ASYMMETRIC MASSIVE MIMO CHANNEL ESTIMATION METHOD BASED ON CO-PRIME ARRAY

Abstract

A downlink channel estimation method based on a co-prime array in asymmetric massive MIMO architecture is provided. First, an uplink and downlink asymmetric receiving and transmitting system model based on a co-prime array is established, and a deviation of the frequency domain direction caused by array broadband signals is observed; then, uplink receiving is performed to estimate an uplink channel, and channel parameters such as the number of paths, the angle of arrival and the path gain are recovered; and finally, a downlink channel is reconstructed based on the channel parameters recovered according to the uplink channel. By means of the high angular resolution of the co-prime array, the problem that a recovered uplink channel cannot be directly used for pre-coding of a downlink channel is solved.

Claims

1. An asymmetric massive MIMO channel estimation method based on a co-prime array, comprising: S1: establishing an uplink and downlink asymmetric massive MIMO system based on a co-prime array, wherein the uplink and downlink asymmetric massive MIMO system comprises a base station provided with ultra-large-scale antennas and users of K antennas, the number of the antennas of the base station is M, all the antennas of the base station have transmitting radio-frequency links, only N receiving radio-frequency links are available to be connected to N antennas to receive uplink signals, and the users communicate with the base station by means of frequency points; M=mn+1, and N=m+n1, where m<n, and m and n are co-prime; selecting uplink receiving antennas according to a co-prime array, and connecting the selected uplink receiving antennas to the receiving radio-frequency links; S2: receiving and estimating, by the base station, uplink channel information of part of the antennas, and constructing, after the uplink channel information is transformed to a frequency domain and is screened and rearranged, a virtual linear uniform array; S3: constructing a group least absolute shrinkage and selection operator based on compressive sensing by means of spatial sparse characteristics to estimate a direction of arrival; S4: reconstructing a partial array manifold matrix according to the estimated direction of arrival, and estimating path gain according to instantaneous channel information observed in the frequency domain later; and S5: reconstructing a complete uplink channel according to the estimated path gain and direction of arrival, and transferring it to a downlink channel based on reciprocity.

2. The asymmetric massive MIMO channel estimation method based on a co-prime array according to claim 1, wherein in S1, the uplink receiving antennas are selected specifically by: successively selecting n antennas which are a (2n+1).sup.th antenna, a (3n+1).sup.th antenna, . . . , and a (mn+1).sup.th antenna, where N=m+n1, a distance d between the antennas is .sub.min/2, and .sub.min is a wavelength corresponding to a subcarrier with a maximum frequency in each frequency point.

3. The asymmetric massive MIMO channel estimation method based on a co-prime array according to claim 2, wherein in S2, receiving and estimating, by the base station, uplink channel information of part of the antennas and constructing, after the uplink channel information is transformed to a frequency domain and is screened and rearranged, a virtual linear uniform array specifically comprise: S201: within P successive symbol durations, respectively performing -point FFT on P groups of discrete time-domain signals received by an uplink array to obtain frequency domain signals on P groups of frequency points, wherein a column vector x.sub.p,q with a length N1 is denoted as the frequency domain signal corresponding to a q.sup.th frequency point in a P.sup.th group of signals; S202: performing autocorrelation processing on the P frequency domain signals on each frequency point to obtain NN autocorrelation matrixes: $R_q=\frac{1}{P}\underset{p=1}{\overset{P}{.Math.}}{x}_{p,q}{x}_{p,q}^H,$ $\mathrm{for}$ $q=1,.Math.,Q$ classifying and averaging array elements at repetitive positions in R.sub.q, and then arranging the array elements in sequence to form a column vector y.sub.q with a length M1; and S203: forming a column vector with a length M by virtual array signals on all the frequency points:
y.sub.f=[y.sub.1.sup.T, . . . y.sub.i . . . ,].sup.T where, a column vector y.sub.i with a length M is the frequency signal on an i.sup.th frequency point.

