CN103107969B - Incremental iterative time-varying channel evaluation and inter carrier interference (ICI) elimination method of fast orthogonal frequency division multiplexing (OFDM) system - Google Patents

Abstract

An incremental iterative time-varying channel evaluation and inter carrier interference (ICI) elimination method of fast orthogonal frequency division multiplexing (OFDM) system is applied in the field of wireless communication channel evolution, and is used for channel evaluation based on pilot frequency in the circumstance that a severe ICI influence of a time-varying channel occurs. The incremental iterative time-varying channel evaluation and ICI elimination method of fast OFDM system is characterized in that the sum of an ICI and a channel noise (SIN) is taken as a denosing object of a Kalman wave filter, and the ICI influence when the Kalman wave filter evaluates is eliminated. In addition, an incremental mode is used by data used for iteration, the number of the sub-carrier waves used for measurement increases slowly along two sides of each pilot frequency point in an iterative process, and thus the influence caused by the ICI is suppressed. The performance of the incremental iterative time-varying channel evaluation and ICI elimination method of fast OFDM system is improved significantly compared with an existing algorithm in the circumstance that signal noise ratio (SNR) is small.

Description

A kind of progressive iteration time-varying harmonic detection of fast change ofdm system and ICI removing method

Technical field

The present invention relates to a kind of progressive OFDM iterative channel estimation method eliminated with ICI.Belong to the association area of channel estimation studies in radio communication.

Technical background

OFDM (Orthogonal Frequency Division Multiplexing, OFDM) be the one of multi-carrier modulation, its thought channel is divided into several mutually orthogonal subcarriers, convert serial data at a high speed to parallel many groups low rate data streams, be adjusted to respectively on these subcarriers and transmit, to improve the availability of frequency spectrum.If the signal bandwidth on subcarrier is less than the correlation bandwidth of channel, then subcarrier can regard flatness decline as, thus eliminates intersymbol interference.Due to its high spectrum utilization and good antijamming capability, OFDM technology has been widely used in the audio frequency of broadcast type, video field and commercial signal communication system, and main application comprises: the digital audio broadcasting (DAB), digital video broadcasting (DVB), high definition TV (HDTV), wireless lan (wlan) etc. of asymmetrical Digital Subscriber Loop (ADSL), etsi standard.

OFDM technology can be subject to the frequency selective characteristic decline caused by channel multi-path time delay simultaneously, and the impact of the time selective fading caused by the doppler spread of channel, and systematic function is declined.Frequency selective characteristic causes change thus have influence on its amplitude and phase place the time of advent of Received signal strength.Selection of time characteristic causes the orthogonality between ofdm system subcarrier to be affected, and causes the interference (intersubcarrier interference, ICI) between subcarrier, causes the hydraulic performance decline of system.Particularly in high-speed mobile situation, in an OFDM symbol, channel also can great changes will take place, and the impact of ICI can be more serious.

For this reason, there is multiple channel estimation method at present, estimated by the method inserting pilot tone and difference.But these algorithms may be inapplicable in the ofdm system of high-speed mobile.In the recent period, basis expansion model (Basis Expansion Model, BEM) algorithm is widely used in simulation time-frequency doubly selective channel, according to the difference of used base, complex exponential base BEM algorithm (CE-BEM) can be divided into, discrete cosine transform BEM(DTC-BEM), polynomial basis BEM(P-BEM), the spherical BEM(DPS-BEM of discrete expansion) and discrete Karhuen-LoeveBEM(KL-BEM).Among these algorithms, P-BEM algorithm performance is best.In order to reduce ICI, be suggested from technology for eliminating.By by information MAP on one group of subcarrier, producing ICI from eliminating, but the reduction of spectrum efficiency can be caused.Separately have algorithm to join in channel estimating by Data Detection, Data Detection for the iterative algorithm in channel estimating and date restoring, thus improves the effect estimated.Namely iterative algorithm wherein considers the iterative algorithm of the Kalman filtering of Given information.Data Detection Algorithm carries out QR decomposition to channel matrix, revises the error of data to eliminate ICI.But because ICI can affect the accuracy of frequency domain estimation, under the environment of fast moving, need to carry out a large amount of iteration, the result of channel estimating is also inaccurate when signal to noise ratio (snr) is lower.

Summary of the invention

1. fast progressive iteration time-varying harmonic detection and the ICI removing method becoming ofdm system, it is characterized in that, in the channel estimating of ofdm system, using the denoising object of ICI and noise sum SIN as Kalman filter, from only using pilot point information, increase the information being used for iterative computation progressively, realize according to following steps:

Step (1), transmitting terminal produces and sends data, is inserted into by pilot data sends in data according to Comb Pilot mode:

Transmitting terminal is set as follows: s represents s OFDM symbol, s=1, and 2 ..., s ... S, each OFDM symbol comprises N number of subcarrier, n=1, and 2 ..., n ..., N, wherein comprises N _pindividual frequency pilot sign and N _dindividual data symbol, N _d+ N _p=N, n _p=1,2 ..., N _p, the location matrix of pilot tone on frequency domain is expressed as: wherein and ensure N _p>=L, L are the maximum of channel multi-path number l, i.e. l=1,2 ..., l ..., L, N _pindividual pilot tone to be inserted among N number of carrier wave by average and remain unchanged in transmitting procedure, and in N number of carrier wave, pilot point symbol is expressed as ${x_p}^{\left(s\right)}=x^{\left(s\right)}\left(P_s\right)={[{x_{p_1}}^{\left(s\right)},{x_{p_2}}^{\left(s\right)},\·\·\·,{x_{{p_N}_p}}^{\left(s\right)}]}^T,$

Step (2), data are sent to receiving terminal by ofdm system, after receiving terminal removes Cyclic Prefix, carry out modeling according to the following steps with polynomial basis extended model P-BEM to channel:

Step (2.1), utilizes polynomial basis extended model P-BEM to describe and has the two time dispersive channel selecting characteristic of time-frequency, then the channel impulse response h in the n-th subcarrier l footpath of s OFDM symbol ^(s)(n, l) is expressed as:

h ^(s)(n,l)＝QC _l ^(s)+ξ _l ^(s)(n),0≤n≤N-1，

Wherein, ξ _l ^(s)represent the model error in the l footpath of each OFDM symbol during modeling, its value is less than 10 ^-3, ignoring when calculating, namely thinking h ^(s)(n, l)=QC _l ^(s), Q is the orthogonal basis function matrix of a N × B, C _l ^(s)then by B coefficient corresponding to basic function the vector of composition ${C_l}^{\left(s\right)}={[c_{1,l}^{\left(s\right)},c_{2,l}^{\left(s\right)},\·\·\·,c_{b,l}^{\left(s\right)},\·\·\·,c_{B,l}^{\left(s\right)}]}^T,$ f _maxthe highest frequency of channel, T _sthe sampling time,

Step (2.2), is expressed as following form by the Received signal strength at receiving terminal:

y ^(s)＝H ^(s)x ^(s)+W ^(s)，

Wherein, x ^(s)=[x ₁ ^(s), x ₂ ^(s)x _n ^(s)] ^t, y ^(s)=[y ₁ ^(s), y ₂ ^(s)..., y _n ^(s)] ^tto represent on frequency domain that s is removed the transmission signal after Cyclic Prefix and Received signal strength, W respectively ^(s)the white noise on its frequency domain, H ^(s)the channel matrix of N × N:

Wherein, each element of matrix be the channel impulse response of multipath channel and, account form is as follows:

$H^{\left(s\right)}(m,k)=\underset{l=0}{\overset{L-1}{\mathrm{\Σ}}}{G_l}^{\left(s\right)}(M,K)e^{-j2\mathrm{\π}(\frac{k-1}{N}-\frac{1}{2}){\mathrm{\τ}}_l},$

M, k represent above-mentioned matrix H ^(s)the value of m capable k row, m=1,2 ..., m ..., M, M≤N, k=1,2 ..., k ..., K, K≤N, τ _lthe time delay in l footpath, G _l ^(s)(M, K) is the corresponding frequency domain presentation matrix of Channel Impulse, and its each element is calculated as follows:

${G_l}^{\left(s\right)}(m,k)=\frac{1}{N}\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}{h}^{\left(s\right)}(n,l)e^{-j2\mathrm{\π}(m-k)n/N},$

