CN113740797B - High-precision single-snapshot target arrival angle estimation method under lens array - Google Patents
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Abstract
The application discloses a high-precision single-snapshot target arrival angle estimation method under a lens array, relates to the technical field of array signal processing, and aims at solving the problems that in the prior art, as DoA is continuously distributed in space and array element arrangement of the lens array is fixed, energy of an arrival signal is inevitably diffused into the whole array, so that energy leakage is caused, and further estimation performance loss is caused. The DOA estimation under the single snapshot condition can be realized under the lens array system. The method effectively solves the problem of inherent energy leakage of the lens array, which results in estimation performance loss, and greatly improves the accuracy of DoA estimation.
Description
Technical Field
The application relates to the technical field of array signal processing, in particular to a high-precision single-snapshot target arrival angle estimation method under a lens array.
Background
The estimation of the arrival angle of a target based on an antenna array is widely used in various fields such as radar, sonar, wireless communication, imaging, and the like. In highly dynamic environments such as autopilot, only a fraction of the data shots (even a single shot) can be used to estimate the DoA due to rapid changes in relative distance, speed and angle, which results in the failure of conventional spatial spectrum estimation algorithms. By exploiting the spatial sparsity of the arrival signals, compressed sensing techniques have been applied in recent years to solve the single snapshot problem. However, when the true target direction is not exactly at the preset discrete grid point, the compressed sensing algorithm may generate a base mismatch error, resulting in performance loss.
Meanwhile, the amplification antenna can obtain higher spatial resolution, spectrum utilization rate and energy efficiency, and has become a development trend of future radar and communication systems. In contrast to conventional multiple-input multiple-output (MIMO) systems, massive MIMO cannot be equipped with a unique radio frequency chain for each antenna. The radio frequency chain comprises a frequency spreader, a digital signal processor and other components, and huge hardware complexity and energy loss can be generated. In order to reduce the required radio frequency chains, students at home and abroad propose a new array system, namely a lens array. While lens arrays can greatly reduce the number of rf chains required without significant loss of performance, the problem of DoA estimation under such arrays becomes quite challenging. Because of the limitation of the rf chain, only a portion of the received data may be used to estimate the DoA, which renders the conventional DoA estimation method ineffective.
Furthermore, the current DoA estimation of the lens array is mostly built under ideal conditions, i.e. assuming that the spatial signal arrival angle is exactly in a pre-set discrete spatial direction, i.e. the signal energy is exactly concentrated on a single array element. However, it is described in the literature (On the power leakage problem in millimeter-wave massive MIMO with lens antenna arrays, IEEE trans. Signalprocess. Vol.67, no.18, pp.4730-4744, sept. 2019.) that since the DoA is continuously distributed in space, and the array element arrangement of the lens array is fixed, the energy of the arriving signal inevitably spreads throughout the array, causing an energy leakage problem. The energy leakage can cause the performance of the angle estimation algorithm under existing lens arrays to be significantly reduced or even disabled. Under the above background, the application provides a method for estimating the DOA of a lens array under a single snapshot condition. Compared with the traditional array signal processing method, the method has the following advantages: (1) On the premise of no obvious performance loss, the hardware complexity and the energy consumption of the large-scale MIMO system are greatly reduced, and the possibility is provided for the practical application of expanding the number of antennas; (2) the DOA estimation under the single snapshot condition can be realized; (3) The method solves the problem of inherent energy leakage of the lens array, which causes the loss of estimation performance, and greatly improves the accuracy of DoA estimation.
Disclosure of Invention
The purpose of the application is that: aiming at the problems that in the prior art, the DoA is continuously distributed in space and the array element arrangement of the lens array is fixed, the energy of an arrival signal is inevitably diffused into the whole array, so that the energy leakage is caused, and the estimated performance loss is caused, the high-precision single snapshot target arrival angle estimation method under the lens array is provided.
The technical scheme adopted by the application for solving the technical problems is as follows:
a high-precision single-snapshot target arrival angle estimation method under a lens array comprises the following steps:
step one: an electromagnetic lens is arranged at the front end of the lens array structure, and N is arranged on the front end of the lens array structure t The array elements are arranged in a semicircular area at the focal point of the lens, N t The value range is [32,256 ]]Then the array element antenna is connected with N RF The radio frequency chains are connected through an electronic switch, wherein N RF =5, and finally the space frequency domain interval [ -1, 1] is defined by the set lens array structure]Average divided into N t Angle theta n ，n＝1,2,…,N t ，N t Among the array elements, the spacing between the array elements satisfies d=λ (sin θ n -sinθ n-1 ) 2, λ is the wavelength of the emitted signal;
step two: connecting a radio frequency chain with a corresponding antenna subset in the lens array structure to obtain received signal data on the antenna subset;
step three: constructing a DOA estimation problem based on atomic norm minimization according to the received signal data on the antenna subset, and solving a dual problem of the DOA estimation problem based on atomic norm minimization to obtain a solution of the dual problem;
step four: constructing a triangular polynomial function taking a solution of the dual problem as a coefficient and taking a space angle as an independent variable, and obtaining the DoA estimation by carrying out maximum value search on the triangular polynomial function.
