CN108037481B - Robustness gradable sparse array frequency and DOA estimation method and device - Google Patents

Abstract

The invention discloses a robustness gradable sparse array frequency and DOA estimation method and a device, wherein the method comprises the following steps: acquiring a parameter set of corrected frequency, amplitude and phase according to the relaxed reciprocal element sparse array and the Tsui spectrum corrector; constructing a first remainder array according to the corrected frequency, performing frequency reconstruction by combining a robustness-oriented remainder system, and obtaining a frequency estimation value and a wavelength through average operation on the frequency; constructing a mean vector according to the corrected phase information and amplitude information, obtaining phase estimation of signals on the array elements according to the relation between the phase and the mean vector, and obtaining two phase difference values by making a difference; and constructing a second remainder array according to the two phase difference values, carrying out DOA reconstruction by combining a robustness-oriented remainder system to obtain an intermediate parameter, and calculating a DOA estimation value by combining an estimation formula. The device comprises: relaxed mutual element sparse array, ADC sampler, DSP and display device. The invention utilizes the relaxin sparse array to complete frequency and DOA estimation.

Description

Robustness gradable sparse array frequency and DOA estimation method and device

Technical Field

The invention relates to the technical field of array signal analysis and processing, in particular to a method and a device for estimating sparse array frequency and DOA (direction of arrival) with gradable robustness, which are applied to anti-noise robustness.

Background

The joint estimation of the frequency and the azimuth of arrival (DOA) of the incident signal is radar^[1]Wireless communication system^[2]And electronic warfare, etc., but the difficulty of the estimation gradually increases with the increase of the frequency of the incident signal. For example, the current radar operating frequency band is gradually transited from the S band and the C band to the X band and the K band, and the signal wavelength is gradually shortened from the meter level, the decimeter level and the centimeter level. This leads to two significant problems: first, the space domain nyquist sampling theorem requires that the antenna array element spacing is not less than half the signal wavelength, so for the short wavelength case, the array elements have to be densely arranged, which results inThe very serious coupling effect between array elements is inevitably caused; second, the time domain nyquist sampling theorem requires that the sampling rate is not lower than twice the highest frequency of the signal, so that the conventional analog-to-digital converter (ADC) cannot meet the requirements in both sampling rate and power consumption with the increase of the operating frequency band.

A frequency and DOA joint estimation scheme based on time and space undersampling is a fundamental approach to solve the above problem. This scheme mainly considers two basic issues: the method comprises the following steps of sparse array element arrangement and configuration and design of frequency and DOA parameter reconstruction algorithm.

In terms of sparse array element arrangement and configuration, minimum cooperative array has appeared earlier^[3]Array of minimum voids^[4]Although these sparse arrays can reduce the coupling effect between array elements, the array structure has no closed derivation form and is difficult to obtain engineering application. In recent years, Vaidyanathan proposed sparse nested arrays^[5]A pixel array^[6]And their improved versions, these arrays do not guarantee that all array elements are sparsely distributed, which means that inter-array element coupling cannot be completely eliminated.

In terms of the design of frequency and DOA parameter reconstruction algorithms, literature^[7]An angle and frequency joint estimator is proposed that employs multi-resolution ESPRIT. Wherein, two array element distances of a long base line and a short base line are considered. Where the long baseline represents a half wavelength, which means that the spatial undersampling condition cannot be met. Therefore, such an estimator can only be used to detect low frequency electromagnetic waves. Another example is a frequency-space-frequency algorithm based on a tree structure of a spatial decomposition of matrix features^[8]The algorithm is only applicable to dense uniform linear arrays. Document [9 ]]-[10]Only DOA estimation is involved and no frequency estimation can be performed.

Literature^[11]A mutual element array is selected as a sparse array, and Chinese Remainder Theorem (CRT) is introduced into frequency and DOA joint estimation under space-time under-sampling for the first time, but the algorithm needs to perform multiple times of under-sampling on a single array element, consumes more snapshot data, and needs to perform multiple times of search for reconstruction, so that data processing is performedThe dressing efficiency is not high; to increase the efficiency of the treatment, the literature^[12]The frequency and arrival angle joint estimation algorithm under single-time space-time domain parallel undersampling is provided, the algorithm replaces a classical mutualin array with a relaxed mutualin array, replaces multiple undersampling with single undersampling, and uses a closed robust Chinese remainder theorem^[13]The Chinese remainder theorem based on search is replaced, so that higher data processing efficiency is obtained, and the parameter estimation precision is improved. The noise robustness of these estimators is not high enough.

The noise robustness can be improved starting from two basic problems that improve the estimator. In improving the 1 st basic problem (i.e. sparse array element arrangement and configuration), it can be realized by increasing the number of array elements and the number of snapshots collected per array element, however, this means increasing the burden of consuming system cost, and is often not allowed by engineering application. Thus, improving the 2 nd basic problem (i.e., improving the reconstruction algorithm) is a viable approach to improving noise robustness.

Reference to the literature

[1]L.Xu,J.Li,and P.Stoica,Target detection and parameter estimation for MIMO radar systems[J].IEEE Transactions on Aerospace and Electronic Systems,2008,44(3):927–939.

[2]Y.Li,N.SESHADRI,S.ARIYAVISITAKUL,Channel estimation for OFDM systems with transmitter diversity in mobile wireless channels[J].IEEE Journal on Selected areas in communications,1999,17(3):461–471.

