CN106453163A - Massive MIMO (Multiple Input Multiple Output) channel estimation method - Google Patents
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Abstract
The invention belongs to the technical field of wireless communication, and particularly relates to a channel estimation algorithm for a multi-user massive MIMO (Multiple Input Multiple Output) system under a frequency division duplex (FDD) mode. In the multi-user massive MIMO system, channel estimation is realized by a sparse signal recovering technology through an inference method based on Bayes compressed sensing, and channel estimation overhead of the FDD massive MIMO system can be lowered greatly.
Description
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a channel estimation algorithm of a multi-user large-scale Multiple Input Multiple Output (MIMO) system in a Frequency Division Duplex (FDD) mode.
Background
The massive MIMO system is one of the key technologies of the fifth generation mobile communication system, and its main advantages are: system capacity increases as the number of antennas increases; reducing the power of the transmitted signal; the optimum performance can be achieved by a simple current precoder and detector; and the areas among the channels are orthogonalized, so that the intra-cell co-channel interference is eliminated.
These advantages are achieved on the premise that the Base Station (BS) is aware of the Channel State Information (CSIT). In a Time Division Duplex (TDD) system, channel estimation is performed at a user equipment (MS) using reciprocity of uplink and downlink channels. The channel estimation overhead is independent of the number of massive antenna array antennas at the base station side and is only related to the number of users. Therefore, in the TDD system, the overhead of channel estimation does not burden the system. For an FDD massive MIMO system, the channel estimation process is as follows: the base station broadcasts pilot signals to the users, and the mobile users estimate CSIT using the received signals and feed back to the base station. In this case, the number of pilot signals is proportional to the number of antennas of the base station, and since the number of antennas is huge in a large-scale MIMO system, a conventional channel estimation method (such as a least square method) will face huge training overhead, so that the training time becomes long, even exceeds the desired interference time of the channel, and the channel estimation loses meaning.
In the multi-user MIMO system, due to the huge difference in the number of antennas between the base station and the user, the base station and the user react to the scattering effect quite differently, and the sparsity of the propagation path at the base station and the richness of the propagation path at the user are presented. Meanwhile, due to the fact that scattering signals of the same scatterer are partially received among different users, partial correlation characteristics exist among channels of the users, and therefore joint sparsity of channels of the multi-user large-scale MIMO system is achieved.
Compressed sensing is a completely new signal sampling theory, which uses sparsity of a signal, acquires discrete samples of the signal by random sampling under the condition of far less than the Nyquist rate, projects the discrete samples of the original signal under few measurements by using the sparse characteristic of the original signal under certain base, and recovers the original signal by a nonlinear algorithm, so that the compressed sensing theory can keep maximum signal information by the least measurements. Sparse Bayesian Learning (SBL) was originally proposed in 2001 by Tipping of microsoft research as a machine Learning algorithm and was subsequently introduced into the Sparse signal recovery field (BCS).
Bayesian compressed sensing is an algorithm for adding sparse prior to signals by using a probability method and deducing signal recovery by using a Bayesian statistical inference method. Due to the high Bayesian flexibility, the method can adapt to various different signal priors by changing the form of probability priors. The bayesian framework provides a number of useful inference methods, such as: ExpectationMaximation (EM), Variable Expectation Maximation (VEM), Maximil Likeliod (ML). The EM algorithm is a method for solving parameter maximum likelihood estimation proposed by Dempster, Laind and Rubin in 1977, can estimate parameters from incomplete data sets, and is a very simple and practical learning algorithm. The main purpose of the EM algorithm is to provide a simple iterative algorithm to compute the posterior density function, which has the greatest advantage of simplicity and stability, but is prone to fall into local optima. The VEM algorithm is a generalized EM algorithm, originally proposed by the BEAL M j. in its paper "variational algorithms for adaptive Bayesian Inference", and is mainly applied in complex statistical models in the field of Bayesian estimation and machine learning.
