CN104052691A - MIMO-OFDM system channel estimation method based on compressed sensing - Google Patents

Abstract

The invention provides an MIMO-OFDM system channel estimation method based on compressed sensing. The MIMO-OFDM system channel estimation method based on compressed sensing is mainly applied to channel estimation when a receiving terminal is provided with a two-dimensional antenna array. According to the MIMO-OFDM system channel estimation method based on compressed sensing, the time delay, incidence angle and gain of each path of a space channel are estimated in sequence, and channel estimation accuracy can be improved effectively. The MIMO-OFDM system channel estimation method based on compressed sensing comprises the following steps that 1, an initially-estimated value of a channel frequency domain response vector of each pilot frequency sub-carrier is obtained according to the least square criterion; 2, by means of the sparsity of the channel frequency domain response vectors in a time delay domain, the time delay of each path of the channel and an estimated value of a channel time domain response vector of each path of the channel are estimated on the basis of the compressed sensing theory; 3, by means of the sparsity of the channel time domain response vectors in a two-dimensional angle domain, the incidence angle of each path of the channel is estimated on the basis of the compressed sensing theory; 4, the gain coefficient of each path of the channel is estimated according to the least square criterion; 5, estimated values of channel frequency domain responses of all the sub-carriers and antennas are obtained.

Description

MIMO-OFDM system channel estimation method based on compressed sensing

Technical field

The present invention relates to the MIMO-OFDM wireless communication system that receiving terminal is equipped with two-dimensional antenna array, particularly the MIMO-OFDM system channel estimation problem based on compressive sensing theory.

Background technology

Multiple-input and multiple-output (MIMO) technology is at transmitting terminal and receiving terminal configuration multiple antenna, by the combination with multiplex technique or diversity technique etc., make full use of the multipath characteristics of scatter channel, in independent, the parallel data flow of space transmission multichannel, in the situation that not increasing system bandwidth, improve exponentially capability of wireless communication system and link reliability, improved the transmission rate of system.Therefore, MIMO technology is subject to extensive concern, is considered to one of important breakthrough of Modern wireless communication and key technology that future wireless system must adopt.In order to meet growing user data demand, antenna configuration number constantly increases, and as extensive mimo system, and two-dimensional antenna array is by the choose reasonable that is this system antenna configuration.

OFDM (OFDM) is a kind of orthogonal multiple carrier modulation technique, has the efficient availability of frequency spectrum.Development along with radio communication, in order to meet people's demand growing to high-rate service, system bandwidth constantly increases, and the frequency selectivity of channel is more outstanding, traditional balancing technique not only complexity is high, and is difficult to eliminate completely the caused intersymbol interference of multidiameter fading channel.Ofdm system converts wideband frequency Selective Fading Channel to a series of arrowbands flat fading channel, effectively solves the problem of intersymbol interference, at aspects such as realizing high speed data transfer, has unique advantage.Therefore, the system architecture based on MIMO and OFDM arises at the historic moment.

Compressed sensing, claims again compression sampling, is a new sampling theory, by the sparse characteristic of exploitation signal, under the condition much smaller than Nyquist sample rate, by stochastical sampling, obtain the discrete sample of signal, then by the perfect reconstruction signal of non-linear algorithm for reconstructing.Due in actual scattering environments, for broadband signal, wireless channel often consists of several main paths, therefore wireless channel can be considered as to a time delay domain condition of sparse channel, utilizes compressive sensing theory to estimate channel response with less number of pilots.Meanwhile, because user is limited to the incident angle number of base station end aerial array, so exploitation channel is in the sparse property of angle domain, can utilize equally compressive sensing theory to obtain the estimation of channel.

Summary of the invention

Technical problem: the invention provides a kind of number of pilots that effectively reduces, there is the MIMO-OFDM system channel estimation method based on compressed sensing of more over-evaluating meter resolution.

Technical scheme: the MIMO-OFDM system channel estimation method based on compressed sensing of the present invention, comprises the following steps:

A) utilize criterion of least squares, obtain the initial estimate of each pilot sub-carrier upper signal channel frequency domain response vector;

B) utilize the initial estimate of the channel frequency domain response vector that described step obtains in a) in the sparse property of time delay domain, based on compressive sensing theory, estimate the estimated value of the time delay in each path of channel and the channel time domain response vector in each path;

C) utilize described step b) in the estimated value of the channel time domain response vector estimated in the sparse property in two dimension angular territory, based on compressive sensing theory, estimate the incidence angle in each path of channel, described incidence angle comprises the vertical angle of pitch and horizontal azimuth;

D) utilize initial estimate, the step b of the channel frequency domain response vector that described step obtains in a)) in time delay, the step c in each path of estimating) incidence angle in each path of estimating, adopt criterion of least squares, estimate the gain coefficient in each path of channel;

E) by described step b) in time delay, the step c in each path of estimating) incidence angle and the steps d in each path of estimating) and in the gain coefficient in estimated each path, the multipath channel models of substitution channel frequency domain response, obtains the estimated value of the channel frequency domain response on all subcarriers, all antennas.

In the preferred version of the inventive method, step b) idiographic flow is:

First, by channel path time delay 0 to uniform discrete between maximum path time delay, obtain minimum time delay interval and be Δ τ and discrete after path number be N _τ, the Fourier transform relation of utilizing channel frequency domain response and channel time domain to respond, is the product of base vector and channel time domain matrix by the channel frequency domain response vector representation on each subcarrier.

