CN1878045A - Method for estimating arrival direction of user coherent multi-path signals in array antenna CDMA system - Google Patents

Abstract

The invention discloses an estimating method of multi-path signal wave reaching direction for array antenna CDMA system user coherent, which comprises the following steps: first, utilizing the added decoding-expanding and mating filter group of each array element of array antenna to separate user multi-path signal; obtaining output vector of mating filter of array antenna; second, proceeding summation for output vectors; then, forming data block of continual sampling of vector sum; utilizing the constant-mode algorithm of iterative least square method projection to estimate user spatial characteristic vector; then, estimating corresponding covariance matrix through forward or backward spatial smoothing method to form covariance matrix; finally, applying multi-signal classification algorithm for spatial smoothing covariance matrix to estimate multi-path signal wave reaching direction of user coherent.

Description

Array antenna CDMA system user coherent multi-path signal Wave arrival direction estimating method

Technical field

The invention belongs to code division multiple access cdma cellular field of wireless communications.

Background technology

The cdma cellular communication technology is simple with its frequency planning, power system capacity is big, ability of anti-multipath is strong, good communication quality, electromagnetic interference are little etc., and characteristics demonstrate huge development potentiality, are the mainstream technologys of future mobile communications.If particularly in cdma system, use array antenna can improve capacity, spectrum efficiency, communication quality, the coverage of system significantly and high-precision wireless location service is provided.The direction of arrival of user multipaths signal estimates that the user radio location technology that wave beam to down link forms, reduces to disturb and estimates based on angle has important function in the array antenna CDMA system, is one of key technology of array antenna CDMA system.

At present, some array antenna CDMA system user multipath signal Wave arrival direction estimating methods have been proposed, but these method hypothesis user multipaths signals are independently each other, but in the cdma system of reality, each multipath signal of same user often may be concerned with, and therefore existing method of estimation can't solve the direction of arrival estimation problem of cdma system user coherent multi-path signal well.

Summary of the invention

The present invention has proposed a kind of array antenna CDMA system user coherent multi-path signal Wave arrival direction estimating method for solving the problems of the technologies described above, this method by utilizing the cdma system subscriber signal dexterously intrinsic characteristic and the space characteristics of user's coherent multi-path signal, solved the direction of arrival estimation problem of array antenna CDMA system user coherent multi-path signal effectively.

The technical scheme that a kind of array antenna CDMA system user of the present invention coherent multi-path signal direction of arrival is estimated may further comprise the steps:

1) signal that receives of each array element of array antenna comprises the stack of each user's signal and noise, at first, utilize the despreading that connects after each array element of array antenna and matched filter banks that each array element is received total baseband signal and carry out despreading and matched filter processing, realize the separation of user multipaths signal, obtain the array antenna matched filter output vector of user multipaths signal;

2) secondly, the array antenna matched filter output vector of user multipaths signal is carried out summation operation, obtain all footpath signals of user the output of array antenna matched filter vector and;

3) then, based on to the vector of array antenna matched filter output and the formed data block of continuous sampling, utilize the constant modulus algorithm of iterative least square projection, obtain user's space characteristics vector;

4) afterwards, the pairing covariance matrix of space characteristics vector is used forward direction/back to the space smoothing method, form the covariance matrix of a space smoothing;

5) last, the space smoothing covariance matrix of subscriber signal is used the multiple signal classification algorithm that direction of arrival is estimated, the direction of arrival that obtains user's coherent multi-path signal is estimated.

Below process that direction of arrival of the present invention is estimated discussed, with the concrete implication of illustrating each step of method of estimation of the present invention and the meaning of related symbol.