Disclosure of Invention
In a multi-user large-scale MIMO system, the invention realizes channel estimation by using a sparse signal recovery technology based on an inference method of Bayesian compressed sensing, and can greatly reduce the cost of channel estimation of an FDD large-scale MIMO system.
For ease of understanding, the models and functions used by the present invention are first introduced:
FDD multi-user massive MIMO channel estimation system model:
it is assumed that the channel to be estimated is flat block fading, i.e. the channel state is unchanged for a certain period of time. The system has a BS configured with a massive antenna array with N antennas, K MSs each with M antennas, the mathematical model for FDD multiuser massive MIMO channel estimation can be represented as Yj＝HjX+NjWherein Y isjA received signal matrix representing the jth MS, HjDenotes a channel matrix between the BS and the j-th MS, X is a pilot signal, NjIs a received noise signal matrix.
Standard compressed sensing mathematical model:
y-ax + n, wherein A is a measuring matrix with the size of m × n, y is a compressed signal with the dimension of m × 1, x is a sparse signal with the dimension of n × 1, the sparsity is s, namely only s < n elements in x are nonzero, the rest elements are all 0, n is system noise with the dimension of m × 1, andits elements obey mean value of 0 and variance of sigma2M < n.
The Bayes compressed sensing model is characterized in that by maximizing an edge likelihood function:
by passingGet a priori parameters α and β, i.e.Where μ i represents the sparse signal xiMean value of (V)iiRepresenting a sparse signal xiThe variance of (a); representing sparse signals<||Yi-φXi||2>The average value of (a) of (b),representing sparse signals<||Yi-φXi||2>The variance of (c).
Obtaining a parameter k through a variable integral Bayes expectation maximization method, wherein the formula is as follows:
wherein the parameter k obeys a bernoulli distribution.
Both the BS end and the MS end are configured with Uniform Linear Arrays (ULAs), and according to the virtual angle domain transformation of the MIMO channel, the channel corresponding to each MS is decomposed into:wherein, UR∈CM×MAnd UT∈CN×NAngle domain transformation unitary matrix and unitary matrix of MS end and BS end respectivelyArray UTThe (p, q) element of (a) is:p,q∈[0,N-1]unitary matrix URThe (a, b) element of (a, b) isa,b∈[0,M-1]，Is the channel matrix in the angular domain. In a large-scale antenna array, the antenna array,have the same sparse support set, i.e. their non-zero elements are exactly the same position and the non-zero elements obey a complex gaussian distribution of zero mean unit variance. There is also a partially correlated relationship between different channel matrices corresponding to different MSs, i.e., there is an intersection between sparse support sets of MSs. Denote the sparse support set for the jth MS channel as ΩjThen, thenIs a common sparse support set for each MS.
A massive MIMO channel estimation method comprises the following steps:
s1, initializing, specifically:
s11, BS broadcasts T pilot signals X to K MSs by T time slotsP＝[x(1),x(2),...,x(T)]∈CN×TWherein N is the number of antennas of the BS, and pilot signal X in the MIMO channel estimation mathematical modelPA compressed sensing measurement matrix converted into an angle domain, denoted by the symbol phi, havingUnitary matrixp,q∈[0,N-1]，ΦH∈CN×TIs a slave setIn the method, the pilot signal power of each time slot is extracted according to equal probability, and P is the pilot signal power of each time slotHRepresenting a conjugate transpose;
s12, K MSs receiving signal matrix is { RjIn which R isjA received signal matrix representing the jth MS, j 1, 2.., K;
s13, converting the signsWherein the unitary matrixa,b∈[0,M-1]M is the number of antennas of MS,. phi.jIs a conjugate transpose of an angle domain channel matrix ofΕjIs an equivalent Gaussian noise matrix, NjIs a received noise signal matrix;
s2, performing joint estimation on the sparse support sets of each user, namely jointly estimating the sparse support sets of K MSs by utilizing a multitask BCS algorithm to obtain K estimated channel sparse support sets, wherein the K estimated channel sparse support sets are expressed as omega1,Ω2,...ΩK；
S3, iterative estimation of each user sparse support set, specifically:
s31, setting an iteration control variable N common to the MS sparse support setsiterAnd the maximum number of iterations Nset；
