CN102624420B - Subspace zero forcing code assist method for suppressing code division multiple access (CDMA) system digit narrowband interference - Google Patents

Abstract

In order to solve a problem that a computation complexity is high when existing direct zero forcing (ZF) code assist method is used to suppress digit narrowband interference in a code division multiple access (CDMA) system, the invention provides a subspace ZF code assist method. The method comprises the following steps: receiving a wireless communication signal and carrying out down conversion on the signal so as to obtain an intermediate frequency signal; digitizing the intermediate frequency signal and demodulating a digital signal to a baseband signal; carrying out chip matching filtering on the baseband signal so as to extract a sampling signal; carrying out windowing storage on the sampling signal so as to obtain a signal vector and carrying out interference suppression to the signal vector. Performance of the subspace ZF code assist method provided in the invention is similar with the direct ZF code assist method but computation complexity is lower than the direct ZF code assist method so that high-performance digit narrowband interference suppression with the low computation complexity can be realized.

Description

Suppress the subspace ZF code householder method that cdma system numeral arrowband disturbs

Technical field

The present invention relates to suppress the method that digital arrowband disturbs in cdma wireless communication system.The present invention be more particularly directed to solve the high problem of existing direct ZF (ZF, Zero Forcing) code householder method computation complexity.

Background technology

The reason that spread spectrum system is used widely in wireless channel is its frequency selective fading that can effectively cause anti-multipath and the superior function in Ta Gong road channel, wherein representative core technology is code division multiple access (CDMA, Code Division Multiple Access) technology.It is the interference that often gets involved spread spectrum system that arrowband disturbs, and wherein the interference of digital arrowband is a kind of novel arrowband interference type.Although spread spectrum system self possesses certain antijamming capability, effectively interference mitigation technology can significantly improve systematic function.

Initial spread spectrum Anti-Jamming Technique originates from 20 century 70s, until the end of the eighties, the main focus of Anti-Jamming Technique is in the directly-enlarging system Suppression of narrow band interference based on prediction/estimation filtering and frequency domain filtering, scientific research personnel's achievement that the Milstein of take is master is the highest, as the summary of document " L B Milstein; Interference rejectiontechniques in spread spectrum communication, IEEE Proceedings, 1988 ".Enter the mid-90, arrival along with CDMA research boom, with the scientific research personnel headed by Poor and Rusch, focus has been transferred to disturb in associating inhibition of cdma system based on technology such as linear prediction, nonlinear prediction and Multiuser Detection more, as the summary of document " H V Poor; L A Rusch; Narrowbandinterference suppression in spread spectrum CDMA, IEEE PersonalCommunication, 1994 ".20th century, the scientific research personnel such as Wang further develop into cdma system interference mitigation technology Predicting Technique, transform domain technology and code ancillary technique, as the summary of document " Xiaodong Wang; H V Poor; Wireless Communication Systems-AdvancedTechniques for Signal Reception; Beijing:Publishing House of Electronics Industry, 2005 ".In above each technology, Predicting Technique comprises linear prediction and nonlinear prediction Liang great branch, its research concentrates in the improvement that receives structure, but due to the processing mode of having taked by bit, the typical problem of existence is that the error rate is high, as document " J Wang; L B Milstein; Adaptive LMS filters forcellular CDMA overlay situations, IEEE Select Areas Commun, 1996 ".Under this viewpoint, a code ancillary technique that utilizes signal code feature to carry out piece processing seems especially effective, and it is that multi-user system is disturbed one of the most promising technology of inhibition, and in this field, the achievement of Poor and Wang is the highest.In existing code ancillary technique, direct ZF (ZF, Zero Forcing) code householder method is due to excellent performance and be easy to self adaptation and realize and to have obtained broad research, as document " S Buzzi; M Lops, H V Poor, Code-Aided Interference Suppression for DS/CDMA Overlay Systems; IEEEProcessing, 2002 ".But directly computation complexity is high, the problem of waste system resource because matrix inversion exists for ZF code ancillary technique.

Accordingly, reduce direct ZF code householder method computation complexity, the method that does not reduce systematic function simultaneously significantly needs.

Summary of the invention

Technology of the present invention is dealt with problems and is: provide a kind of and can suppress the subspace ZF code householder method that in cdma system, digital arrowband disturbs, can reduce existing direct ZF code householder method computation complexity, the Signal to Interference plus Noise Ratio of the high output of keeping system simultaneously performance.

Technical solution of the present invention is: subspace ZF (ZF, ZeroForcing) the code householder method of high-performance low computational complexity, comprises the following steps:

(1) receive wireless communication signals, comprise that CDMA signal, white noise and digital arrowband disturb.

(2) described wireless communication signals is down-converted to intermediate-freuqncy signal.

(3) intermediate-freuqncy signal described in digitlization, to provide digital signal.

(4) by described digital demodulation signal, so that baseband signal to be provided.

(5) by described baseband signal envelope r (t) by cutting general matched filtering so that sampled signal r (m) to be provided, wherein m is sampled signal label and m=0,1,2 ...

Sampled signal r (m) can be modeled as:

r(m)＝y(m)+i(m)+ε(m)

＝y ₀(m)+z(m)+i(m)+ε(m)

Y in formula (m) represents CDMA sampled signal, comprises the signal component y of desired user 0 ₀(m) and multiple access disturb the signal component z (m) of (MAI, Multiple Access Interference); I (m) representative digit arrowband interference sample signal; ε (m) represents that power spectral density is white Gaussian noise sampled signal, and system synchronization.

CDMA sampled signal can be modeled as:

$y\left(m\right)=\underset{k=0}{\overset{K_z}{\mathrm{\Σ}}}{A}_k\underset{n=-\∞}{\overset{\∞}{\mathrm{\Σ}}}{b}_k\left(n\right)s_k(m-\mathrm{nN})$

Wherein the sampled signal model of desired user 0 and MAI is respectively

$y_0\left(m\right)=A_0\underset{n=-\∞}{\overset{\∞}{\mathrm{\Σ}}}{b}_0\left(n\right)s_0(m-\mathrm{nN})$

$z\left(m\right)=\underset{k=1}{\overset{K_z}{\mathrm{\Σ}}}{A}_k\underset{n=-\∞}{\overset{\∞}{\mathrm{\Σ}}}{b}_k\left(n\right)s_k(m-\mathrm{nN})$

K in formula _zrepresent MAI number of users (K _z>=1), A _krepresent that k user receives signal amplitude, A ₀for desired user receives signal amplitude, b _k(n) represent k subscriber signal stream (1 or-1), b ₀(n) be expectation subscriber signal stream, s _krepresent k user's direct sequence spread spectrum codes sampled value, s ₀for desired user direct sequence spread spectrum codes sampled value, before sampling, time domain frequency expansion sequence is

$s_k\left(t\right)=\frac{1}{\sqrt{N}}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{s}_{k,j}{\mathrm{\ψ}}_c(t-j{T}_c)$

{ s in formula _{k, j}: j=1 ..., the spreading code that N} is k user (1 or-1), and k=0,1 ... K _z, ψ _c() is duration T _creturn-change waveform, N=T _b/ T _cfor spreading gain, T _bfor the signal period, T _cfor the spreading code cycle, and spreading code is independent of signal.