Further, in the second step, the connection between the rf chain and the corresponding antenna subset in the lens array structure is performed by an antenna selection rule, where the specific steps of the antenna selection rule are as follows:
first, N is switched on and off by an electronic switch RF The radio frequency chains are sequentially connected with N t The elements being connected and receiving signals, i.e. each radio frequency chain being connectedThe antennas are then used to obtain the received data representation of the whole array antenna +.>M represents the snapshot number of the received signal, and then obtains the sum of the signal power received by each antenna, and the sum is expressed as:
where |X (: m) | represents the absolute value of the mth column data of matrix X,
by usingIndicating the number of the antenna, searching the antenna reception power X P Maximum value of>The antenna number indicating the maximum amplitude of the received signal, the index set of antenna selection is:
wherein c represents the number of antennas selected in the subset and satisfies c.ltoreq.N RF Antenna selection matrixExpressed as:
where i and j represent the ith row and jth column of the antenna selection matrix,
then, the antenna component with the largest amplitude of the received signal is extracted from the vector X P And (3) selecting the strongest signal amplitude in the residual data again, repeating the process to obtain all K antenna subsets selected by the DoA, wherein K represents the known signal source number, and the selection matrix of all incoming wave signals is represented as follows:
if the number of the sources is unknown, the termination condition of the repeated process is as follows:
wherein ,XP (q) represents X P The q-th element of the group,representing a subset of antennas selected by all K doas, η represents a scaling parameter of the energy selection threshold, η is greater than 80%.
Further, the subset of antennas selected by all K doas is expressed as:
further, the DoA estimation problem based on atomic norm minimization constructed in the third step is expressed as:
where ε represents the regularization parameter, y represents the low-dimensional received data,representing the original subset->Induced->Is represented by atomic norms of (1), U represents a number comprising N t Discrete fourier transform matrix of orthogonal basis, ψ n Represents the discrete spatial frequency, vector b= [0,1, …, N t -1] T ，/>Representing the data vector to be restored, U H Representing the conjugate transpose of U.
Further, the atom setInduced->The atomic norms of (2) are expressed as:
c a representing coefficients, a representing atoms.
Further, the low-dimensional received data y is expressed as:
y＝WX＝WU H A(Φ)X+WN
where X and N represent discrete data forms of the received signal and noise, respectively, and A (Φ) represents a manifold matrix of the array response.
Further, the dual problem in the third step is expressed as:
wherein Representing the real part, V representing the solution of the dual problem, Q representing the intermediate variable of the dual problem, V H Represents the conjugate transpose of V.
Further, the dual problem of solving the DOA estimation problem based on atomic norm minimization is solved by a CVX toolkit.
Further, the triangular polynomial function is expressed as:
wherein f represents a spatial frequency,represents the conjugate of the i-th element in vector V, e jπ(i-1)f Representing a trigonometric function.
Further, the DoA estimate is expressed as:
wherein ,represents a rough estimate of DoA, h k Representing maximum search interval,/->Antenna index indicating maximum received signal power, < ->Representing the DoA estimate.
The beneficial effects of the application are as follows:
1. the hardware complexity and the energy consumption of the large-scale MIMO system are greatly reduced, and meanwhile, the estimation performance is ensured to have no obvious loss.
2. DoA estimation under single snapshot condition can be realized under lens array system
3. The method effectively solves the problem of inherent energy leakage of the lens array, which results in estimation performance loss, and greatly improves the accuracy of DoA estimation.
Drawings
FIG. 1 is a diagram of the overall structure of the present application;
FIG. 2 is a schematic view of a lens array according to the present application;
FIG. 3 is a schematic diagram of the lens array energy focusing characteristics and antenna selection of the present application;
fig. 4 is a graph showing the performance contrast of the single snapshot DoA estimation of the present application under the condition of snr=10db, compared with the conventional uniform linear array system;
fig. 5 is a graph showing the performance contrast of the single snapshot DoA estimation of the present application under the condition of snr=15 dB with the conventional uniform linear array system;
FIG. 6 is a graph showing the comparison of channel estimation performance under the present application and existing lens array system.