Step (2.3), carries out modeling again according to P-BEM model by Received signal strength, and the expression formula be expressed as with P-BEM coefficient is as follows:

y ^(s)＝Φ ^(s)g ^(s)+W ^(s)，

Wherein,

G ^(s)=[C ₁ ^{(s) T}, C ₂ ^{(s) T}c _l ^{(s) T}] ^t, represent the coefficient matrix in P-BEM algorithm,

after representing modeling again, the coefficient matrix relevant to sending data, its computational methods are as follows:

$Z_l^{\left(s\right)}=\frac{1}{N}[D_1\mathrm{diag}\left(x^{\left(s\right)}\right){\mathrm{\Γ}}_l,\·\·\·,D_b\mathrm{diag}\left(x^{\left(s\right)}\right){\mathrm{\Γ}}_l,\·\·\·,D_B\mathrm{diag}\left(x^{\left(s\right)}\right){\mathrm{\Γ}}_l],$ Wherein,

${\mathrm{\Γ}}_l={\left[\begin{array}{cccc}{e}^{-j2\mathrm{\π}(\frac{p_1}{N}-\frac{1}{2}){\mathrm{\τ}}_l}& e^{-j2\mathrm{\π}(\frac{p_2-1}{N}-\frac{1}{2}){\mathrm{\τ}}_l}& \·\·\·& e^{-j2\mathrm{\π}(\frac{{p_N}_p-1}{N}-\frac{1}{2}){\mathrm{\τ}}_l}\end{array}\right]}^T,$ The Fourier transform in l footpath,

Γ=[Γ ₁, Γ ₂..., Γ _l], represent total Fourier transform matrix in L footpath,

Diag (x ^(s)) represent with vector x ^(s)for the matrix of diagonal element,

Step (3), utilizes AR model to carry out modeling to channel BEM coefficient:

Step (3.1), is calculated as follows C _l ^(s)correlation matrix:

$R_{C_l}^{\left(j\right)}={\left({\left(Q\right)}^{H}Q\right)}^{-1}{\left(Q\right)}^H{R}_{h(n,l)}^{\left(j\right)}Q{\left({\left(Q\right)}^{H}Q\right)}^{-1},$

Wherein, j represents relevant exponent number, namely carries out the mark space of the OFDM symbol of related operation, and the value of j is [-1,0,1], represent the C of current ofdm signal respectively _l ^(s)with the C of previous symbol _l ^(s-1)correlation matrix, the C of current ofdm signal _l ^(s)autocorrelation matrix, the C of current ofdm signal _l ^(s)with the C of a rear symbol _l ^(s+1) correlation matrix.() ^hrepresent Hermitian computing, $R_{h(n,l)}^{\left(j\right)}=E\left[h(n,l)h^{*}(n+j,l)\right]={\mathrm{\σ}}_{h(n,l)}^2{J}_0\left(2\mathrm{\π}{f}_d{T}_{s}j\right),$ Wherein E [] represents average, J ₀() represents the zero Bessel function of the first kind, f _d=vf _cthe maximum doppler frequency that/c is the translational speed of terminal when being v, f _cbe carrier frequency, c is the light velocity, represent the variance of the channel impulse response in l footpath, and suppose

Step (3.2), obtains the state transition equation of channel P-BEM parameter according to Yule-Walker equation:

g _(s)＝Ag _(s-1)+U _(s)，

Ofdm system is sent the time sequencing g of symbol ^(s)regard state migration procedure g in control system as _(s), i.e. g ^(s)=g _(s), state transition equation coefficient A=diag (a ₁, a ₂..., a _l... a _l), diag (x) expression take vector x as the matrix of diagonal element, U _(s)represent the modeling error of the AR model of s OFDM symbol;

Step (4), initialization is carried out to Kalman filter and calculates initial renewal equation:

Step (4.1), according to the following formula initialization is carried out to Kalman filter:

$g_{\left(0\right|0)}=0_{\mathrm{LB},1},$ $P_{\left(0\right|0)}=\mathrm{diag}(R_{C_1}^{\left(0\right)},R_{C_2}^{\left(0\right)}\·\·\·R_{C_L}^{\left(0\right)}),$

Form as and P _(s|s)the previous s of middle subscript all represents that current state is g _(s), a rear s represents s OFDM symbol, p _(0|0)the initial value for calculating, represent the g of OFDM symbol _(s)initial value, P _(0|0)represent corresponding error correlation matrix, O _{lB, 1}the null matrix of LB × 1,

Step (4.2), is calculated as follows the initial time renewal equation of Kalman:

i＝1，s＝1，

${\hat{g}}_{\left(s\right)}=A{\hat{g}}_{\left(0\right|0)},$

P _(s)＝AP _(0|0)(A) ^H+V[U _(s)]，

I represents iterations, represent state estimation g in Kalman equation _(s)intermediate variable, P _(s)represent intermediate variable corresponding error correlation matrix; Covariance matrix is represented, V [U with V [] _(s)]=diag (u ₁, u ₂u _l),

Step (5), carry out first time iterative channel estimation computing, now iterations i=1, only use the subcarrier place at pilot point place to receive data in current iteration and do channel estimating, data except the subcarrier of pilot point place on other subcarriers are considered as ICI, eliminate unknown data to the impact of pilot tone place channel estimating by SIN method, realize the pilot aided Kalman channel estimating without ICI interference, concrete steps are as follows:

Step (5.1), only the Received signal strength of carrier position corresponding for each pilot point in Received signal strength is used for calculating, and Received signal strength is divided into each pilot point data on sub-carriers, data on other subcarrier except pilot point subcarrier, to the interference of each pilot point place subcarrier and noise three part, are shown below:

${y_p}^{\left(s\right)}=y^{\left(s\right)}\left(P_s\right)={H^{\left(s\right)}}_{[P_s,P_s]}{x_{p_{n_p}}}^{\left(s\right)}+{H^{\left(s\right)}}_{[P_s,d_{n_p{n}^{\′}}]}{x_{d_{n_p{n}^{\′}}}}^{\left(s\right)}+W^{\left(s\right)}\left(P_s\right)$

Wherein, $P_s=[p_1,p_2,\·\·\·,p_{N_p}],$ ${x_{d_{n_p{n}^{\′}}}}^{\left(s\right)}={[x^{\left(s\right)}\left(d_{11}\right),x^{\left(s\right)}\left(d_{12}\right),\·\·\·{,x}^{\left(s\right)}\left(d_{{1N}^{\′}}\right),x^{\left(s\right)}\left(d_{21}\right),\·\·\·,x^{\left(s\right)}\left(d_{N_p{N}^{\′}}\right)]}^T,$ n'=1,2 ..., N' represents the distance between each adjacent pilot point, a N _p× N _punit matrix, σ ²white Gaussian noise W ^(s)variance, in above formula Section 2 be data on other subcarrier except pilot point subcarrier to the interference ICI of pilot point place subcarrier,

Step (5.2), is considered to interchannel noise W by data ICI distracter ^(s)(P _s) a part as the denoising object of filter, the method that the algorithm in step (2) is estimated according to SIN is rewritten, order the Kalman observational equation that then SIN estimates is expressed as:

$y_{p\left(s\right)}={{\mathrm{\Φ}}^{\mathrm{SIN}}}_{\left(s\right)}{g}_{\left(s\right)}+W_{\left(s\right)}^{\mathrm{SIN}},$

Wherein:

${{\mathrm{\Φ}}^{\mathrm{SIN}}}_{\left(s\right)}=\frac{1}{N}[{z_1^{\left(s\right)}}_{\mathrm{SIN}},{Z_2^{\left(s\right)}}_{\mathrm{SIN}}\·\·\·{Z_L^{\left(s\right)}}_{\mathrm{SIN}}],$

${Z_l^{\left(s\right)}}_{\mathrm{SIN}}=\frac{1}{N}[D_1^{\mathrm{SIN}}\mathrm{diag}\left({x_p}^{\left(s\right)}\right){\mathrm{\Γ}}_l^{\mathrm{SIN}}\·\·\·D_B^{\mathrm{SIN}}\mathrm{diag}\left({x_p}^{\left(s\right)}{\mathrm{\Γ}}_l^{\mathrm{SIN}}\right)],$

${\mathrm{\Γ}}_l^{\mathrm{SIN}}={\left[\begin{array}{cccc}{e}^{-j2\mathrm{\π}(\frac{p_1}{N}-\frac{1}{2}){\mathrm{\τ}}_1}& e^{-j2\mathrm{\π}(\frac{p_2-1}{N}-\frac{1}{2}){\mathrm{\τ}}_l}& \·\·\·& e^{-j2\mathrm{\π}(\frac{{p_N}_p-1}{N}-\frac{1}{2}){\mathrm{\τ}}_l}\end{array}\right]}^T,$