1. the separation of user multipaths signal

A. the received signal of array antenna

Investigate one and go up line asynchronous multipath channel array antenna CDMA system.Certain cellular cell has K user launching the BPSK spread-spectrum signal by multipath channel separately in the supposing the system.Like this, k the signal indication that the user launched is:

s _k(t)=A _kb _k(t) c _k(t) in [formula 1] formula, A _kThe amplitude of representing k subscriber signal, b _k(t) bit signal of k user's transmission of expression, c _k(t) k user's of expression frequency spreading wave

$c_k\left(t\right)=\underset{g=0}{\overset{G-1}{\mathrm{\Σ}}}{c}_{\mathrm{kg}}p(t-g{T}_c)$

In [formula 2] formula, c _Kg∈ 1, and+1} (g=0 ..., G-1) be its spreading code, p (t) cuts general pulse, and it cuts the general cycle is T _c, G is defined as G=T _b/ T _cSpreading gain, T _bBe the bit interval time, its frequency spreading wave has normalized energy, promptly ${\∫}_0^{T_b}{\left|c_k\left(t\right)\right|}^2=1.$

Suppose that base station array antenna has N array element, customer mobile terminal adopts single antenna.Like this, the baseband multi-path channel between k user transmitter and base station receiver represents that with the many output of single input SIMO channels its impulse response vector is:

$h_k\left(t\right)=\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{\mathrm{\α}}_{k,l}\left(t\right)a_{k,l}\left({\mathrm{\θ}}_{k,l}\left(t\right)\right)\mathrm{\δ}(t-{\mathrm{\τ}}_{k,l})$

[formula 3] wherein, L is user's a multipath number, δ (t) is the delta function, α _{K, l}And τ _{K, l}Be respectively the multiple decay and the time delay of k user l footpath signal.

$a_{k,l}\left({\mathrm{\θ}}_{k,l}\right)={[a_{k,l,1}\left({\mathrm{\θ}}_{k,l}\right),...,a_{k,l,N}\left({\mathrm{\θ}}_{k,l}\right)]}^T/\sqrt{N}$

[formula 4] is that corresponding k user l footpath signal direction of arrival is θ _{K, l}Array vector.

Like this, base station array antenna array element 1 ..., array element N receives total baseband signal and is:

$y\left(t\right)={[y_1\left(t\right),...,y_N\left(t\right)]}^T$

$=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{s}_k\left(t\right)*h_k\left(t\right)+w\left(t\right)$

$=\underset{i=-\∞}{\overset{\∞}{\mathrm{\Σ}}}\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{A}_k{b}_k\left(i\right)\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{\mathrm{\α}}_{k,l}{a}_{k,l}{c}_k(t-i{T}_b-{\mathrm{\τ}}_{k,l})+w\left(t\right)$

$=\underset{i=-\∞}{\overset{\∞}{\mathrm{\Σ}}}\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{\mathrm{\μ}}_{k,l}{b}_k\left(i\right)a_{k,l}{c}_k(t-i{T}_b-{\mathrm{\τ}}_{k,l})+w\left(t\right)$

In [formula 5] formula, O ^TThe computing of expression transposition, * represents convolution, μ _{K, l}=A _kα _{K, l}Be the complex magnitude of k user l footpath signal of being received, w (t) is that average is 0, and covariance matrix is σ ²I _NThe additive white Gaussian noise vector, I _NIt is the unit matrix of N * N.

B. the despreading of user multipaths signal and matched filter processing

To cdma system, each CDMA user has been assigned with unique spreading code, utilize the priori of CDMA user's spreading code, user multipaths signal is carried out despreading and matched filter processing, realize effective separation of user multipaths signal and the inhibition that multiple access is disturbed.

The despreading matched filtering output vector of user k l footpath signal array antenna is:

$Y_{k,l}\left(i\right)={\∫}_{(i-1)T_b+{\mathrm{\τ}}_{k,l}}^{i{T}_b+{\mathrm{\τ}}_{k,l}}{y\left(t\right)c}_k(t-i{T}_b-{\mathrm{\τ}}_{k,l})\mathrm{dt}$

$={\∫}_{(i-1)T_b+{\mathrm{\τ}}_{k,l}}^{i{T}_b+{\mathrm{\τ}}_{k,l}}\{\underset{k^{\′}=1}{\overset{K}{\mathrm{\Σ}}}\underset{l^{\′}=1}{\overset{L}{\mathrm{\Σ}}}{\mathrm{\μ}}_{k^{\′},l^{\′}}{b}_{k^{\′}}\left(i\right)a_{k^{\′},l^{\′}}\left({\mathrm{\θ}}_{k^{\′},l^{\′}}\right)c_{k^{\′}}(t-i{T}_b-{\mathrm{\τ}}_{k^{\′},l^{\′}})+w\left(t\right)\}{c}_k(t-i{T}_b-{\mathrm{\τ}}_{k,l})\mathrm{dt}$

