CN104360305A - Radiation source direction finding positioning method of uniting compressed sensing and signal cycle stationary characteristics - Google Patents

Abstract

The invention provides a radiation source direction finding positioning method of uniting compressed sensing and signal cycle stationary characteristics, and belongs to the array signal processing field. The radiation source direction finding positioning method of uniting the compressed sensing and the signal cycle stationary characteristics is characterized by using a zero mean non-stationary random process as an incidence signal, and obtaining cycle frequency of the incidence signal, and includes: using a sensor array to observe the incidence signal so as to obtain an observation signal; then, using a gauss observation matrix to compress the observation signal into a low dimension vector so as to obtain a compressed observation signal; for the compressed observation signal, calculating a cycle autocorrelation matrix of the incidence signal according to the cycle frequency; performing feature subspace decomposition on the cycle autocorrelation matrix so as to obtain a signal subspace and a noise subspace; using the noise subspace to perform angle spectrum estimation in a value range of the incidence signal theta, and using the theta value corresponding to the maximum value of angle spectrum PUMUSIC as the finally estimated incidence signal. The radiation source direction finding positioning method of uniting the compressed sensing and the signal cycle stationary characteristics can avoid a fuzzy angle problem.

Description

The radiation source DF and location method of associating compressed sensing and signal cycle smooth performance

Technical field

The invention belongs to Array Signal Processing field, be specifically related to a kind of based on the classical super resolution algorithm multiple signal classification MUSIC algorithm in DOA estimation, the basis of cyclo-stationary MUSIC (Cyclic MUSIC) algorithm adds the element of compressed sensing.

Background technology

Along with going deep into gradually of DOA Estimation Study, find that many estimated signal all have the cyclostationarity of time domain.Utilize the cyclostationarity of signal to carry out DOA estimation to signal, greatly can improve the DOA estimated performance of algorithm.Incoming signal can be divided into useful signal and undesired signal, the cycle frequency of useful signal is cycle frequency to be measured, and it is not signal and noise two parts of cycle frequency to be measured that undesired signal comprises cycle frequency.Utilize cyclostationarity effectively can suppress interference, compared with the DOA estimation method of routine, have advantages such as selecting direction finding ability, antijamming capability, multi signal processing power.

MUSIC algorithm, as the DOA algorithm for estimating of classics, has the advantage of super-resolution, is combined by the cyclostationarity of signal creates Cyclic MUSIC algorithm with the super-resolution of MUSIC algorithm, greatly can improve the performance that DOA estimates.

Along with people are to the sustainable growth of the quantity of information requirement, also increasing to the intractability of signal, in order to reduce storage, process and the cost of signal transmission, need to compress original signal with less sampling rate reconstruction signal.Along with the proposition that compressed sensing CS (Compressed Sensing) is theoretical, as long as signal has openness on certain transform domain, just can will receive high dimensional signal with one with the incoherent observing matrix of this transform-based projects on lower dimensional space, then reconstructs original signal by optimization method.

For Cyclic MUSIC algorithm, angular resolution after its angle direction finding can not be infinitely small, measure incident angle difference be less than requirement differential seat angle will angle of arrival fuzzy, and super-resolution with huge computational complexity for cost, if therefore CS theory can be applied in Cyclic MUSIC algorithm, then for the efficiency improving algorithm, reduce computation complexity, there is important theory significance and engineering practice value.

Summary of the invention

In view of this, the present invention proposes the radiation source DF and location method of associating compressed sensing and signal cycle smooth performance, the selection direction finding of cycle frequency can be utilized to estimate the incident angle of different cycle frequency incoming signal respectively, avoid direction ambiguity problem.

For achieving the above object, technical scheme of the present invention is:

S1, with zero-mean nonstationary random process x (t) for incoming signal, obtain x (t) cycle frequency α, α=m/T ₀, m is an integer, T ₀for x (t) autocorrelation function cycle.

S2, employing sensor array carry out observation to incoming signal and obtain observation signal x ∈ R ^{m × N}, wherein M is the array number of sensor array, and N is the sampling number for observation signal;

Then use Gauss's observing matrix φ by observation signal x ∈ R ^{m × N}the low dimensional vector of boil down to, obtains the observation signal y ∈ R after compressing ^{l × N}, L is the array number after compression.

