CN116131964A - Microwave photon-assisted space-frequency compressed sensing frequency and DOA estimation method - Google Patents
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Abstract
The invention discloses a microwave photon-assisted space-frequency compressed sensing frequency and DOA estimation method, which specifically comprises the following steps: setting a uniform linear array containing N array elements, and modulating a pseudo-random binary sequence on continuous wave light by a first Mach-Zehnder modulator on an optical carrier wave emitted by a continuous wave laser source on each channel branch; the output of the first Mach-Zehnder modulator modulates an upper radio frequency signal through the second Mach-Zehnder modulator, and after photoelectric conversion is carried out through the balance photoelectric detector, a baseband part is reserved through a low-pass filter, and then sampling is carried out through a low-rate analog-to-digital converter; and finally, the sampled N paths of sample sequences enter a digital signal processor to be recovered, and the synchronous orthogonal matching pursuit algorithm for solving the problem of multiple observation vectors is utilized to carry out the joint estimation of the microwave signal frequency and DOA. The invention can carry out joint estimation on the frequency and DOA multi-parameter of the broadband microwave signal, has simple structure and is easy to realize.
Description
Technical Field
The invention belongs to the field of array signal processing parameter estimation, and particularly relates to a microwave photon-assisted space-frequency compressed sensing frequency and DOA estimation method.
Background
Microwave signals are widely applied to modern electronic technology, the frequency is the most basic parameter [1] for describing the signals, and the estimation method of many other parameters is based on the known frequency. The direction of arrival (Direction of Arrival, DOA) estimate [2] of the signal is a specific direction of arrival for determining a plurality of signals of interest within a certain spatial region, and particularly when the desired signal and the interfering signal overlap spectrally, accurate direction finding localization of the signal source is possible. Implementing joint estimation of frequency and DOA is therefore not only a research hotspot in array signal processing but is also an important solution to meet the current ever-complicating electromagnetic spectrum environment awareness applications. The traditional joint estimation method is generally based on a subspace decomposition spectrum estimation algorithm, such as a MUSIC algorithm [3] and an ESPRIT algorithm [4], aiming at a narrow-band signal, the algorithm is large in calculation amount, and the sampling of the signal is required to meet the Nyquist sampling theorem, namely the sampling frequency is required to be not less than twice the highest frequency of the signal. As the frequency range of the signal is larger and larger, for example, the bandwidth of the main working signal of the electronic warfare is distributed between 2 GHz and 18GHz, which puts great pressure on the current analog-digital conversion system. While some high sampling rate analog-to-digital converters have been developed, the high cost, power consumption, remain problematic. With the advent of compressed sensing technology [5], some undersampling methods are gradually applied to frequency and DOA estimation, literature [6] combines the inter-mass frequency and a single sparse inter-mass array with compressed sampling technology to obtain DOA estimation; document [7] proposes a sampling structure of cascades, sub-nyquist sampling is performed by taking array elements in a uniform linear array as each channel of a modulation broadband converter (Modulated Wideband Converter, MWC), the structure is expanded to an L-shaped array to perform frequency and DOA estimation, and a combined recovery algorithm based on an ESPRIT method is provided, so that accuracy is high, but the structure is complex, and the L-shaped array is required to estimate frequency and one-dimensional arrival angle; document [8] proposes dividing the array structure into two parts, wherein a reference array element is used as a standard structure of the MWC for frequency estimation and signal recovery, and other array elements assist in DOA estimation by using a MUSIC algorithm, but pairing processing of frequency and DOA estimation is still required; document [9] proposes an improved uniform linear array structure-based selection of adding a symmetrical branch structure to each antenna to improve the DOA estimation performance. Both of the above undersampling methods require that the pseudo-random binary sequence (Pseudo Random Binary Sequence, PRBS) rate is not less than the nyquist rate, thus placing high demands on the mixer. In recent years, due to the advantages of large instantaneous bandwidth, low loss, light weight, low time jitter, strong electromagnetic interference resistance and the like, researchers propose to modulate an electric signal on an optical wave by using a Mach-Zehnder Modulator, MZM (Mach-Zehnder modulator) to realize photonic broadband signal spectrum sensing. The authors in document [10] propose an optical implementation of the MWC, the computer simulation results having a better ability to benefit high frequency signals than electronic solutions; document [11] proposes the acquisition of radar pulses with photon assistance, reconstructing rectangular pulses, chirped pulses and pulse streams; the authors in document [12] add photon time stretching techniques to the random demodulation structure, effectively reducing the PRBS rate and mixer speed; document [13] uses a single two-electrode MZM to solve the non-zero mean value of the observation matrix, simplifies the construction of the compressed sensing model and improves the recovery performance. Most of the above using microwave photon techniques only concern the perception of the signal spectrum and do not involve the estimation of the signal DOA.