Detailed Description
It should be noted that, in particular, the various embodiments of the present disclosure may be combined with each other without conflict.
The first embodiment is as follows: referring to fig. 1, a method for estimating an arrival angle of a high-precision single-shot object in a lens array according to the present embodiment includes the following steps:
step one: the number of antennas in each antenna subset c is determined based on the array element settings and the desired reserved signal energy ratio.
Step two: amplitude and vector X for receiving single snapshot data from an antenna P The maximum value is selected, and the antenna index corresponding to the maximum value is set asThe index set for a selected antenna can be expressed as:
without loss of generality, c is taken as an odd number in order to ensure symmetry. Then the antenna selection matrixCan be expressed as:
then, the selected antenna component is derived from vector X P If the process is repeated by selecting again the strongest signal amplitude in the remaining data, then all K of the multiple DoA-selected antenna subsets may be successively obtained, which may be represented as
In the case where the number of sources is unknown, the termination condition for this iterative process may be selected as:
where η is a predetermined scaling parameter as the energy selection threshold. After the data of the antenna subset to be received is obtained through the antenna selection mode, a switch in a selection network can be controlled, a radio frequency link is connected with a corresponding antenna, and the obtained low-dimensional received data is recorded as y.
Step three: constructing the following optimization problem according to the low-dimensional received data y obtained in the step two:
where epsilon is the regularization parameter,u represents N t The dual problem of problem (5) can be expressed as:
wherein Representing the real part of a. The semi-positive programming problem can be solved with a CVX toolkit to obtain the value of the dual variable v.
Step four: with the dual variable v as a coefficient, constructing the following triangular polynomial function with the space angle as an independent variable:
where f represents the spatial frequency. In addition, in the antenna selection process of the second step, the DoA can be estimated roughly from the following equation:
thus, it is possible to be in the intervalPerforming a maximum search on the function (8) to obtain an accurate estimate of the DoA as:
step one, the number c of antennas in each antenna subset is selected according to the signal energy distribution of the lens array, and the related quotation is as follows [1]:
and (5) lemma: for incoming wave direction phi in beam space k The sum P of the c strongest energy components of the signal at the receiving element c With the whole array receiving the total energy P T The ratio between them has the following bound:
furthermore, once phi is determined k Is the strongest energy location of (2)The other c-1 components will be uniformly located around it.
According to the above quotients we can keep only c antennas out of all antennas with a suitable energy ratio. For example, for a 64 element antenna, if only the 4 antennas receiving the strongest energy are reserved, more than 90% of the energy is reserved. Therefore, the lens array can not obviously lose performance under the condition of greatly reducing hardware complexity and energy consumption.
Step two, according to the working principle schematic diagrams of the lens array shown in fig. 2 and 3, an electromagnetic lens is placed at the front end of the receiving array element, and the function of the electromagnetic lens mathematically corresponds to that of the electromagnetic lens containing N t The discrete Fourier transform matrix of each orthogonal basis is expressed as:
wherein b= [0,1, …, N t -1] T ，n＝1,2,…,N t Representing pre-divided discrete spatial frequencies, N t Is the number of antennas. Definition s (t) = [ s ] 1 (t),s 2 (t),…,s K (t)] T For complex-valued signals arriving from the spatial K DoA directions, the received signal for a lens array element can be expressed as:
x(t)＝U H A(Φ)s(t)+n(t) (12)
wherein n (t) is subject to complex Gaussian distributionIs equal to a (phi) = [ a (phi) 1 ),…,a(φ K )]Manifold matrix, phi, representing array response i ＝sin(θ i ) Spatial frequency value representing the angle of DOA, θ= [ θ ] 1 ,…,θ K ]The DoA direction of the K signals is indicated. a (phi) is a guiding vector of the central symmetry uniform linear array, which can be written as:
where d denotes the element spacing, λ is the signal wavelength, and we usually take d/λ=1/2.
Subsequently, the energy vector X of the received signal P The method can be calculated according to the following formula:
where |x (: M) | represents the absolute value of the mth column of data in matrix X, M represents the number of snapshots of the received signal, the application is primarily directed to the single snapshot case where m=1. Next, from X P The maximum value is selected, and the antenna index corresponding to the maximum value is set asThe index set for a selected antenna can be expressed as:
without loss of generality, c is taken as an odd number in order to ensure symmetry. Then the antenna selection matrixCan be expressed as:
then, the selected antenna component is derived from vector X P If the process is repeated by selecting again the strongest signal amplitude in the remaining data, then all K of the multiple DoA-selected antenna subsets may be successively obtained, which may be represented as
In the case where the number of sources is unknown, the termination condition for this iterative process may be selected as:
where η is a predetermined scaling parameter as the energy selection threshold. After obtaining the data of the antenna subset to be received in the above antenna selection manner, a switch in the selection network may be controlled, and the radio frequency link is connected with the corresponding antenna, so that the obtaining of the low-dimensional received data y may be expressed as:
y＝WX＝WU H A(Φ)X+WN (19)
where X and N are discrete data forms of the received signal and noise, respectively.