$=\underset{k^{\′}=1}{\overset{K}{\mathrm{\Σ}}}\underset{l^{\′}=1}{\overset{L}{\mathrm{\Σ}}}{\mathrm{\μ}}_{k^{\′},l^{\′}}{\mathrm{\α}}_{k^{\′},l^{\′}}\left({\mathrm{\θ}}_{k^{\′},l^{\′}}\right)b_{k^{\′}}\left(i\right){\mathrm{\ρ}}_{k,k^{\′},l,l^{\′}}+w_{k,l}\left(i\right)$

[formula 6]

In the formula, ${\∫}_{(i-1)T_b+{\mathrm{\τ}}_{k,l}}^{i{T}_b+{\mathrm{\τ}}_{k,l}}{c}_k(t-{\mathrm{iT}}_b-{\mathrm{\τ}}_{k,l})c_{k^{\′}}(t-{\mathrm{iT}}_b-{\mathrm{\τ}}_{k^{\′},l^{\′}})\mathrm{dt}={\mathrm{\ρ}}_{k,k^{\′},l{,l}^{\′}},{\mathrm{\ρ}}_{k,k,l,l}=1,$

${\∫}_{(i-1)T_b+{\mathrm{\τ}}_{k,l}}^{i{T}_b+{\mathrm{\τ}}_{k,l}}w\left(t\right)c_k(t-{\mathrm{iT}}_b-{\mathrm{\τ}}_{k,l})\mathrm{dt}=w_{k,l}\left(i\right).$

C. the summation of array antenna matched filter output vector

To the summation of the array antenna matched filter output vector of user multipaths signal, obtain the vector of all L footpath signal array antenna matched filter outputs of user k and be:

$Y_k\left(i\right)=\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{Y}_{k,l}\left(i\right)=\underset{l=1}{\overset{L}{\mathrm{\Σ}}}\{{\mathrm{\μ}}_{k,l}{a}_{k,l}\left({\mathrm{\θ}}_{k,l}\right)b_k\left(i\right)+v_{k,l}\left(i\right)\}$

$=b_k\left(i\right)\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{\mathrm{\μ}}_{k,l}{a}_{k,l}\left({\mathrm{\θ}}_{k,l}\right)+\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{v}_{k,l}\left(i\right)$

$=a_k{b}_k\left(i\right)+v_k\left(i\right)$

[formula 7]

In the formula, $a_k=\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{\mathrm{\μ}}_{k,l}{a}_{k,l}\left({\mathrm{\θ}}_{k,l}\right)$ Be the space characteristics vector of subscriber signal, $v_k\left(i\right)=\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{v}_{k,l}\left(i\right).$

2. user's coherent multi-path signal direction of arrival is estimated

A. space characteristics is estimated

In the algorithm of subspace, for determining direction of arrival, must construct a space characteristics covariance matrix, make its signal subspace by space characteristics vector a _kOpen into, it is carried out feature decomposition, obtain direction of arrival.Be the space characteristics of estimating user signal, to the vector of all footpath signal array antenna despreadings and matched filtering outputs of user k with sample, according to formula 7, its sampling is output as:

Z _k(O)=a _kb _k(O)+I _k(O) in [formula 8] formula, Z _k(O)=[Y _k(1) ..., Y _k(O)] be N * O order array input data matrix, b _k(O)=[b _k(1) ..., b _k(O)] be 1 * O rank signal waveform matrixes, I _k(O)=[v _k(1) ..., v _k(O)] be N * O rank interference plus noise matrix, O is a bit sample length.

