CN101534177B - RUMSWF based low-complexity reduced rank balancing method in MIMO system - Google Patents

Abstract

The invention provides a RUMSWF based low-complexity reduced rank balancing method in an MIMO system, which is improved from an MSWF based self-adapting reduced rank linear balancing method and is a reduced rank self-adapting MIMO linear balancing method which realizes a multilevel Weiner filter based on a rectangular block matrix and by a related subtraction structure. By improving the block matrix of the unitary multilevel Weiner filter, a rectangular matrix block of the square block matrix is selected as the block matrix, and the number of dimension of a received signal is reduced step by step in the forward recursive decomposition of the unitary multilevel Weiner filter, thereby reducing the iteration complexity of the self-adapting balancing and simultaneously increasing the convergence rate. The theoretical analysis and simulation result show that the low-complexity quick reduced rank self-adapting balancing method has the advantages of low complexity and quick convergence rate. In a V-BLAST system provided with 4 transmitting antennas and 8 receiving antennas and adopting the BPSK modulation, by only utilizing one half of complexity of the multilevel Weiner filter based balancing method, the error code performance which is only 0.78 dB lower than that of the multilevel Weiner filter based balancing method can be achieved.

Description

In the mimo system based on the low complex degree contraction equalization methods of RUMSWF

Technical field

The invention belongs to the channel equalization method in the wireless communication technology field mimo system, be specifically related to a kind of low complex degree contraction equalization methods based on RUMSWF (Rectangle Unitary Multistage Wiener Filter).

Background technology

In decades in the past, the communication technology has obtained development fast and has used widely, has greatly promoted The development in society and economy, is changing people's life style.And along with the development of society and the raising of people's material life and spiritual life level, people grow with each passing day to the demand of capability of wireless communication system.Traditional wireless communication system adopts single transmit antenna and single reception antenna, is called the single output of single input (SISO) system.The SISO system has the bottleneck that can not break through---Shannon capacity limit on channel capacity, can not satisfy the demand of new generation of wireless capability of communication system and reliability.Multi-aerial transmission system---MIMO (the Multiple Input Multiple Output) communication technology of handling during in conjunction with sky; The new way that addresses this problem is provided, and it all adopts many antennas at the Radio Link two ends, can make full use of space resources; Need not to increase under the situation of frequency spectrum resource and transmitting power; Promote capability of communication system and reliability exponentially, be regarded as the key technology that the next generation wireless communication system must adopt, caused countries in the world scholars' very big concern.

The MIMO technology is conceptive very simple, any one wireless communication system, so long as all use many antennas at the two ends of Radio Link, perhaps aerial array has just constituted a mimo system.E.Telatar and J.Foshini have proved respectively that mimo system and SIMO are wireless and have compared with the MISO wireless system that can obtain huge channel capacity, this channel capacity has broken through the bottleneck of conventional channel capacity, is the popularization of C.E.Shannon channel capacity.But meanwhile, the complexity of mimo system also can increase along with the increase of dual-mode antenna number, and therefore advanced signal processing technology is to realize the key of mimo system maximum capacity.Along with the continuous popularization that deepens continuously and use of research, the contraction method in the mimo system, particularly the detection method research based on the contraction signal processing have become present research focus and difficult point.

The MIMO input is the branch that present input field receives much concern, and has delivered more than 600 piece scientific paper in important so far periodical and the meeting at home and abroad, and about 70 remainder patents.The most frequently used detection method comprises maximum likelihood detection method (MLD), linearity test method and demixing time space V-BLAST (the Vertical-Bell Laboratories Layered Space Time) method that was proposed by people such as the breadboard J.Foschini of the U.S. BELL of Lucent company in 1996 in the mimo system.Because in the MIMO input, the performance of speed and reliability and method and the balance between the complexity or trade-off problem are the key factor that can this technology of decision really be suitable for practical application all the time.Therefore, under the prerequisite that satisfies certain performance index requirement, the complexity that reduces method has as much as possible just become the emphasis of our concern, and the research of dimension reduction method just can reach this purpose.

The thought of dimensionality reduction or contraction signal processing has quite long developing history; Can trace back to H.Hotelling; The early stage work of doing of C.E.Shannon and L.L.Scharf, and obtained application in various degree in Array Signal Processing, radar, Multiuser Detection field etc.At present the achievement in research of dimension reduction method is attributable to following two types: the MIMO contraction method of handling based on the MIMO contraction method of signal subspace thought, based on multilevel signal.