[3]TAYLOR H,GOLOMB S W.Rulers part I[J].Univ.Southern Calif.,Los Angeles,CSI Tech.Rep,1985(85-05):01.

[4]MOFFET A.Minimum-redundancy linear arrays[J].IEEE Transactions on antennas and propagation,1968,16(2):172-175.

[5]PAL P,VAIDYANATHAN P P.Nested arrays:A novel approach to array processing with enhanced degrees of freedom[J].IEEE Transactions on Signal Processing,2010,58(8):4167-4181.

[6]VAIDYANATHAN P P,PAL P.Sparse sensing with co-pprime samplers and arrays[J].IEEE Transactions on Signal Processing,2011,59(2):573-86.

[7]LEMMA A N,VAN DER VEEN A-J,DEPRETTERE E F.Analysis of joint angle-frequency estimation using ESPRIT[J].IEEE Transactions on Signal Processing,2003,51(5):1264-83.[8]LIN J-D,FANG W-H,WANG Y-Y,et al.FSF MUSIC for joint DOA and frequency estimation and its performance analysis[J].IEEE Transactions on Signal Processing,2006,54(12):4529-42.

[9]C.Liu,P.Vaidyanathan,Remarks on the spatial smoothing step in coarray music[J].IEEE Signal Processing Letters,2015,22(9):1438-1442.

[10]P.Vaidyanathan,P.Pal,Sparse sensing with co-prime samplers and arrays[J].IEEE Transactions on Signal Processing,2011,59(2):573-586.

[11]H Liang,H Zhang.New method for joint estimation of multi-target frequency and azimuth under space-time under-sampling[J].Journal of Northwestern Polytechnical University,2012,30(5):694-698.

[12]X Huang,M Liu,L Yang,K Liu,T Liu.Joint estimation of frequency and direction of arrival under the single-and-parallel spatial-temporal undersampling condition[J].Acta Physica Sinica,2017,66(18):188401.

[13]W.Wang,X.-G.Xia,A closed-form robust chinese remainder theorem and its performance analysis[J].IEEE transactions on Signal Processing,2010,58(11):5655–5666.

Disclosure of Invention

The invention provides a method and a device for estimating frequency and DOA of a sparse array with gradable robustness, which finish frequency and DOA estimation by utilizing a relaxed mutual element sparse array under the condition that a space domain and a time domain are highly undersampled, and are described in detail as follows:

a robustness scalable sparse array frequency and DOA estimation method, the estimation method comprising the steps of:

acquiring a parameter set of corrected frequency, amplitude and phase according to the relaxed reciprocal element sparse array and the Tsui spectrum corrector;

constructing a first remainder array according to the corrected frequency, performing frequency reconstruction by combining a robustness-oriented remainder system, and obtaining a frequency estimation value and a wavelength through average operation on the frequency;

constructing a mean vector according to the corrected phase information and amplitude information, obtaining phase estimation of signals on the array elements according to the relation between the phase and the mean vector, and obtaining two phase difference values by making a difference;

and constructing a second remainder array according to the two phase difference values, carrying out DOA reconstruction by combining a robustness-oriented remainder system to obtain an intermediate parameter, and calculating a DOA estimation value by combining an estimation formula.

The acquiring of the corrected parameter group of frequency, amplitude and phase according to the relaxed reciprocal element sparse array and the Tsui spectrum corrector specifically comprises:

doing M to signal samples of relaxed mutualin sparse array_fAnd point DFT, using a Tsui spectrum corrector to perform frequency and phase correction on the DFT result to obtain the parameter group of the corrected frequency, amplitude and phase.

The method comprises the steps of constructing a first remainder array according to corrected frequencies, performing frequency reconstruction by combining a robustness-oriented remainder system, and obtaining a frequency estimation value and a wavelength through average operation of frequencies, wherein the frequency estimation value and the wavelength specifically comprise the following steps:

and constructing a first remainder array according to the corrected frequency, substituting the first remainder array and the corresponding modulus value into a robustness-oriented remainder system for frequency reconstruction, and averaging 3 frequencies by using the frequency estimation value to obtain a frequency estimation value and a wavelength of the incident signal.

The relaxed mutilin sparse array comprises:

3 sparse array of array elements, each array element is provided with two ADC samplers, and from a certain specific moment, the two ADCs of each array element are respectively sampled by f_s1,f_s2The incident signal is parallel undersampled at two sampling rates, and the fast beat number acquired by each array element is M_f。

The method further comprises the following steps:

robustness ranking of frequency estimation and robustness ranking of DOA estimation.

Further, the robustness ranking setting of the frequency estimation specifically includes:

fast array element beat number M_fPrime number pair { eta₁,η₂Y value of substituting TRRNS₁,Υ₂H, the parameters and given frequency robustness grading parameters j are used_fSubstituting into TRRNS model to determine corresponding residue error tolerance tau_jSum frequency reconstruction ceiling

Further, the robustness ranking setting of the DOA estimation specifically includes:

by M_θAnd prime number pair { gamma₁,Γ₂Y value of substituting TRRNS₁,Υ₂H, these parameters are then ranked with the given DOA robustness j_DSubstituting the TRRNS model to determine the corresponding residue error tolerance tau_jSum N value reconstruction ceiling

A robustness scalable sparse array frequency and DOA estimation apparatus, the apparatus comprising: loose mutual element sparse array, ADC sampler, DSP, display device,

when the signal is incident on the relaxed reciprocal element sparse array, two ADC samplers on each array element are respectively expressed by f_s1，f_s2Performing parallel undersampling on the data, and inputting the obtained data into a DSP device;

and finally, obtaining the frequency of the incident signal and the DOA estimated value, and displaying the result on a display device.