Under given this data block, adopt earlier and carry out the estimation of space characteristics based on the constant modulus algorithm of iterative least square projection, concrete estimating step is as follows:

(1) gives an a at random _{K, 0}, j=0;

(2)j＝j+1；

· $b_{k,j}={\left(a_{k,j-1}^H{a}_{k,j-1}\right)}^{-1}{a}_{k,j-1}^H{Z}_k;$

With [b _{K, j}] all elements project into immediate value on the unit circle (hard restriction);

· $a_{k,j}={Z_k{b}_{k,j}^H\left(b_{k,j}{b}_{k,j}^H\right)}^{-1};$

(3) with a _{K, j}Every row divided by first element values of this row;

(4) repeating step 2 and 3 is up to a _{K, j}And a _{K, i-1}Fully approaching.

Thus, the estimated value of space characteristics will be obtained

B. space characteristics Estimation of covariance matrix

In mobile communication system, owing to often may be concerned with between each multipath signal of same user, therefore directly apply to the array antenna CDMA system with traditional based on subspace such as multiple signal classification method with by direction of arrival algorithm for estimating such as invariable rotary technology estimated signal parameters, estimated performance will be subjected to very big influence, even can't estimate.Therefore, before feature decomposition, need carry out front and back, obtain the space characteristics covariance matrix of space smoothing, with the reliability that guarantees to estimate on average.

The space characteristics vector

Pairing covariance matrix R _{F, k}For:

$R_{f,k}\left(P\right)=\underset{p=1}{\overset{P}{\mathrm{\Σ}}}\left({\hat{a}}_k(p:N-P+p){\hat{a}}_k{(p:N-P+p)}^H\right)$

[formula 9]

To R _{F, k}Use forward direction/back to the space smoothing method, form the covariance matrix of a space smoothing:

$R_{\mathrm{fb},k}\left(P\right)=R_{f,k}\left(P\right)+J{R}_{f,k}^{*}\left(P\right)J$

[formula 10]

In the formula, () ^HThe computing of expression conjugate transpose, () ^*The expression conjugate operation, J be except that the back-diagonal element be that all the other elements are 0 permutation matrix 1, P is smoothing factor (a submatrix columns).

C. direction of arrival is estimated

The space smoothing covariance matrix of subscriber signal is used the multiple signal classification method that following direction of arrival is estimated, the direction of arrival that obtains user's coherent multi-path signal is estimated.Concrete estimating step is:

(1) to space smoothing covariance matrix R _{Fb, k}Carry out feature decomposition

R _{Fb, k}In V=V Λ [formula 11] formula, Λ=diag{ λ ₁, λ ₂..., λ _N-P+1, λ ₁〉=... 〉=λ _N-P+1Be characteristic value, V=[q ₁..., q _N-P+1] be R _{Fb, k}The matrix that corresponding characteristic vector is formed.

(2) computer memory spectrum

${\hat{P}}_{\mathrm{MU}}\left(\mathrm{\θ}\right)=\frac{a_k^H\left(\mathrm{\θ}\right)a_k\left(\mathrm{\θ}\right)}{a_k^H\left(\mathrm{\θ}\right)V_n{V}_n^H{a}_k\left(\mathrm{\θ}\right)}$

[formula 12]

In the formula, V _n=[q _L+1, q _L+2..., q _N-P+1].

The pairing θ value of L the peak-peak estimated value that is exactly each coherent multi-path signal direction of arrival of user k.

Beneficial effect of the present invention: at first, the present invention has made full use of the priori that cdma system each user has been assigned with unique spreading code, by user multipaths signal is carried out despreading and matched filter processing, realized effective separation of user multipaths signal and the inhibition that multiple access is disturbed; Secondly, estimation to user's coherent multi-path signal direction of arrival is directly to utilize the matched filter banks and the output thereof that connect after each array element of array antenna to realize, and be the necessary link of cdma system subscriber signal demodulating process to the despreading and the matched filter processing of user multipaths signal, so method have handle directly, simple advantage; In addition, the estimation of each coherent multi-path signal direction of arrival of user is based on feature decomposition to the space smoothing covariance matrix realizes, guaranteed the reliability that each coherent multi-path signal direction of arrival of user is estimated; At last, to adopting the system of N element array antenna, can estimate the direction of arrival of 2N/3 relevant multipath simultaneously to this method of arbitrary user, and cdma system is less than 2N/3 usually to the multipath component number that same user utilized, RAKE receiver as the third generation (3G) cdma mobile communication has been utilized 4 multipath components, adopt the array antenna of 6 array elements just can effectively estimate to the direction of arrival of same each coherent multi-path signal of user, the array antenna that adopts 9 array elements just can effectively estimate the direction of arrival of 6 coherent multi-path signals of same user, so this method is very suitable is applied in the array antenna CDMA system.