MIMO contraction method based on signal subspace thought: its core is exactly with received signal vector projection on the dimensionality reduction subspace, with the convergence rate and the reduction computation complexity of raising method.Select different contraction conversion (being the contraction subspace) can obtain different contraction performances.Typical subspace choosing method has proper subspace, based on the contraction processing method of Krylov subspace, based on the contraction processing method of orthogonal subspaces projection.At present, the most frequently used method of choosing of contraction subspace composition characteristic vector has principal component analysis method (Principal ComponentMethod) and cross-spectrum to estimate method (Cross Spectral Method), and they all are based on the method for characteristic value decomposition.Principal component analysis method has only been used the second-order statistics of observation data, and its performance is not ideal.Cross-spectrum is estimated method and is had more robustness with respect to principal component analysis method, but still the covariance matrix of vector is made characteristic value decomposition to received signal, makes that its computation complexity is higher.

MIMO contraction method based on the multilevel signal processing: multistage wiener filter (MSWF-Multistagewinner filter) is proposed by Goldstein and Reed the earliest; It has promoted traditional Weiner filter structure; Form a nested chain by the scalar Weiner filter; Corresponding method is broken down into forward recursion and backward recursion equation; As long as the D level at the forward recursion equation of multistage wiener filter is blocked, just can obtain the multistage wiener filter of contraction, promptly realized the dimension-reduction treatment of signal.Multistage wiener filter has two kinds of ways of realization in real system: based on the method (LMS-Least Mean Square) of gradient with based on the invert method of (SMI-SampleMatrix Inverse) of sample matrix.Usually, the convergence rate of gradient method depends on the conditional number of covariance matrix.Under the less situation of reception antenna number, the conditional number of covariance matrix is bigger, thereby makes the convergence rate of gradient method very slow.And the SMI method requires sample autocorrelation matrix is inverted, and therefore when the dual-mode antenna number was a lot, its operand was very high.

The various MIMO detection methods of above-mentioned research; Usually need understand channel condition information accurately at receiving terminal; In the application corresponding to reality, just need in sending data, add a large amount of pilot tones, channel circumstance complicated and changeable estimated with auxiliary receiver.This just causes the rate of information throughput of mimo system greatly to reduce, and this also becomes the MIMO detection method is moved towards practical applications by theoretical research a major obstacle simultaneously.Meanwhile, the adaptive equalization technique in the frequency selectivity mimo channel is quite important, and for adaptive equilibrium method, computation complexity and convergence rate are two important indicators of balancing method performance.Fast convergence rate can allow receiver to make judgement faster.Particularly in time varying channel, we require the convergence rate of method faster than the pace of change of channel, respond faster and follow the tracks of so that equalizer is made fast-changing channel.So this just needs the design dimension reduction method with minimum tap number (minimizing computation complexity), reaches (less training sequence) and stable convergence fast.So research has low complex degree, can be applied in the time varying channel, do not influence detect performance in, can significantly reduce the training sequence traffic volume detection method---the dimension-reduction treatment method is extremely important.The present invention has proposed improved low complex degree contraction equalization methods based on RUMSWF in a kind of mimo system on the basis based on the dimensionality reduction adaptive MIMO linear equalizing method of multistage wiener filter.The method has been accelerated convergence rate in the iteration complexity that reduces adaptive equalization, and is far smaller than under the situation that receives the signal dimension at the progression of contraction Weiner filter, and this method just can reach the performance of approximate full rank mean square error.

Summary of the invention

It is high to the objective of the invention is to overcome traditional equalization methods complexity, and the shortcoming that convergence rate is slow provides in a kind of mimo system the low complex degree contraction equalization methods based on RUMSWF.