Secondly, the initial estimate of the channel frequency domain response vector on all pilot sub-carriers is arranged in to a matrix in order, is designated as channel frequency domain matrix; All base vectors are arranged in to a matrix according to identical order, are designated as projection matrix; Thereby by channel frequency domain Matrix Estimation value representation be:

$\tilde{H}=\mathrm{\ΞA}+W---\left(12\right)$

Wherein, represent channel frequency domain Matrix Estimation value, Ξ is projection matrix, and A is channel time domain matrix, and W is noise matrix;

Finally, according to formula (12), adopt compressive sensing theory to solve channel time domain matrix, the channel time domain matrix solving is N altogether _τoK, find non-zero row vector wherein, the number L of described non-zero row vector is the channel path sum estimating, l non-zero row vector is the estimated value of the channel time domain response vector in l path, l the corresponding path delay in path is (m-1) Δ τ, wherein, l is the sequence number of non-zero row vector, and m is the channel time domain matrix line number m at l non-zero row vector place.

In the preferred version of the inventive method, step c) idiographic flow is:

First, by vertical angle of pitch uniform discrete, obtain minimum angles and be spaced apart Δ θ, the angle number after discrete is N _θ; By horizontal azimuth uniform discrete, obtain minimum angles and be spaced apart Δ φ, the angle number after discrete is N _φ, utilize the two-dimensional Fourier transform relation between channel time domain response and path incidence angle, the channel time domain response vector estimated value table in each path is shown:

${\widehat{\mathrm{\α}}}_l=P{\mathrm{\γ}}_l+w---\left(18\right)$

Wherein, be the channel time domain response vector estimated value in l path, P is projection matrix, γ _lbe the path complex gain vector in l path, w is noise vector;

Then calculate respectively in accordance with the following methods the incidence angle in each path: for l path, utilize formula (18), adopt compressive sensing theory to solve the estimated value that obtains path complex gain vector, according to the peaked position of element in the complex gain vector of path, calculate the incidence angle in l path, described incidence angle comprises the vertical angle of pitch and horizontal azimuth.

In the above-mentioned preferred version of the inventive method, step c) in, every row element arrangement mode and path complex gain vector γ in described projection matrix _lmiddle arrangement of elements mode is identical, is according to the order sequence of the Kronecker product of the vertical angle of pitch and horizontal azimuth institute respective path and obtains;

The method of calculating the incidence angle in l path is: according to the peaked position s of element in the complex gain vector of path, the vertical angle of pitch that obtains l path is horizontal azimuth is wherein, n _φ=mod (s, N _φ), n _θ=(s-n _φ)/N _φ+ 1, mod (x, y) represents that x is to y complementation.

In the another kind of preferred version of the inventive method, step c) in, arrangement of elements mode and path complex gain vector γ in described projection matrix _lmiddle arrangement of elements mode is identical, is according to the order of the Kronecker product of horizontal azimuth and vertical angle of pitch institute respective path;

The method of calculating the incidence angle in l path is: according to the peaked position s of element in the complex gain vector of path, the vertical angle of pitch that obtains l path is horizontal azimuth is wherein, n _θ=mod (s, N _θ), n _φ=(s-n _θ)/N _θ+ 1.

Beneficial effect: compared with prior art, tool has the following advantages in the present invention:

1, channel estimation methods of the present invention is on the basis of least-squares estimation, further estimated to characterize the parameter (time delay, incidence angle and the gain coefficient that comprise path) of the characteristic of channel, its channel estimation results has significantly and improves compared to least-squares estimation.

2, traditional MIMO-OFDM system channel estimation scheme, as least-squares estimation, number of pilots in an OFDM symbol must be not less than channel time domain length, thereby guarantee that pilot tone is less than coincidence frequency interval at the distribution interval of frequency domain, otherwise can cause that channel estimation results is at the aliasing of time domain.The present invention has utilized the sparse property of channel in time delay domain, and in conjunction with the theory of compressed sensing, number of pilots can be less than channel time domain length, thereby has reduced pilot-frequency expense.

3, traditional incident angle estimation scheme based on subspace algorithm, as MUSIC algorithm, needs a large amount of sample estimate covariance battle arrays.Limited when number of samples, or sample is while having correlation, and estimated performance is very poor, and the number of the incidence angle that can differentiate is less than number of antennas.The present invention utilizes channel in the sparse property in two dimension angular territory, in conjunction with the theory of compressed sensing, estimates incidence angle, not only can effectively reduce observation sample number, and not be subject to the impact of sample correlations and number of antennas, has more wide application.

The present invention adopts the method based on compressed sensing to obtain the estimation of channel parameter, take full advantage of channel in the sparse property in time delay domain and two dimension angular territory, estimated result compares to least-squares estimation tool and increases significantly, reduced pilot-frequency expense simultaneously, for broadband and extensive mimo system, be with a wide range of applications.

Accompanying drawing explanation

Fig. 1 is receiving terminal antenna array configuration schematic diagram.

Embodiment

In order to make those skilled in the art person understand better the present invention, below in conjunction with embodiment and Figure of description, the technical scheme in the present invention is carried out to clear, complete description explanation, should understand these embodiment only for the embodiment of technical solution of the present invention is described, and be not used in, limit the scope of the invention.After having read the present invention, those skilled in the art all fall within to the modification of various equivalents of the present invention and replacement the protection range that the application's claim limits.