Description of drawings

Fig. 1 is the procedure chart that a kind of arbitrary user k of array antenna CDMA system coherent multi-path signal direction of arrival is estimated;

Fig. 2 is a method of the present invention and to the spatial spectrum output of despreading and matched filter and that directly use traditional multiple signal classification method;

Fig. 3 is the relation curve of the root-mean-square error RMSE of Wave arrival direction estimating method of the present invention to signal to noise ratio snr.

Embodiment

The present invention is described in further detail below in conjunction with accompanying drawing.

The method according to this invention can be applied to the CDMA mobile communication system of any employing array antenna.

Fig. 1 has provided this method and has been applied to the process that the array antenna CDMA system estimates arbitrary user k coherent multi-path signal direction of arrival.Concrete estimating step is as follows:

1) at first, with base station array antenna array element 1 ..., array element N receives total baseband signal y (t)=[y ₁(t) ..., y _N(t)] ^TSend into separately despreading and matched filter pack module 11, by pairing despreading of each multipath signal and matched filter 11-1, ..., the despreading of 11-L realizes separating of user multipaths signal with matched filter processing, obtains the array antenna matched filter output vector Y of user k l footpath signal _{K, l}(i),

$Y_{k,l}\left(i\right)={\∫}_{(i-1)T_b+{\mathrm{\τ}}_{k,j}}^{i{T}_b+{\mathrm{\τ}}_{k,l}}y\left(t\right)c_k(t-i{T}_b-{\mathrm{\τ}}_{k,l})\mathrm{dt}$

In the formula, c _k(t) be k user's frequency spreading wave, T _bBe bit interval time, τ _{K, l}Be the time delay of k user l footpath signal, its result offers summation module 12;

2) secondly, in summation module 12, to the array antenna matched filter output vector Y of user multipaths signal _{K, l}(i) carry out summation operation, obtain the vector and the Y of all L footpath signal array antenna matched filter outputs of user k _k(i),

$Y_k\left(i\right)=\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{Y}_{k,l}\left(i\right)$

3) then, in space characteristics vector module 13, based on to Y _k(i) the formed data block Z of an O continuous sampling _k(O)=[Y _k(1) ..., Y _k(O)], utilize the constant modulus algorithm of iterative least square projection to obtain the space characteristics vector of user k

Tool

The body estimating step is as follows:

(1) gives an a at random _{K, 0}, j=0;

(2)j＝j+1；

· $b_{k,j}={\left(a_{k,j-1}^H{a}_{k,j-1}\right)}^{-1}{a}_{k,j-1}^H{Z}_k;$

With [b _{K, j}] all elements project into immediate value on the unit circle (hard restriction);

· $a_{k,j}={Z_k{b}_{k,j}^H\left(b_{k,j}{b}_{k,j}^H\right)}^{-1};$

(3) with a _{K, j}Every row divided by first element values of this row;

(4) repeating step (2) and (3) are up to a _{K, j}And a _{K, i-1}Fully approaching; In the formula, b _k(O)=[b _k(1) ..., b _k(O)] be 1 * O rank signal waveform matrixes, thus, will obtain the estimated value of space characteristics

4) afterwards, in space characteristics covariance matrix module 14, to the space characteristics vector Pairing covariance matrix R _{F, k}

$R_{f,k}\left(P\right)=\underset{p=1}{\overset{P}{\mathrm{\Σ}}}\left({\hat{a}}_k(p:N-P+p){\hat{a}}_k{(p:N-P+p)}^H\right)$

Use forward direction/back to the space smoothing method, form the covariance matrix of a space smoothing:

$R_{\mathrm{fb},k}\left(P\right)=R_{f,k}\left(P\right)+J{R}_{f,k}^{*}\left(P\right)J$

In the formula, () ^HThe computing of expression conjugate transpose, () ^*The expression conjugate operation, J be except that the back-diagonal element be that all the other elements are 0 permutation matrix 1, P is smoothing factor (a submatrix columns);

5) last, in direction of arrival estimation module 15, the space smoothing covariance matrix of subscriber signal is used the multiple signal classification algorithm that direction of arrival is estimated, the direction of arrival that obtains user's coherent multi-path signal estimates that concrete estimating step is:

(1) to space smoothing covariance matrix R _{Fb, k}Carry out feature decomposition

R _{Fb, k}In the V=V Λ formula, Λ=diag{ λ ₁, λ ₂..., λ _N-P+1, λ ₁〉=... 〉=λ _N-P+1Be characteristic value, V=[q ₁..., q _N-P+1] be R _{Fb, k}The matrix that corresponding characteristic vector is formed;

(2) computer memory spectrum

${\hat{P}}_{\mathrm{MU}}\left(\mathrm{\θ}\right)=\frac{a_k^H\left(\mathrm{\θ}\right)a_k\left(\mathrm{\θ}\right)}{a_k^H\left(\mathrm{\θ}\right)V_n{V}_n^H{a}_k\left(\mathrm{\θ}\right)}$

In the formula, V _n=[q _L+1, q _L+2..., q _N-P+1], The pairing θ value of L the peak-peak estimated value that is exactly each coherent multi-path signal direction of arrival of user k.

For investigating a kind of array antenna CDMA system user multipath signal Wave arrival direction estimating method proposed by the invention, method has been carried out Computer Simulation research.In emulation, having adopted array element distance is the even equidistant 6 array element linear array antennas of half-wavelength, in order to carry out space smoothing, array is divided into 25 yuan of overlapping subarrays.Consider that the cdma system matched filter separates user multipaths signal with chip period, so the time delay of user multipaths signal is chosen by the integral multiple of chip period.The multiple attenuation coefficient of the channel of user's coherent multi-path signal is by the rayleigh distributed picked at random, and spreading code is that the length of picked at random is 8 PN sequence.Supposing the system has 4 CDMA users, and each user has 4 relevant multipaths, and the direction of arrival of the relevant multipath of desired user is respectively 18 °, 58 °, 98 ° and 138 °, the direction of arrival picked at random of each relevant multipath of other 3 users.Sampling length is 50.

Fig. 2 is a method of the present invention and to the spatial spectrum output of despreading and matched filter and that directly use traditional multiple signal classification method.Can clearly find out from Fig. 2, adopt method of the present invention to realize effective estimation desired user coherent multi-path signal direction of arrival, and the almost utter failure of traditional method.

Be further to estimate the performance of the inventive method, to 1000 times independently simulation result carried out on average having adopted root-mean-square error RMSE as evaluation index,

$\mathrm{RMSE}=\sqrt{\frac{1}{D}\underset{d=1}{\overset{D}{\mathrm{\Σ}}}\frac{1}{L}\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{({\widehat{\mathrm{\θ}}}_{k,l}-{\mathrm{\θ}}_{k,l})}^2},l=1,...,L$

[formula 13] wherein, D is the number of times of independent experiment.

Can find out that from Fig. 3 the root-mean-square error RMSE that adopts method of the present invention that CDMA user's coherent multi-path signal direction of arrival is estimated is more and more littler with the increase of signal to noise ratio snr, shows that method of the present invention is very effective, its result is suitable for practical application.