Numeral arrowband interference sample signal can be modeled as:

$i\left(m\right)=\underset{k=1}{\overset{K_i}{\mathrm{\Σ}}}{A}_{\mathrm{ik}}\frac{1}{\sqrt{N}}\underset{n_i=-\∞}{\overset{\∞}{\mathrm{\Σ}}}{b}_{\mathrm{ik}}\left(n_i\right)\mathrm{\υ}(m-n_i{N}_{\mathrm{vk}})$

K in formula _irepresentative digit arrowband disturbs number, A _ikrepresent that k digital arrowband disturbs reception signal amplitude, b _ik(n) represent k digital narrow-band interference signal stream (1 or-1), the duration is T _ik, i.e. digital arrowband interference period.Here T _ik> > T _cand N _vk=T _b/ T _ikfor integer, υ () representation unit height rectangular pulse.

(6) by described sampled signal r (m) by windowing memory, for n transmitted signal, processing interval [nT _b, (n+1) T _b] in to sampled signal r (m) windowing obtain (N * 1) dimension windowing vector r (n)=[r (nN+N-1), r (nN+N-2) ..., r (nN)] ^t, wherein n is transmitted signal label and n=0,1,2 ..., T _bfor the signal period, N is spreading gain.

Windowing vector r (n) can be modeled as:

r(n)＝y(n)+i(n)+ε(n)

＝y ₀(n)+z(n)+i(n)+ε(n)

Y in formula (n) is CDMA windowing signal, comprises the signal component y of desired user 0 ₀and the signal component z of MAI (n) (n), i (n) is that digital arrowband disturbs windowing signal, and ε (n) is white Gaussian noise windowing signal.

CDMA windowing vector can be modeled as:

$y\left(n\right)=\underset{k=0}{\overset{K_z}{\mathrm{\Σ}}}{A}_k{b}_k\left(n\right)s_k$

The windowing signal model that wherein comprises desired user 0 and MAI

y ₀(n)＝A ₀b ₀(n)s ₀

In formula $s_k=\frac{1}{\sqrt{N}}{[s_{k,N-1},s_{k,N-2},\·\·\·,s_{k,0}]}^T,$ $s_0=\frac{1}{\sqrt{N}}{[s_{0,N-1},s_{0,N-2},\·\·\·,s_{0,0}]}^T.$

Numeral arrowband disturbs windowing vector to be modeled as:

$i\left(n\right)=\underset{k=1}{\overset{K_i}{\mathrm{\Σ}}}{A}_{\mathrm{ik}}{s}_{\mathrm{ik}}$

In formula and wherein each symbol repeats N _ik=T _ik/ T _cindividual element, N _ik=T _ik/ T _cfor digital arrowband obstacle gain.

(7) described windowing vector r (n) is carried out to the subspace ZF code auxiliary filter of high-performance low computational complexity, comprise the steps:

Step 1: estimate statistics autocorrelation matrix

R _rr(n)＝E{r(n)r ^T(n)|b}

＝R _yy(n)+R _ii(n)+R _εε(n)

＝R _yy0(n)+R _zz(n)+R _ii(n)+R _εε(n)

R in formula _yy(n)=E{y (n) y ^t(n) be } CDMA windowing signal autocorrelation matrix, comprise the autocorrelation matrix of desired user 0 autocorrelation matrix R with MAI _zz(n)=E{z (n) z ^t(n) }, R _ii(n)=E{i (n) i ^t(n) be } that digital arrowband disturbs windowing signal autocorrelation matrix, R _{ε ε}(n)=E{ ε (n) ε ^t(n) } be white Gaussian noise windowing autocorrelation matrix.

FI estimates CDMA autocorrelation matrix

$R_{\mathrm{yy}}=\underset{k=0}{\overset{K_z}{\mathrm{\Σ}}}{A}_k^2{s}_k{s}_k^T$

The autocorrelation matrix that comprises desired user 0 and MAI

$R_{\mathrm{yy}0}=A_0^2{s}_0{s}_0^T$

Estimative figure arrowband disturbs autocorrelation matrix

$R_{\mathrm{ii}}=\underset{k=1}{\overset{K_i}{\mathrm{\Σ}}}{A}_{\mathrm{ik}}^{\′2}{s}_{\mathrm{ik}}{s}_{\mathrm{ik}}^T$

Estimate white Gaussian noise autocorrelation matrix

$R_{\mathrm{\ϵ\ϵ}}\left(n\right)={\mathrm{\σ}}_{\mathrm{\ϵ}}^2{I}_N$

I in formula _nrepresent N dimension diagonal matrix.

Step 2: autocorrelation matrix Eigenvalues Decomposition

$R_{\mathrm{rr}}=U_s{\mathrm{\Λ}}_s{U}_s^T+{\mathrm{\σ}}_{\mathrm{\ϵ}}^2{U}_{\mathrm{\ϵ}}{U}_{\mathrm{\ϵ}}^T$

Λ in formula _s=diag{ λ ₁, λ ₂..., λ _kcomprise K=1+K _z+ K _ithe individual characteristic value that is greater than diagonal matrix, U _s={ u ₁, u ₂..., u _k] be the matrix that a corresponding K orthogonal vectors form, meet u _ε=[u _k+1, u _k+2..., u _n] be N-K characteristic value the matrix that corresponding orthogonal vectors form, for CDMA user disturbs the virtual CDMA subspace of opening with digital arrowband, its quadrature component is U _εthe noise subspace opened of row.