The noise-resistant robustness gradable sparse array frequency and DOA estimation method and device provided by the invention have the following functional advantages if applied to the field of practical engineering:

1) hardware cost reduction

The loose inter-element sparse array provided by the invention can realize the frequency and DOA estimation of high anti-noise performance only by 3 array elements without the need of dense arrangement (the array element interval is half wavelength) of the traditional uniform linear array;

in addition, the invention removes the limitation of Nyquist sampling law through the undersampling process, and can work even in a higher frequency band, thereby further reducing the hardware requirement.

2) Improving data utilization

The invention can complete the work by utilizing two ADC samplers respectively configured on 3 array elements to carry out single parallel undersampling, and greatly improves the data utilization rate compared with a multi-time and long-time sampling method.

3) Improving noise immunity robustness and optimizing array element spacing

By adopting the reconstruction algorithm for the robust remainder system, which is provided by the invention, and combining with the frequency spectrum correction, the hierarchical adjustment of robustness is realized, the anti-noise performance of the robust remainder system is improved to a great extent, and the array element spacing is adjusted corresponding to different robustness levels, so that the array sparsity is ensured, and the space is fully utilized.

Drawings

FIG. 1 is a block diagram of a relaxed mutualin sparse array;

FIG. 2 is a flow diagram of noise immunity robustness scalable mutual prime array frequency and DOA estimation;

FIG. 3 is a schematic diagram showing the relationship between the frequency detection success probability and the SNR;

FIG. 4 is a diagram illustrating the relationship between the angle of arrival (DOA) detection success probability and SNR;

FIG. 5 is a diagram comparing DOA estimated RMSE for different estimators;

fig. 6 is a schematic structural diagram of a robustness scalable sparse array frequency and DOA estimation apparatus.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention are described in further detail below.

In order to solve the problems in the background art, the embodiments of the present invention provide a robustness-oriented remainder system (TRRNS), in which a basic reconstruction can be implemented by only providing a pair of modulus values and a pair of remainders (i.e., the number L of reconstruction channels is 2), and different levels of reconstruction robustness can be "customized" according to needs from the pair of modulus values. The reconstruction system gives the following elicitations: on the premise of not increasing hardware complexity and system cost, the frequency and DOA estimation under space-time undersampling with higher robustness and more flexibility can be realized by simply modifying the configuration of the array element spacing and the sampling rate according to the requirement of the robustness-oriented remainder system on the gradable robustness and combining the remainder system reconstruction algorithm oriented to the robustness.

In addition, the embodiment of the invention is also based on a novel relaxed reciprocal element sparse array, realizes the frequency and DOA joint estimation with gradable anti-noise robustness by means of space-time domain undersampling and combining the spectrum correction and the TRRNS reconstruction algorithm provided by the embodiment of the invention, saves the hardware cost and greatly improves the anti-noise robustness of the device.

The embodiment of the invention relates to a method for measuring target frequency and DOA (direction of arrival) by injecting a single source signal into a novel relaxed mutual prime sparse array, performing undersampling processing on the array, and performing frequency spectrum correction and robust-oriented remainder system algorithm reconstruction.

Example 1

A robust scalable sparse array frequency and DOA estimation method, see fig. 1 and 2, comprising the steps of:

101: setting a relaxed mutualin sparse array;

referring to fig. 1, the relaxed mutilin sparse array includes: 3 sparse array of array elements, each array element is provided with two ADC samplers, and from a certain specific moment, the two ADCs of each array element are respectively sampled by f_s1,f_s2The incident signal is parallel undersampled at two sampling rates, and the fast beat number acquired by each array element is M_f。

102: making M of signal samples on 3 array elements_fPoint DFT, using Tsui frequency spectrum corrector to correct frequency and phase of DFT result, obtaining parameter group of corrected frequency, amplitude and phase;

wherein the corrected frequency, amplitude and phase parametersFor combined use

And l is 1,2,3.

The Tsui spectrum corrector is well known to those skilled in the art, and the embodiments of the present invention will not be described in detail.

103: constructing a first remainder array according to the corrected frequency, substituting the first remainder array and the corresponding modulus value into a robustness-oriented remainder system for frequency reconstruction, obtaining a frequency estimation value of each array element, averaging the frequency estimation values to 3 frequencies, and finally obtaining a frequency estimation value of the incident signal

And the incident signal wavelength;

wherein the corrected frequency is used

Indicating that the first remainder array is

For frequency estimation

Indicating, wavelength of incident signal

Further, the details of the robust residue number oriented system are shown in embodiment 2, and are not described herein.

104: constructing a mean vector according to the phase information and the amplitude information obtained in the step 102, obtaining phase estimation of a signal on the ith array element according to the relation between the phase and the mean vector, and obtaining two phase difference values by making a difference;

wherein the mean vector is used

Expressed, the relationship of the phase and mean vectors is

105: constructing a second remainder array according to the two phase difference values, substituting the second remainder array and the corresponding modulus value into a robustness oriented remainder system for DOA reconstruction to obtain an intermediate parameter, and calculating a DOA estimation value according to an estimation formula

Wherein the second remainder array is used

Representing intermediate parameters by

Expressed by the estimation formula of

Is an intermediate quantity (see formula (29)),

in order to be the wavelength of the incident signal,

an intermediate amount (see formula (14)).