${\mathrm{\Γ}}^{\mathrm{SIN}}=\left[\begin{array}{cccc}{{\mathrm{\Γ}}_1}^{\mathrm{SIN}},& {{\mathrm{\Γ}}_2,}^{\mathrm{SIN}}& \·\·\·,& {{\mathrm{\Γ}}_l}^{\mathrm{SIN}}\end{array}\right]$

Step (5.3), calculates covariance matrix

Suppose in calculating that ICI is white Gaussian noise, order because both noise and ICI are separate, so $V\left[W_{\left(s\right)}^{\mathrm{SIN}}\right]=U_{\mathrm{ICI}}+V\left[W^{\left(s\right)}\left(P_s\right)\right];$

U _iCIthe calculating formula of each element in matrix is:

$U_{\mathrm{ICI}}(m,k)=R_{\mathrm{ICI}}^{\left(j\right)}\≈4{\mathrm{\π}}^2{T_s}^2{E}_s\left(\underset{l=0}{\overset{L-1}{\mathrm{\Σ}}}{\mathrm{\σ}}_{h(n,l)}^2{\mathrm{\σ}}_{D_l}\right)\mathrm{\ρ}(\mathrm{\α},\mathrm{rag},N),$

Wherein, the capable k row of m of m, k representing matrix, E _sthe power sending data, be power be P _vtime the general function of Doppler power, f is transmission frequency, and α represents that most marginal date for iteration is apart from the distance of each corresponding pilot point, be 0, rag is the precision calculated when first time calculates, rag=[0,1,2,3], and:

ρ(α,rag，N)=ρ(0,rag,N)-ρ ₁(α,rag,N)，

Step (5.4), calculates kalman gain K by following three formulas respectively _(s), s OFDM symbol transfers to state state estimation matrix and with corresponding covariance matrix P _(s|s), form observation renewal equation group, wherein, Φ=Φ ^sIN, $W_{\left(s\right)}=W_{\left(s\right)}^{\mathrm{SIN}},$

K _(s)＝P _(s)(Φ _(s)) ^H(Φ _(s)P _(s)(Φ _(s)) ^H+V[W _(s)]) ^-1，

${\hat{g}}_{\left(s\right|s)}={\hat{g}}_{\left(s\right)}+K_{\left(s\right)}(y_{\left(s\right)}-{\mathrm{\Φ}}_{\left(s\right)}{\hat{g}}_{\left(s\right)}),$

P _(s|s)＝P _(s)-K _(s)Φ _(s)P _(s)，

Step (5.5), calculates channel matrix H according to following formula ^(s)estimated value:

$H^{\left(s\right)}=\frac{1}{N}\underset{b=1}{\overset{B}{\mathrm{\Σ}}}{D}_b\mathrm{diag}\left(\mathrm{\Γ}{\hat{g}}_{\left(s\right|s)}\right),$

Step (5.6), utilizes following formula to carry out QR decomposition to channel matrix, obtains matrix R ^(s):

H ^(s)＝IR ^(s)

Wherein I is a unit matrix, R ^(s)a upper triangular matrix,

Step (5.7), by following formula, QR Data Detection is carried out to data:

Wherein y ' ^(s)=(I) ^hy ^(s), with the result after the detected value of data and detected value planisphere quantize respectively, [] _{m, k}represent the capable k row of m of matrix, [] _mm element of vector, [] _kbe a kth element of vector, O () represents demodulation computing, m, k representing matrix H ^(s)the value of m capable k row, m=1,2 ..., m ..., M, M≤N, k=1,2 ..., k ..., K, K≤N,

Step (6), iterations i=i+1, during iterative computation number of times i>1, the data that subcarrier place receives that the subcarrier at second time iteration pilot point place place is adjacent with its both sides do channel estimating, data on its remaining sub-carriers are considered as ICI, thereafter the data for calculating that at every turn increase of iteration, be the data that last iteration receives for the subcarrier place of the subcarrier both sides at data place calculated, data on its remaining sub-carriers are considered as ICI, and it is as described below that SIN method carries out iterative channel estimation computing:

Step (6.1), Received signal strength is divided into pilot point place subcarrier data, for the subcarrier data at data place calculated, not for the data that calculate to pilot point with for the interference of data place subcarrier that calculates and noise four part, be shown below:

In above formula, Section 3 is the ICI interference after upgrading,

Step (6.2), the method described in step (5.2) calculates Φ ^sIN _(s),

Step (6.3), increase with iterations, the data for iteration increase, and now upgrade covariance matrix U _iCIbe calculated as follows:

$U_{\mathrm{ICI}}\≈4{\mathrm{\π}}^2{T_s}^2{E}_s\left(\underset{l=0}{\overset{L-1}{\mathrm{\Σ}}}{\mathrm{\σ}}_{h(n,l)}^2{\mathrm{\σ}}_{D_l}\right)[\frac{1}{2}\mathrm{\ρ}(A+m,\mathrm{rag},N)+\frac{1}{2}\mathrm{\ρ}(A-m,\mathrm{rag},N)]$

Wherein, A+m represent on the right side of pilot point for the data that the calculate distance to corresponding pilot point, A-m represent on the left of pilot point for the data that the calculate distance to the pilot point of correspondence,

Step (6.4), calculates kalman gain K by the described method of step (5.5) _(s), s OFDM symbol transfers to state state estimation matrix and with corresponding covariance matrix P _(s|s), form observation renewal equation group, wherein, Φ=Φ ^sIN,

K _(s)＝P _(s)(Φ _(s)) ^H(Φ _(s)P _(s)(Φ _(s)) ^H+V[W _(s)]) ^-1，

${\hat{g}}_{\left(s\right|s)}={\hat{g}}_{\left(s\right)}+K_{\left(s\right)}(y_{\left(s\right)}-{\mathrm{\Φ}}_{\left(s\right)}{\hat{g}}_{\left(s\right)}),$

P _(s|s)＝P _(s)-K _(s)Φ _(s)P _(s)，

Step (6.5), calculates the estimated value H of channel matrix by step (5.5) described method ^(s):

$H^{\left(s\right)}=\frac{1}{N}\underset{b=1}{\overset{B}{\mathrm{\Σ}}}{D}_b\mathrm{diag}\left(\mathrm{\Γ}{\hat{g}}_{\left(s\right|s)}\right),$

Step (6.6), carries out QR decomposition by step (5.6) described method to channel matrix and obtains R ^(s):

H ^(s)＝IR ^(s)，

Step (6.7), by step (5.7) described method, QR Data Detection is carried out to data:

Step (7), judge whether that whether all data are all for iteration, if so, then algorithm terminates, if not, then continue,

Step (8), by judging the number of times of iteration, determine the input data the need of increasing iterative algorithm, evaluation algorithm is as follows:

Setting step delta, relatively iterations i and Δ μ+2, wherein, $\mathrm{\&mu;}=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,\mathrm{\&Delta;}\&CenterDot;\mathrm{\&mu;}+2<\frac{N}{N_p},$ If i=Δ μ+2, then select for data for calculating that the data at the subcarrier place of the subcarrier both sides at data place calculated newly add as next iteration, with together with the data that calculate, bring SIN algorithm into, be brought in step (6) and again count;

If i ≠ Δ μ+2, then not increasing the data for calculating, returning step (6) and carrying out iteration;

Terminate.

