CN108896974B - Improved MIMO array high-resolution spatial spectrum estimation method - Google Patents

Improved MIMO array high-resolution spatial spectrum estimation method Download PDF

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CN108896974B
CN108896974B CN201810458847.2A CN201810458847A CN108896974B CN 108896974 B CN108896974 B CN 108896974B CN 201810458847 A CN201810458847 A CN 201810458847A CN 108896974 B CN108896974 B CN 108896974B
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刘雄厚
樊宽
孙超
杨益新
卓颉
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Northwestern Polytechnical University
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Abstract

The invention provides an improved MIMO array high-resolution space spectrum estimation method, aiming at overcoming the defect of the detection capability of the MIMO array high-resolution space spectrum estimation method based on the transmission diversity smoothing in the prior art under the environment of multiple targets and low signal-to-noise ratio, a uniform transmission linear array and a uniform receiving linear array are designed according to the de-coherence effect of the transmission diversity smoothing characteristic, matched filtering and time domain truncation processing are carried out when echo is processed to improve the signal-to-noise ratio, and simultaneously subarray smoothing is carried out by combining the array element spacing relation of the designed transmission linear array and receiving linear array to increase the degree of freedom, so that the detection performance superior to that of the existing transmission diversity smoothing MIMO array high-resolution space spectrum estimation method is obtained under the environment of multiple targets and low signal-to-noise ratio.

Description

Improved MIMO array high-resolution spatial spectrum estimation method
Technical Field
The invention relates to an array signal processing method.
Background
The high-resolution spatial spectrum estimation method of the active array system has important significance for multi-target detection (Stoica P, Moses R L. spectral analysis of signals [ M ]. Upper Saddle River, NJ: Pearson Prentice Hall, 2005.). Because the traditional active array system uses a single waveform and has higher correlation among multi-target echoes, the multi-target echoes on a receiving array need to be subjected to subarray smooth decorrelation coherent processing when high-resolution spatial spectrum estimation is used. However, when the number of targets is large and the receiving aperture of the active array is small, more sub-arrays need to be divided to obtain the desired decorrelation effect, which may result in a loss of the receiving aperture, and thus, the multi-target detection capability is insufficient.
In view of the shortcomings of the conventional active array system, a MIMO array can be used to obtain a stronger multi-target resolution capability to some extent (Li J, Stoica P, Xu L, et al.on parameter identification of MIMO radar [ J ]. IEEE Signal Processing Letters,2007,14(12):968 and 971.). The MIMO array irradiates a target by using a plurality of orthogonal waveforms in a pulse period, obtains the smooth characteristic of transmit diversity when the number of transmit array elements is more than or equal to the number of the target, and can estimate the target azimuth by directly utilizing high-resolution DOA estimation methods such as MVDR and MUSIC on the basis of automatic decorrelation of echoes from different targets (namely, linear independence of vector groups formed by echo signals). This method is called as a transmit diversity smoothing MIMO array high-resolution spatial spectrum estimation method.
However, when the number of targets is large, the number of transmit array elements of the MIMO array is smaller than the number of targets, and at this time, the transmit diversity smooth MIMO array high-resolution spatial spectrum estimation method faces the problem of insufficient degree of freedom. In addition, when the target distance is far, the signal-to-noise ratio of the echo is low, and the performance of the high-resolution spatial spectrum estimation method using the MIMO array is seriously reduced. Therefore, how to effectively detect more targets at a longer distance is an urgent problem to be solved by the existing MIMO array high-resolution spatial spectrum estimation method based on transmit diversity smoothing.