Embodiment 1:

1, system model

This programme is considered MIMO-OFDM system.Fig. 1 is receiving terminal antenna configuration schematic diagram, is not general, adopts two-dimensional antenna uniform surface battle array, and wherein horizontal direction has N _hroot antenna, vertical direction has N _vroot antenna, adjacent antenna spacing is d.Time domain multipath channel response matrix is

$Q\left(\mathrm{\τ}\right)=\underset{l=0}{\overset{L-1}{\mathrm{\Σ}}}{\mathrm{\β}}_{l}a\left({\mathrm{\θ}}_l\right)a^T\left({\mathrm{\φ}}_l\right)\mathrm{\δ}(\mathrm{\τ}-{\mathrm{\τ}}_l)---\left(1\right)$

Wherein, δ (τ) represents Kronecker impulse function, the footpath number that L is multipath channel, τ _l, β _lbe respectively time delay and the gain coefficient in l path. for the time domain channel matrix of user to aerial array.Suppose that user distance aerial array is enough far away, incident wave is plane wave, and the vertical direction in l footpath and horizontal direction steering vector are respectively

$a\left({\mathrm{\θ}}_l\right)={[1,e^{-j2\mathrm{\π}d\cos \left({\mathrm{\θ}}_l\right)/\mathrm{\λ}},\·\·\·,e^{-j2\mathrm{\π}(N_v-1)d\cos \left({\mathrm{\θ}}_l\right)/\mathrm{\λ}}]}^T$

$a\left({\mathrm{\φ}}_l\right)={[1,e^{-j2\mathrm{\π}d\sin \left({\mathrm{\θ}}_l\right)\cos \left({\mathrm{\φ}}_l\right)/\mathrm{\λ}},\·\·\·,e^{-j2\mathrm{\π}(N_h-1)d\sin \left({\mathrm{\θ}}_l\right)\cos \left({\mathrm{\φ}}_l\right)/\mathrm{\λ}}]}^T$

Wherein, θ _l∈ [0, pi/2], φ _l∈ [0, π] is respectively vertical angle of pitch angle and the horizontal azimuth in l footpath, and λ is incident wave wavelength.The multipath channel models of utilizing Fourier transform to obtain channel frequency domain response is:

$\begin{array}{c}{H}_k={\∫}_{-\∞}^{+\∞}Q\left(\mathrm{\τ}\right)e^{-j2\mathrm{\πk}({\mathrm{\τ}}_l/t_s)/N_c}\mathrm{d\τ}\\ =\underset{l=0}{\overset{L-1}{\mathrm{\Σ}}}{\mathrm{\β}}_{l}a\left({\mathrm{\θ}}_l\right)a^T\left({\mathrm{\φ}}_l\right)e^{-j2\mathrm{\πk}({\mathrm{\τ}}_l/t_s)/N_c}\end{array}---\left(2\right)$

Wherein, t _sfor the sampling period, N _cfor the number of OFDM symbol subcarrier, H _kbe the channel frequency domain matrix of k subcarrier, the element representative of consumer that its v is capable, h is listed as, to vertical direction v root antenna, the channel frequency domain response of horizontal direction h root antenna on k subcarrier, is expressed as

$H_{v,h,k}=\underset{l=0}{\overset{L-1}{\mathrm{\Σ}}}{\mathrm{\α}}_{v,h,l}{e}^{-j2\mathrm{\πk}({\mathrm{\τ}}_l/t_s)/N_c}---\left(3\right)$

Wherein, user to vertical direction v root antenna, horizontal direction h root antenna in the channel time domain response in l path is

${\mathrm{\α}}_{v,h,l}={\mathrm{\β}}_l{e}^{-j2\mathrm{\π}(v-1)d\cos \left({\mathrm{\θ}}_l\right)/\mathrm{\λ}}{e}^{-j2\mathrm{\π}(h-1)d\sin \left({\mathrm{\θ}}_l\right)\cos \left({\mathrm{\φ}}_l\right)/\mathrm{\λ}}---\left(4\right)$

Suppose that user's number is 1 and is equipped with single antenna, system model is

Y _k＝H _kX _k+Z _k (5)

Wherein, x _krepresent respectively k the reception data on subcarrier and send data, Z _kfor additive white Gaussian noise matrix.To formula (5) equal sign left and right matrix-vector,

y _k＝h _kX _k+z _k (6)

Wherein, y _k=vec (Y _k), h _k=vec (H _k), z _k=vec (Z _k), vec () representing matrix vectorization operator.

2, channel initial estimation

Suppose that user's pilot symbol transmitted is X _k, it is y that receiving terminal receives pilot data _k, according to system model formula (6), utilizing criterion of least squares, the initial estimate that obtains each pilot sub-carrier upper signal channel frequency domain response vector is

${\hat{h}}_k=y_k/X_k=h_k+z_k/X_k=h_k+w_k---\left(7\right)$

Suppose that pilot tone is uniformly distributed at frequency domain, wherein pilot interval is k _p, pilot tone number is N _p, pilot set is { 0, k _p..., (N _p-1) k _p.This channel estimation methods is simple, but precision is limited.Next, this programme will estimate time delay, incidence angle and the gain coefficient of the every paths of multipath channel successively based on this initial estimation result, thereby obtain more accurate channel estimation results.

3, time delay is estimated

If channel path maximum delay is τ _max, because every channel path time delay is all at 0～τ _maxbetween random distribution, can be by channel path time delay 0 to τ _maxbetween uniform discrete, discrete interval is Δ τ, the path number after discrete is wherein, be expressed as the result that a is rounded up, by formula (3), can obtain being expressed as of channel frequency domain response

$H_{v,h,k}=\underset{{\mathrm{\τ}}_l\∈\mathrm{\Γ}}{\mathrm{\Σ}}{\mathrm{\α}}_{v,h,l}{e}^{-j2\mathrm{\πk}({\mathrm{\τ}}_l/t_s)/N_c}---\left(8\right)$

Wherein, time delay set Γ's is chosen for

Γ＝{0,Δτ,2Δτ,…,(N _τ-1)Δτ} (9)

The channel frequency domain response of all antennas on k subcarrier is gathered together, be designated as channel frequency domain response vector, be expressed as

h _k＝Au _k (10)

