CN105978674A - FDD large-scale MIMO channel estimation pilot frequency optimization method based on compressed sensing - Google Patents

Abstract

The invention discloses an FDD large-scale MIMO channel estimation pilot frequency optimization method based on compressed sensing, and the method comprises the steps: firstly enabling a channel to be modeled into a formula in a large-scale MIMO system: Y=HX+N, wherein H (shown in the description) is a channel matrix, X (shown in the description) is a pilot frequency matrix, Y (shown in the description) is a receiving signal matrix, and N (shown in the description) is channel noise, M is the number of transmitting antennas, and T is the number of pilot frequencies; secondly carrying out the conversion of the channel matrix, and solving the conjugate matrix (shown in the description) of Y, wherein the conjugate matrix (shown in the description) of the channel matrix represents the conversion form of the channel matrix, the conjugate matrix (shown in the description) of the pilot frequency matrix represents the conversion form of the pilot frequency matrix, and the conjugate matrix (shown in the description) of the receiving signal matrix represents the conversion form of the receiving signals of a receiving end; and finally solving an optimal pilot frequency matrix. Because the conjugate matrix (shown in the description) of the channel matrix is a sparse vector, a channel estimation problem can be modeled into a compressed sensing reconstruction problem shown in the description, wherein ||*||<1> represents 1-norm, ||*||<2> represents 2-norm, and epsilon is greater than zero and less than one. The method can guarantee that the FDD MIMO downlink channel estimation based on compressed sensing can remarkably reduce the mean square error of channel estimation, and improves the channel estimation performance.

Description

The pilot frequency optimization method that under FDD based on compressed sensing, extensive mimo channel is estimated

Technical field

The channel that the present invention relates to communication system pilot aided is estimated and pilot design technical field, particularly relates to a kind of base The pilot frequency optimization method that extensive mimo channel is estimated under the FDD of compressed sensing.

Background technology

In Modern wireless communication, (Frequency Division Duplexing FDD) extensive MIMO under FDD Degree of freedom in system increases, diversity that multiple antennas brings and spatial multiplexing gain, it is possible to significantly improve spectrum efficiency and energy efficiency.Base station In order to obtain spatial multiplex gains and array gain, base station transmitting terminal or user's receiving terminal need known channel state information (CSI, Channel state information), this is accomplished by estimating to obtain by channel.The extensive mimo system of tdd mode In, base station can obtain channel uplink CSI, and channel reciprocity makes the channel of downlink estimate to become relatively to hold Easily.One challenge of the extensive mimo system of fdd mode is exactly number of pilots to be increased and linear increase along with launching number of antennas, Cause pilot-frequency expense huge, reduce communication system efficiency, and accurately the CSI of estimating down-ward link is not easy to.Due to FDD For delay-sensitive system, more efficiently and current most of Cellular Networks all have employed FDD in use, therefore under research FDD more Estimate necessary for effective channel.

Base station substantial amounts of transmitting antenna causes limited local to scatter.Along with the increase of transmitting antenna, channel presents openness Matter.The sparse property utilizing channel implicit carries out channel estimation, it is possible to reduce the number of pilot tone, thus improves the effective of system Property.

Compressed sensing is widely used at signal and image processing field.Compressed sensing is based on by echo signal rarefaction and select Selecting suitable calculation matrix, sparse signal sampling and compression are carried out simultaneously, only need to transmit a small amount of data, receiving terminal is according to phase Matrix should be recovered recovered by signal.Compressive sensing theory has shown superior performance in terms of channel estimation.On big rule In mould mimo system, it is possible to use compressed sensing reconstruction algorithm carries out channel estimation, thus reduces the quantity of pilot tone.

Summary of the invention

The technical problem to be solved is for defect involved in background technology, it is provided that a kind of based on pressure The pilot frequency optimization method that under the FDD of contracting perception, extensive mimo channel is estimated so that the optimal pilot matrix of acquisition is estimated by channel The MSE of meter significantly reduces, and improves the performance that channel is estimated.

