CN1845640A - Wireless channel blind estimation method based on wavelet shrinkage and HMM - Google Patents

Abstract

The blind estimation method for fast-decay wireless channel based on wavelet transformation comprises: (1) determining the depth and convergent order of wavelet decomposition; (2) pre-calculating C(P, n, M) as time-varying discrete wavelet basis function, and selecting proper initial value; (3) modifying time-domain BW algorithm to construct Kullback-Leibler information measure on wavelet domain, and iterative computing till convergence; (4) reconstructing wavelet to obtain h(n, k) as the time-varying pulse response of wireless channel.

Description

A kind of wireless channel blind estimation method based on wavelet shrinkage and HMM

Technical field

The present invention relates to the blind estimating method of rapid fading wireless channel, specifically, is a kind of signal that only receives according to receiving terminal, and the channel characteristics of rapid fading wireless channel is carried out blind estimation approach.

Background technology

Channel estimating is the basis of various communication system signal processing technologies.Whether the root a tree name needs pilot signal, can be divided into three kinds: blind Channel Estimation, non-blind Channel Estimation and semi-blind channel estimation.Blind Channel Estimation be utilize channel output and with the relevant statistical information of input, estimate channel parameter, Channel Transmission efficient height, the bandwidth that helps saving communication system need not to know under the situation of pilot tone or training sequence.

General blind channel estimation method, what be primarily aimed at is the time-independent situation of channel characteristics, related method mainly comprises high-order statistic, subspace, cyclo-stationary etc.These methods can not be directly used in the time dependent occasion of channel characteristics, and in addition, these methods require many received signals usually, otherwise the performance of blind Channel Estimation can be affected.

For the limited occasion of received signal, the performance of maximum likelihood (Maximum Likelihood) class blind estimating method is sorrow, but computation complexity is very big.Traditional BW algorithm approaches maximum likelihood class blind estimating method on performance, and its computation complexity can greatly be reduced.But the BW algorithm can only be used for the time-independent occasion of channel characteristics.

If the variation of channel characteristics is slow, can on above-mentioned the whole bag of tricks, be changed, introduce the self adaptation step, but wireless channel for rapid fading, or because auto-adaptive parameter is too small, cause the pace of change of channel characteristics can exceed the time of self adaptation convergence, or, cause serious reforming phenomena because auto-adaptive parameter is excessive.Even adopted automatic adjustment technologies, the channel for non-rule changes still can cause " hysteresis " effect.Finally cause channel estimation error and increase, the error rate uprises.

In order to solve the blind estimation problem of fast fading channel, this specification adopts wavelet decomposition, the thought of wavelet shrinkage and wavelet reconstruction technology, at HMM (Hidden Markov Model, HMM) on the basis, propose a kind of new method, the signal that receives according to receiving terminal only obtains the feature of wireless channel.

Summary of the invention

The blind estimating method that the purpose of this invention is to provide a kind of rapid fading wireless channel, this method is based on wavelet transformation and HMM.This method is in conjunction with the advantage of the two, by wavelet decomposition, wavelet shrinkage and wavelet reconstruction, the time channel characteristics that becomes be converted to the wavelet transformation characteristic of field that becomes when non-, thereby the spy 6 that can obtain the rapid fading wireless channel better levies, and then reduces the error rate of communication system.

The objective of the invention is to realize by following technical step:

1 input signal sequence s (n) for transmitting terminal, the output sequence x (n) of receiving terminal, the time become channel impulse response h (k), there is following relation in n:

$x\left(n\right)=\underset{k=0}{\overset{L}{\mathrm{\Σ}}}h(n,k)s(n-k)+v\left(n\right)={s_n}^T{h}_n+v\left(n\right)---\left(1\right)$

n＝0，1，.，N-1

s _n＝[s(n)，s(n-1)，...，s(n-L)] ^Th _n＝[h(n，0)，...，h(n，L)] ^T

(n k) carries out discrete wavelet and decomposes to h

$h(n,k)=\underset{m=0}{\overset{N/2^P}{\mathrm{\Σ}}}{\mathrm{\ζ}}_{P,m}\left(k\right)C_0^P(2^{P}m-n)$

$+\underset{i=1}{\overset{P}{\mathrm{\Σ}}}\underset{m=0}{\overset{N/2^P}{\mathrm{\Σ}}}{\mathrm{\ξ}}_{l,m}\left(k\right)C_1^{\left(l\right)}(2^{l}m-n)---\left(2\right)$

$=c{(P,n)}^{T}w(P,k)$

Wherein, ξ _{L, m}(k), ζ _{P, m}(k) be respectively the approximate component and the details component of wavelet decomposition, P is the wavelet decomposition degree of depth.

