CN108259398A - The channel estimation methods of COMPLEX MIXED model based on variational Bayesian - Google Patents
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- H—ELECTRICITY
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- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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Abstract
The invention belongs to wireless communication technology fields, particularly relate to a kind of channel estimation methods of the COMPLEX MIXED model based on variational Bayesian.The sparsity structure of extensive mimo channel is utilized in the method for the present invention,And its similitude of adjacent channel sparsity structure,And each antenna is reasonably divided into each submatrix,Maximally utilise the correlation between each channel,Innovatively construct the sparse model (multilayer prior model) of extensive mimo channel,Introducing probability event comes control channel position and belongs to completely shared,Submatrix shares position or non-shared position,Propose the channel estimation method (being abbreviated as Complex_Mixture_VBI) of the COMPLEX MIXED model based on variational Bayesian,While and OMP,ASSP,The channel estimation methods such as Geniu LS are compared,The present invention substantially increases the accuracy of channel estimation,Under certain condition,It may be such that channel estimation errors reach 10‑3, and do not need to any prior information.
Description
Technical field
The invention belongs to wireless communication technology fields, particularly relate to a kind of complexity based on variational Bayesian
The channel estimation methods of mixed model.
Background technology
Extensive MIMO (Multiple Input Multiple Output, multiple-input and multiple-output) system is to move in the 5th generation
One of key technology of dynamic communication system, main advantage is：Power system capacity increases as antenna amount increases；Reduce hair
Send signal power；Simple linear precoder can be optimal performance with detector；Tend to orthogonalization between channel, therefore
Eliminate co-channel interference in cell.
The premise for realizing these advantages is base station (BS) channel knowledge status information (CSIT).In time division duplex (TDD) system
In system, channel estimation is carried out in user terminal (MS) using the reciprocity of uplink and downlink channel.For the extensive mimo systems of FDD,
The flow of channel estimation is：To each user's broadcast pilot, mobile subscriber estimates that CSIT is then anti-using signal is received for base station
It is fed back to base station.In this case, pilot signal number is directly proportional to antenna for base station number, due in extensive mimo system, antenna
Enormous amount, conventional channel estimation methods (such as least square method) will face huge training expense so that the training time becomes
Length, the even more than coherence time of channel so that channel estimation loses meaning.
Compressed sensing is a kind of completely new signal sampling theory, it is openness using signal, much smaller than Nyquist
In the case of rate, the discrete sample of signal is obtained with stochastical sampling, utilizes sparse spy of the original signal below certain bases
Property, it is projected under seldom measurement, original signal is restored by nonlinear algorithm, therefore compressive sensing theory can lead to
It crosses minimum measurement and retains maximum signal message.Management loading (Sparse Bayesian Learning, SBL) is most
It was just proposed as a kind of machine learning algorithm by the Tipping of Microsoft Research in 2001, is subsequently introduced into sparse signal
Recovery field (BCS).
Bayes's compressed sensing is the method using probability, increases sparse prior to signal, is inferred by Bayesian statistics
Method, derive signal restore algorithm.Due to Bayes's flexibility ratio height, can by changing the form of probability priori, with
Adapt to a variety of different signal priori.Bayesian frame provides a variety of useful estimating methods, such as：Expectation
Maximization(EM)、Variational Expectation Maximization(VEM)、Maximal Likelihood
(ML)、Variational Bayes Inference(VEM).EM algorithms are Dempster, and Laind, Rubin were carried in 1977
What is gone out seeks a kind of method of parameter Maximum-likelihood estimation, it can estimate parameter from incomplete data set, is a kind of
Very simple and practical learning algorithm.The main purpose of EM algorithms is to provide a simple iterative algorithm and calculates posterior density letter
Number, its great advantage are simple and stablize, but be easily trapped into local optimum.VEM algorithms are the EM algorithms of generalization, are earliest
By BEAL M J. in its paper《Variational Algorithms for Approximate Bayesian
Inference》In proposed, be mainly used in statistical model complicated in Bayesian Estimation and machine learning field.
Lot of experiments shows that wireless broadband channel has the openness of delay domain (delay domain), is advising greatly
Adjacent transmission antenna and a user show closely similar path delay values in mould mimo system, i.e., different transmitting antenna tools
There is similar sparse path.
Invention content
The purpose of the present invention is to propose to a kind of channel estimation methods based on bayesian algorithm.It is of the invention mainly to utilize compression
The similitude of openness and adjacent antenna the sparsity structure of perception principle and extensive mimo channel, in bayesian algorithm
On the basis of propose a kind of improved bayesian algorithm, the accuracy of channel estimation is improved with this.
