CN108365874A - Based on the extensive MIMO Bayes compressed sensing channel estimation methods of FDD - Google Patents

Abstract

The invention belongs to wireless communication technology fields, provide one kind and being based on the extensive MIMO Bayes compressed sensing channel estimation methods of FDD, for obtaining accurate channel state information.The present invention designs the Gaussian prior model of one mode coupling, to describe common sparsity between different antennae, coefficient wherein in channel vector is divided into some isometric groups, and every group there are one common hyper parameter, every group in this way of coefficients just to possess identical sparsity；In turn, by expectation maximization step, Bayesian inference is carried out based on alternative manner, wherein channel coefficients are as hidden variable, and hyper parameter is as unknown parameter；Finally, using the Posterior Mean of obtained channel vector as the estimation of channel.Emulation shows that BCS methods proposed by the present invention are largely better than congenic method, and can reach the performance bounds that ideal least-squares algorithm is baseline.

Description

Channel Estimation Method Based on FDD Massive MIMO Bayesian Compressive Sensing

technical field

The invention belongs to the technical field of wireless communication, and in particular relates to a method for estimating a compressed sensing channel based on a sparse Bayesian model.

Background technique

Due to the great spatial freedom brought by large-scale antennas, massive MIMO (Multiple-Input Multiple-Output, Multiple-Input Multiple-Output) systems can improve spectrum and energy efficiency by several orders of magnitude; therefore, it is widely considered It is one of the key technologies of the next generation wireless system.

In order to give full play to the characteristics of massive MIMO, the base station needs to accurately obtain uplink and downlink CSI (Channel State Information). The downlink CSI is the same; therefore, only the terminal needs to transmit the uplink pilot, and the base station estimates the corresponding signal CSI; when the pilot sequence is properly designed, the base station can accurately estimate the channel. However, in Frequency Division Duplexing (FDD, Frequency Division Duplexing) mode, channel reciprocity does not hold. The traditional way to obtain downlink CSI is to perform channel estimation at the user end and feed it back to the base station; due to the large number of antennas in the base station, There are many unknown coefficients to be estimated in the downlink channel; therefore, direct downlink channel estimation will cause excessive training and calculation overhead.

In order to avoid the unfavorable factors of obtaining downlink CSI in massive MIMO systems, most researchers so far have adopted TDD mode; however, FDD has many advantages compared with TDD, especially for communication symmetry and delay-sensitive applications; therefore massive MIMO Obtaining the FDD downlink CSI is very challenging and important. In order to reduce the training and calculation burden, some methods based on compressed sensing have been proposed; one of the schemes is to feed back the compressed measurement value of downlink CSI from each user to the base station first, and then the base station adopts a method based on Orthogonal Matching Pursuit (OMP, Orthogonal Matching Pursuit ) algorithm to jointly estimate the channel matrix of multiple users; however, this algorithm only considers gently fading channels, so it can only be applied to narrowband systems. In order to deal with frequency selective channels in broadband systems, an Adaptive Structured Subspace Pursuit algorithm (ASSP, Adaptive Structured Subspace Pursuit) was proposed. Due to the common sparsity of different antennas, the ASSP algorithm can achieve such The performance boundary of the algorithm, and has a moderate training overhead; but the performance of the ASSP algorithm is determined by the threshold p _th , which needs to be carefully adjusted according to the signal-to-noise ratio; and the signal-to-noise ratio is not a priori that can be obtained, so it greatly limits ASSP Practical applications of algorithms.

Based on this, the present invention provides an improved Bayesian compressed sensing channel estimation method based on FDD massive MIMO.

Contents of the invention

The object of the present invention is to provide an improved Bayesian Compressive Sensing channel estimation method based on FDD massive MIMO, which is based on the BCS (Bayesian Compressive Sensing, Bayesian Compressive Sensing) method for estimating FDD massive MIMO wideband CSI.