For achieving the above object, the technical scheme that the present invention adopts is:

1) foundation of system model: for number of transmit antennas is that M, reception antenna number are the frequency selectivity mimo system of N, supposes that its channel exponent number is L, and then channel impulse response is:

$H=\underset{l=0}{\overset{L-1}{\mathrm{\Σ}}}{H}_l\mathrm{\δ}(i-l)$

H wherein _lBeing N * M dimension, is the corresponding channel fading coefficient matrix in l bar time delay path, if k moment emission signal vector s (k) is independent identically distributed M dimensional vector s (k)=[s ₁(k) ..., s _M(k)] ^T, then N ties up received signal vector y (k)=[y ₁(k) ..., y _N(k)] ^TRepresent as follows:

$y\left(k\right)=\underset{l=0}{\overset{L}{\mathrm{\Σ}}}{H}_{l}s(k-l)+n\left(k\right)$

N (k)=[n wherein ₁(k) ..., n _N(k)] ^TFor N ties up independent identically distributed additivity white complex gaussian noise process;

The treated length that makes equalizer is N _f, with emission signal vector, received signal vector and noise vector at k=0 ..., N _f-1 carries out the time domain expansion constantly, that is $\tilde{s}\left(k\right)={\left[\begin{array}{ccc}{s}^T\left(k\right)& \·\·\·& s^T(k-N_f-L)\end{array}\right]}^T,$ $\tilde{y}\left(k\right)={\left[\begin{array}{cccc}{y}^T\left(k\right)& y^T(k-1)& \·\·\·& y^T(k-N_f)\end{array}\right]}^T,$ $\tilde{n}\left(k\right)={\left[\begin{array}{ccc}{n}^T\left(k\right)& \·\·\·& n^T(k-N_f)\end{array}\right]}^T,$ So obtain following matrix representation forms:

$\tilde{y}\left(k\right)=\tilde{H}\left(k\right)\tilde{s}\left(k\right)+\tilde{n}\left(k\right)$

Wherein

It is multipath channel matrix H by N * M dimension _lThe L line diagonal matrix that constitutes;

2) establish s ₁Be reference signal, forgetting factor is λ, k constantly the tenth of the twelve Earthly Branches multistage wiener filter be input as received signal vector $x_0\left(k\right)=\tilde{y}\left(k\right),$ Carry out the renewal of normalization associated vector and blocking matrix:

$h_1\left(k\right)=\tilde{y}\left(k\right){\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="H2009100218725E00012.png"\; state="\{\{state\}\}">s</figure-callout>}}_1^{*}\left(k\right)+\mathrm{\&lambda;}{h}_1(k-1)$

$B_1\left(k\right)=I_N^{(N-1)}-h_1^{(N-1)}\left(k\right)h_1^H\left(k\right);$

3) to i=1 ..., D, using the forward recursion equation has

$d_i\left(k\right)=h_i^H{x}_{i-1}\left(k\right),1\&le;i\&le;D$

$x_i\left(k\right)=B_i{x}_{i-1}\left(k\right)=x_{i-1}^{(N-i)}\left(k\right)-h_i^{(N-i)}{d}_i\left(k\right),1\&le;i\&le;D$

$h_{i+1}\left(k\right)=x_i\left(k\right){\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="H2009100218725E00012.png"\; state="\{\{state\}\}">d</figure-callout>}}_1^{*}\left(k\right)+\mathrm{\&lambda;}{h}_{i+1}(k-1)$

$B_{i+1}\left(k\right)=I_{N-i}^{(N-i-1)}-h_{i+1}^{(N-i-1)}\left(k\right)h_{i+1}^H\left(k\right)$

In the formula, subscript ^*The expression conjugation, h _iBe (N-i+1) * 1 dimensional vector, x _i(k) be the N-i dimensional vector, promptly along with the increase x of filter order _i(k) dimension reduces step by step;

4) to i=1 ..., D uses the backward recursion equation, and is identical with equalization methods based on UMSWF

d _D(k)＝ε _D(k)

$w_i\left(k\right)=\frac{{\mathrm{\&epsiv;}}_i\left(k\right)d_{i-1}^{*}\left(k\right)}{{\left|{\mathrm{\&epsiv;}}_i\left(k\right)\right|}^2}$

${\mathrm{\&epsiv;}}_{i-1}\left(k\right)=d_{i-1}\left(k\right)-w_i^{*}{\mathrm{\&epsiv;}}_i\left(k\right)$

In the formula, d _i(k) expression i level scalar ideal signal, w _iBe weight vector, just by vector x _I-1(k) estimate scalar d _I-1(k) Weiner filter, ε _iBe the error signal of each grade, the ideal signal d of D level _D(k) be ε _D, the then output of equalizer

Be:

${\hat{s}}_1\left(k\right)=w_1^{*}\left(k\right){\mathrm{\&epsiv;}}_1\left(k\right).$

The blocking matrix that the present invention is based on multistage wiener filter at tenth of the twelve Earthly Branches in the self adaptation contraction linear equalizing method of MSWF improves, and the rectangular matrix-block that adopts (N-i) * (N-i+1) dimension is as blocking matrix, make the MSWF forward recursion decompose in observation signal vector x at different levels _i(k) dimension reduces step by step, and this rectangular matrix-block comes from the square blocking matrix that subtracts each other implementation structure simultaneously, therefore possesses the advantage of square blocking matrix simultaneously, does not need independently to find the solution blocking matrix.The present invention is applied to RUMSWF to have reduced the complexity of equalization methods in the contraction adaptive equalization, has accelerated the convergence rate of equalization methods, makes it have good performance.Particularly at transmitting antenna, reception antenna is more and contraction exponent number when higher, RUMSWF can effectively reduce the number of times that the MSWF forward recursion is taken advantage of in decomposing again, thereby greatly reduces the complexity of method, has accelerated convergence rate.Theory analysis and emulation experiment show that this improves equalization methods at the self adaptation contraction equalization methods that all is superior to aspect complexity and the convergence rate based on MSWF.

Description of drawings

Fig. 1 is a self-adaptive linear equalisation device structured flowchart in the mimo system;

Fig. 2 is the implementation structure figure of RUMSWF (Rectangle Unitary Multistage Wiener Filter);

Fig. 3 is the contraction linear equalizer error code curve chart based on three kinds of multistage wiener filters;

Fig. 4 is two kinds of self-adaptive reduced-dimensions equalization methods and RLS method convergence rate comparison diagram.

Embodiment

Below in conjunction with accompanying drawing the present invention is done further explain.

Referring to Fig. 1, at first provide the system model of self-adaptive linear equalisation device in the mimo system.For number of transmit antennas is that M, reception antenna number are the frequency selectivity mimo system of N, supposes that its channel exponent number is L, so channel impulse response can be expressed as:

$H=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{H}_l\mathrm{\&delta;}(i-l)$

H wherein _lBeing N * M dimension, is the corresponding channel fading coefficient matrix in l bar time delay path.If k emission signal vector s (k) constantly is independent identically distributed M dimensional vector s (k)=[s ₁(k) ..., s _M(k)] ^T, then N ties up received signal vector y (k)=[y ₁(k) ..., y _N(k)] ^TRepresent as follows:

$y\left(k\right)=\underset{l=0}{\overset{L}{\mathrm{\&Sigma;}}}{H}_{l}s(k-l)+n\left(k\right)$

N (k)=[n wherein ₁(k) ..., n _N(k)] ^TFor N ties up independent identically distributed additivity white complex gaussian noise process.

The treated length that makes equalizer is N _f, with emission signal vector, received signal vector and noise vector at k=0 ..., N _f-1 carries out the time domain expansion constantly, that is $\tilde{s}\left(k\right)={\left[\begin{array}{ccc}{s}^T\left(k\right)& \&CenterDot;\&CenterDot;\&CenterDot;& s^T(k-N_f-L)\end{array}\right]}^T,$ $\tilde{y}\left(k\right)={\left[\begin{array}{cccc}{y}^T\left(k\right)& y^T(k-1)& \&CenterDot;\&CenterDot;\&CenterDot;& y^T(k-N_f)\end{array}\right]}^T,$ $\tilde{n}\left(k\right)={\left[\begin{array}{ccc}{n}^T\left(k\right)& \&CenterDot;\&CenterDot;\&CenterDot;& n^T(k-N_f)\end{array}\right]}^T,$ So obtain following matrix representation forms:

$\tilde{y}\left(k\right)=\tilde{H}\left(k\right)\tilde{s}\left(k\right)+\tilde{n}\left(k\right)$

Wherein

It is multipath channel matrix H by N * M dimension _lThe L line diagonal matrix that constitutes.