The channel frequency domain vector of k subcarrier wherein $h_k={[H_{\mathrm{1,1},k},H_{\mathrm{1,2},k},\·\·\·,H_{\mathrm{2,1},k},\·\·\·,H_{N_v,N_h,k}]}^T,$ Base vector ${\mathrm{\μ}}_k={[0,\·\·\·,e^{-j2\mathrm{\πk}((N_{\mathrm{\τ}}-1)\mathrm{\Δ\τ}/t_s)/N_c}]}^T,$ Channel time domain matrix

$A=\left[\begin{array}{ccccc}{\mathrm{\α}}_{\mathrm{1,1,1}}& & \·\·\·& & {\mathrm{\α}}_{N_v,N_h,1}\\ {\mathrm{\α}}_{\mathrm{1,1,2}}& & \·\·\·& & {\mathrm{\α}}_{N_v,N_h,2}\\ \·& & & & \·\\ \·& & & & \·\\ \·& & & & \·\\ {\mathrm{\α}}_{\mathrm{1,1},N_{\mathrm{\τ}}}& & \·\·\·& & {\mathrm{\α}}_{N_v,N_h,N_{\mathrm{\τ}}}\end{array}\right]$

According to formula (7) and formula (10), the initial estimate of channel frequency domain response vector is expressed as

${\tilde{h}}_k={\mathrm{Au}}_k+w_k---\left(11\right)$

The initial estimate of the channel frequency domain response vector on all pilot sub-carriers is arranged in to channel frequency domain matrix in order all base vectors are arranged in to projection matrix Ξ according to identical order, thus obtain by channel frequency domain Matrix Estimation value representation, be:

$\tilde{H}=\mathrm{\ΞA}+W---\left(12\right)$

Wherein, $\tilde{H}={[{\tilde{h}}_0^T,{\tilde{h}}_{k_p}^T,\·\·\·,{\tilde{h}}_{(N_p-1)k_p}^T]}^T,\mathrm{\Ξ}={[u_0^T,u_{k_p}^T,\·\·\·,u_{(N_p-1)k_p}^T]}^T,$ because the most elements of channel time domain matrix A are 0, be a sparse matrix, so formula (12) be the initial estimate of channel frequency domain response vector at the rarefaction representation of time delay domain, based on compressive sensing theory, solve channel time domain matrix A and be

$\hat{A}=\underset{A}{\min }\{\frac{1}{2}{\left|\right|\tilde{H}-\mathrm{\ΞA}\left|\right|}_2^2+\mathrm{\μ}{\left|\right|A\left|\right|}_1\}---\left(13\right)$

Wherein, μ is regularization parameter, this value choose the precision that affects signal reconstruction, || || ₁, || || ₂1-norm and the 2-norm of difference representing matrix.At solved channel time domain matrix in, if certain a line is not null vector, there is a corresponding time delay path, as channel time domain matrix m capable be l non-zero row vector, the channel time domain response vector estimated value of l paths is

${\widehat{\mathrm{\α}}}_l={[{\widehat{\mathrm{\α}}}_{\mathrm{1,1},m},\·\·\·,{\widehat{\mathrm{\α}}}_{N_v,N_h,m}]}^T---\left(14\right)$

Corresponding path delay is estimated as suppose channel time domain matrix middle non-zero row vector altogether individual, the channel path estimating adds up to the corresponding delay set estimating is

$\widehat{\mathrm{\Γ}}=\{{\widehat{\mathrm{\τ}}}_1,{\widehat{\mathrm{\τ}}}_2,\·\·\·,{\widehat{\mathrm{\τ}}}_{\hat{L}}\}---\left(15\right)$

4, incidence angle is estimated

Due to vertical angle of pitch random distribution between 0～0.5 π, by vertical angle of pitch uniform discrete, minimum angles is spaced apart Δ θ, and the angle number after discrete is wherein, be expressed as the result that a is rounded downwards; Due to horizontal azimuth random distribution between 0～π, by horizontal azimuth uniform discrete, minimum angles is spaced apart Δ φ, and the angle number after discrete is by (4), channel time domain response can be expressed as

${\mathrm{\α}}_{v,h,l}=\underset{{\mathrm{\θ}}_q\∈\mathrm{\Θ}}{\mathrm{\Σ}}\underset{{\mathrm{\φ}}_s\∈\mathrm{\Φ}}{\mathrm{\Σ}}{\mathrm{\γ}}_{\mathrm{lqs}}{e}^{-j2\mathrm{\π}(v-1)d\cos \left({\mathrm{\θ}}_q\right)/\mathrm{\λ}}{e}^{-j2\mathrm{\π}(h-1)d\sin \left({\mathrm{\θ}}_q\right)\cos \left({\mathrm{\φ}}_s\right)/\mathrm{\λ}}---\left(16\right)$

Wherein, angle set Θ, Φ is chosen for

$\begin{array}{c}\mathrm{\Θ}=\{\mathrm{\Δ\θ},2\mathrm{\Δ\θ},\·\·\·,N_{\mathrm{\θ}}\mathrm{\Δ\θ}\}\\ \mathrm{\Φ}=\{\mathrm{\Δ\φ},2\mathrm{\Δ\φ},\·\·\·,N_{\mathrm{\φ}}\mathrm{\Δ\φ}\}\end{array}---\left(17\right)$

According to the estimated result of formula (14) and formula (16), the channel time domain response vector estimated value table of estimated l paths is shown

${\widehat{\mathrm{\α}}}_l=P{\mathrm{\γ}}_l+w---\left(18\right)$

Wherein, path complex gain vector w is noise vector, and P is projection matrix, is expressed as