Disclosure of Invention
In order to overcome the defect of the detection capability of the MIMO array high-resolution space spectrum estimation method based on the transmission diversity smoothing in the prior art under the environment of multiple targets and low signal to noise ratio, the invention provides an improved MIMO array high-resolution space spectrum estimation method.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
1) a uniform linear array is adopted as a receiving and transmitting array, a transmitting array and a receiving array are arranged on the same straight line, and the geometric centers of the arrays are mutually overlapped; relative of transmitting and receiving arrayThe angle of the far field target is the same; the number M of the transmitting array elements is more than or equal to 2, and the number N of the receiving array elements is more than or equal to 6; the central frequency of operation of the transmit-receive array is f0And the underwater sound velocity is c, the corresponding wavelength lambda is c/f0Array element spacing d of receiving array elementsrλ/2, array element spacing d of transmitting arrayt≥L×drL is the number of sub-arrays divided when the receiving array is subjected to space smoothing;
2) the transmitting array simultaneously transmits a plurality of orthogonal pulse signals and different transmitting signals si(t)、sj(t) do not overlap each other in frequency band and correlation coefficient between them
Figure GDA0003355091190000021
Receiving echo signals, and recording the angle from the p-th target to the transmitting-receiving array as thetapEcho signals on N-element receiving array
Figure GDA0003355091190000022
at(θp) And ar(θp) Array manifold vectors, beta, for the transmit and receive ULA, respectivelypIs the scattering intensity of the pth target, and z (t) is an additive white gaussian noise vector on the receiving array element;
3) matched filtering of received signals by means of the sum of the transmitted signals, the unit impulse response function of the matched filter
Figure GDA0003355091190000023
Wherein T is the pulse width of the transmitting signal; let xn(t) is the echo signal on the n-th receiving array element, then the matched filter output y obtained by the matched filtern(t)＝xn(t) h (t); by yn(t) constructing an output vector y (t) of the array [ y ]1(t) y2(t) … yN(t)]T；
Performing time domain truncation on the output vector after matched filtering, taking the midpoint of the output signal of matched filtering as the center of the truncated signal, and respectively truncating to two sides for a time length of t0Time domain output of t0The value of (A) satisfies [0.2 ] in a predetermined volume1/B，2×1/B]B is single signal bandwidth to obtain N-element uniform linear array
Figure GDA0003355091190000024
Figure GDA0003355091190000025
A rectangular window for intercepting the signal;
carrying out subarray division on the N-element uniform linear array, dividing L subarrays in total, wherein L is more than or equal to P/M, and the length N of a single subarray0N-L + 1; output signal on the first sub-array
Figure GDA0003355091190000031
Output covariance matrix
Figure GDA0003355091190000032
The output of the ith sub-array and the covariance matrix of the corresponding array are yl' (t) and
Figure GDA0003355091190000033
defining the mean of the covariance matrices of the L sub-arrays
Figure GDA0003355091190000034
The corresponding array manifold after smoothing is a sub-array manifold
Figure GDA0003355091190000035
Wherein θ represents a scan angle;
finally obtaining a covariance matrix R according to the smoothingfAnd array manifold aSA(θp) And performing high-resolution spatial spectrum estimation.
The array element spacing d of the transmitting arrayt＝Lmax×drMaximum number of subarrays that can be divided when the receiving array is spatially smoothed
Figure GDA0003355091190000036
The high-resolution spatial spectrum estimation is carried out by adopting MVDR (spatial variance-variance digital radiography), and the spatial spectrum estimation result of the MVDR
Figure GDA0003355091190000037
The high-resolution spatial spectrum estimation is carried out by adopting MUSIC (multiple signal classification), and the covariance matrix R is subjected tofPerforming feature decomposition to obtain noise subspace G corresponding to small feature value, and estimating result by using spatial spectrum obtained by MUSIC
Figure GDA0003355091190000038
The invention has the beneficial effects that: the problem of multi-target high-resolution azimuth estimation is solved by combining the transmit diversity smoothing of the MIMO array and the traditional space smoothing, the ratio of the array element spacing of the transmit-receive array and the transmit-receive array is determined according to the number of the divided sub-arrays, and the maximization of the smooth degree of freedom is ensured; meanwhile, a matched filter which is generated by superposition of the transmitted signals and corresponds to signal design is utilized to carry out pulse compression on the received signals and further carry out time domain truncation on the matched filter output, so that the signal-to-noise ratio of the receiving end is improved, and the azimuth performance under the condition of low signal-to-noise ratio is improved.