The present invention solves above-mentioned technical problem by the following technical solutions:

The pilot frequency optimization method that under FDD based on compressed sensing, extensive mimo channel is estimated, the extensive MIMO of described FDD Channel is flat fading channel, and there is M transmitting antenna base station, and in community, the antenna number of each user is 1, and Base Transmitter is a length of The pilot training sequence of T, described pilot frequency optimization method comprises the following steps:

Step 1), set up channel model Y=HX+N；

Wherein,For channel matrix,For pilot matrix,For receiving signal matrix,For channel additive Gaussian noise,Represent complex vector space；

Step 2), order Make channel model corresponding with compressed sensing model, obtain and compressed sensing model Corresponding channel model

Wherein,It is unitary matrice,Being angle domain channel matrix, P is pilot tone symbol Number signal to noise ratio, (*)^HRepresent and matrix or vector are carried out conjugate transpose；PT is the signal to noise ratio of T frequency pilot sign of transmission；Subscript ω is the symbol of angular frequency, is used for H is described^ωFor channel matrix H in the expression of angle domain；Represent the change of channel matrix Change form,Represent the variation of pilot matrix,Represent receiving terminal and receive the variation of signal；

Step 3), initialize iteration total degree Iter_opt, current iteration number of times q=1, for the first time iteration time pilot matrix Matrix element meets normal distribution, i.e.I=1,2...T, j=1,2...M；

Step 4), seek current gram matrix For current pilot matrix；

Step 5), gram matrix after reducing is calculated according to default coefficient of diminution γ

${\hat{g}}_{ij}={\mathrm{\&gamma;g}}_{ij}$

Wherein, i, j=1,2...M, g_ijFor matrix G_qElement,For matrixElement；

Step 6), use singular value decomposition willContraction, retains maximum front T singular value, and unusual according to this front T Value obtains matrix

Step 7), orderBySquare root factorization obtains Zq, leading when i.e. obtaining next iteration Frequently matrix；

Step 8), current iteration number of times q is added 1；

Step 9), repeated execution of steps 4) to step 8), until current iteration number of times q is equal to iteration total degree Iter_opt；

Step 10), the matrix that input optimizes

The pilot frequency optimization method estimated as extensive mimo channel under present invention FDD based on compressed sensing is further Prioritization scheme, described default coefficient of diminution γ is 0.95.

The pilot frequency optimization method estimated as extensive mimo channel under present invention FDD based on compressed sensing is further Prioritization scheme, described iteration total degree Iter_optIt it is 800 times.

The present invention uses above technical scheme compared with prior art, has following technical effect that

The extensive mimo system of FDD based on compressed sensing channel estimate in, with use stochastic generation unoptimizable lead Frequently matrix is compared, and the optimal pilot matrix using the present invention to obtain can significantly decrease the mean square error (mean that channel is estimated Square error, MSE).Improve the performance that channel is estimated.

Accompanying drawing explanation

Fig. 1 is pilot matrix optimization and the unoptimizable impact on reconstruction performance of different number of pilots；

Fig. 2 is the different pilot matrix optimization launching number of antennas and the unoptimizable impact on reconstruction performance.

Detailed description of the invention

Below in conjunction with the accompanying drawings technical scheme is described in further detail:

The present invention comprises two technical problem underlying, and one is the compressed sensing problem that channel estimation problems is converted into, from And pilot frequency sequence optimization problem is modeled as calculation matrix optimization problem in a compressed sensing；Another is to propose pilot tone optimization to calculate Method, solves this calculation matrix optimization problem, thus obtains the pilot matrix of optimum.Introduce the enforcement of the two part separately below Mode, and illustrate that this pilot distribution method is to improving beneficial effect based on compressed sensing channel estimating performance by emulation.

(1) acquisition of pilot tone Optimality Criteria

Considering the next extensive mimo system of fdd mode, its channel is flat fading channel, and there is M interval half base station The uniform emission antenna of wavelength, in community, each user only has an antenna.The pilot training sequence of a length of T of Base Transmitter. The pilot signal of note i-th time slot isI=1,2 ..., T, then the signal y received on reception antenna_iFor:

y_i=Hx_i+n_i, i=1,2 ..., T (1)

Channel matrixBe as the criterion static channel,For additive Gaussian noise.Note Have:

Y=HX+N (2)

Every pilot time slot signal to noise ratio is designated as P, and the total signal to noise ratio of T pilot time slot is tr (X^HX)=PT.