S3, for the observation signal y after compression, calculate the circulation autocorrelation matrix R of incoming signal y according to cycle frequency α ^α _yy, R ^α _yybe the matrix of a L × L, in this matrix, each element is specially:

${R^{\mathrm{\α}}}_{\mathrm{yy}}(m_1,m_2)=\frac{1}{N}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}y(m_1,n)\×y{(m_2,n)}^{*}\×e^{-j2\mathrm{\π\αn}}$

Wherein * is conjugate operation, m ₁and m ₂value between 1 ~ L; N is sampled point numbering; R ^α _yy(m ₁, m ₂) be matrix R ^α _yyin m ₁oK, m ₂the element of row; Y (m ₁, n) be array element m in y ₁the n-th sample point sampled value; Y (m ₂, n) be array element m in y ₂the n-th sample point sampled value.

S4, to the circulation autocorrelation matrix R in Step3 ^α _yycarry out eigendecomposition, R ^α _yy=U _sd _su _s ^h+ U _nd _nu _n ^h, U _sfor signal subspace, D _sfor the diagonal matrix of signal subspace character pair value composition; U _nfor noise subspace, D _nfor the diagonal matrix of noise subspace character pair value composition.

S5, carry out angular spectrum estimation, angular spectrum wherein a (θ) steering vector, d is array element distance, and λ is incoming signal wavelength; θ is incident angle.

In the span of incident angle θ, to make angular spectrum P _mUSICthe corresponding θ value of getting maximal value is the final incident angle estimated.

Beneficial effect:

The radiation source DF and location method of associating compressed sensing provided by the invention and signal cycle smooth performance, i.e. CS Cyclic MUSIC algorithm, the method utilizes the selection direction finding of cycle frequency to estimate the incident angle of different cycle frequency incoming signal respectively, there is good selection direction finding ability, also avoid direction ambiguity problem simultaneously, improve the angular resolution of MUSIC algorithm.

2, CS Cyclic MUSIC algorithm provided by the present invention carries out direction finding estimation according to the cycle frequency α of signal, therefore, it is possible to tell the measured signal under particular cycle frequency from the mixed signal of multiple complexity, even if the sum of signal of interest and interference is greater than array number, these class methods still correctly can estimate the direction of arrival of all signal of interest.

3, on the basis of above advantage, owing to make use of compressive sensing theory, CS Cyclic MUSIC algorithm is reduced compared to Cyclic MUSIC algorithm on computation complexity, thus improves the application efficiency of algorithm, the engineer applied considerably increasing algorithm is worth.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of this method;

Fig. 2 is that MUSIC algorithm DOA estimates simulation curve figure;

Fig. 3 is that Cyclic MUSIC algorithm DOA estimates simulation curve figure;

Fig. 4 is that CS Cyclic MUSIC algorithm DOA estimates simulation curve figure;

Fig. 5 is DOA algorithm for estimating effectiveness comparison;

Fig. 6 is DOA algorithm for estimating effectiveness comparison;

Fig. 7 is the DOA estimation effect figure of information source number when being more than or equal to array number;

Fig. 8 estimates hardware structure realization figure based on the angular spectrum of compressed sensing framework.

Embodiment

To develop simultaneously embodiment below in conjunction with accompanying drawing, describe the present invention.

Embodiment 1,

The radiation source DF and location method of associating compressed sensing provided by the present invention and signal cycle smooth performance, its process flow diagram as shown in Figure 1, specifically comprises the steps:

Step1, with zero-mean nonstationary random process x (t) for incoming signal, obtain x (t) cycle frequency α, α=m/T ₀, m is an integer, T ₀for the cycle of the autocorrelation function of x (t).

Step2, employing sensor array carry out observation to incoming signal and obtain observation signal x ∈ R ^{m × N}, wherein M is the array number of described sensor array, and N is the sampling number for observation signal.

Then use Gauss's observing matrix φ by described observation signal x ∈ R ^{m × N}be compressed to low dimensional vector y ∈ R ^{l × N}; Wherein y is the observation signal after compression, and L is the array number after compression.

