CN105791185A - Low-rank channel estimation method based on singular value half threshold under large scale MIMO scene - Google Patents

Abstract

The invention discloses a low-rank channel estimation method based on a singular value half threshold under a large scale MIMO scene. The method comprises the following steps that 1) a base station terminal in a TDD large scale MIMO system under an uplink is equipped with N antennas which are placed in an uniform linear array mode, a receiving terminal is M single antenna users, the users emit a pilot signal to a base station and the base station receives the pilot signal Y, wherein a channel vector from a user m to the base station is defined in the description; 2) the base station terminal estimates an uplink channel through the received pilot signal Y and then constructs a rank minimization problem; 3) in the rank minimization problem established in the step2), a punishment factor lambda is introduced; 4) a half threshold singular value iteration algorithm is used to solve the rank minimization problem after the punishment factor lambda is introduced so as to obtain a channel matrix H corresponding to an optimal rank and complete low-rank channel estimation based on the singular value half threshold under the large scale MIMO scene. In the invention, the low-rank channel estimation can be realized, complexity of a solution is low and system robustness is good.

Description

Based on the low rank channel method of estimation of singular value half threshold value under extensive MIMO scene

Technical field

The invention belongs to the line options field, sky of wireless communication system, relate to the low rank channel method of estimation based on singular value half threshold value under a kind of extensive MIMO scene.

Background technology

In extensive mimo wireless communication system, it is considered to base station configuration even linear array, according to scattering environments, the channel vector of the different user of receiving terminal has identical steering vector, and this makes channel between user have stable dependency.Further, owing to the dimension of steering vector is much smaller than antenna for base station number and number of users, this causes that the channel under extensive MIMO scene has low-rank characteristic.

In existing scheme, modal scheme is that the low-rank of non-convex retrains the constraint of laxization nuclear norm, optimization problem is converted into semi definite programming (SDP) problem further and solves.Although, these schemes can avoid direct solution non-convex problem, but, these schemes yet suffer from many deficiencies.On the one hand, nuclear norm is not the best fit approximation of low-rank constraint, the robustness of solution and the accuracy of rand estination is all needed to be further improved；On the other hand, direct solution SDP problem complexity is too high in practice.

In sum, for the low rank channel estimation problem in large scale system, design that a kind of rand estination precision is high and to have the scheme of reasonable complexity be necessary.

Summary of the invention

It is an object of the invention to the shortcoming overcoming above-mentioned prior art, provide the low rank channel method of estimation based on singular value half threshold value under a kind of extensive MIMO scene, the method can be estimated by low rank channel, and the complexity solved is relatively low, and the robustness of system is better.

For reaching above-mentioned purpose, comprise the following steps based on the low rank channel method of estimation of singular value half threshold value under extensive MIMO scene of the present invention:

1) in the extensive mimo system of the TDD under up-link, base station end is equipped with the antenna put of N root even linear array, and receiving terminal is M single-antenna subscriber, and user is to Base Transmitter pilot signalBase station receives pilot signal Y, and wherein, user m to the channel vector of base station is

2) up channel is estimated by base station end by the pilot signal Y received, and then builds order minimization problem again；

3) in step 2) the order minimization problem set up introduces penalty factor λ；

4) adopt half threshold value singular value iterative algorithm to solve the order minimization problem after introducing penalty factor λ, obtain the channel matrix H that optimal rank is corresponding, complete to estimate based on the low rank channel of singular value half threshold value under extensive MIMO scene.

Base station sight to pilot signal Y be:

Y=XH+N (1)

Wherein,For the channel of user to base station end, Ν be user m ∈ 1 ..., the additive white Gaussian noise of M}, and

User m is to the channel vector of base station endFor:

$h_m=\underset{p=1}{\overset{P}{\Σ}}{g}_{m,p}a\left({\mathrm{\θ}}_p\right)---\left(2\right)$

Wherein, P is distinguishable physics footpath number, g_m,pFor the angle spread of path p, θ_pFor the angle of leaving of path p, a (θ_p) for steering vector.