Reference is made to:
[1]Schmidt R.Multiple emitter location and signal parameter estimation[J].IEEE transactions on antennas and propagation,1986,34(3):276-280.
[2] wang Yongliang theory and Algorithm of spatial Spectrum estimation [ M ]. Press, university of Qinghai, inc., 2004.
[3]Schmidt R.Multiple emitter location and signal parameter estimation[J].IEEE transactions on antennas and propagation,1986,34(3):276-280.
[4]Roy R,Kailath T.ESPRIT-estimation of signal parameters via rotational invariance techniques[J].IEEE Transactions on acoustics,speech,and signal processing,1989,37(7):984-995.
[5]Donoho D L.Compressed sensing[J].IEEE Transactions on Information Theory,2006,52(4):1289-1306.
[6]Qin S,Zhang Y D,Amin M G,et al.DOA estimation exploiting a uniform linear array with multiple co-prime frequencies[J].Signal Processing,2017,130:37-46.
[7]Ioushua S S,Yair O,Cohen D,et al.CaSCADE:Compressed carrier and DOA estimation[J].IEEE Transactions on Signal Processing,2017,65(10):2645-2658.
[8]Cui C,Wu W,Wang W Q.Carrier frequency and DOA estimation of sub-Nyquist sampling multi-band sensor signals[J].IEEE sensors journal,2017,17(22):7470-7478.
[9]Chen T,Liu L,Guo L.Joint carrier frequency and DOA estimation using a modified ULA based MWC discrete compressed sampling receiver[J].IET Radar,Sonar&Navigation,2018,12(8):873-881.
[10]Nan H,Gu Y,Zhang H.Optical analog-to-digital conversion system based on compressive sampling[J].IEEE Photonics Technology Letters,2010,23(2):67-69.
[11]Guo Q,Liang Y,Chen M,et al.Compressive spectrum sensing of radar pulses based on photonic techniques[J].Optics express,2015,23(4):4517-4522.
[12]Chi H,Chen Y,Mei Y,et al.Microwave spectrum sensing based on photonic time stretch and compressive sampling[J].Optics Letters,2013,38(2):136-138.
[13]Yang B,Yang S,Cao Z,et al.Photonic compressive sensing of sparse radio frequency signals with a single dual-electrode Mach–Zehnder modulator[J].Optics Letters,2020,45(20):5708-5711.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention provides a microwave photon-assisted space-frequency compressed sensing frequency and DOA estimation method.
The invention relates to a microwave photon-assisted space-frequency compressed sensing frequency and DOA estimation method, which utilizes a uniform linear array structure to sub-sample signals and processes snapshot data through a recovery algorithm, thereby realizing the joint estimation of frequency and DOA, and specifically comprises the following steps:
and setting a uniform linear array comprising N array elements, wherein each channel formed by each array element comprises two Mach-Zehnder modulators, a balance photoelectric detector, a low-pass filter and an analog-to-digital converter, and performing parallel undersampling to obtain N paths of sample sequences.
On each channel branch, an optical carrier wave emitted by a continuous wave laser source firstly passes through a first Mach-Zehnder modulator to modulate a pseudo-random binary sequence on continuous wave light; the output of the first Mach-Zehnder modulator is modulated by a second Mach-Zehnder modulator, the output of the second Mach-Zehnder modulator is subjected to photoelectric conversion by a balanced photoelectric detector, and the output electric signal is in direct proportion to the product of the radio frequency signal and the random signal; the baseband part is reserved through a low-pass filter, and then sampling is carried out by a low-rate analog-to-digital converter; and finally, the sampled N paths of sample sequences enter a digital signal processor to be recovered, and the synchronous orthogonal matching pursuit algorithm for solving the problem of multiple observation vectors is utilized to carry out the joint estimation of the microwave signal frequency and DOA.
Further, the first Mach-Zehnder modulator is in push-pull type, is biased at a quadrature modulation point, has a pseudo-random binary sequence with a fixed period alternating between + -1, and outputs a signal corresponding to the pseudo-random binary sequence with amplitude converted.
Further, the second mach-zehnder modulator is dual-output and is under certain bias conditions to remove unnecessary components.
Further, balanced photodetectors are equivalent to two 3dB optocouplers superimposed with one phase modulator.
Further, the sampling rate of the analog-to-digital converter is more than 2 times the bandwidth of the low-pass filter.