2 carry out dimensionality reduction (reduced-size) for wavelet decomposition handles, and shrinks coefficient of wavelet decomposition ξ _{L, m}(k) and ζ _{P, m}(k), select an integer M who is not more than P, make ξ _i(k) (i＜M) is 0, and other ξ _{L, m}(k) and ζ _{P, m}(k) remain unchanged, thereby construct one with respect to former " being similar to " SPACE V of having living space _M

$V_M=\left\{\begin{array}{c}{t}_n=S_n^T{h}_n^M=S_n^{T}C(P,n,M)W(P,M)\\ n=\mathrm{0,1},\·\·\·N-1\end{array}\right\}$

(3)

Since special 2 property of the time-frequency localization of wavelet transformation, new " being similar to " SPACE V _MCan approach original space well, thereby greatly reduce the computation complexity of method.

This method adopts the Daubechies small echo.

On the wavelet transformed domain, (n, estimation k) is converted into (P, estimation M) to W to h.At this moment, the characteristic parameter of channel is $\mathrm{\ψ}=({\mathrm{\σ}}_v^2,W(P,M)).$ For given list entries F, the likelihood function of the output signal of receiving terminal is:

$f_{\mathrm{\ψ}}\left(X\right|F)=\frac{1}{{\left(2\mathrm{\π}{\mathrm{\σ}}_v^2\right)}^{N/2}}{e}^{-(1/2{\mathrm{\σ}}_v^2)\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}{|x\left(n\right)-{s_n}^T{h}_n^M|}^2---\left(4\right)}$

3 adopt wavelet decomposition and shrink after, successfully the time become impulse response h (n k) is decomposed into two parts, the time become discrete wavelet basic function C (P, n, M) and the wavelet domain coefficients W that becomes when non-(P, M).Therefore, can copy traditional to become situation when non-, make up a HMM.Definition status vector s _n=[s (n), s (n-1) ..., s (n-L)] ^TIf s (n) has X different value, wireless channel can be described with a finite state machine, and this state machine has T=|X| ^LEach state.

The corresponding tlv triple ε of HMM=(A, P, f) as follows:

(1) state transition probability

A＝[a _i，j] a _i，j＝Pr(s _n+1＝Z _j|s _n＝Z _i)1≤i，j≤T (6)

$a_{i,j}=\mathrm{Pr}(s_{n+1}-Z_j|s_n=Z_i)=\left\{\begin{array}{cc}1/\left|X\right|& \mathrm{if}{Z}_i\mathrm{leads\; to}{Z}_j\\ 0& \mathrm{Otherwise}\end{array}\right.$

(2) initial probability

P＝(p _i)?p _i＝Pr(s ₀＝Z _i)＝1/T?1≤i≤T (7)

(3) probability distribution

$f_{\mathrm{\ψ}}\left(x\left(n\right)\right|s_n)=\frac{1}{{\left(2\mathrm{\π}{\mathrm{\σ}}_v^2\right)}^{1/2}}{e}^{-{|x\left(n\right)-S_n^{T}C(P,n,M)W(P,M)|}^2/2-{\mathrm{\σ}}_V^2}$

$\log f_{\mathrm{\ψ}}\left(X\right|F)=\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}\log f_{\mathrm{\ψ}}\left(x\left(n\right)\right|s_n)---\left(8\right)$

$=\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}\underset{j=1}{\overset{T}{\mathrm{\Σ}}}\log f_{\mathrm{\ψ}}\left(x\left(n\right)\right|s_n=Z_j)\mathrm{\δ}(Z_j,s_n)$

$\mathrm{\δ}(Z_j,s_n)=\left\{\begin{array}{cc}1& Z_i=s_n\\ 0& \mathrm{Otherwise}\end{array}\right.$

4 at wavelet transformed domain, and corresponding Kullback-Leibler information measure is defined as

$-\frac{1}{2}\×\frac{1}{{\mathrm{\σ}}_v^{\′2}}\×{|x\left(n\right)-S_j^{T}C(P,n,M)W^{\′}(P,M)|}^2\}$

