CN107422317A

CN107422317A - Low angle target arrival direction estimation method based on smoothing matrix collection

Info

Publication number: CN107422317A
Application number: CN201710656447.8A
Authority: CN
Inventors: 师俊朋; 胡国平; 张小飞; 周豪
Original assignee: Air Force Engineering University of PLA
Current assignee: Air Force Engineering University of PLA
Priority date: 2017-08-03
Filing date: 2017-08-03
Publication date: 2017-12-01
Anticipated expiration: 2037-08-03
Also published as: CN107422317B

Abstract

The invention discloses the low angle target arrival direction estimation method based on smoothing matrix collection, it is related to radar signal and technical field of information processing, it is front and rear to smoothing matrix collection (Forward Backward SMS, FB SMS) method builds new smoothing matrix by rearranging the auto-covariance battle array of the sub- face battle array of each every trade, and algorithm can be by improving the information utilization optimal estimating performance of sample covariance matrix；Spatial diversity smoothing matrix collection (Spatial Differencing SMS, SD SMS) method by the noise to the sub- face battle array of every trade and non-noise part carry out respectively spatial diversity and it is front and rear reduce data degradation to smoothing processing, compared to traditional distinctions algorithm, its coloured noise rejection is more preferable.

Description

Low-angle target two-dimensional DOA estimation method based on smooth matrix set

Technical Field

The invention relates to the technical field of radar signal and information processing, in particular to a low-angle target two-dimensional DOA estimation method based on a smooth matrix set.

Background

Multi-target two-dimensional DOA (pitch angle, azimuth angle) estimation has been widely applied in the fields of radar, sonar, wireless communication, and the like. Two-dimensional DOA estimation is carried out by utilizing array flow patterns such as an L-shaped array, a parallel linear array, a uniform area array and the like, thereby achieving great progress. Among them, subspace-like algorithms are being developed enormously, such as MUSIC, ESPRIT, etc. However, in a low-altitude environment, the coherence characteristics of the direct signal and the reflected signal make the conventional subspace-like algorithm ineffective. The Forward and Backward Spatial Smoothing (FBSS) algorithm can solve the decorrelation through the forward and backward sub-matrix covariance matrix space, but a certain degree of freedom is lost. Therefore, a virtual sub-array is formed by utilizing the uniform area array space smoothing processing to overcome the aperture loss, and great progress is made, such as two-dimensional MUSIC, two-dimensional real-valued ESPRIT algorithm and the like. And the algorithm is used for MIMO radar DOA estimation, joint DOD and DOA estimation and the like. On the basis of a two-dimensional space smoothing algorithm, a new theoretical system is formed by a space difference algorithm for performing difference operation by utilizing forward and backward subarrays, such as initial subarray and backward subarray difference operation, adjacent forward and backward subarray difference operation, forward and backward subarray Hermition difference operation, asymmetric forward and backward difference operation and the like. However, the main disadvantages of the existing spatial smoothing and spatial difference algorithms are:

1. the two-dimensional space smoothing algorithm can only utilize limited data information, and especially for a uniform area array, the quantity of the unused data information is larger. And under color noise conditions, the estimation performance is weak.

2. The two-dimensional spatial difference algorithm generates a large data loss in performing the difference operation and increases as the aperture of the array increases. Therefore, under the condition of large array aperture, the performance of the spatial difference algorithm is weaker than that of the spatial smoothing algorithm for white noise and color noise.

Disclosure of Invention

The embodiment of the invention provides a low-angle target two-dimensional DOA estimation method based on a smooth matrix set, which can solve the problems in the prior art.

A low-angle target two-dimensional DOA estimation method based on a smooth matrix set comprises the following steps:

establishing a low-angle target echo signal model under the condition of uniform area array;

dividing a uniform area array in the low-angle target echo signal model into a plurality of row sub-area arrays in a sliding mode;

under white noise, taking a diagonal line of the covariance matrix of the first row sub-area array as a boundary, extracting data information from top to bottom, and constructing a downlink smooth matrix set according to the extracted data information;

carrying out backward smoothing treatment on the downlink smooth matrix set to obtain a downlink backward smooth matrix set;

taking a diagonal line of the covariance matrix of the first row sub-area array as a boundary, extracting data information from bottom to top, and constructing an uplink smooth matrix set according to the extracted data information;

carrying out backward smoothing treatment on the uplink smoothing matrix set to obtain an uplink backward smoothing matrix set;

extracting downlink forward and backward extraction data of each row sub-area array by using the downlink smooth matrix set and the downlink backward smooth matrix set, and extracting uplink forward and backward extraction data of each row sub-area array by using the uplink smooth matrix set and the uplink backward smooth matrix set;

calculating a final forward and backward space smoothing set according to the downlink forward and backward extraction data and the uplink forward and backward extraction data of each line sub-area array, and solving a DOA estimation value by adopting a two-dimensional ESPRIT algorithm after performing singular value decomposition on the forward and backward space smoothing set;