In summary, in the embodiment of the present invention, through the above steps 101 to 105, frequency and DOA estimation are completed by using the relaxed reciprocal element sparse array under the condition that both the spatial domain and the time domain are highly undersampled, and work can be completed by performing single parallel undersampling by using two ADC samplers respectively configured on 3 array elements, which greatly improves the data utilization ratio compared with the multiple and long-time sampling method.

Example 2

The robust remainder system (TRRNS) -oriented reconstruction process in steps 103 and 105 in embodiment 1 is described in detail below with reference to specific calculation formulas, and is described in detail below:

setting system parameters: m₁＝mΥ₁,M₂＝mΥ₂,M₂＞M₁And m is a common divisor. The system model is

Initialization: the total number of robust rankings J is determined.

Let sigma_-1＝Υ₂,σ₀＝Υ₁. Let i equal to 1, add 1 to i step by step, and calculate sigma recurrently_i＝σ_i-2modσ_i-1Until sigma is satisfied_iUntil 1, assign J to i and record σ₁,...,σ_J。

Inputting: 2 remainder

A robustness ranking parameter j.

And (3) outputting: reconstructed integer

Step 1) calculation

When J is equal to 1, the compound is,

when J is greater than or equal to 2, if J is 1, there are

If J is more than or equal to 1 and less than or equal to J-1,

the equation (1) is calculated.

Accordingly, the number of the first and second electrodes,

the equation (2) is calculated.

Wherein

Indicating a rounding down.

Step 2) utilization of

The following two sets were constructed:

step 3) determining a folding integer

First calculate

To q is₂₁The following discussion is expanded:

(i) if q is₂₁≥σ _j2 in the set S₂If the element x satisfying the following conditions can be found

Then order s₂X. Otherwise let s₂Is a set S₂Is neutral to q₂₁The nearest element, i.e.

And further determined according to the following two formulas

Wherein the content of the first and second substances,

is upsilon₂Mold removing upsilon₁Is inverse of the mode, i.e.

And [. X]"means a rounding operation.

(ii) If q is₂₁＜σ _j2 in the set S₁If the element y can be found, if the element y satisfies the following conditions

Then order s₁If not, let s₁Is a set S₁Neutralization of-q₂₁The nearest element, i.e.

And further determined according to the following two formulas

Wherein the content of the first and second substances,

is upsilon₁Mold removing upsilon₂Is inverse of the mode, i.e.

(iii) If it is

Then order

Step 4) according to the folding integer

Calculating a final reconstruction result

Note: given a robust scaling parameter j, its reconstructed value

The reconstruction upper limit is:

in summary, the embodiments of the present invention, through the above steps, achieve frequency and DOA estimation by using the relaxed reciprocal element sparse array under the condition that both the spatial domain and the time domain are highly under-sampled, and perform single parallel under-sampling by using two ADC samplers respectively configured on 3 array elements, which can complete the work.

Example 3

The schemes in examples 1 and 2 are further described below with reference to specific examples and calculation formulas, which are described in detail below:

301: designing a relaxed mutilin sparse array;

wherein, the relaxed mutual element sparse array is as shown in FIG. 1, and the frequency f of the incident signal is₀Maximum value of f_maxThe unit wavelength is λ ═ c/f_max(c represents the speed of light). The relaxed reciprocal element sparse array in fig. 1 only includes L-3 array elements with an array element spacing d_lThe settings were as follows:

wherein the content of the first and second substances,

the expression of (a) is:

Γ in formulae (13) and (14)₁,...,Γ_l-1Are each a prime number, M_θIs a positive integer, beta is epsilon (0, 1)]。

The main advantages of the configuration of fig. 1 are: the number of the array elements is only 3, so that the hardware cost is reduced to the maximum extent; further, d is affected by the multiplication of the equation (13) as L is larger_lTends to increase (i.e., the array sparsity decreases). Therefore, the embodiment of the invention selects smaller L and increases the parameter beta, thereby further optimizing the array element spacing.

Setting beta, gamma appropriately₁,Γ₂The value can be such that d₁,d₂> λ/2, the sparsity of the relaxed reciprocal element sparse array of FIG. 1 is ensured to be high, and the situation of local dense distribution of array elements can be completely avoided.

In addition, each array element in FIG. 1 is equipped with two ADC samplers, the sampling rate f of which_s1,f_s2Is configured as follows

f_s1＝M_fη₁,f_s2＝M_fη₂ (15)

Wherein eta is₁,η₂Is a relatively prime integer, M_fIs a fast beat number (positive integer). These parameters are set appropriately so that f_s1,f_s2＜＜f₀Therefore, the snapshot data with the highly undersampled time domain is acquired by any array element.

In addition, the design adopts a TRRNS reconstruction algorithm for parameter estimation, the number of reconstruction channels is required to be 2, and when frequency estimation is carried out, each array element in the figure 1 is provided with 2 ADCs, so that the TRRNS reconstruction algorithm is exactly corresponding to the TRRNS algorithm; in the DOA estimation, the remainder required by the algorithm is taken from the phase difference between adjacent array elements, so that 3 array elements in fig. 1 generate two phase difference remainders, which also exactly correspond to the TRRNS algorithm.

