CN104914408B - Frequency based on Chinese remainder theorem, DOA union measuring methods and device - Google Patents
Frequency based on Chinese remainder theorem, DOA union measuring methods and device Download PDFInfo
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Abstract
The invention discloses a kind of frequency based on Chinese remainder theorem, DOA union measuring methods and device, the Nonuniform Linear Array for including L bay is set, the A/D converter on each bay carries out parallel lack sampling, acquisition L roads sample sequence；N point DFT are to L roads sample sequence, line frequency and phasing are entered to DFT results by estimator, obtain the L after correction respectively to frequency estimation and phase estimation value；The reconstruct of line frequency and phase is entered to frequency estimation and phase estimation value, and enclosed Chinese remainder theorem by L, obtains signal frequency and DOA estimate value.The present invention uses the scheme of multi-path low speed rate lack sampling, realizes the measurement to high-frequency signal；The present invention breaches this limitation and devises flexible thinned array arrangement, rationally sets array parameter by combining Practical Project requirement, DOA parameters can be accurately reconstructed using the method for the present invention.
Description
Technical Field
The invention relates to the field of array signal processing, in particular to a method and a device for performing undersampling on an incident signal in a time domain and a space domain by using an antenna array and obtaining high-precision joint estimation of frequency and direction of arrival by processing snapshot data.
Background
The combined estimation of the carrier frequency and the Direction of Arrival (DOA) of a space incident signal is a research hotspot of array signal processing, and is widely applied in various fields such as sonar, radar, wireless communication systems and the like[1]. The two-dimensional extension version of the traditional spectrum estimation algorithm (such as MUSIC and ESPRIT methods) based on subspace decomposition can realize the aim of parameter joint estimation[2-4]However, these methods are relatively computationally intensive, and their theoretical premise requires that the signal sampling in both space and time domains satisfy the nyquist theorem, which is critical for some engineering applications. For example, the wavelength of a Ka-band radar signal is in millimeter level, and array elements need to be densely arranged to meet the condition that the distance between adjacent array elements of the sampling theorem is not greater than the half wavelength of the signal, which not only brings difficulty to hardware installation, but also easily causes mutual coupling of the signal between the adjacent array elements, thereby reducing the measurement and calculation precision; in addition, for time domain sampling, the nyquist theorem requires that the sampling rate must be greater than twice the highest frequency of the signal, which puts a severe requirement on Analog-to-Digital converter (ADC) and system backend data processing performance, and increases the difficulty of engineering implementation and hardware cost. Therefore, it is important to break through the limitation of the array element spacing and effectively reduce the sampling rate, i.e. to find a joint parameter estimation method suitable for the time-space undersamplingMeaning.
Frequency and DOA joint estimation studies in the undersampled case were first found in literature [5 ]]The authors propose to divide the 2-18GHz airborne radar broadband signal into a plurality of 1GHz sub-bands, and to combine the ESPRIT algorithm to perform comprehensive processing to obtain an estimation result; however, this method requires a mixer and a filter bank for each array element, and the hardware cost is high. In recent years, a co-prime spectrum (co-prime spectrum) theory is also applied to parameter estimation under undersampling, however, the current method based on the co-prime spectrum can only realize single parameter measurement of frequency or DOA, and cannot realize joint estimation[6,7]. By the Chinese Remainder Theorem (CRT)[8]It is known that if a positive integer is not greater than the least common multiple of a set of two relatively prime integers, then the integer can be uniquely determined by its remainder after the modulo operation. By utilizing the reconstruction characteristic of the CRT, the problem of solution blurring caused by undersampling can be solved. Document [9]]A robust CRT algorithm is provided and used for estimating the frequency of a complex exponential signal, and the sampling rate is greatly reduced by a multi-path sampling mode; however, in the reconstruction process of the algorithm, multiple two-dimensional searches need to be performed, and meanwhile, the DFT point number of each path of sample needs to be equal to the sampling rate value, the frequency resolution can only be accurate to 1Hz, and a large amount of calculation is consumed; document [10]]By using Candan frequency estimator[11]And closed CRT algorithm[12]In combination, reference [9]The frequency estimation of the undersampled complex exponential signal is popularized to the frequency estimation of a real cosine signal, and the operation amount is reduced under the condition of less snapshot numbers; however, the estimation accuracy of the algorithm at low signal-to-noise ratio is to be improved; document [13]]The CRT is used for signal azimuth estimation under spatial undersampling and the feasibility of the CRT is demonstrated, which lays a foundation for further research and development in the follow-up process, however, in the document [13]]No specific array arrangement scheme and phase residue extraction method is mentioned. Aiming at the defects of high operation complexity, fixed resolution, low precision under low signal-to-noise ratio, lack of specific arrangement scheme of the array and the like of the existing method, the invention combines the closed CRT[12]And AM spectrum estimator[14]A method for frequency and DOA of signal under time-space undersampling is disclosedA method and apparatus for high precision joint measurement.
Reference to the literature
[1]KRIM H,VIBERG M.Two decades of array signal processing research:the parametric approach[J].Signal Processing Magazine,IEEE,1996,13(4):67-94.
[2]WANG S,CAFFERY JR J,ZHOU X.Analysis of a joint space-time DOA/FOAestimator using MUSIC；proceedings of the Personal,Indoor and Mobile RadioCommunications,200112th IEEE International Symposium on,F,2001[C].IEEE.
[3]LEMMA A N,VAN DER VEEN A-J,DEPRETTERE E F.Analysis of joint angle-frequency estimation using ESPRIT[J].Signal Processing,IEEE Transactions on,2003,51(5):1264-83.
[4]LIN J-D,FANG W-H,WANG Y-Y,et al.FSF MUSIC for joint DOA andfrequency estimation and its performance analysis[J].Signal Processing,IEEETransactions on,2006,54(12):4529-42.
[5]ZOLTOWSKI M D,MATHEWS C P.Real-time frequency and 2-D angleestimation with sub-Nyquist spatio-temporal sampling[J].Signal Processing,IEEE Transactions on,1994,42(10):2781-94.
[6]VAIDYANATHAN P P,PAL P.Sparse sensing with co-pprime samplers andarrays[J].IEEE Transactions on Signal Processing,2011,59(2):573-86.
[7]PAL P,VAIDYANATHAN P P.Coprime sampling and the MUSIC algorithm；proceedings of the Digital Signal Processing Workshop and IEEE SignalProcessing Education Workshop(DSP/SPE),2011IEEE,F,2011[C].IEEE.
[8]ARAZI B.A generalization of the Chinese remainder theorem[J].Pacific Journal ofMathematics,1977,70(2):289-96.
[9]LI X,LIANG H,XIA X-G.A robust Chinese remainder theorem with itsapplications infrequency estimation from undersampled waveforms[J].SignalProcessing,IEEE Transactions on,2009,57(11):4314-22.
[10] Frequency estimation of cosine signal under undersampling based on Chinese remainder theorem [ J ] Physics report 2014,63(19):198403-.
[11]CANDAN C.A method for fine resolution frequency estimation fromthree DFT samples[J].Signal Processing Letters,IEEE,2011,18(6):351-4.
[12]WANG W,XIA X-G.A closed-form robust Chinese remainder theorem andits performance analysis[J].Signal Processing,IEEE Transactions on,2010,58(11):5655-66.
[13] Lianghong, ZUGHEN, Yangsheng, generalized and steady Chinese remainder theorem and application thereof in space under-sampled signal DOA estimation [ J ]. proceedings of northwest university of Industrial science 2010,3):409-14.
[14]ABOUTANIOS E,MULGREW B.Iterative frequency estimation byinterpolation on Fourier coefficients[J].Signal Processing,IEEE Transactionson,2005,53(4):1237-42.
Disclosure of Invention
The invention provides a frequency and DOA combined measurement method and a device based on Chinese remainder theorem, which utilizes an antenna array to perform undersampling on an incident signal in a time domain and a space domain, and realizes high-precision combined estimation of frequency and direction of arrival by processing snapshot data, wherein the detailed description is as follows:
a frequency and DOA combined measurement method based on Chinese remainder theorem comprises the following steps:
setting an inhomogeneous linear array comprising L antenna array elements, and performing parallel undersampling on an A/D converter on each antenna array element to obtain L paths of sample sequences;
performing N-point DFT on the L sample sequences, and performing frequency and phase correction on DFT results through an estimator to respectively obtain L corrected frequency estimation values and L corrected phase estimation values;
and reconstructing the frequency and the phase through L pairs of frequency estimation values and phase estimation values and a closed Chinese remainder theorem to obtain the signal frequency and the estimation values of the angle of arrival.
The step of reconstructing the frequency and the phase through the L pair of the frequency estimation value and the phase estimation value and the closed Chinese remainder theorem to obtain the signal frequency and the wave arrival angle estimation value specifically comprises the following steps:
forming a frequency remainder by the L frequency estimation values, and substituting the frequency remainder into a closed Chinese remainder theorem to reconstruct a signal frequency;
and solving L-1 phase difference estimated values according to the L phase estimated values to form phase remainders, substituting the phase remainders into a closed Chinese remainder theorem to reconstruct, and acquiring the estimated value of the angle of arrival by combining signal frequency.
The step of substituting L frequency estimation values into a frequency remainder, and reconstructing the signal frequency by using the closed chinese remainder theorem specifically includes:
acquiring an intermediate variable from the residue array, and calculating a fuzzy multiple through the intermediate variable;
obtaining an estimated value of the signal frequency through a fuzzy multiple and a remainder group;
the step of substituting the closed Chinese remainder theorem for reconstruction and acquiring the estimated value of the angle of arrival by combining the signal frequency specifically comprises the following steps:
selecting any positive integer, substituting the prime number group, the phase remainder group and the positive integer into a closed Chinese remainder theorem to reconstruct a nonnegative integer;
and obtaining an estimated value of the signal wavelength and a non-negative integer by a frequency estimation process to obtain an estimated value of the angle of arrival.
A frequency and DOA combined measuring device based on Chinese remainder theorem, which comprises:
the antenna array elements form an inhomogeneous linear array;
the A/D sampler is arranged on the antenna array element and used for parallel undersampling to obtain an L-path sample sequence;
and the DSP is used for performing N-point DFT on the L-path sample sequence, performing frequency and phase correction on a DFT result through the estimator, respectively obtaining a corrected L-pair frequency estimation value and a corrected phase estimation value, performing frequency and phase reconstruction by closed Chinese remainder theorem, and obtaining the frequency and the angle of arrival estimation value of the incident signal.
Further, the measuring device further includes:
and the output drive and the display circuit thereof are used for outputting the signal frequency and the estimated value of the angle of arrival.
Wherein the DSP comprises:
and the first processor is used for forming frequency remainders by the L frequency estimation values and substituting the frequency remainders into a closed Chinese remainder theorem to reconstruct the frequency of the incident signal.
Further, the DSP comprises:
and the second processor is used for solving L-1 phase difference estimated values from the L phase estimated values to form phase remainders, substituting the phase remainders into a closed Chinese remainder theorem to reconstruct, and acquiring the estimated value of the angle of arrival by combining signal frequency.
Further, the first processor comprises:
the first acquisition module is used for acquiring an intermediate variable from the residue array and calculating a fuzzy multiple through the intermediate variable; and obtaining an estimated value of the signal frequency through fuzzy multiple and remainder groups.
Further, the second processor comprises:
the second acquisition module is used for selecting any positive integer, and substituting the prime number group, the phase remainder group and the positive integer into a closed Chinese remainder theorem to reconstruct a nonnegative integer; and obtaining an estimated value of the signal wavelength and a non-negative integer by a frequency estimation process to obtain an estimated value of the angle of arrival.
The signal frequency and DOA combined measurement method under the space-time undersampling provided by the invention can produce the following effects if being applied to the field of practical engineering:
1) the estimation of the signal frequency under time domain undersampling is realized:
in the conventional frequency measurement method, if the sampling rate does not satisfy the nyquist theorem, frequency ambiguity is caused, and thus an accurate frequency measurement value cannot be obtained. The invention adopts a multi-path low-rate undersampling scheme to realize the measurement of high-frequency signals, and if the L-path sampling rate is set to be fs1～fsLThen the frequency measurement range of the present invention is [0, fmax]Wherein f ismaxIs equal to fs1～fsLThe least common multiple of;
2) the DOA estimation is realized by utilizing the sparse linear array, and the array can be flexibly arranged;
in the classical unambiguous phase measurement method, the spacing between adjacent array elements is required to be less than half the wavelength of the incident signal. The invention breaks through the limitation and designs a flexible sparse array arrangement scheme, and by reasonably setting array parameters by combining with actual engineering requirements, DOA parameters can be accurately reconstructed by adopting the method of the invention;
3) the algorithm efficiency is high, and the parameter measurement precision is high;
the method in the document [9] needs the limiting conditions of multi-snapshot number and large-point DFT, and the method provided by the invention can obtain the frequency and the parameters required by DOA reconstruction by introducing spectrum correction and only processing a small number of snapshots acquired by an array, so that the sample utilization rate and the algorithm efficiency are high, and the limit of fixed frequency resolution is overcome.
Meanwhile, the AM estimator is adopted to replace a Candan estimator sensitive to frequency deviation in the document [10], so that the parameter estimation precision is improved, and a theoretical expression of frequency variance is deduced.
Drawings
FIG. 1 is a flow chart of joint measurement of frequency and DOA of a signal under spatio-temporal undersampling;
FIG. 2 is a schematic diagram of a sparse array arrangement of antennas;
FIG. 3 is a graph of frequency detection probability versus SNR;
FIG. 4 is a graph illustrating the DOA detection probability versus SNR curve;
FIG. 5 is a diagram of a mean square error relationship curve for frequency measurements;
FIG. 6 is a graph showing the mean square error relationship for DOA measurements;
FIG. 7 is a diagram of the hardware configuration of the present invention;
fig. 8 is a flowchart of the DSP internal program.
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.
Example 1
A frequency and DOA joint measurement method based on chinese remainder theorem, referring to fig. 1, the measurement method includes the following steps:
101: setting an inhomogeneous linear array comprising L antenna array elements, and performing parallel undersampling on an A/D converter on each antenna array element to obtain L paths of sample sequences;
102: performing N-point DFT on the L sample sequences, and performing frequency and phase correction on DFT results through an estimator to respectively obtain L corrected frequency estimation values and L corrected phase estimation values;
103: and reconstructing the frequency and the phase through L pairs of frequency estimation values and phase estimation values and a closed Chinese remainder theorem to obtain the signal frequency and the estimation values of the angle of arrival.
The step 103 of reconstructing the frequency and the phase through the L pair frequency estimation value and the phase estimation value and the closed chinese remainder theorem to obtain the signal frequency and the estimation value of the angle of arrival specifically includes:
forming a frequency remainder by the L frequency estimation values, substituting the frequency remainder into a closed Chinese remainder theorem to reconstruct the frequency of the signal, and acquiring the frequency of the incident signal;
and solving L-1 phase difference estimated values according to the L phase estimated values to form phase remainders, substituting the phase remainders into a closed Chinese remainder theorem to reconstruct, and acquiring the estimated value of the angle of arrival by combining signal frequency.
The method comprises the following steps of (1) forming a frequency remainder by using L frequency estimation values, substituting the L frequency estimation values into a closed Chinese remainder theorem to reconstruct the frequency of a signal, and acquiring the frequency of an incident signal:
acquiring an intermediate variable from the residue array, and calculating a fuzzy multiple through the intermediate variable;
obtaining an estimated value of the signal frequency through a fuzzy multiple and a remainder group;
the method comprises the following steps of substituting closed Chinese remainder theorem for reconstruction, and acquiring a wave arrival angle estimated value by combining signal frequency:
selecting any positive integer, substituting the prime number group, the phase remainder group and the positive integer into a closed Chinese remainder theorem to reconstruct a nonnegative integer;
and obtaining an estimated value of the signal wavelength and a non-negative integer by a frequency estimation process to obtain an estimated value of the angle of arrival.
Through the operations of the steps 101-103, the embodiment of the present invention realizes high-precision joint estimation of the frequency and the direction of arrival.
The operation process described in this embodiment is described in detail below with reference to a specific calculation formula and fig. 2, and is described in detail below:
example 2
201: arranging a non-uniform linear array comprising L antenna elements, each element being provided with fs1～fsLThe sampling rate of the method is used for carrying out parallel undersampling on signals, the fast beat number acquired by each array element is N, and an L-path sample sequence is acquired;
arranging the non-uniform linear array as shown in FIG. 2, wherein circles 1-L represent L antenna elements, s1(t)～sL(t) denotes a received signal of each array element, d1～dL-1Representing the spacing of adjacent array elements; each array element is provided with an A/D converter, and the sampling rate corresponding to the array element i is set to be fsiL, requiring fs1～fsLWith greatest common divisor Mf(ii) a And f iss1～fsLDivided by MfAfter the resulti＝fsi/MfL are relatively prime in pairs, and the frequency measurement range of the parameter measurement proposed by the present invention is [0, f ·, n ═ 1max]Wherein f ismax＝lcm(fs1,...,fsL) And lcm (·) means finding the least common multiple (i.e. finding f)s1,...,fsLLeast common multiple of). Spacing d between adjacent antenna elementsjJ 1, L-1 satisfiesη therein1～ηL-1Is a pairwise coprime array, C is a parameter set according to actual requirements and satisfies 0 < C < C0/fmax(c0Is the propagation velocity of electromagnetic wavesRate).
Narrow-band signal s from far-field source in radar, sonar or other applications0(t) may be expressed in the form:
wherein A represents amplitude, f0Is the frequency of the signal or signals,the initial phase of the signal, "j" represents the unit of an imaginary number (the italic "j" represents the number, ranging from 1 to L-1). Considering the noise and the phase shift of the signal on the array, the received signal of the ith array element can be expressed as:
wherein,is the initial phase, ζ, of the signal as it arrives at array element ii(t) is gaussian white noise, and from a certain moment, L array elements carry out parallel sampling to incident signal simultaneously (sampling time can be far less than 1 second, and specific value is set for according to the requirement in practical application), and every array element gathers N snapshots, obtains L way sample sequence:
202: performing N-point DFT on the obtained L-path sample sequence, and utilizing an AM estimator[14]Frequency and phase correction is carried out on the DFT result, and L pairs of frequency estimation value and phase estimation value after correction are respectively obtained
That is, the obtained L path sample sequence is subjected to N point DFT to obtain Si(k)＝DFT(si(N)), k is 0,1, …, N-1, and the frequency estimation value obtained by DFT can be represented as (k))pi+i)·fsiForm of/N, kpiFor spectral peak positions (which can be directly derived from spectral peak searching),ifor the frequency offset value (which can be found by the AM estimator), the spectral correction using the AM estimator is performed as follows:
for the ith path, initializing the frequency offset valueIterative operations were performed as follows:
1) calculating the intermediate variable X-0.5And X0.5
2) Calculating the frequency offset value of the first iteration
Where Re (. cndot.) represents the real part.
Document [14] indicates that the frequency offset estimation value of convergence can be obtained by only iterating more than twice.
Each path is processed in the same way to obtain L frequency deviation estimated valuesFurther, the normalized remainder frequency after each path of correction can be obtained
While utilizing frequency offsetObtaining the correction value of the initial phase of each array element receiving signal
WhereinIs the phase obtained directly from the DFT spectral peak position.
203: substituting L acquired frequency estimated values to form frequency residue, substituting the frequency residue into a closed CRT to reconstruct signal frequency f0Calculating L-1 phase difference estimated values from L phase estimated values to form phase remainders, substituting the phase remainders into a closed CRT for reconstruction, and combining the signal frequency estimated values to obtain a wave arrival angle theta0。
Due to f0＞＞fsiFrequency of signal f0Can be modeled as the following CRT model:
f0＝ni·fsi+(kpi+i)·fsi/N (8)
wherein n isiTo be a fuzzy multiple, f0Corresponding to dividend of CRT, sampling rate f of each array elements1～fsLCorresponding to the modulus of CRT, and the remainder set ri1, L can be obtained from the following formula:
ri＝(kpi+i)·fsi/N (9)
firstly, reconstructing the signal frequency f0；
The closed CRT algorithm proposed in the document [12] is adopted to reconstruct the signal frequency, and the specific flow is as follows:
1) from the remainder group r1～rLCalculating the intermediate variable qi,1：
qi,1＝[(ri-r1)/Mf],2≤i≤L (10)
Wherein [ □]Representing a rounding operation, i.e. a pair (r)i-r1)/MfAnd carrying out rounding operation.
2) Calculating intermediate variables ξi,1：
Wherein,to relate toiIs inverse of the mode (i.e. satisfies)k ∈ Z, Z is a positive integer.
3) Calculating a first blur multiple n1：
Wherein, bi,1Is gamma1/iAboutiModulo inversion of (gamma) (-)1Is an intermediate variable and
4) calculating the remaining blur multiple ni；
ni＝(n1 1-qi,1)/i,2≤i≤L (13)
5) Estimating the frequency f of the signal0：
Measurement of residue as known from closed CRTAnd an ideal value riNeed to satisfy
Can precisely reconstruct f0(MfLarger error tolerance) and gives f0Reconstruction range of
After the measuring range and the number of array elements of engineering requirements are given, proper M is selected according to the formulas (15) and (16)fAnd prime number group1～LFurther determining the sampling rate f of each array elementsi＝Mf i,i＝1,...,L
Meanwhile, the invention provides a theoretical variance closed expression of frequency estimation as
ρ in equation (17) is the signal-to-noise ratio (the relationship with the signal-to-noise ratio SNR in dB is that ρ is 10SNR/10)。
Secondly, obtaining the estimated value of the angle of arrival
It is not difficult to deduce from the array structure of fig. 2 that the phase difference of the received signals of array element i and array element i +1 is:
when array element spacing djGreater than half the wavelength lambda of the signal0At the time of/2, the ratio of the total amount of the carbon atoms,blurring in units of 2 pi, i.e.