Step 3: estimator space ZF filter vector

Setting subspace ZF code auxiliary filter vector is w=[w ₁, w ₂..., w _n] ^t(N * 1 dimension), by w=U _sx substitution ZF code aided algorithm cost function, x is intermediate variable

$\left\{\begin{array}{c}{w}_{\mathrm{ZF}}=\arg \underset{w}{\min }E\left\{{\left|w^T(r\left(n\right)-\mathrm{\ϵ}\left(n\right))\right|}^2\right\}\\ w^T{s}_0=1\end{array}\right.$

Obtain

Making above formula gradient is zero, obtains

$x_{\mathrm{ZF}}=-\frac{\mathrm{\ξ}}{2}{\left(U_s^T(R_{\mathrm{yy}}+R_{\mathrm{ii}})U_s\right)}^{-1}{U}_s^T{s}_0$

By above formula substitution constraints the limited Lagrange factor generation time above formula obtaining, can obtain

$x_{\mathrm{ZF}}=\frac{{\left(U_s^T(R_{\mathrm{yy}}+R_{\mathrm{ii}})U_s\right)}^{-1}{U}_s^T{s}_0}{s_0^T{U}_s{\left(U_s^T(R_{\mathrm{yy}}+R_{\mathrm{ii}})U_s\right)}^{-1}{U}_s^T{s}_0}$

According to u wherein _swith U _εthe character of quadrature, can obtain

$U_s^T(R_{\mathrm{yy}}+R_{\mathrm{ii}})U_s=U_s^T(R_{\mathrm{rr}}-{\mathrm{\σ}}_{\mathrm{\ϵ}}^2{I}_N)U_s$

$=U_s^T(U_s{\mathrm{\Λ}}_s{U}_s^T+{\mathrm{\σ}}_{\mathrm{\ϵ}}^2{U}_{\mathrm{\ϵ}}{U}_{\mathrm{\ϵ}}^T-{\mathrm{\σ}}_{\mathrm{\ϵ}}^2{I}_N)U_s$

$={\mathrm{\Λ}}_s-{\mathrm{\σ}}_{\mathrm{\ϵ}}^2{I}_K$

The x that above two formulas are obtained _zFsubstitution w=U _sx, can estimator space ZF code aided algorithm filter vector expression formula

$w_{\mathrm{ZF}}=\frac{{U_s\left({{\mathrm{\Λ}}_s-\mathrm{\σ}}_{\mathrm{\ϵ}}^2{I}_K\right)}^{-1}{U}_s^T{s}_0}{s_0^T{U}_s{({\mathrm{\Λ}}_s-{\mathrm{\σ}}_{\mathrm{\ϵ}}^2{I}_K)}^{-1}{U}_s^T{s}_0}$

Step 4: direct-detection symbol judgement

According to direct-detection rule

${\hat{b}}_0\left(n\right)=w_{\mathrm{ZF}}^{T}r\left(n\right)$

After detection, carry out symbol judgement and obtain useful information.

The present invention's beneficial effect is compared with prior art:

The present invention has realized the high-performance low computational complexity filtering that cdma system numeral arrowband disturbs.The subspace ZF code householder method matrix inversion part providing is improved to K dimension diagonal matrix (K < N) by N * N dimension non-singular matrix of existing direct ZF code householder method, greatly reduce system-computed complexity, kept the height output Signal to Interference plus Noise Ratio performance close with direct ZF code householder method simultaneously.

Accompanying drawing explanation

The cdma system that the existing direct ZF code householder method of describing Fig. 1 suppresses to disturb by digital arrowband receives block diagram;

The subspace ZF code householder method that Fig. 2 describes high-performance low computational complexity suppresses the cdma system reception block diagram disturbing by digital arrowband;

Subspace ZF code householder method and existing direct ZF code householder method that Fig. 3 describes high-performance low computational complexity suppress the performance simulation correlation curve that digital arrowband disturbs;

Fig. 4 describes algorithm implementing procedure figure of the present invention.

Embodiment

In detailed description of the present invention, with reference to appended drawing, these accompanying drawings are explained specific exemplary embodiment, invention can be implemented in these exemplary embodiments below.These embodiment describe with sufficient details, to allow those skilled in the art to implement the present invention, but can utilize other embodiment, and can make changing with other of logic, machinery, electrical equipment, and do not depart from standard of the present invention.Therefore, detailed description below should not be considered restrictive, and scope of the present invention is limited by appended claims only.

The embodiment of subspace ZF code householder method comprises the following steps:

(1) receive wireless communication signals, comprise that CDMA signal, white noise and digital arrowband disturb.

(2) described wireless communication signals is down-converted to intermediate-freuqncy signal.

(3) intermediate-freuqncy signal described in digitlization, to provide digital signal.

(4) by described digital demodulation signal, so that baseband signal to be provided.

(5) by described baseband signal envelope r (t) by cutting general matched filtering so that sampled signal r (m) to be provided, wherein m is sampled signal label and m=0,1,2 ...

Sampled signal r (m) can be modeled as:

r(m)＝y(m)+i(m)+ε(m)

＝y ₀(m)+z(m)+i(m)+ε(m)

Y in formula (m) represents CDMA sampled signal, comprises the signal component y of desired user 0 ₀(m) and multiple access disturb the signal component z (m) of (MAI, Multiple Access Interference); I (m) representative digit arrowband interference sample signal; ε (m) represents that power spectral density is white Gaussian noise sampled signal, and system synchronization.

CDMA sampled signal can be modeled as:

$y\left(m\right)=\underset{k=0}{\overset{K_z}{\mathrm{\&Sigma;}}}{A}_k\underset{n=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{b}_k\left(n\right)s_k(m-\mathrm{nN})$

Wherein the sampled signal model of desired user 0 and MAI is respectively

$y_0\left(m\right)=A_0\underset{n=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{b}_0\left(n\right)s_0(m-\mathrm{nN})$

$z\left(m\right)=\underset{k=1}{\overset{K_z}{\mathrm{\&Sigma;}}}{A}_k\underset{n=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{b}_k\left(n\right)s_k(m-\mathrm{nN})$

K in formula _zrepresent MAI number of users (K _z>=1), A _krepresent that k user receives signal amplitude, A ₀for desired user receives signal amplitude, b _k(n) represent k subscriber signal stream (1 or-1), b ₀(n) be expectation subscriber signal stream, s _krepresent k user's direct sequence spread spectrum codes sampled value, s ₀for desired user direct sequence spread spectrum codes sampled value, before sampling, time domain frequency expansion sequence is

$s_k\left(t\right)=\frac{1}{\sqrt{N}}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{s}_{k,j}{\mathrm{\&psi;}}_c(t-j{T}_c)$

{ s in formula _{k, j}: j=1 ..., the spreading code that N} is k user (1 or-1), and k=0,1 ... K _z, ψ _c() is duration T _cnormalization waveform, N=T _b/ T _cfor spreading gain, T _bfor the signal period, T _cfor the spreading code cycle, and spreading code is independent of signal.

