maximum number of iterations is reached or the error is less than the preset threshold, the output