The basic principle and the implementation scheme of the invention are verified by computer numerical simulation, and the result shows that: the method provided by the invention can effectively solve the detection problem of the MIMO array high-resolution spatial spectrum estimation method based on the transmit diversity smoothing under the environment of multiple targets and low signal to noise ratio.
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FIG. 1 is an array structure and signal propagation model for MIMO;
FIG. 2 is a schematic diagram of conventional spatial smoothing (forward smoothing) subarray partitioning;
FIG. 3 is a flow chart of an embodiment of the present invention;
FIG. 4 is a transmitted signal spectrum used in an implementation example;
FIG. 5 is a time domain diagram of a signal received by array element No. 1 in an embodiment example;
FIG. 6 shows the time domain output of the received signal of array element No. 1 after matched filtering;
fig. 7 shows the time domain output after the signal received by the array element No. 1 is processed by matched filtering and time domain truncation in the embodiment;
FIG. 8 shows the element spacing d of the transceiver arrayt＝drA spatial spectrum estimation result in the absence of matched filtering processing;
FIG. 9 shows the element spacing d of the transceiver arrayt＝drThe space spectrum estimation result is obtained when matched filtering processing is carried out;
FIG. 10 shows the element spacing d of the transceiver arrayt＝drThe space spectrum estimation result is obtained during matched filtering and time domain truncation processing;
FIG. 11 shows the element spacing d of the transmitter and receiver arrayt＝5drA spatial spectrum estimation result in the absence of matched filtering processing;
FIG. 12 shows the element spacing d of the transceiver arrayt＝5drThe space spectrum estimation result is obtained when matched filtering processing is carried out;
FIG. 13 shows the element spacing d of the transmitter and receiver arrayt＝5drThe space spectrum estimation result is obtained during matched filtering and time domain truncation processing.
Detailed Description
The present invention will be further described with reference to the following drawings and examples, which include, but are not limited to, the following examples.
The main contents of the invention are:
1. and designing an array type of the MIMO array. The transmitting array is an M-element uniform linear array with array element spacing equal to integral multiple of half wavelength of signals (the product of the array element spacing and the number of sub-arrays must be more than or equal to) and the receiving array is an N-element uniform linear array with array element spacing equal to half wavelength. The transmitting uniform linear array and the receiving uniform linear array are collinear and the geometric centers are superposed with each other (the array design is the prior art, but the subsequent sub-array division mode is determined).
2. A plurality of transmitting array elements in a transmitting linear array simultaneously transmit a plurality of orthogonal pulses with the same bandwidth, a receiving linear array collects multi-target echoes, the MIMO array echoes are subjected to matched filtering and time domain truncation, the sum of all transmitting signals is used for carrying out matched filtering processing on the echoes, meanwhile, time domain truncation is carried out on the matched filtering output, and data with a large signal-to-noise ratio in the matched filtering output is extracted. The extraction range of time domain truncation is: with matched filteringThe time length between the midpoint and the two sides is t0Time domain output of t0The value of (A) satisfies [ 0.2X 1/B, 2X 1/B]And B is the bandwidth of a single pulse signal.
3. And constructing a covariance matrix by using the matched filtering output extracted by time domain truncation, and simultaneously performing decorrelation on multi-target echo by using sub-array smoothing processing. When the subarray is processed smoothly, the number of the divided subarrays is larger than or equal to the ratio of the target number to the number of the transmitting array elements. And for the echo covariance matrix after the coherence resolution, a high-resolution spatial spectrum estimation method is used for obtaining a multi-target spatial spectrum estimation result.
4. A high-resolution space spectrum estimation method of the transmit diversity smooth MIMO array and a space spectrum estimation result of the improved method under the environment with multiple targets and low signal to noise ratio are provided through computer numerical simulation, so that the method provided by the invention can obtain good space spectrum estimation performance.