Definition ${\mathrm{\γ}}_j^{\left(i\right)}\left(n\right)=\underset{F\∈F}{\mathrm{\Σ}}{f}_{{\mathrm{\ψ}}^{\left(i\right)}}(X,F)\mathrm{\δ}(Z_j,s_n)$

At above-mentioned HMM, according to the Kullback-Leibler information measure, traditional time domain BW algorithm is improved, find the solution in the enterprising row iteration of new wavelet field.Concrete steps are as follows:

(1) iteration initialization according to desired precision, is determined wavelet decomposition degree of depth P, wavelet shrinkage exponent number M, and calculate corresponding $C(P,n,M)=I_{D+1}\⊗c{(P,n)}_M^T,$ Choose an iteration initial parameter

${\mathrm{\ψ}}^{\left(0\right)}=({\mathrm{\σ}}_v^{2\left(0\right)},W^{\left(0\right)}(P,M))$

(2) calculate γ _j ⁽ⁱ⁾(n)

(3) choose ψ ', the Q (ψ in feasible (9) ⁽ⁱ⁾, ψ ') and maximum, corresponding ψ ' is exactly ψ ⁽ⁱ⁺¹⁾Order ${\▿}_{{\mathrm{\σ}}_v^{\′2}}Q({\mathrm{\ψ}}^i,{\mathrm{\ψ}}^{\′})=0$ And  _{W ' (P, M)}Q (ψ ⁱ, ψ ')=0, ψ can be obtained ⁽ⁱ⁺¹⁾, expression formula is as follows: W ⁽ⁱ⁺¹⁾(P, M)=Ψ ^-1Γ

$\mathrm{\Ψ}=\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}\underset{j=1}{\overset{T}{\mathrm{\Σ}}}{\mathrm{\γ}}_j^{\left(i\right)}\left(n\right){\left(A_{(P,j,n,M)}{A_{(P,j,n,M)}}^H\right)}^{*}$

$\mathrm{\Γ}=\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}\underset{j=1}{\overset{T}{\mathrm{\Σ}}}{\mathrm{\γ}}_j^{\left(i\right)}\left(n\right)x\left(n\right){\left(A_{(P,j,n,M)}\right)}^{*}$

${\mathrm{\σ}}_v^{2(i+1)}=\frac{1}{N}\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}\underset{j=1}{\overset{T}{\mathrm{\Σ}}}{\mathrm{\γ}}_j^{\left(i\right)}\left(n\right)$

$\×{|x\left(n\right)-S_j^{T}C(P,n,M)W^{(i+1)}(P,M)|}^2$

Wherein, $A_{(P,j,n,M)}=S_j^{T}C(P,n,M)$

(4) repeating step (2) and (3), up to $\mathrm{\ψ}({\mathrm{\σ}}_v^2,W(P,M))$ Convergence.

(5) can by formula (2) calculate h (n, k).

(6) obtain list entries if desired, (n k) calculates, and can adopt the Viterbi algorithm to calculate most probable list entries owing to h.

Simulation calculation shows compared with the rapid fading wireless channel blind estimation method of other type, no matter the method that this paper proposes is the error rate, and channel tracking performance or computation complexity all have greatly improved.

Description of drawings

Fig. 1 is the structure chart of wavelet decomposition and wavelet shrinkage among the present invention.

Fig. 2 is the calculation process schematic diagram of the inventive method

Embodiment

Fig. 1 illustrates the structure chart of wavelet decomposition and wavelet shrinkage.

1 selects wavelet decomposition degree of depth P and wavelet shrinkage exponent number M

At first, must determine wavelet decomposition degree of depth P and wavelet shrinkage exponent number M.Wavelet decomposition degree of depth P has bigger influence to the computation complexity of the method that this paper proposed, the P value is too small, at this moment, if the signal points N of receiving terminal is excessive, can cause W (P, M) coefficient in is too much, computation complexity improves, the P value is excessive, if N is less, then can cause performance for estimating channel to descend.A large amount of l-G simulation tests show that the P value is proper by following value:

P=[log ₂(N)] wherein N is that the received signal of receiving terminal is counted

Equally, the value difference of wavelet shrinkage exponent number M can be to " approximation space " V _MCause different influences with former degree of approximation of having living space, it would be desirable M=1, like this, V _MCan perfectly approach former having living space, but corresponding calculated complexity maximum, if get M=P, so, computation complexity is minimum, but corresponding precision is also minimum.Following Several Factors is depended in the selection of M:

(1) the maximum Dopple frequency displacement f of sampling period T and wireless channel _d

(2) wavelet decomposition degree of depth P.