Numeral arrowband interference sample signal can be modeled as:

$i\left(m\right)=\underset{k=1}{\overset{K_i}{\mathrm{\&Sigma;}}}{A}_{\mathrm{ik}}\frac{1}{\sqrt{N}}\underset{n_i=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{b}_{\mathrm{ik}}\left(n_i\right)\mathrm{\&upsi;}(m-n_i{N}_{\mathrm{vk}})$

K in formula _irepresentative digit arrowband disturbs number, A _ikrepresent that k digital arrowband disturbs reception signal amplitude, b _ik(n) represent k digital narrow-band interference signal stream (1 or-1), the duration is T _ik, i.e. digital arrowband interference period.Here T _ik> > T _cand N _vk=T _b/ T _ikfor integer, υ () representation unit height rectangular pulse.

(6) by described sampled signal r (m) by windowing memory, for n transmitted signal, processing interval [nT _b, (n+1) T _b] in to sampled signal r (m) windowing obtain (N * 1) dimension windowing vector r (n)=[r (nN+N-1), r (nN+N-2) ..., r (nN)] ^t, wherein n is transmitted signal label and n=0,1,2 ..., T _bfor the signal period, N is spreading gain.

Windowing vector r (n) can be modeled as:

r(n)＝y(n)+i(n)+ε(n)

＝y ₀(n)+z(n)+i(n)+ε(n)

Y in formula (n) is CDMA windowing signal, comprises the signal component y of desired user 0 ₀and the signal component z of MAI (n) (n), i (n) is that digital arrowband disturbs windowing signal, and ε (n) is white Gaussian noise windowing signal.

CDMA windowing vector can be modeled as:

$y\left(n\right)=\underset{k=0}{\overset{K_z}{\mathrm{\&Sigma;}}}{A}_k{b}_k\left(n\right)s_k$

The windowing signal model that wherein comprises desired user 0 and MAI

y ₀(n)＝A ₀b ₀(n)s ₀

In formula $s_k=\frac{1}{\sqrt{N}}{[s_{k,N-1},s_{k,N-2},\&CenterDot;\&CenterDot;\&CenterDot;,s_{k,0}]}^T,$ $s_0=\frac{1}{\sqrt{N}}{[s_{0,N-1},s_{0,N-2},\&CenterDot;\&CenterDot;\&CenterDot;,s_{0,0}]}^T.$

Numeral arrowband disturbs windowing vector to be modeled as:

$i\left(n\right)=\underset{k=1}{\overset{K_i}{\mathrm{\&Sigma;}}}{A}_{\mathrm{ik}}{s}_{\mathrm{ik}}$

In formula and wherein each symbol repeats N _ik=T _ik/ T _cindividual element, N _ik=T _ik/ T _cfor digital arrowband obstacle gain.

(7) described windowing vector r (n) is carried out to the subspace ZF code auxiliary filter of high-performance low computational complexity, comprising:

First: estimate statistics autocorrelation matrix

R _rr(n)＝E{r(n)r ^T(n)|b}

＝R _yy(n)+R _ii(n)+R _εε(n)

＝R _yy0(n)+R _zz(n)+R _ii(n)+R _εε(n)

R in formula _yy(n)=E{y (n) y ^t(n) be } CDMA windowing signal autocorrelation matrix, comprise the autocorrelation matrix of desired user 0 autocorrelation matrix R with MAI _zz(n)=E{z (n) z ^t(n) }, R _ii(n)=E{i (n) i ^t(n) be } that digital arrowband disturbs windowing signal autocorrelation matrix, R _{ε ε}(n)=E{ ε (n) ε ^t(n) } be white Gaussian noise windowing autocorrelation matrix.

Estimate CDMA autocorrelation matrix

$R_{\mathrm{yy}}=\underset{k=0}{\overset{K_z}{\mathrm{\&Sigma;}}}{A}_k^2{s}_k{s}_k^T$

The autocorrelation matrix that comprises desired user 0 and MAI

$R_{\mathrm{yy}0}=A_0^2{s}_0{s}_0^T$

Estimative figure arrowband disturbs autocorrelation matrix

$R_{\mathrm{ii}}=\underset{k=1}{\overset{K_i}{\mathrm{\&Sigma;}}}{A}_{\mathrm{ik}}^{\&prime;2}{s}_{\mathrm{ik}}{s}_{\mathrm{ik}}^T$

Estimate white Gaussian noise autocorrelation matrix

$R_{\mathrm{\&epsiv;\&epsiv;}}\left(n\right)={\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}^2{I}_N$

I in formula _nrepresent N dimension diagonal matrix.

Secondly: autocorrelation matrix Eigenvalues Decomposition

$R_{\mathrm{rr}}=U_s{\mathrm{\&Lambda;}}_s{U}_s^T+{\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}^2{U}_{\mathrm{\&epsiv;}}{U}_{\mathrm{\&epsiv;}}^T$

Λ in formula _s=diag{ λ ₁, λ ₂..., λ _kcomprise K=1+K _z+ K _ithe individual characteristic value that is greater than diagonal matrix, U _s=[u ₁, u ₂..., u _k] be the matrix that a corresponding K orthogonal vectors form, meet u _ε=[u _k+1, u _k+2..., u _n] be N-K characteristic value the matrix that corresponding orthogonal vectors form, for CDMA user disturbs the virtual CDMA subspace of opening with digital arrowband, its quadrature component is U _εthe noise subspace opened of row.

Again: estimator space ZF filter vector

Setting subspace ZF code auxiliary filter vector is w=[w ₁, w ₂..., w _n] ^t(N * 1 dimension), by w=U _sx substitution ZF code aided algorithm cost function, x is intermediate variable

$\left\{\begin{array}{c}{w}_{\mathrm{ZF}}=\arg \underset{w}{\min }E\left\{{\left|w^T(r\left(n\right)-\mathrm{\&epsiv;}\left(n\right))\right|}^2\right\}\\ w^T{s}_0=1\end{array}\right.$

Obtain

Making above formula gradient is zero, obtains

$x_{\mathrm{ZF}}=-\frac{\mathrm{\&xi;}}{2}{\left(U_s^T(R_{\mathrm{yy}}+R_{\mathrm{ii}})U_s\right)}^{-1}{U}_s^T{s}_0$

By above formula substitution constraints the limited Lagrange factor generation time above formula obtaining, can obtain

$x_{\mathrm{ZF}}=\frac{{\left(U_s^T(R_{\mathrm{yy}}+R_{\mathrm{ii}})U_s\right)}^{-1}{U}_s^T{s}_0}{s_0^T{U}_s{\left(U_s^T(R_{\mathrm{yy}}+R_{\mathrm{ii}})U_s\right)}^{-1}{U}_s^T{s}_0}$