For the ease of understanding of the those skilled in that art to technical solution of the present invention, the compression used first to the present invention
Perception principle and bayesian algorithm and system model illustrate.
Standard compression sensing mathematics model：Y=Α x+n.Wherein, Α is the perception matrix that size is n × m, and y is tieed up for n × 1
Compressed signal, x are the sparse signal that m × 1 is tieed up, and there was only k ＜ ＜ m element non-zeros in degree of rarefication k, i.e. x, remaining element is complete
Portion be 0, n be the system noise of the dimension of n × 1 and its element to obey mean value be 0, variance σ2Gaussian Profile.
Improved bayesian algorithm is based on variational Bayesian algorithm, and variational Bayesian algorithm is a kind of solves most
The algorithm of big Posterior distrbutionp passes through constantly iteration, the mean value and variance of the hidden variable under the conditions of obtaining known to sample.
The present invention is based on extensive mimo systems, it is assumed that it is flat block decline to need the channel estimated, i.e., at certain section
Interior channel status is constant, considers OFDM (Orthogonal Frequency Division Multiplexing, orthogonal frequency
Multiplexing) technology.
In transmitting terminal, there are one base station BS, each BS is is configured with NtThe extensive antenna array of root antenna, base station utilize Nt
Root antenna sends training sequence (non-orthogonal pilot), and the present invention is designed using the non-orthogonal pilot based on compressive sensing theory, it
The pilot tone of different transmitting antennas is allowed to occupy identical subcarrier, and using the sparse characteristic of channel, for channel estimation
Number of pilots can greatly reduce.And traditional orthogonal pilot design is based on classical Nyquist sampling thheorems, different transmittings
The pilot tone of antenna needs very high pilot-frequency expense in occupation of different subcarriers.
The designing scheme of non-orthogonal pilot is following (by taking an OFDM symbol as an example)：
The number of one OFDM symbol sub-carriers is N, and the number of pilot sub-carrier is Np, the set ξ of pilot sub-carrier
It is chosen from { 1,2 ... N }, it is all identical to all transmitting antennas.The pilot frequency sequence of n-th of transmitting antenna symbol PnIt representsNtThe pilot tone of a transmitting antennaByIt forms,Obey [0,2 π) independent same distribution it is equal
Even distribution.Sets of pilot sub-carriersI (i) is from set { 1,2 ... N } with intervalIt is equidistant to choose,WhereinI is taken herein0=1.
In receiving terminal, single user is considered, user has single reception antenna, and user carries out channel estimation by receiving signal.
After removing protection interval and discrete Fourier transform, an OFDM symbol receives signalIt is expressed as follows：
Wherein, 1. diag (Pn) represent vector PnDiagonalization；②It is a DFT matrix, FL/ξExpression takes F's
Preceding L row, N is taken according to ξ in FpRow,③Φn=diag (Pn)FL/ξ, 4. as r=1, hn,rTurn to hn,Additivity is high
This white noiseIn expression formula, | | h | |2=Nt*L；NoiseIn each element to obey mean value be 0, side
Difference is β-1Multiple Gauss distribution, β obey Gamma distribution β~Gamma (a, b).
The present invention utilizes the similitude of the openness and sparsity structure of extensive mimo system adjacent channel, lower mask body point
The two properties of channel are analysed, and build layering prior model:
In the downlink, the delay domain channel impulse response between n-th of transmitting antenna and user's reception antenna is as follows：
hn,r=[hn,r(1),hn,r(2),…hn,r(L)]T,1≤n≤Nt
WhereinR is mark of the OFDM symbol in time domain, and L is equivalent channel length.There is measurement result to show,
Different transmitting antennas and a user show closely similar path delay values, i.e., different transmitting antennas have similar sparse
Path, degree of rarefication ΩrIt represents, support (hn,r) represent hn,rIn sparse support number.