under color noise, after data information is extracted from top to bottom by taking a diagonal line of a covariance matrix of a first row sub-area array as a boundary, carrying out difference operation on a noise part of the extracted data information, and simultaneously carrying out forward and backward smoothing on a non-noise part to obtain a downlink difference sub-array;

after data information is extracted from bottom to top by taking a diagonal line of the covariance matrix of the first row sub-area array as a boundary, carrying out difference operation on a noise part of the extracted data information, and simultaneously carrying out forward and backward smoothing on a non-noise part to obtain an uplink difference sub-array;

respectively extracting a downlink difference smooth matrix set and an uplink difference smooth matrix set of each row sub-area array by using the downlink difference sub-array and the uplink difference sub-array;

and calculating a final space difference smooth matrix set according to the downlink difference smooth matrix set and the uplink difference smooth matrix set, and solving the DOA estimation value for the space difference smooth matrix set by adopting a two-dimensional ESPRIT algorithm.

The low-angle target two-dimensional DOA estimation method based on the smooth matrix set in the embodiment of the invention has the following advantages:

FB-SMS utilizes more sample covariance matrix information, and the estimation performance of the FB-SMS is better than that of a traditional spatial smoothing method;

SD-SMS utilizes the difference operation of the autocovariance array (noise part) and the forward and backward processing of the cross covariance array (non-noise part) to effectively restrain color noise, reduces the data loss of the difference operation and obviously improves the estimation performance.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.

FIG. 1 is a model of an established low-angle target echo signal;

FIG. 2(a) is a schematic diagram of a first row sub-area array;

FIG. 2(b) is a schematic diagram of a covariance matrix of a first row sub-area matrix;

FIG. 3 shows simulation results of FB-SMS;

FIG. 4 shows simulation results of SD-SMS;

FIG. 5 is a graph showing the variation of the mean square error with the SNR under white noise;

FIG. 6 is a graph showing the variation of mean square error with fast beat under white noise;

FIG. 7 is a graph showing the variation of mean square error with signal-to-noise ratio under color noise;

FIG. 8 is a graph of mean square error versus fast beat number for color noise.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

The embodiment of the invention provides a low-angle target two-dimensional DOA estimation method based on a smooth matrix set, which comprises the following steps:

establishing a low-angle target echo signal model, wherein the established model is as shown in figure 1, the multipath effect is an ideal mirror reflection model and ignores atmospheric refraction and earth curvature influence, the uniform area array is provided with M × N antenna array elements, the interval between adjacent array elements is half wavelength, the height of the uniform area array is h, K uncorrelated far-field narrow-band signal sources s_k(t) K is 1,2, …, and K has an incident angle of (α)_k,θ_k). The echo signal is composed of a direct signal and a reflected signal, and the model is specifically as follows:

in the formula, theta_dkAnd theta_rkThe direct and reflected elevation angles, theta, of the kth target, respectively_dk≈-θ_rk＝θ_k，α_kAt an azimuth angle of β_kIs the multipath reflection coefficient; u_k＝sinθ_kcosα_k，v_k＝sinθ_ksinα_k(ii) a Z (t) is a mean of 0 and a variance of σ²Independent white Gaussian noise, β for easy calculation_k＝exp[j(π-2πΔR_k/λ)]，ΔR_k≈2h sinθ_k，ΔR_kIs the difference in multipath distance. The echo signal is vectorized and expressed as:

x(t)＝vec(X(t))＝(A_xοA_y)s(t)+z(t) (2)

in the formula, z (t) vec (z (t)). Is provided withFormula (2) may be represented as:

when the fast beat number is L (t ═ 1,2, …, L), the covariance matrix of the echo signals x (t) can be expressed as:

wherein A is A_xοA_y，R_s＝E[s(t)s^H(t)]Is a signal source covariance matrix.

And under the white noise condition, dividing the uniform area array into a plurality of row sub-area arrays. Taking the first row sub-area array as an example, taking a covariance matrix diagonal line of the first row sub-area array as a boundary, extracting data information from top to bottom and constructing a downlink smooth matrix set; then, extracting data information from bottom to top and constructing a corresponding forward and upward smooth matrix set; and similarly, constructing a downlink and uplink smooth matrix set corresponding to each row sub-area array.