Steering vector a (θ_p) expression formula be:

$a\left({\mathrm{\θ}}_p\right)={\[1,e^{-j2\mathrm{\π}\frac{D}{\mathrm{\λ}}cos\left({\mathrm{\θ}}_p\right)},\mathrm{...},e^{-j2\mathrm{\π}\frac{D}{\mathrm{\λ}}(M-1)cos\left({\mathrm{\θ}}_p\right)}\]}^T---\left(3\right)$

Step 2) the order minimization problem that builds is:

S.t.Y=XH+N

Wherein, the order that rank (H) is channel matrix H.

Step 2) the relaxing of low-rank estimation problem that build be:

S.t.Y=XH+N.

Give in formula (5) again and introduce penalty factor λ, then low-rank estimation problem is converted to:

The method have the advantages that

Under extensive MIMO scene of the present invention based on the low rank channel method of estimation of singular value half threshold value when concrete operations, up channel is estimated by base station end by the pilot signal Y received, and build order minimization problem, again through introducing penalty factor, order minimum problem is converted, then the order minimum problem after conversion is solved again through half threshold value singular value iterative algorithm, obtain the channel matrix H that optimal rank is corresponding, it should be noted that, the present invention adopts half threshold value singular value iterative algorithm to solve order minimum problem, thus effectively reducing the complexity solved, and make system have higher robustness.

Accompanying drawing explanation

Fig. 1 is the structure chart of extensive mimo system of the present invention；

The scattergram of the real part of real part and real channel coefficient modulus value in the channel coefficients modulus value of present invention when Fig. 2 is SNR=25dB in emulation experiment；

The scattergram of the imaginary part of imaginary part and real channel coefficient modulus value in the channel coefficients modulus value of present invention when Fig. 3 is SNR=25dB in emulation experiment；

Fig. 4 is the MSE Performance comparision figure of the present invention and other channel estimation method.

Detailed description of the invention

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

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

1) in the extensive mimo system of the TDD under up-link, base station end is equipped with the antenna put of N root even linear array, and receiving terminal is M single-antenna subscriber, and user is to Base Transmitter pilot signalBase station receives pilot signal Y, and wherein, user m to the channel vector of base station isWherein

Base station sight to pilot signal Y be:

Y=XH+N (1)

Wherein,For the channel of user to base station end, Ν be user m ∈ 1 ..., the additive white Gaussian noise of M}, and

User m is to the channel vector of base station endFor:

$h_m=\underset{p=1}{\overset{P}{\Σ}}{g}_{m,p}a\left({\mathrm{\θ}}_p\right)---\left(2\right)$

Wherein, P is distinguishable physics footpath number, g_m,pFor the angle spread of path p, θ_pFor the angle of leaving of path p, a (θ_p) for steering vector, steering vector a (θ_p) expression formula be:

$a\left({\mathrm{\θ}}_p\right)={\[1,e^{-j2\mathrm{\π}\frac{D}{\mathrm{\λ}}cos\left({\mathrm{\θ}}_p\right)},\mathrm{...},e^{-j2\mathrm{\π}\frac{D}{\mathrm{\λ}}(M-1)cos\left({\mathrm{\θ}}_p\right)}\]}^T---\left(3\right)$

2) up channel is estimated by base station end by the pilot signal Y received, and then builds order minimization problem again, wherein

Order minimization problem is:

S.t.Y=XH+N

Wherein, the order that rank (H) is channel matrix H.

3) in step 2) the order minimization problem set up introduces penalty factor λ, wherein

Step 2) the relaxing of low-rank estimation problem that build be:

S.t.Y=XH+N.

Give in formula (5) again and introduce penalty factor λ, then low-rank estimation problem is converted to:

4) adopt half threshold value singular value iterative algorithm to solve the order minimization problem after introducing penalty factor λ, obtain the channel matrix H that optimal rank is corresponding, complete to estimate based on the low rank channel of singular value half threshold value under extensive MIMO scene.