As shown in fig. 3, the technical scheme adopted by the present invention can be divided into the following steps, and each step of the present invention is described in detail below:
step 1) mainly relates to the array structure design of the MIMO array, and the related specific content is as follows:
the transmitting array and the receiving array are arranged on the same straight line, and the geometric centers of the arrays are mutually overlapped. The angles of the transceiving arrays relative to the far-field targets are the same, and if P targets with the same target characteristics exist in a far-field environment, a signal propagation diagram of the structure of the MIMO array relative to the P-th target is shown in fig. 1. The number of the transmitting array elements generally satisfies M is more than or equal to 2, and the number of the receiving array elements satisfies N is more than or equal to 6. Suppose the MIMO array operates at a center frequency f0And the underwater sound velocity is c, the corresponding wavelength lambda is c/f0Array element spacing d of receiving array elementsrSatisfying a half-wavelength arrangement, i.e. drλ/2. Array element spacing d of transmitting arraytThe number L of sub-arrays and the spacing d of elements of the receiving array, which are divided when the receiving array performs spatial smoothing (the spatial smoothing used in this embodiment refers to the conventional forward smoothing technique), are usedrJointly, it is decided that:
dt≥L×dr (1)
in the formula, x represents a simple number multiplication. In other words, after the number L of sub-arrays is determined, the array element pitch of the transmission array elements must satisfy the condition of expression (1) in order to obtain the maximum degree of freedom for the smoothing process. The number of sub-arrays required by the smoothing processing is determined according to the number P of coherent targets existing in the actual situation, but the array element spacing d of the transmitting arraytIs determined in advance. Therefore, for M-transmission and N-reception MIMO array, the maximum number L of sub-arrays which can be divided can be determinedmaxDetermine dtThus, it can be seen that:
Figure GDA0003355091190000061
in the formula
Figure GDA0003355091190000062
This means taking the smallest positive integer equal to or greater than the value in the symbol. On the basis of ensuring that the smoothness freedom degree can reach the maximum, the size of a transmitting array needs to be reduced as much as possible, and then the space between transmitting array elements is determined:
dt＝Lmax×dr (3)
the transmitting array element spacing determined according to the formula (3) can ensure that the degree of freedom of the known array for smoothing processing is the maximum within the range of the number of sub-arrays which can be divided.
Step 2) mainly relates to signal transmission and echo acquisition of the MIMO array, and the related specific contents are as follows:
the transmitting linear array simultaneously transmits a plurality of orthogonal pulse signals. Taking frequency-division linear frequency-modulated signal (LFM) as an example, different transmission signals si(t) do not overlap each other in frequency band, and correlation coefficient ρ of the frequency bandsijThe following relationship is satisfied:
Figure GDA0003355091190000063
in the formula (I), the compound is shown in the specification,E[.]express the mathematical expectation, | - | express the modulus, [.]cRepresenting the conjugation;
let the angle from the p-th target to the MIMO array be θp(angle of target to array normal). To simplify the analysis, only the influence of the scattering intensity of the target on the echo intensity is considered, ignoring the doppler shift of the echo and the diffusion loss and medium absorption loss. Therefore, the echo signal x (t) on the N-ary receiving array can be expressed as:
Figure GDA0003355091190000064
wherein [.]TRepresenting a transposition operation, at(θp) And ar(θp) Array manifold vectors, beta, for the transmit and receive ULA, respectivelypIs the scattering intensity of the pth target, and z (t) is the additive white gaussian noise vector on the receiving array element.