302: reconstructing a frequency estimation model and TRRNS;

considering the factors of noise and phase shift, the received signal on the l-th array element is not expressed as:

wherein the content of the first and second substances,

indicating the phase, ξ, of the signal arriving at the array element_l(t) denotes zero-mean white Gaussian noise, A₀Representing the signal amplitude. Let t be n/f_s1，t＝n/f_s2Substitution of formula (16) to obtain two lengths M_fThe sequence of (a):

therein, ζ₁(n)、ζ₂(n) are zero-mean white gaussian noise on the two ADC samplers, respectively.

F in equation (17) due to undersampling₀/f_s1And f₀/f_s2Are necessarily greater than 1, so that there is:

wherein the content of the first and second substances,

is a normalized remainder; n is₁,n₂Are respectively folding integers;

is a positive integer.

For convenience of presentation, let:

wherein the content of the first and second substances,

is a modulus value, eta is a relatively prime integer,

is the remainder, that is,

is the normalized remainder.

Substituting formulae (15) and (19) for formula (18), there are:

formula (20) is completely in accordance withA robust residue number system (TRRNS) oriented model, in which,

the values of the modulus are used as the modulus values,

is a remainder, n₁,n₂Is the folded integer to be estimated.

For the snapshot sequence x acquired at the l-th array element (l ═ 1,2,3)_l,1(n),x_l,2(n) obtaining a frequency estimate of the array element by

And phase estimation

And final incident signal frequency estimation

By means of spectral correctors (e.g. Tusi correctors, the correction procedure of which is described in the literature [11 ]]) Two normalized frequency estimates of equation (20) may be calculated

Further adjusting the modulus

Remainder

And the later mentioned robustness ranking parameter j_fSubstituting TRRNS reconstruction Process, the folding integer n can be determined₁,n₂And thus the frequency on the array element is estimated as:

the Tusi corrector may also provide phase and amplitude correction results

And

further, the following averaging operation is performed to construct a combined vector

The phase angle is taken to obtain the phase estimation value of the first array element

Here, ang represents the angle calculation.

Estimated for each array element

The final frequency estimate of the incident signal is obtained by averaging:

accordingly, the wavelength of the incident signal is estimated as

(c is the speed of light).

303: angle of arrival (DOA) estimation model and TRRNS reconstruction;

assuming a far-field narrow-band signal s₀(t) at an angle θ₀Incident on the sparse array antenna shown in fig. 1, the theoretical phase difference between the ith array element and the (l + 1) th array element can be expressed as:

due to the array element spacing d₁,d₂> λ/2, therefore

It must contain 2 pi whole-cycle ambiguities, i.e.:

n_lrepresents an unknown integer number of bits that is,

observed phase calculated from equation (22)

The estimated value is obtained, so that after the difference value is subjected to modulo division by 2 pi, the expected value of (0,2 pi) of the formula (25) can be obtained]Phase difference within range

Namely:

combining the formulas (24), (25) and (26) in order, comprising:

in the case where formula (13) is substituted for formula (27), there are:

in order to ensure that the water-soluble organic acid,

simultaneous (28), (29) to obtain:

substituting the modulus value and the remainder into a TRRNS model to obtain a reconstructed value

Further, the obtained wavelength estimation value is substituted into an equation (29), and the arrival azimuth angle estimation can be obtained:

304: a joint estimator overall flow path;

the flow of noise-resistant robust scalable relatively prime array frequency and DOA estimation proposed by the embodiment of the present invention is shown in fig. 2. As can be seen from FIG. 2, only 3 undersampled sequence pairs { x ] of sparse array elements are needed_l,1(n),x_l,2(n), l ═ 1,2,3} is fed into estimator, and after being processed by frequency and phase estimator based on TRRNS reconstruction and spectrum correction, the frequency estimation value output by the estimator

Simple averaging to input/output frequency estimation of a transmitted signal

Phase estimation value output thereto

Difference, 2 pi modular division and corresponding factor phaseAfter multiplication and TRRNS reconstruction and inverse trigonometric operation processing, the estimated value of the arrival azimuth angle can be output

It should be noted that the present invention uses TRRNS algorithm for frequency and DOA reconstruction, and fig. 2 is composed of 3 input parameters (j)_f,j_DAnd β) for noise immunity robustness adjustment. Wherein the robust scaling parameter j_fAnd a relatively prime integer pair { η₁,η₂Cooperate for adjusting the frequency estimation

Noise immunity robustness of; robust scaling parameter j_DAnd a prime integer pair { Γ₁,Γ₂The coordination is used for adjusting the noise immunity robustness of DOA estimation; in addition, as mentioned above, considering that estimator robustness is inversely proportional to array sparsity, a parameter β is set for making a trade-off between the two. The mechanism of adjustment of the above parameters is given below.

305: noise immunity robustness adjustment mechanism.