Accompanying drawing explanation

Fig. 1 is the ofdm system that the present invention is suitable for;

Fig. 2 is general principle flow chart of the present invention;

Fig. 3 is the progressive step-length schematic diagram related in the present invention.Wherein Fig. 3 (a) represents Received signal strength when calculating for the first time, and wherein 1. namely the part of black represents frequency place subcarrier 3. the subcarrier at ICI place is represented ${x_{d_{n_p{n}^{\&prime;}}}}^{\left(s\right)}={[x^{\left(s\right)}\left(d_{11}\right),x^{\left(s\right)}\left(d_{12}\right),\&CenterDot;\&CenterDot;\&CenterDot;,x^{\left(s\right)}\left(d_{{1N}^{\&prime;}}\right),x^{\left(s\right)}\left(d_{21}\right),\&CenterDot;\&CenterDot;\&CenterDot;,x^{\left(s\right)}\left(d_{N_p{N}^{\&prime;}}\right)]}^T;$ Fig. 3 (b) represents Received signal strength during second time calculating, wherein 1. represents pilot point place subcarrier 2. represent that current iteration newly adds the subcarrier at the data place of calculating with 3. represent the subcarrier at ICI place, 4. represent α, namely for the distance between the data at the most edge of iteration and pilot point, now α=1,5. represents the distance between pilot point fig. 3 (c) represents iterations i=Δ μ+2, and Received signal strength during i > 2, wherein 1. represent the data place subcarrier of last time for calculating

${x^{\left(s\right)}\left(p_{N_p}\right)+[x^{\left(s\right)}\left(d_{11}\right),x^{\left(s\right)}\left(d_{12}\right),\&CenterDot;\&CenterDot;\&CenterDot;,x^{\left(s\right)}\left(d_{1(i-1)}\right),\&CenterDot;\&CenterDot;\&CenterDot;x^{\left(s\right)}\left(d_{n_{p}1}\right),\&CenterDot;\&CenterDot;\&CenterDot;,x^{\left(s\right)}\left(d_{n_{p(i-1)}}\right),\&CenterDot;\&CenterDot;\&CenterDot;,x^{\left(s\right)}\left(d_{N_p(i-1)}\right)]}^T,$ 2. represent that current iteration newly adds the subcarrier at the data place of calculating with 4. α is represented, now, α=Δ+1;

Fig. 4 be the present invention with based on Kalman but the performance comparison of the channel estimation method of untreated ICI.Wherein

with to represent respectively in conventional method 1 time, 3 times and result after 10 iteration,

With represent the result after crossing of the present invention 1 time, 3 times and 10 iteration, represent data whole known time,

The theoretical value upper limit of this kind of algorithm.

Embodiment

The progressive iteration time-varying harmonic detection of fast change ofdm system and ICI removing method, it is characterized in that, in the channel estimating of ofdm system, using the denoising object of ICI and noise sum SIN as Kalman filter, from only using pilot point information, increase the information being used for iterative computation progressively, realize according to following steps:

Step (1), transmitting terminal produces and sends data, is inserted into by pilot data sends in data according to Comb Pilot mode:

Transmitting terminal is set as follows: s represents s OFDM symbol, s=1, and 2 ..., s ... S, each OFDM symbol comprises N number of subcarrier, n=1, and 2 ..., n ..., N, wherein comprises N _pindividual frequency pilot sign and N _dindividual data symbol, N _d+ N _p=N, n _p=1,2 ..., N _p, the location matrix of pilot tone on frequency domain is expressed as: wherein and ensure N _p>=L, L are the maximum of channel multi-path number l, i.e. l=1,2 ..., l ..., L, N _pindividual pilot tone to be inserted among N number of carrier wave by average and remain unchanged in transmitting procedure, and in N number of carrier wave, pilot point symbol is expressed as ${x_p}^{\left(s\right)}=x^{\left(s\right)}\left(P_s\right)={[{x_{p_1}}^{\left(s\right)},{x_{p_2}}^{\left(s\right)},\&CenterDot;\&CenterDot;\&CenterDot;,{x_{{p_N}_p}}^{\left(s\right)}]}^T,$

Step (2), data are sent to receiving terminal by ofdm system, after receiving terminal removes Cyclic Prefix, carry out modeling according to the following steps with polynomial basis extended model P-BEM to channel:

Step (2.1), utilizes polynomial basis extended model P-BEM to describe and has the two time dispersive channel selecting characteristic of time-frequency, then the channel impulse response h in the n-th subcarrier l footpath of S OFDM symbol ^(s)(n, l) is expressed as:

h ^(s)(n,l)＝QC _l ^(s)+ξ _l ^(s)(n),0≤n≤N-1，

Wherein, ξ ₁ ^(s)represent the model error in the l footpath of each OFDM symbol during modeling, its value is less than 10 ^-3, ignoring when calculating, namely thinking h ^(s)(n, l)=QC _l ^(s), Q is the orthogonal basis function matrix of a N × B, C _l ^(s)then by B coefficient corresponding to basic function the vector of composition ${{C_l}^{\left(s\right)}=[c_{1,l}^{\left(s\right)},c_{2,l}^{\left(s\right)},\&CenterDot;\&CenterDot;\&CenterDot;,c_{b,l}^{\left(s\right)},\&CenterDot;\&CenterDot;\&CenterDot;,c_{B,l}^{\left(s\right)}]}^T,$ f _maxthe highest frequency of channel, T _sthe sampling time,

Step (2.2), is expressed as following form by the Received signal strength at receiving terminal:

y ^(s)＝H ^(s)x ^(s)+W ^(s)，

Wherein, x ^(s)=[x ₁ ^(s), x ₂ ^(s)x _n ^(s)] ^t, y ^(s)=[y ₁ ^(s), y ₂ ^(s)..., y _n ^(s)] ^tto represent on frequency domain that s is removed the transmission signal after Cyclic Prefix and Received signal strength, W respectively ^(s)the white noise on its frequency domain, H ^(s)the channel matrix of N × N:

Wherein, each element of matrix be the channel impulse response of multipath channel and, account form is as follows:

$H^{\left(s\right)}(m,k)=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{G_l}^{\left(s\right)}(M,K)e^{-j2\mathrm{\&pi;}(\frac{k-1}{N}-\frac{1}{2}){\mathrm{\&tau;}}_l},$

M, k represent above-mentioned matrix H ^(s)the value of m capable k row, m=1,2 ..., m ..., M, M≤N, k=1,2 ..., k ..., K, K≤N, τ _lthe time delay in l footpath, G _l ^(s)(M, K) is the corresponding frequency domain presentation matrix of Channel Impulse, and its each element is calculated as follows:

$G_l^{\left(s\right)}(m,k)=\frac{1}{N}\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{h}^{\left(s\right)}(n,l)e^{-j2\mathrm{\&pi;}(m-k)n/N},$

Step (2.3), carries out modeling again according to P-BEM model by Received signal strength, and the expression formula be expressed as with P-BEM coefficient is as follows:

y ^(s)＝Φ ^(s)g ^(s)+W ^(s)，

Wherein,

G ^(s)=[C ₁ ^{(s) T}, C ₂ ^{(s) T}c _l ^{(s) T}] ^t, represent the coefficient matrix in PBEM algorithm,

after representing modeling again, the coefficient matrix relevant to sending data, its computational methods are as follows:

$Z_l^{\left(s\right)}=\frac{1}{N}[D_1\mathrm{diag}\left(x^{\left(s\right)}\right){\mathrm{\&Gamma;}}_l,\&CenterDot;\&CenterDot;\&CenterDot;,D_b\mathrm{diag}\left(x^{\left(s\right)}\right){\mathrm{\&Gamma;}}_l,\&CenterDot;\&CenterDot;\&CenterDot;,D_B\mathrm{diag}\left(x^{\left(s\right)}\right){\mathrm{\&Gamma;}}_l],$ Wherein,

${\mathrm{\&Gamma;}}_l={\left[\begin{array}{cccc}{e}^{-j2\mathrm{\&pi;}(\frac{p_1}{N}-\frac{1}{2}){\mathrm{\&tau;}}_l}& e^{-j2\mathrm{\&pi;}(\frac{p_2-1}{N}-\frac{1}{2}){\mathrm{\&tau;}}_l}& \&CenterDot;\&CenterDot;\&CenterDot;& e^{-j2\mathrm{\&pi;}(\frac{{p_N}_p-1}{N}-\frac{1}{2}){\mathrm{\&tau;}}_l}\end{array}\right]}^T,$ The Fourier transform in l footpath,

Γ=[Γ ₁, Γ ₂..., Γ _l], represent total Fourier transform matrix in L footpath,

Diag (x ^(s)) represent with vector x ^(s)for the matrix of diagonal element,

Step (3), utilizes AR model to carry out modeling to channel BEM coefficient:

Step (3.1), is calculated as follows C _l ^(s)correlation matrix:

$R_{C_l}^{\left(j\right)}={\left({\left(Q\right)}^{H}Q\right)}^{-1}{\left(Q\right)}^H{R}_{h(n,l)}^{\left(j\right)}Q{\left({\left(Q\right)}^{H}Q\right)}^{-1},$