To achieve the above object, the technical solution adopted in the present invention is:

A method for channel estimation based on FDD massive MIMO Bayesian compressed sensing, characterized in that it comprises the following steps:

Set the number of antennas of the base station as M, adopt the OFDM technology, the base station selects N _p pilot subcarriers to send training symbols, the training symbol vector sent by the mth antenna is p _m , and the pilot subcarriers The position set of is expressed as The base station communicates with a single user, and the channel between the mth antenna of the base station and the user is expressed as:

h _m ＝[h _m,1 ,h _m,2 ,...,h _m,L ] ^T , m=1,2,...,M

Wherein, h _{m, l} represent the lth multipath in h _m , l=1,2,...,L, L represents the channel length;

Step 1. Initialize channel variance Noise variance β ⁽⁰⁾ , upper limit of iteration number N _T , preset error η;

Step 2. Iterative calculation using EM method:

Step E:

Γ ⁽ⁿ⁾ ＝(D ^(n-1) ) ^-1 -β ^(n-1) (D ^(n-1) ) ^-1 A ^H (I+β ^(n-1) A(D ^{(n-1 )} ) ^-1 A ^H ) ^-1 A(D ^(n-1) ) ^-1

μ ⁽ⁿ⁾ = β ^(n-1) Γ ⁽ⁿ⁾ A ^H y

where D represents the diagonal variance matrix:

D=diag([α ₁ ^(n-1) I _1×M ,…,α _l ^(n-1) I _1×M ,…,α _L ^(n-1) I _1×M ] ^T ),I _{1 ×M} is a unit vector;

A represents the measurement matrix:

A＝[A ₁ ,A ₂ ,...,A _L ], A _l ＝[Φ ₁ (l),Φ ₂ (l),...,Φ _M (l)], Φ _m (l) is column l of Φ _m , Collected by location in F _L The selected N _p columns, F _L is composed of the first L columns of the discrete Fourier transform matrix F; ● ^H represents the conjugate transpose operation;

y is the received signal;

M step:

Among them, m _l ⁽ⁿ⁾ ＝[μ ⁽ⁿ⁾ _(l-1)M+1 ,…,μ ⁽ⁿ⁾ _(l-1)M+M ] ^T , μ ⁽ⁿ⁾ _t is μ ⁽ⁿ⁾ The tth element, V _l is the posterior variance matrix of x _l , the (p, t)th element of V _l V _l (p, t) = Γ((l-1)M+p, (l-1 )M+t), Γ(i,j) is the (i,j)th element of Γ, Indicates the sparse vector of the block after the channel adjusts the element position, where x _l,m =h _m,l ,

Termination Judgment:

like, or n=N _T , then terminate the iteration;

output channel estimate

The beneficial effects of the present invention are:

The present invention provides an improved Bayesian compressed sensing channel estimation method based on FDD massive MIMO, which is used to obtain accurate channel state information, so as to give full play to a large-scale multiple-input multiple-output (MIMO, multiple-inputmultiple e-output) system potential. The present invention proposes an improved Bayesian Compressive Sensing (BCS, BayesianCompressive Sensing) method for estimating channel state information (CSI, Channel State Information) in frequency division multiplexing massive MIMO; The Gaussian prior model is used to describe the common sparsity between different antennas, in which the coefficients in the channel vector are divided into groups of equal length, and each group has a common hyperparameter, so that the coefficients of each group have the same sparsity Furthermore, through the step of EM (expectationmaximization), Bayesian inference is performed based on an iterative method, in which the channel coefficient is used as a hidden variable, and the hyperparameter is used as an unknown parameter; finally, the obtained posterior mean of the channel vector as an estimate of the channel. The simulation shows that the BCS method proposed by the present invention is superior to similar methods to a large extent, and can reach the performance boundary of the ideal least squares (LS, LeastSquares) algorithm as the baseline.

Description of drawings

Figure 1 shows the sparse pattern of a massive MIMO channel.

Figure 2 is an illustration of the prior model, in which the double-ring circles are observed data, the single-ring circles are hidden variables, and the boxes are unknown parameters.

Fig. 3 is a diagram showing the variation of MSE performance of various algorithms with SNR in the embodiment, N _p /N=0.22, k=6.

FIG. 4 is a diagram showing the variation of MSE performance of various algorithms with pilot frequency ratio N _p /N in the embodiment, SNR=20dB, k=6.