1) Robustness ranking for TRRNS reconstruction

Note that the frequency reconstruction model of equation (20) and the DOA reconstruction model of equation (30) may be written collectively as follows:

wherein M is₁＝mΥ₁,M₂＝mΥ₂(Υ₁,Υ₂A pair of relatively prime integers). TRRNS reconstitution is characterized by: allowing trade-off of two remainders r by lowering the reconstruction ceiling of N₁,r₂In particular, given a robustness ranking parameter j, the actual remainder is allowed

Satisfies the following conditions:

let two element number satisfy upsilon₂＞Υ₁Residual error tolerance τ for TRRNS reconstruction_jThe values of (A) are:

wherein σ_jThe value can be calculated recursively (let σ be)_-1＝Υ₂,σ₀＝Υ₁)：

σ_j＝σ_j-2modσ_j-1,j＝1,2,... (36)

The presence of J satisfies: sigma₁＞…＞σ_J＝1 (37)

Therefore, the classification parameter J satisfies that J is more than or equal to 1 and less than or equal to J.

2) Setting robustness of frequency estimation in a grading mode;

fast array element beat M of formula (15)_fPrime number pair { eta₁,η₂Y value of substituting TRRNS₁,Υ₂H, the parameters and given frequency robustness grading parameters j are used_fSubstituting into TRRNS model to determine the residue error tolerance tau_jSum frequency reconstruction ceiling

3) The robustness of the DOA estimation is set hierarchically.

By M of formula (29)_θAnd prime number pair { gamma₁,Γ₂Y value of substituting TRRNS₁,Υ₂H, these parameters are then ranked with the given DOA robustness j_DSubstituting into TRRNS model to determine the residue error tolerance tau_jSum N value reconstruction ceiling

Unlike frequency estimation, DOA estimation is not a TRRNS reconstruction value N valueInstead, the value of N is taken into account in the computational arcsine result as shown in equation (32). Considering that in engineering applications it is desirable that the arcsine range can reach its upper limit of pi/2, this is correspondingly required in equation (32)

The upper value limit is close to 1. As mentioned previously, when the robustness against noise of TRRNS reconstruction is improved (corresponding to the robust ranking parameter j)_DReduced), N value reconstruction ceiling

Will be reduced to maintenance

The value is close to 1, and the objective requirement is reduced

The value of beta should be reduced as can be inferred from the combination of equation (14).

Consider β ∈ (0, 1)]Therefore, β ═ 1 corresponds to the worst robustness case (i.e., the case of the robustness ranking parameter J ═ J), and at this time, the TRRNS reconstruction upper limit is the CRT upper limit (two modulus values M)_θΓ₁,M_θΓ₂Least common multiple of) so that there is:

accordingly, when the robustness ranking parameter takes j_DWhen the integer is less than J, beta should be taken to be equal to the reconstruction upper limit thereof

The directly proportional values, namely:

in summary, in the embodiment of the present invention, through the above steps 301 to 305, the frequency and DOA estimation is completed by using the relaxed reciprocal element sparse array under the condition that both the spatial domain and the time domain are highly under-sampled, and the work can be completed by performing single parallel under-sampling by using two ADC samplers respectively configured on 3 array elements, which greatly improves the data utilization ratio compared with the multiple and long-time sampling method.

Example 4

The noise-resistant robustness gradable sparse array frequency and DOA estimation device provided by the embodiment of the invention corresponds to the methods in the embodiments 1 to 3, and is described in detail as follows:

referring to fig. 3, the estimation apparatus includes: the system comprises a loose mutual element sparse array, an ADC sampler, a DSP and an output display device.

The measurement process is as follows: when the signal is incident on the relaxed reciprocal element sparse array, two ADC samplers on each array element are respectively expressed by f_s1，f_s2And performing parallel undersampling on the received signals, inputting the obtained data into a DSP device, processing the data according to the algorithm provided by the invention to finally obtain the frequency and DOA estimated value of the incident signals, and displaying the result on a display device.

In the embodiment of the invention, the DSP internal storage system stores the core algorithm of the invention, which determines the robustness, accuracy and stability of the whole measuring system. The following functions are assumed in the whole measurement process:

1. operating a core algorithm, performing frequency spectrum correction on a signal sequence obtained by sampling of each array element ADC, and calling a robustness-oriented remainder system algorithm, thereby realizing detection of frequency and DOA;

2. the measurement results are input to the driving and display module.

In the embodiment of the present invention, except for the specific description of the model of each device, the model of other devices is not limited, as long as the device can perform the above functions.

In summary, the embodiments of the present invention implement, through the above devices, that frequency and DOA estimation are completed by using a relaxed reciprocal element sparse array under the condition that both the spatial domain and the time domain are highly undersampled, and work can be completed by performing single parallel undersampling by using two ADC samplers respectively configured on 3 array elements, which greatly improves data utilization ratio compared with the multiple and long-time sampling method.

Example 4

The methods of examples 1 to 3 and the apparatus of example 4 were validated in the following in combination with specific experimental data, fig. 4-5, as described in detail below:

one, frequency estimation performance comparison of different noise immunity robustness levels

1) The time domain undersampling parameters in the array are set as follows:

make snapshot number M that every array element ADC gathered_f1024, prime number pair { η₁,η₂{7101,7106} (corresponding to a sampling rate { f }_s1,f_s2J {7.271424,7.276544} MHz, M_f，{η₁,η₂Y and y substituting TRRNS₁,Υ₂According to the equations (36) and (37), a total hierarchical robustness number J ═ 2 can be calculated. Let frequency robustness rank parameter j _f1 and j _f2, the corresponding upper limit of the frequency reconstruction can be calculated from (12) as

So as not to make f_max10GHz, the unit wavelength λ of the array of fig. 1 is c/f_max＝3cm。

2) The signal parameters of equation (16) are set as:

f₀8GHz (corresponding wavelength λ)₀＝3.75cm)，A₀＝2，

In addition, the signal-to-noise ratio test interval is set to be SNR E [ -25,5 [ -S [ ]]dB, carrying out 2000 Monte Carlo tests on each SNR condition, respectively carrying out frequency estimation by using a robustness non-grading algorithm based on a closed CRT and the method, and if the measurement error of a certain test satisfies

The detection is deemed to be successful, otherwise the detection is deemed to be failed. Fig. 4 shows the detection success rate curves of two frequency estimators.

