CN100345402C - High resolution estimation method for incoming wave direction of mobile communication system - Google Patents

Abstract

The present invention relates to a high resolution estimation method of the incoming wave direction of mobile communication systems, which comprises the following steps: the channel information of each antenna array element is estimated; then, the channel information of each user of each antenna array element is used for forming the signal covariance matrix of each user; characteristic decomposition is carried out to the signal covariance matrix of each user, and signal subspace and noise subspace are separated; the incoming wave direction is sought in the noise subspace for accurately seeking the multi-path direction of each user. DOA numbers estimated by the method of the present invention far and away breakthrough the limitation of the number of the antenna array elements; the method of the present invention has the advantages of less calculating amount and easy project realization.

Description

A kind of mobile communcations system arrival bearing's high-resolution method of estimation

Technical field

The present invention relates to high-resolution estimation approach or the device of a kind of TD-SCDMA super many DOA of system, this method is applicable to other cdma communication field simultaneously.

Background technology

In wireless telecommunication system, often need to estimate mobile subscriber's arrival bearing (DOA), to satisfy various application need, locate as the mobile subscriber, wave beam forming, or the like, DOA estimates it generally is to realize by the received signal of the aerial array of many array elements is carried out Combined Treatment.Traditional DOA estimation technique, as the MUSIC algorithm, ESPRIT algorithm and be basic improved Root-MUSIC etc. with the MUSIC algorithm, the DOA number that can estimate is subjected to the restriction of the array number of aerial array, and M root array element can only be estimated M-1 DOA.And in practice, consider cost and complexity, and the aerial array that adopt the base station is generally 4-8 root array element, that is to say, and in the antenna array system of 8 array elements of reality, traditional DOA method of estimation can only be estimated maximum 7 DOA.This can not satisfy the demand, because in wireless communications environment, base station often needs to communicate by letter simultaneously with tens to tens users simultaneously, and also there is multipath in the communication environments of these subscriber signals, and the DOA number that needs to estimate is usually more than 7.According to spectrum correlation, the DOA number that can estimate is not subjected to the restriction of array number based on the improved circulation MUSIC of MUSIC algorithm algorithm, but the data volume that requires is bigger, calculation of complex.

Therefore, prior art has defective, and awaits improving and development.

Summary of the invention

The object of the present invention is to provide a kind of mobile communcations system arrival bearing's high-resolution method of estimation, can estimate to high-resolution each user's multipath arrival bearing, and the DOA number that multipotency is estimated is several times as much as the array number of aerial array, be (M-1) K, wherein M is the array number of aerial array, K is user's number, and the method amount of calculation that the present invention proposes is few, is easy to Project Realization.

Technical scheme of the present invention is:

A kind of mobile communcations system arrival bearing's high-resolution method of estimation, it may further comprise the steps: the channel information that estimates each user on each bay, utilize the channel information of each user on each bay to constitute each user's signal covariance matrix then, again each user's signal covariance matrix is carried out feature decomposition, separation signal subspace and noise subspace, noise subspace search arrival bearing, each user's multipath direction is accurately searched for then.

Described method, wherein, described method is further comprising the steps of:

A) estimating user channel response value: utilize the displacement vector of Midamble sign indicating number known in each time slot to constitute matrix G, estimate the channel response value of all users on M unit array element, the channel response value on the m root array element is:

${\hat{h}}^{\left(m\right)}={\left(G^{H}G\right)}^{-1}{G}^H\·r^{\left(m\right)}---\left(4\right);$

B) obtain channel matrix on this relevant position according to the midamble sign indicating number displacement of user k;

C) ask for the correlation matrix of the channel matrix of user k:

${R_{\mathrm{hh}}}^{\left(k\right)}=H^{\left(k\right)}\·H^{\left(k\right)H}=\left[\begin{array}{c}{h}^{(k,1)}\\ h^{(k,2)}\\ \·\\ \·\\ \·\\ h^{(k,M)}\end{array}\right]\left[\begin{array}{cccc}{h}^{{(k,1)}^{*}}& h^{{(k,2)}^{*}}& \·\·\·& \end{array},h^{{(k,M)}^{*}}\right];$

