CN103746947A - Phase noise estimation method - Google Patents

Abstract

The invention belongs to the technical field of wireless communication, and particularly relates to a method for realizing the phase noise estimation by an iteration method in a wireless communication system. According to the method, firstly, the equivalent discrete time domain channel impulse response is estimated through channel estimation sequences, then, a CPE (common phase error) of the phase noise is estimated through interpolation, and finally, the phase noise estimation is realized by the iteration method, so the phase noise is compensated, the reliability of the system is improved, and the bit error rate is reduced.

Description

A kind of method of estimation of phase noise

Technical field

The invention belongs to wireless communication technology field, the method by iteration of being specifically related in wireless communication system realizes phase noise and estimates.

Background technology

Modern digital communication systems has corresponding use frequency range, and system need to just can be delivered in transmission medium after being transferred to designated frequency band on information sequence, and receiving terminal needs reception signal to be down-converted to base band to facilitate subsequent treatment.So all need to produce corresponding carrier wave to complete corresponding up-conversion and down-conversion operation at transmitting terminal and receiving terminal.Yet carrier wave is not desirable, owing to producing crystal oscillator and the phase-locked loop of carrier wave, there is certain stability, thereby caused year > ripple frequency and target frequency to have random difference in short-term, and then cause produced sine wave signal generation random phase saltus step, show as phase noise.

Phase noise, is actually a kind of sign to frequency source frequency stability.Generally, frequency stability is divided into long-term frequency stability and short-term frequency stability.So-called short-term frequency stability, refers to the phase fluctuation or the frequency fluctuation that by random noise, are caused.Frequency slow drift as for causing because of temperature, aging etc., is referred to as long-term frequency stability.Conventionally main consideration is short-term stability problem, can think that phase noise is exactly short-term frequency stability, only two kinds of different expression modes of a physical phenomenon.For oscillator, frequency stability is that it produces a kind of of same frequency and measures within the scope of whole official hour.If there is instantaneous variation in signal frequency, can not remain unchanged, signal source just exists unsteadiness so, and cause is exactly phase noise.

If there is no phase noise, the whole power of oscillator all should concentrate on centre frequency place so.But the appearance of phase noise in adjacent frequency, has produced sideband by a part of power expansion of oscillator.Phase noise is normally defined the dBc/Hz value at a certain given deviation frequency place, wherein, and this frequency place power of dBc Shi YidBWei unit and the ratio of gross power.Oscillator phase noise at a certain deviation frequency place is defined as signal power in this 1Hz of frequency place bandwidth and the gross power ratio of signal.

Current research major part concentrates in ofdm system.On the whole, have based on feedback with without the phase noise compensation algorithm feeding back.In ofdm system, phase noise can produce common phase error (CPE) and inter-carrier interference (ICI); In SC-FDE system, produce common phase error (CPE) and intersymbol interference (ISI), cause the error rate to increase.

Summary of the invention

The object of the present invention is to provide a kind of method of utilizing iteration to realize the estimation of phase noise in wireless communication system.

In order to describe easily content of the present invention, first the definition that belongs to of using in the present invention is described:

Special word (UW, Unique Word).In order to carry out synchronous or parameter Estimation etc. at receiving terminal, at transmitting terminal, send have some particular characteristics, to the known special sequence of receiving terminal.

Object of the present invention realizes as follows:

S1, utilize channel estimation sequence to realize channel estimating, obtain the impulse response estimated value of equivalent time domain channel

S2, receiving terminal are estimated phase noise by iteration, comprising:

S21, UW is defined, make the length of UW be greater than the length of equivalent time domain channel, described UW is added in the data sequence that will transmit and is gone;

S22, the i UW reception signal during by channel can approximate representation be:

$y\_{\mathrm{uw}}_{\left(i\right)}\left(n\right)\≈\frac{a\_{\mathrm{uw}}_{\left(i\right)}}{a}{\hat{h}}_0*{\mathrm{UW}}_{\left(i\right)}+w_{\left(i\right)},$ $\mathrm{length}\left({\hat{h}}_0\right)-1\≤n\≤\mathrm{length}{\left(\mathrm{UW}\right)}_i-1,$ We can, by the UW in transmission data sequence, take the method for interpolation to estimate the phase noise constant of i data block and the ratio of a transmitting between i UW and i+1 UW like this: $\frac{a\left(i\right)}{a}=\frac{1}{2}\×(\frac{a\_{\mathrm{uw}}_{\left(i\right)}}{a}+\frac{a\_{\mathrm{uw}}_{(i+1)}}{a});$