The beneficial technical effects of the invention are as follows:
the invention utilizes a uniform linear array structure to form a modulation broadband converter sampling structure, utilizes microwave photon technology to support, mixes frequencies by a Mach-Zehnder modulator, estimates frequency and DOA by a synchronous orthogonal matching pursuit algorithm through signals after photoelectric conversion, and the frequency and DOA estimation does not involve pairing problems. The invention has simple structure and easy realization.
Drawings
FIG. 1 is a schematic diagram of the microwave photon assisted space-frequency compressed sensing frequency and DOA estimation method of the present invention.
Fig. 2 is a graph of incident single signal spectra.
Fig. 3 is a graph of incident single signal spectral recovery.
Fig. 4 is a graph of incident single signal DOA estimation.
Fig. 5 is a graph of incident multi-signal spectra.
Fig. 6 is a graph of incident multi-signal spectral recovery.
Fig. 7 is a graph of incident multi-signal DOA estimation.
Detailed Description
The invention will now be described in further detail with reference to the drawings and to specific examples.
The structure realized by the microwave photon assisted space frequency compressed sensing frequency and DOA estimation method is shown in figure 1, a uniform linear array comprising N antenna array elements is arranged, each channel of each array element comprises two Mach-Zehnder modulators, and a balanced photoelectric detector, a low-pass filter and a low-rate analog-to-digital converter are used for parallel sampling to obtain N paths of sample sequences.
And expanding an array manifold matrix in a linear equation obtained by the N paths of sample sequences to form a dictionary matrix according to a certain sequence, wherein the assumed frequency and the arrival angle are positioned on the divided frequency and angle grids.
And converting the infinite observation vector problem into a multi-observation vector problem with the same support set by using a continuous finite module, and solving the multi-observation vector problem by using a synchronous orthogonal matching pursuit algorithm to obtain the estimation results of frequency and angle.
Consider that x (t) is a continuous-time real signal that contains M unknown frequencies, which in the time domain can be written as:
wherein f i Is the i-th unknown frequency, V i Is the amplitude phi i Is the initial phase and is assumed to be 0. Since the frequency is unknown, the frequency f should be sampled at the Nyquist frequency Nyq Sampling, the signal received by the kth array element of the uniform linear array can be expressed as:
wherein τ k (θ i ) Representing the advance or delay of the k-th element received signal relative to the reference element, the fourier transform is:
the optical carrier of the continuous wave light is assumed to be written as:
wherein P is c Is the average optical power omega c Is the angular frequency, the pseudo-random binary sequence is modulated on the optical carrier by a first mach-zehnder modulator biased at the quadrature bias point, the output can be expressed as:
wherein p (T) is a period T p Pseudo-random binary sequences alternating between + -1, V π Is a half-wave voltage of a Mach-Zehnder modulator, and outputs a modulated upper signal x by a second Mach-Zehnder modulator k (t) the second mach-zehnder modulator is dual-output, biased at the quadrature bias point, dc-suppressed to obtain a better mixing product, the output may be expressed as:
where φ (t) is the relative phase shift between the two arms:
φ(t)＝π[V bias +x k (t)]/V π (7)
wherein V is bias Representing the dc bias voltage.
The output optical signal is subjected to photoelectric conversion by a balance photoelectric detector:
wherein R is the responsivity of the balanced photoelectric detector, C is a constant of parameters such as modulation depth, link loss and the like, and under the condition of small signal approximation, the output photocurrent is proportional to p' (t) x k (t), p' (t) is considered the same except for a pseudo-random binary sequence of varying magnitude, expressed as:
p'(t)＝cos 2 [πp(t)/V π +π/4] (9)
at a pass cutoff frequency of 1/(2T) s ) After a low pass filter of (2)，T s And T is p Equal, only the baseband component is retained, and then passed through a sampling frequency of 1/T s The analog-to-digital converter of (a) performs compressed sampling to obtain N sampling sequences y 1 [n],y 2 [n],...,y N [n]Sampling sequence y on any one channel k [n]The Discrete-time fourier transform (DTFT) of (a) may be expressed as:
wherein f p Is a pseudo-random sequence period T p Reciprocal of c l Is the fourier series coefficient of p' (t), and represents the signal vector S as:
by definition of Y [ n ]]＝[y 1 [n],y 2 [n],...,y N [n]] T . A linear system consisting of a sequence of samples of all channels is spectrally represented in the form of a matrix:
Y(f)＝A(f,θ)S(f) (12)
wherein the array manifold matrix A is represented as
Assuming that the frequencies are all located in a frequency grid
In which L=f Nyq And/2 delta, delta being the spacing of the frequency grid. Also, the angle is divided into S parts { alpha } 1 ,α 2 ,...,α S And assuming that the true DOA is located on the angular grid. Thus, by expanding array manifold matrix A into dictionary matrix G, its first, n, s terms can be written as
g l,n,s ＝exp[j2πd(n-1)lΔsin(α s )/c] (14)
Where c is the speed of light, so the array manifold becomes:
g is an extended array manifold matrix and its corresponding frequency and angular position is known, i.e., frequency is in terms of [ -LΔL.DELTA.]The DOA corresponding to each frequency grid is formed according to { alpha } 1 ,α 2 ,…,α S The order of }, equation (12) becomes
Y(f)＝G(f,θ)X(f) (16)
Wherein X (f) is a sparse vector, because the frequencies are continuous, the above-mentioned underdetermined equation belongs to the infinite observation vector problem, which is constructed as a multiple observation vector problem with continuous finite modules and with the same support set between them, a frame V is constructed by the sampling sequence y [ n ], expressed as
By choosing V through feature decomposition, a multiple observation vector problem v=gu can be constructed that can be solved by any multiple observation vector compressed sensing algorithm, such as a synchronous orthogonal matching pursuit algorithm, once its support set is found, the frequency and DOA are estimated.