$=\left[\begin{array}{cccc}{h}^{(k,1)}{h}^{{(k,1)}^{*}}& h^{(k,1)}{h}^{{(k,2)}^{*}}& \·\·\·& h^{(k,1)}{h}^{{(k,M)}^{*}}\\ h^{(k,2)}{h}^{{(k,1)}^{*}}& h^{(k,2)}{h}^{{(k,2)}^{*}}& \·\·\·& h^{(k,2)}{h}^{{(k,M)}^{*}}\\ \·& \·& & \·\\ \·& \·& \·\·\·& \·\\ \·& \·& & \·\\ h^{(k,M)}{h}^{{(k,1)}^{*}}& h^{(k,M)}{h}^{{(k,2)}^{*}}& \·\·\·& h^{(k,M)}{h}^{{(k,M)}^{*}}\end{array}\right]---\left(7\right)$

D) this correlation matrix is carried out feature decomposition;

E) according to the size ordering of characteristic value, get minimum M-L _kIndividual characteristic value characteristic of correspondence vector is formed spatial noise:

$V_n^{\left(k\right)}=\left[\begin{array}{cccc}{g}_1^{\left(k\right)}& g_2^{\left(k\right)}& \·\·\·& g_{M-L_k}^{\left(k\right)}\end{array}\right]---\left(9\right);$

F) the direction vector a (θ in the l of user k footpath _l ^(k)), l=1...L _k, can be expressed as

$a\left({\mathrm{\θ}}_l^{\left(k\right)}\right)={\left(\begin{array}{cccc}{e}^{j\frac{2\mathrm{\πr}}{\mathrm{\λ}}\cos {\mathrm{\θ}}_l^{\left(k\right)}}& e^{j\frac{2\mathrm{\πr}}{\mathrm{\λ}}\cos \left({\mathrm{\θ}}_l^{\left(k\right)}\frac{2\mathrm{\π}(\mathrm{ka}-1)}{\mathrm{Ka}}\right)}& ...& e^{j\frac{2\mathrm{\π}2}{\mathrm{\λ}}\cos \left({\mathrm{\θ}}_l^{\left(k\right)}\frac{2\mathrm{\π}(\mathrm{Ka}-1)}{\mathrm{Ka}}\right)}\end{array}\right)}^T---\left(10\right)$

Because the l of user k directly belongs to signal space, therefore have

$a{\left({\mathrm{\θ}}_l^{\left(k\right)}\right)}^H{V}_n{V}_n^{H}a\left({\mathrm{\θ}}_l^{\left(k\right)}\right)=0$

So, the L of user k _kThe arrival bearing of individual incoming signal can make an estimate by the peak value of determining the MUSIC spatial spectrum, and is specific as follows:

Order

$P\left({\mathrm{\θ}}_l^{\left(k\right)}\right)=\frac{1}{a_l^{\left(k\right)H}{V}_n^{\left(k\right)}{V}_n^{\left(k\right)H}{a}_l^{\left(k\right)}}---\left(11\right)$

Or

$P\left({\mathrm{\θ}}_l^{\left(k\right)}\right)=\frac{a_l^{\left(k\right)H}{a}_l^{\left(k\right)}}{a_l^{\left(k\right)H}{V}_n^{\left(k\right)}{V}_n^{\left(k\right)H}{a}_l^{\left(k\right)}}---\left(12\right)$

Make θ from 0 to 360 degree value, calculate P (θ) value, get the L of P (θ) _kThe L of individual peak value correspondence _kIndividual θ value is θ _l ^(k), l=1...L _k

G) repeating step b)-f), estimate the arrival bearing of all users (k=1....K).

A kind of mobile communcations system arrival bearing's provided by the present invention high-resolution method of estimation, thought in conjunction with traditional MUSIC, utilize the channel information of each user on each bay to constitute each user's signal covariance matrix, again each user's signal covariance matrix is carried out feature decomposition, separation signal subspace and noise subspace, then noise subspace search arrival bearing, the DOA number of estimating is broken through the restriction of aerial array array number far away, and amount of calculation is few, is easy to Project Realization.