$P=\left[\begin{array}{ccc}{\mathrm{\ψ}}_{\mathrm{1,1,1,1}}& \·\·\·& {\mathrm{\ψ}}_{\mathrm{1,1},N_{\mathrm{\θ}},N_{\mathrm{\φ}}}\\ \·& & \·\\ \·& & \·\\ \·& & \·\\ {\mathrm{\ψ}}_{N_v,N_h,\mathrm{1,1}}& \·\·\·& {\mathrm{\ψ}}_{N_v,N_h,N_{\mathrm{\θ}},N_{\mathrm{\φ}}}\end{array}\right]---\left(19\right)$

Wherein, ${\mathrm{\ψ}}_{i,j,q,s}=e^{-j2\mathrm{\π}(i-1)d\cos \left({\mathrm{\θ}}_q\right)/\mathrm{\λ}}{e}^{-j2\mathrm{\π}(j-1)d\sin \left({\mathrm{\θ}}_q\right)\cos \left({\mathrm{\φ}}_s\right)/\mathrm{\λ}},$ φ _s＝sΔφ，θ _q＝qΔθ。Due to path complex gain vector γ _lin to only have an element be not 0, be a sparse vector, so formula (18) is that the estimated value of channel time domain response vector is at the rarefaction representation in two dimension angular territory, based on compressive sensing theory solution path complex gain vector γ _lfor

${\widehat{\mathrm{\γ}}}_l=\underset{{\mathrm{\γ}}_l}{\min }\{\frac{1}{2}{\left|\right|{\widehat{\mathrm{\α}}}_l-{\mathrm{P\γ}}_l\left|\right|}_2^2+\mathrm{\μ}{\left|\right|{\mathrm{\γ}}_l\left|\right|}_1\}---\left(20\right)$

The estimated path complex gain vector going out the size of incident angle has been reflected in the residing position of middle element maximum.According to vectorial γ _lthe arrangement mode of middle element, can calculate the vertical angle of pitch and horizontal azimuth.If the path complex gain vector estimating the peaked position of middle element is s,

(1) if path complex gain vector γ _lthe arrangement mode of middle element is the order of the Kronecker product of the vertical angle of pitch and horizontal azimuth institute respective path, first, for each vertical angle of pitch, by horizontal azimuth order from small to large, arranges path complex gain, and obtaining a length is N _φvector; Then, according to vertical angle of pitch order from small to large, arranging above-mentioned length is N _φvector, obtaining a length is N _θn _φvector, be expressed as

The corresponding vertical angle of pitch of l paths and horizontal azimuth is estimated as

${\widehat{\mathrm{\θ}}}_l=n_{\mathrm{\θ}}\mathrm{\Δ\θ},{\widehat{\mathrm{\φ}}}_l=n_{\mathrm{\φ}}\mathrm{\Δ\φ}$

Wherein, n _φ=mod (s, N _φ), n _θ=(s-n _φ)/N _φ+ 1, mod (x, y) represents that x is to y complementation.

(2) if path complex gain vector γ _lthe arrangement mode of middle element is horizontal azimuth and the order of the Kronecker product of vertical angle of pitch institute respective path, first, for each horizontal azimuth, by vertical angle of pitch order from small to large, arranges path complex gain, and obtaining a length is N _θvector; Then, according to horizontal azimuth order from small to large, arranging above-mentioned length is N _θvector, obtaining a length is N _θn _φvector, be expressed as

The corresponding vertical angle of pitch of l paths and horizontal azimuth is estimated as

${\widehat{\mathrm{\θ}}}_l=n_{\mathrm{\θ}}\mathrm{\Δ\θ},{\widehat{\mathrm{\φ}}}_l=n_{\mathrm{\φ}}\mathrm{\Δ\φ}$

Wherein, n _θ=mod (s, N _θ), n _φ=(s-n _θ)/N _θ+ 1.

Estimate successively the set of the incident angle of paths (the vertical angle of pitch and horizontal azimuth) is

$\begin{array}{c}\widehat{\mathrm{\Θ}}=\{{\widehat{\mathrm{\θ}}}_1,{\widehat{\mathrm{\θ}}}_2,\·\·\·,{\widehat{\mathrm{\θ}}}_L\}\\ \widehat{\mathrm{\Φ}}=\{{\widehat{\mathrm{\φ}}}_1,{\widehat{\mathrm{\φ}}}_2,\·\·\·,{\widehat{\mathrm{\φ}}}_L\}\end{array}---\left(21\right)$

5, gain coefficient is estimated

According to the estimated value of the incidence angle in the estimated value of the time delay in the initial estimate of channel frequency domain response, each path, each path, by formula (3) and formula (4), can be obtained

${\tilde{H}}_{v,h,k}=\underset{l=0}{\overset{\hat{L}-1}{\mathrm{\Σ}}}{\mathrm{\β}}_l{e}^{-j2\mathrm{\π}(v-1)d\cos \left({\mathrm{\θ}}_l\right)/\mathrm{\λ}}{e}^{-j2\mathrm{\π}(h-1)d\sin \left({\widehat{\mathrm{\θ}}}_l\right)\cos \left({\widehat{\mathrm{\φ}}}_l\right)/\mathrm{\λ}}{e}^{-j2\mathrm{\πk}({\widehat{\mathrm{\τ}}}_l/t_s)/N_c}+W_{v,h,k}---\left(22\right)$

Wherein, w _{v, h, k}be respectively user to initial estimate and the noise of horizontal direction h root antenna, the channel frequency domain response of vertical direction v root antenna on k subcarrier, be respectively time delay, horizontal azimuth and the vertical angle of pitch in estimated l the path going out, β _lit is the gain coefficient in l path.The initial estimate of the channel frequency domain response on all pilot sub-carriers is arranged in to column vector, according to formula (22),