According to u wherein _swith U _εthe character of quadrature, can obtain

$U_s^T(R_{\mathrm{yy}}+R_{\mathrm{ii}})U_s=U_s^T(R_{\mathrm{rr}}-{\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}^2{I}_N)U_s$

$=U_s^T(U_s{\mathrm{\&Lambda;}}_s{U}_s^T+{\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}^2{U}_{\mathrm{\&epsiv;}}{U}_{\mathrm{\&epsiv;}}^T-{\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}^2{I}_N)U_s$

$={\mathrm{\&Lambda;}}_s-{\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}^2{I}_K$

The x that above two formulas are obtained _zFsubstitution w=U _sx, can estimator space ZF code aided algorithm filter vector expression formula

$w_{\mathrm{ZF}}=\frac{{U_s\left({{\mathrm{\&Lambda;}}_s-\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}^2{I}_K\right)}^{-1}{U}_s^T{s}_0}{s_0^T{U}_s{({\mathrm{\&Lambda;}}_s-{\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}^2{I}_K)}^{-1}{U}_s^T{s}_0}$

Last: direct-detection symbol judgement

According to direct-detection rule

${\hat{b}}_0\left(n\right)=w_{\mathrm{ZF}}^{T}r\left(n\right)$

After detection, carry out symbol judgement and obtain useful information.

The cdma system that the existing direct ZF code householder method of describing Fig. 1 suppresses to disturb by digital arrowband receives block diagram, down conversion module 101, direct ZF code auxiliary filter module 102 and direct ZF code auxiliary filter vector calculation module 103, consists of.

As shown in the figure, the wireless communication signals 105 that antenna 104 receives comprises that useful signal CDMA signal, digital arrowband disturb and white Gaussian noise.Antenna 104 is coupled to down conversion module 101.In down conversion module 101, first by band pass filter 106, process wireless communication signals 105, the frequency of wanting is selected on this filter optimization ground, for example, with the frequency of CDMA signal correction connection.Band pass filter 106 is coupled to amplifier 107, and this amplifier amplifies the signal from band pass filter 106.Blender 108 mixes the output of amplifier 107 with the oscillator signal from local oscillator 109.Like this, the output signal of blender 108 down-conversion amplifiers 107, to provide intermediate-freuqncy signal 110.After initial down-conversion, by modulus a/d transducer 111, intermediate-freuqncy signal 110 is transformed into digital signal 112.Because QPSK signal can be regarded as the stack of two quadrature 2PSK signals, so go demodulation with the crossing coherent carrier of two-way.Wherein a road signal enters blender 115 and mixes with the signal from digital controlled oscillator 113, and another road signal enters blender 116 and with the signal after pi/2 phase shift 114 mixes from digital controlled oscillator 113.Blender 115 is connected respectively to low pass filter 117 and low pass filter 118 with the signal of blender 116 outputs.Thereafter, the output signal of the output signal of low pass filter 117 and low pass filter 118 is connected respectively to sampling decision device 119 and sampling decision device 120, and by the output signal of sampling decision device 119 and sampling decision device 120 after parallel/serial device 121 conversion, become baseband signal 122 outputs.

Like this, band pass filter 106, amplifier 107, blender 108, local oscillator 109 have completed the process that is down-converted to intermediate-freuqncy signal, modulus a/d transducer 111, digital controlled oscillator 113, pi/2 phase shift 114, blender 115,116, low pass filter 117,118, sampling decision device 119,120, parallel/serial device 121 have completed the process that is down-converted to baseband signal by intermediate-freuqncy signal.Above process has completed down conversion module 101.

Existing direct ZF code householder method is carried out filtering by direct ZF code auxiliary filter module 102.Baseband signal 122 envelope r (t) are cut to general matched filtering sampling 123, sampled signal r (m) 124 is provided.By sampled signal r (m) 124 by windowing memory 125, to sampled signal r (m) 124 windowings obtain (N * 1) dimension windowing vector r (n)=[r (nN+N-1), r (nN+N-2) ..., r (nN)] ^t126.The filter vector element w that direct ZF code auxiliary filter vector calculation module 103 is obtained ₁131, w ₂132...w _n13N sends into linear combination estimator 1:w with element r (nN+N-1) 141, r (nN) 142...r (nN+N-2) 14N of windowing vector r (n) 126 respectively ₁r (nN+N-1) 151, linear combination estimator 2:w ₂r (nN+N-2) 152... linear combination estimator N:w _nr (nN) 15N, obtains linear combination signal through adder 161 finally, to bit estimated signal send into symbol judgement device 162, obtain useful signal 163.

Like this, and general filtering sampling 123; Sampling windowing storage 125; 2 152... linear combinations estimation N 15N are estimated in linear combination estimation 1 151, linear combination; Adder 161; Symbol judgement device 162 has formed direct ZF code auxiliary filter module 102 jointly.

The direct required filter vector element w of ZF code auxiliary filter module 102 ₁131, w ₂132...w _n13N is provided by direct ZF code auxiliary filter vector calculation module 103.According to channel estimating principle, windowing vector r (n) 126 is sent into and estimates statistics autocorrelation matrix computing module 127R _rr(n)=E{r (n) r ^t(n) | b}=R _yy(n)+R _ii(n)+R _{ε ε}(n)=R _yy0(n)+R _zz(n)+R _ii(n)+R _{ε ε}(n).Send estimating the relevant parameter that statistics autocorrelation matrix computing module 127 obtains into the direct ZF filter vector computing module 128 of estimation finally by the filter vector element w that estimates that direct ZF filter vector computing module 128 obtains ₁131, w ₂132...w _n13N sends into direct ZF code auxiliary filter module 102.

Like this, estimate statistics autocorrelation matrix computing module 127, add up direct ZF filter vector computing module 128 and formed direct ZF code auxiliary filter vector calculation module 103.

The subspace ZF code householder method that Fig. 2 describes high-performance low computational complexity suppresses the cdma system reception block diagram disturbing by digital arrowband, down conversion module 201, subspace ZF code auxiliary filter module 202 sum of subspace ZF code auxiliary filter vector calculation modules 203, consists of.