S23, for receiving signal, remove and receive signal frequency domain after CP and can be with matrix representation: Y _{n * 1}=A _{n * N}h _{n * N}x _{n * 1}+ W _{n * 1}, A wherein _{n * N}for the toeplitz matrix that phase noise frequency domain forms, H _{n * N}for the diagonal matrix of estimating that the frequency domain of channel forms, X _{n * 1}for the matrix that transmission data frequency domain forms, Y _{n * 1}the matrix forming for receiving the frequency domain of signal, W _{n * 1}matrix for white Gaussian noise frequency domain structure;

S24, reception signal time-domain representation are: y _{n * 1}=diag (p _{n * 1}) h _{n * N}x _{n * 1}+ w _{n * 1}, wherein, y _{n * 1}receive the matrix of the time domain formation of signal, diag (p _{n * N}) diagonal matrix that forms for phase noise time domain, h _{n * N}for the toeplitz matrix that the time domain of channel forms, x _{n * 1}for the matrix that transmission data time domain forms, w _{n * 1}the matrix being configured to for noise time domain;

S25, structure interpolating matrix P _{n * N}, make p _{n * 1}=P _{n * N}c _{s * 1}, will as initial condition structure A _{1, N * N}, utilize Y _{n * 1}=A _{n * N}h _{n * N}x _{n * 1}+ W _{n * 1}and y _{n * 1}=diag (p _{n * 1}) h _{n * N}x _{n * 1}+ w _{n * 1}and p _{n * 1}the mould value of element is 1 these three conditions, and constantly iterative estimate goes out

by interpolation, obtain

thereby the method for having utilized iteration has realized the estimation of phase noise.

The invention has the beneficial effects as follows: the present invention first passes through channel estimation sequence, estimate equivalent dispersion time domain channel impulse response, then by Interpolate estimation, go out the common phase error (CPE) of phase noise, finally by the method for iteration, realize the estimation of phase noise, thereby compensation phase noise, the reliability of raising system, reduces the error rate.

Accompanying drawing explanation

Fig. 1 is the single-carrier frequency domain equalization system illustraton of model that affected by phase noise that the present invention uses

Fig. 2 is the phase noise statistical model figure that the present invention uses;

Fig. 3 utilizes this phase noise method of estimation to realize the flow chart of eliminating phase noise impact in single carrier frequency domain equalization communication system.

Embodiment

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described:

S1, utilize channel estimation sequence to realize channel estimating, comprising:

S11, channel estimation sequence are the sequences consisting of some known symbols, and for example in 802.11.ad standard, single carrier channel estimated sequence is [Gb ₁₂₈,-Ga ₁₂₈, Gb ₁₂₈,-Ga ₁₂₈,-Gb ₁₂₈, Ga ₁₂₈,-Gb ₁₂₈,-Ga ₁₂₈,-Gb ₁₂₈], and the channel estimation sequence of ofdm system is [Gb ₁₂₈, Ga ₁₂₈,-Gb ₁₂₈,-Ga ₁₂₈,-Gb ₁₂₈,-Ga ₁₂₈, Gb ₁₂₈,-Ga ₁₂₈,-Gb ₁₂₈], Ga wherein ₁₂₈and Gb ₁₂₈that Gray's sequence forms.

The form that S12, the signal indication that we can obtain time domain at receiving terminal are matrix: y _{n * 1}=A _{n * N}h _{n * N}x _{n * 1}+ w _{n * 1}, wherein, y _{n * 1}be the form of N * 1 column vector, it is subject to the impact of phase noise and white Gaussian noise.A _{n * N}the diagonal matrix that is a N * N consists of phase noise, h _{n * N}teoplitz (toeplitz) matrix being formed by equivalent time domain channel impulse response, x _{n * 1}n * 1 column vector being formed by transmission data, w _{n * 1}it is the noise vector of N * 1.

S13, we both can utilize some conventional channel estimations technique, the for example channel estimating based on Serial relation, least square method (LS) channel estimating etc., also can utilize the method for some reasonable novelties to realize channel estimating, as orthogonal matching pursuit algorithm (OMP, Orthogonal Matching Pursuit).