Description of drawings

Fig. 1, Fig. 2 are the effect schematic diagrames of mobile communcations system arrival bearing's of the present invention high-resolution method of estimation.

Embodiment

Specify the inventive method with examples of implementation below.

The core concept of the inventive method is, at first estimate the channel information of each user on each bay, then in conjunction with the thought of traditional MUSIC algorithm, utilize the channel information of each user on each bay to constitute each user's signal covariance matrix, again each user's signal covariance matrix is carried out feature decomposition, separation signal subspace and noise subspace noise subspace search arrival bearing, are accurately searched for each user's multipath direction come out then.

Be the inventive method to be done describe in further detail below.

To the cdma system of discrete input and output, setting up departments altogether has K user to insert k the signal s that the user sent ^(k)(t) can be expressed as

$s^{\left(k\right)}\left(t\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{d_n}^{\left(k\right)}\·\underset{q=1}{\overset{Q}{\mathrm{\Σ}}}{c_q}^{\left(k\right)}\·g_c\{t-[(n-1)Q+q\left]T_c\right\}---\left(1\right)$

Wherein, d _n ^(k)The data symbol that the expression user sends; The symbolic number that n sends for the user, Q is a spread spectrum coefficient, T _cBe chip duration, g _c(τ) be the chip impulse response, c _q ^(k)It is k user's spread-spectrum code chip value.

If the aerial array (even linear array, circle battle array or other stream shape) of M unit is used in the base station, the reception data x on m array element then ^(m)(t) be

$x^{\left(m\right)}\left(t\right)=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\underset{l=1}{\overset{L_k}{\mathrm{\Σ}}}{a}_l^{(k,m)}{s}^k\left(t\right)\·h_l^{(k,m)}(\mathrm{\τ},t)+n\left(t\right)---\left(2\right)$

Wherein, L _kIt is the multipath number that k subscriber signal arrives receiving terminal; h _l ^{(k, m)}(τ, t) be the equivalent channel impulse response that k user's l directly arrives antenna m array element, it has comprised the influence of aerial fading channel and receiving terminal channel model, information such as the Doppler frequency-shift that contains the Rayleigh fading, multidiameter delay of amplitude, causes because of the travelling carriage high-speed mobile, angle spread are time varying channels; α _l ^{(k, m)}Be the array factor that k user's l directly arrives antenna m array element, mainly to reach the angle relevant with the ripple of array pitch and signal for it; N (t) is an additive noise.

Then the synthetic matrix of the received signal of M root antenna is

X＝[x ⁽¹⁾(t)?x ⁽²⁾(t)?...?x ^(M)(t)] ^T (3)

Wherein, T is a transposition.

According to the TD-SCDMA physical layer protocol, the Midamble sign indicating number of K user in time slot forms the window length W=[128/K of displacement by a basic Midamble sign indicating number displacement], this W value all is prior known for base station and user.According to the Steiner channel estimation methods, utilize Midamble sign indicating number known in each time slot to constitute the G matrix, estimate the channel response value of all users on m root array element:

${\hat{h}}^{\left(m\right)}={\left(G^{H}G\right)}^{-1}{G}^H\·r^{\left(m\right)}---\left(4\right)$

R wherein ^(m)Be m the received signal x on the array element ^(m)In corresponding to the part of Midamble sign indicating number;

The estimation channel value of representing m array element; G represents the matrix that Midamble displacement vector constitutes.Channel response on the associating M root array element:

Each user is according to the displacement of the Midamble sign indicating number of oneself, In the channel value of corresponding M * W is arranged, shown in the mark of (5).K user's channel matrix

$H^{\left(k\right)}=\left[\begin{array}{ccc}{h}_1^{(k,1)}& \·\·\·& h_W^{(k,1)}\\ h_1^{(k,2)}& \·\·\·& h_W^{(k,2)}\\ \·& \·& \·\\ \·& \·& \·\\ \·& \·& \·\\ h_1^{(k,M)}& \·\·\·& h_W^{(k,M)}\end{array}\right]---\left(6\right)$

By formula (4) estimated channel response, not only comprise time delay and decline information, also comprise angle information, be the h in the formula (2) _l ^{(k, m)}(τ, t) and α _l ^{(k, m)}Two product.