Claims (1)

1. an array antenna CDMA system user coherent multi-path signal Wave arrival direction estimating method is characterized in that, the estimation of arbitrary user k coherent multi-path signal direction of arrival be may further comprise the steps:

1) at first, with base station array antenna array element 1 ..., array element N receives total baseband signal y (t)=[y ₁(t) ..., y _N(t)] ^TSend into separately despreading and matched filter pack module (11), by pairing despreading of each multipath signal and matched filter (11-1), ..., despreading (11-L) realizes separating of user multipaths signal with matched filter processing, obtains the array antenna matched filter output vector Y of user k l footpath signal _{K, l}(i),

$Y_{k,l}\left(i\right)={\∫}_{(i-1)T_b+{\mathrm{\τ}}_{k,l}}^{{\mathrm{iT}}_b+{\mathrm{\τ}}_{k,l}}y\left(t\right)c_k(t-i{T}_b-{\mathrm{\τ}}_{k,l})\mathrm{dt}$

In the formula, c _k(t) be k user's frequency spreading wave, T _bBe bit interval time, τ _{K, l}Be the time delay of k user l footpath signal, its result offers summation module (12);

2) secondly, in summation module (12), to the array antenna matched filter output vector Y of user multipaths signal _{K, l}(i) carry out summation operation, obtain the vector and the Y of all L footpath signal array antenna matched filter outputs of user k _k(i),

$Y_k\left(i\right)=\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{Y}_{k,l}\left(i\right)$

3) then, in space characteristics vector module (13), based on to Y _k(i) the formed data block Z of an O continuous sampling _k(O)=[Y _k(1) ..., Y _k(O)], utilize the constant modulus algorithm of iterative least square projection to obtain the space characteristics vector of user k

Concrete estimating step is as follows:

(1) gives an a at random _{K, 0}, j=0;

(2)j＝j+1；

· $b_{k,j}={\left(a_{k,j-1}^H{a}_{k,j-1}\right)}^{-1}{a}_{k,j-1}^H{Z}_k;$

With [b _{K, j}] all elements project into immediate value on the unit circle, hard restriction;

· $a_{k,j}=Z_k{b}_{k,j}^H{\left(b_{k,j}{b}_{k,j}^H\right)}^{-1};$

(3) with a _{K, j}Every row divided by first element values of this row;

(4) repeating step (2) and (3) are up to a _{K, j}And a _{K, i-1}Fully approaching;

In the formula, b _k(O)=[b _k(1) ..., b _k(O)] be 1 * O rank signal waveform matrixes, thus, will obtain the estimated value of space characteristics

4) afterwards, in space characteristics covariance matrix module (14), to the space characteristics vector

Pairing covariance matrix R _{F, k}

$R_{f,k}\left(P\right)=\underset{p=1}{\overset{P}{\mathrm{\Σ}}}\left({\hat{a}}_k(p:N-P+p){\hat{a}}_k{(p:N-P+p)}^H\right)$

Use forward direction/back to the space smoothing method, form the covariance matrix of a space smoothing:

$R_{\mathrm{fb},k}\left(P\right)=R_{f,k}\left(P\right)+{\mathrm{JR}}_{f,k}^{*}\left(P\right)J$

In the formula, () ^HThe computing of expression conjugate transpose, () ^*The expression conjugate operation, J be except that the back-diagonal element be that all the other elements are 0 permutation matrix 1, P is that smoothing factor is the submatrix columns;

5) last, in direction of arrival estimation module (15), the space smoothing covariance matrix of subscriber signal is used the multiple signal classification algorithm that direction of arrival is estimated, the direction of arrival that obtains user's coherent multi-path signal estimates that concrete estimating step is:

(1) to space smoothing covariance matrix R _{Fb, k}Carry out feature decomposition

R _fb，kV＝VΛ

In the formula, Λ=diag{ λ ₁, λ ₂..., λ _N-P+1, λ ₁〉=... 〉=λ _N-P+1Be characteristic value, V=[q ₁..., q _N-P+1] be R _{Fb, k}The matrix that corresponding characteristic vector is formed;

(2) meter waits spatial spectrum

${\hat{P}}_{\mathrm{MU}}\left(\mathrm{\θ}\right)=\frac{a_k^H\left(\mathrm{\θ}\right)a_k\left(\mathrm{\θ}\right)}{a_k^H\left(\mathrm{\θ}\right)V_n{v}_n^H{a}_k\left(\mathrm{\θ}\right)}$

In the formula, V _n=[q _L+1, q _L+2..., q _N-P+1], The pairing θ value of L the peak-peak estimated value that is exactly each coherent multi-path signal direction of arrival of user k.