4. The asymmetric massive MIMO channel estimation method based on a co-prime array according to claim 3, wherein a specific selection process in S202 comprises: from one end of a complete array, denoting serial numbers of the antennas as 0, 1, 2, . . . , M1, making the serial number of an activated uplink antenna array as a set {p.sub.1, p.sub.2, . . . , P.sub.N} with a length N, and arranging the set by column to form a matrix T.sub.c with a length NN: $T_c=\underset{N\mathrm{columns}}{\underset{}{\left[\begin{array}{ccc}{p}_1& .Math.& p_1\\ .Math.& .Math.& .Math.\\ p_N& .Math.& p_N\end{array}\right]}}$ wherein, elements in the autocorrelation matrix R.sub.q are in one-to-one correspondence with elements in R.sub.tab=T.sub.cT.sub.c.sup.T, that is, an element [R.sub.q].sub.i,j in the i.sup.th row and j.sup.th column of R.sub.q is an element at the position [R.sub.tab].sub.i,j of the virtual array.

5. The asymmetric massive MIMO channel estimation method based on a co-prime array according to claim 4, wherein in S3, an estimation problem is constructed by means of the group least absolute shrinkage and selection operator based on compressive sensing and is solved in an ADMM optimization framework to estimate the direction of arrival, which specifically comprises: S301: constructing an observation matrix =[A.sub.1, . . . A.sub.i, . . . , A.sub.w, ] of M(w+1) within a preset incident angle interval [.sub.l, .sub.r], wherein .sub.l, .sub.r are a left angle boundary and a right angle boundary respectively and meet 0.sub.l<.sub.r, w is the number of grid points within an estimation interval [.sub.l, .sub.r], a sub-matrix A.sub.i of M is an observation matrix on an i.sup.th grid point, is a matrix used for noise estimation, and the sub-matrixes are generated by: $A_i=\left[\begin{array}{ccc}{a}_{i,1}& .Math.& 0\\ .Math.& & .Math.\\ 0& .Math.& a_{i,Q}\end{array}\right],\stackrel{\_}{I}=\left[\begin{array}{ccc}{e}_1& .Math.& 0\\ .Math.& & .Math.\\ 0& .Math.& e_1\end{array}\right],$ a.sub.i,q is a steering vector of the q.sup.th frequency point on the i.sup.th and point, and: $a_{i,q}={\left[1,e^{-j2\frac{d}{{}_q}\cos \left({}_l+\text{?}\frac{{}_r-{}_l}{w}\right)},.Math.,e^{-j2\frac{d}{{}_q}\cos \left({}_l+\text{?}\frac{{}_r-{}_l}{w}\right)\left(M-1\right)}\right]}^T,$ $e_1={\left[1,0,.Math.,0\right]}^T,$ $\text{?}\text{indicates text missing or illegible when filed}$ where, the length of e.sub.l is M, j is an imaginary unit, i is a sequence of the grid points, $\frac{{}_r-{}_l}{w}$ is a distance between the grid points, ${}_l+i\frac{{}_r-{}_l}{w}$ is an angle represented by the i.sup.th grid point, and .sub.q is a wavelength corresponding to the q.sup.th frequency point; S302: writing out a linear regression problem constrained by L21 norm in the ADMM framework based on compressive sensing: $\underset{\stackrel{}{x}0}{\min }\frac{1}{2}\stackrel{}{A}\stackrel{\_}{x}-{\stackrel{}{y}}_f{}_2^2+{}_1\underset{i=1}{\overset{w+1}{.Math.}}{z}_i{}_2$ $\begin{array}{cc}s.t.