Since adjacent transmitting antenna has similar sparse path, the phase of the sparsity structure of channel between each antenna is utilized
Like property, antenna is uniformly divided into K submatrix, the similitude of condition of sparse channel is embodied in completely shared position and shares position with submatrix
On.NtRoot antenna shares Ωc1A degree of rarefication claims this Ωc1A position is completely shared position；NtRoot antenna is evenly divided into K groups,
Every group of antenna number M=Nt/ K, all antennas in kth group share Ωc2A degree of rarefication claims this Ωc2A position shares position for submatrix
(or the shared position in part) is put, is left Ω-Ωc1-Ωc2A position is non-shared position, between each antenna independently of each other.One
In OFDM symbol, base station and user terminal channel show certain sparse characteristic, as shown in Figure 1, equivalent channel length L in Fig. 1
=15, degree of rarefication Ω=6, completely shared degree of rarefication Ωc1=3, submatrix shares degree of rarefication Ωc2=2, each antenna is non-shared sparse
Spend Ωp=1, hk,mRepresent the delay domain channel impulse response between n-th antenna of kth group and user's reception antenna, wherein k
∈[1,K],n∈[1,Nt]。
The probability Distribution Model of h can be expressed as：
Wherein hk,mRepresent the m root antennas of k-th of submatrix,hm,l,kRepresent hk,mL-th of position member
Element；zm,l,kDetermine that everybody is set to completely shared position on each antenna or submatrix shares position or non-shared position, zm,l,k=1 table
L-th of position for showing kth group submatrix m root antennas is completely shared position, zm,l,k=2 represent kth group submatrix m root antennas
L-th of position shares position, z for submatrixm,l,kL-th of position of=3 expression kth group submatrix m root antennas is non-shared position,
I.e. for zm,l,kThree events may occur：zm,l,k=1 (event 1), zm,l,k=2 (events 2), zm,l,k=3 (events 3), and thing
Part 1, event 2, event 3 are exclusive events, i.e.,WhereinTable respectively
Show the probability of generation event 1, event 2, event 3.1 [z of expression formulam,l,k=1] position is characterized as completely shared position, and thing occurs
The probability of part 1 ishm,l,kIt is completely shared, it is 0 to obey mean value, and variance isMultiple Gauss distributionSimilarly, 1 [z of expression formulam,l,k=2] it characterizes the position and shares position for submatrix, event 2 occurs
Probability behm,l,kIt is that submatrix shares, it is 0 to obey mean value, and variance isMultiple Gauss distributionSimilarly, 1 [z of expression formulam,l,k=3] position is characterized as non-shared position, and event 3 occurs
Probability behm,l,kIt is non-shared.It is to sum up told, hm,l,kProbability Distribution Model as shown in figure 4, its expression formula
It is as follows：
Based on the considerations of above-mentioned sparsity structure, the present invention proposes the COMPLEX MIXED model based on variational Bayesian
Channel estimation method (is abbreviated as Complex_Mixture_VBI), and the present invention can be realized by following scheme, realizes step such as
Under：
S1, initialization, specially：
S11, BS are to MS broadcast pilotsWherein, NtFor the antenna number of BS, by mimo channel
Pilot signal P in estimation mathematical model is converted into compressed sensing calculation matrix, represents there is Φ with symbol Φn=diag (Pn)
FL/ξ,WhereinIt is a DFT matrix.
The reception signal of S12, MS are y=Φ h+w, and wherein channel vector isAdditivity
White Gaussian noiseAnd have | | h | |2=Nt*L。
If S13, hm,l,kIt is completely shared, it is 0 to obey mean value, and variance isMultiple Gauss distributionIf hm,l,kIt is that submatrix shares, it is 0 to obey mean value, and variance is's
Multiple Gauss is distributedαc2m,l=c20/d20；If hm,l,kIt is non-shared, obeying mean value is
0, variance isMultiple Gauss distributionNoise
In each element to obey mean value be 0, variance β-1Multiple Gauss distribution, β obey Gamma distribution β~Gamma (a, b), β=
a0/b0, wherein a0, b0, c10, d10, c20, d20, e0, f0For the parameter of initialization, general value is smaller.
S2, excessively following step realize the iteration of variation bayesian algorithm：
S21, setting maximum iteration are Niter, iteration ends thresholding Thr, initialization zm,l.kFor completely shared position or
Submatrix share or the possibility of non-shared position be it is identical, i.e.,Initialize each parameter point
It Wei not a0,b0,c10,d10,c20,d20,e0,f0；
S22, the mean value u of Posterior distrbutionp of h and variance ∑ are calculated：
∑=(<β>φHφ+Dc1+Dc2+Dp)-1
U=<β>∑φHy
Wherein,
The mean value u of S23, h Posterior distrbutionp is as estimated value, the completely shared parameter alpha of updatec1Parameter alpha is shared with submatrixc2With
Non-shared parameter alphap, and calculate<lnαc1l>、<lnαc2k,l>、<lnαpm,l,k>。
Wherein, um,l,kRepresent the mean value of l-th of position channel vector of kth group m root antennas, ∑m,l,kRepresent kth group
The variance of l-th of position channel vector of m root antennas.