Step 4) in adopt half threshold value singular value iterative algorithm to solve the concrete operations introducing the order minimization problem after penalty factor λ to be:

According to threshold value representation theory, based on l_1/2The threshold value iteration of the low rand estination of regularization is expressed as:

B^(k+1)=H^(k)+μX^H(XH^(k)-Y)(7)

To B^(k+1)It is Svd to decompose,

[UDV]=Svd (B^(k+1))(8)

Utilizing half threshold operator, the iteration obtaining channel matrix H is expressed:

H^(k+1)=U*diag (H_μ(σ))V^H](9)

Wherein, σ is B^(k+1)Singular value, H_μ() is half threshold operator, definition:

H_μ(σ)=[h_λ(σ₁),h_λ(σ₂),...,h_λ(σ_N)]^T(10)

The more new formula of penalty factor is:

${\mathrm{\λ}}^{(k+1)}=min\{{\mathrm{\λ}}^{\left(k\right)},\frac{\sqrt{96}}{9\mathrm{\μ}}{\left({\[\mathrm{\σ}\left(H_k\right)\]}_r\right)}^{\frac{3}{2}}\}---\left(13\right)$

[σ(H_k)]_rFor to H_kDuring singular value descending, index is the singular value of r, then

${\mathrm{\μ}}^{\left(k\right)}={\mathrm{\μ}}^{\left(0\right)}=\frac{1-\mathrm{\ϵ}}{\left|\right|X|{|}_2^2},\mathrm{\ϵ}\∈(0,1)---\left(14\right)$

Iteration performs above-mentioned steps, when reaching maximum iteration time or error less than a certain thresholding, and output

L-G simulation test

Simulation parameter is as shown in table 1, simulation result as shown in Figure 2, Figure 3 and Figure 4 shown in, by Fig. 2, Fig. 3 and Fig. 4 it can be seen that the present invention has higher robustness referring now to prior art.

Table 1

Claims (6)

1. based on the low rank channel method of estimation of singular value half threshold value under an extensive MIMO scene, it is characterised in that comprise the following steps:

1) in the extensive mimo system of the TDD under up-link, base station end is equipped with the antenna put of N root even linear array, and receiving terminal is M single-antenna subscriber, and user is to Base Transmitter pilot signalBase station receives pilot signal Y, and wherein, user m to the channel vector of base station is

2) up channel is estimated by base station end by the pilot signal Y received, and then builds order minimization problem again；

3) in step 2) the order minimization problem set up introduces penalty factor λ；

4) adopt half threshold value singular value iterative algorithm to solve the order minimization problem after introducing penalty factor λ, obtain the channel matrix H that optimal rank is corresponding, complete to estimate based on the low rank channel of singular value half threshold value under extensive MIMO scene.

2. based on the low rank channel method of estimation of singular value half threshold value under extensive MIMO scene according to claim 1, it is characterised in that base station sight to pilot signal Y be:

Y=XH+N (1)

Wherein,For the channel of user to base station end, N be user m ∈ 1 ..., the additive white Gaussian noise of M}, and

3. based on the low rank channel method of estimation of singular value half threshold value under extensive MIMO scene according to claim 2, it is characterised in that user m is to the channel vector of base station endFor:

$h_m=\underset{p=1}{\overset{P}{\Σ}}{g}_{m,p}a\left({\mathrm{\θ}}_p\right)---\left(2\right)$

Wherein, P is distinguishable physics footpath number, g_m,pFor the angle spread of path p, θ_pFor the angle of leaving of path p, a (θ_p) for steering vector.

4. based on the low rank channel method of estimation of singular value half threshold value under extensive MIMO scene according to claim 3, it is characterised in that steering vector a (θ_p) expression formula be:

$a\left({\mathrm{\θ}}_p\right)={\[1,e^{-j2\mathrm{\π}\frac{D}{\mathrm{\λ}}cos\left({\mathrm{\θ}}_p\right)},\mathrm{...},e^{-j2\mathrm{\π}\frac{D}{\mathrm{\λ}}(M-1)cos\left({\mathrm{\θ}}_p\right)}\]}^T---\left(3\right)$

5. based on the low rank channel method of estimation of singular value half threshold value under extensive MIMO scene according to claim 4, it is characterised in that step 2) the order minimization problem that builds is:

S.t.Y=XH+N

Wherein, the order that rank (H) is channel matrix H.

6. based on the low rank channel method of estimation of singular value half threshold value under extensive MIMO scene according to claim 5, it is characterised in that step 2) the relaxing of low-rank estimation problem that build be:

S.t.Y=XH+N

Give in formula (5) again and introduce penalty factor λ, then low-rank estimation problem is converted to: