CN101764772B - Channel equalization method and communication system thereof based on precoding - Google Patents

Abstract

The invention provides a channel equalization method based on precoding. The method comprises that geometric mean decomposition is carried out on the extended channel matrix H of an original channel matrix H, R matrix, P matrix and Q matrix are obtained and then equalization is carried out, at a sending end, T-H precoding processing is carried out on modulated data according to the R matrix and the data after the T-H precoding is sent and filtered according to the P matrix and at a receiving end, the data after frequency domain signal processing is received and filtered according to the Q matrix. The invention further provides a communication system based on the precoding, which comprises a geometric mean decomposition module based on H, a receiving filtering module and a sending filtering module added to the sending end. The invention can eliminate error floor under high SNR and improve the system performance under low SNR and is compatible with a single or multiple carrier waves communication system. The invention also provides flexible gang scheme so that the system can obtain excellent performance under low complexity.

Description

A kind of channel equalization method and communication system thereof based on precoding

Technical field

The invention belongs to WiMAX access technology field, specifically propose a kind of channel equalization method based on precoding, and a kind of communication system based on precoding.

Background technology

Channel equalization technique is adopted by 3G long evolving system LTE as a kind of effective anti-multipath decline of high-speed radiocommunication technology that is used for.When data transmission rate is very high, because the multipath maximum delay substantially exceeds duration of single transmission symbol, cause the stack of tens of even hundreds of symbols before the data of receiving sometime are, it is difficult unusually therefore to recover original data stream at receiving terminal.From mathematics in essence, channel equalizer at first estimates the corresponding matrix of impulse of channel by channel estimation module, again the signal that receives is carried out the channel matrix inversion operation, thus the data of recovering.Traditional channel equalization technique mainly carries out in time domain, but along with the data transmission rate of Modern Communication System is more and more higher, the complexity of time domain equalization also increases thereupon, often needs hundreds of delayers and multiplier, and this is to be difficult to realize in the process of high-speed data flow transmission.And on the other hand, the high speed circuit of fast fourier transform algorithm FFT realize to make such as OFDM, MC-CDMA based on the new technology emerge in multitude of frequency-domain operations.This type of technology is to shine upon and load at frequency domain, and real transmission course but is to finish in time domain, so transmitting terminal need carry out the IFFT operation.As everyone knows, the IFFT operation can cause serious peak-to-average force ratio problem, so use frequency-domain equalization technology, then FFT and IFFT operation can both be finished at receiver, thereby effectively solves the problem of peak-to-average force ratio.

Channel equalization can be carried out according to multiple criterion, and it is four kinds of the most frequently used criterions that ZF ZF (Zero-Forcing), Minimum Mean Square Error MMSE (Minimum-Mean-Square-Error), high specific merge MRC (Maximum-Ratio-Combining), equal gain combining EGC (Equal-Gain-Combining).Wherein, use the ZF criterion to carry out channel equalization and can eliminate intersymbol interference ISI (Inter-Symbol Interference) fully, but cost is possible put noise very big at some frequency, causes the globality loss of energy.Can not amplify noise and use the MMSE criterion to carry out channel equalization, but can not eliminate ISI fully, need further handle the residual ISI that exists.The prior art updated plan is to adopt T-H (Tomlinson-Harashima) precoding to remove residual ISI at transmitting terminal.

Fig. 1 is based on the time-frequency equilibrium system signal flow chart of original channel Matrix QR Decomposition in the prior art.At transmitting terminal, transmitter at first carries out MQAM modulation to data, and data enter the T-H precoding module and go here and there the pre-elimination that symbol disturbs then, after the data behind the coding add Cyclic Prefix, go out by antenna transmission.At receiving terminal, the operation of Cyclic Prefix at first removed the data of receiving by receiver, by FFT data transaction is arrived frequency domain then, utilize pilot data to carry out channel estimating, after obtaining each footpath channel gain, utilize ZF, Minimum Mean Square Error, high specific to merge and carry out frequency domain equalization, because transmitting terminal has been done the T-H precoding with these different criterions of equal gain combining, so can fully eliminate ISI behind the frequency domain equalization this moment, thereby recover initial data.

Fig. 2 has the 4QAM analogous diagram of comparing independent MMSE frequency domain equalization based on the time-frequency equilibrium scheme of original channel Matrix QR Decomposition now, and wherein, ordinate BER represents bit error rate, and abscissa Eb/No represents signal to noise ratio.As can be seen from the figure, though three kinds of time-frequency equilibrium schemes based on the original channel Matrix QR Decomposition are not so good as the MMSE frequency domain equalization under low signal-to-noise ratio, but raising along with signal to noise ratio, their performance advantage will progressively embody, as seen from the figure, after signal to noise ratio surpassed 12dB, the MMSE frequency domain equalization performance lagged behind three kinds of time-frequency equilibrium schemes based on the original channel Matrix QR Decomposition gradually.So, the elimination that utilizes the T-H precoding technique to carry out residual ISI can bring significantly improving of performance, and the raising of this performance will further be strengthened along with the rising of order of modulation, as shown in Figure 3, under the 16QAM modulation, three kinds of time-frequency equilibrium schemes based on the original channel Matrix QR Decomposition have all surmounted optimum MMSE frequency domain equalization.Reason is under the high order modulation, and residual ISI is to the deterioration of the systematic function highly significant that will become, thereby seriously contains error performance.As can be seen from the figure, time-frequency equilibrium scheme slope under high s/n ratio based on the original channel Matrix QR Decomposition is not very precipitous, it is flat mistake in various degree to have occurred, this is owing to adopted the QR decomposition technique in these schemes, can cause the signal to noise ratio of some sub data flow of data block afterbody to be starkly lower than the data of head like this, be that received signal to noise ratio is inhomogeneous, make the tail data of low signal-to-noise ratio under high s/n ratio, to tie down systematic function.As shown in Figure 4, the flat schematic diagram of mistake that Fig. 4 occurs under high s/n ratio for the time-frequency equilibrium scheme based on the original channel Matrix QR Decomposition, no matter how signal to noise ratio improves in this case, and always the effective signal-to-noise ratio of some data does not reach requirement; Simultaneously, from figure, it can also be seen that,, amplified noise simultaneously though prior art can be eliminated ISI fully, the zone of low signal-to-noise ratio in making, systematic function is still lower.

Summary of the invention

Purpose of the present invention is to propose a kind of channel equalization method based on precoding, and a kind of communication system based on precoding, and it is flat to eliminate the mistake that produces under high s/n ratio, can improve the systematic function under the low signal-to-noise ratio again.

The channel equalization method based on precoding that the present invention proposes comprises:

Step S100 is according to the extended channel matrices of original channel matrix H

Carry out geometric mean and decompose, obtain upper triangular matrix R, unitary matrice P and unitary matrice Q;

For multicarrier system, step S100 specifically comprises:

Step S101 is to described extended channel matrices

Earlier according to formula

Carry out characteristic value decomposition, obtain the extension feature value matrix of biconjugate corner structure

Wherein

Be N _C* N _CFourier's matrix, N _CBe the contained symbolic number of data block;

Step S102 is to the extension feature value matrix of described biconjugate corner structure

Carry out geometric mean and decompose, obtain Q, R, three matrixes of P;

Step S200 carries out equilibrium according to R matrix, P matrix and Q matrix, comprising:

Step S201 at transmitting terminal, carries out the T-H precoding according to the R matrix to the data after modulating earlier;

Step S202 at transmitting terminal, sends filtering according to the data of P matrix after to the T-H precoding;

Step S203, at receiving terminal, the data after according to the Q matrix frequency-region signal being handled accept filter.

The present invention also proposes a kind of communication system based on precoding simultaneously, comprises transmitting terminal and receiving terminal; Described transmitting terminal comprises modulation module, T-H precoding module, increases cyclic prefix module and transmitting antenna, and described receiving terminal comprises reception antenna, removes cyclic prefix module, frequency-region signal processing module, the module that accepts filter, delivery module and demodulation module; It is characterized in that described communication system also comprises: based on the geometric mean decomposing module of extended channel, described transmitting terminal also comprises the transmission filtration module;

Described geometric mean decomposing module based on extended channel is used for the extended channel matrices to the original channel matrix H

Carry out geometric mean and decompose, obtain upper triangular matrix R, unitary matrice P and unitary matrice Q, and described R matrix is sent to the T-H precoding module, described P matrix is sent to the transmission filtration module, described Q matrix is sent to the module that accepts filter; For multicarrier system, described process of carrying out the geometric mean decomposition specifically comprises:

To described extended channel matrices Earlier according to formula

Carry out characteristic value decomposition, obtain the extension feature value matrix of biconjugate corner structure

Wherein

Be N _C* N _CFourier's matrix, N _CBe the contained symbolic number of data block;

Extension feature value matrix to described biconjugate corner structure

Carry out geometric mean and decompose, obtain Q, R, three matrixes of P;

Described transmission filtration module is used to receive described P matrix, and sends filtering according to the data of described P matrix after to the T-H precoding;

Extended channel matrices according to the original channel matrix H Described geometric mean decomposing module based on extended channel is decomposed acquisition upper triangular matrix R, unitary matrice P and unitary matrice Q;

Transmitting terminal, described T-H precoding module carry out the T-H precoding according to the described R matrix that receives to the data after the modulation; Described transmission filtration module sends filtering according to described P matrix to the data after the T-H precoding;

At receiving terminal, the described module that accepts filter accepts filter to the data after the frequency-region signal processing according to described Q matrix.

In the prior art, the signal strength signal intensity of the conclusive judgement variable of received signal is that the diagonal element diag{R} that fully decomposes the R matrix that obtains by QR is determined, because being the element of diag{R} afterbody, the defective that QR decomposes to reduce rapidly, and the element value of head is than mean value height, the intensity that promptly means the signal reception is good at first half, but has sacrificed the intensity of latter half data.The geometric mean that the present invention adopts decomposes, and obtains R, P, three matrixes of Q, carries out equilibrium according to these three matrixes.The intensity of conclusive judgement variable that can obtain received signal by reasoning and calculation is by the diagonal element of R matrix

Decision, and resulting upper triangular matrix R matrix, element values all on its diagonal all equate, thereby mean that promptly not existing QR decomposition diag{R} afterbody element to diminish rapidly produces the flat situation of mistake.Because the entire system performance determined by differing from most a circuit-switched data intensity, thus the present invention can thoroughly weed out errors flat, thereby improved the entire system performance.In addition, geometric mean of the present invention decompose to as if the extended channel matrices of original channel matrix, final judgment variables

Not only depend on Also with

The variance information σ relevant, that this has comprised noise has embodied the balance that the MMSE criterion is made between noise amplification and elimination ISI, do not exist the prior art noise to amplify the lower situation of systematic function that causes.Thereby it is flat to realize eliminating the mistake that produces under high s/n ratio, can improve the systematic function under the low signal-to-noise ratio again.

Description of drawings

Fig. 1 is the time-frequency equilibrium system signal flow chart based on the original channel Matrix QR Decomposition;

The time-frequency equilibrium scheme that Fig. 2 is based on the original channel Matrix QR Decomposition is compared the 4QAM analogous diagram of independent MMSE frequency domain equalization;

Fig. 3 is the 16QAM analogous diagram that three kinds of time-frequency equilibrium schemes based on the original channel Matrix QR Decomposition are compared independent MMSE frequency domain equalization;

The flat schematic diagram of mistake that Fig. 4 occurs under high s/n ratio for the time-frequency equilibrium scheme based on the original channel Matrix QR Decomposition;

The channel equalization method flow chart that Fig. 5 proposes for the present invention based on precoding;

Fig. 6 is the error rate analogous diagram of QR-THP and MMSE-GMD-THP single carrier equalizing system;

Fig. 7 is the value distribution schematic diagram of the diag{R} after decomposing through grouping MMSE-GMD;

Fig. 8 is the single-carrier system schematic diagram that decomposes based on the extended channel matrices geometric mean;

Fig. 9 is a T-H precoding module schematic diagram;

Figure 10 is the multicarrier system schematic diagram that decomposes based on the extended channel matrices geometric mean.

Embodiment

Baseband signal model used in the present invention is described below:

Channel model is the multipath Rayleigh fading channel, τ _lBe channel tap time delay, h _lBe channel gain.

$h\left(t\right)=\underset{l=0}{\overset{L-1}{\mathrm{\Σ}}}{h}_l\mathrm{\δ}(t-{\mathrm{\τ}}_l)$

Because the use of cyclic prefix CP (Cyclic Prefix), make the linear convolution of data and interchannel be converted into circular convolution, therefore whole channel matrix can be write as the form of Toeplize matrix, and this matrix has a large amount of 0 elements to exist, and is sparse matrix:

$H=\left[\begin{array}{cccccc}{h}_0& & & h_{L-1}& ...& h_1\\ h_1& {\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="H2009101933113E00012.png,H2009101933113E00022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0& & & & ...\\ ...& h_1& & & & h_{L-1}\\ h_{L-1}& ...& ...& & & \\ & h_{L-1}& ...& h_0& & \\ & & & h_1& {\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="H2009101933113E00012.png,H2009101933113E00022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0& \\ 0& & & ...& h_1& {\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="H2009101933113E00051.png"\; state="\{\{state\}\}">h</figure-callout>}}_1\end{array}\right]$

If the data after ovennodulation be s}, and through the data after the T-H precoding be x}, then received signal r can be write as:

$r=\sqrt{E_s}\mathrm{Hx}+n$

Wherein, the energy of the Es unit of representative modulation symbol, n represents white Gaussian noise.

Following elder generation briefly introduces doing based on the frequency domain equalization scheme of original channel Matrix QR Decomposition:

The first step: received signal is transformed into frequency domain, carries out the frequency domain equalization operation.By IFFT data transaction is returned time domain behind the frequency domain equalization, this moment, data can be expressed as:

$\hat{r}=\sqrt{E_s}\hat{H}x+\hat{n}$

Wherein, Be the equivalent channel matrix behind the frequency domain equalization.Current programme has adopted following QR decomposition technique to this equivalence channel matrix, obtains R matrix and Q matrix:

$\hat{H}=\mathrm{QR}$

Second step: utilize the R matrix that obtains, can obtain the needed key parameter B of T-H precoding:

B＝diag{R} ^-1R-I

Thereby sending signal can be write as:

x＝s-Bx+2Mz _t

Wherein, 2Mz _tDie lifter operation in the expression T-H precoding processing, die lifter carries out following operation respectively to the real part imaginary part of signal:

Immediate integer is got in representative downwards, and M has different values according to the difference of modulation system.

Then, received signal r can be write as according to the new expression formula that sends signal x:

$\hat{r}=\sqrt{E_s}\mathrm{QR}{(I+B)}^{-1}s+n$

$=\sqrt{E_s}\mathrm{QR}{\left(\mathrm{diag}{\left\{R\right\}}^{-1}R\right)}^{-1}s+n$

$=\sqrt{E_s}Q\left[\mathrm{diag}\right\{R\left\}\right]s+n$

The 3rd step, utilize the Q matrix that obtains, r carries out partial-equilibrium to received signal, and carries out modulo operation 2Mz simultaneously _r, to eliminate the influence that sends die lifter:

$\stackrel{\&OverBar;}{r}=Q^H\hat{r}+2M{z}_r$

$=\sqrt{E_s}\left[\mathrm{diag}\right\{R\left\}\right]s+2M(z_t+z_r)+Q^{H}n$

$=\sqrt{E_s}\left[\mathrm{diag}\right\{R\left\}\right]s+n$

As from the foregoing, the conclusive judgement variable of received signal r Signal strength signal intensity determined by the diagonal element diag{R} of R matrix fully. and the defective of current Q R decomposition technique is that the element value of diag{R} afterbody can reduce rapidly, and the element value of its head is than mean value height, as shown in Figure 4.It is relatively good that on behalf of received signal intensity, this forwardly divide, but sacrificed the intensity of rear section data.Because the overall performance of system is determined by a poorest circuit-switched data signal strength signal intensity, so can cause serious system's error performance mistake flat like this.

In addition, because the original channel matrix H is a sparse matrix that contains a large amount of 0 elements, and the equivalent channel matrix behind the frequency domain equalization

It is a dense matrix.Therefore, select directly sparse matrix H to be carried out channel decomposing, can significantly reduce the amount of calculation of matrix decomposition on the one hand, on the other hand, decomposing the resulting upper triangular matrix R in back also will be a sparse matrix.From above-mentioned QR decomposition technique in conjunction with the briefly introducing of the processing method of frequency domain equalization as can be seen, upper triangular matrix R is the direct sources of the required key parameter of T-H precoding module, the sparse characteristic of R matrix will effectively reduce the number of taps of T-H precoding module needed multiplier and delayer in physics realization, thereby significantly reduce system complexity.

In addition, owing to can unify to be expressed as based on the balanced weights of ZF/MMSE criterion:

For the ZF criterion,

It is the employed original channel matrix H of current Q R decomposing scheme.

And, following extended matrix is arranged for the MMSE criterion:

$\stackrel{\&OverBar;}{H}={[H,\mathrm{\&sigma;I}]}^T$

Obtain easily, the generalized inverse of this extended channel matrices is

The balanced weights of this classical just MMSE criterion.

This shows, if based on extended channel

Carrying out GMD and decompose, then is a kind of MMSE equilibrium in essence, because the balance an of the best has been done in the MMSE equilibrium between noise amplification and interference eliminated, so performance obviously is better than the ZF equilibrium.For GMD decompose and can be write as

$\stackrel{\&OverBar;}{H}=\stackrel{\&OverBar;}{Q}\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H={\left[\begin{array}{cc}{Q}_1& Q_2\end{array}\right]}^T\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H$

Because

${\stackrel{\&OverBar;}{Q}}^H\stackrel{\&OverBar;}{H}=\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H=\left[\begin{array}{cc}{Q_1}^H& {Q_2}^H\end{array}\right]\left[\begin{array}{c}H\\ \mathrm{\&sigma;I}\end{array}\right]$

Thereby

${Q_1}^H=\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H-\mathrm{\&sigma;}{Q_2}^H$

Therefore channel can resolve into following form:

$H=Q_1(\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H-\mathrm{\&sigma;}{Q_2}^H)$

The present invention then proposes a kind of extended channel matrices to the original channel matrix and carries out the geometric mean decomposition, and as shown in Figure 5, Fig. 5 is the channel equalization method flow chart based on precoding that the present invention proposes, and is specific as follows:

Step S100 is according to the extended channel matrices of original channel matrix H

Carry out geometric mean and decompose, obtain upper triangular matrix R, unitary matrice P and unitary matrice Q;

Step S200 carries out equilibrium according to R matrix, P matrix and Q matrix, comprising:

Step S201 at transmitting terminal, carries out the T-H precoding according to the R matrix to the data after modulating earlier;

Step S202 at transmitting terminal, sends filtering according to the data of P matrix after to the T-H precoding;

Step S203, at receiving terminal, the data after according to the Q matrix frequency-region signal being handled accept filter.

Be described with specific embodiment below.

Embodiment 1:

Present embodiment is a single carrier implementation of the present invention.The detailed process of signal processing is as described below:

Step S100 is according to the extended channel matrices of original channel matrix H

Carry out geometric mean and decompose, obtain upper triangular matrix R, unitary matrice P and unitary matrice Q.According to the mathematics pertinent literature, the decomposition of the geometric mean of matrix makes GMD (Geometry Mean Decomposition) decompose again.Present embodiment is direct extended channel matrices to original channel H

Carry out GMD and decompose, process is as follows:

$\stackrel{\&OverBar;}{H}=\stackrel{\&OverBar;}{Q}\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H={\left[\begin{array}{cc}{Q}_1& Q_2\end{array}\right]}^T\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H$

Wherein, can get upper triangular matrix R, unitary matrice P and unitary matrice Q after the decomposition.Element value all equates on the diagonal of R matrix:

$r_{i,i}={\left(\underset{i=1}{\overset{\mathrm{Nc}}{\mathrm{\&Pi;}}}{\mathrm{\&lambda;}}_1\right)}^{1/\mathrm{Nc}}$

r _{I, i}Element on the expression diagonal, λ _iBe the channel expansion matrix

I characteristic value, N _CRepresent the number of symbols in the data block.

Step S200 carries out equilibrium according to R matrix, P matrix and Q matrix.Because this step can be divided into for three steps and realize, then be described with three steps, balanced process specifically comprises:

Step S201 at transmitting terminal, carries out the T-H precoding according to the R matrix to the data after modulating earlier.Transmitting terminal carries out the QAM modulation to data after, utilize the R matrix that obtains, can obtain the required key parameter B of T-H precoding:

$B=\mathrm{diag}{\left\{\stackrel{\&OverBar;}{R}\right\}}^{-1}\stackrel{\&OverBar;}{R}-I$

Then can be write as through the output signal after the T-H precoding:

x＝s-Bx+2Mz _t

Step S202 at transmitting terminal, sends filtering according to the data of P matrix after to the T-H precoding, obtains sending signal

Sending filtered data can add cyclic prefix CP and send from antenna.

Step S203, at receiving terminal, the data after according to the Q matrix frequency-region signal being handled accept filter, according to sending signal

Received signal can be write as:

$\hat{r}=\sqrt{E_s}H\stackrel{\&OverBar;}{x}+n$

$=\sqrt{E_s}{Q}_1(\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H-\mathrm{\&sigma;}{Q_2}^H)\stackrel{\&OverBar;}{x}+n$

$=\sqrt{E_s}{Q}_1(\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H-\mathrm{\&sigma;}{Q_2}^H)\left[\stackrel{\&OverBar;}{P}{(I+B)}^{-1}s\right]+n$

$=\sqrt{E_s}{Q}_1(\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H-\mathrm{\&sigma;}{Q_2}^H)\left[\stackrel{\&OverBar;}{P}{\left(\mathrm{diag}{\left\{\stackrel{\&OverBar;}{R}\right\}}^{-1}\stackrel{\&OverBar;}{R}\right)}^{-1}s\right]+n$

$=\sqrt{E_s}{Q}_1(\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H-\mathrm{\&sigma;}{Q_2}^H)\stackrel{\&OverBar;}{P}{\stackrel{\&OverBar;}{P}}^{-1}\mathrm{diag}\left(\stackrel{\&OverBar;}{R}\right)s+n$

$=\sqrt{E_s}{Q}_1(\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H-\mathrm{\&sigma;}{Q_2}^H){\left(\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H\right)}^{-1}\mathrm{diag}\left(\stackrel{\&OverBar;}{R}\right)s+n$

$=\sqrt{E_s}{Q}_1\left[(I-\mathrm{\&sigma;}{Q_2}^H{\left(\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H\right)}^{-1})\right]\mathrm{diag}\left(\stackrel{\&OverBar;}{R}\right)s+n$

Data after according to the Q matrix frequency-region signal being handled accept filter, and carry out modulo operation 2Mz simultaneously _r, to eliminate the influence that sends die lifter, get:

$\stackrel{\&OverBar;}{r}={Q_1}^H\hat{r}+2M{z}_r$

$=\sqrt{E_s}[(I-\mathrm{\&sigma;}{Q_2}^H{\left(\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H\right)}^{-1}]\mathrm{diag}\left(\stackrel{\&OverBar;}{R}\right)s+2M(z_t+z_r)+{Q_1}^{H}n$

$=\sqrt{E_s}\left[\mathrm{diag}\left(\stackrel{\&OverBar;}{R}\right)\right]s-\sqrt{E_s}\left[\mathrm{\&sigma;}{Q_2}^H{\left(\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H\right)}^{-1}\mathrm{diag}\left(\stackrel{\&OverBar;}{R}\right)\right]s+{Q_1}^{H}n$

The present invention adopts extended channel matrices is carried out the geometric mean decomposition, obtains R, P, three matrixes of Q, carries out equilibrium according to these three matrixes.From the expression formula of the conclusive judgement variable of above-mentioned received signal as can be seen, judgment variables

Mainly by

Decision, and resulting upper triangular matrix R matrix, element values all on its diagonal all equate, thereby mean that promptly not existing QR decomposition diag{R} afterbody element to diminish rapidly produces the flat situation of mistake.Because the entire system performance determined by differing from most a circuit-switched data intensity, thus the present invention can thoroughly weed out errors flat, thereby improved the entire system performance.In addition, geometric mean decomposes among the present invention to as if extended channel matrices

Final judgment variables

Also with

The variance information σ relevant, that this has comprised noise has embodied the balance that the MMSE criterion is made between noise amplification and elimination ISI.Thereby it is flat to realize eliminating the mistake that produces under high s/n ratio, can improve the systematic function under the low signal-to-noise ratio again.

As shown in Figure 6, Fig. 6 is the error rate analogous diagram of QR-THP and MMSE-GMD-THP single carrier equalizing system.Wherein, QR-THP refers to that to the equalization methods of prior art based on the original channel Matrix QR Decomposition MMSE-GMD-THP refers to the equalization methods that decomposes based on the extended channel matrices geometric mean of the present invention.As seen from the figure, MMSE-GMD-THP performance under low signal-to-noise ratio is better than QR-THP, this is because when low signal-to-noise ratio, noise amplifies more serious than the influence of ISI, thereby dominate the error rate of whole system, therefore the strategy based on the MMSE criterion can obtain better error performance as MMSE-GMD-THP, and the strategy based on the ZF criterion as prior art is then relatively poor relatively.But, in the high s/n ratio zone, the no longer leading systematic function of the influence that noise amplifies, and the unbalance systematic function that makes of interchannel signal to noise ratio is limited by a poorest subchannels separately.Therefore, the geometric mean decomposition strategy that the present invention adopts, can the balance high s/n ratio under each subchannels, have very superior performance.

Embodiment 2:

Present embodiment is a multicarrier implementation of the present invention, promptly realizes on ofdm system.The detailed process of signal processing is as described below:

The original channel matrix H is the circular matrix of a Toeplitz, and according to the character of matrix: any circular matrix can be decomposed by Fourier's matrix exgenvalue, obtains following channel decomposing form then:

$H=F_{\mathrm{Nc}}^H{\mathrm{\&Lambda;}}_H{F}_{\mathrm{Nc}}$

Wherein, F is Fourier's matrix of Nc * Nc, Λ _HBe the eigenvalue matrix of channel matrix, Nc is the contained symbolic number of data block.Therefore extended channel matrices has following decomposed form:

$\stackrel{\&OverBar;}{H}=F_{\mathrm{Nc}}^H{\stackrel{\&OverBar;}{\mathrm{\&Lambda;}}}_H{F}_{\mathrm{Nc}}$

Wherein

Extension feature value matrix for the biconjugate corner structure.Owing to Fourier's matrix can be realized fast by IFFT conversion and FFT conversion, therefore, to extended channel matrices GMD decompose the extension feature value matrix can be reduced to the biconjugate corner structure

GMD decompose.Because Λ _H, σ I is diagonal matrix, and the complexity of GMD algorithm itself will lower greatly, and process is as follows:

${\stackrel{\&OverBar;}{\mathrm{\&Lambda;}}}_H=\stackrel{\&OverBar;}{Q}\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H={\left[\begin{array}{cc}{Q}_1& Q_2\end{array}\right]}^T\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H$

Because

${\stackrel{\&OverBar;}{Q}}^H{\stackrel{\&OverBar;}{\mathrm{\&Lambda;}}}_H=\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H=\left[\begin{array}{cc}{Q_1}^H& {Q_2}^H\end{array}\right]\left[\begin{array}{c}{\mathrm{\&Lambda;}}_H\\ \mathrm{\&sigma;I}\end{array}\right]$

Thereby

${Q_1}^H{\mathrm{\&Lambda;}}_H=\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H-\mathrm{\&sigma;}{Q_2}^H$

So eigenvalue matrix Λ of channel _HCan resolve into following form:

${\mathrm{\&Lambda;}}_H=Q_1(\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H-\mathrm{\&sigma;}{Q_2}^H)$

So, specific as follows based on the channel equalization method of precoding:

Step S100 is according to the extended channel matrices of original channel matrix H Carry out geometric mean and decompose, obtain upper triangular matrix R, unitary matrice P and unitary matrice Q.The present invention is for the implementation of multicarrier, is divided into for two steps to finish whole geometric mean decomposable process:

Step S101 is to extended channel matrices

Earlier according to formula

Carry out characteristic value decomposition, obtain the extension feature value matrix of biconjugate corner structure

Wherein

Be N _C* N _CFourier's matrix, N _CBe the contained symbolic number of data block;

Step S102 is to the extension feature value matrix of biconjugate corner structure Carry out geometric mean and decompose, obtain Q, R, three matrixes of P;

Step S200 carries out equilibrium according to R, P, three matrixes of Q, specifically be divided into three the step realize:

Step S201 at transmitting terminal, according to the R matrix, carries out the T-H precoding to the data after the modulation.

Step S202 sends filtering according to the data of P matrix after to the T-H precoding.

This two step is identical with corresponding step among the embodiment 1, is not repeated in this description at this.

Data are carried out after the Filtering Processing, execution in step: carry out the OFDM modulation to sending filtered data.Be with the above matrix of signal times herein

The physical significance of this Mathematical treatment is promptly carried out the OFDM modulation to data for carrying out the IFFT operation.So this moment, received signal can be expressed as:

$r={\mathrm{HF}}_{\mathrm{Nc}}^H+\stackrel{\&OverBar;}{P}x+n$

At receiving terminal, execution in step: the data of removing Cyclic Prefix are carried out the OFDM demodulation.This process is to received signal is multiplied by matrix F _Nc, the physical significance of this Mathematical treatment is promptly carried out the OFDM demodulation to data, the received signal after the demodulation for carrying out the FFT operation

Can be expressed as:

$\hat{r}=F_{\mathrm{Nc}}r$

Wherein, received signal

Can be written as:

$\hat{r}=\sqrt{E_s}\left(F_{\mathrm{Nc}}\right)H\left(F_{\mathrm{Nc}}^{H}P\right)x+\left(F_{\mathrm{Nc}}\right)n$

$=\sqrt{E_s}{\mathrm{\&Lambda;}}_H\stackrel{\&OverBar;}{P}x+\left(F_{\mathrm{Nc}}\right)n$

$=\sqrt{E_s}{Q}_1(\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H-\mathrm{\&sigma;}{Q_2}^H)\left[\stackrel{\&OverBar;}{P}{(I+B)}^{-1}s\right]+\left(F_{\mathrm{Nc}}\right)n$

$=\sqrt{E_s}{Q}_1(\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H-\mathrm{\&sigma;}{Q_2}^H)\left[\stackrel{\&OverBar;}{P}{\left(\mathrm{diag}{\left\{\stackrel{\&OverBar;}{R}\right\}}^{-1}\stackrel{\&OverBar;}{R}\right)}^{-1}s\right]+\left(F_{\mathrm{Nc}}\right)n$

$=\sqrt{E_s}{Q}_1(\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H-\mathrm{\&sigma;}{Q_2}^H)\stackrel{\&OverBar;}{P}{\stackrel{\&OverBar;}{R}}^{-1}\mathrm{diag}\left(\stackrel{\&OverBar;}{R}\right)s+\left(F_{\mathrm{Nc}}\right)n$

$=\sqrt{E_s}{Q}_1(\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H-\mathrm{\&sigma;}{Q_2}^H){\left(\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H\right)}^{-1}\mathrm{diag}\left(\stackrel{\&OverBar;}{R}\right)s+\left(F_{\mathrm{Nc}}\right)n$

$=\sqrt{E_s}{Q}_1\left[(I-\mathrm{\&sigma;}{Q_2}^H{\left(\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H\right)}^{-1})\right]\mathrm{diag}\left(\stackrel{\&OverBar;}{R}\right)s+\left(F_{\mathrm{Nc}}\right)n$

Execution in step S203 again after the demodulation carries out frequency-region signal to the data after the OFDM demodulation and handles, and the data after according to the Q matrix frequency-region signal being handled again accept filter:

$\stackrel{\&OverBar;}{r}={Q_1}^H\hat{r}$

Then the judgment variables of final received signal can be expressed as:

$\stackrel{\&OverBar;}{r}={Q_1}^H\hat{r}+2M{z}_r$

$=\sqrt{E_s}\left[\right(I-\mathrm{\&sigma;}{Q_2}^H{\left(\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H\right)}^{-1}]\mathrm{diag}\left(\stackrel{\&OverBar;}{R}\right)s+2M(z_t+z_r)+{Q_1}^{H}n$

$=\sqrt{E_s}\left[\mathrm{diag}\left(\stackrel{\&OverBar;}{R}\right)\right]s-\sqrt{E_s}\left[\mathrm{\&sigma;}{Q_2}^H{\left(\stackrel{\&OverBar;}{R}{\stackrel{\&OverBar;}{P}}^H\right)}^{-1}\mathrm{diag}\left(\stackrel{\&OverBar;}{R}\right)\right]s+{Q_1}^{H}n$

Equally as can be seen, judgment variables

Mainly by

Decision, and judgment variables

Also with

The variance information σ relevant, that this has comprised noise has embodied the balance that the MMSE criterion is made between noise amplification and elimination ISI.Thereby it is flat to realize eliminating the mistake that produces under high s/n ratio, can improve the systematic function under the low signal-to-noise ratio again.Present embodiment proposes technical scheme, operates the channel diagonalization by utilizing IFFT/FFT, comes down to have realized a multi-carrier OFDM systems, and promptly the technical program can be used with multi-carrier OFDM systems compatible fully.

Mention in the foregoing, to the extended matrix of original channel matrix

Can carry out bidiagonalization by Fourier's matrix earlier, promptly carry out:

As the further improvement of the foregoing description, can also be with the biconjugate corner structure

In eigenvalue matrix Λ _HCarry out the grouping coupling of characteristic value, to obtain the new feature value matrix

To the new feature value matrix

In each grouping matrix carry out geometric mean and decompose.With eigenvalue matrix Characteristic value on the diagonal coupling of dividing into groups is in order to obtain the received signal intensity of respectively the dividing into groups balance of trying one's best, and this is mainly by making up big characteristic value and little characteristic value.For example: be with eigenvalue matrix Synthetic one group of on the diagonal the 1st and the 8th element set then will First main diagonal element and the 8th main diagonal element adjust to the adjacent position and get final product.After combining, matrix F _NcAlso to do corresponding row and adjust in proper order, with F _NcFirst row and the 8th be listed as and adjust to the adjacent position, with the reposition of corresponding primitive character value.

The FNc that the note ordering is good, Λ _HFor

Right In each grouping matrix carry out GMD and decompose, remember that first group is ∑ _iThereby, obtain:

∑ _i＝Q _iR _iP _i ^H

Therefore whole channel matrix can be write as:

$\hat{H}={{\hat{F}}_{\mathrm{Nc}}}^H{\mathrm{QRP}}^H{\hat{F}}_{\mathrm{Nc}}$

Wherein:

Q＝diag{Q _i| _{i＝1，2，...，k}}

R＝diag{R _i| _{i＝1，2，...，k}}

P＝diag{P _i| _{i＝1，2，...，k}}

The follow-up signal processing procedure is identical with embodiment 2 corresponding steps, does not repeat them here.Fig. 7 is the value distribution schematic diagram of the diag{R} after decomposing through grouping MMSE-GMD, and as seen from the figure, it is many more to divide into groups, and complexity is low more, but the signal strength signal intensity of one group of the poorest data also can be low more, thereby performance is poor more.And grouping more after a little while, and the signal strength signal intensity of one group of the poorest data can be high more, and performance is good more, but this is to be cost with the complexity.This prioritization scheme provides the degree of freedom of a balance between performance and complexity, be highly suitable in the practical application and adjust accordingly according to system situation.

Embodiment 3:

The present invention also proposes a kind of communication system based on precoding, comprises transmitting terminal and receiving terminal; Transmitting terminal comprises modulation module, T-H precoding module, increases cyclic prefix module and antenna, and receiving terminal comprises antenna, removes cyclic prefix module, frequency-region signal processing module, the module that accepts filter, delivery module and demodulation module; Aforementioned these modules exist in the existing communication system, no longer are repeated in this description.The key of native system is that this communication system also comprises: based on the geometric mean decomposing module of extended channel, and described transmitting terminal also comprises the transmission filtration module.As shown in Figure 8, Fig. 8 is the single-carrier system schematic diagram that decomposes based on the extended channel matrices geometric mean.Decomposition is meant and uses the geometric mean decomposition technique based on the extended channel matrices geometric mean, and the extended channel matrices of original channel matrix is decomposed.

Be used for extended channel matrices based on the geometric mean decomposing module of extended channel to the original channel matrix H Carry out geometric mean and decompose, obtain upper triangular matrix R, unitary matrice P and unitary matrice Q, and the R matrix is sent to the T-H precoding module, the P matrix is sent to the transmission filtration module, the Q matrix is sent to the module that accepts filter.

Send filtration module and be used to receive described P matrix, and send Filtering Processing according to the data of described P matrix after to the T-H precoding.

Extended channel matrices according to the original channel matrix H

Decompose acquisition upper triangular matrix R, unitary matrice P and unitary matrice Q based on the geometric mean decomposing module of extended channel.

Transmitting terminal, T-H precoding module carry out the T-H precoding according to the R matrix that receives to the data after the modulation; Send filtration module according to the P matrix, the data after the T-H precoding are sent filtering.

At receiving terminal, the module that accepts filter accepts filter to the data after the frequency-region signal processing according to the Q matrix.

Below the several key modules based on the communication system of precoding are described:

The T-H precoding module as shown in Figure 9, Fig. 9 is a T-H precoding module schematic diagram.Represent that with s x represents the data through the T-H precoding through the data after the modulation module QAM modulation.Data after the QAM modulation are gone here and there through a feedback filter and are accorded with the pre-elimination of disturbing, and feedback filter is to carry out this pre-process of eliminating according to the R matrix.Owing to can make the dynamic range of signal strengthen in this process, and transmitted power also can improve, and therefore inserts a die lifter in the output of filter, and this die lifter is responsible for the dynamic range of signal is limited in [M, M] between, M has different values according to different QAM modulation.

After the signal process T-H precoding module, need through sending filtration module.The parameter of this transmission filtration module is from the R matrix that decomposes acquisition based on the geometric mean decomposing module of extended channel.

The signal that the frequency-region signal processing module is responsible for receiving is converted to frequency domain by FFT, carries out synchronously operations such as channel estimating and frequency domain equalization then.But different with traditional scheme, frequency domain signal processing module frequency domain balancing technique of the present invention is an alternative mode, with the present single-carrier frequency domain equalization system of compatibility), also comprise other frequency domain technique simultaneously, synchronous as frequency domain, frequency domain channel estimation etc.The frequency-region signal processing module can return conversion of signals to time domain by IFFT, enters the follow-up module that accepts filter then.

The module that accepts filter accepts filter the parameter handled equally from the geometric mean decomposing module based on extended channel to data, can realize this module with filter.

Wherein, for the feedback filter in the T-H precoding module and the module that accepts filter, its physical structure is identical with traditional scheme, but it is different with traditional scheme on parameter acquiring, be the parameter of utilizing QR to decompose to obtain the feedback filter in the T-H precoding module and the module that accepts filter in the prior art, and the present invention decompose by the geometric mean based on extended channel to obtain these parameters.

Set forth the native system course of work below by specific implementation process:

Step S101 obtains channel information.Concerning closed-loop system and open cycle system, the process that obtains channel information is different.To closed-loop system, transmitting terminal at first sends training sequence channel is trained; Receiving terminal utilizes this known training sequence again, with classical channel estimation method wireless channel is estimated, obtains channel information; Receiving terminal is given transmitting terminal with this feedback of channel information at last.The divided ring system, the TDD system of time division duplex for example, transmitting terminal utilizes the channel information of the channel information estimating down-ward link of up link directly according to the symmetry of uplink downlink, under this pattern, need not receiving terminal and gives transmitting terminal with feedback of channel information.

Step S102 is according to the channel information that obtains, based on the geometric mean decomposing module of the extended channel extended channel matrices to the original channel matrix H

Carry out geometric mean and decompose, obtain R matrix, P matrix and Q matrix.

Step S103, modulation module carries out the QAM modulation to the data that receive, and the data after will modulating then are sent to the T-H precoding module.

Step S104, the T-H precoding module is carried out the T-H precoding according to the R matrix that receives to the data after the modulation, promptly carries out the elimination of ISI, and the result with the T-H precoding is sent to transmission filtering mould certainly then.

Step S105 sends filtration module according to the P matrix that receives, and the data after the T-H precoding are sent filtering.Increase cyclic prefix module then and add CP, and send from antenna to sending filtered data.

Step S106, the receiving terminal antenna receives data, removes cyclic prefix module the data that receive are removed CP, and it is sent into the frequency-region signal processing module.The frequency-region signal processing module will be exported the result and be sent to the module that accepts filter after the data of removing CP are carried out the frequency-region signal processing.

Step S107, the module that accepts filter accepts filter to the data after the frequency-region signal processing according to the Q matrix that receives.Data after accepting filter then enter the delivery module, enter demodulation module at last and carry out QAM demodulation and judgement, recover original transmission information.

Said process has briefly been described the single-carrier system course of work of decomposing based on the extended channel matrices geometric mean.As the multicarrier system implementation of the foregoing description, transmitting terminal also comprises the OFDM modulation module, and this module is used for carrying out the OFDM modulation to sending filtered data; Receiving terminal also comprises the OFDM demodulation module, and this module is used for the data that receive are carried out the OFDM demodulation.Like this, the application channel equalization method based on precoding of the present invention is feasible equally on multicarrier system.As shown in figure 10, Figure 10 is the multicarrier system schematic diagram that decomposes based on the extended channel matrices geometric mean.

In the multicarrier system, for the step S105 of the foregoing description, the transmission filtration module sends according to P logm certificate after the filtering, and the OFDM modulation module carries out the IFFT operation to these data, promptly carries out the OFDM modulation.Increase cyclic prefix module then data are added CP, and send from antenna.

In the multicarrier system, for the step S106 of the foregoing description, the receiving terminal antenna receives data, removes the processing that cyclic prefix module is removed CP to the data that receive, and the OFDM demodulation module carries out the FFT operation to data then, promptly carries out the OFDM demodulation.Data through the FFT operation are admitted to the frequency-region signal processing module again.After signal is handled through frequency-region signal, enter the module that accepts filter.

So far, the channel equalization method based on precoding of the present invention's proposition can be realized with the mode of multicarrier system equally.In embodiment 1 and 2, description is arranged owing to carry out balanced process according to R, P, Q matrix in the said process, no longer repeat at this.

Above-described embodiment of the present invention does not constitute the qualification to protection range of the present invention.Any modification of being done within the spirit and principles in the present invention, be equal to and replace and improvement etc., all should be included within the claim protection range of the present invention.

Claims (6)

1. the channel equalization method based on precoding is characterized in that, comprising:

Step S100 is according to the extended channel matrices of original channel matrix H Carry out geometric mean and decompose, obtain upper triangular matrix R, unitary matrice P and unitary matrice Q;

For multicarrier system, step S100 specifically comprises:

Step S101 is to described extended channel matrices

Earlier according to formula

Carry out characteristic value decomposition, obtain the extension feature value matrix of biconjugate corner structure

Wherein

Be N _C* N _CFourier's matrix, N _CBe the contained symbolic number of data block;

Step S102 is to the extension feature value matrix of described biconjugate corner structure

Carry out geometric mean and decompose, obtain Q, R, three matrixes of P;

Step S200 carries out equilibrium according to described R matrix, P matrix and Q matrix, comprising:

Step S201 at transmitting terminal, carries out the T-H precoding according to described R matrix to the data after modulating earlier;

Step S202 at transmitting terminal, sends filtering according to the data of described P matrix after to the T-H precoding;

Step S203, at receiving terminal, the data after according to described Q matrix frequency-region signal being handled accept filter.

2. the channel equalization method based on precoding according to claim 1 is characterized in that, for single-carrier system, among the step S100, according to the extended channel matrices of original channel matrix H

The process of carrying out the geometric mean decomposition specifically comprises: to described extended channel matrices

According to formula Directly carrying out geometric mean decomposes.

3. the channel equalization method based on precoding according to claim 1 is characterized in that, carries out in the balanced process according to described R matrix, P matrix and Q matrix:

Also comprise step after the step S202:, carry out the OFDM modulation to sending filtered data at transmitting terminal;

Also comprise step before the step S203:, the data of removing Cyclic Prefix are carried out the OFDM demodulation at receiving terminal.

4. the channel equalization method based on precoding according to claim 3 is characterized in that, among the step S102 to the extension feature value matrix of described biconjugate corner structure

The process of carrying out the geometric mean decomposition also comprises: with the extension feature value matrix of described biconjugate corner structure

In eigenvalue matrix Λ _HCarry out the grouping coupling of characteristic value, to obtain the new feature value matrix To described new feature value matrix

In each grouping matrix carry out geometric mean and decompose.

5. the communication system based on precoding comprises transmitting terminal and receiving terminal; Described transmitting terminal comprises modulation module, T-H precoding module, increases cyclic prefix module and transmitting antenna, and described receiving terminal comprises reception antenna, removes cyclic prefix module, frequency-region signal processing module, the module that accepts filter, delivery module and demodulation module; It is characterized in that described communication system also comprises: based on the geometric mean decomposing module of extended channel, described transmitting terminal also comprises the transmission filtration module;

Described geometric mean decomposing module based on extended channel is used for the extended channel matrices to the original channel matrix H

Carry out geometric mean and decompose, obtain upper triangular matrix R, unitary matrice P and unitary matrice Q, and described R matrix is sent to the T-H precoding module, described P matrix is sent to the transmission filtration module, described Q matrix is sent to the module that accepts filter; For multicarrier system, described process of carrying out the geometric mean decomposition specifically comprises:

To described extended channel matrices

Earlier according to formula

Carry out characteristic value decomposition, obtain the extension feature value matrix of biconjugate corner structure

Wherein

Be N _C* N _CFourier's matrix, N _CBe the contained symbolic number of data block;

Extension feature value matrix to described biconjugate corner structure

Carry out geometric mean and decompose, obtain Q, R, three matrixes of P;

Described transmission filtration module is used to receive described P matrix, and sends filtering according to the data of described P matrix after to the T-H precoding;

Extended channel matrices according to the original channel matrix H

Described geometric mean decomposing module based on extended channel is decomposed acquisition upper triangular matrix R, unitary matrice P and unitary matrice Q;

Transmitting terminal, described T-H precoding module carry out the T-H precoding according to the described R matrix that receives to the data after the modulation; Described transmission filtration module sends filtering according to described P matrix to the data after the T-H precoding;

Receiving terminal, the described module that accepts filter accept filter to the data after the frequency-region signal processing according to described Q matrix.

6. the communication system based on precoding according to claim 5 is characterized in that, for the implementation of multicarrier system, described transmitting terminal also comprises the OFDM modulation module, and described receiving terminal also comprises the OFDM demodulation module; Described OFDM modulation module is used for carrying out the OFDM modulation to sending filtered data; Described OFDM demodulation module is used for carrying out the OFDM demodulation through the data of removing Cyclic Prefix.

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