Step 3) mainly uses matched filtering, time domain truncation and subarray smoothing to obtain the expected spatial spectrum estimation performance, and the related specific contents are as follows:
the sum of the transmitted signals is used for carrying out matched filtering processing on the received signals, and the received signals on the array elements are formed by linearly superposing M orthogonal transmitted signals and noise. According to the characteristics, the following matched filter is designed, and the unit impulse response function of the matched filter is as follows:
Figure GDA0003355091190000071
where T is the pulse width of the transmit signal. Let xn(t) is the echo signal on the n-th receiving array element, and the matched filtering output obtained by the matched filter of the formula (6) is:
yn(t)＝xn(t)*h(t) (7)
in the formula, a represents convolution. By yn(t) constructing an output vector y (t) of the array, namely:
y(t)＝[y1(t) y2(t) … yN(t)]T (8)
in order to further improve the output signal-to-noise ratio, the output vector after matched filtering is subjected to time domain truncation. Because the energy output by the matched filtering is mainly concentrated in the middle main lobe part, the midpoint of the output signal of the matched filtering is taken as the center of the intercepted signal, and the intercepting time length to two sides is t0Time domain output of t0The value of (A) satisfies [ 0.2X 1/B, 2X 1/B]And B is the single signal bandwidth. The whole signal interception process can be expressed as y (t) and rectangular window
Figure GDA0003355091190000072
The form of multiplication:
Figure GDA0003355091190000073
rectangular window
Figure GDA0003355091190000074
The specific expression of (1) is:
Figure GDA0003355091190000075
when the number of coherent targets is far larger than the number of transmitting array elements, the signals are subjected to space smoothing before being estimated by using a high-resolution algorithm. Taking traditional spatial smoothing (forward smoothing) as an example, carrying out subarray division on an N-element uniform linear array, wherein L subarrays are divided, and the number of the subarrays needs to meet the following requirements:
L≥P/M (11)
length N of a single subarray0Comprises the following steps:
N0＝N-L+1 (12)
a schematic diagram of the subarray division is shown in fig. 2. With the output signal y on the first sub-array1' (t) is an example:
Figure GDA0003355091190000081
the output covariance matrix of the subarray
Figure GDA0003355091190000082
Can be written as:
Figure GDA0003355091190000083
by analogy, the output of the L (L ═ 1,2, …, L) th sub-array and the covariance matrix of the corresponding array are y, respectivelyl' (t) and
Figure GDA0003355091190000084
defining the mean value of the covariance matrixes of the L sub-matrixes as an output covariance matrix after forward spatial smoothing:
Figure GDA0003355091190000085
the corresponding array manifold after smoothing is a subarray array manifold:
Figure GDA0003355091190000086
where θ represents the scan angle.
Finally obtaining a covariance matrix R according to the smoothingfAnd array manifold aSA(θp) And performing high-resolution spatial spectrum estimation through high-resolution algorithms such as MVDR and MUSIC. Wherein the spatial spectrum estimation result of MVDR is obtained from equation (17):
Figure GDA0003355091190000087
for covariance matrix RfPerforming feature decomposition to obtain noise subspace G corresponding to small feature value, and estimating result by using spatial spectrum obtained by MUSICThen represented by equation (18):
Figure GDA0003355091190000088
in the implementation example, the computer is used for carrying out numerical simulation to check the effect of the method provided by the invention. In the verification method, two high-resolution algorithms of MVDR and MUSIC are adopted to carry out azimuth estimation on the target.
1) Setting target parameters and simulation conditions
Assuming that a plurality of targets with the same parameters exist in the environment and are uniformly distributed in a space angle relative to the transceiving array, the total number P of the targets is 12, and the angle interval between adjacent targets is 10 °. The MIMO array adopts a uniform linear array with 3 transmitting and 18 receiving, and the geometric centers of the array are overlapped. Array element spacing d of receiving arrayrArranged according to half wavelength, array element spacing d of transmitting arraytThe requirement according to equation (3) is set to dt＝5dr. Center frequency f of MIMO array operation0The frequency division chirp signals with 3 frequency bands not overlapping each other are used as the transmission signals, and are orthogonal to each other, the central frequency difference Δ f is 2kHz, the bandwidth B of a single signal is 2kHz, and the frequency spectrum of the transmission signals is shown in fig. 4. The signal sampling frequency is 4 times Fs (Fs to 4 f) of the center frequency0The sampling time Ts is 0.1 s. The noise is white Gaussian noise with the frequency band level, and the SNR is-15 dB.