Fig. 5 is a diagram showing the variation of MSE performance of various algorithms with channel sparsity k in the embodiment, SNR=20dB, N _p /N=0.22.

Detailed ways

Below in conjunction with accompanying drawing and example the present invention is described in detail as follows:

This embodiment provides a channel estimation method based on FDD massive MIMO Bayesian compressed sensing, specifically as follows:

Channel model:

Assuming that a base station with M antennas communicates with a single user, under frequency selective fading, the channel between the mth antenna of the base station and the user can be expressed as:

h _m ＝[h _m,1 ,h _m,2 ,...,h _m,L ] ^T , m=1,2,...,M (1)

Among them, h _m,l represents the lth multipath in h _m , and L represents the channel length; due to the high resolution brought by the broadband system, L is usually large, but due to the limited dispersion in the physical propagation environment, only A small number of multipaths is meaningful, and the other channel coefficients are approximately 0; in other words, the channel vector It is generally sparse; moreover, the channels of different antennas at the massive MIMO base station usually have correlation; thus, the channels of different transmission antennas have a common sparse pattern; the support set of sparse channels is Ω _m ={l:|h _{m, l} |≠0}; as shown in Figure 1, it is a sparse mode of a massive MIMO channel, where L=12, Ω={1,4,10}, and |Ω|=3, it can be seen that

Receive signal model:

Using Orthogonal Frequency Division Multiplexing (OFDM, Orthogonal Frequency Division Multiplexing) technology, the base station selects N _p pilot subcarriers to send training symbols, and the UE performs channel estimation after receiving the signals; among the total N subcarriers, The N _p pilot subcarriers are evenly placed; the position set of pilot subcarriers is expressed as in, is a downward rounding operation; the training symbol vector sent by the mth antenna is Among them, the random variable Uniform distribution subject to independent and identical distribution

At the user end, the received signal is removed from the cyclic prefix, converted to the frequency domain, and the vector expression of the processed received signal is:

in, For the processed received signal, Represents a complex vector with N _p rows and one column, N _p is the number of pilots, diag(·) represents the diagonal matrix whose elements are located on its diagonal, Collected by location in F _L The selected N _p columns are composed, and _FL consists of a discrete Fourier transform (DFT, Discrete Fourier Transform) matrix The first L columns of is a 0-mean complex Gaussian noise vector;

For the convenience of analysis, (2) is expressed as

in and

In order to reflect the correlation of the sparse mode among different antennas and facilitate the calculation, the columns of Φ and the elements in h are rearranged to make the channel have block sparsity. The rearranged measurement matrix is denoted by A, and the block sparse channel is denoted by x, we get :

y=Ax+w (4)

in, is the lth column of Φ _m ; x _l ＝[h _1,l ,h _2,l ,...,h _M,l ]∈C ^M×1 , that is, the vector x _l consists of The lth element of each vector in ; according to the correlation between different antenna channels, the elements in x _l have the same sparsity; let the support set of x be S, get:

y＝A _S x _S +w (5)

Among them, A _S is composed of columns selected by A according to the support set S, and x _S is composed of non-zero elements selected by X according to S;

Assuming that the user terminal S is known, the estimate of x _S in the ideal state is:

in, It is the generalized inverse of Moore-Penrose; this estimation scheme is called the ideal least squares (LS, Least Squares) method, and this method is used as the performance baseline of the simulation in the present invention.

The improved BCS method of the present invention:

For the compressed sensing model in formula (4), y, A, x and w are real-valued when processed by the traditional BCS method, while the channel is complex-valued; moreover, the elements in x are independent of each other, that is, Different elements in x have different hyperparameters; making the traditional BCS method unsuitable for the current problem and requiring more hyperparameters; therefore, the present invention improves it.