And thirdly, considering the condition that the received data is single snapshot m=1, the gridless compressed sensing algorithm based on the atomic norm shows good performance when solving the off-grid and single snapshot problems. First, define an atom set as:
wherein a (f) represents a guiding vector of the central symmetry uniform linear array, f is a corresponding spatial frequency component, and the expression is the same as the expression (13). From the form of equation (12), it is apparent that the array received data X can be seen as the product of a predetermined discrete fourier transform matrix and a sparse non-negative combination of the elements in the atomic set, namely:
wherein ψk Representing the phase of the kth spatial frequency component, i.es k Representing the complex amplitude of the spatial component. Thus, a group of atoms can be obtained>Induced->The atomic norms of (2) are:
in order to recover the received signals of the array, the following optimization problem is constructed from the low-dimensional received data y obtained in step two:
where epsilon is the regularization parameter,since the original subset is a set defined in the spatial continuous domain, the problem is an infinite-dimensional continuous parameter estimation problem and cannot be directly solved. Furthermore, our objective is to estimate the direction of the DoA without the need to recover the entire received data. Therefore, the optimization problem (23) can be converted into a dual problem, and then an accurate DoA estimated value can be obtained through the relationship between the dual variable and the space frequency. Its dual problem can be expressed as:
wherein Representing the real part of a. The problem (24) is a standard semi-positive programming problem, and the value of the dual variable v can be easily obtained by using a CVX tool kit.
Step four: with the dual variable v as a coefficient, constructing the following triangular polynomial function with the space angle as an independent variable:
and f represents the spatial frequency, and the DoA value to be estimated is the angle value corresponding to the maximum value search of the equation (7) in the airspace. It should be noted that, in the conventional atomic norm minimization, the root equation is generally used to directly obtain the DoA estimation value, but in the lens array, this method is ineffective. Since the lens array obtains signal data after fourier transformation, many false roots appear in the root-finding process, and the value of the DoA cannot be estimated accurately. In addition, in the antenna selection process of the second step, the DoA can be estimated roughly from the following equation:
thus, it is possible to be in the intervalPerforming a maximum search on the function (25) to obtain an accurate estimate of the DoA as:
the effectiveness of the application can be demonstrated by the following simulations:
simulation conditions and Contents
1 under the condition of SNR=10dB, the method provided by the application is compared with a single snapshot DoA estimation performance contrast curve under a traditional uniform linear array system
Consider a lens array comprising 65 array elements, with c=5 antennas selected among the subset of antennas to ensure that more than 90% of the energy can be retained for each DoA. Assuming that the number of signal sources is K=3, the DOA angle is θ= [ -32.8881 °,25.2773 °,69.3903 °]And simultaneously, the normalized signal energy is selected, and the signal strengths of different incoming wave directions are ensured to be the same.Representing the manner in which the signal to noise ratio (dB) is defined. Furthermore, root mean square error is used as a measure for evaluating the estimated performance of the DoA, which is defined as +.>P represents Monte Carlo experiments at this time, < >>Representing an estimate of the kth target, θ, in the p-th experiment k Is a true value. P is taken 500 Monte Carlo experiments, the signal to noise ratio is 10dB, the number of radio frequency chains is 15 to 65, and the interval is 10.
2 under the condition of SNR=15 dB, the method provided by the application is compared with a single snapshot DoA estimation performance contrast curve under a traditional uniform linear array system
Consider a lens array comprising 65 array elements, with c=5 antennas selected among the subset of antennas to ensure that more than 90% of the energy can be retained for each DoA. Assuming that the number of signal sources is K=3, the DOA angle is θ= [ -32.8881 °,25.2773 °,69.3903 °]And simultaneously, the normalized signal energy is selected, and the signal strengths of different incoming wave directions are ensured to be the same.Representing the manner in which the signal to noise ratio (dB) is defined. Furthermore, root mean square error is used as a measure for evaluating the estimated performance of the DoA, which is defined as +.>P represents Monte Carlo experiments at this time, < >>Representing an estimate of the kth target, θ, in the p-th experiment k Is a true value. P is taken 500 Monte Carlo experiments, the signal to noise ratio is 15dB, the number of radio frequency chains is 15 to 65, and the interval is 10.