Construction of Q in the x-and y-directions, respectively_xAnd Q_yA forward sub-array with array elements of P_xAnd P_yThen the uniform area array can be divided into Q_xQ_yA sub-array of size P_x×P_y，Q_x＝M-P_x+1，Q_y＝N-P_y+1. Q th_xq_yThe sub-area array may be represented as:

in the formula,andrespectively an array flow pattern matrix A_xAnd A_yFront P of_xAnd P_yLine composition q_x＝1,…,Q_x，q_y＝1,…,Q_y，Is the corresponding noise vector. At this time, each row sub-area array is composed of Q_yAnd (4) forming a sub-area array. Take the first row sub-area array as an example, set asx_1,nIs x_nFront P of_xLine, N ═ 1, …, N. Taking the diagonal line of the covariance matrix as a boundary, extracting the data information of each column from top to bottom, and then extracting the nth column (n is 1, …, Q)_y-1) can be represented as:

wherein,

z₁(t)，z_1,n(t) are the corresponding noise vectors respectively,remaining P_yColumn data can be expressed as:

as can be seen from (6) and (10), the reconstructed downlink forward smoothing matrix set can be represented as:

wherein,to improve estimation performance and decorrelation performance, matrix R is aligned₁The backward smoothing treatment can obtain:

wherein,d_k＝(M-1)u_k+(N-1)v_kthe set of downlink backward smoothing matrices obtained from (12) and (13) is:

similarly, taking diagonal line as boundary, extracting each column of data information from bottom to topThe columns are as follows:

wherein,

whereinThen the last P_yColumn data can be expressed as:

as can be seen from (18) and (20), the reconstructed uplink forward sliding matrix set can be represented as:

wherein,the set of uplink backward smoothing matrices is:

the q th can be obtained by the same method_xThe forward and backward smooth matrix set of the downlink and the uplink of the sub-area array is as follows:

wherein

The final forward-backward spatial smoothing set (FB-SMS) from (20) - (23) is:

matrix set R^fbHas the following properties: when Q is_xQ_y＞2K，Q_x＞1，Q_y> 1, matrix R^fbIs 2K. Then to R^fbAfter Singular Value Decomposition (SVD), a two-dimensional ESPRIT algorithm may be employed to solve for the DOA estimate.

Under color noise, as can be seen from equations (6) and (15), only the first subarray contains the noise matrix, and the other subarrays are composed of the cross-correlation matrix.

The difference operation is performed on the noise part of equation (6), and there are:

other cross-correlation sub-arrays (non-noise parts) can be processed using a forward and backward spatial smoothing technique:

wherein,from (27) and (28), the nth column (n: 1, …, Q)_y-1) the difference matrix of the data can be represented as:

remaining P_yThe difference matrix for column data can be expressed as:

wherein,the set of downlink spatial difference smoothing matrices (SD-SMS) available from (29) and (31) is:

then extracting data information from bottom to top to construct an uplink difference smoothing matrix set of

Wherein,

in the same way, the q th_xThe downlink and uplink difference smooth matrix sets corresponding to the row sub-area arrays are respectively

Wherein,

then, from equations (36) and (37):

to R^dAnd a DOA estimated value can be obtained by adopting a two-dimensional ESPRIT algorithm.

To illustrate the applicability of the present invention, simulations are now performed as follows. The simulation conditions are as follows: the height of the uniform area array is h-20M, the number of the array elements is M-N-12, the wavelength of the signal is 1M, and the power of the incident signal isThe color noise is a second-order AR model with coefficients a ═ 1, -0.7,0.6](ii) a Monte carlo simulation times 300.

Experiment 1, simulation results of FB-SMS and SD-SMS are respectively shown in FIG. 3 and FIG. 4, the simulation times are 100, and the target positions are α respectively₁＝[10°,20°,40°]，θ₁＝[20°,35°,50°]And α₂＝[5°,15°,25°]，θ₂＝[25°,35°,45°](ii) a Dimension P of subarray_x＝P_yThe SNR is 5dB, and the fast beat rate is 500L, 9. As can be seen from fig. 3 and 4, the FB-SMS and the SD-SMS can accurately estimate all the target positions in both white noise and color noise.

Experiment 2: and (5) analyzing the performance under the white noise condition. The algorithm (FB-SM) of the invention is performed under the condition of white noise in the experimentS, SD-SMS), FBSS algorithm, space difference algorithm (AFB-SDS) and CRB mean square error (RMSE) curve as a function of signal-to-noise ratio and snapshot number. FIG. 5 shows the variation of the mean square error with the signal-to-noise ratio, the size of the subarray P_x＝P_y9, the snapshot number L is 500; FIG. 6 shows the variation of mean square error with fast beat number, the size of subarray P_x＝P_yThe SNR is 5dB for 9. As can be seen from fig. 5 and 6, under white noise conditions, the FB-SMS algorithm estimates better performance due to utilizing more data information; SD-SMS is estimated to perform less than FBSS due to greater data loss; the SD-SMS only adopts difference operation on the autocorrelation matrix, and the AFB-SDS adopts difference operation on the covariance of the subarrays, so that the data loss of the SD-SMS is lower than that of the AFB-SMS, and the estimation performance is better.