As shown in the figure, the wireless communication signals 205 that antenna 204 receives comprises that useful signal CDMA signal, digital arrowband disturb and white Gaussian noise.Antenna 204 is coupled to down conversion module 201.In down conversion module 201, first by band pass filter 206, process wireless communication signals 205, the frequency of wanting is selected on this filter optimization ground, for example, with the frequency of CDMA signal correction connection.Band pass filter 206 is coupled to amplifier 207, and this amplifier amplifies the signal from band pass filter 206.Blender 208 mixes the output of amplifier 207 with the oscillator signal from local oscillator 209.Like this, the output signal of blender 208 down-conversion amplifiers 207, to provide intermediate-freuqncy signal 210.After initial down-conversion, by modulus a/d transducer 211, intermediate-freuqncy signal 210 is transformed into digital signal 212.Because QPSK signal can be regarded as the stack of two quadrature 2PSK signals, so go demodulation with the crossing coherent carrier of two-way.Wherein a road signal enters blender 215 and mixes with the signal from digital controlled oscillator 213, and another road signal enters blender 216 and with the signal after pi/2 phase shift 214 mixes from digital controlled oscillator 213.Blender 215 is connected respectively to low pass filter 217 and low pass filter 218 with the signal of blender 216 outputs.Thereafter, the output signal of the output signal of low pass filter 217 and low pass filter 218 is connected respectively to sampling decision device 219 and sampling decision device 220, and by the output signal of sampling decision device 219 and sampling decision device 220 after parallel/serial device 221 conversion, become baseband signal 222 outputs.

Like this, band pass filter 206, amplifier 207, blender 208, local oscillator 209 have completed the process that is down-converted to intermediate-freuqncy signal, modulus a/d transducer 211, digital controlled oscillator 213, pi/2 phase shift 214, blender 215,216, low pass filter 217,218, sampling decision device 219,220, parallel/serial device 221 have completed the process that is down-converted to baseband signal by intermediate-freuqncy signal.Above process has completed down conversion module 201.

Subspace ZF code householder method is carried out filtering by subspace ZF code auxiliary filter module 202.Baseband signal 222 envelope r (t) are cut to general matched filtering sampling 223, sampled signal r (m) 224 is provided.By sampled signal r (m) 224 by windowing memory 225, to sampled signal r (m) 224 windowings obtain (N * 1) dimension windowing vector r (n)=[r (nN+N-1), r (nN+N-2) ..., r (nN)] ^t226.The filter vector element w that subspace ZF code auxiliary filter vector calculation module 203 is obtained ₁231, w ₂232...w _n23N sends into linear combination estimator 1:w with element r (nN+N-1) 241, r (nN) 242...r (nN+N-2) 24N of windowing vector r (n) 226 respectively ₁r (nN+N-1) 251, linear combination estimator 2:w ₂r (nN+N-2) 252... linear combination estimator N:w _nr (nN) 25N, obtains linear combination signal through adder 261 finally, by bit estimated signal send into symbol judgement device 262, obtain useful signal 263.

Like this, and general filtering sampling 223; Sampling windowing storage 225; 2 252... linear combinations estimation N 25N are estimated in linear combination estimation 1 251, linear combination; Adder 261; Symbol judgement device 262 has formed subspace ZF code auxiliary filter module 202 jointly.

The filter vector element w that subspace ZF code auxiliary filter module 202 is required ₁231, w ₂232...w _n23N is provided by subspace ZF code auxiliary filter vector calculation module 203.According to channel estimating principle, windowing vector r (n) 226 is sent into and estimates statistics autocorrelation matrix computing module 227R _rr(n)=E{r (n) r ^t(n) | b}=R _yy(n)+R _ii(n)+R _zz(n)=R _yy0(n)+R _zz(n)+R _ii(n)+R _{ε ε}(n).Send estimating the autocorrelation matrix that statistics autocorrelation matrix computing module 227 obtains into autocorrelation matrix Eigenvalues Decomposition module 228 the relevant parameter again autocorrelation matrix Eigenvalues Decomposition module 228 being obtained is sent into estimator space ZF filter vector computing module 229 the filter vector element w finally estimator space ZF filter vector computing module 229 being obtained ₁231, w ₂232...w _n23N sends into subspace ZF code auxiliary filter module 202.

Like this, estimate statistics autocorrelation matrix computing module 227, autocorrelation matrix Eigenvalues Decomposition module 228, statistics subspace ZF filter vector computing module 229 has formed subspace ZF code auxiliary filter vector calculation module 203.

Subspace ZF code householder method and existing direct ZF code householder method that Fig. 3 describes high-performance low computational complexity suppress the performance simulation correlation curve that digital arrowband disturbs, and wherein comprise respectively the simulation comparison curve to single-tone disturbs and multitone disturbs.

The cdma system that simulated conditions is set spreading gain N=63 comprises 4 users, and wherein user 0 is desired user, signal power, i.e. unit signal energy other MAI and desired user constant power; CDMA spreading code is all chosen the Gold sequence of coefficient correlation 1/N.Channel circumstance white Gaussian noise power spectral density be that the relative ambient noise power of signal power is 20dB (after despreading).Interference power is with " J " expression, and unit is dB.Set and only exist a digital arrowband to disturb, N _v=4 and-10dB≤J≤30dB.Output Signal to Interference plus Noise Ratio (SINR, Signal to Interference and Noise Rate) has reflected the ratio of desired signal and interference and noise power in system output mixed signal, the dB of unit.

As shown in Figure 3, SINR 301 expression system output SINR, J 302 represents interference power.When disturbing as the interference of digital arrowband, the performance 303 of subspace ZF code householder method is close with the performance 304 of direct ZF code householder method.This has also proved for digital arrowband and has disturbed, the subspace ZF code householder method that the present invention proposes is with directly ZF code householder method performance is close, but its matrix inversion part is improved to K dimension diagonal matrix (K < N) by N * N dimension non-singular matrix of existing direct ZF code householder method, greatly reduces system-computed complexity.Illustrate that ZF code householder method more existing direct ZF code householder method in subspace has significant advantage.

Fig. 4 is the flow chart of method.In step 401, wireless communication signals 205 is down-converted to intermediate-freuqncy signal 210.In step 402, first use modulus a/d transducer 211 that intermediate-freuqncy signal 210 is digitized as to digital signal, carry out thereafter QPSK demodulation output baseband signal 222.In step 403, baseband signal 222 is obtained to sampled signal r (m) 224 by cutting general matched filtering sampler 223.In step 404, sampled signal r (m) 224 is obtained to windowing vector r (n) 226 by windowing memory 225.In step 405, by estimation, add up autocorrelation matrix computing module 227 counting statistics autocorrelation matrix R _rr(n)=E{r (n) r ^t(n) | b}=R _yy(n)+R _ii(n)+R _{ε ε}(n)=R _yy0(n)+R _zz(n)+R _ii(n)+R _{ε ε}(n).In step 406, by 228 pairs of autocorrelation matrix characteristic values of autocorrelation matrix Eigenvalues Decomposition module, decompose in step 407, by estimator space ZF filter vector computing module 229, calculate subspace ZF filter vector in step 408, the filter vector element w that subspace ZF code auxiliary filter vector calculation module 203 is obtained ₁231, w ₂232...w _n23N sends into linear combination estimator 1:w with element r (nN+N-1) 241, r (nN) 242...r (nN+N-2) 24N of windowing vector r (n) 226 respectively ₁r (nN+N-1) 251, linear combination estimator 2:w ₂r (nN+N-2) 252... linear combination estimator N:w _nr (nN) 25N, obtains linear combination signal through adder 261 in step 409, by bit estimated signal send into symbol judgement device 262, obtain useful signal 263.In step 410, symbolic label increases progressively n=n+1.In step 411, judge whether n is greater than transmitted signal information sum, if so, process ends, if not, as from 411 send to return to arrow indicated.