$\tilde{H}=\mathrm{E\β}+W---\left(23\right)$

Wherein, $\tilde{H}={[{\tilde{H}}_{\mathrm{1,1,1}},{\tilde{H}}_{\mathrm{2,1,1}},\·\·\·,{\tilde{H}}_{N_v,\mathrm{1,1}},{\tilde{H}}_{\mathrm{1,2,1}},\·\·\·,{\tilde{H}}_{H_v,N_h,1},{\tilde{H}}_{\mathrm{1,1},k_p},\·\·\·,{\tilde{H}}_{N_v,N_h,(N_p-1)k_p}]}^T,$ The path delay and the incidence angle that according to formula (15) and formula (21), obtain, matrix E builds as follows

Wherein, ${\widehat{\mathrm{\ψ}}}_{i,j,l}=e^{-j2\mathrm{\π}(i-1)d\cos \left({\widehat{\mathrm{\θ}}}_l\right)/\mathrm{\λ}}{e}^{-j2\mathrm{\π}(j-1)d\sin \left({\widehat{\mathrm{\θ}}}_l\right)\cos \left({\widehat{\mathrm{\φ}}}_l\right)/\mathrm{\λ}}{\widehat{\mathrm{\ξ}}}_{k,l}=e^{-j2\mathrm{\πk}({\widehat{\mathrm{\τ}}}_l/t_s)/N_c}.$ Adopt criterion of least squares, obtain channel gain coefficient and be

$\widehat{\mathrm{\β}}={\left(E^{H}E\right)}^{-1}{E}^H\tilde{H}$

6, channel estimating

According to estimated path delay, incidence angle and gain coefficient, the multipath channel models of substitution channel frequency domain response (2), the estimated value that obtains the channel frequency domain response on all subcarriers and antenna is:

$\begin{array}{c}{\hat{H}}_{v,h,k}=\underset{l=0}{\overset{\hat{L}-1}{\mathrm{\Σ}}}{\widehat{\mathrm{\β}}}_l{e}^{-j2\mathrm{\π}(v-1)d\cos \left({\widehat{\mathrm{\θ}}}_l\right)/\mathrm{\λ}}{e}^{-j2\mathrm{\π}(h-1)d\sin \left({\widehat{\mathrm{\θ}}}_l\right)\cos \left({\widehat{\mathrm{\φ}}}_l\right)/\mathrm{\λ}}{e}^{-j2\mathrm{\πk}({\widehat{\mathrm{\τ}}}_l/t_s)/N_c}\\ 1\≤v\≤H_v,1\≤h\≤N_h,0\≤k\≤N_c-1\end{array}---\left(24\right)$

Embodiment 2:

According to compressive sensing theory, can obtain formula (13) and formula (20), adopt optimized algorithm to solve.The present embodiment provides OMP Algorithm for Solving formula (13) and formula (20), is specially:

A. initialization residual $r_{v,h}^{\left(0\right)}={\tilde{H}}_{v,h}={[{\tilde{H}}_{v,h,0},{\tilde{H}}_{v,h,k_p},\·\·\·,{\tilde{H}}_{v,h,(N_p-1)k_p}]}^T,$ K wherein _pfor pilot interval, N _pfor pilot tone number, for user is to vertical direction v root antenna, horizontal direction h root antenna is at the initial estimate of the channel frequency domain response of k subcarrier.The set of initialization time delay index iterations t=1.Make Ψ ⁽⁰⁾for empty matrix.Suppose that multipath number L is known.

B. in the t time iteration, by solving following formula, find the location index in t time delay footpath:

Wherein, be the j row of projection matrix Ξ, projection matrix Ξ is expressed as

$\mathrm{\Ξ}=\left[\begin{array}{cccc}{\mathrm{\ξ}}_{\mathrm{0,1}}& {\mathrm{\ξ}}_{\mathrm{0,2}}& \·\·\·& {\mathrm{\ξ}}_{0,N_{\mathrm{\τ}}}\\ {\mathrm{\ξ}}_{k_p,1}& {\mathrm{\ξ}}_{k_p,2}& \·\·\·& {\mathrm{\ξ}}_{k_p,N_{\mathrm{\τ}}}\\ \·& \·& & \·\\ \·& \·& & \·\\ \·& \·& & \·\\ {\mathrm{\ξ}}_{(N_p-1)k_p,1}& {\mathrm{\ξ}}_{(N_p-1)k_p,2}& \·\·\·& {\mathrm{\ξ}}_{(N_p-1)k_p,N_{\mathrm{\τ}}}\end{array}\right]$

Wherein, ${\mathrm{\ξ}}_{k,l}=e^{-j2\mathrm{\πk}({\mathrm{\τ}}_l/t_s)/N_c},{\mathrm{\τ}}_l=(l-1)\mathrm{\Δ\τ},$ T _sfor the sampling interval.

C. preserve the estimated result of the t time iteration:

D. solve the channel time domain response vector in the path that has completed time delay estimation ${\mathrm{\α}}_{v,h}^{\left(t\right)}(1\≤v\≤N_v,1\≤h\≤N_h):$

${\widehat{\mathrm{\α}}}_{v,h}^{\left(t\right)}=\underset{{\mathrm{\α}}_{v,h}}{\arg \min }{\left|\right|{\tilde{H}}_{v,h}-{\mathrm{\Ψ}}^{\left(t\right)}{\mathrm{\α}}_{v,h}\left|\right|}_2$

E. upgrade residual volume

${\stackrel{\widehat{~}}{H}}_{v,h}^{\left(t\right)}={\mathrm{\Ψ}}^{\left(t\right)}{\widehat{\mathrm{\α}}}_{v,h}^{\left(t\right)},r_{v,h}^{\left(t\right)}={\tilde{H}}_{v,h}-{\stackrel{\widehat{~}}{H}}_{v,h}^{\left(t\right)}$