In order to describe the common sparsity of the elements in _xl , the variable _αl is introduced as a hyperparameter shared by all elements in _xl ; Where x _l,m =h _m,l , assuming that the prior of x _l,m is a complex Gaussian distribution with a mean of 0 and a variance of 1/α _l ; its probability density function is:

It can be seen from the above formula that when α _l has a large value, x _l,m tends to 0, and when α _l is a small value, the probability of x _l,m is a large value is high, so adjust a _l according to y properly , can adaptively control the sparsity of x _l,m ;

Because α _l is shared by all elements in x _l , they have the same sparsity. Based on the above formula, the probability density function of the prior information of x is:

That is to say, x is a complex Gaussian vector with 0 mean value, the diagonal variance matrix D=diag([α ₁ I _1×M ,…,α _L I _1×M ] ^T ), and I _1×M is a unit vector;

According to the signal model (4) and prior information (8), to estimate the channel x from the received signal y, the present invention puts it into the EM framework for solution, regards y as an observation vector, x as a hidden variable, and As an unknown parameter, where 1/β is the variance of the 0-mean Gaussian noise vector w, the model diagram is shown in Figure 2; the EM algorithm works in an iterative manner, and during the nth iteration, the expectation (E, Expectation) step is involved and the maximization (M, Maximization) step, the posterior probability of x is updated in the E step, and the parameter θ that maximizes the expectation is estimated in the M step; in summary, the EM method iterates between the following two steps:

Step E: Calculate p(x|y; θ ^(n-1) ) (9)

M-step: Estimation

The posterior probability of x in the E step is calculated by the following formula:

Among them, p(x; θ ^(n-1) ) is the prior probability density function of x, p(y; θ ^(n-1) ) represents the probability density of y, in the process of calculating the mean and variance of the posterior probability , can be treated as a constant; θ ^(n-1 ) is the set of estimated parameters after the n-1th iteration, and the expectation in the M step is calculated by the following formula:

Among them, lnp(x,y; θ ^(n-1) )=ln(p(y|x; θ ^(n-1) )p(x; θ ^(n-1) )), the symbol <·> means · About the expectation of the posterior probability p(x|y; θ ^(n-1) );

For the sake of illustration, θ or its superscript will be ignored below if there is no ambiguity;

In step E, the integrated signal model (4) and Gaussian noise w are easily obtained:

Take the logarithm of (11) to get:

lnp(x|y; θ) = lnp(y|x; θ)+lnp(x; θ)+const=-(x-μ) ^H Γ ^-1 (x-μ)+const (14)

Among them, const is a constant that is not related to x;

Bringing (8) and (13) into (11) to calculate the posterior probability p(x|y; θ) of x, combined with formula (14), the mean value μ and variance Γ of the posterior probability of x are obtained as:

It can be seen from (14) that the posterior probability of x obeys the complex Gaussian distribution, the mean vector is μ, and the variance matrix is Γ;

It should be noted that in the E step, the parameter θ is calculated and known in the previous iteration, and the iteration mark is omitted here for the sake of brevity;

In the M step, the objective function Q(x,θ)=<ln(p(y|x;θ)p(x;θ))>, bring (8), (13) into Q(x,θ) , calculated to get:

Understand that the expectation is calculated on the posterior probability p(x|y; θ), so the size of Q(x, θ) depends on θ;

Finding the solution that makes the derivative of Q(x,θ) with respect to a _l is 0, we get

in, l=1,2,...,L, μt is the tth element of μ; is the posterior variance matrix of x _l , the (p, t)th element of V _l V _l (p, t) = Γ ((l-1)M+p, (l-1)M+t), Γ (i, j) is the (i, j)th element of Γ; from formula (17), it can be seen that a _l is inversely proportional to ||x _l || ² : the posterior mean of <||x _l || ² >, that is When <||x _l || ² > is large, α _l is small, which makes the elements in xl have large values; on the other hand, when <||x _l || ² > is small, α _l is large , which will cause the elements in x _l to be smaller and close to the mean value 0; moreover, due to the use of a common hyperparameter α _l , the elements in x _l have a common sparsity;

Similarly, by setting the derivative of Q(x,θ) with respect to β to be 0, we derive

Among them, tr( ) is the trace of matrix ; it is easy to see that the above calculation has completed one iteration;

It should be noted that in the M step, μ and Γ are calculated and known in the E step of this iteration, and the iteration mark is omitted here for the sake of brevity;

In the above EM algorithm, initialization parameters are required at the beginning of the iteration Maximum number of iterations N _T , error η; run iterations until the number of iterations reaches N _T , or reaches the corresponding iteration termination condition, that is Among them, μ ⁽ n) is the posterior mean after the nth iteration;