Ask the channel correlation matrix of user k

${R_{\mathrm{hh}}}^{\left(k\right)}=H^{\left(k\right)}\·H^{\left(k\right)H}=\left[\begin{array}{c}{h}^{(k,1)}\\ h^{(k,2)}\\ \·\\ \·\\ \·\\ h^{(k,M)}\end{array}\right]\left[\begin{array}{cccc}{h}^{{(k,1)}^{*}}& h^{{(k,2)}^{*}}& \·\·\·& h^{{(k,M)}^{*}}\end{array}\right]$

$=\left[\begin{array}{cccc}{h}^{(k,1)}{h}^{{(k,1)}^{*}}& h^{(k,1)}{h}^{{(k,2)}^{*}}& \·\·\·& h^{(k,1)}{h}^{{(k,M)}^{*}}\\ h^{(k,2)}{h}^{{(k,1)}^{*}}& h^{(k,2)}{h}^{{(k,2)}^{*}}& \·\·\·& h^{(k,2)}{h}^{{(k,M)}^{*}}\\ \·& \·& & \·\\ \·& \·& \·\·\·& \·\\ \·& \·& & \·\\ h^{(k,M)}{h}^{{(k,1)}^{*}}& h^{(k,M)}{h}^{{(k,2)}^{*}}& \·\·\·& h^{(k,M)}{h}^{{(k,M)}^{*}}\end{array}\right]---\left(7\right)$

Wherein, R _Hh ^(k)The channel autocorrelation matrix of representing k user;

H ^(k)The channel matrix of representing k user;

h ^{(k, x)}, x=1......M represents the channel estimation vector corresponding to user k of x antenna; Checking easily, covariance matrix R _Hh ^(k)Be the Hermitian matrix, its characteristic value is a nonnegative value.Make eigenvalue ₁〉=λ ₂〉=... 〉=λ _M〉=0, its feature decomposition value can be write as $R_{\mathrm{hh}}^{\left(k\right)}=\mathrm{U\Σ}{U}^H=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\λ}}_i{u}_i{u_i}^H.$ In the formula, U=[u ₁, u ₂..., u _M] form for characteristic vector unitary matrice (be that each vectorial mould is 1, mutually orthogonal between the vector, and UU ^H=I is the orthogonal matrix of plural number).∑=diag[λ ₁, λ ₂..., λ _M] diagonal matrix that constitutes for characteristic value.If M characteristic value is arranged in order by size, then preceding L _k(L _k≤ W) individual multipath power with user k is relevant.From L _kThe little characteristic value of+1 beginning is determined at noise fully, and its value approximates σ ², promptly ${\mathrm{\λ}}_{L_k+1}\≈{\mathrm{\λ}}_{L_k+2}\≈...\≈{\mathrm{\λ}}_M\≈{\mathrm{\σ}}^2.$

Suppose that the effective multipath of each user counts L _kLess than array number M (this is very reasonably to suppose, general multipath number is between 2-4, and array number is between 4-8), R _Hh ^(k)L is arranged _kThe corresponding multipath signal number of individual big characteristic value has M-L _kIndividual minimal eigenvalue is corresponding to noise power.Will with L _kIndividual big characteristic value characteristic of correspondence vector u _l ^(k), l=1 ..., L _k, they constitute the multipath signal space, with M-L _kIndividual minimal eigenvalue characteristic of correspondence vector g _j ^(k), j=1:M-L _k, they are noise vectors, constitute spatial noise.Multipath signal space and spatial noise quadrature that is to say

$\left\{\begin{array}{cccc}{u}_1^{\left(k\right)}& u_2^{\left(k\right)}& \·\·\·& u_{L_k}^{\left(k\right)}\end{array}\right\}\⊥\left\{\begin{array}{cccc}{g}_1^{\left(k\right)}& g_2^{\left(k\right)}& \·\·\·& g_{M-L_k}^{\left(k\right)}\end{array}\right\}---\left(8\right)$

The structure noise matrix

$V_n^{\left(k\right)}=\left[\begin{array}{cccc}{g}_1^{\left(k\right)}& g_2^{\left(k\right)}& \·\·\·& g_{M-L_k}^{\left(k\right)}\end{array}\right]---\left(9\right)$