S24, update position selection parameter
Wherein, ηc2m,l,k=<lnαc2k,l>-<αc2k,l><||hm,l,k||2>
S25, pass through expression formula | | hn-hn-1|-|hn-1-hn-2||<||hn-hn-1|-|h1-h0| | whether * Thr judgements iteration
Convergence if meeting condition, stops the mean value u of iteration and h Posterior distrbutionps as estimated value, otherwise repeatedly step S22~S25.
The beneficial effects of the invention are as follows：Compared with conventional method, extensive MIMO is dexterously utilized in method of the invention
The sparsity structure of channel and its similitude of adjacent channel sparsity structure, and each antenna is reasonably divided into each submatrix, most
The correlation between each channel is utilized to limits, innovatively constructs the sparse model (multilayer of extensive mimo channel
Prior model), it introduces probability event and comes that control channel position belongs to completely shared, submatrix shares position or non-shared position
It puts, it is proposed that the channel estimation method of the COMPLEX MIXED model based on variational Bayesian (is abbreviated as Complex_
Mixture_VBI), while compared with the channel estimation methods such as OMP, ASSP, Geniu-LS, the present invention substantially increases channel and estimates
The accuracy of meter under certain condition, may be such that channel estimation errors reach 10-3, and do not need to any prior information.
Description of the drawings
Fig. 1 is the openness schematic diagram of COMPLEX MIXED model of extensive mimo channel；
Fig. 2 is the COMPLEX MIXED model system figure of extensive mimo channel；
Fig. 3 inventive algorithm flow charts；
Fig. 4 inventive algorithms and common BCS are (i.e._ SBL), ideal BCS (i.e. Enhanced_SBL), OMP, ASSP,
Geniu-LS algorithms are in different resource ratio NpPerformance comparison figure under/N；
Fig. 5 inventive algorithms and common BCS are (i.e._ SBL), ideal BCS (i.e. Enhanced_SBL), OMP, ASSP,
Performance comparison figure of the Geniu-LS algorithms under different sparsity structures.
Fig. 6 is the performance comparison of inventive algorithm and Geniu-LS and Mixture_VBI algorithms under different signal-to-noise ratio
Figure.
Specific embodiment
With reference to specific drawings and examples, the present invention is described in further detail：
Embodiment
Launch party's antenna for base station number is set as N in this examplet=32, submatrix group number K=4, submatrix internal antenna number M=Nt/ K=
8, recipient is single user, is gathered around there are one reception antenna, equivalent channel length L=64, degree of rarefication s=10, Signal to Noise Ratio (SNR)=
20dB, sub-carrier number N=1024.
Fig. 3 is this example channel estimation flow chart, and according to flow chart, algorithm can be emulated using above-mentioned parameter.
S1, initialization, specially：
S11, BS are to MS broadcast pilotsMimo channel is estimated into the pilot tone in mathematical model
Signal P is converted into compressed sensing calculation matrix, there is Φn=diag (Pn)FL/ξ,For channel vector, hnIt is
Sparse, and each hnBetween sparsity structure have similitude.
The reception signal of S12, MS are additive white Gaussian noise, and have for y=Φ h+w, w | | h | |2=Nt*L。
If S13, hm,l,kBe it is completely shared,αc1l~Gamma (c1l,d1l), αc1l=c10/
d10；If hm,l,kIt is that submatrix shares,αc2m,l~Gamma (c2m,l,d2m,l), αc2m,l=c20/d20,
If hm,l,kBe it is non-fully shared,αpm,l,k~Gamma (em,l,k,fm,l,k), αpm,l,k=e0/f0；
Noiseβ~Gamma (a, b), β=a0/b0。
S2, excessively following step realize Complex_Mixture_VBI algorithms：
S21, setting maximum iteration are Niter=100, iteration ends thresholding Thr=10-3, initialize zm,l,kIt is complete
Shared position or submatrix share or the possibility of non-shared position be it is identical, i.e.,Initially
It is respectively a to change each parameter0=10-4, b0=10-6, c10=10-2, d10=10-6, c20=10-2, d20=10-6, e0=10-2, f0=
10-6。
S22, the mean value u of Posterior distrbutionp of h and variance ∑ are calculated：
∑=(<β>φHφ+Dc1+Dc2+Dp)-1
U=<β>∑φHy
Wherein,
The mean value u of S23, h Posterior distrbutionp is as estimated value, the completely shared parameter alpha of updatec1Parameter alpha is shared with submatrixc2With
Non-shared parameter alphap, and calculate<lnαc1l>、<lnαc2k,l>、<lnαpm,l,k>。
S24, update position selection parameter
Wherein, ηc2m,l,k=<lnαc2k,l>-<αc2k,l><||hm,l,k||2>
S25, update noise parameter
S26, pass through expression formula | | hn-hn-1|-|hn-1-hn-2||<||hn-hn-1|-|h1-h0| | whether * Thr judgements iteration
Convergence, if meeting condition, stops iteration, otherwise repeatedly step S22~S25.