To above system model, establish s ₁Be reference signal, forgetting factor is λ, k constantly the tenth of the twelve Earthly Branches multistage wiener filter be input as received signal vector $x_0\left(k\right)=\tilde{y}\left(k\right).$ Then N ties up the observation signal vector x ₀(k) through becoming D dimension desired signal behind the D level forward recursion equation, can get D rank contraction RUMSWF by Fig. 2

$d\left(k\right)={[d_1\left(k\right),d_2\left(k\right),\&CenterDot;\&CenterDot;\&CenterDot;,d_D\left(k\right)]}^T=T_D^H{x}_0\left(k\right)$ ()

$T_D=[{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="H2009100218725E00012.png"\; state="\{\{state\}\}">h</figure-callout>}}_1,h_2{\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="H2009100218725E00012.png"\; state="\{\{state\}\}">B</figure-callout>}}_1,\&CenterDot;\&CenterDot;\&CenterDot;,h_{D-1}\underset{i=D-2}{\overset{1}{\mathrm{\&Pi;}}}{B}_i,h_D\underset{i=D-1}{\overset{1}{\mathrm{\&Pi;}}}{B}_i]=[{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="H2009100218725E00012.png"\; state="\{\{state\}\}">t</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="H2009100218725E00021.png"\; state="\{\{state\}\}">t</figure-callout>}}_2,\&CenterDot;\&CenterDot;\&CenterDot;,t_D]$

$B_i=I-h_i{h}_i^H$

$d_i\left(k\right)=h_i^H{x}_{i-1}\left(k\right),1\&le;i\&le;N-1$

x _i(k)＝B _ix _i-1(k)＝x _i-1(k)-h _id _i(k)，1≤i≤N-1

d _D(k)＝ε _D(k)

Wherein, d _i(k) expression i level scalar ideal signal.h ₁..., h _NBe the normalized crosscorrelation vector, be desired signal and observation signal vector normalized crosscorrelation vector.I-h _ih _i ^HBe blocking matrix B _i, satisfy B _ih _i=0, i=1 ..., N * N of N ties up positive square matrix, and its order is N-i.Define the subscript of matrix or vector simultaneously ⁽ⁱ⁾It is capable that its preceding i is got in expression, i.e. h ₁ ^(N-1)Expression amount of orientation h ₁Preceding N-1 capable.MSWF adopts when subtracting each other the structure realization, ${\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="H2009100218725E00012.png"\; state="\{\{state\}\}">B</figure-callout>}}_1=I-h_1{h}_1^H,$ Satisfy $B_1^{N-1}{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="H2009100218725E00012.png"\; state="\{\{state\}\}">h</figure-callout>}}_1=0.$ Use B here, ₁ ^N-1Replace ${\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="H2009100218725E00012.png"\; state="\{\{state\}\}">B</figure-callout>}}_1=I-h_1{h}_1^H,$ Promptly get B ₁Preceding N-1 capable of (N-1) * N dimension blocking matrix.This substitutes and has kept

Full detail and do not have any loss, this is because B ₁Order be N-1.Proof N ties up square blocking matrix B below _iOrder be N-i.By B _iBe (N-i+1) * (N-i+1) dimension matrix, h _iFor (N-i+1) * 1 dimensional vector, satisfy B _ih _i=0, promptly be equivalent to seek and satisfy $[{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="H2009100218725E00012.png"\; state="\{\{state\}\}">b</figure-callout>}}_1,\&CenterDot;\&CenterDot;\&CenterDot;,b_{N-i+1}]\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="h\; i"\; filenames="H2009100218725E00012.png"\; state="\{\{state\}\}">h</figure-callout>}}_i\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ h_{i(N-i+1)}\end{array}\right]=0$ The number of independent vector of 1 * (N-i+1) dimension, be prone to know that the vectorial number of the independence of existence is N-i, i.e. B by the linear algebra knowwhy _iOrder be N-i.So adopt (N-i) * (N-i+1) to tie up rectangular matrix B _i ^(N-i)Can keep as blocking matrix

Full detail and do not have any loss.This implementation structure has utilized the advantage of rectangular blocking matrix on the one hand simultaneously, can reduce the dimension of received signal vector step by step, has adopted on the other hand and has subtracted each other structure; Do not need to find the solution separately blocking matrix; So both can reduce memory space, help reducing amount of calculation again, as calculating x _i(k)=B _ix _I-1(k) amount of calculation that needs is O (N ²), subtract each other Structure Calculation x and utilize _i(k)=x _I-1(k)-h _id _i(k) amount of calculation that needs is merely O (N).