& \stackrel{}{z}=\stackrel{}{x}\end{array},$ where, a column vector x=[x.sub.1.sup.T, . . . , x.sub.w+1.sup.T].sup.T with a length (w+1) is a target variable to be solved and represents the magnitude of energy of the frequency points on the estimated grid points, x.sub.i is a sub-vector formed by elements from element (i1)+1 to element iQ of x, z.sub.i is a sub-vector formed by elements from element (i1)+1 to element iQ of z, z=[z.sub.1.sup.T, . . . , z.sub.w+1.sup.T].sup.T is an auxiliary variable, .sub.t is a penalty coefficient, and a formula of a (k+1).sup.th iteration of the problem is: ${\stackrel{}{x}}^{\left(k+1\right)}={\left(\left({\stackrel{}{A}}^H\stackrel{}{A}\right)+I\right)}^{-1}\left[\left({\stackrel{}{A}}^H{\stackrel{}{y}}_f\right)+{\stackrel{}{u}}^{\left(k\right)}+{\stackrel{}{z}}^{\left(k\right)}\right]$ $z_i^{\left(k+1\right)}=\left(1-\frac{{}_t}{x_i^{\left(k+1\right)}-\frac{1}{}{u}_i^{\left(k\right)}{}_2}\right)\left(x_i^{\left(k+1\right)}-\frac{1}{}{u}_i^{\left(k\right)}\right),\mathrm{for}i=1,2,.Math.,w+1$ ${\stackrel{}{u}}^{\left(k+1\right)}={\stackrel{}{u}}^{\left(k\right)}+\left({\stackrel{}{z}}^{\left(k+1\right)}-{\stackrel{}{x}}^{\left(k+1\right)}\right)$ where, I is a unit matrix, =[u.sub.1.sup.T, . . . , u.sub.w+1.sup.T].sup.T is an auxiliary variable, u.sub.i is a sub-vector formed by elements from element (i1)+1 to element i of , is an iteration step, x.sub.i.sup.(k+1) is a sub-vector formed by elements from element (i1)+1 to element i of a vector x.sup.(k+1) generated by the (k+1).sup.th iteration, and a convergence condition is: ${\stackrel{}{x}}^{\left(k+1\right)}-{\stackrel{}{x}}^{\left(k\right)}{}_2,$ x.sup.(k) is a vector obtained by a k.sup.th iteration of the target variable x, and is a convergence threshold, which is a small constant greater than 0; and S303: calculating an energy distribution vector x.sub.L1(2)=[x.sub.1.sub.2, . . . x.sub.w+1.sub.2].sup.T of the estimated grid points according to a solution x=[x.sub.1.sup.T, . . . , x.sub.w+1.sup.T].sup.T obtained in S302, sorting elements in x.sub.L1(2), denoting sorted x.sub.L1(2) as {tilde over (x)}.sub.L1(2), and selecting first {circumflex over (L)} elements in {tilde over (x)}.sub.L1(2), which meet: $\frac{\underset{i=1}{\overset{\hat{L}-1}{.Math.}}{\left[{\stackrel{}{x}}_{L1\left(2\right)}\right]}_i}{{\stackrel{}{x}}_{L1\left(2\right)}{}_1}<\frac{\underset{i=1}{\overset{\hat{L}}{.Math.}}{\left[{\stackrel{}{x}}_{L1\left(2\right)}\right]}_i}{{\stackrel{}{x}}_{L1\left(2\right)}{}_1},$ where, is a path recovery threshold and meets 0<<1, a set formed by subscripts, corresponding to the recovered {circumflex over (L)} elements, in the vector x.sub.L1(2) is denoted as L={.sub.1, .sub.2, . . . .sub.l . . . , .sub.{circumflex over (L)}}, .sub.l is an original index of an l.sup.th selected element in x.sub.L1(2), and a vector of the direction of arrival of {circumflex over (L)} paths in space is: $\stackrel{}{}=\left[{}_l+{\tilde{i}}_1\frac{{}_r-{}_l}{w},{}_l+{\tilde{i}}_2\frac{{}_r-{}_l}{w},.Math.,{}_l+{\tilde{i}}_L\frac{{}_r-{}_l}{w}\right].$