The mean value and estimate of variance of S3, the extensive mimo channel of output, Estimation of Mean value u are extensive MIMO letters
The final estimated result in road.
Consider that channel sparsity structure is in Fig. 4：Completely shared sc1=5, submatrix shares sc2=3, non-shared sp=2, it incite somebody to action this
Invent the Complex_Mixture_VBI algorithms proposed, comparison Naive-SBL (reset condition BCS) and Enhanced-SBL (reasons
Think state BCS) and Geniu-LS, ASSP, OMP, three kinds of methods different length pilot sub-carrier number NpUnder, wherein leading
Frequency sub-carrier number ratio Np/ N=0.5:0.1:1, the mean error of 100 accidental channels is tested, Pth in corresponding ASSP methods
It is that 400, thresholding epsilon is set as 0.05 to be set as ending iterations in 0.06, OMP methods.It can be seen from the figure that this
The performance of Complex_Mixture_VBI algorithms estimation channel that invention proposes is far superior to ASSP, OMP, and with number of resources
Increase and approach hypothetic algorithm；In addition it will be seen that Enhanced-SBL algorithms in the case where only considering perfect channel model
Poor-performing, consider that the Naive-SBL algorithm performances of reset condition are suitable with OMP.
In Fig. 5, by Complex_mixture_VBI proposed by the present invention (3 mixed model of state), Naive-SBL is compared
(reset condition BCS) is with Enhanced-SBL (perfect condition BCS) and Geniu-LS, ASSP, OMP, three kinds of methods in difference
Under the conditions of sparse, the mean error of 100 accidental channels is tested.Fixed resource number Np=round (N*0.8) is completely shared dilute
Dredge degree sc1=5, independent variable is non-shared degree of rarefication sp, variation range sp=[0:1:5].It can be seen from the figure that with channel
The change of sparsity structure, the increase of privately owned positional number in channel, ASSP, Enhanced-SBL, Complex_mixture_VBI are calculated
The performance of method continuously decreases, and OMP, Naive-SBL method are unaffected, mainly since channel is utilized in first three methods
Sparsity structure with the complication of sparsity structure, estimates reduced performance.But algorithm proposed by the present invention can still keep preferable
Performance, it is minimum with the gap of hypothetic algorithm.
In Fig. 6 main contrast's Complex_mixture_VBI algorithms proposed by the present invention (being abbreviated as in figure " state 3 ") with
Performance of the Mixture_VBI algorithms (being abbreviated as in figure " state 2 ") under different Signal to Noise Ratio (SNR), and compare hypothetic algorithm
Geniu-LS tests the mean error of each algorithm under 100 accidental channels.Wherein channel sparsity structure：Completely shared sc1=5,
Submatrix shares sc2=3, non-shared sp=2, Geniu-LS and pilot sub-carrier number N in Complex_mixture_VBI methodspIf
Put Np=round (N*0.8), K submatrix works respectively in Mixture_VBI methods, and pilot sub-carrier number is identical in each submatrix,
Consider following 4 kinds of situations：NpIt is respectively set to Np=round (N*0.2), Np=round (N*0.4), Np=round (N*
0.6)、Np=round (N*0.8), signal-to-noise ratio variation range SNR=[0:5:30].It is it can be seen from the figure that identical in number of resources
In the case of, the performance of Complex_mixture_VBI methods more approaches ideal method, and Mixture_VBI methods need more
More resources could more approach ideal method.(being abbreviated as in figure " state 3 ").