Experiment 3: and (5) analyzing the performance under the condition of color noise. FIG. 7 shows the variation of RMSE with signal to noise ratio, P_x＝P_y9, L500; FIG. 8 shows the variation of RMSE with fast beat number, P_x＝P_ySNR is 5dB for 9. As can be seen from fig. 7 and 8, SD-SMS has better estimation performance than FB-SMS when the color noise is a second-order AR model. This is because SD-SMS can effectively reduce the influence of the off-diagonal elements of the color noise covariance matrix. Wherein, the FB-SMS performance is superior to the FBSS due to the utilization of more data information; AFB-SDS performs the weakest, due to the large data loss.

As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.

The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the invention.

It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims

1. A low-angle target two-dimensional DOA estimation method based on a smooth matrix set is characterized by comprising the following steps:

2. The method of claim 1, wherein the multipath effects are an ideal specular reflection model and neglect atmospheric refraction and earth curvature effects, the uniform area array has M × N antenna elements, adjacent elements are spaced by a half wavelength, and the height of the uniform area array is h, K uncorrelated far-field narrow-band signal sources s_k(t), K is 1,2, …, and the incident angle of K is (α)_k,θ_k) Wherein α_kAnd theta_kThe azimuth angle and the elevation angle of the kth target are respectively, the echo signal is composed of a direct signal and a reflected signal, and the model specifically comprises the following steps:

<mrow> <mtable> <mtr> <mtd> <mrow> <mi>X</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <msub> <mi>a</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> <mo>,</mo> <msub> <mi>&theta;</mi> <mrow> <mi>d</mi> <mi>k</mi> </mrow> </msub> <mo>)</mo> </mrow> <msubsup> <mi>a</mi> <mi>y</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> <mo>,</mo> <msub> <mi>&theta;</mi> <mrow> <mi>d</mi> <mi>k</mi> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>s</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <msub> <mi>a</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> <mo>,</mo> <msub> <mi>&theta;</mi> <mrow> <mi>r</mi> <mi>k</mi> </mrow> </msub> <mo>)</mo> </mrow> <msubsup> <mi>a</mi> <mi>y</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> <mo>,</mo> <msub> <mi>&theta;</mi> <mrow> <mi>r</mi> <mi>k</mi> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>&beta;</mi> <mi>k</mi> </msub> <msub> <mi>s</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>Z</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <msub> <mi>a</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> <mo>,</mo> <msub> <mi>&theta;</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <msubsup> <mi>a</mi> <mi>y</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> <mo>,</mo> <msub> <mi>&theta;</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>s</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <msub> <mi>a</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> <mo>,</mo> <mo>-</mo> <msub> <mi>&theta;</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <msubsup> <mi>a</mi> <mi>y</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> <mo>,</mo> <mo>-</mo> <msub> <mi>&theta;</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>&beta;</mi> <mi>k</mi> </msub> <msub> <mi>s</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>Z</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>

in the formula, theta_dkAnd theta_rkThe direct and reflected elevation angles, theta, of the kth target, respectively_dk≈-θ_rk＝θ_k，α_kAt an azimuth angle of β_kIs the multipath reflection coefficient; u_k＝sinθ_kcosα_k，v_k＝sinθ_ksinα_k(ii) a Z (t) is a mean of 0 and a variance of σ²Independent white Gaussian noise, β for easy calculation_k＝exp[j(π-2πΔR_k/λ)]，ΔR_k≈2h sinθ_k，ΔR_kFor the multipath distance difference, the echo signal is vectorized and expressed as:

in the formula,

<mrow> <msub> <mi>A</mi> <mi>y</mi> </msub> <mo>=</mo> <msubsup> <mrow> <mo>&lsqb;</mo> <msub> <mi>a</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>v</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>a</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <mo>-</mo> <msub> <mi>v</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>a</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>v</mi> <mi>K</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>a</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <mo>-</mo> <msub> <mi>v</mi> <mi>K</mi> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow> <mrow> <mi>N</mi> <mo>&times;</mo> <mn>2</mn> <mi>K</mi> </mrow> <mi>T</mi> </msubsup> <mo>,</mo> <mi>s</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mrow> <mo>&lsqb;</mo> <msub> <mi>s</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>&beta;</mi> <mn>1</mn> </msub> <msub> <mi>s</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>s</mi> <mi>K</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>&beta;</mi> <mi>K</mi> </msub> <msub> <mi>s</mi> <mi>K</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow> <mrow> <mn>2</mn> <mi>K</mi> <mo>&times;</mo> <mn>1</mn> </mrow> <mi>T</mi> </msubsup> <mo>,</mo> </mrow>

z (t) vec (Z (t)), whereinFormula (2) may be represented as:

when the fast beat number is L, t is 1,2, …, L, the covariance matrix of the echo signal x (t) can be expressed as:

<mrow> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo>=</mo> <mi>E</mi> <mo>&lsqb;</mo> <mi>x</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msup> <mi>x</mi> <mi>H</mi> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mo>=</mo> <mfrac> <mn>1</mn> <mi>L</mi> </mfrac> <munderover> <mo>&Sigma;</mo> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>L</mi> </munderover> <mi>x</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msup> <mi>x</mi> <mi>H</mi> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>AR</mi> <mi>s</mi> </msub> <msup> <mi>A</mi> <mi>H</mi> </msup> <mo>+</mo> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <msub> <mi>I</mi> <mrow> <mi>M</mi> <mi>N</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>

in the formula,R_s＝E[s(t)s^H(t)]is a signal source covariance matrix.