Wherein n isjIs a multiple of the phase ambiguity (x),representing ideal phase difference measurements, combining (18) (19) and taking phase measurement errors into accountjTo obtain
Wherein,is the angle of incidence of the signal (i.e. DOA),for the phase difference measurement, it can be obtained by processing the result of equation (7), i.e.
Wherein mod is a modulo division operation to ensure non-negativity of the remainder of the CRT, and two sides of equation (20) are simultaneously multiplied by a parameter d0/(2πdj) To obtain
Wherein d isjIs the spacing of adjacent array elements, d0Are defined parameters, the values of which are respectively defined as
Wherein M isθC is a non-negative constant according to the actual value, η1～ηL-1Two by two are mutually prime. The left end of equation (23) is usedIs shown, i.e.
Definition of
Mj＝d0/dj＝Mθηj(27)
Equation (23) can be converted into the following CRT model
Wherein M isjA value representing the modulus required for the CRT,is the CRT remainder.
From CRT reconstruction range
Substituting the formulas (24) and (26) into the formula (30) to obtain
0≤C＜λ0/sinθ0(31)
If the given frequency measurement range is (0, f)max]Angle of incidence of signal θ0Has a distribution range of (0, pi/2)]Then, the value range of the non-negative constant C is easily derived:
0＜C＜c0/fmax(32)
wherein c is0Is the propagation velocity of the electromagnetic wave. In practical application, the value of C should be selected within the range of formula (32) as required.
The corresponding module and the remainder are substituted into CRT to reconstruct(CRT solving process is similar to frequency estimation process and is not described here), and then the estimation value of the angle of arrival of the signal is obtained
WhereinCan be derived from the frequency estimation result.
Example 3
A frequency and DOA combined measuring device based on chinese remainder theorem, referring to fig. 3, the measuring device includes:
the L antenna array elements form a uniform linear array;
the A/D sampler is arranged on the antenna array element and used for parallel undersampling to obtain an L-path sample sequence;
and the DSP is used for performing N-point DFT on the L paths of sample sequences, performing frequency and phase correction on DFT results through the estimator, respectively obtaining L pairs of frequency estimation values and phase estimation values after correction, performing frequency and phase reconstruction by closed Chinese remainder theorem, and obtaining the sampling rate and the arrival angle estimation values of the antenna array elements.
Further, the measuring device further includes:
and the output drive and display circuit thereof are used for outputting the signal frequency and the estimated value of the angle of arrival.
Wherein, the DSP includes:
and the first processor is used for forming frequency remainders by the L frequency estimated values and substituting the frequency remainders into a closed Chinese remainder theorem to reconstruct the sampling rate of the antenna array element.
Further, the DSP includes:
and the second processor is used for solving L-1 phase difference estimated values from the L phase estimated values to form phase remainders, substituting the phase remainders into a closed Chinese remainder theorem to reconstruct, and acquiring the estimated value of the angle of arrival by combining signal frequency.
Further, the first processor comprises:
the first acquisition module is used for acquiring an intermediate variable from the residue array and calculating a fuzzy multiple through the intermediate variable; obtaining an estimated value of the signal frequency through a fuzzy multiple and a remainder group; and acquiring the sampling rate of each antenna array element by combining the range between the remainder measurement value and the ideal value through the estimation value of the signal frequency.
Further, the second processor comprises:
the second acquisition module is used for selecting any positive integer, substituting the mass array, the phase remainder array and the positive integer into a closed Chinese remainder theorem to reconstruct a nonnegative integer; and obtaining an estimated value of the signal wavelength and a non-negative integer by a frequency estimation process to obtain an estimated value of the angle of arrival.
Through the circuit device, the embodiment of the invention realizes high-precision joint estimation of the frequency and the direction of arrival.
The structure of the measuring apparatus in embodiment 3 is described in detail below with reference to the flowchart of the measuring apparatus, and is described in detail below:
example 4
Referring to fig. 3 and 4, the joint measuring apparatus for signal frequency and DOA under spatio-temporal undersampling proposed by the present invention comprises: antenna array element, A/D sampler, DSP, output driver and its display device.
The narrow-band signal s (t) of the space far field reaches each antenna array element at a certain angle to obtain an array receiving signal s (t) { s }1(t),...,sL(t) the A/D converter on each antenna element is respectively set by fs1～fsLThe received signal is sampled in parallel at the rate, the obtained snapshot is input to a DSP device, and the frequency and DOA measurement of the signal are obtained through processing by an internal algorithm of the DSP deviceAnd finally, outputting the result by means of the output drive and the display circuit thereof.
Wherein, the DSP is a core component and completes the following functions in the whole measuring process:
1) calling a core algorithm, completing DFT of each array element signal sample, correcting frequency and phase by using an AM estimator, and calling a closed CRT algorithm to realize measurement of frequency and DOA;
2) adjusting the sampling rate f of each array element in time according to the actual situations1～fsLSo as to meet the engineering requirements;
3) and outputting the measurement result to a driving and displaying module.
The main factors that determine the accuracy, complexity and stability of the system of fig. 3 are the core measurement algorithms stored in the program memory inside the DSP 3. The internal program flow of the DSP3 device is shown in fig. 4, and is specifically divided into the following steps:
roughly estimating the frequency of an incident signal, and setting a frequency measurement range and the sampling rate of each array element according to engineering requirements;
a CPU main controller in the DSP reads snapshot data from an I/O port and enters an internal RAM;
the direct current component in the signal to be measured can reduce the measurement accuracy by removing the direct current processing, so the direct current influence needs to be eliminated;
the measurement of parameters according to the flow of fig. 1 is the core part of the DSP algorithm, by which the frequency of the incident signal and the DOA measurement will be obtained. Judging whether the measurement result meets the engineering requirement, if not, resetting the frequency measurement range and the sampling rate according to the result and the actual requirement; and if the obtained result meets the requirement, outputting the result to driving or display equipment through a DSP output bus.
Example 5
Scheme according to figure 1Arranging an inhomogeneous linear array containing 4 antenna elements with sampling rate fs1＝29KHz，fs2＝31KHz，fs3＝33KHz，fs437KHz (corresponding to CRT parameter M)f＝1000，＝[29，31，33，37]). The maximum measurable frequency f from equation (16)max1.097679GHz, which is much larger than the sampling rate (4 orders of magnitude higher).
Assume further that the incident angle θ0Is in the range of (0,90 DEG)]Setting C to 0.2 according to equation (32) and letting η to [7, 11, 13]]The distance between adjacent array elements is d from the formula (25)1＝28.6m，d2＝18.2m，d315.4 m. It is readily known that the minimum half wavelength for a frequency in the measurement range is about 0.14m, which is much smaller than the minimum array spacing. The experiment was carried out with the probability of detection PdAnd Root Mean Square Error (RMSE) are used for inspecting the parameter estimation performance of the invention, and the fact that the array elements have the same receiving characteristics and are independent from each other and the noise is white Gaussian noise with zero mean value is assumed. The number of snapshots N acquired in each simulation is 1024, and 1000 Monte Carlo tests are performed under each SNR condition.
Firstly, the anti-noise performance of the measurement scheme of the invention is inspected, and in each test, the incidence angle theta0Randomly from (0,90 DEG)]Medium and uniform selection, frequency f0Randomly from [0, fmax]And (4) selecting. When the frequency estimation value is satisfiedIf so, the measurement is considered to be successful, otherwise, the measurement is considered to be failed. Similarly, when the DOA estimate isSatisfy the requirement ofWhen the detection is regarded as successful, fig. 5 and fig. 6 show the frequency detection probability and the DOA detection probability respectively as the changes of the SNR. As can be seen from FIG. 5, when the SNR is>The frequency detection has reached 100% success probability at 15dB, and FIG. 6 shows that, when SNR is high>At 0dB, the method is adoptedThe estimated value of the arrival angle can be successfully detected.
Then, the accuracy of parameter estimation of the present invention is examined, and the incident angle is fixed to θ0At 58 °, frequency fixed to f0Other parameters were unchanged at 858833689.15 Hz. In terms of frequency estimation, reference [12]]The proposed method is compared to the method of the present invention. FIGS. 7 and 8 show the mean square error versus SNR curves for the frequency estimate and the DOA estimate, respectively, as can be seen from FIG. 5 when SNR is>At-10 dB, the root mean square error of the frequency measurement value obtained by the invention is only about 0.6Hz, the precision is obviously improved along with the increase of SNR, and the performance is better than that of the document [12]]The proposed method; the frequency measurements are matched to the theoretical error curve given, and FIG. 8 shows the SNR when>The measured value of the incident angle obtained by the method has high precision at 0 dB.
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.
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 (2)
1. A frequency and DOA combined measurement method based on Chinese remainder theorem is characterized by comprising the following steps:
setting an inhomogeneous linear array comprising L antenna array elements, and performing parallel undersampling on an A/D converter on each antenna array element to obtain L paths of sample sequences;
performing N-point DFT on the L sample sequences, and performing frequency and phase correction on DFT results through an AM estimator to respectively obtain L corrected frequency estimation values and L corrected phase estimation values;
reconstructing frequency and phase through L pair of frequency estimation value and phase estimation value and closed Chinese remainder theorem to obtain signal frequency and estimation value of angle of arrival;
the step of reconstructing the frequency and the phase through the L pair of the frequency estimation value and the phase estimation value and the closed Chinese remainder theorem to obtain the signal frequency and the wave arrival angle estimation value specifically comprises the following steps:
forming a frequency remainder by the L frequency estimation values, and substituting the frequency remainder into a closed Chinese remainder theorem to reconstruct a signal frequency;
calculating L-1 phase difference estimated values from the L phase estimated values to form phase remainders, substituting the phase remainders into a closed Chinese remainder theorem to reconstruct, and acquiring a DOA estimated value by combining signal frequency;
the step of substituting L frequency estimation values into a closed Chinese remainder theorem to reconstruct the signal frequency comprises the following steps:
acquiring an intermediate variable from the residue array, and calculating a fuzzy multiple through the intermediate variable;
obtaining an estimated value of the signal frequency through a fuzzy multiple and a remainder group;
the step of substituting the closed Chinese remainder theorem for reconstruction and acquiring the estimated value of the angle of arrival by combining the signal frequency specifically comprises the following steps:
selecting any positive integer, substituting the prime number group, the phase difference remainder group and the positive integer into a closed Chinese remainder theorem to reconstruct a nonnegative integer;
obtaining an estimated value of signal wavelength and a non-negative integer by a frequency estimation process to obtain an estimated value of a wave arrival angle;
fix the incident angle at theta0At 58 °, frequency fixed to f0858833689.15Hz when SNR>At-10 dB, the root mean square error of the frequency measurements obtained by the present method is only 0.6 Hz.
2. A frequency and DOA combined measuring device based on Chinese remainder theorem is characterized in that the measuring device comprises:
the antenna array elements form an inhomogeneous linear array;
the A/D sampler is arranged on the antenna array element and used for parallel undersampling to obtain an L-path sample sequence;
the DSP is used for performing N-point DFT on the L-path sample sequence, performing frequency and phase correction on a DFT result through an AM estimator, respectively obtaining a corrected L-pair frequency estimation value and a corrected phase estimation value, performing frequency and phase reconstruction through a closed Chinese remainder theorem, and obtaining the frequency and the angle of arrival estimation value of an incident signal;
the DSP includes:
the first processor is used for forming frequency remainders by the L frequency estimated values and substituting the frequency remainders into a closed Chinese remainder theorem to reconstruct the frequency of the incident signal;
the DSP includes:
the second processor is used for solving L-1 phase difference estimated values from the L phase estimated values to form phase remainders, substituting the phase remainders into a closed Chinese remainder theorem to reconstruct, and acquiring an estimated value of the angle of arrival by combining signal frequency;
the measuring device further includes:
the output drive and display circuit thereof are used for outputting signal frequency and an estimated value of the angle of arrival;
the first processor comprises:
the first acquisition module is used for acquiring an intermediate variable from the residue array and calculating a fuzzy multiple through the intermediate variable; obtaining an estimated value of the signal frequency through a fuzzy multiple and a remainder group;
the second processor comprises:
the second acquisition module is used for selecting any positive integer, and substituting the prime number group, the phase remainder group and the positive integer into a closed Chinese remainder theorem to reconstruct a nonnegative integer; obtaining an estimated value of signal wavelength and a non-negative integer by a frequency estimation process to obtain an estimated value of a wave arrival angle;
fix the incident angle at theta0At 58 °, frequency fixed to f0858833689.15Hz when SNR>At-10 dB, the root mean square error of the frequency measurements obtained by the present method is only 0.6 Hz.
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