Wherein, j represents relevant exponent number, namely carries out the mark space of the OFDM symbol of related operation, and the value of j is [-1,0,1], represent the C of current ofdm signal respectively _l ^(s)with the C of previous symbol _l ^(s-1)correlation matrix, the C of current ofdm signal _l ^(s)autocorrelation matrix, the C of current ofdm signal _l ^(s)with the C of a rear symbol _l ^(s+1) correlation matrix.() ^hrepresent Hermitian computing, $R_{h(n,l)}^{\left(j\right)}=E\left[h(n,l)h^{*}(n+j,l)\right]={\mathrm{\&sigma;}}_{h(n,l)}^2{J}_0\left(2\mathrm{\&pi;}{f}_d{T}_{s}j\right),$ Wherein E [] represents average, J ₀() represents the zero Bessel function of the first kind, f _d=vf _cthe maximum doppler frequency that/c is the translational speed of terminal when being v, f _cbe carrier frequency, c is the light velocity, represent the variance of the channel impulse response in l footpath, and suppose

Step (3.2), obtains the state transition equation of channel P-BEM parameter according to YuleWalker equation:

g _(s)＝Ag _(s-1)+U _(s)，

Ofdm system is sent the time sequencing g of symbol ^(s)regard state migration procedure g in control system as _(s), i.e. g ^(s)=g _(s), state transition equation coefficient A=diag (a ₁, a ₂..., a _l... a _l), diag (x) expression take vector x as the matrix of diagonal element, U _(s)represent the modeling error of the AR model of s OFDM symbol;

Step (4), initialization is carried out to Kalman filter and calculates initial renewal equation:

Step (4.1), according to the following formula initialization is carried out to Kalman filter:

${\hat{g}}_{\left(0\right|0)}=0_{LB,1},P_{\left(0\right|0)}=\mathrm{diag}(R_{C_1}^{\left(0\right)},R_{C_2}^{\left(0\right)}\&CenterDot;\&CenterDot;\&CenterDot;R_{C_L}^{\left(0\right)}),$

Form as and P _(s|s)the previous s of middle subscript all represents that current state is g _(s), a rear s represents s OFDM symbol, p _(0|0)the initial value for calculating, represent the g of OFDM symbol _(s)initial value, P _(0|0)represent corresponding error correlation matrix, O _{lB, 1}the null matrix of LB × 1,

Step (4.2), is calculated as follows the initial time renewal equation of Kalman:

i＝1，s＝1，

${\hat{g}}_{\left(s\right)}=A{\hat{g}}_{\left(0\right|0)},$

P _(s)＝AP _(0|0)(A) ^H+V[U _(s)]，

I represents iterations, represent state estimation g in Kalman equation _(s)intermediate variable, P _(s)represent intermediate variable corresponding error correlation matrix; Covariance matrix is represented, V [U with V [] _(s)]=diag (u ₁, u ₂u _l),

Step (5), carry out first time iterative channel estimation computing, now iterations i=1, only use the subcarrier place at pilot point place to receive data in current iteration and do channel estimating, data except the subcarrier of pilot point place on other subcarriers are considered as ICI, eliminate unknown data to the impact of pilot tone place channel estimating by SIN method, realize the pilot aided Kalman channel estimating without ICI interference, concrete steps are as follows:

Step (5.1), only the Received signal strength of carrier position corresponding for each pilot point in Received signal strength is used for calculating, and Received signal strength is divided into each pilot point data on sub-carriers, data on other subcarrier except pilot point subcarrier, to the interference of each pilot point place subcarrier and noise three part, are shown below:

${y_p}^{\left(s\right)}=y^{\left(s\right)}\left(P_s\right)={H^{\left(s\right)}}_{[P_s,P_s]}{x_{{p_n}_p}}^{\left(s\right)}+{H^{\left(s\right)}}_{[P_s,d_{n_p{n}^{\&prime;}]}}{x_{d_{n_p{n}^{\&prime;}}}}^{\left(s\right)}+W^{\left(s\right)}\left(P_s\right)$

Wherein, $P_s=[p_1,p_2,\&CenterDot;\&CenterDot;\&CenterDot;,{p_N}_p],$ ${x_{d_{n_p{n}^{\&prime;}}}}^{\left(s\right)}={[x^{\left(s\right)}\left(d_{11}\right),x^{\left(s\right)}\left(d_{12}\right),\&CenterDot;\&CenterDot;\&CenterDot;{,x}^{\left(s\right)}\left(d_{{1N}^{\&prime;}}\right),x^{\left(s\right)}\left(d_{21}\right),\&CenterDot;\&CenterDot;\&CenterDot;,x^{\left(s\right)}\left(d_{N_p{N}^{\&prime;}}\right)]}^T,$ n'=1,2 ..., N' represents the distance between each adjacent pilot point, a N _p× N _punit matrix, σ ²white Gaussian noise W ^(s)variance, in above formula Section 2 be data on other subcarrier except pilot point subcarrier to the interference ICI of pilot point place subcarrier,

Step (5.2), is considered to interchannel noise W by data ICI distracter ^(s)(P _s) a part as the denoising object of filter, the method that the algorithm in step (2) is estimated according to SIN is rewritten, order the Kalman observational equation that then SIN estimates is expressed as:

$y_{p\left(s\right)}={{\mathrm{\&Phi;}}^{\mathrm{SIN}}}_{\left(s\right)}{g}_{\left(s\right)}+W_{\left(s\right)}^{\mathrm{SIN}},$

Wherein:

${{\mathrm{\&Phi;}}^{\mathrm{SIN}}}_{\left(s\right)}=\frac{1}{N}[{z_1^{\left(s\right)}}_{\mathrm{SIN}},{Z_2^{\left(s\right)}}_{\mathrm{SIN}}\&CenterDot;\&CenterDot;\&CenterDot;{Z_L^{\left(s\right)}}_{\mathrm{SIN}}],$

${Z_l^{\left(s\right)}}_{\mathrm{SIN}}=\frac{1}{N}[D_1^{\mathrm{SIN}}\mathrm{diag}\left({x_p}^{\left(s\right)}\right){\mathrm{\&Gamma;}}_l^{\mathrm{SIN}}\&CenterDot;\&CenterDot;\&CenterDot;D_B^{\mathrm{SIN}}\mathrm{diag}\left({x_p}^{\left(s\right)}\right){\mathrm{\&Gamma;}}_l^{\mathrm{SIN}}],$

${\mathrm{\&Gamma;}}_l^{\mathrm{SIN}}={\left[\begin{array}{cccc}{e}^{-j2\mathrm{\&pi;}(\frac{p_1}{N}-\frac{1}{2}){\mathrm{\&tau;}}_l}& e^{-j2\mathrm{\&pi;}(\frac{p_2-1}{N}-\frac{1}{2}){\mathrm{\&tau;}}_l}& \&CenterDot;\&CenterDot;\&CenterDot;& e^{-j2\mathrm{\&pi;}(\frac{{p_N}_p-1}{N}-\frac{1}{2}){\mathrm{\&tau;}}_l}\end{array}\right]}^T,$

Γ ^SIN＝[Γ ₁ ^SIN,Γ ₂, ^SIN…,Γ _l ^SIN]

Step (5.3), calculates covariance matrix

Suppose in calculating that ICI is white Gaussian noise, order because both noise and ICI are separate, so $V\left[W_{\left(s\right)}^{\mathrm{SIN}}\right]=U_{\mathrm{ICI}}+V\left[W^{\left(s\right)}\left(P_S\right)\right];$

U _iCIthe calculating formula of each element in matrix is:

$U_{\mathrm{ICI}}(m,k)=R_{\mathrm{ICI}}^{\left(j\right)}\&ap;4{\mathrm{\&pi;}}^2{T_s}^2{E}_s\left(\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_{h(n,l)}^2{\mathrm{\&sigma;}}_{D_l}\right)\mathrm{\&rho;}(\mathrm{\&alpha;},\mathrm{rag},N),$

Wherein, the capable k row of m of m, k representing matrix, E _sthe power sending data, be power be P _vtime the general function of Doppler power, f is transmission frequency, and α represents that most marginal date for iteration is apart from the distance of each corresponding pilot point, be 0, rag is the precision calculated when first time calculates, rag=[0,1,2,3], and:

ρ(α,rag，N)=ρ(0,rag,N)-ρ ₁(α,rag,N)

Step (5.4), calculates kalman gain K by following three formulas respectively _(s), s OFDM symbol transfers to state state estimation matrix and with corresponding covariance matrix P _(s|s), form observation renewal equation group, wherein, Φ=Φ ^sIN $W_{\left(s\right)}=W_{\left(s\right)}^{\mathrm{SIN}},$