3. The method of claim 2, wherein the step of dividing the uniform area array in the low-angle target echo signal model into a plurality of row sub-area arrays in a sliding manner comprises:

construction of Q in the x-and y-directions, respectively_xAnd Q_yA forward sub-array with array elements of P_xAnd P_yThen the uniform area array can be divided into Q_xQ_yAn array of rows of sub-areas of size P_x×P_y，Q_x＝M-P_x+1，Q_y＝N-P_y+1, q th_xq_yThe row sub-area array can be represented as:

in the formula, andrespectively an array flow pattern matrix A_xAnd A_yFront P of_xAnd P_yLine composition q_x＝1,…,Q_x，q_y＝1,…,Q_y， For the corresponding noise vector, at this time, each row sub-area array is composed of Q_yThe first row sub-area array can be set asx_1,nIs x_nFront P of_xLine, N ═ 1, …, N.

4. The method of claim 3, wherein extracting data information from top to bottom with a diagonal of the covariance matrix of the first row sub-area array as a boundary under white noise, and constructing a set of downlink smoothing matrices from the extracted data information comprises:

taking the diagonal line of the covariance matrix as a boundary, extracting data information of each column from top to bottom, so that the nth column, n is 1, …, and Q_y-1, which can be represented as:

<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mo>{</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo>+</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <msubsup> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> <mi>H</mi> </msubsup> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>2</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo>+</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <msubsup> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> <mi>H</mi> </msubsup> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <msubsup> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> <mi>H</mi> </msubsup> <mo>}</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <msub> <mi>&Phi;</mi> <mi>y</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <msub> <mi>&Pi;</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>+</mo> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <msub> <mi>C</mi> <mi>n</mi> </msub> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <msub> <mi>&Pi;</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>+</mo> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <msub> <mi>C</mi> <mi>n</mi> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>

wherein,

<mrow> <msub> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msubsup> <mi>A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>+</mo> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <msub> <mi>I</mi> <mrow> <msub> <mi>P</mi> <mi>x</mi> </msub> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>

as can be seen from equations (6) and (10), the reconstructed downlink forward smoothing matrix set can be represented as:

<mrow> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>=</mo> <mo>&lsqb;</mo> <msub> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>&rsqb;</mo> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <mo>{</mo> <msub> <mi>&Pi;</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>&Pi;</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msubsup> <mi>A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>}</mo> <mo>+</mo> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <msub> <mi>C</mi> <mn>0</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>

wherein,

the step of performing backward smoothing processing on the downlink smoothing matrix set to obtain a downlink backward smoothing matrix set specifically includes:

to improve estimation performance and decorrelation performance, matrix R is aligned₁The backward smoothing treatment can obtain:

<mrow> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> <mi>b</mi> </msubsup> <mo>=</mo> <msub> <mi>J</mi> <mrow> <msub> <mi>Q</mi> <mi>x</mi> </msub> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> <mo>*</mo> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&Pi;</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> <mo>*</mo> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>+</mo> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <msub> <mi>C</mi> <mi>n</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> <mi>b</mi> </msubsup> <mo>=</mo> <msub> <mi>J</mi> <mrow> <msub> <mi>Q</mi> <mi>x</mi> </msub> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> <mi>b</mi> </msubsup> <msub> <mi>J</mi> <mrow> <msub> <mi>Q</mi> <mi>x</mi> </msub> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&Theta;A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>+</mo> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <msub> <mi>I</mi> <mrow> <msub> <mi>P</mi> <mi>x</mi> </msub> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>

wherein,d_k＝(M-1)u_k+(N-1)v_kfrom equations (12) and (13), the set of backward smoothing matrices is:

<mrow> <msubsup> <mi>R</mi> <mn>1</mn> <mi>b</mi> </msubsup> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <mo>{</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&Pi;</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> <mo>*</mo> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>,</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&Pi;</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> <mo>*</mo> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&Pi;</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> <mo>*</mo> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>,</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&Pi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&Theta;A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>}</mo> <mo>+</mo> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <msub> <mi>C</mi> <mn>0</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow>

taking a diagonal line of the covariance matrix of the first row sub-area array as a boundary, extracting data information from bottom to top, and constructing an uplink smooth matrix set according to the extracted data information specifically comprises the following steps:

taking diagonal lines as boundaries, extracting each line of data information from bottom to top The columns are as follows:

<mrow> <msub> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> </mrow> </msub> <mo>=</mo> <mo>{</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <msubsup> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> </mrow> <mi>H</mi> </msubsup> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <msubsup> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> </mrow> <mi>H</mi> </msubsup> <mo>}</mo> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <msub> <mi>&Phi;</mi> <mi>y</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <msub> <mover> <mo>&Pi;</mo> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>+</mo> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <msub> <mover> <mi>C</mi> <mo>&OverBar;</mo> </mover> <mi>n</mi> </msub> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <msub> <mover> <mo>&Pi;</mo> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>+</mo> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <msub> <mover> <mi>C</mi> <mo>&OverBar;</mo> </mover> <mi>n</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow>

wherein,

<mrow> <msub> <mover> <mo>&Pi;</mo> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> </mrow> </msub> <mo>=</mo> <mo>{</mo> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> </mrow> </msubsup> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>,</mo> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> </mrow> </msubsup> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> </mrow> </msubsup> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow>

whereinThen the last P_yColumn data can be expressed as:

<mrow> <msub> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>+</mo> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <msub> <mi>I</mi> <mrow> <msub> <mi>P</mi> <mi>x</mi> </msub> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow>

as can be seen from equations (15) and (17), the reconstructed uplink forward sliding matrix set can be represented as:

<mrow> <msub> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <mn>1</mn> </msub> <mo>=</mo> <mo>&lsqb;</mo> <msub> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> </mrow> </msub> <mo>,</mo> <msub> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>&rsqb;</mo> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <mo>{</mo> <msub> <mover> <mo>&Pi;</mo> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mover> <mo>&Pi;</mo> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>}</mo> <mo>+</mo> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <msub> <mover> <mi>C</mi> <mo>&OverBar;</mo> </mover> <mn>0</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow>

wherein,

carrying out backward smoothing treatment on the uplink smoothing matrix set to obtain an uplink backward smoothing matrix set, wherein the step of obtaining the uplink backward smoothing matrix set specifically comprises the following steps:

the set of uplink backward smoothing matrices is:

<mrow> <mtable> <mtr> <mtd> <mrow> <msubsup> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <mn>1</mn> <mi>b</mi> </msubsup> <mo>=</mo> <mo>&lsqb;</mo> <msubsup> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> </mrow> <mi>b</mi> </msubsup> <mo>,</mo> <msubsup> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>b</mi> </msubsup> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msubsup> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> <mi>b</mi> </msubsup> <mo>,</mo> <msubsup> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> <mi>b</mi> </msubsup> <mo>&rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <mo>{</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mover> <mi>&Pi;</mi> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> </mrow> <mi>b</mi> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mover> <mi>&Pi;</mi> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> <mi>b</mi> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>,</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&Theta;A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>}</mo> <mo>+</mo> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <msub> <mover> <mi>C</mi> <mo>&OverBar;</mo> </mover> <mn>0</mn> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>19</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>

5. the method of claim 4, wherein the qth_xThe forward and backward smooth matrix set of the downlink and the uplink of each row sub-area array is as follows:

<mrow> <msub> <mi>R</mi> <msub> <mi>q</mi> <mi>x</mi> </msub> </msub> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <mo>{</mo> <msub> <mi>&Pi;</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&Pi;</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>&Pi;</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>}</mo> <mo>+</mo> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <msub> <mi>C</mi> <mn>0</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>20</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>R</mi> <msub> <mi>q</mi> <mi>x</mi> </msub> <mi>b</mi> </msubsup> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <mo>{</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&Pi;</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mn>1</mn> </mrow> <mo>*</mo> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>,</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&Pi;</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mn>2</mn> </mrow> <mo>*</mo> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&Pi;</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> <mo>*</mo> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&Theta;A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>}</mo> <mo>+</mo> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <msub> <mi>C</mi> <mn>0</mn> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>21</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <msub> <mi>q</mi> <mi>x</mi> </msub> </msub> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <mo>{</mo> <msub> <mover> <mo>&Pi;</mo> <mo>&OverBar;</mo> </mover> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mi>N</mi> </mrow> </msub> <mo>,</mo> <msub> <mover> <mo>&Pi;</mo> <mo>&OverBar;</mo> </mover> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mover> <mo>&Pi;</mo> <mo>&OverBar;</mo> </mover> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mi>N</mi> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msubsup> <mi>&Phi;</mi> <mi>s</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>}</mo> <mo>+</mo> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <msub> <mover> <mi>C</mi> <mo>&OverBar;</mo> </mover> <mn>0</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>22</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msubsup> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <msub> <mi>q</mi> <mi>x</mi> </msub> <mi>b</mi> </msubsup> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <mo>{</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mover> <mo>&Pi;</mo> <mo>&OverBar;</mo> </mover> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mi>N</mi> </mrow> <mo>*</mo> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mover> <mo>&Pi;</mo> <mo>&OverBar;</mo> </mover> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mi>N</mi> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> <mo>*</mo> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>,</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>&Theta;A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>}</mo> <mo>+</mo> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <msub> <mover> <mi>C</mi> <mo>&OverBar;</mo> </mover> <mn>0</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>23</mn> <mo>)</mo> </mrow> </mrow>