This RUMSWF is applied in the adaptive equilibrium method, and step is following:

1) at first, carry out the renewal of normalization associated vector and blocking matrix:

$h_1\left(k\right)=\tilde{y}\left(k\right){\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="H2009100218725E00012.png"\; state="\{\{state\}\}">s</figure-callout>}}_1^{*}\left(k\right)+\mathrm{\&lambda;}{h}_1(k-1)$

$B_1\left(k\right)=I_N^{(N-1)}-h_1^{(N-1)}\left(k\right)h_1^H\left(k\right);$

2) to i=1 ..., D, using the forward recursion equation has

$d_i\left(k\right)=h_i^H{x}_{i-1}\left(k\right),1\&le;i\&le;D$

$x_i\left(k\right)=B_i{x}_{i-1}\left(k\right)=x_{i-1}^{(N-i)}\left(k\right)-h_i^{(N-i)}{d}_i\left(k\right),1\&le;i\&le;D$

$h_{i+1}\left(k\right)=x_i\left(k\right){\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="H2009100218725E00012.png"\; state="\{\{state\}\}">d</figure-callout>}}_1^{*}\left(k\right)+\mathrm{\&lambda;}{h}_{i+1}(k-1)$

$B_{i+1}\left(k\right)=I_{N-i}^{(N-i-1)}-h_{i+1}^{(N-i-1)}\left(k\right)h_{i+1}^H\left(k\right)$

In the formula, subscript ^*The expression conjugation, h _iBe (N-i+1) * 1 dimensional vector, x _i(k) be the N-i dimensional vector, promptly along with the increase x of filter order _i(k) dimension reduces step by step;

3) to i=1 ..., D uses the backward recursion equation, and is identical with equalization methods based on UMSWF

d _D(k)＝ε _D(k)

$w_i\left(k\right)=\frac{{\mathrm{\&epsiv;}}_i\left(k\right)d_{i-1}^{*}\left(k\right)}{{\left|{\mathrm{\&epsiv;}}_i\left(k\right)\right|}^2}$

${\mathrm{\&epsiv;}}_{i-1}\left(k\right)=d_{i-1}\left(k\right)-w_i^{*}{\mathrm{\&epsiv;}}_i\left(k\right)$

To sum up, equalizer is output as:

${\hat{s}}_1\left(k\right)={\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="H2009100218725E00012.png"\; state="\{\{state\}\}">w</figure-callout>}}_1^{*}\left(k\right){\mathrm{\&epsiv;}}_1\left(k\right).$

Fig. 3 and Fig. 4 have provided the performance simulation of the method.

Simulated conditions: consider a transmitting antenna M=4, the V-BLAT system of reception antenna N=8, each antenna transmits and adopts the BPSK modulation and have equal transmitting power.Channel model is the frequency selectivity rayleigh fading channel, channel exponent number L=3, the i.e. length N of equalizer processes _f=3, each footpath power equates and power spectrum is the Jakes spectrum, each antenna to the multipath fading coefficient separate, and to obey variance be 1 multiple Gaussian distribution, no chnnel coding.Noise is that average is 0 white complex gaussian noise, and power changes with signal to noise ratio.In emulation, the bit number of fixing each frame is 1000, and wherein preceding 200 bits are used for channel estimating, adopts minimum mean square error criterion to estimate each channel parameter in the channel estimating.Adopt Monto Carlo emulation technology to carry out emulation.

The signal to noise ratio snr of trunnion axis definition is defined as the average signal-to-noise ratio of output among Fig. 3, promptly $\mathrm{SNR}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{SNR}}_i,$ SNR wherein _iBe the signal power that receives of i root antenna and the ratio of noise power.Main investigation is improved based on the RUMSWF equalization methods and based on UMSWF equalization methods error performance difference in the emulation.Fig. 3 has provided the order (progression is represented with D) of multistage wiener filter when getting different value, based on the error code curve of the equalization methods of two kinds of MSWF.We can find out by figure, and when SNR changed from low to high, in order to obtain full rank Wiener filtering performance, two kinds of required necessary level number averages of MSWF were increasing gradually.Simultaneously; Comprehensive D=4, D=8, the curve under three kinds of situation of D=16; The error performance that can see the UMSWF equalization methods slightly is superior to the equalization methods based on RUMSWF; This is because we have done modification choosing of blocking matrix, and MSWF is equivalent to receiving the subspace projection of signal phasor to a low dimension, and its performance depends on to a great extent whether the projection subspace can well the approximate signal subspace.And be that to have got the preceding N-i of the positive square matrix of (N-i+1) * (N-i+1) dimension capable based on the blocking matrix of getting of the equalization methods of RUMSWF; If the capable subspace of opening of this N-i just is the orthogonal signalling subspace; Be that the capable vector of this N-i is independently vectorial for linearity; The full detail that then this N-i is capable can express