S14, we take Least Square Method in Frequency Domain LS channel estimating as example (equivalent time domain channel impulse response length is less than N), F _{n * N}normalized N * N Fourier matrix, $F(k,i)=\frac{1}{\sqrt{N}}\×\exp \{-j2\mathrm{\πki}/N\},0\≤k\≤N-\mathrm{1,0}\≤i\≤N-1.$ Frequency domain receives signal matrix and is expressed as Y _{n * 1}=aX _{n * N}h _{n * 1}+ W _{n * 1}, wherein, Y _{n * 1}=F _{n * N}y _{n * 1}, X _{n * N}be a diagonal matrix, its main diagonal element is by time domain transmission data x _{n * 1}the X that conversion obtains through N point fft _{n * 1}, H _{n * 1}n * 1 matrix, H _{n * 1}=F _{n * N}h _{n * 1}, h _{n * 1}after equivalent time domain channel impulse response h, to add 0 N * 1 matrix forming.W _{n * 1}noise in time domain w _{n * 1}after changing, N point normalization fft obtains.Here we think that phase noise is a constant a, so

through N point normalization ifft, obtain again

then by setting threshold value, obtain the equivalent time domain channel impulse response of estimating

here

a is phase noise constant.

S2, receiving terminal are estimated phase noise by iteration, comprising:

S21, by channel estimating, we have obtained the impulse response of the equivalent time domain channel estimated

here we take block transfer of data as example, have defined the sequence of UW for having known before us, and we are added to UW in the data sequence that will transmit and go, and realize and remove intersymbol interference.

S22, we suppose that UW length is greater than equivalent time domain channel length, here we know in the data sequence of transmission UW, UW is equivalent time domain channel impulse response h and UW convolution by channel essence, but it is subject to the impact of phase noise and white Gaussian noise simultaneously, here we think that the phase noise being subject in UW sequence is that (the phase noise constant that different UW are subject to is different for a constant, here can think phase noise constant actual be the common phase error CPE of phase noise), the reception signal of i UW during by channel can approximate representation be: $y\_{\mathrm{uw}}_{\left(i\right)}\left(n\right)\≈\frac{a\_{\mathrm{uw}}_{\left(i\right)}}{a}{\hat{h}}_0*{\mathrm{UW}}_{\left(i\right)}+w_{\left(i\right)},$ $\mathrm{length}\left({\hat{h}}_0\right)-1\≤n\≤\mathrm{length}{\left(\mathrm{UW}\right)}_i-1,$ We can, by the UW in transmission data sequence, take the method for interpolation to estimate the phase noise constant of i data block and the ratio of a transmitting between i UW and i+1 UW like this: $\frac{a\left(i\right)}{a}=\frac{1}{2}\×(\frac{a\_{\mathrm{uw}}_{\left(i\right)}}{a}+\frac{a\_{\mathrm{uw}}_{(i+1)}}{a}).$

S23, for receiving signal, remove and receive signal frequency domain after CP and can be with matrix representation: Y _{n * 1}=A _{n * N}h _{n * N}x _{n * 1}+ W _{n * 1}, A wherein _{n * N}for the toeplitz matrix that phase noise frequency domain forms, H _{n * N}for the diagonal matrix of estimating that the frequency domain of channel forms, X _{n * 1}for the matrix that transmission data frequency domain forms, Y _{n * 1}the matrix forming for receiving the frequency domain of signal, W _{n * 1}matrix for white Gaussian noise frequency domain structure.Correspondingly, receiving signal time-domain representation is: y _{n * 1}=diag (p _{n * 1}) h _{n * N}x _{n * 1}+ w _{n * 1}, wherein, y _{n * 1}receive the matrix of the time domain formation of signal, diag (p _{n * N}) diagonal matrix that forms for phase noise time domain, h _{n * N}for the toeplitz matrix that the time domain of channel forms, x _{n * 1}for the matrix that transmission data time domain forms, w _{n * 1}the matrix being configured to for noise time domain.In order to reduce complexity, by structure interpolating matrix P _{n * N}, make p _{n * 1}=P _{n * N}c _{s * 1}.We as initial condition structure A _{1, N * N}, utilize Y _{n * 1}=A _{n * N}h _{n * N}x _{n * 1}+ W _{n * 1}and y _{n * 1}=diag (p _{n * 1}) h _{n * N}x _{n * 1}+ w _{n * 1}and p _{n * 1}the mould value of element is 1 these three conditions.By continuous iterative estimate, go out by interpolation, obtain

thereby the method for having utilized iteration has realized the estimation of phase noise.

Fig. 1 is the single-carrier frequency domain equalization system illustraton of model that affected by phase noise that the present invention uses.

Fig. 1 transmitting terminal is used single carrier piecemeal transmission (Single-Carrier Block Transmission, SCBT), and bit stream adds the piecemeal transmission of protection interval after chnnel coding, digit mapping.In SC-FDE system; protection is spaced apart known special word (UW) and forms; the benefit of doing is like this known array that the equivalent cycle prefix (Cyclic Prefix, CP) that both formed next piece also can be used as receiving terminal parameter Estimation, has improved data transmission efficiency.

Signal is subject to receiving terminal noise effect after channel, enters numeric field and process after sampling.From digital receiver, the equivalent channel of digital signal process comprises the matched filter of the formed filter of transmitter, physical propagation channel and receiver.The sampled signal of digital receiver is subject to the property the taken advantage of impact of additive white Gaussian noise (Addictive White Gaussian Noise, AWGN) Additive effect in channel and phase noise.

Receiver, the train of signal that receives conversion, removes equivalent CP and to frequency domain, carries out frequency domain equalization by FFT, then through IFFT turn back to that time domain is adjudicated, digital demodulation and channel-decoding, finally send bit stream to terminal.

If go here and there and change after user data be s _i=[s _i(0), s _i(1) ..., s _i(N _s-1)] ^Τ, wherein [] ^Τthe transposition of representing matrix or vector, N _sthe length of user data in i data block.U=[u (0), u (1) ..., u (N _cp-1)] ^Τthat the length of inserting between data is N _cpuW.After user data, add i data block: x of UW complete _i=[s _i(0) ..., s _i(N _s-1), u (0) ..., u (N _c-1)] ^Τ, the length N of data block wherein _b=N _s+ N _cp.The UW inserting, as the equivalent CP of next data block, adds the growth data piece of equivalent CP

take matrix representation as:

${\stackrel{\‾}{x}}_i=T_c{x}_i---(0-1)$

In formula, T _c=[0 _{ncp * (Nb-Ncp)}, I _ncp; I _nb] be by N _cp* (N _b-N _cp) null matrix, N _cp* N _cpunit matrix and N _b* N _b(the N that forms of unit matrix _b+ N _cp) * N _bcyclic Prefix matrix.At UW, make in the SC-FDE system of equivalent CP growth data piece

in fact by i data block x _iform with the afterbody UW in i-1 data block.

I growth data piece of transmitting terminal

the equivalent dispersion CIR of process is h _i=[h _i(0), h _i(1) ... h _i(L-1)] ^Τ, wherein L is the maximum length of channel.Suppose ideal synchronisation, remove it and receive data block r _ithe time domain that obtains of CP receive Additive effect and the phase noise that signal is subject to additive white Gaussian noise

phase place deflection impact, φ wherein _ibe that average is 0, variance is

stable Gaussian phase noise.Go the matrix notation of the time domain reception signal after CP:

y _i＝A _iH _ix _i+n _i

In formula, A _i=diag{ φ _ithe diagonal matrix that formed by the phase place deflection of phase noise, here diag{[] ^Τrepresent to using vector as its cornerwise diagonal matrix.H _in _b* N _bcirculation Toeplitz matrix, its first row is h _iadding 0, to extend to length be N _bchannel vector.N _in _b* 1 AWGN vector, it is 0 by average, variance is

separate AWGN form.To mistake! Do not find Reference source.N is carried out on both sides _bpoint FFT obtains frequency domain reception signal:

Y _i＝Fy _i

＝Φ _iHH _iX _i+N _i

In formula, Y _i=[Y _i(0), Y _i(1) ..., Y _i(N _b-1)] ^Τthe frequency domain that is data block receives signal.F and F ^hrepresent respectively N _b* N _bnormalization discrete Fourier transform (DFT) (Discrete Fourier Transform, DFT) matrix and normalization inverse discrete fourier transform (Inverse Discrete Fourier Transform, IDFT) matrix, wherein [] ^Ηthe conjugate transpose of representing matrix or vector.The k+1 of F is capable, n+1 is listed as (0≤k, n≤N _b-1) element: and there is FF ^h=F ^hf=I, wherein I is N _b* N _bunit matrix.Φ _in _b* N _bcirculation Toeplitz matrix, its first row is phase noise φ _in _bthe 1/N of point DFT _b.HH _i=diag{[H _i(0), H _i(1) ..., H _{i (}n _b-1)] ^Τ, H wherein _i(k) (0≤k≤N _b-1) be h _in _bpoint DFT.X _i=[X _i(0), X _i(1) ..., X _i(N _b-1)] ^Τx _in _bpoint DFT, in like manner, N _ifor frequency domain additive white Gaussian noise, be n _in _bpoint DFT.