K _(s)＝P _(s)(Φ _(s)) ^H(Φ _(s)P _(s)(Φ _(s)) ^H+V[W _(s)]) ^-1，

${\hat{g}}_{\left(s\right|s)}={\hat{g}}_{\left(s\right)}+K_{\left(s\right)}(y_{\left(s\right)}-{\mathrm{\&Phi;}}_{\left(s\right)}{\hat{g}}_{\left(s\right)}),$

P _(s|s)＝P _(s)-K _(s)Φ _(s)P _(s)，

Step (5.5), calculates channel matrix H according to following formula ^(s)estimated value:

$H^{\left(s\right)}=\frac{1}{N}\underset{b=1}{\overset{B}{\mathrm{\&Sigma;}}}{D}_b\mathrm{diag}\left(\mathrm{\&Gamma;}{\hat{g}}_{\left(s\right|s)}\right),$

Step (5.6), utilizes following formula to carry out QR decomposition to channel matrix, obtains matrix R ^(s):

H ^(s)＝IR ^(s)

Wherein I is a unit matrix, R ^(s)a upper triangular matrix,

Step (5.7), by following formula, QR Data Detection is carried out to data:

Wherein y ' ^(s)=(I) ^hy ^(s), with the result after the detected value of data and detected value planisphere quantize respectively, [] _{m, k}represent the capable k row of m of matrix, [] _mm element of vector, [] _kbe a kth element of vector, O () represents demodulation computing, m, k representing matrix H ^(s)the value of m capable k row, m=1,2 ..., m ..., M, M≤N, k=1,2 ..., k ..., K, K≤N,

Step (6), iterations i=i+1, during iterative computation number of times i>1, the data that subcarrier place receives that the subcarrier at second time iteration pilot point place place is adjacent with its both sides do channel estimating, data on its remaining sub-carriers are considered as ICI, thereafter the data for calculating that at every turn increase of iteration, be the data that last iteration receives for the subcarrier place of the subcarrier both sides at data place calculated, data on its remaining sub-carriers are considered as ICI, and it is as described below that SIN method carries out iterative channel estimation computing:

Step (6.1), Received signal strength is divided into pilot point place subcarrier data, for the subcarrier data at data place calculated, not for the data that calculate to pilot point with for the interference of data place subcarrier that calculates and noise four part, be shown below:

In above formula, Section 3 is the ICI interference after upgrading,

Step (6.2), the method described in step (5.2) calculates Φ ^sIN _(s),

Step (6.3), increase with iterations, the data for iteration increase, and now upgrade covariance matrix U _iCIbe calculated as follows:

$U_{\mathrm{ICI}}\&ap;4{\mathrm{\&pi;}}^2{{T_s}^{2}E}_s\left(\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_{h(n,l)}^2{\mathrm{\&sigma;}}_{D_l}\right)[\frac{1}{2}\mathrm{\&rho;}(A+m,\mathrm{rag},N)+\frac{1}{2}\mathrm{\&rho;}(A-m,\mathrm{rag},N)]$

Wherein, A+m represent on the right side of pilot point for the data that the calculate distance to corresponding pilot point, A-m represent on the left of pilot point for the data that the calculate distance to the pilot point of correspondence,

Step (6.4), calculates kalman gain K by the described method of step (5.5) _(s), s OFDM symbol transfers to state state estimation matrix and with corresponding covariance matrix P _(s|s), form observation renewal equation group, wherein, Φ=Φ ^sIN,

K _(s)＝P _(s)(Φ _(s)) ^H(Φ _(s)P _(s)(Φ _(s))H+V[W _(s)]) ^-1，

${\hat{g}}_{\left(s\right|s)}={\hat{g}}_{\left(s\right)}+K_{\left(s\right)}(y_{\left(s\right)}-{\mathrm{\&Phi;}}_{\left(s\right)}{\hat{g}}_{\left(s\right)}),$

P _(s|s)＝P _(s)-K _(s)Φ _(s)P _(s)，

Step (6.5), calculates the estimated value H of channel matrix by step (5.5) described method ^(s):

$H^{\left(s\right)}=\frac{1}{N}\underset{b=1}{\overset{B}{\mathrm{\&Sigma;}}}{D}_b\mathrm{diag}\left(\mathrm{\&Gamma;}{\hat{g}}_{\left(s\right|s)}\right),$

Step (6.6), carries out QR decomposition by step (5.6) described method to channel matrix and obtains R ^(s):

H ^(s)＝IR ^(s)，

Step (6.7), by step (5.7) described method, QR Data Detection is carried out to data:

Step (7), judge whether that whether all data are all for iteration, if so, then algorithm terminates, if not, then continue,

Step (8), by judging the number of times of iteration, determine the input data the need of increasing iterative algorithm, evaluation algorithm is as follows:

Setting step delta, relatively iterations i and Δ μ+2, wherein, $\mathrm{\&mu;}=\mathrm{1,2}\&CenterDot;\&CenterDot;\&CenterDot;,\mathrm{\&Delta;}\&CenterDot;\mathrm{\&mu;}+2<\frac{N}{N_p},$ If i=Δ μ+2, then select for data for calculating that the data at the subcarrier place of the subcarrier both sides at data place calculated newly add as next iteration, with together with the data that calculate, bring SIN algorithm into, be brought in step (6) and again count;

If i ≠ Δ μ+2, then not increasing the data for calculating, returning step (6) and carrying out iteration;

Terminate.

Claims (1)

1. fast progressive iteration time-varying harmonic detection and the ICI removing method becoming ofdm system, it is characterized in that, in the channel estimating of ofdm system, using the denoising object of ICI and noise sum SIN as Kalman filter, from only using pilot point information, increase the information being used for iterative computation progressively, realize according to following steps:

Step (1), transmitting terminal produces and sends data, is inserted into by pilot data sends in data according to Comb Pilot mode:

Transmitting terminal is set as follows: s represents s OFDM symbol, s=1, and 2 ..., s ... S, each OFDM symbol comprises N number of subcarrier, n=1, and 2 ..., n ..., N, wherein comprises N _pindividual frequency pilot sign and N _dindividual data symbol, N _d+ N _p=N, n _p=1,2 ..., N _p, the location matrix of pilot tone on frequency domain is expressed as: wherein and ensure N _p>=L, L are the maximums of channel multi-path number l, namely n _pindividual pilot tone to be inserted among N number of carrier wave by average and remain unchanged in transmitting procedure, and in N number of carrier wave, pilot point symbol is expressed as ${x_p}^{\left(s\right)}=x^{\left(s\right)}\left(P_s\right)={[{x_{p_1}}^{\left(s\right)},{x_{p_2}}^{\left(s\right)},\&CenterDot;\&CenterDot;\&CenterDot;,{x_{p_{N_p}}}^{\left(s\right)}]}^T,$

Step (2), data are sent to receiving terminal by ofdm system, after receiving terminal removes Cyclic Prefix, carry out modeling according to the following steps with polynomial basis extended model P-BEM to channel:

Step (2.1), utilizes polynomial basis extended model P-BEM to describe to have the two time dispersive channel selecting characteristic of time-frequency, then and the ^sthe channel impulse response h in the n-th subcarrier l footpath of individual OFDM symbol ^(s)(n, l) is expressed as:

h ^(s)(n,l)＝QC _l ^(s)+ξ _l ^(s)(n),0≤n≤N-1，

Wherein, ξ _l ^(s)represent the model error in the l footpath of each OFDM symbol during modeling, its value is less than 10 ^-3, ignoring when calculating, namely thinking h ^(s)(n, l)=QC _l ^(s), Q is the orthogonal basis function matrix of a N × B, C _l ^(s)then by B coefficient corresponding to basic function the vector of composition f _maxthe highest frequency of channel, T _sthe sampling time,

Step (2.2), is expressed as following form by the Received signal strength at receiving terminal:

y ^(s)＝H ^(s)x ^(s)+W ^(s)，

Wherein, x ^(s)=[x ₁ ^(s), x ₂ ^(s)x _n ^(s)] ^t, y ^(s)=[y ₁ ^(s), y ₂ ^(s)..., y _n ^(s)] ^tto represent on frequency domain that s is removed the transmission signal after Cyclic Prefix and Received signal strength, W respectively ^(s)the white noise on its frequency domain, H ^(s)the channel matrix of N × N:

Wherein, each element of matrix be the channel impulse response of multipath channel and, account form is as follows:

$H^{\left(s\right)}(m,k)=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{G_l}^{\left(s\right)}(M,K)e^{-j2\mathrm{\&pi;}(\frac{k-1}{N}-\frac{1}{2}){\mathrm{\&tau;}}_l},$