3. The present application compares the channel estimation performance with the existing lens array system
Consider a lens array comprising 65 array elements, with c=5 antennas selected among the subset of antennas to ensure that more than 90% of the energy can be retained for each DoA. Assuming that the number of signal sources is K=3, the DOA angle is θ= [ -32.8881 °,25.2773 °,69.3903 °]Simultaneous selection of normalized signalsEnergy and ensuring the same signal intensity in different incoming wave directions.Representing the manner in which the signal to noise ratio (dB) is defined. Furthermore, the root mean square error of the normalized channel estimate, defined as +.> P represents Monte Carlo experiments at this time, < >>Representing an estimate of the kth target, θ, in the p-th experiment k Is a true value. P is taken 500 Monte Carlo experiments, the signal to noise ratio is from 0dB to 20dB, and the interval is 5dB. For comparison purposes, assume that the OMP and SD algorithms being compared have 20 snapshots of data and that an ideal DoA angle θ is set 1 ＝[-17.9202°,0°,27.4864°]。
(II) simulation results
1. The application compares with the single snapshot DoA estimation performance contrast curve under the traditional uniform linear array system under the condition of SNR=10dB
The single snapshot DoA estimation algorithm of the present application and a conventional Uniform Linear Array (ULA) array at snr=10 dB is given in fig. 4. The application can greatly reduce the number of the required radio frequency chains, and in the simulation, the number of the radio frequency chains required by the application is always Kc=15. The number of rf chains required for the conventional ULA array algorithm is the same as the number of antennas with respect to the present application, and thus the simulation increases the number of rf chains for the conventional algorithm from 15 to 65.PR represents a rotation vector algorithm, MUSIC represents a single fast afraid MUSIC algorithm, FIIB represents a fast iterative interpolation beamforming algorithm. As can be seen from fig. 4, in the case of snr=10 dB, the angle estimation performance of the present application is always better than other comparison algorithms, although the radio frequency chains of the ULA array reach 65 array elements, which are the same as the number of antennas of the present application.
2. The application compares with the single snapshot DoA estimation performance contrast curve under the traditional uniform linear array system under the condition of SNR=15 dB
The single snapshot DoA estimation algorithm of the present application with a conventional Uniform Linear Array (ULA) array at snr=15 dB is given in fig. 5. The application can greatly reduce the number of the required radio frequency chains, and in the simulation, the number of the radio frequency chains required by the application is always Kc=15. The number of rf chains required for the conventional ULA array algorithm is the same as the number of antennas with respect to the present application, and thus the simulation increases the number of rf chains for the conventional algorithm from 15 to 65.PR represents a rotation vector algorithm, MUSIC represents a single fast afraid MUSIC algorithm, FIIB represents a fast iterative interpolation beamforming algorithm. As can be seen from fig. 5, the single-fast MUSIC algorithm is superior to the present application when the rf chain exceeds 35 in the case of snr=15 dB. Although the comparison algorithm is superior to the present application when assembling a larger number of rf chains, the ULA array structure consumes a lot of energy and a huge hardware complexity. At low radio frequency chains, contrast algorithm performance is greatly reduced or even disabled. Meanwhile, the algorithms are designed under ULA system, and the algorithms fail under lens array system.
3. The present application compares the channel estimation performance with the existing lens array system
Fig. 6 shows a comparison between the channel estimation algorithm under existing lens array system and the present application. Where OMP represents the orthogonal matching pursuit algorithm in standard compressed sensing techniques and SD represents the support set detection algorithm. Because the two algorithms can only directly recover channel data and cannot perform angle estimation, the application estimates the signal complex amplitude reconstruction signal for comparison through a least square method after estimating the angle for comparison. Furthermore, both methods require accumulation of pilots, which fail in the case of a single snapshot, so the data of 20 snapshots of both methods are presented in simulation for comparison. As can be seen from fig. 6, while OMP performs the same as the present application under ideal conditions, OMP and SD algorithms will cause a significant performance penalty once there is a spectrum leakage problem. This is because the proposals of SD and OMP take advantage of the sparsity of the beam space channels, which are not strictly sparse when there is spectrum leakage, due to the spread of signal energy into the entire array, which results in estimation errors.
It should be noted that the detailed description is merely for explaining and describing the technical solution of the present application, and the scope of protection of the claims should not be limited thereto. All changes which come within the meaning and range of equivalency of the claims and the specification are to be embraced within their scope.
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