As shown in fig. 4, for the test curve ('o' mark) of the CRT-based robust non-scalable algorithm, the SNR threshold of-6 dB, which is the signal-to-noise ratio with a frequency detection success rate of 100%; for the method, the robustness grading parameter j_fThe test curve ('mark') corresponding to 2 substantially coincides with the curve for the CRT reconstruction case (as mentioned above, the upper limit of the CRT reconstruction is the special case j_fDue to TRRNS reconstruction ceiling at J), and a robust ranking parameter J)_fThe signal-to-noise ratio threshold for the test curve (' # mark) corresponding to 1 is then-15 dB for SNR compared to j_fThe noise immunity robustness is greatly improved because of the reduction of about 9dB in the case of 2.

Two, DOA estimation performance comparison of different noise-resistant robust levels

Let the incident wave reach angle theta₀On the basis of the time domain undersampling parameter setting, the spatial domain undersampling parameter of the formula (13) is set as follows: m _θ2, a prime integer pair { Γ₁,Γ₂J {13,22}, and M is equal to_θ、{Γ₁,Γ₂Y and y replacing TRRNS₁,Υ₂According to the equations (36) and (37), a total hierarchical robustness number J ═ 3 can be calculated.

Let the robust ranking parameter j_DThe TRRNS reconstruction upper limit can be obtained as 1,2,3

The beta values are calculated to be 0.10,0.23,1 respectively by the combination formula (39), and the array element pitch { d) is calculated by the formula (13)₁,d₂Are respectively

Still at SNR ∈ [ -25,5]Performing Monte Carlo test in dB test interval, if DOA measurement error of a certain test is satisfied

The detection is deemed to be successful, otherwise the detection is deemed to be failed. FIG. 5 shows a CRT based robustness non-scalable DOA estimator and a DOA in an embodiment of the invention, respectivelyDetection success rate curve of estimator.

As shown in fig. 5, for the test curve ('mark') of the CRT-based robust non-scalable algorithm, the SNR threshold of 0dB is the signal-to-noise ratio for which the DOA detection success rate reaches 100%; for the method, the robust grading parameter j_DThe test curve ('□' label) for 3 coincides with the curve for the CRT reconstruction case, the robust scaling parameter j _D2 and j_DThe threshold signal-to-noise ratio of the test curve (marked with ' ∘ ', ') corresponding to 1 is-9 dB SNR and-10 dB SNR, respectively, i.e. the noise robustness is improved by 9dB and 10dB, respectively, compared to the case where the CRT is not scalable.

Root mean square error performance comparison of three or more DOA estimators

To further reveal the anti-noise robustness of the estimator, the Root Mean Square Error (RMSE) of the present fractal DOA estimator is compared to that of a closed CRT based DOA estimator (following the above-mentioned null and time domain undersampling parameter settings). In addition, unlike the two estimators based on sparse reciprocal element arrays, for reference, the two estimators are compared with the conventional estimator based on a λ/2-pitch Uniform Linear Array (ULA) (the DOA estimation is obtained by using the classical MUSIC decomposition method), the number of array elements of the three estimators is equal to L, which is equal to 3, and the arrival azimuth angle is equal to θ₀45 degrees, and the signal-to-noise ratio test interval is set as SNR E [ -15,30 [ -]dB. The DOA anti-noise robust grading parameter of the method is taken as j_DThe RMSE curves for the different estimators are compared as shown in fig. 6(a), (b), (c), respectively, 1,2,3.

From the RMSE curves of fig. 6, the following conclusions can be drawn.

1) For the estimator of the method ('prime' notation), the noise robust scaling parameter j_DThe SNR thresholds corresponding to 1,2, and 3 are-13 dB, -7dB, and 4dB, respectively, and are lower than the SNR threshold (5dB) in the CRT reconstruction ('Δ'. mark), and therefore, higher robustness is obtained (j `)_DThe smaller the value, the higher the degree of noise immunity robustness improvement).

2) The RMSE curves of the estimators of the embodiments of the invention for the 3 robustness levels are all higher than for the CRT reconstruction case (i.e., the former estimateThe accuracy of the meter is inferior to the latter), and j_DThe smaller the value, the more significant the degree of accuracy degradation. This can be seen as the cost of the improved robustness achieved by the estimator of embodiments of the present invention.

3) Although with j_DThe smaller the value, the less accurate the DOA estimator designed by the embodiment of the present invention will be, but even in the worst case (j) where the accuracy is deteriorated_D1), the RMSE curve is still lower than that based on conventional ULA ('o' mark). And for j_DIn the case of 1, the signal-to-noise threshold is substantially identical to the RMSE curve of the conventional ULA (again, SNR-13 dB).