Wherein, V _n ^(k)Expression user k spatial noise;

L _kThe multipath number of expression user k;

M represents array number;

g _x ^(k), x=1,2 ..., M-L _k, the M-L that expression is minimum _kIndividual characteristic value characteristic of correspondence vector;

According to (8) formula, we can get $u_l^{\left(k\right)H}{V}_n{V}_n^H{u}_l^{\left(k\right)}=0.$ Direction vector a (the θ in the l footpath of user k _l ^(k)), l=1...L _kCan be expressed as

$a\left({\mathrm{\θ}}_l^{\left(k\right)}\right)={\left(\begin{array}{cccc}{e}^{j\frac{2\mathrm{\πr}}{\mathrm{\λ}}\cos {\mathrm{\θ}}_l^{\left(k\right)}}& e^{j\frac{2\mathrm{\πr}}{\mathrm{\λ}}\cos \left({\mathrm{\θ}}_l^{\left(k\right)}\frac{2\mathrm{\π}(\mathrm{ka}-1)}{\mathrm{Ka}}\right)}& ...& e^{j\frac{2\mathrm{\π}2}{\mathrm{\λ}}\cos \left({\mathrm{\θ}}_l^{\left(k\right)}\frac{2\mathrm{\π}(\mathrm{Ka}-1)}{\mathrm{Ka}}\right)}\end{array}\right)}^T---\left(10\right)$

Wherein, the ka span is ka=1...Ka, expression antenna sequence number, and Ka is the antenna sum;

θ _l ^(k)The arrival bearing in the l footpath of expression user k; R represents the circular array radius; λ represents optical wavelength;

Because the l of user k directly belongs to signal space, therefore have

$a{\left({\mathrm{\θ}}_l^{\left(k\right)}\right)}^H{V}_n{V}_n^{H}a\left({\mathrm{\θ}}_l^{\left(k\right)}\right)=0$

So, the L of user k _kThe DOA of individual incoming signal can make an estimate by the peak value of determining the MUSIC spatial spectrum.

Specific as follows:

Order

$P\left({\mathrm{\θ}}_l^{\left(k\right)}\right)=\frac{1}{a_l^{\left(k\right)H}{V}_n^{\left(k\right)}{V}_n^{\left(k\right)H}{a}_l^{\left(k\right)}}---\left(11\right)$

Or

$P\left({\mathrm{\θ}}_l^{\left(k\right)}\right)=\frac{a_l^{\left(k\right)H}{a}_l^{\left(k\right)}}{a_l^{\left(k\right)H}{V}_n^{\left(k\right)}{V}_n^{\left(k\right)H}{a}_l^{\left(k\right)}}---\left(12\right)$

Wherein, a _l ^(k)Any direction vector of expression θ span [0,360];

Make θ from 0 to 360 degree value, calculate P (θ) value, get the L of P (θ) _kThe L of individual peak value correspondence _kIndividual θ value is θ _l ^(k), l=1:L _k

In general, with L _kIndividual big characteristic value characteristic of correspondence vector $a_l^{\left(k\right)}=a\left({\mathrm{\θ}}_l^{\left(k\right)}\right),$ L=1:L _k, be steering vector, they directly can be used for wave beam as descending weight vectors and form.But in emulation, find, the wave beam that the method forms has a shortcoming, each weight vector of trying to achieve exactly is strictly not corresponding one by one with arrival bearing, they also have the response of certain amplitude ground in other direction except own direction, make when the wave beam that forms is used to launch like this, then echo signal be transmitted into simultaneously other directly upwards and other user side upwards, form interference.In addition, in the environment of macrocell, angle spread is generally 45 °, makes that two multipath directions of same user may be very close, and the wave beam that form this moment then can not separate by two footpath signals.If estimate each arrival bearing DOA directly accurately with method of the present invention, the array response vector that adopts this direction then can be avoided the problems referred to above largely as weight vectors.