In actually used, virtual angular domain represents can make nonlinear channel model parameters approximately linear, carries out channel Virtual representation processes so that being analyzed and estimating.The virtual representation of non-selective mimo channel is:

$H=A_R{H}^{\mathrm{\&omega;}}{A}_T^H---\left(3\right)$

Being unitary matrice, M is to launch number of antennas.It it is angle domain channel square Battle array.Because base station exists local scattering effect, H^ωIt is sparse.

Formula (2) is converted to compressed sensing model.Will

WithSubstitution formula (2), obtains:

$\stackrel{\&OverBar;}{Y}=\stackrel{\&OverBar;}{X}\stackrel{\&OverBar;}{H}+\stackrel{\&OverBar;}{N}---\left(6\right)$

Formula (6) is corresponding with there being the compressed sensing model (7) made an uproar:

Y=Ds+N (7)

Wherein the s of T × 1 is sparse signal,For recovering matrix,For additive Gaussian noise.Sparse Signal s Solve problems can be converted into:

$\begin{array}{ccc}{\hat{s}}_0=\arg min\left|\right|s|{|}_1& s.t.& \left|\right|y-Ds|{|}_2\&le;\mathrm{\&epsiv;}\end{array}---\left(8\right)$

ε is the normal number close to zero.

Can obtain: pilot matrixCorresponding to calculation matrix D,It is sparse signal, corresponding to s.Thus, channel is estimated ParameterProblem can be converted into sparse signal Problems of Reconstruction in compressive sensing theory.Meanwhile, the optimization problem of pilot frequency sequence also may be used It is converted into the calculation matrix optimization problem of compressed sensing.

In order to compressed sensing problem solving, if recovering matrix D to meet orthogonal property (Mutual Incoherence Property, MIP), the most just can be with the biggest probability accurate reconstruction sparse signal.Therefore, compressed sensing problem solving and survey Moment matrix optimization problem can be with MIP as foundation.

Matrix is recovered for oneIts cross correlation value is defined as inner product between two maximum different lines and returns One absolute value changed, i.e.

$\mathrm{\&mu;}\left\{D\right\}={\max }_{1\&le;i,j\&le;M,i\&NotEqual;j}\frac{|<d_i,d_j>|}{\left|\right|d_i|{|}_2\&CenterDot;|\left|d_j\right|{|}_2}---\left(9\right)$

{ D} reflects similarity maximum between two row of calculation matrix to cross correlation value μ.The another kind of performance of cross correlation value Form is as follows: gram matrix G=D^HD, D are the form after row normalization.The off-diagonal element g of G_{I, j}For what formula (9) occurred Inner product, cross-correlation number is the maximum of off-diagonal element.Cross correlation value represents dependency maximum between matrix element, existing Document shows, cross correlation value is the least, and reconstruction error is the least.Therefore, to directly affect compressed sensing extensive in the reduction of cross correlation value Double calculation method reconstruction performance.

(2) pilot matrix optimized algorithm

Pilot matrix is carried out by reducing the μ t of gram matrix GOptimization.The core concept optimized is to choose suitably Optimize the thresholding t element to G | g_ij| reduce, i.e. for more than t value | g_ij| it is optimized, t ∈ [0,1).Reduction equation Become:

${\hat{g}}_{ij}={\mathrm{\&gamma;g}}_{ij},\left|g_{ij}\right|\&GreaterEqual;t=0---\left(10\right)$

γ is decay factor, takes 0.95.Matrix after being reduced For matrixElement.Due toOrder may More than the line number of pilot matrix, in order to it is carried out the pilot matrix that square root factorization obtains optimizing, need to use singular value to divide Solve (Singular Value Decomposition, SVD) and the order of G is reduced to T.The detailed process of contraction is as follows: at the q time repeatedly Dai Zhong, use SVD willContraction retains front T singular value,

U_TAnd V_MBeing respectively the unitary matrice of T × T and M × M, ∑ diagonal is singular value, and bySquare root divides Solution obtains Z_q, orderMore than the process such as reduction and contraction needs iteration repeatedly, so that cross-correlation number is reduced to metastable Value.Iteration terminates us and obtains the matrix through optimizingFinal optimizing pilot matrix X is obtained finally according to formula (5)_opt。 Pilot tone optimizes detailed process as shown in algorithm 1:

Algorithm 1: the optimized algorithm of pilot matrix

Input: pilot matrixThe Gaussian matrix that it is randomly generated, matrix elementi =1,2...M, j=1,2...T, meet independent same distribution.It is often gone and represents the pilot tone sequence that every, base station antenna transmission number is T Row.