In each iteration, the computational complexity mainly depends on the calculation of Γ in (15); if Γ is directly calculated, it will lead to higher complexity The present invention uses Woodbury identity to calculate Γ, the calculation of Γ is expanded as:

Γ＝D ^-1 -βD ^-1 A ^H (I+βAD ^-1 A ^H ) ^-1 AD ^-1 (19)

Its complexity is Therefore, the overall complexity of the proposed BCS method is Wherein _N is the number of iterations actually used in the iteration; ASSP algorithm is adopted as comparative example 1 in the present embodiment, and the complexity of ASSP algorithm is Under typical settings _Np = 410, _Np /N = 0.2, M = 64, |Ω| = 6 (used in the following simulations), the two methods have similar complexity;

If you do not take advantage of the common sparsity in {x _l }, set independent hyperparameters for each element in x, that is, the original BCS algorithm, as comparison example 2; the hyperparameter set is Using a similar derivation one can get:

n=1,2,...,ML, where Γ _n is the nth element on the diagonal of Γ; the calculation of the posterior probability of x and β still uses the original formula.

During the simulation, the system parameters were set as number of antennas M=64, channel length L=64, number of pilots N=2048, and sparsity |Ω|=k. Now according to a complex Gaussian distribution with 0 mean and unit variance, k elements are randomly selected as the channel The non-zero element in , 1≤m≤M is the antenna serial number, k is the channel sparsity, and the other Lk elements in h _m are set to 0. The obtained channel is normalized so that ||x|| ² =ML, and x is the adjusted channel in (4). The simulation compares the original BCS method, ASSP algorithm, improved BCS algorithm and ideal LS algorithm. Wherein, in the original BCS algorithm, the initial hyperparameter is set to 100, and in the ASSP algorithm, the threshold is set to p _th =0.06, and in the improved BCS method of the present invention, the initial hyperparameter is set to The number of iterations and the error are set as N _T =20, η=10- ³ .

The simulation process is briefly described as follows:

Step 1. Generate the corresponding original sparse channel according to the above description

Step 2. Follow the x _l ＝[h _1,l ,h _2,l ,...,h _M,l ]∈CM× ¹ Form the sparse channel generated in step 1 into x in formula (4) to describe the channel The common sparsity of x makes x have block sparsity, which is convenient for algorithm calculation;

Step 3. Generate corresponding 0-mean Gaussian random noise w according to the set SNR value;

In this case, the formula for calculating the normalized signal-to-noise ratio of the signal is

According to this formula, the variance of the noise can be obtained, so that the variance of the real and imaginary parts of the noise is Generate the corresponding 0-mean complex Gaussian noise w;

Step 4. According to Build the measurement matrix in (4), where is the lth column of Φ _m , The form of the DFT matrix is as follows

in 1≤i≤N _p , 0≤k≤L-1.

Step 5 generates the corresponding received signal y according to formula (4) y=Ax+w.

Step 6 Input y and A into the four algorithms mentioned above for channel estimation, and calculate the corresponding MSE, the formula is as follows

Where ||x|| ₂ is the operator two-norm of x. Figures 3, 4, and 5 are plotted by adjusting SNR, N _p /N, and k, respectively.

The pseudocode of the improved BCS method is as follows

Enter y, A

initialization

iterative calculation

step:

step:

Termination Judgment::

if Or n=N _T , terminate the iteration.

output

Description of simulation results

As shown in FIG. 3 , the channel estimation Mean Squared Error (MSE, Mean Squared Error) performance changes with the signal-to-noise ratio, where N _p /N=0.22, k=6. It can be seen that the curve of the proposed improved BCS almost coincides with that of the ideal LS in the entire SNR region shown. In contrast, when the SNR<25dB, the gap between the ASSP algorithm and the ideal LS algorithm is relatively large. When SNR≥25dB, the curves of ASSP algorithm, improved BCS algorithm and ideal LS algorithm are relatively close. Compared with the ASSP algorithm and the improved BCS algorithm, the original BCS algorithm does not take advantage of the inherent common sparsity of massive MIMO channels, so there is a certain loss in performance compared to the ideal LS baseline.