Claims (1)
1. miscellaneous mixed model channel estimation methods are onlapped based on variational Bayesian, including：
Transmitting terminal：
Each base station is configured with NtThe extensive antenna array of a antenna, base station utilize NtA antenna sends training sequence, the training
Sequence is the non-orthogonal pilot based on compressive sensing theory, that is, the pilot tone of different transmitting antennas is allowed to occupy identical sub- load
Wave；Then for sending signal, if the number of an OFDM symbol sub-carriers is N, the number of pilot sub-carrier is Np, pilot tone
The set ξ of carrier wave chooses from { 1,2 ... N }, all identical to all transmitting antennas, and the pilot frequency sequence of n-th of transmitting antenna is used
Symbol PnIt represents,NtThe pilot tone of a transmitting antennaByIt forms,Obey [0,2 π) it is only
The vertical same distribution that is evenly distributed, sets of pilot sub-carriers areI (i) is from set { 1,2 ... N } with interval
It is equidistant to choose,Wherein
Base station is to user's broadcast pilotPilot signal P is converted into compressed sensing calculation matrix, is used
Symbol Φ is represented, there is Φn=diag (Pn)FL/ξ,Wherein, diag
(Pn) represent vector PnDiagonalization；It is a DFT matrix, FL/ξExpression takes the preceding L of F to arrange, and N is taken in F according to ξp
Row,
Receiving terminal：
Setting user has single reception antenna, receives signal and is：
Y=Φ h+w
Wherein, channel vector isAdditive white Gaussian noiseAnd have | | h | |2=
Nt*L；
It is characterized in that, receiving terminal includes the following steps the method for estimation of channel：
S1, openness and sparsity structure the similitude according to extensive mimo system adjacent channel build prior model, specifically
For：
Due to adjacent transmitting antenna have similar sparse path, using between each antenna the sparsity structure of channel it is similar
Property, degree of rarefication is set as Ω, NtRoot antenna shares Ωc1A degree of rarefication claims this Ωc1A position is completely shared position；By NtRoot
Antenna is uniformly divided into K submatrix, every group of antenna number M=Nt/ K, all antennas in kth group share Ωc2A degree of rarefication, claims this
Ωc2A position shares position for submatrix, is left Ω-Ωc1-Ωc2Position is non-shared position, between each antenna mutually solely；Using
hk,mRepresent the delay domain channel impulse response between n-th antenna of kth group and user's reception antenna, wherein k ∈ [1, K], n
∈[1,Nt]；The probability Distribution Model for then building h is：
Wherein hk,mRepresent the m root antennas of k-th of submatrix,hm,l,kRepresent hk,mL-th of position element；
zm,l,kDetermine that everybody is set to completely shared position on each antenna or submatrix shares position or non-shared position, and using zm,l,k=1
L-th of position for representing kth group submatrix m root antennas is completely shared position, and probability of happening ishm,l,kIt is complete
Shared, it is 0 to obey mean value, and variance isMultiple Gauss distributionzm,l,k=2 represent kth
L-th of position of group submatrix m root antennas shares position for submatrix, and probability of happening ishm,l,kIt is that submatrix shares,
It is 0 to obey mean value, and variance isMultiple Gauss distributionzm,l,k=3 represent kth group
L-th of position of battle array m root antennas is non-shared position, and probability of happening ishm,l,kIt is non-shared；Then hm,l,k's
Probability Distribution Model is：
S2, given initial value：
Setting maximum iteration is Niter, iteration ends thresholding Thr, initialization zm,l.kIt is shared for completely shared position or submatrix
Or the possibility of non-shared position be it is identical, i.e.,
S3, the mean value u of Posterior distrbutionp and variance ∑ that channel h is obtained using equation below：
∑=(<β>φHφ+Dc1+Dc2+Dp)-1
U=<β>∑φHy
Wherein,
S4, using the mean value u of h Posterior distrbutionps as estimated value, the completely shared parameter alpha of updatec1, submatrix share parameter alphac2With it is non-shared
Parameter alphap, and calculate<lnαc1l>、<lnαc2k,l>、<lnαpm,l,k>：
S5, update position selection parameter
Wherein,
S6, pass through expression formula | | hn-hn-1|-|hn-1-hn-2||<||hn-hn-1|-|h1-h0| | whether * Thr judgements iteration restrains, if
Meet condition, then stop iteration, the mean value u of h Posterior distrbutionps as estimated value and is entered step into S7, otherwise repeatedly step S3~
S5；
S7, the mean value and estimate of variance for exporting channel, Estimation of Mean value u are the final estimation knot of extensive mimo channel
Fruit.
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