S32, initial value given:
receiving a signal matrix Y; a prior probability matrix of X, the elements of the matrix obeying a mean value ofVariance ofComplex gaussian distribution ofCommon sparse support and non-common sparse support parametersComplex gaussian distribution variance of noiseIn accordance with Bernoulli distribution, with an initial probability ofEmpirical value ofAnd an intermediate variable initialized to 0
S33, assuming that the prior probability of Z follows the mean value of Z, the received signal Z without noise is Φ XVariance ofComplex gaussian distribution ofObtaining the posterior probability of Z from the prior probability of Z, wherein the obedient mean value of the probability isVariance ofComplex gaussian distribution ofUpdate the rule as(Is composed ofThe reciprocal of (d);
s34, combining the posterior probabilities of Z with the intermediate variablesDeducing the prior probability of X
S35, posterior probability of Z, common sparse parameter and non-common sparse parameterNoise variance parameterSelecting parametersBy intermediate variablesTo obtain updated posterior probability of X
S36, updating initial parameter valueIterating S33-S35 until an iterative control variable N is satisfiediterAnd the maximum number of iterations NsetCan obtain the channel state information of each user comprising the common sparse support and the non-common sparse support
S4, multi-user large-scale MIMO channel estimation, wherein the channel estimation result of each user isThe sparse support part of X is obtained by the Bayes compressed sensing iteration method provided by the invention when a certain set condition is met, the rest part is all 0, and the set condition is an empirical condition.
Further, the obtaining of the K estimated channel sparse support sets Ω in S21,Ω2,...ΩKThe method comprises the following specific steps;
s21, supposing that M receiving antennas of each user have the same sparse support set, the sparse support degrees of K MSs are S, for different users K, the number of common sparse support positions is Sc, and the number of non-common sparse support positions is S-Sc, wherein Sc is a symbol representing the number of sparse support positions, and S-Sc represents the unique number of non-common sparse support positions of each user;
s22, according to the Bayes compressed sensing algorithm, setting the sparse channel compliance parameter of the jth MS to be αj＝[αj1,αj2,...,αji,...,αjN]TIn which the element α isjiSharing sparse support for multiple usersOr for exclusive sparse supportI.e. joint probability density functionWherein, m is 1,2jIndicating the channel between the jth MS and the BS,i-th element, empirical value, representing channel vectorThe initial values obey a Bernoulli distribution, each element kiProbability of beingi＝1,2,…N；
S23, jointly considering K MSs according toDeriving a set of parameters for a common sparse support locationUpdate rule ofParameter set of non-common sparse support locationsUpdate rule ofWherein, representing the m-th sparse signalThe average value of (a) of (b),representing the m-th sparse signalM 1,2, … K;
s24, the noise obeys the mean value of 0 and the variance of 0Complex gaussian distribution of (c), parameter βmIs updated by the formula
S25, jointly considering K MSs, the update formula of the common distribution parameter K of different users isWherein,wherein, pi is kiInitial probability of 0;
s26, inputting the compressed sensing measurement matrix phi and the angle domain received signal matrix Y in S13, and performing joint iterative estimation on the parameters of S23-S25 to obtain a sparse support set omega of different users.
Further, the updating of the initial parameter value S36The specific process is as follows: the posterior probability of X obtained in S34 is substituted into the parameter updating formula in S23-S25.
The invention has the beneficial effects that:
the method avoids the process of direct matrix inversion of the posterior probability of X in the EM algorithm, greatly simplifies the operation amount, and improves the operation speed and the operation precision. Meanwhile, compared with channel estimation methods such as OMP, ST-BCS, SOMP, JOMP and the like, the method improves the accuracy of channel estimation, and can ensure that the error of channel estimation reaches 10 under certain conditions-3The method of the invention can be used to realize large-scale MIMO channel estimation in practice.