M, k represent above-mentioned matrix H ^(s)the value of m capable k row, m=1,2 ..., m ..., M, M≤N, k=1,2 ..., k ..., K, K≤N, τ _lthe time delay in l footpath, G _l ^(s)(M, K) is the corresponding frequency domain presentation matrix of Channel Impulse, and its each element is calculated as follows:

${G_l}^{\left(s\right)}(m,k)=\frac{1}{N}\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{h}^{\left(s\right)}(n,l)e^{-j2\mathrm{\&pi;}(m-k)n/N},$

Step (2.3), carries out modeling again according to P-BEM model by Received signal strength, and the expression formula be expressed as with P-BEM coefficient is as follows:

y ^(s)＝Φ ^(s)g ^(s)+W ^(s)，

Wherein,

G ^(s)=[C ₁ ^{(s) T}, C ₂ ^{(s) T}c _l ^{(s) T}] ^t, represent the coefficient matrix in P-BEM algorithm,

after representing modeling again, the coefficient matrix relevant to sending data, its computational methods are as follows:

$Z_l^{\left(s\right)}=\frac{1}{N}[D_1\mathrm{diag}\left(x^{\left(s\right)}\right){\mathrm{\&Gamma;}}_l,\&CenterDot;\&CenterDot;\&CenterDot;,D_b\mathrm{diag}\left(x^{\left(s\right)}\right){\mathrm{\&Gamma;}}_l,\&CenterDot;\&CenterDot;\&CenterDot;,D_B\mathrm{diag}\left(x^{\left(s\right)}\right){\mathrm{\&Gamma;}}_l],$ Wherein,

${\mathrm{\&Gamma;}}_l={\left[\begin{array}{cccc}{e}^{-j2\mathrm{\&pi;}(\frac{p_1}{N}-\frac{1}{2}){\mathrm{\&tau;}}_l}& e^{-j2\mathrm{\&pi;}(\frac{p_2-1}{N}-\frac{1}{2}){\mathrm{\&tau;}}_l}& ...& e^{-j2\mathrm{\&pi;}(\frac{p_{N_p}-1}{N}-\frac{1}{2}){\mathrm{\&tau;}}_l}\end{array}\right]}^T,$ The Fourier transform in l footpath,

Γ=[Γ ₁, Γ ₂..., Γ _l], represent total Fourier transform matrix in L footpath,

Diag (x ^(s)) represent with vector x ^(s)for the matrix of diagonal element,

Step (3), utilizes AR model to carry out modeling to channel BEM coefficient:

Step (3.1), is calculated as follows C _l ^(s)correlation matrix:

$R_{C_l}^{\left(j\right)}={\left({\left(Q\right)}^{H}Q\right)}^{-1}{\left(Q\right)}^H{R}_{h(n,l,)}^{\left(j\right)}Q{\left({\left(Q\right)}^{H}Q\right)}^{-1},$

Wherein, j represents relevant exponent number, namely carries out the mark space of the OFDM symbol of related operation, and the value of j is [-1,0,1], represent the C of current ofdm signal respectively _l ^(s)with the C of previous symbol _l ^(s-1)correlation matrix, the C of current ofdm signal _l ^(s)autocorrelation matrix, the C of current ofdm signal _l ^(s)with the C of a rear symbol _l ^(s+1)correlation matrix () ^hrepresent Hermitian computing, $R_{h(n,l)}^{\left(j\right)}=E\left[h(n,l)h^{*}(n+j,l)\right]={\mathrm{\&sigma;}}_{h(n,l)}^2{J}_0\left(2\mathrm{\&pi;}{f}_d{T}_{s}j\right),$ Wherein E [] represents average, J ₀() represents the zero Bessel function of the first kind, f _d=vf _cthe maximum doppler frequency that/c is the translational speed of terminal when being v, f _cbe carrier frequency, c is the light velocity, represent the variance of the channel impulse response in l footpath, and suppose

Step (3.2), obtains the state transition equation of channel P-BEM parameter according to Yule-Walker equation:

g _(s)＝Ag _(s-1)+U _(s)，

Ofdm system is sent the time sequencing g of symbol ^(s)regard state migration procedure g in control system as _(s), i.e. g ^(s)=g _(s), state transition equation coefficient A=diag (a ₁, a ₂..., a _l... a _l), diag (x) expression take vector x as the matrix of diagonal element, U _(s)represent the modeling error of the AR model of s OFDM symbol;

Step (4), initialization is carried out to Kalman filter and calculates initial renewal equation:

Step (4.1), according to the following formula initialization is carried out to Kalman filter:

${\hat{g}}_{\left(0\right|0)}=0_{\mathrm{LB},1},P_{\left(0\right|0)}=\mathrm{diag}(R_{C_1}^{\left(0\right)},R_{C_2}^{\left(0\right)}\&CenterDot;\&CenterDot;\&CenterDot;R_{C_L}^{\left(0\right)}),$

Form as with the previous s of middle subscript all represents that current state is g _(s), a rear s represents s OFDM symbol, p _(O|O)the initial value for calculating, represent the g of OFDM symbol _(s)initial value, P _(O|O)represent corresponding error correlation matrix, 0 _{lB, 1}the null matrix of LB × 1,

Step (4.2), is calculated as follows the initial time renewal equation of Kalman:

i＝1，s＝1，

${\hat{g}}_{\left(s\right)}=A{\hat{g}}_{\left(0\right|0)},$

P _(s)＝AP _(0|0)(A) ^H+V[U _(s)]，

I represents iterations, represent state estimation g in Kalman equation _(s)intermediate variable, P _(s)represent intermediate variable corresponding error correlation matrix; Covariance matrix is represented, V [U with V [] _(s)]=diag (u ₁, u ₂u _l),

Step (5), carry out first time iterative channel estimation computing, now iterations i=1, only use the subcarrier place at pilot point place to receive data in current iteration and do channel estimating, data except the subcarrier of pilot point place on other subcarriers are considered as ICI, eliminate unknown data to the impact of pilot tone place channel estimating by SIN method, realize the pilot aided Kalman channel estimating without ICI interference, concrete steps are as follows:

Step (5.1), only the Received signal strength of carrier position corresponding for each pilot point in Received signal strength is used for calculating, and Received signal strength is divided into each pilot point data on sub-carriers, data on other subcarrier except pilot point subcarrier, to the interference of each pilot point place subcarrier and noise three part, are shown below:

Wherein, $P_s=[p_1,p_2,\&CenterDot;\&CenterDot;\&CenterDot;,p_{N_p}],{x_{d_{n_p{n}^{\&prime;}}}}^{\left(s\right)}={[x^{\left(s\right)}\left(d_{11}\right),x^{\left(s\right)}\left(d_{12}\right),\&CenterDot;\&CenterDot;\&CenterDot;x^{\left(s\right)}\left(d_{1N^{\&prime;}}\right),x^{\left(s\right)}\left(d_{21}\right),\&CenterDot;\&CenterDot;\&CenterDot;x^{\left(s\right)}\left(d_{N_p{N}^{\&prime;}}\right)]}^T,$ $N^{\&prime;}=\frac{N}{N_p},n^{\&prime;}=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,N^{\&prime;}$ Represent the distance between adjacent each pilot point, $V\left[W^{\left(s\right)}\left(P_s\right)\right]={\mathrm{\&sigma;}}^2{I}_{N_p},$ a N _p× N _punit matrix, σ ²white Gaussian noise W ^(s)variance, in above formula Section 2 be data on other subcarrier except pilot point subcarrier to the interference ICI of pilot point place subcarrier,

Step (5.2), is considered to interchannel noise W by data ICI distracter ^(s)(P _s) a part as the denoising object of filter, the method that the algorithm in step (2) is estimated according to SIN is rewritten, order the Kalman observational equation that then SIN estimates is expressed as:

$y_{p\left(s\right)}={{\mathrm{\&Phi;}}^{\mathrm{SIN}}}_{\left(s\right)}{g}_{\left(s\right)}+W_{\left(s\right)}^{\mathrm{SIN}},$

Wherein:

${{\mathrm{\&Phi;}}^{\mathrm{SIN}}}_{\left(s\right)}=\frac{1}{N}[{Z_1^{\left(s\right)}}_{\mathrm{SIN}},{Z_2^{\left(s\right)}}_{\mathrm{SIN}}\&CenterDot;\&CenterDot;\&CenterDot;{Z_L^{\left(s\right)}}_{\mathrm{SIN}}],$