This means that the DOA estimator proposed by the present invention has high application value: the precision of the array element space-based ultra wideband noise-free linear array is improved compared with that of a traditional ULA estimator with dense array element space, but the noise-resistant robustness is not reduced, and due to the fact that a loose cross element sparse array is adopted, compared with the ULA condition with dense array elements, cross coupling among the array elements is eliminated.

Those skilled in the art will appreciate that the drawings are only schematic illustrations of preferred embodiments, and the above-described embodiments of the present invention are merely provided for description and do not represent the merits of the embodiments.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (5)

1. A sparse array frequency and DOA estimation method is characterized by comprising the following steps of applying the estimation method to noise robustness:

acquiring a parameter set of corrected frequency, amplitude and phase according to the relaxed reciprocal element sparse array and the Tsui spectrum corrector;

constructing a first remainder array according to the corrected frequency, performing frequency reconstruction by combining a robustness-oriented remainder system, and obtaining a frequency estimation value and a wavelength through average operation on the frequency;

constructing a mean vector according to the corrected phase information and amplitude information, obtaining phase estimation of signals on the array elements according to the relation between the phase and the mean vector, and obtaining two phase difference values by making a difference;

constructing a second remainder array according to the two phase difference values, carrying out DOA reconstruction by combining a robustness-oriented remainder system to obtain an intermediate parameter, and calculating a DOA estimation value by combining an estimation formula;

wherein the robust residue number system is modeled as

M₁＝mΥ₁,M₂＝mΥ₂,M₂＞M₁，

m is common divisor, upsilon₁,Υ₂Is a relatively prime integer pair, r₁,r₂Is a remainder, n₁,n₂Are respectively folding integers;

let two element number satisfy upsilon₂＞Υ₁Reconstructed residue error tolerance τ_jThe values of (A) are:

wherein σ_jThe value is calculated recursively as follows, let σ_-1＝Υ₂,σ₀＝Υ₁；

σ_j＝σ_j-2modσ_j-1,j＝1,2,...

There is a robust hierarchical total number J that satisfies: sigma₁＞…＞σ_J＝1

Therefore, the grading parameter J satisfies J is more than or equal to 1 and less than or equal to J;

wherein the method further comprises:

setting robustness of frequency estimation and setting robustness of DOA estimation in a grading way;

the robustness grading setting of the frequency estimation specifically comprises the following steps:

fast beat number M by array element_fPrime number pair { eta₁,η₂Replacement of m value, { upsilon }₁,Υ₂}，η₁,η₂Is a relatively prime integer, f_s1＝M_fη₁,f_s2＝M_fη₂，f_s1,f_s2For the sampling rate, a robust scaling parameter j_fAnd a relatively prime integer pair { η₁,η₂Cooperate for adjusting the frequency estimation

Robustness against noise, will norm

Remainder

And a robustness ranking parameter j_fSubstituting the parameters into a robust residue number system model, and then combining the parameters with a given frequency robustness grading parameter j_fDetermining a corresponding residue error tolerance τ_jAnd the frequency estimation on the array element is:

wherein the content of the first and second substances,

the values of the modulus are used as the modulus values,

is a normalized remainder;

the robustness grading setting of the DOA estimation specifically comprises the following steps:

by positive integers M_θAnd prime number pair { gamma₁,Γ₂Replacement of the m-value, { γ } for the robustness-oriented remainder system₁,Υ₂}，Γ₁,Γ₂Mutually prime, and then rank these parameters with given DOA robustnessParameter j_DSubstituting into a model of a robust residue number system to determine a corresponding residue error tolerance tau_jSum N value reconstruction ceiling

Is an intermediate parameter.

2. The sparse array frequency and DOA estimation method according to claim 1, wherein the obtaining of the set of corrected frequency, amplitude and phase parameters from the relaxed reciprocal sparse array and the Tsui spectrum corrector is specifically:

doing M to signal samples of relaxed mutualin sparse array_fAnd point DFT, using a Tsui spectrum corrector to perform frequency and phase correction on the DFT result to obtain the parameter group of the corrected frequency, amplitude and phase.

3. The sparse array frequency and DOA estimation method according to claim 1, wherein the first remainder array is constructed according to the corrected frequency, frequency reconstruction is performed in combination with a robust-oriented remainder system, and the frequency estimation value and the wavelength are obtained by averaging the frequency:

and constructing a first remainder array according to the corrected frequency, substituting the first remainder array and the corresponding modulus value into a robustness-oriented remainder system for frequency reconstruction, and averaging 3 frequencies by using the frequency estimation value to obtain a frequency estimation value and a wavelength of the incident signal.

4. A sparse array frequency and DOA estimation method as claimed in claim 1 wherein said relaxed mutualin sparse array comprises:

3 sparse array of array elements, each array element is provided with two ADC samplers, and from a certain specific moment, the two ADCs of each array element are respectively sampled by f_s1,f_s2The incident signal is parallel undersampled at two sampling rates, and the fast beat number acquired by each array element is M_f。

5. A sparse array frequency and DOA estimation apparatus, the apparatus comprising: loose mutual element sparse array, ADC sampler, DSP, display device,

when the signal is incident on the relaxed reciprocal element sparse array, two ADC samplers on each array element are respectively expressed by f_s1，f_s2Performing parallel undersampling on the data, and inputting the obtained data into a DSP device;

finally, the frequency and DOA estimated value of the incident signal are obtained, and the result is displayed on a display device;

the DSP is adapted to perform the estimation method of any one of claims 1-4.

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