Drawings
Fig. 1 is a diagram of joint sparsity of a multi-user massive MIMO channel and its physical view.
Fig. 2 is a flow chart of the algorithm of the present invention.
FIG. 3 is a graph comparing the performance of the multi-user massive MIMO system with the rest of sparse signal reconstruction algorithms implemented at different training costs.
FIG. 4 is a graph comparing the performance of the multi-user massive MIMO system with different SNR for the algorithm of the present invention and the rest of sparse signal reconstruction algorithms.
Detailed Description
The present invention will be described in further detail with reference to specific examples.
Fig. 1 is a diagram of a multiuser massive MIMO channel.
Assuming that the number K of users is 20, the base station and the user terminal are each configured with a Uniform Linear Array (ULA), and the number N of base station antennas is 160, and the number of user antennas is the same and M is 2. It is assumed that the number of sparse supports (sparsity) of each user channel is the same and S is 15, and the common number of sparse supports Sc is 8.
Fig. 2 is a flow chart of multiuser massive MIMO channel estimation, according to which the algorithm can be simulated using the above parameters.
S1, initializing, specifically:
s11, BS broadcasts T pilot signals X to 20 MSs by T time slotsP＝[x(1),x(2),...,x(T)]∈CN×TWherein, the number N of the antennas of the BS is 160, and pilot signals X in the MIMO channel estimation mathematical model are usedPA compressed sensing measurement matrix converted into an angle domain, denoted by the symbol phi, having(Represents XPConjugate transpose of) unitary matrixp,q∈[0,N-1]，ΦH∈CN×T(ΦHRepresenting phi conjugate transpose), i.e., a slave setExtracting with equal probability, wherein P is pilot signal power of each time slot;
s12, 20 MS received signal matrix is { Rj},RjA received signal matrix (j ═ 1, 2.., 20) representing the jth MS;
s13, converting the signsWherein the unitary matrixa,b∈[0,M-1]The number of antennas M of MS is 2, phi denotes a compressed sensing measurement matrix, XjIs a conjugate transpose of an angle domain channel matrix ofΕjIs an equivalent Gaussian noise matrix, NjIs a received noise signal matrix;
s2, performing joint estimation on the sparse support sets of each user, namely jointly estimating the sparse support sets of 20 MSs by using a multitask BCS algorithm to obtain 20 estimated channel sparse support sets, wherein the 20 estimated channel sparse support sets are expressed as omega1,Ω2,...Ω20The method specifically comprises the following steps:
s21, assuming that 2 receiving antennas of each user have the same sparse support set, the sparse support degrees of 20 MSs are all 15, and for different users, the number of common sparse support positions is 8, and the number of non-common sparse support positions is 7;
s22, according to the Bayes compressed sensing algorithm, setting the sparse channel compliance parameter of the jth MS to be αj＝[αj1,αj2,...,αji,...,αjN]TIn which the element α isjiSharing sparse support for multiple usersOr for exclusive sparse supportI.e. joint probability density functionWherein, m is 1,2jIndicating the channel between the jth MS and the BS,i (i ═ 1,2, … 160) th element representing a channel vector, an empirical valueThe initial values obey a Bernoulli distribution, each element kiProbability of being(i＝1,2,…160)；
S23, jointly considering 20 MSs according toDeriving a set of parameters for a common sparse support locationUpdate rule of(Representing the m-th sparse signalThe average value of (a) of (b),representing the m-th sparse signalM 1,2, … 20), a set of parameters for the non-common sparse support locationUpdate rule ofWherein,
s24, the noise obeys the mean value of 0 and the variance of 0(m 1, 2.., 20), then parameter βmIs updated toIs composed of
S25, jointly considering 20 MSs, the update formula of the common distribution parameter k of different users isWherein,
s26, inputting the compressed sensing measurement matrix phi and the angle domain received signal matrix Y in S13, and performing joint iterative estimation on the parameters of S23-S25 to obtain a sparse support set omega of different users.