6. The asymmetric massive MIMO channel estimation method based on a co-prime array according to claim 5, wherein in Step 4, reconstructing a partial array manifold matrix according to the estimated direction of arrival and estimating path gain according to instantaneous channel information observed in the frequency domain later specifically comprise: S401: performing FFT on time-domain signals on N actual receiving antennas to obtain Q frequency domain column vector signals with a length N, which are denoted as {tilde over (y)}.sub.q, wherein q is the q.sup.th frequency point; constructing the partial array manifold matrix .sub.q of uplink receiving antennas on the frequency points, wherein q is the q.sup.th frequency point:
.sub.q=[.sub.1,q,.sub.2,q, . . . .sub.i,q . . . ,.sub.{circumflex over (L)},q] where, .sub.1,q, .sub.2,q, .sub.i,q and .sub.{circumflex over (L)},q are steering vectors of the actual activated uplink antennas: ${\tilde{a}}_{i,q}={\left[e^{-j2\frac{d}{{}_q}{p}_1\cos \left({}_l+i\frac{{}_r-{}_l}{w}\right)},e^{-j2\frac{d}{{}_q}{p}_2\cos \left({}_l+i\frac{{}_y-{}_l}{w}\right)},.Math.,e^{-j2\frac{d}{{}_q}{p}_n\cos \left({}_l+i\frac{{}_y-{}_l}{w}\right)},.Math.e^{-j2\frac{d}{{}_q}{p}_N\cos \left({}_l+i\frac{{}_r-{}_l}{w}\right)}\right]}^T$ p.sub.n is a sequence corresponding to the selected antennas in the uplink array, p.sub.n{0, 1, 2, . . . , M1}, iL; S402: sequentially solving path gain of the paths on the frequency points, wherein a gain vector {circumflex over ()}.sub.q of the {circumflex over (L)} paths on the q frequency points is: ${\stackrel{}{}}_q={\left({}_q^H{}_q+I\right)}^{-1}{}_q^H{\stackrel{}{y}}_q$ where, each element in {circumflex over ()}.sub.q corresponds to the path gain of each path, is a minimal constant for ensuring nonsingularity of the matrix during an inversion process.

7. The asymmetric massive MIMO channel estimation method based on a co-prime array according to claim 6, wherein in S5, reconstructing a complete uplink channel according to the path gain estimated in S402 and the direction of arrival estimated in S303 and transferring it to a downlink channel based on reciprocity specifically comprise: respectively reconstructing complete M{circumflex over (L)} array manifold matrixes of the uplink receiving antennas on the Q frequency points by: $\widehat{A_q}=\left[{}_{1,q},{}_{2,q},.Math.{}_{i,q}.Math.,{}_{\stackrel{}{L},q}\right],\mathrm{for}q=1,2,.Math.,Q$ where, .sub.i,q is a complete steering vector of the q.sup.th frequency point at an i.sup.th angle: ${}_{i,q}={\left[1,e^{-j2\frac{d}{{}_q}\cos \left({}_l+i\frac{{}_r-{}_l}{w}\right)},.Math.,e^{-j2\frac{d}{{}_q}\left(M-1\right)\cos \left({}_l+i\frac{{}_r-{}_l}{w}\right)}\right]}^T,iL,$ reconstructing M1 complete channels of all the antennas: ${\stackrel{}{h}}_q={}_q{}_q,\mathrm{for}q=1,2,.Math.,Q;$ in a time division duplex mode, .sub.q is a downlink channel matrix corresponding to the q.sup.th frequency point, and a complete downlink channel is:
=[.sub.1, . . . .sub.q . . . ,.sub.Q] where, .sub.1 is a downlink channel matrix corresponding to the first frequency point, and .sub.Q is the downlink channel matrix corresponding to the q.sup.th frequency point.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0051] FIG. 1 is a flow diagram of the invention.

[0052] FIG. 2 is a schematic diagram of the selection of uplink receiving antennas according to the invention.

DETAILED DESCRIPTION

[0053] The technical solution of the invention will be described in further detail below in conjunction with accompanying drawings. The following embodiment is implemented based on the technical solution of the invention and provides a detailed implementation and a specific operation process, but the protection scope of the invention is not limited to the following embodiment.