${Z_l^{\left(s\right)}}_{\mathrm{SIN}}=\frac{1}{N}[D_1^{\mathrm{SIN}}\mathrm{diag}\left({x_p}^{\left(s\right)}\right){\mathrm{\&Gamma;}}_l^{\mathrm{SIN}}\&CenterDot;\&CenterDot;\&CenterDot;D_B^{\mathrm{SIN}}\mathrm{diag}\left({x_p}^{\left(s\right)}\right){\mathrm{\&Gamma;}}_l^{\mathrm{SIN}}],$

${\mathrm{\&Gamma;}}_l^{\mathrm{SIN}}={\left[\begin{array}{cccc}{e}^{-j2\mathrm{\&pi;}(\frac{p_1}{N}-\frac{1}{2}){\mathrm{\&tau;}}_l}& e^{-j2\mathrm{\&pi;}(\frac{p_2-1}{N}-\frac{1}{2}){\mathrm{\&tau;}}_l}& \&CenterDot;\&CenterDot;\&CenterDot;& e^{-j2\mathrm{\&pi;}(\frac{p_{N_p}-1}{N}-\frac{1}{2}){\mathrm{\&tau;}}_l}\end{array}\right]}^T,$

${\mathrm{\&Gamma;}}^{\mathrm{SIN}}=\left[\begin{array}{cccc}{{\mathrm{\&Gamma;}}_1}^{\mathrm{SIN}},& {{\mathrm{\&Gamma;}}_2,}^{\mathrm{SIN}}& \&CenterDot;\&CenterDot;\&CenterDot;,& {{\mathrm{\&Gamma;}}_l}^{\mathrm{SIN}}\end{array}\right]$

Step (5.3), calculates covariance matrix

Suppose in calculating that ICI is white Gaussian noise, order because both noise and ICI are separate, so $V\left[W_{\left(s\right)}^{\mathrm{SIN}}\right]=U_{\mathrm{ICI}}+V\left[W^{\left(s\right)}\left(P_s\right)\right];$

U _iCIthe calculating formula of each element in matrix is:

$U_{\mathrm{ICI}}(m,k)=R_{\mathrm{ICI}}^{\left(j\right)}\&ap;4{\mathrm{\&pi;}}^2{T_s}^2{E}_s\left(\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_{h(n,l)}^2{\mathrm{\&sigma;}}_{D_l}\right)\mathrm{\&rho;}(\mathrm{\&alpha;},\mathrm{rag},N),$

Wherein, the capable k row of m of m, k representing matrix, E _sthe power sending data, be power be P _vtime the general function of Doppler power, f is transmission frequency, and α represents that most marginal date for iteration is apart from the distance of each corresponding pilot point, be 0, rag is the precision calculated when first time calculates, rag=[0,1,2,3], and:

ρ(α,rag,N)＝ρ(0,rag,N)-ρ ₁(α,rag,N)，

Step (5.4), calculates kalman gain K by following three formulas respectively _(s), s OFDM symbol transfers to state state estimation matrix and with corresponding covariance matrix P _(s|s), form observation renewal equation group, wherein, Φ=Φ ^sIN, $W_{\left(s\right)}=W_{\left(s\right)}^{\mathrm{SIN}},$

K _(s)＝P _(s)(Φ _(s)) ^H(Φ _(s)P _(s)(Φ _(s)) ^H+V[W _(s)]) ^-1，

${\hat{g}}_{\left(s\right|s)}={\hat{g}}_{\left(s\right)}+K_{\left(s\right)}(y_{\left(s\right)}-{\mathrm{\&Phi;}}_{\left(s\right)}{\hat{g}}_{\left(s\right)}),$

P _(s|s)＝P _(s)-K _(s)Φ _(s)P _(s)，

Step (5.5), calculates channel matrix H according to following formula ^(s)estimated value:

$H^{\left(s\right)}=\frac{1}{N}\underset{b=1}{\overset{B}{\mathrm{\&Sigma;}}}{D}_b\mathrm{diag}\left(\mathrm{\&Gamma;}{\hat{g}}_{\left(s\right|s)}\right),$

Step (5.6), utilizes following formula to carry out QR decomposition to channel matrix, obtains matrix R ^(s):

H ^(s)＝IR ^(s)

Wherein I is a unit matrix, R ^(s)a upper triangular matrix,

Step (5.7), by following formula, QR Data Detection is carried out to data:

Wherein y ^{' (s)}=(I) ^hy ^(s), with the result after the detected value of data and detected value planisphere quantize respectively, [] _m,krepresent the capable k row of m of matrix, [] _mm element of vector, [] _kbe a kth element of vector, O () represents demodulation computing, m, k representing matrix H ^(s)the value of m capable k row, m=1,2 ..., m ..., M, M≤N, k=1,2 ..., k ..., K, K≤N,

Step (6), iterations i=i+1, during iterative computation number of times i>1, the data that subcarrier place receives that the subcarrier at second time iteration pilot point place place is adjacent with its both sides do channel estimating, data on its remaining sub-carriers are considered as ICI, thereafter the data for calculating that at every turn increase of iteration, be the data that last iteration receives for the subcarrier place of the subcarrier both sides at data place calculated, data on its remaining sub-carriers are considered as ICI, and it is as described below that SIN method carries out iterative channel estimation computing:

Step (6.1), Received signal strength is divided into pilot point place subcarrier data, for the subcarrier data at data place calculated, not for the data that calculate to pilot point with for the interference of data place subcarrier that calculates and noise four part, be shown below:

In above formula, Section 3 is the ICI interference after upgrading,

Step (6.2), the method described in step (5.2) calculates Φ ^sIN _(s),

Step (6.3), increase with iterations, the data for iteration increase, and now upgrade covariance matrix U _iCIbe calculated as follows:

$U_{\mathrm{ICI}}\&ap;4{\mathrm{\&pi;}}^2{T_s}^2{E}_s\left(\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_{h(n,l)}^2{\mathrm{\&sigma;}}_{D_l}\right)[\frac{1}{2}\mathrm{\&rho;}(A+m,\mathrm{rag},N)+\frac{1}{2}\mathrm{\&rho;}(A-m,\mathrm{rag},N)]$

Wherein, A+m represent on the right side of pilot point for the data that the calculate distance to corresponding pilot point, A-m represent on the left of pilot point for the data that the calculate distance to the pilot point of correspondence,

Step (6.4), calculates kalman gain K by the described method of step (5.5) _(s), s OFDM symbol transfers to state state estimation matrix and with corresponding covariance matrix P _(s|s), form observation renewal equation group, wherein, Φ=Φ ^sIN, $W_{\left(s\right)}=W_{\left(s\right)}^{\mathrm{SIN}},$

K _(s)＝P _(s)(Φ _(s)) ^H(Φ _(s)P _(s)(Φ _(s)) ^H+V[W _(s)]) ^-1，

${\hat{g}}_{\left(s\right|s)}={\hat{g}}_{\left(s\right)}+K_{\left(s\right)}(y_{\left(s\right)}-{\mathrm{\&Phi;}}_{\left(s\right)}{\hat{g}}_{\left(s\right)}),$

P _(s|s)＝P _(s)-K _(s)Φ _(s)P _(s)，

Step (6.5), calculates the estimated value H of channel matrix by step (5.5) described method ^(s):

$H^{\left(s\right)}=\frac{1}{N}\underset{b=1}{\overset{B}{\mathrm{\&Sigma;}}}{D}_b\mathrm{diag}\left(\mathrm{\&Gamma;}{\hat{g}}_{\left(s\right|s)}\right),$

Step (6.6), carries out QR decomposition by step (5.6) described method to channel matrix and obtains R ^(s):

H ^(s)＝IR ^(s)，

Step (6.7), by step (5.7) described method, QR Data Detection is carried out to data:

Step (7), judge whether that whether all data are all for iteration, if so, then algorithm terminates, if not, then continue,

Step (8), by judging the number of times of iteration, determine the input data the need of increasing iterative algorithm, evaluation algorithm is as follows:

Setting step delta, relatively iterations i and Δ μ+2, wherein, if i=Δ μ+2, then select for data for calculating that the data at the subcarrier place of the subcarrier both sides at data place calculated newly add as next iteration, with together with the data that calculate, bring SIN algorithm into, be brought in step (6) and again count;

If i ≠ Δ μ+2, then not increasing the data for calculating, returning step (6) and carrying out iteration;

Terminate.