S3, iterative estimation of each user sparse support set, specifically:
s31, setting an iteration control variable N common to the MS sparse support setsiter＝10-3Maximum number of iterations NsetIs 200;
s32, initial value given:
receiving a signal matrix Y; a prior probability matrix of X, the elements of the matrix obeying a mean value ofVariance ofComplex gaussian distribution ofCommon sparse support and non-common sparse support parametersComplex gaussian distribution variance of noiseIn accordance with Bernoulli distribution, with an initial probability ofEmpirical value ofAnd an intermediate variable initialized to 0
S33, assuming that the prior probability of Z follows the mean value of Z, the received signal Z without noise is Φ XVariance ofComplex gaussian distribution ofObtaining the posterior probability of Z from the prior probability of Z, wherein the obedient mean value of the probability isVariance ofComplex gaussian distribution ofUpdate the rule as(Is composed ofThe reciprocal of (d);
s34 posterior probability combination of ZIntermediate variablesDeducing the prior probability of X
S35, posterior probability of Z, common sparse parameter and non-common sparse parameterNoise variance parameterSelecting parametersBy intermediate variablesTo obtain updated posterior probability of X
S36, updating initial parameter valueIterating S33-S35 until an iterative control variable N is satisfiediterAnd the maximum number of iterations NsetCan obtain the channel state information of each user comprising the common sparse support and the non-common sparse support
S4, multi-user large-scale MIMO channel estimation, wherein the channel estimation result of each user isThe sparse support part of X is obtained by the Bayes compressed sensing iteration method provided by the invention when a certain set condition is met, the rest part is all 0, and the set condition is an empirical condition.
Fig. 3 is a comparison graph of the performance of the method of the present invention when applied to multi-user massive MIMO channel estimation and the performance of other sparse signal recovery algorithms applied to the same channel estimation for different overheads. It can be seen from the figure that the algorithm of the present invention achieves the optimal performance when the base station sends the pilot signal 45 times, and the estimation error is greatly reduced compared with the algorithms of LS (least square method), OMP, SOMP, ST-BCS, and joomp (Joint OMP). The remaining algorithms require the base station to transmit more pilot signals to achieve optimal performance. By contrast, the algorithm of the present invention is demonstrated to have significant advantages in reducing the multi-user massive MIMO channel estimation overhead, making the realization of massive MIMO channel estimation in practice possible.
Fig. 4 is a graph comparing the performance of the algorithm of the present invention when applied to multi-user massive MIMO channel estimation with the performance of other sparse signal recovery algorithms applied to the same channel estimation for different signal-to-noise ratios. The invention is demonstrated to perform consistently in different signal-to-noise ratio environments. The same conclusions can be drawn as in fig. 3 at different signal-to-noise ratios.