accurately; And if the capable vector of this N-i is non-linear independently vector; Then the capable expression signal subspace fully accurately of this N-i is still very little owing to this approximate error, so the difference of two kinds of methods is also less.The suitable difference of error performance of seeing two kinds of methods equally from the simulation result of Fig. 3 is about 1dB; Especially at the high s/n ratio place; Almost indifference exists, but the complexity of the open method of the present invention is more much lower than the adaptive equilibrium method based on MSWF, and table 1 is seen in concrete analysis.

The complexity of three kinds of equalization methods of table 1 (complex multiplication operation number of times) contrast

Can find out that from table 1 improved RUMSWF adaptive equilibrium method lacks MDN than each level of multiplication number of times of UMSWF adaptive equilibrium method _fD (D+1) is inferior, and the multiplication number of times reduces MN altogether in the whole balanced renewal process _f[1 ²* 2+2 ²* 3+ ... (D-1) ²* D] inferior.This shows that improving the total computation complexity of equalization methods reduces more considerable.

Fig. 4 is mainly relatively based on the dimensionality reduction RLS equalization methods of RUMSWF and convergence rate based on the dimensionality reduction RLS equalization methods of UMSWF, simultaneously the convergence rate of these two kinds of methods with conventional RLS adaptive approach compared.In emulation, fixing signal to noise ratio snr=10dB, forgetting factor λ=0.998; Be used for eliminating the influence of current input vector; To the past data exponential weighting, make iteration trend towards reducing the importance of sampled data in the past, so the forgetting factor representative is a kind of temporal correlation through it.Other simulated conditions are identical with error performance emulation.The mean square error of two kinds of methods is as shown in Figure 4 with the change curve of iterations.Can find out by figure; Convergence rate based on the dimensionality reduction RLS equalization methods of RUMSWF slightly is superior to the adaptive equilibrium method based on MSWF; This is owing to will reach same error performance; Than much lower based on the complexity of MSWF, so convergence rate slightly is superior to the method based on MSWF based on the iteration complexity of the dimensionality reduction RLS equalization methods of RUMSWF.We can find out that the convergence rate of the two all obviously is superior to conventional RLS method simultaneously, and order D is more little, and convergence rate is fast more.Needed search time when convergence rate is meant the method iteration near optimal solution, it can regard the search speed of method as.Conventional RLS adaptive approach is searched for optimal solution in whole signal subspace, its convergence rate is directly proportional with the dimension of subspace.Dimensionality reduction RLS adaptive approach is then different, and it greatly reduces the scope of search through subspace projection, has accelerated the convergence rate of method, and projection subspace dimension is low more, restrains fast more.Yet dimensionality reduction RLS method can only be sought the local optimum point in the dimensionality reduction subspace, and the search of conventional RLS method method is global optimum's point, so the MSE performance of dimensionality reduction RLS method is poorer than the performance of full rank RLS method, this point also can be found out from Fig. 4.From figure, can find out that also dimensionality reduction RLS method does not reach the mean square error performance of RLS when D is too small at last.

Claims (1)

1.MIMO based on the low complex degree contraction equalization methods of RUMSWF, it is characterized in that in the system:

1) foundation of system model: for number of transmit antennas is that M, reception antenna number are the frequency selectivity mimo system of N, supposes that its channel exponent number is L, and then channel impulse response is:

$H=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{H}_l\mathrm{\&delta;}(i-l)$

H wherein _lBeing N * M dimension, is the corresponding channel fading coefficient matrix in l bar time delay path, if k moment emission signal vector s (k) is independent identically distributed M dimensional vector s (k)=[s ₁(k) ..., s _M(k)] ^T, then N ties up received signal vector y (k)=[y ₁(k) ..., y _N(k)] ^TRepresent as follows:

$y\left(k\right)=\underset{l=0}{\overset{L}{\mathrm{\&Sigma;}}}{H}_{l}s(k-l)+n\left(k\right)$

N (k)=[n wherein ₁(k) ..., n _N(k)] ^TFor N ties up independent identically distributed additivity white complex gaussian noise process;

The treated length that makes equalizer is N _f, with emission signal vector, received signal vector and noise vector at k=0 ..., N _f-1 carries out the time domain expansion constantly, that is $\tilde{s}\left(k\right){\left[\begin{array}{ccc}{s}^T\left(k\right)& \&CenterDot;\&CenterDot;\&CenterDot;& s^T(k-N_f-L)\end{array}\right]}^T,$ $\tilde{y}\left(k\right)={\left[\begin{array}{cccc}{y}^T\left(k\right)& y^T(k-1)& \&CenterDot;\&CenterDot;\&CenterDot;& y^T(k-N_f)\end{array}\right]}^T,$ $\tilde{n}\left(k\right)={\left[\begin{array}{ccc}{n}^T\left(k\right)& \&CenterDot;\&CenterDot;\&CenterDot;& n^T(k-N_f)\end{array}\right]}^T,$ So obtain following matrix representation forms:

$\tilde{y}\left(k\right)=\tilde{H}\left(k\right)\tilde{s}\left(k\right)+\tilde{n}\left(k\right)$

Wherein

It is multipath channel matrix H by N * M dimension _lThe L line diagonal matrix that constitutes;

2) establish s ₁Be reference signal, forgetting factor is λ, k constantly the tenth of the twelve Earthly Branches multistage wiener filter be input as received signal vector

Carry out the renewal of normalization associated vector and blocking matrix:

$h_1\left(k\right)=\tilde{y}\left(k\right)s_1^{*}\left(k\right)+{\mathrm{\&lambda;h}}_1(k-1)$

$B_1\left(k\right)=I_N^{(N-1)}-h_1^{(N-1)}\left(k\right)h_1^H\left(k\right);$

In the formula, () ⁱThe preceding i that matrix or vector are got in expression is capable, as

Expression amount of orientation h ₁Preceding N-1 capable;

3) to i=1 ..., D, using the forward recursion equation has

$d_i\left(k\right)=h_i^H{x}_{i-1}\left(k\right),$ 1≤i≤D

$x_i\left(k\right)=B_i{x}_{i-1}\left(k\right)=x_{i-1}^{(N-i)}\left(k\right)-h_i^{(N-i)}{d}_i\left(k\right),$ 1≤i≤D

$h_{i+1}\left(k\right)=x_i\left(k\right)d_1^{*}\left(k\right)+{\mathrm{\&lambda;h}}_{i+1}(k-1)$

$B_{i+1}\left(k\right)=I_{N-i}^{(N-i-1)}-h_{i+1}^{(N-i-1)}\left(k\right)h_{i+1}^H\left(k\right)$

In the formula, D is the progression that blocks of filter, and subscript * representes conjugation, () ⁱThe preceding i that matrix or vector are got in expression is capable, h _iBe (N-i+1) * 1 dimensional vector, x _i(k) be the N-i dimensional vector, promptly along with the increase x of filter order _i(k) dimension reduces step by step;

4) to i=1 ..., D uses the backward recursion equation, and is identical with equalization methods based on UMSWF

d _D(k)＝ε _D(k)

$w_i\left(k\right)=\frac{{\mathrm{\&epsiv;}}_i\left(k\right)d_{i-1}^{*}\left(k\right)}{{\left|{\mathrm{\&epsiv;}}_i\left(k\right)\right|}^2}$

${\mathrm{\&epsiv;}}_{i-1}\left(k\right)=d_{i-1}\left(k\right)-w_i^{*}{\mathrm{\&epsiv;}}_i\left(k\right)$

In the formula, d _i(k) expression i level scalar ideal signal, w _iBe weight vector, just by vector x _I-1(k) estimate scalar d _I-1(k) Weiner filter, ε _iBe the error signal of each grade, the ideal signal d of D level _D(k) be ε _D, the then output of equalizer

Be:

${\hat{s}}_1\left(k\right)=w_1^{*}\left(k\right){\mathrm{\&epsiv;}}_1\left(k\right).$

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