wherein

<mrow> <msub> <mover> <mo>&Pi;</mo> <mo>&OverBar;</mo> </mover> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> </mrow> </msub> <mo>=</mo> <mo>{</mo> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>P</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>25</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>

6. The method of claim 5, wherein computing a final forward and backward spatial smoothing set from the downlink forward and backward extracted data and the uplink forward and backward extracted data of each row sub-area array comprises:

<mrow> <msup> <mi>R</mi> <mrow> <mi>f</mi> <mi>b</mi> </mrow> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msub> <mi>Q</mi> <mi>x</mi> </msub> </mrow> </mfrac> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>Q</mi> <mi>x</mi> </msub> </munderover> <mo>{</mo> <mo>&lsqb;</mo> <msub> <mi>R</mi> <msub> <mi>q</mi> <mi>x</mi> </msub> </msub> <mo>,</mo> <msub> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <msub> <mi>q</mi> <mi>x</mi> </msub> </msub> <mo>&rsqb;</mo> <mo>+</mo> <mo>&lsqb;</mo> <msubsup> <mi>R</mi> <msub> <mi>q</mi> <mi>x</mi> </msub> <mi>b</mi> </msubsup> <mo>,</mo> <msubsup> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <msub> <mi>q</mi> <mi>x</mi> </msub> <mi>b</mi> </msubsup> <mo>&rsqb;</mo> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>26</mn> <mo>)</mo> </mrow> </mrow>

to R^fbAfter singular value decomposition, a two-dimensional ESPRIT algorithm is adopted to solve the DOA estimated value.

7. The method of claim 4, wherein the difference operation is performed on the noise portion of equation (6) by:

the non-noise part of other cross-correlation sub-arrays can be processed by adopting a forward and backward spatial smoothing technology:

<mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>{</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>2</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo>+</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <msubsup> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> <mi>H</mi> </msubsup> <mo>+</mo> <msub> <mi>J</mi> <mrow> <msub> <mi>Q</mi> <mi>x</mi> </msub> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>2</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo>+</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>*</mo> </msup> <msubsup> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> <mi>T</mi> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>}</mo> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msub> <mi>A</mi> <mi>P</mi> </msub> <mrow> <mo>(</mo> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mi>n</mi> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>n</mi> </mrow> </msubsup> <mo>+</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mo>-</mo> <mi>n</mi> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <mi>x</mi> </msub> </mrow> </msubsup> <mo>)</mo> </mrow> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>28</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> <mi>d</mi> </msubsup> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <msub> <mi>&Gamma;</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>29</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&Gamma;</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mo>{</mo> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>-</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>n</mi> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>T</mi> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>(</mo> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <msub> <mi>Q</mi> <mi>y</mi> </msub> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>n</mi> </mrow> </msubsup> <mo>+</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mo>-</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <mi>x</mi> </msub> </mrow> </msubsup> <mo>)</mo> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>/</mo> <mn>2</mn> <mo>}</mo> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>30</mn> <mo>)</mo> </mrow> </mrow>

remaining P_yThe difference matrix for column data can be expressed as:

<mrow> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> <mi>d</mi> </msubsup> <mo>=</mo> <msub> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>-</mo> <msub> <mi>J</mi> <mrow> <msub> <mi>Q</mi> <mi>x</mi> </msub> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> <mo>*</mo> </msubsup> <msub> <mi>J</mi> <mrow> <msub> <mi>Q</mi> <mi>x</mi> </msub> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <msub> <mi>&Gamma;</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>31</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msubsup> <mi>R</mi> <mn>1</mn> <mi>d</mi> </msubsup> <mo>=</mo> <mo>&lsqb;</mo> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> <mi>d</mi> </msubsup> <mo>,</mo> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> <mi>d</mi> </msubsup> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> <mi>d</mi> </msubsup> <mo>,</mo> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> <mi>d</mi> </msubsup> <mo>&rsqb;</mo> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <mo>{</mo> <msub> <mi>&Gamma;</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&Gamma;</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>&Gamma;</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&Gamma;</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>32</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msubsup> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <mn>1</mn> <mi>d</mi> </msubsup> <mo>=</mo> <mo>&lsqb;</mo> <msubsup> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> </mrow> <mi>d</mi> </msubsup> <mo>,</mo> <msubsup> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>d</mi> </msubsup> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msubsup> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> <mi>d</mi> </msubsup> <mo>,</mo> <msubsup> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> <mi>d</mi> </msubsup> <mo>&rsqb;</mo> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <mo>{</mo> <msub> <mover> <mi>&Gamma;</mi> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> </mrow> </msub> <mo>,</mo> <msub> <mover> <mi>&Gamma;</mi> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mover> <mi>&Gamma;</mi> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mover> <mi>&Gamma;</mi> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>33</mn> <mo>)</mo> </mrow> </mrow>