Claims (1)

1. suppress the subspace ZF code householder method that cdma system numeral arrowband disturbs, it is characterized in that comprising:

(1) receive wireless communication signals;

(2) described wireless communication signals is down-converted to intermediate-freuqncy signal;

(3) intermediate-freuqncy signal described in digitlization, to provide digital signal;

(4) by described digital demodulation signal, so that baseband signal to be provided;

(5) by described baseband signal envelope r (t) by cutting general matched filtering so that sampled signal r (m) to be provided, wherein m is sampled signal label and m=0,1,2

Sampled signal r (m) can be modeled as:

r(m)＝y(m)+i(m)+ε(m)

＝y ₀(m)+z(m)+i(m)+ε(m) (1)

Y in formula (m) represents CDMA sampled signal, comprises the signal component y of desired user 0 ₀(m) and multiple access disturb the signal component z (m) of MAI (Multiple Access Interference); I (m) representative digit arrowband interference sample signal; ε (m) represents that power spectral density is white Gaussian noise sampled signal, , and system synchronization;

Wherein CDMA sampled signal can be modeled as:

$y\left(m\right)=\underset{k=0}{\overset{K_z}{\mathrm{\&Sigma;}}}{A}_k\underset{n=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{b}_k\left(n\right)s_k(m-\mathrm{nN})---\left(2\right)$

Wherein the sampled signal model of desired user 0 and MAI is respectively:

$y_0\left(m\right)=A_0\underset{n=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{b}_0\left(n\right)s_0(m-\mathrm{nN})---\left(3\right)$

$z\left(m\right)=\underset{k=1}{\overset{K_z}{\mathrm{\&Sigma;}}}{A}_k\underset{n=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{b}_k\left(n\right)s_k(m-\mathrm{nN})---\left(4\right)$

K in formula _zrepresent MAI number of users (K _z>=1), A _krepresent that k user receives signal amplitude, A ₀represent that desired user receives signal amplitude, b _k(n) represent k subscriber signal stream (1 or-1), b ₀(n) represent desired user signal stream, s _krepresent k user's direct sequence spread spectrum codes sampled value, s ₀represent desired user direct sequence spread spectrum codes sampled value, before sampling, time domain frequency expansion sequence is:

$S_k\left(t\right)=\frac{1}{\sqrt{N}}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{S}_{k,j}{\mathrm{\&psi;}}_c(t-{\mathrm{jT}}_c)---\left(5\right)$

{ s in formula _{k, j}: j=1 ..., the spreading code that N} is k user (1 or-1), and k=0,1 ... K _z, ψ _c() is duration T _cnormalization waveform, N=T _b/ T _cfor spreading gain, T _bfor the signal period, T _cfor the spreading code cycle, and spreading code is independent of signal;

Numeral arrowband interference sample signal can be modeled as:

$i\left(m\right)=\underset{k=1}{\overset{K_i}{\mathrm{\&Sigma;}}}{A}_{\mathrm{ik}}\frac{1}{\sqrt{N}}\underset{n_i=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{b}_{\mathrm{ik}}\left(n_i\right)\mathrm{\&upsi;}(m-n_i{N}_{\mathrm{vk}})---\left(6\right)$

K in formula _irepresentative digit arrowband disturbs number, A _ikrepresent that k digital arrowband disturbs reception signal amplitude, b _ik(n) represent k digital narrow-band interference signal stream (1 or-1), the duration is T _ik, T _ikrepresent k digital narrow-band interference signal stream duration, i.e. digital arrowband interference period, here T _ik> > T _cand N _vk=T _b/ T _ikfor integer, υ () representation unit height rectangular pulse;

(6) by described sampled signal r (m) by windowing memory, for n transmitted signal, processing interval [nT _b, (n+1) T _b] in to sampled signal r (m) windowing obtain N * 1 dimension windowing vector r (n)=[r (nN+N-1), r (nN+N-2) ..., r (nN)] ^t, wherein n is transmitted signal label and n=0,1,2 ..., T _bfor the signal period, N is spreading gain;

Windowing vector r (n) can be modeled as:

r(n)＝y(n)+i(n)+ε(n) (7)

＝y ₀(n)+z(n)+i(n)+ε(n)

Y in formula (n) is CDMA windowing signal, comprises the signal component y of desired user 0 ₀and the signal component z of MAI (n) (n), i (n) is that digital arrowband disturbs windowing signal, and ε (n) is white Gaussian noise windowing signal;

CDMA windowing vector can be modeled as:

$y\left(n\right)=\underset{k=0}{\overset{K_z}{\mathrm{\&Sigma;}}}{A}_k{b}_k\left(n\right)s_k---\left(8\right)$

The windowing signal model that wherein comprises desired user 0 and MAI:

y ₀(n)＝A ₀b ₀(n)s ₀ (9)

$z\left(n\right)=\underset{k=1}{\overset{K_z}{\mathrm{\&Sigma;}}}{A}_k{b}_k\left(n\right)s_k---\left(10\right)$

In formula $s_k=\frac{1}{\sqrt{N}}{[s_{k,N-1},s_{k,N-2},...,s_{k,0}]}^T,s_0=\frac{1}{\sqrt{N}}{[s_{0,N-1},s_{0,N-2},...,s_{\mathrm{0,0}}]}^T;$

Numeral arrowband disturbs windowing vector to be modeled as:

$i\left(n\right)=\underset{k=1}{\overset{K_i}{\mathrm{\&Sigma;}}}{A}_{\mathrm{ik}}{s}_{\mathrm{ik}}---\left(11\right)$

In formula $s_{\mathrm{ik}}\left(n\right)=\frac{1}{\sqrt{N}}{[b_{\mathrm{ik}}(N_{\mathrm{vk}}-1)...,b_{\mathrm{ik}}(N_{\mathrm{vk}}-2)...,...,b_{\mathrm{ik}}\left(0\right)...]}^T,$ And wherein each symbol repeats N _ik=T _ik/ T _cindividual element, N _ik=T _ik/ T _cfor digital arrowband obstacle gain, T _ikbe k digital narrow-band interference signal stream duration, i.e. digital arrowband interference period;