Step 1), askTry to achieve from X according to formula (5)

Step 2), optimizeObtainInitialize iterations q=1, putIteration Iter altogether_opt=800 times.

Step 2.1), seek gram matrix G_q: byTry to achieve；

Step 2.2), askGram matrix after reducing is obtained according to formula (10)

Step 2.3), seek Z_q: use SVD willContraction, retains maximum front T singular value and obtains matrixAnd bySquare root factorization obtains Z_q,

Step 2.4), it is judged that: if q reaches Iter_optSecondary, jump out circulation, obtain the matrix optimizedOtherwise, put Q=q+1, skips to step 2.1).

Step 3), the pilot matrix that will optimizeOutput.

In lower joint, the same pilot matrix phase being not optimised of pilot matrix that we will be obtained by algorithm 1 by emulation explanation Ratio, can make under the extensive MIMO of FDD based on the orthogonal tracking of coupling (Orthogonal Matching Pursui t, OMP) Downlink channels is estimated to obtain less mean square error, so that system obtains higher channel estimating performance.

(3) simulation result

Need based on emulation, the virtual angular domain channel matrix H used in emulation^ωUse the spatial Channel Model of 3GPP (Spatial Channel Model SCM) also generates based on city microcellulor scene.Pilot length is T, Base Transmitter antenna Number is M, signal degree of rarefication K.In emulation, pilot frequency sequence uses time division way to send.Channel matrix H^ωIt is sparse, makes sparse Degree K is 6.As shown in formula (2), Base Transmitter signal Y to user, convert a signal into according to formula (4) and meet compressed sensing model FormDue to receiving terminal known pilot X, be converted to according to formula (5)For formula (6), we rebuild calculation according to compressed sensing Method OMP recovers channel matrixThrough being converted to channel matrix H, complete channel and estimate.We use normalization MSE to weigh The quality of amount sparse signal restorability.MSE is defined as:

$MSE=\frac{E\&lsqb;{\mathrm{\&Sigma;}}_k|{\stackrel{\&OverBar;}{H}}_k-{\widehat{\stackrel{\&OverBar;}{H}}}_k{|}^2\&rsqb;}{E\&lsqb;{\mathrm{\&Sigma;}}_k|{\stackrel{\&OverBar;}{H}}_k{|}^2\&rsqb;}---\left(12\right)$

WhereinRepresent sparse signalMiddle kth element,Represent reconstructionMiddle kth element.We are from difference Number of pilots and different two aspects of number of antennas of launching carry out simulation analysis.

1) impact on channel estimating performance of the optimizing pilot matrix in the case of first we study different number of pilots.Base Transmitting number of antennas M of standing elects 200 as, chooses number of pilots T and is respectively 20,30 and 40.Simulation result is as shown in Figure 1.Result table Bright, under different number of pilots, all there is difference clearly in the reconstruction performance between the optimizing and do not optimize of pilot tone.At SNR it is During 25dB, when using 20 pilot tones and 30 pilot tones, use the pilot tone optimized so that MSE reduces by 1～2dB；When SNR is bigger Time, MSE can decline further.It should be noted that when pilot number is 30 use optimizing pilot matrix channel estimate MSE and Use when pilot number is 40 be not optimised the MSE of pilot matrix very close to.Namely on the premise of identical reconstruction performance, use The pilot tone optimized can make the quantity of pilot tone reduce, thus improves the effectiveness of system.It addition, can be seen that from simulation curve Come, along with the increase of number of pilots, it is clear that this effect of optimization can gradually weaken.