[0054] This embodiment provides an asymmetric massive MIMO channel estimation method based on a co-prime array, which, as show in FIG. 1, comprises the following steps: [0055] S1: establishing an uplink and downlink asymmetric massive MIMO system based on a co-prime array, wherein the uplink and downlink asymmetric massive MIMO system comprises a base station provided with ultra-large-scale antennas (the number of the antennas is M) and users of K antennas, all the antennas of the base station have transmitting radio-frequency links, only N(N<<M, KN) receiving radio-frequency links are available to be connected to N antennas to receive uplink signals, and the users communicate with the base station by means of Q frequency points; M=mn+1, and N=m+n1, where m<n, and m and n are co-prime: selecting uplink receiving antennas according to a co-prime array, and connecting the selected uplink receiving antennas to the receiving radio-frequency links, wherein the uplink receiving antennas are selected specifically by: successively selecting n antennas which are a (2n+1).sup.th antenna, a (3n+1).sup.th antenna . . . and a (mn+1).sup.th antenna, wherein N=m+n1 (m and n are two co-prime numbers used for designing the number of uplink antennas and the number of downlink antennas in asymmetric arrays), a distance d between the antennas is .sub.min/2, and .sub.min is a wavelength corresponding to a subcarrier with a maximum frequency in each frequency point. [0056] S2: receiving and estimating, by the base station, uplink channel information of part of the antennas, and constructing, after the uplink channel information is transformed to a frequency domain and is screened and rearranged, a virtual linear uniform array, which specifically comprise: [0057] S201: within P successive symbol durations, respectively performing Q-point fast Fourier transform (FFT) on P groups of Q discrete time-domain signals received by an uplink array to obtain frequency domain signals on the P groups of Q frequency points, wherein a column vector x.sub.p,q with a length N1 is denoted as the frequency domain signal corresponding to a q.sup.th frequency point in a P.sup.th group of signals; [0058] S202: performing autocorrelation processing on the P frequency domain signals on each frequency point to obtain NN autocorrelation matrixes:

[00017]$R_q=\frac{1}{P}\underset{p=1}{\overset{P}{.Math.}}{x}_{p,q}{x}_{p,q}^H,$$\mathrm{for}$$q=1,.Math.,Q,$

[0059] Classifying (the upper triangle corresponding to a negative lag is grounded) and averaging array elements at repetitive positions in R.sub.q, and then arranging the array elements in sequence to form a column vector y.sub.q with a length M1, wherein [].sup.H represents conjugate transposition, and [].sup.T represents transposition; a specific selection process comprises:

[0060] From one end of a complete array, denoting serial numbers of the antennas as 0, 1, 2, . . . , M1, denoting the serial number of an activated uplink antenna array as a set {p.sub.1, p.sub.2, . . . , P.sub.N} with a length N, and arranging the set by column to form a matrix T.sub.c with a length NN:

[00018]$T_c=\underset{N\mathrm{columns}}{\underset{}{\left[\begin{array}{ccc}{p}_1& .Math.& p_1\\ .Math.& .Math.& .Math.\\ p_N& .Math.& p_N\end{array}\right]}}$ [0061] Wherein, elements in the autocorrelation matrix R.sub.q are in one-to-one correspondence with elements in R.sub.tab=T.sub.cT.sub.c.sup.T, that is, an element [R.sub.q].sub.i,j in the i.sup.th row and j.sup.th column of R.sub.q is an element at the position [R.sub.tab].sub.i,j of the virtual array; [0062] S203: forming a column vector with a length M by virtual array signals on all the frequency points:

y.sub.f=[y.sub.1.sup.T, . . . y.sub.i . . . ,].sup.T,

[0063] Where, a column vector y.sub.i with a length M is the frequency signal on an i.sup.th frequency point, and [].sup.T represents transposition; [0064] S3: constructing a group least absolute shrinkage and selection operator based on compressive sensing by means of spatial sparse characteristics to estimate a direction of arrival, which specifically comprise: [0065] S301: constructing an observation matrix =[A.sub.1, . . . A.sub.i, . . . , A.sub.w, ] of M(w+1) within a preset incident angle interval [.sub.l,.sub.r], wherein .sub.l,.sub.r are a left angle boundary and a right angle boundary respectively and meet 0.sub.l<.sub.r, the two angle boundaries are obtained through an angle domain detection method such as discrete Fourier transform (DFT); if the detection is not performed, l=0, .sub.r=; w is the number of grid points within an estimation interval [.sub.l,.sub.r], and with the increase of w, the accuracy of an estimation result is higher, and the complexity is also improved; a sub-matrix A.sub.i of Mis an observation matrix on an i.sup.th grid point, is a matrix used for noise estimation, and the sub-matrixes are generated by:

[00019]$A_i=\left[\begin{array}{ccc}{a}_{i,1}& .Math.& 0\\ .Math.& & .Math.\\ 0& .Math.& a_{i,Q}\end{array}\right],$$\stackrel{\_}{I}=\left[\begin{array}{ccc}{e}_1& .Math.& 0\\ .Math.& & .Math.\\ 0& .Math.& e_1\end{array}\right],$

[0066] Where, all ellipses are 0, a.sub.i,1 is a steering vector of the first frequency point on the i.sup.th grid point, a.sub.i,Q is a steering vector of the .sup.th frequency point on the i.sup.th grid point, a.sub.i,q is a steering vector of the q.sup.th frequency point on the i.sup.th grid point, and:

[00020]$a_{i,q}={\left[1,e^{-j2\frac{d}{{}_q}\cos \left({}_l+i\frac{{}_r-{}_l}{w}\right)},.Math.,e^{-j2\frac{d}{{}_q}\cos \left({}_l+i\frac{{}_r-{}_l}{w}\right)\left(M-1\right)}\right]}^T,$$e_1={\left[1,0,.Math.,0\right]}^T,$

[0067] Where, the length of e.sub.1 is M, j is an imaginary unit, i is a sequence of the grid points,

[00021]$\frac{{}_r-{}_l}{w}$

is a distance between the grid points,

[00022]${}_l+i\frac{{}_r-{}_l}{w}$

is an angle represented by the i.sup.th grid point, and .sub.q is a wavelength corresponding to the q.sup.th frequency point; [0068] S302: writing out a linear regression problem constrained by L21 norm in an alternating direction method of multipliers (ADMM) framework based on compressive sensing:

[00023]$\underset{\stackrel{}{x}0}{\min }\frac{1}{2}{.Math.\stackrel{}{A}\stackrel{}{x}-{\stackrel{}{y}}_f.Math.}_2^2+{}_t\underset{i=1}{\overset{w+1}{.Math.}}{.Math.z_i.Math.}_2,$$s.t.\stackrel{}{z}=\stackrel{}{x},$

[0069] Where, a column vector x=[x.sub.1.sup.T, . . . , x.sub.w+1.sup.T].sup.T with a length (w+1) is a target variable to be solved and represents the magnitude of energy of the frequency points on the estimated grid points, x.sub.1 is a sub-vector formed by elements from element (11)+1 to element 1of x, x.sub.w+1 is a sub-vector formed by elements from element (w+11)+1 to element w+1 of x, x.sub.i is a sub-vector formed by elements from element (i1)+1 to element i of x, z.sub.1 is a sub-vector formed by elements from element (11)+1 to element 1 in z, z.sub.w+1 is a sub-vector formed by elements from element (w+11)+1 to element (w+1)in z, z.sub.i is a sub-vector formed by elements from element (i1)+1 to element iQ of z, z=[z.sub.1.sup.T, . . . , z.sub.w+1.sup.T].sup.T is an auxiliary variable, .sub.t is a penalty coefficient, .sub.2 represents taking the 2-norm of a target vector, and a formula of a (k+1).sup.th iteration of the problem is:

[00024]${\stackrel{}{x}}^{\left(k+1\right)}={\left(\left({\stackrel{}{A}}^H\stackrel{}{A}\right)+I\right)}^{-1}\left[\left({\stackrel{}{A}}^H{\stackrel{}{y}}_f\right)+{\stackrel{}{u}}^{\left(k\right)}+{\stackrel{}{z}}^{\left(k\right)}\right],$$z_i^{\left(k+1\right)}=\left(1-\frac{{}_t}{{.Math.x_i^{\left(k+1\right)}-\frac{1}{}{u}_i^{\left(k\right)}.Math.}_2}\right)\left(x_i^{\left(k+1\right)}-\frac{1}{}{u}_i^{\left(k\right)}\right),$$\mathrm{for}$$i=1,2,.Math.,w+1,$${\stackrel{}{u}}^{\left(k+1\right)}={\stackrel{}{u}}^{\left(k\right)}+\left({\stackrel{}{z}}^{\left(k+1\right)}-{\stackrel{}{x}}^{\left(k+1\right)}\right),$