(7) described windowing vector r (n) is carried out to the filtering of high-performance low computational complexity, wherein the filtering of high-performance low computational complexity refers to and takes subspace ZF (ZF, Zero Forcing) code householder method, comprises the steps:

Step 1: estimate statistics autocorrelation matrix:

R _rr(n)＝E{r(n)r ^T(n)|b}

＝R _yy(n)+R _ii(n)+R _εε(n) (12)

＝R _yy0(n)+R _zz(n)+R _ii(n)+R _εε(n)

R in formula _yy(n)=E{y (n) y ^t(n) be } CDMA windowing signal autocorrelation matrix, comprise the autocorrelation matrix of desired user 0 autocorrelation matrix R with MAI _zz(n)=E{z (n) z ^t(n) }, R _ii(n)=E{i (n) i ^t(n) be } that digital arrowband disturbs windowing signal autocorrelation matrix, R _{ε ε}(n)=E{ ε (n) ε ^t(n) } be white Gaussian noise windowing autocorrelation matrix;

Estimate CDMA autocorrelation matrix:

$R_{\mathrm{yy}}=\underset{k=0}{\overset{K_z}{\mathrm{\&Sigma;}}}{A}_k^2{s}_k{s}_k^T---\left(13\right)$

The autocorrelation matrix that comprises desired user 0 and MAI:

$R_{\mathrm{yy}0}=A_0^2{s}_0{s}_0^T---\left(14\right)$

$R_{\mathrm{zz}}=\underset{k=1}{\overset{K_z}{\mathrm{\&Sigma;}}}{A}_k^2{s}_k{s}_k^T---\left(15\right)$

Estimative figure arrowband disturbs autocorrelation matrix:

$R_{\mathrm{ii}}=\underset{k=1}{\overset{K_i}{\mathrm{\&Sigma;}}}{A}_{\mathrm{ik}}^{\&prime;2}{s}_{\mathrm{ik}}{s}_{\mathrm{ik}}^T---\left(16\right)$

Estimate white Gaussian noise autocorrelation matrix:

$R_{\mathrm{\&epsiv;\&epsiv;}}\left(n\right)={\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}^2{I}_N---\left(17\right)$

K in formula _zrepresent MAI number of users, A _krepresent that k user receives signal amplitude, s _krepresent spreading code windowing vector, A ₀represent that desired user receives signal amplitude, s ₀represent desired user direct sequence spread spectrum codes windowing vector, K _irepresentative digit arrowband disturbs number, represent that k digital arrowband disturbs reception signal amplitude, s _ikrepresentative digit narrow-band interference signal stream windowing vector, represent white Gaussian noise power spectral density, I _nrepresent N dimension diagonal matrix;

Step 2: autocorrelation matrix Eigenvalues Decomposition:

$R_{\mathrm{rr}}=U_s{\mathrm{\&Lambda;}}_s{U}_s^T+{\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}^2{U}_{\mathrm{\&epsiv;}}{U}_{\mathrm{\&epsiv;}}^T---\left(18\right)$

Λ in formula _s=diag{ λ ₁, λ ₂..., λ _kcomprise K=1+K _z+ K _ithe individual characteristic value that is greater than diagonal matrix, U _s=[u ₁, u ₂..., u _k] be the matrix that a corresponding K orthogonal vectors form, meet u _ε=[u _k+1, u _k+2..., u _n] be N-K characteristic value the matrix that corresponding orthogonal vectors form, for CDMA user disturbs the virtual CDMA subspace of opening with digital arrowband, its quadrature component is U _εthe noise subspace opened of row;

Step 3: estimator space ZF filter vector

Setting subspace ZF code auxiliary filter vector is w=[w ₁, w ₂..., w _n] ^t(N * 1 dimension), by w=U _sx substitution ZF code aided algorithm cost function, x is intermediate variable:

$\begin{array}{c}{w}_{\mathrm{ZF}}=\arg \underset{w}{\min }\left\{\right|w^T(r\left(n\right)-\mathrm{\&epsiv;}\left(n\right)){|}^2\}\\ w^T{s}_0=1\end{array}---\left(19\right)$

Obtain:

In formula, ξ is Lagrange factor, and making formula (20) gradient is zero, obtains:

$x_{\mathrm{ZF}}=-\frac{\mathrm{\&xi;}}{2}{\left(U_s^T(R_{\mathrm{yy}}+R_{\mathrm{ii}})U_s\right)}^{-1}{U}_s^T{s}_0---\left(21\right)$

By formula (21) substitution constraints the limited Lagrange factor generation time formula (21) obtaining, can obtain

$x_{\mathrm{ZF}}=\frac{{\left(U_s^T(R_{\mathrm{yy}}+R_{\mathrm{ii}})U_s\right)}^{-1}{U}_s^T{s}_0}{s_0^T{U}_s{\left(U_s^T(R_{\mathrm{yy}}+R_{\mathrm{ii}})U_s\right)}^{-1}{U}_s^T{s}_0}---\left(22\right)$

According to u wherein _swith U _εthe character of quadrature, can obtain:

$\begin{array}{c}{U}_s^T(R_{\mathrm{yy}}+R_{\mathrm{ii}})U_s=U_s^T(R_{\mathrm{rr}}-{\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}^2{I}_N)U_s\\ =U_s^T(U_s{\mathrm{\&Lambda;}}_s{U}_s^T+{\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}^2{U}_{\mathrm{\&epsiv;}}{U}_{\mathrm{\&epsiv;}}^T-{\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}^2{I}_N)U_s\\ ={\mathrm{\&Lambda;}}_s-{\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}^2{I}_K\end{array}---\left(23\right)$

I in formula _kfor k dimension diagonal matrix, bring formula (23) into formula (22) and obtain x _zF, by x _zFsubstitution w=U _sx, can obtain:

$w_{\mathrm{ZF}}=\frac{U_s{({\mathrm{\&Lambda;}}_s-{\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}^2{I}_K)}^{-1}{U}_s^T{s}_0}{s_0^T{U}_s{({\mathrm{\&Lambda;}}_s-{\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}^2{I}_K)}^{-1}{U}_s^T{s}_0}--\left(24\right)$

Formula (24) is subspace ZF code aided algorithm filter vector expression formula;

Step 4: direct-detection symbol judgement

Regular according to direct-detection:

${\hat{b}}_0\left(n\right)=w_{\mathrm{ZF}}^{T}r\left(n\right)---\left(25\right)$

After detection, carry out symbol judgement and obtain useful information, in formula for the useful information obtaining.