If do not consider the impact of noise item, frequency domain receives signal Y _i(k) be only subject to H _i(k) impact and be not subject to other frequency of transmitted signal X _i(l), l ≠ k crosstalks, and now the complexity of frequency domain equalization reduces greatly with respect to time domain equalization.Frequency domain receives signal Y _in after frequency domain equalization _bpoint IFFT turns back to time domain and obtains:

${\tilde{x}}_i=F^H{C}_i{\mathrm{\Φ}}_{i}H{H}_i{\mathrm{Fx}}_i+{\tilde{n}}_i$

Here, C _i=diag{[C _i(0), C _i(1) ..., C _i(N _b-1)] ^Τn _b* N _bfrequency domain equalization coefficient matrix,

be time domain AWGN through the noise of linear transformation, its result is still AWGN.

Fig. 2 is the phase noise statistical model figure that the present invention uses.

Phase noise generally uses its power spectral density (PSD) to characterize, and communication standard IEEE802.15.3c and IEEE802.11ad have provided " pole/zero " model about phase noise PSD:

$\mathrm{PSD}\left(f\right)=\mathrm{PSD}\left(0\right)\frac{1+{(f/f_Z)}^2}{1+{(f/f_p)}^2}$

In formula, f represents the frequency at offset carrier center.PSD (0) is a constant, IEEE802.15.3c and IEEE802.11ad standard respectively value-87dbc/Hz and-90dbc/Hz.F _p=1MHz is pole frequency, f _z=100MHz is zero frequency.

We regard stable Gaussian look phase noise as this coloured noise of band limit for height that the white Gaussian noise of zero-mean obtains by low pass filter as.The mould of this low pass filter transfer function square can be decomposed into:

${\left|H\left(f\right)\right|}^2=\frac{1+{(f/f_Z)}^2}{1+{(f/f_p)}^2}=\frac{1+j(f/f_Z)}{1+j(f/f_p)}\frac{1-j(f/f_Z)}{1-j(f/f_p)}$

From above formula, choose the transfer function of a systems stabilisation, obtain the transfer function H(s of simulation low-pass filter):

$H\left(s\right)=\frac{1+\mathrm{as}}{1+\mathrm{bs}}$

S=j Ω=j2 π f wherein, a=1/2 π f _z, b=1/2 π f _p, f _pand f _zbe respectively

pole frequency and zero frequency.We utilize Bilinear transformation method to realize analog filter and are converted into digital filter:

constant C=π (f wherein _p+ f _z)/tan (π (f _p+ f _z)/2f _s) make at (f _p+ f _zit is linear that the analog frequency at this Frequency point place)/2 is transformed into numerical frequency.Can obtain the transfer function of digital filter thus:

$H\left(z\right)=\frac{(1+\mathrm{aC})+(1-\mathrm{aC})z^{-1}}{(1+\mathrm{bC})+(1-\mathrm{bC})z^{-1}}.$

Fig. 3 utilizes the phase noise method of estimation of this iteration to realize the flow chart of eliminating phase noise impact in single carrier frequency domain equalization communication system.

We can utilize channel estimation sequence to estimate equivalent time domain channel impulse response a is phase noise constant, and h is actual equivalent time domain channel impulse response.Then Interpolate estimation goes out the phase noise constant of i data block and the ratio of a transmitting between i UW and i+1 UW

we know that the time domain after CP receives the matrix notation of signal: y _i=A _ih _ix _i+ n _i.Here we

as initial condition, construct $A_{1,i}=\left[\begin{array}{ccc}\frac{a\left(i\right)}{a}& ...& ...\\ ...& \frac{a\left(i\right)}{a}& ...\\ ...& ...& \frac{a\left(i\right)}{a}\end{array}\right].$ For the system of single carrier frequency domain equalization, data block length is N _bx _imiddle length is N _cpuW be known.Thereby can realize the matrix that time domain after CP receives signal by fractionation can be transformed to $y_i=A_i{\stackrel{\‾}{H}}_{1,i}{\stackrel{\‾}{x}}_i+A_i{\stackrel{\‾}{H}}_{2,i}{\stackrel{\‾}{x}}_{\mathrm{cp}}+n_i.$ We can estimate like this