Step3, for the observation signal y after compression, calculate the circulation autocorrelation matrix R of incoming signal y according to cycle frequency α ^α _yy, R ^α _yybe the matrix of a L × L, in this matrix, each element is specially:

${R^{\mathrm{\α}}}_{\mathrm{yy}}(m_1,m_2)=\frac{1}{N}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}y(m_1,n)\×y{(m_2,n)}^{*}\×e^{-j2\mathrm{\π\αn}}$

Wherein * is conjugate operation, m ₁and m ₂value between 1 ~ L; N is sampled point numbering; R ^α _yy(m ₁, m ₂) be matrix R ^α _yyin m ₁oK, m ₂the element of row; Y (m ₁, n) be array element m in y ₁the n-th sample point sampled value; Y (m ₂, n) be array element m in y ₂the n-th sample point sampled value.

Step4, to the circulation autocorrelation matrix R in Step3 ^α _yycarry out eigendecomposition, R ^α _yy=U _sd _su _s ^h+ U _nd _nu _n ^h, U _sfor signal subspace, Ds is the diagonal matrix of signal subspace character pair value composition; U _nfor noise subspace, Dn is the diagonal matrix of noise subspace character pair value composition.

Step5, carry out angular spectrum estimation, angular spectrum wherein a (θ) steering vector, d is array element distance, and λ is incoming signal wavelength.

θ is incident angle, in the span of incident angle, makes angular spectrum P _mUSICthe θ value of getting maximal value is the final incident angle estimated.

The calculated amount that MUSIC algorithm is huge is because need to carry out Eigenvalues Decomposition to the covariance matrix of observation signal, CS theory is added in MUSIC algorithm in above-mentioned steps, the dimension of signal was decreased before carrying out Eigenvalues Decomposition, decrease the complexity of Eigenvalues Decomposition, it also reduce the complexity that whole DOA estimates.Specifically: the computation complexity of MUSIC algorithm is o (M ³), and the complexity of MUSIC algorithm is after compression o (L ³), wherein L is the array number after compression.Compression multiple larger, the raising of complexity is more obvious.

Embodiment 2,

The present embodiment, by the basis of embodiment 1, by the feature of simulating, verifying CS Cyclic MUSIC algorithm performance, emulates with MUSIC algorithm, Cyclic MUSIC algorithm and CS CyclicMUSIC algorithm for incoming signal respectively.

When incoming signal is two arrowband AM signals, incident angle is respectively 40 ° and 43 °, and the cycle frequency of two AM signals is respectively 1000Hz and 750Hz, and signal to noise ratio (S/N ratio) is 5dB, time delay τ is 24 sampling periods.

Wherein Fig. 2, Fig. 3 and Fig. 4 are respectively MUSIC algorithm, Cyclic MUSIC algorithm and CS Cyclic MUSIC algorithm DOA provided by the invention estimation simulation curve figure;

Can be seen by simulation curve, in Fig. 2, MUSIC algorithm has all carried out DOA estimation to the signal of two on incident array, there are two spectrum peaks, when in Fig. 3 and Fig. 4, Cyclic MUSIC algorithms selection cycle frequency is 1000Hz, angle estimation value is 43 °, when selecting cycle frequency to be 750Hz, angle estimation value is 40 °, and cycle frequency is misfitted and can not be estimated.

The compression factor that the present embodiment adopts in CS Cyclic MUSIC algorithm is 4, does not reduce, also demonstrate the validity of compressive sensing theory after being compressed by Received signal strength to the accuracy that DOA estimates.In above-mentioned simulation algorithm, the CS Cyclic MUSIC algorithm time used is 0.031623, and the algorithm time of uncompressed is 0.183629s, also can find out that computation complexity reduces from the time.

Above emulated data is put into a figure to compare, as Fig. 5, shown in Fig. 6: from Fig. 5, Fig. 6 can find out when incoming signal two arrival bearings relatively, on the side direction curve of MUSIC algorithm can not clear resolution two spectrum peak time, CS Cyclic MUSIC has carried out estimating accurately to incoming signal, effectively inhibit interference, have better estimated performance than MUSIC algorithm.

When incoming signal be an arrowband AM signal and three undesired signals time, incident angle is respectively 40 °, 50 °, 60 ° and 20 °, and the cycle frequency of narrow band signal is respectively 600Hz, and incident angle is 20 °, and number of arrays is 4.

As seen from Figure 7, when the information source number of incoming signal is more than or equal to array number, MUSIC algorithm truly can not measure the direction of incoming wave signal, but Cyclic MUSIC algorithm CS Cyclic MUSIC algorithm effectively inhibits the signal outside cycle frequency 600Hz, has carried out DOA estimation to measured signal accurately.Result shows: CS Cyclic MUSIC performance in multi signal process is given prominence to.