F. make t=t+1.If t≤L, returns to step b and carries out next iteration; Otherwise, continue.

G. step b～step f has searched out L paths altogether, and the path delay location index set wherein estimating is Λ ^(L).For l ∈ Λ arbitrarily ^(L), there is a paths, its time delay is corresponding path gain is user to the estimated value of the channel time domain response vector of the l paths on all antennas is

Time delay estimates that set sequence is

$\widehat{\mathrm{\Γ}}=\{{\widehat{\mathrm{\τ}}}_1,{\widehat{\mathrm{\τ}}}_2,\·\·\·,{\widehat{\mathrm{\τ}}}_L\}$

H. for the estimated L paths going out, search for successively corresponding incidence angle, wherein, the incident angle index value of l paths is

$s=\underset{j=1,\·\·\·,N_{\mathrm{\θ}}{N}_{\mathrm{\φ}}}{\arg \max }|\⟨{\widehat{\mathrm{\α}}}_l,p_j\⟩|$

Wherein, p _jj row for projection matrix P.Projection matrix P is provided by following formula

$P=\left[\begin{array}{ccc}{\mathrm{\ψ}}_{\mathrm{1,1,1,1}}& \·\·\·& {\mathrm{\ψ}}_{\mathrm{1,1},N_{\mathrm{\θ}},N_{\mathrm{\φ}}}\\ \·& & \·\\ \·& & \·\\ \·& & \·\\ {\mathrm{\ψ}}_{N_v,N_h,\mathrm{1,1}}& \·\·\·& {\mathrm{\ψ}}_{N_v,N_h,N_{\mathrm{\θ}},N_{\mathrm{\φ}}}\end{array}\right]$

Wherein, ${\mathrm{\ψ}}_{i,j,q,s}=e^{-2\mathrm{\π}(i-1)d\cos \left({\mathrm{\θ}}_q\right)/\mathrm{\λ}}{e}^{-j2\mathrm{\π}(j-1)d\sin \left({\mathrm{\θ}}_q\right)\cos \left({\mathrm{\φ}}_s\right)/\mathrm{\λ}},{\mathrm{\φ}}_s=(s-1)/b,$ θ _q=(q-1)/c, the minimum antenna distance that d is even antenna plane, λ is carrier wavelength.According to the sortord of row vector element in projection matrix P, can be in the hope of corresponding incidence angle, wherein, every row element arrangement mode and path complex gain vector γ above in projection matrix P _lmiddle arrangement of elements mode is identical, therefore

(1) if path complex gain vector γ _lthe arrangement mode of middle element is the order of the Kronecker product of the vertical angle of pitch and horizontal azimuth institute respective path, first, for each vertical angle of pitch, by horizontal azimuth order from small to large, arranges path complex gain, and obtaining a length is N _φvector; Then, according to vertical angle of pitch order from small to large, arranging above-mentioned length is N _φvector, obtaining a length is N _θn _φvector, be expressed as

${\mathrm{\γ}}_l={[{\mathrm{\γ}}_{l11},{\mathrm{\γ}}_{l12},\·\·\·,{\mathrm{\γ}}_{l1N_{\mathrm{\φ}}},{\mathrm{\γ}}_{l21},{\mathrm{\γ}}_{l22},\·\·\·{\mathrm{\γ}}_{l2N_{\mathrm{\φ}}},\·\·\·,{\mathrm{\γ}}_{l{N}_{\mathrm{\θ}}1},\·\·\·,{\mathrm{\γ}}_{l{N}_{\mathrm{\θ}}{N}_{\mathrm{\φ}}}]}^T$

The corresponding vertical angle of pitch of l paths and horizontal azimuth is estimated as

${\widehat{\mathrm{\θ}}}_l=n_{\mathrm{\θ}}\mathrm{\Δ\θ},{\widehat{\mathrm{\φ}}}_l=n_{\mathrm{\φ}}\mathrm{\Δ\φ}$

Wherein, n _φ=mod (s, N _φ), n _θ=(s-n _φ)/N _φ+ 1, mod (x, y) represents that x is to y complementation.

(2) if the arrangement mode of element is horizontal azimuth and the order of the Kronecker product of vertical angle of pitch institute respective path in path complex gain vector γ l, first, for each horizontal azimuth, by vertical angle of pitch order from small to large, arrange path complex gain, obtaining a length is N _θvector; Then, according to horizontal azimuth order from small to large, arranging above-mentioned length is N _θvector, obtaining a length is N _θn _φvector, be expressed as

${\mathrm{\γ}}_l={[{\mathrm{\γ}}_{l11},{\mathrm{\γ}}_{l12},\·\·\·,{\mathrm{\γ}}_{l{N}_{\mathrm{\θ}}1},{\mathrm{\γ}}_{l12},{\mathrm{\γ}}_{l22},\·\·\·{\mathrm{\γ}}_{l{N}_{\mathrm{\θ}}2},\·\·\·,{\mathrm{\γ}}_{l1N_{\mathrm{\φ}}},\·\·\·,{\mathrm{\γ}}_{l{N}_{\mathrm{\θ}}{N}_{\mathrm{\φ}}}]}^T$

The corresponding vertical angle of pitch of l paths and horizontal azimuth is estimated as

${\widehat{\mathrm{\θ}}}_l=n_{\mathrm{\θ}}\mathrm{\Δ\θ},{\widehat{\mathrm{\φ}}}_l=n_{\mathrm{\φ}}\mathrm{\Δ\φ}$

Wherein, n _θ=mod (s, N _θ), n _φ=(s-n _θ)/N _θ+ 1.