As shown in FIG. 4 , the impact of training resources on performance is described, where the signal-to-noise ratio SNR=20dB, k=6. As expected, as the number of pilots N _p increases, all methods exhibit better performance. Similar to Fig. 3, the improved BCS algorithm reaches the performance boundary of ideal LS. However, ASSP algorithm needs more pilot overhead to achieve the performance of ideal LS. It can be seen that the MSE of the ASSP algorithm decreases greatly between N _p /N=0.21 and N _p /N=0.23, which means that in order to achieve reliable channel estimation, the algorithm needs to select N _p empirically.

As shown in Fig. 5, the influence of the channel sparsity k on the estimation performance is described, where SNR=20dB, N _p /N=0.22. As k increases, more meaningful elements of x need to be estimated. Therefore, for all methods, the estimation performance is worse for larger k. Although the performance of the improved BCS suffers as the sparsity increases, it is still very close to the ideal LS baseline.

Combining the results of Figures 3, 4, and 5, it can be concluded that the improved BCS algorithm can achieve performance close to the ideal baseline. Compared with the ASSP algorithm, it can handle channel estimation with a larger sparse level with better performance under smaller SNR and training overhead.

The above is only a specific embodiment of the present invention. Any feature disclosed in this specification, unless specifically stated, can be replaced by other equivalent or alternative features with similar purposes; all the disclosed features, or All method or process steps may be combined in any way, except for mutually exclusive features and/or steps.

Claims (1)

1. The improved Bayesian compressed sensing channel estimation method based on the FDD large-scale MIMO is characterized by comprising the following steps of:

setting the number of antennas of the base station as M, adopting the orthogonal frequency division multiplexing technology, and selecting N by the base station_pThe training symbols are sent by pilot frequency sub-carriers, the training symbol vector sent by the m antenna is p_mExpressing the position set of pilot subcarriers asBase station and single userAnd performing communication, wherein the channel between the mth antenna of the base station and the user is represented as:

h_m＝[h_m,1,h_m,2,...,h_m,L]^T，m＝1,2,...,M

wherein h is_m,lRepresents h_mThe L-th multipath, L1, 2, L represents the channel length;

step 1, initializing channel variancesum noise variance β⁽⁰⁾Upper limit of iteration number N_Tpresetting an error eta;

step 2, adopting an EM method to carry out iterative computation:

e, step E:

Γ⁽ⁿ⁾＝(D^(n-1))^-1-β^(n-1)(D^(n-1))^-1A^H(I+β^(n-1)A(D^(n-1))^-1A^H)^-1A(D^(n-1))^-1

μ⁽ⁿ⁾＝β^(n-1)Γ⁽ⁿ⁾A^Hy

where D represents the diagonal variance matrix:

D＝diag([α₁ ^(n-1)I_1×M,…,α_l ^(n-1)I_1×M,…,α_L ^(n-1)I_1×M]^T)，I_1×Mis a unit vector;

a denotes the measurement matrix:

A＝[A₁,A₂,...,A_L]，A_l＝[Φ₁(l),Φ₂(l),...,Φ_M(l)]，Φ_m(l) Is phi_mThe first column of (a) is, from F_LAccording to location setSelected N_pColumn composition, F_LThe first L columns of the discrete Fourier transform matrix F are formed; a^HRepresenting a conjugate transpose operation;

y is a received signal;

and M:

wherein m is_l ⁽ⁿ⁾＝[μ⁽ⁿ⁾ _(l-1)M+1,…,μ⁽ⁿ⁾ _(l-1)M+M]^T、μ⁽ⁿ⁾ _tIs mu⁽ⁿ⁾The t-th element of (V)_lIs x_lA posterior variance matrix of, V_lThe (p, t) -th element V of_lΓ ((l-1) M + p, (l-1) M + t), Γ (i, j) is the (i, j) th element of Γ,vector representing block sparse after channel adjustment element position, where x_l,m＝h_m,l；

And (4) termination judgment:

if the number of the first-time-series terminal,or N ═ N_TThen the iteration is terminated;

outputting the channel estimation value