[0070] Where, I is a unit matrix, =[u.sub.1.sup.T, . . . , u.sub.w+1.sup.T].sup.T is an auxiliary variable, u.sub.1 is a sub-vector formed by elements from element (11)+1 to element 1of , u.sub.w+1 is a sub-vector formed by elements from element (w+11)+1 to element (w+1) of , u.sub.i is a sub-vector formed by elements from element (i1)+1 to element iof , the definition of u.sub.i is similar to that of x.sub.i, the superscript of ().sup.(k) represents a variable value of a k.sup.th iteration, is an iteration step and may be a constant value, () represents taking a rear part of a complex number, x.sub.1.sup.(k+1) is a sub-vector formed by elements from element (i1)+1 to element iof a vector x.sup.(k+1) generated by the (k+1).sup.th iteration, and a convergence condition is:

[00025]${.Math.{\stackrel{}{x}}^{\left(k+1\right)}-{\stackrel{}{x}}^{(k}.Math.}_2,$

[0071] x.sup.(k) is a vector obtained by a k.sup.th iteration of the target variable x, and is a convergence threshold, which is a small constant greater than 0; [0072] S303: calculating an energy distribution vector x.sub.L1(2)=[x.sub.1.sub.2, . . . , x.sub.w+1.sub.2].sup.T of the estimated grid points (in the spatial direction) according to a solution x=[x.sub.1.sup.T, . . . , x.sub.w+1.sup.T].sup.T obtained in S302, sorting elements in x.sub.L1(2), denoting sorted x.sub.L1(2) as {tilde over (x)}.sub.L1(2), and selecting first {circumflex over (L)} elements in {tilde over (x)}.sub.L1(2), which meet:

[00026]$\frac{\underset{i=1}{\overset{\widehat{L}-1}{.Math.}}{\left[{\stackrel{}{x}}_{L1\left(2\right)}\right]}_i}{{.Math.{\stackrel{}{x}}_{L1\left(2\right)}.Math.}_1}<\frac{\underset{i=1}{\overset{\widehat{L}}{.Math.}}{\left[{\stackrel{}{x}}_{L1\left(2\right)}\right]}_i}{{.Math.{\stackrel{}{x}}_{L1\left(2\right)}.Math.}_1},$

[0073] Where, is a path recovery threshold and meets 0<<1, .sub.1 represents taking the 1-norm of the target vector, [].sub.i represents an i.sup.th element of the vector, a set formed by subscripts, corresponding to the recovered {circumflex over (L)} elements, in the vector x.sub.L1(2) is denoted as L={.sub.1, .sub.2, . . . .sub.l . . . , .sub.{circumflex over (L)}}, .sub.1 is an original index of the first element in x.sub.L1(2), .sub.2 is an original index of the second element in x.sub.L1(2), .sub.{circumflex over (L)} is an original index of an {circumflex over (L)}.sup.th selected element in x.sub.L1(2), .sub.l is an original index of an l.sup.th selected element in x.sub.L1(2), and a vector of the direction of arrival of {circumflex over (L)} paths in space is:

[00027]$\hat{}=\left[{}_l+{\tilde{i}}_1\frac{{}_r-{}_l}{w},{}_l+{\tilde{i}}_2\frac{{}_r-{}_1}{w},.Math.,{}_l+{\tilde{i}}_{\hat{L}}\frac{{}_r-{}_l}{w}\right].$ [0074] S4: reconstructing a partial array manifold matrix according to the estimated direction of arrival, and estimating path gain according to instantaneous channel information observed in the frequency domain later, which specifically comprise: [0075] S401: performing FFT on time-domain signals on N actual receiving antennas to obtain Q frequency domain column vector signals with a length N, which are denoted as {tilde over (y)}.sub.q, wherein 9 is the q.sup.th frequency point; constructing the partial array manifold matrix .sub.q (the size is NL) is of uplink receiving antennas on the frequency points, wherein q is the q.sup.th frequency point:

.sub.q=[.sub.1,q,.sub.2,q, . . . .sub.i,q . . . ,.sub.{circumflex over (L)},q],

[0076] Where, .sub.1,q, .sub.2,q, .sub.i,q and .sub.{circumflex over (L)},q are steering vectors of the actual activated uplink antennas:

[00028]${\tilde{a}}_{i,q}=[e^{-j2\frac{d}{{}_q}{p}_1\cos \left({}_l+i\frac{{}_r-{}_l}{w}\right)},e^{-j2\frac{d}{{}_q}{p}_2\cos \left({}_l+i\frac{{}_r-{}_l}{w}\right)},.Math.,e^{-j2\frac{d}{{}_q}{p}_n\cos \left({}_l+i\frac{{}_r-{}_l}{w}\right)},.Math.e^{{-j2\frac{d}{{}_q}{p}_N\cos \left({}_l+i\frac{{}_r-{}_l}{w}\right)]}^T,}$ [0077] p.sub.n is a sequence corresponding to the selected antennas in the uplink array, p.sub.n{0,1, 2 . . . , M1}, iL; [0078] S402: sequentially solving path gain of the paths on the Q frequency points, wherein a gain vector {circumflex over ()}.sub.q of the {circumflex over (L)} paths on the q frequency points is:

[00029]${\widehat{}}_q={\left({}_q^H{}_q+I\right)}^{-1}{}_q^H{\tilde{y}}_q,$

[0079] Where, each element in {circumflex over ()}.sub.q corresponds to the path gain of each path, is a minimal constant for ensuring nonsingularity of the matrix during an inversion process; [0080] S5: reconstructing a complete uplink channel according to the estimated path gain and direction of arrival, and transferring it to a downlink channel based on reciprocity, which specifically as follows:

[0081] In S5, reconstructing a complete uplink channel according to the path gain estimated in S402 and the direction of arrival estimated in S303 and transferring it to a downlink channel based on reciprocity specifically comprise:

[0082] Respectively reconstructing complete M{circumflex over (L)} array manifold matrixes of the uplink receiving antennas on the Q frequency points by:

[00030]${}_q=\left[{\hat{a}}_{1,q},{\hat{a}}_{2,q},.Math.{\hat{a}}_{i,q}.Math.,{\hat{a}}_{\hat{L},q}\right],$$\mathrm{for}$$q=1,2,.Math.,Q,$

[0083] Where, .sub.1,q is a complete steering vector of the q.sup.th frequency point at a first angle, .sub.2,q is a complete steering vector of the q.sup.th frequency point at a second angle, .sub.{circumflex over (L)},q is a complete steering vector of the q.sup.th frequency point at an L.sup.th angle, and .sub.i,q is a complete steering vector of the q.sup.th frequency point at an i.sup.th angle:

[00031]${\hat{a}}_{i,q}={\left[1,e^{-j2\frac{d}{{}_q}\cos \left({}_l+i\frac{{}_r-{}_l}{w}\right)},.Math.,e^{-j2\frac{d}{{}_q}\left(M-1\right)\cos \left({}_l+i\frac{{}_r-{}_l}{w}\right)}\right]}^T,iL,$

[0084] Reconstructing M1 complete channels of all the antennas:

[00032]${\widehat{h}}_q={}_q{\hat{}}_q,$$\mathrm{for}$$q=1,2,.Math.,Q.$

[0085] In a time division duplex mode, .sub.q is a downlink channel matrix corresponding to the q.sup.th frequency point, and a complete downlink channel is:

=[.sub.1, . . . .sub.q . . . ,.sub.Q]

[0086] Where, .sub.1 is a downlink channel matrix corresponding to the first frequency point, and .sub.Q is the downlink channel matrix corresponding to the q.sup.th frequency point.

[0087] The above embodiment is merely a specific one of the invention; and protection scope of the invention is not limited to the above embodiment. Any transformations or substitutions obtained by those skilled in the art within the technical scope of the invention should fall within the scope of the invention. Thus, the protection scope of the invention should be subject to the claims.