In order to reduce phase noise unknown number number, we utilize an interpolating matrix P to realize φ _i=Pc _i, c _ibe a column vector, it has constructed φ after multiplying each other with interpolating matrix _i.Therefore go the matrix of the time domain reception signal after CP can be transformed to y _i=diag (Pc _i) H _ix _i+ n _i.Utilize y _i=diag (Pc _i) H _ix _i+ n _iwith phase noise mould value be 1 these two conditions, estimate c _{2, i}.And then utilize φ _i=Pc _iwith

estimate

utilize y _i=diag (Pc _i) H _ix _i+ n _iwith phase noise mould value be that 1 these two conditions are estimated c _{3, i}, so constantly iteration realizes, until meet the condition of convergence.Thereby estimated

utilize φ _i=Pc _i, obtained the phase noise of estimating

by compensation phase noise, obtained going the matrix of the time domain reception signal after CP: y _i=H _ix _i+ n _i.Do afterwards frequency domain equalization and obtained transmission

Claims (1)

1. a method of estimation for phase noise, is characterized in that, comprises the following steps: S1, utilize channel estimation sequence to realize channel estimating, obtain the impulse response estimated value of equivalent time domain channel

S2, receiving terminal are estimated phase noise by iteration, comprising:

S21, UW is defined, make the length of UW be greater than the length of equivalent time domain channel, described UW is added in the data sequence that will transmit and is gone;

S22, the i UW reception signal during by channel can approximate representation be:

$y\_{\mathrm{uw}}_{\left(i\right)}\left(n\right)\≈\frac{a\_{\mathrm{uw}}_{\left(i\right)}}{a}{\hat{h}}_0*{\mathrm{UW}}_{\left(i\right)}+w_{\left(i\right)},$ $\mathrm{length}\left({\hat{h}}_0\right)-1\≤n\≤\mathrm{length}{\left(\mathrm{UW}\right)}_i-1,$ We can, by the UW in transmission data sequence, take the method for interpolation to estimate the phase noise constant of i data block and the ratio of a transmitting between i UW and i+1 UW like this: $\frac{a\left(i\right)}{a}=\frac{1}{2}\×(\frac{a\_{\mathrm{uw}}_{\left(i\right)}}{a}+\frac{a\_{\mathrm{uw}}_{(i+1)}}{a});$

S23, for receiving signal, remove and receive signal frequency domain after CP and can be with matrix representation: Y _{n * 1}=A _{n * N}h _{n * N}x _{n * 1}+ W _{n * 1}, A wherein _{n * N}for the toeplitz matrix that phase noise frequency domain forms, H _{n * N}for the diagonal matrix of estimating that the frequency domain of channel forms, X _{n * 1}for the matrix that transmission data frequency domain forms, Y _{n * 1}the matrix forming for receiving the frequency domain of signal, W _{n * 1}matrix for white Gaussian noise frequency domain structure;

S24, reception signal time-domain representation are: y _{n * 1}=diag (p _{n * 1}) h _{n * N}x _{n * 1}+ w _{n * 1}, wherein, y _{n * 1}receive the matrix of the time domain formation of signal, diag (p _{n * N}) diagonal matrix that forms for phase noise time domain, h _{n * N}for the toeplitz matrix that the time domain of channel forms, x _{n * 1}for the matrix that transmission data time domain forms, w _{n * 1}the matrix being configured to for noise time domain;

S25, structure interpolating matrix P _{n * N}, make p _{n * 1}=P _{n * N}c _{s * 1}, will as initial condition structure A _{1, N * N}, utilize Y _{n * 1}=A _{n * N}h _{n * N}x _{n * 1}+ W _{n * 1}and y _{n * 1}=diag (p _{n * 1}) h _{n * N}x _{n * 1}+ w _{n * 1}and p _{n * 1}the mould value of element is 1 these three conditions, and constantly iterative estimate goes out

by interpolation, obtain thereby the method for having utilized iteration has realized the estimation of phase noise.

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