The set that estimates successively the incident angle (the vertical angle of pitch and horizontal azimuth) of L paths is

$\begin{array}{c}\widehat{\mathrm{\Θ}}=\{{\widehat{\mathrm{\θ}}}_1,{\widehat{\mathrm{\θ}}}_2,\·\·\·,{\widehat{\mathrm{\θ}}}_L\}\\ \widehat{\mathrm{\Φ}}=\{{\widehat{\mathrm{\φ}}}_1,{\widehat{\mathrm{\φ}}}_2,\·\·\·,{\widehat{\mathrm{\φ}}}_L\}\end{array}.$

Claims (5)

1. the MIMO-OFDM system channel estimation method based on compressed sensing, is characterized in that, the method comprises the following steps:

A) utilize criterion of least squares, obtain the initial estimate of each pilot sub-carrier upper signal channel frequency domain response vector;

B) utilize the initial estimate of the channel frequency domain response vector that described step obtains in a) in the sparse property of time delay domain, based on compressive sensing theory, estimate the estimated value of the time delay in each path of channel and the channel time domain response vector in each path;

C) utilize described step b) in the estimated value of the channel time domain response vector estimated in the sparse property in two dimension angular territory, based on compressive sensing theory, estimate the incidence angle in each path of channel, described incidence angle comprises the vertical angle of pitch and horizontal azimuth;

D) utilize initial estimate, the step b of the channel frequency domain response vector that described step obtains in a)) in time delay, the step c in each path of estimating) incidence angle in each path of estimating, adopt criterion of least squares, estimate the gain coefficient in each path of channel;

E) by described step b) in time delay, the step c in each path of estimating) incidence angle and the steps d in each path of estimating) and in the gain coefficient in estimated each path, the multipath channel models of substitution channel frequency domain response, obtains the estimated value of the channel frequency domain response on all subcarriers and antenna.

2. a kind of MIMO-OFDM system channel estimation method based on compressed sensing according to claim 1, is characterized in that described step b) idiographic flow be:

First, by channel path time delay 0 to uniform discrete between maximum path time delay, obtain minimum time delay interval and be Δ τ and discrete after path number be N _τ, the Fourier transform relation of utilizing channel frequency domain response and channel time domain to respond, is the product of base vector and channel time domain matrix by the channel frequency domain response vector representation on each subcarrier;

Secondly, the initial estimate of the channel frequency domain response vector on all pilot sub-carriers is arranged in to a matrix in order, is designated as channel frequency domain matrix; All base vectors are arranged in to a matrix according to identical order, are designated as projection matrix; Thereby by channel frequency domain Matrix Estimation value representation be:

$\tilde{H}=\mathrm{\ΞA}+W---\left(12\right)$

Wherein, represent channel frequency domain Matrix Estimation value, Ξ is projection matrix, and A is channel time domain matrix, and W is noise matrix;

Finally, according to formula (12), adopt compressive sensing theory to solve channel time domain matrix, the channel time domain matrix solving is N altogether _τoK, find non-zero row vector wherein, the number L of described non-zero row vector is the channel path sum estimating, l non-zero row vector is the estimated value of the channel time domain response vector in l path, l the corresponding path delay in path is (m-1) Δ τ, wherein, l is the sequence number of non-zero row vector, and m is the channel time domain matrix line number m at l non-zero row vector place.

3. a kind of MIMO-OFDM system channel estimation method based on compressed sensing according to claim 1 and 2, is characterized in that described step c) idiographic flow be:

First, by vertical angle of pitch uniform discrete, obtain minimum angles and be spaced apart Δ θ, the angle number after discrete is N _θ, by horizontal azimuth uniform discrete, obtaining minimum angles and be spaced apart Δ φ, the angle number after discrete is N _φ, utilize the two-dimensional Fourier transform relation between channel time domain response and path incidence angle, the channel time domain response vector estimated value table in each path is shown:

${\widehat{\mathrm{\α}}}_l=P{\mathrm{\γ}}_l+w---\left(18\right)$

Wherein, be the channel time domain response vector estimated value in l path, P is projection matrix, γ _lbe the path complex gain vector in l path, w is noise vector;

Then calculate respectively in accordance with the following methods the incidence angle in each path: for l path, utilize formula (18), adopt compressive sensing theory to solve the estimated value that obtains path complex gain vector, according to the peaked position of element in the complex gain vector of path, calculate the incidence angle in l path, described incidence angle comprises the vertical angle of pitch and horizontal azimuth.

4. a kind of MIMO-OFDM system channel estimation method based on compressed sensing according to claim 3, is characterized in that described step c) in, every row element arrangement mode and path complex gain vector γ in described projection matrix P _lmiddle arrangement of elements mode is identical, is according to the order sequence of the Kronecker product of the vertical angle of pitch and horizontal azimuth institute respective path and obtains;

The method of calculating the incidence angle in l path is: according to the peaked position s of element in the complex gain vector of path, the vertical angle of pitch that obtains l path is horizontal azimuth is wherein, n _φ=mod (s, N _φ), n _θ=(s-n _φ)/N _φ+ 1, mod (x, y) represents that x is to y complementation.

5. a kind of MIMO-OFDM system channel estimation method based on compressed sensing according to claim 3, is characterized in that described step c) in, every row element arrangement mode and path complex gain vector γ in described projection matrix P _lmiddle arrangement of elements mode is identical, is according to the order sequence of the Kronecker product of horizontal azimuth and vertical angle of pitch institute respective path and obtains;

The method of calculating the incidence angle in l path is: according to the peaked position s of element in the complex gain vector of path, the vertical angle of pitch that obtains l path is horizontal azimuth is wherein, n _θ=mod (s, N _θ), n _φ=(s-n _θ)/N _θ+ 1.