Wherein,

<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>&Gamma;</mi> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> </mrow> </msub> <mo>=</mo> <mo>{</mo> <mrow> <mo>(</mo> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> </mrow> </msubsup> <mo>+</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>-</mo> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <mi>x</mi> </msub> </mrow> </msubsup> <mo>)</mo> </mrow> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>/</mo> <mn>2</mn> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>...</mn> <mo>,</mo> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>-</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>}</mo> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>34</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mover> <mi>&Gamma;</mi> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>R</mi> <mi>s</mi> </msub> <mo>-</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <mi>&Theta;</mi> <mo>)</mo> </mrow> <msubsup> <mi>A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>35</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>5

8. the method of claim 7, wherein the qth is obtainable according to equations (32) and (33), the qth_xThe downlink and uplink difference smooth matrix sets corresponding to the row sub-area arrays are respectively as follows:

<mrow> <msubsup> <mi>R</mi> <msub> <mi>q</mi> <mi>x</mi> </msub> <mi>d</mi> </msubsup> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <mo>{</mo> <msub> <mi>&Gamma;</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&Gamma;</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>&Gamma;</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&Gamma;</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>36</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msubsup> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <msub> <mi>q</mi> <mi>x</mi> </msub> <mi>d</mi> </msubsup> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <mo>{</mo> <msub> <mover> <mi>&Gamma;</mi> <mo>&OverBar;</mo> </mover> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mover> <mi>&Gamma;</mi> <mo>&OverBar;</mo> </mover> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mover> <mi>&Gamma;</mi> <mo>&OverBar;</mo> </mover> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mover> <mi>&Gamma;</mi> <mo>&OverBar;</mo> </mover> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>37</mn> <mo>)</mo> </mrow> </mrow>

wherein,

<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&Gamma;</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mo>{</mo> <mrow> <mo>(</mo> <msub> <mi>R</mi> <mi>s</mi> </msub> <mo>-</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>n</mi> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <mo>-</mo> <msub> <mi>P</mi> <mi>x</mi> </msub> <mo>+</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <mo>)</mo> </mrow> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>,</mo> <mn>...</mn> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>(</mo> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <msub> <mi>Q</mi> <mi>y</mi> </msub> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>n</mi> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <mo>+</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mo>-</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <mo>-</mo> <msub> <mi>P</mi> <mi>x</mi> </msub> <mo>+</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <mo>)</mo> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>/</mo> <mn>2</mn> <mo>}</mo> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>38</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mi>&Gamma;</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <mo>-</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mi>&Theta;</mi> <mo>)</mo> </mrow> <msubsup> <mi>A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>39</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>&Gamma;</mi> <mo>&OverBar;</mo> </mover> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> </mrow> </msub> <mo>=</mo> <mo>{</mo> <mrow> <mo>(</mo> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>P</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>+</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>-</mo> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <msub> <mi>P</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>...</mn> <mo>,</mo> <mrow> <mo>(</mo> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <mo>-</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>y</mi> <mrow> <mover> <mi>n</mi> <mo>&OverBar;</mo> </mover> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <msub> <mi>P</mi> <mi>x</mi> </msub> </mrow> </msubsup> <mo>)</mo> </mrow> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>}</mo> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>40</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mover> <mi>&Gamma;</mi> <mo>&OverBar;</mo> </mover> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <mo>-</mo> <msup> <mi>&Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mi>&Theta;</mi> <mo>)</mo> </mrow> <msubsup> <mi>A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>41</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>

9. the method of claim 8, wherein a final set of spatial difference smoothing matrices is established based on the sets of downlink and uplink difference smoothing matrices corresponding to the respective row sub-area arrays:

<mrow> <msup> <mi>R</mi> <mi>d</mi> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>Q</mi> <mi>x</mi> </msub> </mfrac> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>Q</mi> <mi>x</mi> </msub> </munderover> <mo>{</mo> <msubsup> <mi>R</mi> <msub> <mi>q</mi> <mi>x</mi> </msub> <mi>d</mi> </msubsup> <mo>,</mo> <msubsup> <mover> <mi>R</mi> <mo>&OverBar;</mo> </mover> <msub> <mi>q</mi> <mi>x</mi> </msub> <mi>d</mi> </msubsup> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>42</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>

and solving the DOA estimated value by adopting a two-dimensional ESPRIT algorithm.