The invention adopts MATLAB tool simulation, and numerical simulation verifies the correctness and feasibility of the invention. Nyquist frequency f in simulation Nyq 10GHz, n=30 array elements are set, the array element spacing r=0.03 m, i.e. half wavelength corresponding to the highest frequency of 5GHz, the signal duration is 1.9499us, the amplitude is 0.6V, the signal-to-noise ratio is 10db, the f of prbs p = 51.28MHz. The average power of the laser is 1mW, and the half-wave voltage of the Mach-Zehnder modulator is 5V, so that the condition of small signal approximation is satisfied. The divided frequency grid is 100MHz and the angle grid is 10 °. Simulation verifies the incidence condition of single signals, and FIG. 2 shows that the original incidence signal frequency is 2.1GHz, fig. 3 and 4 show the recovery of the spectrum and the estimation of the DOA, respectively. Further testing of the multiple signal estimation, fig. 5 shows the frequencies of the incident signals at 0.5ghz,2.7ghz,4.8ghz, respectively, corresponding angles of arrival at 30 °,30 °,70 °. Fig. 6 and 7 show the spectrum and the DOA estimation, respectively.
Claims (6)
1. The utility model provides a microwave photon-assisted space-frequency compression perception frequency and DOA architecture and estimation method, which is characterized in that a uniform linear array structure is utilized to sub-sample signals, snapshot data is processed through a recovery algorithm, thereby realizing frequency and DOA joint estimation, and the method is specifically as follows:
setting a uniform linear array comprising N array elements, wherein each channel formed by each array element comprises two Mach-Zehnder modulators, a balance photoelectric detector, a low-pass filter and an analog-to-digital converter, and performing parallel undersampling to obtain N paths of sample sequences;
on each channel branch, an optical carrier wave emitted by a continuous wave laser source firstly passes through a first Mach-Zehnder modulator to modulate a pseudo-random binary sequence on continuous wave light; the output of the first Mach-Zehnder modulator is modulated by a second Mach-Zehnder modulator, the output of the second Mach-Zehnder modulator is subjected to photoelectric conversion by a balanced photoelectric detector, and the output electric signal is in direct proportion to the product of the radio frequency signal and the random signal; the baseband part is reserved through a low-pass filter, and then sampling is carried out by a low-rate analog-to-digital converter; and finally, the sampled N paths of sample sequences enter a digital signal processor to be recovered, and the synchronous orthogonal matching pursuit algorithm for solving the problem of multiple observation vectors is utilized to carry out the joint estimation of the microwave signal frequency and DOA.
2. A method of microwave photon assisted space frequency compressed sensing frequency and DOA estimation as defined in claim 1 wherein the first mach-zehnder modulator is push-pull biased at quadrature modulation point with a fixed period of pseudo-random binary sequence alternating between ± 1, the output signal corresponding to the amplitude transformed pseudo-random binary sequence.
3. A method of microwave photon assisted spatial frequency compressed sensing (plc) and DOA estimation as defined in claim 1 wherein said second mach-zehnder modulator is dual-output, under specific bias conditions to remove unwanted components.
4. The method for estimating space-frequency compressed sensing frequency and DOA as defined in claim 1, wherein the balanced photodetector is equivalent to two 3dB optical couplers superimposed with one phase modulator.
5. The method for microwave photon assisted spatial frequency compressed sensing and DOA estimation according to claim 1, wherein the sampling rate of the analog-to-digital converter is more than 2 times the bandwidth of the low pass filter.
6. The microwave photon assisted space frequency compressed sensing frequency and DOA estimation method according to claim 1, wherein each antenna unit adopts the same path of binary pseudo-random sequence to realize sensing of different phases of space domain radio frequency signals.
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