Claims (3)
1. A massive MIMO channel estimation method is characterized by comprising the following steps:
s1, initializing, specifically:
s11, BS broadcasts T pilot signals X to K MSs by T time slotsP＝[x(1),x(2),...,x(T)]∈CN×TWherein N is the number of antennas of the BS, and pilot signal X in the MIMO channel estimation mathematical modelPA compressed sensing measurement matrix converted into an angle domain, denoted by the symbol phi, havingUnitary matrixp,q∈[0,N-1]，ΦH∈CN×TIs a slave setIn the method, the pilot signal power of each time slot is extracted according to equal probability, and P is the pilot signal power of each time slotHRepresenting a conjugate transpose;
s12, K MSs receiving signal matrix is { RjIn which R isjA received signal matrix representing the jth MS, j 1, 2.., K;
s13, converting the signsWherein the unitary matrixa,b∈[0,M-1]M is the number of antennas of MS,. phi.jIs a conjugate transpose of an angle domain channel matrix ofΕjIs an equivalent Gaussian noise matrix, NjIs a received noise signal matrix;
s2, performing joint estimation on the sparse support sets of each user, namely jointly estimating the sparse support sets of K MSs by utilizing a multitask BCS algorithm to obtain K estimated channel sparse support sets, wherein the K estimated channel sparse support sets are expressed as omega1,Ω2,...ΩK；
S3, iterative estimation of each user sparse support set, specifically:
s31, setting an iteration control variable N common to the MS sparse support setsiterAnd the maximum number of iterations Nset；
S32, initial value given:
receiving a signal matrix Y; a prior probability matrix of X, the elements of the matrix obeying a mean value ofVariance ofComplex gaussian distribution ofCommon sparse support and non-common sparse support parametersComplex gaussian distribution variance of noiseIn accordance with Bernoulli distribution, with an initial probability ofEmpirical value ofAnd an intermediate variable initialized to 0
S33, assuming that the prior probability of Z follows the mean value of Z, the received signal Z without noise is Φ XVariance ofComplex gaussian distribution ofAfter obtaining Z from the prior probability of ZProbability is tested, the probability obeys the mean value ofVariance ofComplex gaussian distribution ofUpdate the rule as(Is composed ofThe reciprocal of (d);
s34, combining the posterior probabilities of Z with the intermediate variablesDeducing the prior probability of X
S35, posterior probability of Z, common sparse parameter and non-common sparse parameterNoise variance parameterSelecting parametersBy intermediate variablesTo obtain updated posterior probability of X
S36, updating initial parameter valueIterating S33-S35 until an iterative control variable N is satisfiediterAnd the maximum number of iterations NsetCan obtain the channel state information of each user comprising the common sparse support and the non-common sparse support
S4, multi-user large-scale MIMO channel estimation, wherein the channel estimation result of each user isThe sparse support part of X is obtained by the Bayes compressed sensing iteration method provided by the invention when a certain set condition is met, the rest part is all 0, and the set condition is an empirical condition.
2. The massive MIMO channel estimation method according to claim 1, wherein: s2, obtaining K estimated channel sparse support sets omega1,Ω2,...ΩKThe method comprises the following specific steps;
s21, supposing that M receiving antennas of each user have the same sparse support set, the sparse support degrees of K MSs are S, for different users K, the number of common sparse support positions is Sc, and the number of non-common sparse support positions is S-Sc, wherein Sc is a symbol representing the number of sparse support positions, and S-Sc represents the unique number of non-common sparse support positions of each user;
s22, according to the Bayes compressed sensing algorithm, setting the sparse channel obedience of the jth MSParameter is αj＝[αj1,αj2,...,αji,...,αjN]TIn which the element α isjiSharing sparse support for multiple usersOr for exclusive sparse supportI.e. joint probability density functionWherein, m is 1,2jIndicating the channel between the jth MS and the BS,i-th element, empirical value, representing channel vectorThe initial values obey a Bernoulli distribution, each element kiProbability of beingi＝1,2,…N；
S23, jointly considering K MSs according toDeriving a set of parameters for a common sparse support locationUpdate rule ofParameter set of non-common sparse support locationsUpdate rule ofWherein, representing the m-th sparse signalThe average value of (a) of (b),representing the m-th sparse signalM 1,2, … K;
s24, the noise obeys the mean value of 0 and the variance of 0Complex gaussian distribution of (c), parameter βmIs updated by the formula
S25, jointly considering K MSs, the update formula of the common distribution parameter K of different users isWherein,wherein, pi is kiInitial probability of 0;
s26, inputting the compressed sensing measurement matrix phi and the angle domain received signal matrix Y in S13, and performing joint iterative estimation on the parameters of S23-S25 to obtain a sparse support set omega of different users.
3. The massive MIMO channel estimation method according to claim 1, wherein: updating initial parameter values S36The specific process is as follows: the posterior probability of X obtained in S34 is substituted into the parameter updating formula in S23-S25.
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