2) Matched filtering and time-domain truncation
And designing a corresponding matched filter according to the transmitting signal, and performing matched filtering processing on the receiving signal to improve the signal-to-noise ratio. And performing time-domain truncation on the matched filtering output sequence, wherein the time-domain truncation is performed according to t0The truncation is performed in the range of 1/B, i.e. 150 points on either side of the centre of the output sequence. Fig. 4, 5 and 6 are the actual received signal of array element No. 1 and the time domain output after matched filtering and the time domain output after truncation, respectively.
3) Dividing subarrays and spatially smoothing
And carrying out subarray division on the receiving array, wherein the number L of subarrays is 4(L is more than or equal to P/M, P is 12, and M is 3). By matched filtering, choppingBreaking the processed signals to obtain 4 sub-array output covariance matrixes, and then calculating the mathematical average of the 4 sub-array output covariance matrixes to obtain an array output covariance matrix R after smoothingf. And finally, respectively carrying out high-resolution spatial spectrum estimation by adopting MVDR and MUSIC.
In order to embody the respective functions of the three parts of array design, matched filtering and time domain truncation, the invention respectively provides the high-resolution spatial spectrum estimation results of the MIMO array under a plurality of different simulation conditions, and the array design part adopts the conventional MIMO array (the array element spacing of the transmitting-receiving array is equal to the half wavelength d)t＝drλ/2) was compared to the array design of the present invention.
Fig. 8 to fig. 13 total 6 diagrams respectively show the high-resolution spatial spectrum estimation results of the MIMO array obtained by using MVDR and MUSIC under different processing flows. Wherein fig. 13 is a diagram of spatial spectrum estimation obtained by adopting all the designs of the present invention, and fig. 8 is a diagram of conventional MIMO array high-resolution spatial spectrum estimation based on transmit diversity smoothing before improvement. FIG. 9 is added with the matched filtering process proposed by the present invention as compared to FIG. 8, FIG. 10 is added with the time-domain truncation process as compared to FIG. 9, and FIGS. 8 to 10 all use the conventional array design, i.e., dt＝drλ/2. FIGS. 11 to 13 all adopt the array design proposed by the present invention satisfying dt＝5dr2.5 λ, and fig. 12 and 13 are the results obtained by adding the steps of matched filtering and time-domain truncation processing successively to the processing flow of fig. 11. The overview of fig. 8 and fig. 11, fig. 9 and fig. 12, fig. 10 and fig. 13 can form 3 groups of comparisons about array design, and it is obvious that more smooth degrees of freedom can be obtained by using the array design proposed by the present invention, so that the high-resolution spatial spectrum estimation performance of two high-resolution algorithms under the multi-objective condition is better; comparing fig. 11 and fig. 12, it can be seen that the performance of improving the high-resolution spatial spectrum estimation can be improved by using the matched filter provided by the present invention to perform matched filtering, and then, in combination with fig. 13, it can be seen that the performance of two high-resolution algorithms can be further improved by performing truncation processing on the basis of matched filtering, and thus, the performance of the low-signal algorithm is greatly improvedDetectability at noise ratio.
According to the embodiment, the maximization of the smooth degree of freedom is realized by designing the transmitting-receiving array element spacing of the MIMO array, the receiving signal-to-noise ratio is successively improved by utilizing a plurality of transmitting signals to design a matched filter at a receiving end and adopting a time domain truncation mode, and the problem of the direction estimation of the MIMO array high-resolution space spectrum estimation method based on the transmit diversity smoothing under the environment of multiple targets and low signal-to-noise ratio is effectively solved.