Fig. 8 estimates hardware structure realization figure based on the angular spectrum of compressed sensing framework, the corresponding broadband receiver passage of each antenna, as can be seen from Figure 8, when sampling instant t, M sensor array element collects signal vector x (t)={ x in t ₁(t), x ₂(t) ..., x _m(t) }, a compression sampling matrix based on CS act on this array element, like this after channel to channel adapter, M × 1 dimensional signal vector x (t) has originally been compressed on signal vector y (t) of L × 1 dimension, m compressed signal vector y _mt () is by original N number of array element x ₁(t), x ₂(t) ..., x _mt () gets weighting respectively summation obtains, and after baseband signal digital sample, obtains discrete sampling version y _m.

Meanwhile, when number of probes is less than or equal to incoming signal number, it also can accurately estimate by the DOA algorithm for estimating of cyclo-stationary signal.On the basis of first step signal compression, the DOA carrying out Cyclic MUSIC algorithm estimates, can reduce the step of Subspace Decomposition in a large number, thus reduces the complexity estimated.

In compressive sensing theory, sampling and the compression of signal are carried out with low rate simultaneously, make the sampling of sensor and assess the cost greatly to reduce, and signaling protein14-3-3 process is a process optimizing calculating. therefore, this theory indicates the effective way of simulating signal Direct Sampling boil down to digital form, has direct information sampling nature.Because any signal all has compressibility theoretically, as long as its corresponding rarefaction representation space can be found, just effectively can carry out compression sampling, this theory will bring once new revolution to signal sampling method. first pass through observing matrix, Received signal strength is compressed to lower dimension, for next step DOA estimates ready.

Compressive sensing theory combines both can retain in MUSIC algorithm with the DOA algorithm for estimating of cyclo-stationary signal and also can reduce computation complexity to the accurate location of signal arrival bearing by the present invention, and can not have an impact to the performance of signal, be with a wide range of applications.

In sum, these are only preferred embodiment of the present invention, be not intended to limit protection scope of the present invention.Within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (1)

1. combine the radiation source DF and location method of compressed sensing and signal cycle smooth performance, it is characterized in that, the method comprises the steps:

S1, with zero-mean nonstationary random process x (t) for incoming signal, obtain x (t) cycle frequency α, α=m/T ₀, m is an integer, T ₀for the cycle of the autocorrelation function of x (t);

S2, employing sensor array carry out observation to described incoming signal and obtain observation signal x ∈ R ^{m × N}, wherein M is the array number of described sensor array, and N is the sampling number for observation signal;

Then use Gauss's observing matrix φ by described observation signal x ∈ R ^{m × N}the low dimensional vector of boil down to, obtains the observation signal y ∈ R after compressing ^{l × N}, L is the array number after compression;

S3, for the observation signal y after compression, calculate the circulation autocorrelation matrix R of incoming signal y according to cycle frequency α ^α _yy, R ^α _yybe the matrix of a L × L, in this matrix, each element is specially:

${R^{\mathrm{\α}}}_{\mathrm{yy}}(m_1,m_2)=\frac{1}{N}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}y(m_1,n)\×y{(m_2,n)}^{*}\×e^{-j2\mathrm{\π\αn}}$

Wherein * is conjugate operation, m ₁and m ₂value between 1 ~ L; N is sampled point numbering; R ^α _yy(m ₁, m ₂) be matrix R ^α _yyin m ₁oK, m ₂the element of row; Y (m ₁, n) be array element m in y ₁the n-th sample point sampled value; Y (m ₂, n) be array element m in y ₂the n-th sample point sampled value;

S4, to the circulation autocorrelation matrix R in Step3 ^α _yycarry out eigendecomposition, R ^α _yy=U _sd _su _s ^h+ U _nd _nu _n ^h, U _sfor signal subspace, D _sfor the diagonal matrix of signal subspace character pair value composition; U _nfor noise subspace, D _nfor the diagonal matrix of noise subspace character pair value composition;

S5, carry out angular spectrum estimation, angular spectrum wherein a (θ) steering vector, d is array element distance, and λ is incoming signal wavelength; θ is incident angle;

In the span of incident angle θ, to make angular spectrum P _mUSICthe corresponding θ value of getting maximal value is the final incident angle estimated.