The concrete operations step of the inventive method is as follows:

1. with Steiner method estimating user channel response value, see (4) formula;

2. obtain channel matrix on the relevant position according to the midamble sign indicating number displacement of user k;

3. ask for the correlation matrix of user k channel matrix, see (7) formula;

4. to the correlation matrix feature decomposition;

5. according to the size ordering of characteristic value, get minimum M-L _kIndividual characteristic value characteristic of correspondence vector is formed spatial noise (9) formula;

6. get θ and equal 0 to 360 degree, calculate a (θ) and P (θ), see (10) formula and (11) formula, get the L of P (θ) _kThe L of individual peak value correspondence _kIndividual θ value is the L of user k _kThe DOA of individual incoming signal estimates, is designated as θ _l ^(k), l=1:L _k

Repeating step 2 to 6, the DOA that draws all users estimates.

Suppose that the number of users that the TD-SCDMA system communicates by letter simultaneously is 5, every user has 4 multipaths, each footpath energy distribution is [0-3-6-9] dB, total like this comes wave number=5*4=20, and 8 array elements circle array antenna receives array radius 0.5 λ, arrival bearing user produces at random, angle spread scope 45, user moving speed 0km/h, input signal-to-noise ratio Eb/NO are 10dB.

Then the estimation procedure of user DOA is as follows:

1 uses 8 array numbers channel impulse response according to estimates respectively;

Corresponding channel matrix is obtained in 2 positions according to the 1st user's midamble sign indicating number displacement correspondence.

3 ask the correlation matrix of channel matrix.

4 pairs of correlation matrix feature decomposition.

The 5 size orderings according to characteristic value are divided into signal space and spatial noise with characteristic vector.

6 utilize the spatial noise matrix at 360 degree space search DOA, obtain the 1st user's multipath arrival bearing, as shown in Figure 1.

7 the 2nd users to the, 5 users' DOA estimates to repeat the 2nd and went on foot for the 6th step.

As depicted in figs. 1 and 2, shown the wherein arrival bearing in all 4 footpaths of the 1st user and the 2nd user respectively, indicated actual DOA on the figure so that contrast with the result.Other 3 users' result is similar, just repeats no more.From simulation result as can be seen the present invention can effectively estimate 20 DOA of 5 whole users.

Should be understood that above-mentioned description at specific embodiment is too concrete, can not therefore limit patent and ask for protection scope that the patent scope of asking for protection should be as the criterion with claims.

Claims (2)

1. a mobile communcations system arrival bearing high-resolution method of estimation, it may further comprise the steps: the channel information that estimates each user on each bay, utilize the channel information of each user on each bay to constitute each user's signal covariance matrix then, again each user's signal covariance matrix is carried out feature decomposition, separation signal subspace and noise subspace, noise subspace search arrival bearing, each user's multipath direction is accurately searched for then.

2. method according to claim 1 is characterized in that, described method is further comprising the steps of:

A) estimating user channel response value: utilize the displacement vector of Midamble sign indicating number known in each time slot to constitute matrix G, estimate the channel response value of all users on M unit array element, the channel response value on the m root array element is:

${\hat{h}}^{\left(m\right)}={\left(G^{H}G\right)}^{-1}{G}^H\·r^{\left(m\right)}---\left(4\right);$

Wherein,

The estimation channel value of representing m array element;

G represents the matrix that Midamble displacement vector constitutes;

r ^(m)Represent in m the reception data on the array element part corresponding to the Midamble sign indicating number;

B) obtain channel matrix on this relevant position according to the midamble sign indicating number displacement of user k;

C) ask for the correlation matrix of the channel matrix of user k:

${R_{\mathrm{hh}}}^{\left(k\right)}=H^{\left(k\right)}\·H^{\left(k\right)H}=\left[\begin{array}{c}{h}^{(k,1)}\\ h^{(k,2)}\\ \·\\ \·\\ \·\\ h^{(k,M)}\end{array}\right]\left[\begin{array}{cccc}{h}^{(k,1)*}& h^{(k,2)*}& \·\·\·& h^{(k,M)*}\end{array}\right];$