2), when we study Base Transmitter number of antennas difference, channel is estimated the improvement situation of MSE by pilot matrix optimization. Considering that number of pilots is 30, Base Transmitter number of antennas is respectively 100,200 and 300.As seen from Figure 2, send out along with base station Penetrating the increase of number of antennas, the restorability of channel matrix declines.But in the case of three kinds of different transmitting number of antennas, Normal SNR is more than under 15dB signal communication environments, and the optimization of pilot matrix can obtain good reconstruction effect.At SNR it is During 25dB, in the case of three kinds are launched number of antennas, use the pilot matrix optimized can reduce letter than unoptimizable pilot matrix The MSE about 1.5dB that road is estimated.When SNR is bigger, this value will can reach 4dB.From Fig. 2 simulation curve it can also be seen that base station When transmitting number of antennas is more, the MSE performance improvement that optimizing pilot brings is the biggest.

From emulation it can be seen that when high s/n ratio, i.e. when SNR is more than 15dB, either number of pilots changes still Base Transmitter antenna changes, and uses the pilot frequency sequence optimized can effectively reduce the MSE that channel is estimated.

It is understood that unless otherwise defined, all terms used herein (include skill to those skilled in the art of the present technique Art term and scientific terminology) have with the those of ordinary skill in art of the present invention be commonly understood by identical meaning.Also It should be understood that those terms defined in such as general dictionary should be understood that have with in the context of prior art The consistent meaning of meaning, and unless defined as here, will not explain by idealization or the most formal implication.

Above-described detailed description of the invention, has been carried out the purpose of the present invention, technical scheme and beneficial effect further Describe in detail, be it should be understood that the detailed description of the invention that the foregoing is only the present invention, be not limited to this Bright, all within the spirit and principles in the present invention, any modification, equivalent substitution and improvement etc. done, should be included in the present invention Protection domain within.

Claims (3)

1. the pilot frequency optimization method that under FDD based on compressed sensing, extensive mimo channel is estimated, the extensive MIMO of described FDD believes Road is flat fading channel, and there is M transmitting antenna base station, and in community, the antenna number of each user is 1, a length of T of Base Transmitter Pilot training sequence, it is characterised in that described pilot frequency optimization method comprises the following steps:

Step 1), set up channel model Y=HX+N；

Wherein,For channel matrix,For pilot matrix,For receiving signal matrix, For channel additive Gaussian noise,Represent complex vector space；

Step 2), order Make channel model corresponding with compressed sensing model, obtain and compressed sensing model Corresponding channel model

Wherein,It is unitary matrice,Being angle domain channel matrix, P is frequency pilot sign Signal to noise ratio, (*)^HRepresent and matrix or vector are carried out conjugate transpose；PT is the signal to noise ratio of T frequency pilot sign of transmission；Subscript ω is The symbol of angular frequency, is used for H is described^ωFor channel matrix H in the expression of angle domain；Represent the conversion shape of channel matrix Formula,Represent the variation of pilot matrix,Represent receiving terminal and receive the variation of signal；

Step 3), initialize iteration total degree Iter_opt, current iteration number of times q=1, for the first time iteration time pilot matrix Matrix element meets normal distribution, i.e.I=1,2...T, j=1,2...M；

Step 4), seek current gram matrix For current pilot matrix；

Step 5), gram matrix after reducing is calculated according to default coefficient of diminution γ

${\hat{g}}_{ij}={\mathrm{\&gamma;g}}_{ij}$

Wherein, i, j=1,2...M, g_ijFor matrix G_qElement,For matrixElement；

Step 6), use singular value decomposition willContraction, retains maximum front T singular value, and obtains according to this front T singular value Obtain matrix

Step 7), orderBySquare root factorization obtains Z_q, i.e. obtain pilot tone square during next iteration Battle array；

Step 8), current iteration number of times q is added 1；

Step 9), repeated execution of steps 4) to step 8), until current iteration number of times q is equal to iteration total degree Iter_opt；

Step 10), the matrix that input optimizes

The pilot frequency optimization method that under FDD based on compressed sensing the most according to claim 1, extensive mimo channel is estimated, It is characterized in that, described default coefficient of diminution γ is 0.95.

The pilot frequency optimization method that under FDD based on compressed sensing the most according to claim 1, extensive mimo channel is estimated, It is characterized in that, described iteration total degree Iter_optIt it is 800 times.