Claims (4)

1. An improved MIMO array high-resolution spatial spectrum estimation method is characterized by comprising the following steps:
1) a uniform linear array is adopted as a receiving and transmitting array, a transmitting array and a receiving array are arranged on the same straight line, and the geometric centers of the arrays are mutually overlapped; the angles of the transceiving arrays relative to the far-field target are the same; the number M of the transmitting array elements is more than or equal to 2, and the number N of the receiving array elements is more than or equal to 6; the central frequency of operation of the transmit-receive array is f0And the underwater sound velocity is c, the corresponding wavelength lambda is c/f0Array element spacing d of receiving array elementsrλ/2, array element spacing d of transmitting arrayt≥L×drL is the number of sub-arrays divided when the receiving array is subjected to space smoothing;
2) the transmitting array simultaneously transmits a plurality of orthogonal pulse signals and different transmitting signals si(t)、sj(t) do not overlap each other in frequency band and correlation coefficient between them
Figure FDA0003355091180000011
i,j＝1,2…M,i≠j；
Wherein E [.]Express the mathematical expectation, [.]cRepresenting the conjugation;
receiving echo signals, and recording the angle from the p-th target to the transmitting-receiving array as thetapEcho signals on N-element receiving array
Figure FDA0003355091180000012
at(θp) And ar(θp) Array manifold for transmitting ULA and receiving ULA respectivelyAmount, betapIs the scattering intensity of the pth target, z (t) is an additive white Gaussian noise vector on the receiving array element, and P represents the number of coherent targets;
3) matched filtering of received signals by means of the sum of the transmitted signals, the unit impulse response function of the matched filter
Figure FDA0003355091180000013
Wherein T is the pulse width of the transmitting signal; let xn(t) is the echo signal on the n-th receiving array element, then the matched filter output y obtained by the matched filtern(t)＝xn(t) h (t); by yn(t) constructing an output vector y (t) of the array [ y ]1(t) y2(t) … yN(t)]T；
Performing time domain truncation on the output vector after matched filtering, taking the midpoint of the output signal of matched filtering as the center of the truncated signal, and respectively truncating to two sides for a time length of t0Time domain output of t0The value of (A) satisfies [ 0.2X 1/B, 2X 1/B]B is single signal bandwidth to obtain N-element uniform linear array
Figure FDA0003355091180000014
Figure FDA0003355091180000015
A rectangular window for intercepting the signal;
carrying out subarray division on the N-element uniform linear array, dividing L subarrays in total, wherein L is more than or equal to P/M, and the length N of a single subarray0N-L + 1; output signal on the first sub-array
Figure FDA0003355091180000021
Output covariance matrix
Figure FDA0003355091180000022
The output of the l-th sub-array and the covariance matrix of the corresponding array are y'l(t) and
Figure FDA0003355091180000023
defining the mean of the covariance matrices of the L sub-arrays
Figure FDA0003355091180000024
The corresponding array manifold after smoothing is a sub-array manifold
Figure FDA0003355091180000025
Wherein θ represents a scan angle;
finally obtaining a covariance matrix R according to the smoothingfAnd array manifold aSA(θp) And performing high-resolution spatial spectrum estimation.
2. The improved MIMO array high-resolution spatial spectrum estimation method of claim 1, wherein: the array element spacing d of the transmitting arrayt＝Lmax×drMaximum number of subarrays that can be divided when the receiving array is spatially smoothed
Figure FDA0003355091180000026
3. The improved MIMO array high-resolution spatial spectrum estimation method of claim 1, wherein: the high-resolution spatial spectrum estimation is carried out by adopting MVDR (spatial variance-variance digital radiography), and the spatial spectrum estimation result of the MVDR
Figure FDA0003355091180000027
4. The improved MIMO array high-resolution spatial spectrum estimation method of claim 1, wherein: the high-resolution spatial spectrum estimation is carried out by adopting MUSIC (multiple signal classification), and the covariance matrix R is subjected tofPerforming feature decomposition to obtain noise subspace G corresponding to small feature value, and estimating result by using spatial spectrum obtained by MUSIC
Figure FDA0003355091180000028
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