$=\left[\begin{array}{cccc}{h}^{(k,1)}{h}^{(k,1)*}& h^{(k,1)}{h}^{(k,2)*}& \·\·\·& h^{(k,1)}{h}^{(k,M)*}\\ h^{(k,2)}{h}^{(k,1)*}& h^{(k,2)}{h}^{(k,2)*}& \·\·\·& h^{(k,2)}{h}^{(k,M)*}\\ \·& \·& & \·\\ \·& \·& \·\·\·& \·\\ \·& \·& & \·\\ h^{(k,M)}{h}^{(k,1)*}& h^{(k,M)}{h}^{(k,2)*}& \·\·\·& h^{(k,M)}{h}^{(k,M)*}\end{array}\right]---\left(7\right)$

Wherein, R _Hh ^(k)The channel autocorrelation matrix of representing k user;

H ^(k)The channel matrix of representing k user;

h ^{(k, x)}, x=1......M represents the channel estimation vector corresponding to user k of x antenna;

D) this correlation matrix is carried out feature decomposition;

E) according to the size ordering of characteristic value, get minimum M-L _kIndividual characteristic value characteristic of correspondence vector is formed spatial noise:

$V_n^{\left(k\right)}=\left[\begin{array}{cccc}{g}_1^{\left(k\right)}& g_2^{\left(k\right)}& \·\·\·& g_{M-L_k}^{\left(k\right)}\end{array}\right]---\left(9\right);$

Wherein, V _n ^(k)Expression user k spatial noise;

L _kThe multipath number of expression user k;

M represents array number;

g _x ^(k), x=1,2 ..., M-L _K, the M-L that expression is minimum _kIndividual characteristic value characteristic of correspondence vector; F) the direction vector a (θ in the l of user k footpath _l ^(k)), l=1...L _k, can be expressed as

$a\left({\mathrm{\θ}}_l^{\left(k\right)}\right)={\left(\begin{array}{cccc}{e}^{j\frac{2\mathrm{\πr}}{\mathrm{\λ}}\cos {\mathrm{\θ}}_l^{\left(k\right)}}& e^{j\frac{2\mathrm{\πr}}{\mathrm{\λ}}\cos ({\mathrm{\θ}}_l^{\left(k\right)}-\frac{2\mathrm{\π}(\mathrm{ka}-1)}{\mathrm{Ka}})}& \·\·\·& e^{j\frac{2\mathrm{\πr}}{\mathrm{\λ}}\cos ({\mathrm{\θ}}_l^{\left(k\right)}-\frac{2\mathrm{\π}(\mathrm{Ka}-1)}{\mathrm{Ka}})}\end{array}\right)}^T---\left(10\right)$

Wherein, the ka span is ka=1...Ka, expression antenna sequence number, and Ka is the antenna sum;

θ _l ^(k)The arrival bearing in the l footpath of expression user k;

R represents the circular array radius;

λ represents optical wavelength;

Because the l of user k directly belongs to signal space, therefore have

$a{\left({\mathrm{\θ}}_l^{\left(k\right)}\right)}^H{V}_n{V}_n^{H}a\left({\mathrm{\θ}}_l^{\left(k\right)}\right)=0$

So, the L of user k _kThe arrival bearing of individual incoming signal can make an estimate by the peak value of determining the MUSIC spatial spectrum, and is specific as follows:

Order

$P\left({\mathrm{\θ}}_l^{\left(k\right)}\right)=\frac{1}{a_l^{\left(k\right)H}{V}_n^{\left(k\right)}{V}_n^{\left(k\right)H}{a}_l^{\left(k\right)}}---\left(11\right)$

Or

$P\left({\mathrm{\θ}}_l^{\left(k\right)}\right)=\frac{a_l^{\left(k\right)H}{a}_l^{\left(k\right)}}{a_l^{\left(k\right)H}{V}_n^{\left(k\right)}{V}_n^{\left(k\right)H}{a}_l^{\left(k\right)}}---\left(12\right)$

Wherein, a _l ^(k)Any direction vector of expression θ span [0,360];

Make θ from 0 to 360 degree value, calculate P (θ) value, get the L of P (θ) _kThe L of individual peak value correspondence _kIndividual θ value is θ _l ^(k), l=1...L _k

G) repeating step b)-f), estimate the arrival bearing of all users (k=1...K).

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