Patent ID: 11909564
Assignee: SOUTHWEST JIAOTONG UNIVERSITY
Field: Digital communication (Electrical engineering)
Classification: CPC H  Y | IPC H

Claim 0:
1. An angular domain channel estimation method based on matrix reconstruction for a symmetrical nonuniform array, defining that a system comprises a base station with M antennas and a user with a single antenna, wherein the M antennas form a symmetrical nonuniform linear array and the symmetrical nonuniform linear array is divided into a dense symmetrical uniform linear subarray, a first sparse uniform linear subarray and a second sparse uniform linear subarray; the dense symmetrical uniform linear subarray has 2M1+1 array elements; each of the array elements has a spacing d, and d=λ/2, λ being a half of a wavelength; each of the first sparse uniform linear subarray and the second sparse uniform linear subarray comprises M2 array elements, each of the array elements has a spacing (M1+1)d, and M=2(M1+M2)+1; the first sparse uniform linear subarray and the second sparse uniform linear subarray are respectively deployed on two sides of the dense symmetrical uniform linear subarray; an array element in a middle of the dense symmetrical uniform linear subarray is selected as a reference array element, and rest array elements are symmetrically distributed by taking the reference array element as a center; since a wireless channel experiences limited scattering propagation, the channel has a sparse multi-path structure and the user is defined to have L scattering paths; and the channel estimation method comprises:
performing path angle estimation based on a matrix reconstruction method, specifically as follows:
enabling a user side to send a training signal s t at a time t, and in all snapshots, enabling |st|=1, then a receiving signal at a position of a base station antenna being:

yt=htst+nt=Agtst+nt 

wherein ht is a user uplink channel, nt is an additive white Gaussian noise obeying complex Gaussian distribution CN(0,σ2I), σ2I is a variance of the additive white Gaussian noise, and Agt is a form of matrix multiplication of the channel ht:

gt=[g1,t, . . . ,gl,t]TϵCL×1 

A=[a(θ1), . . . ,a(θL))]ϵCM×L 

gl,t being a channel gain of the user at the time t and at an lth scattering path and obeying complex Gaussian distribution gi,t˜CN(0,1), θl representing an angle-of-arrivals of an lth path of the user, and a vector a(θl)ϵCM×1 representing an array manifold vector, l=1, . . . L;
enabling xt=gtstϵCL×1 to obtain a receiving signal covariance matrix:

Ry=EytytH=Rh+σ2I=ARxAH+σ2I 

wherein Rh=EhthtH and Rx=ExtxtH;
vectorizing the covariance matrix Ry to obtain a vector z:

z=vec(Ry)=Ãp+σm2

wherein Ã=A*⊙AϵC|M|2×L, p=[g12σ12, . . . , gL2σL2]T, gl2 and σl2 respectively represent a transmission signal power and a path gain power, 1≤l≤L, σm2 is a noise power, =[e1T, e2T, . . . , eMT]T, ei is a column vector, except that the ith position is 1, the rest are 0, the vector z is equivalent to receiving data with an array manifold matrix (A*⊙A), and array element positions of the vector z are given by a set D=di−dj, i,j=1, 2, . . . , M, di represents a distance from an ith array element to the reference array element, repeated elements in the set D are deleted to obtain a set B, integer elements of the set B correspond to positions of virtual array elements, the repeated data in the receiving data z are removed and corresponding rows are rearranged to cause the rows to correspond to the positions of the virtual array to obtain a new vector:

{tilde over (z)}=ABp+σm2e0 

wherein {tilde over (z)}ϵC|B|×1 is a receiving signal of the virtual array, and ABϵC|B|×L is an array manifold matrix corresponding to the virtual array, |B|=M+2(M1+(M1+1)M2), e0ϵC|B|×1, and except that a central term is 1, the rest are 0;
reconstructing the received data {tilde over (z)} into a covariance matrix, R
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wherein US is a signal subspace formed by a feature vector corresponding to a large feature value, and UN is a noise subspace formed by a feature vector corresponding to a small feature value;
multiplying both sides of the matrix by UN to obtain:

{tilde over (R)}yUN=(A1RxA1H+σm2I)UN=σm2Un,

wherein A1ϵC(|B|+1)/2×L represents an array manifold matrix corresponding to the virtual array and meets:

A1RxA1HUN=0

since a column vector of A1 corresponds to a signal transmitting direction, a direction of a signal source is estimated by the characteristic; based on a multiple signal classification algorithm, defining a spatial spectrum signal Pmusic({circumflex over (θ)}1) as:, P
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wherein in a case that a denominator ã({circumflex over (θ)}l)HUNUNHã({circumflex over (θ)}l) reaches a minimum value, ã({circumflex over (θ)}l) is an lth column vector of the matrix A1, Pmusic({circumflex over (θ)}l) reaches a maximum value, a direction-of-arrivals l is estimated according to a peak value of Pmusic({circumflex over (θ)}l), thereby obtaining all path angle information {circumflex over (θ)}=[{circumflex over (θ)}1, {circumflex over (θ)}2, . . . , {circumflex over (θ)}L]; and
performing path gain estimation, specifically as follows:
obtaining an array manifold matrix Â based on the obtained {tilde over (θ)}, sending a pilot signal ut, estimating path gains in different time blocks based on the obtained Â, and constructing a cost function:, J
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minimizing the cost function to obtain a channel gain estimation ĝt, specifically, by calculating a partial derivative of the cost function relative to ĝt, obtaining:, ∂
    
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wherein T is a time block, then within one time block, the whole channel estimation result expression is:

t=t,t=1, . . . ,T.