(3) V _MApproximate requirement.

Simulation calculation shows that if will reach computational accuracy preferably, the empirical equation that M must satisfy is as follows:

$\frac{2^{P+1-M}}{N}>8f_{d}T$

The initial value of 2 iterative computation ${\mathrm{\ψ}}^{\left(0\right)}=({\mathrm{\σ}}_v^{2\left(0\right)},W^{\left(0\right)}(P,M))$

ψ ⁽⁰⁾The convergence of choosing the method for mentioning for this paper very big influence is arranged, usually, can adopt the impulse response that calculates time-variant wireless channel at the blind estimating method of non-time-variant wireless channel earlier, and calculate an initial value ψ ⁽⁰⁾Although the impulse response of this and actual channel has bigger gap, can be used as the initial value of this method.

3 calculate γ _j ⁽ⁱ⁾(n)

γ _j ⁽ⁱ⁾(n) representative is when the i time iteration, and the probability of occurrence of burst when given state j can adopt front and back in the HMM to algorithm, calculates γ fast _j ⁽ⁱ⁾(n).

When 4 judge iteration convergence

Because method that this paper proposed is a kind of blind estimating method, do not know in advance wireless channel h (n, k), therefore, when judging convergence, must adopt the method for relative accuracy: a large amount of simulation calculation show, can adopt following empirical equation when to judge iteration convergence:

$\frac{\left|\right|W^{(i+1)}(P,M)-W^{\left(i\right)}(P,M)\left|\right|}{\left|\right|W^{(i+1)}(P,M)\left|\right|}<\frac{1}{P{2}^{P+1-M}}$

Claims (2)

1. rapid fading wireless channel blind estimation method based on HMM and wavelet shrinkage.It is characterized in that receiving terminal is not knowing to send under the situation of signal, only, channel characteristics carried out blind estimation according to the signal that receives,

Step:

1) according to sampling time and maximum Dopple frequency displacement, selected wavelet decomposition degree of depth P and wavelet shrinkage exponent number M.

2) employing calculates the impulse response of time-variant wireless channel at the blind estimating method of non-time-variant wireless channel earlier, and then calculates an initial value ψ ⁽⁰⁾Although the impulse response of this and actual channel has bigger gap, can be used as the iteration initial value of this method.

3) HMM of structure on the wavelet field improved the BW algorithm of time domain, is transplanted on the wavelet field, obtains the computing formula of corresponding wavelet domain coefficients (wavelet field characteristic vector).

4) iteration is calculated, and till participating in each parameter convergence that iteration transports, wavelet reconstruction obtains the impulse response and the noise variance of wireless channel.

2. as blind estimating method as described in the right 1, it is characterized in that: according to sampling time and maximum Dopple frequency displacement, the selected wavelet decomposition degree of depth and wavelet shrinkage exponent number, the time varying channel impulse response h (n of time domain, k) be converted into the non-time varying characteristic vector of wavelet field, and then derive corresponding iterative computation formula.

W ⁽ⁱ⁺¹⁾(P，M)＝ψ ^-1Γ

$\mathrm{\&Psi;}=\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{T}{\mathrm{\&Sigma;}}}{\mathrm{\&gamma;}}_j^{\left(i\right)}\left(n\right){\left(A_{(P,j,n,M)}{A_{(P,j,n,M)}}^H\right)}^{*}$

$\mathrm{\&Gamma;}=\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{T}{\mathrm{\&Sigma;}}}{\mathrm{\&gamma;}}_j^{\left(i\right)}\left(n\right)x\left(n\right){\left(A_{(P,j,n,M)}\right)}^{*}$

${\mathrm{\&sigma;}}_v^{2(i+1)}=\frac{1}{N}\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{T}{\mathrm{\&Sigma;}}}{\mathrm{\&gamma;}}_j^{\left(i\right)}\left(n\right)\&times;{|x\left(n\right)-S_j^{T}C(P,n,M)W^{(i+1)}(P,M)|}^2$

$A_{(P,j,n,M)}=S_j^{T}C(P,n,M)$