CN107483130A - A Joint Wideband Spectrum Sensing and Angle of Arrival Estimation Method - Google Patents

Abstract

The invention belongs to radio communication (wireless communication) technical field, more particularly to a kind of joint broader frequency spectrum using time nyquist sampling perceives and angle of arrival (direction of arrival, DOA) method of estimation.One kind joint broader frequency spectrum perceives and angle-of- arrival estimation method：Every antenna channels are only made up of a delay path and an ADC.The signal that each antenna receives is sampled after a default time delay with secondary Nyquist rate.Compared to other sampling frames, the signal that framework proposed by the present invention need not receive antenna is divided into multichannel, therefore, the ADC numbers needed are equal with number of antennas, in addition, the time delay of different antennae can be very random setting, it is only necessary to time delay meet a very wide in range condition, it becomes possible to carry out exactly joint broader frequency spectrum perceive and DOA estimate.In framework proposed by the present invention, just signal is sampled after a simple delay, can significantly find out that this framework has relatively low hardware complexity, and be easily achieved.

Description

A Joint Wideband Spectrum Sensing and Angle of Arrival Estimation Method

technical field

The invention belongs to the technical field of wireless communication (wireless communication), and in particular relates to a joint broadband spectrum sensing and angle-of-arrival (direction-of-arrival, DOA) estimation method using sub-Nyquist sampling.

Background technique

Today, with the rapid development of communication technology, spectrum resources have become extremely scarce and precious, and how to improve spectrum utilization has always been a research hotspot. In the field of signal processing and wireless communication, wideband spectrum sensing technology has been widely studied, and its purpose is to identify the occupancy of spectrum within a large frequency band. In order to further improve the utilization rate of the broadband spectrum, it is also necessary to estimate the DOA of each information source. The sampling frequency of general spectrum sensing technology and DOA estimation algorithm is based on the Nyquist rate. In the problem of wideband spectrum sensing, the sensed signal usually has a large dynamic range in the frequency domain, which puts forward higher requirements on the sampling rate of the ADC (analog-digital converter). The use of a high-speed ADC will result in large power consumption and economic costs, and will form a large amount of sampled data, which will cause trouble for storage and subsequent processing. Therefore, it becomes particularly critical to design a sub-Nyquist rate-based sampling framework to realize joint wideband spectrum sensing and DOA estimation.

For the broadband spectrum sensing problem, the existing methods based on sub-Nyquist sampling technology take advantage of the sparsity of the spectrum and use the compressed sensing method to reconstruct the original signal spectrum, but these methods cannot simultaneously complete the signal DOA estimation.

At present, there are only two types of joint broadband spectrum sensing and DOA estimation schemes based on sub-Nyquist sampling technology, and they use different forms of antenna arrays. The first one was proposed by C.-M.S.See et al. Under its sampling framework, the signal received by each antenna is divided into two channels, and the ADC is used for sub-Nyquist sampling, and one of them needs to be accurately delay. In this sampling framework, the number of ADCs is twice the number of antennas, which increases the cost of hardware implementation. And the delay on each antenna needs to be consistent, but accurate delay is difficult to achieve in reality. The second method was proposed by the team of Y.C.Eldar et al. It is based on the modulated wideband converter (MWC) method, which uses an L-shaped antenna array, and uses the same periodic pseudo-random sequence after each antenna The code is multiplied by the received signal, and then sampled by the ADC after passing through a low-pass filter. This method only considers the reconstruction of the original signal, and the MWC-based system itself is not easy to implement. Considering that only the spectrum occupancy is concerned in the actual broadband spectrum sensing, in the present invention, we do not consider the reconstruction of the original signal, but the reconstruction of the power spectrum of the original signal. We propose a new sub-Nyquist sampling architecture, which is based on ULA (uniform linear array), has relatively simple hardware complexity, and has low requirements for delay accuracy. Using the data obtained by sampling under this architecture, we can model the problem as a tensor decomposition problem, and use CP (CANDECOMP/PARAFAC) decomposition to obtain the corresponding three factor matrices, in which the signal can be efficiently estimated Power spectrum, carrier frequency and DOA.

Contents of the invention

The purpose of the present invention is to design a sub-Nyquist rate sampling architecture with low hardware implementation complexity, and propose a joint broadband spectrum sensing and DOA estimation method based on the architecture. Considering that only the spectrum occupancy is concerned in the actual wideband spectrum sensing, therefore, in the present invention, the reconstruction of the power spectrum of the original signal is considered instead of the reconstruction of the original signal. The present invention proposes a new sub-Nyquist sampling architecture, which is based on ULA (uniform linear array), has relatively simple hardware complexity, and has low requirements on delay accuracy. Using the data obtained by sampling under this framework, the problem can be modeled as a tensor decomposition problem, and the corresponding three factor matrices can be obtained by using CP (CANDECOMP/PARAFAC) decomposition, and the power of the signal can be efficiently estimated in the factor matrix spectrum, carrier frequency and DOA.

For the convenience of description, the system model is first explained:

The framework of the sub-Nyquist sampling based on the uniform array antenna proposed by the present invention is shown in FIG. 1 . In this framework, each antenna channel consists of only one delay channel and one ADC. The signal received by each antenna is sampled at the sub-Nyquist rate after a preset time delay. Compared with other sampling frameworks, the framework proposed by the present invention does not need to divide the signal received by the antenna into multiple channels, so the number of ADCs required is equal to the number of antennas. In addition, the time delay of different antennas can be set at will. Joint wideband spectrum sensing and DOA estimation can be performed accurately only if the time delay satisfies a very broad condition. In comparison, the framework proposed by C.-M.S.See et al. requires accurate time delay, which is difficult to achieve in practice, but under the framework of the present invention, it is only necessary to measure the actual time delay, and this The time-delay data that measure is used in the recovery algorithm that the present invention proposes, and this has reflected the practicability of this invention; In the frame that Y.C.Eldar et al. propose, need receive signal and a periodic pseudo-random sequence code multiplication, through Sampling is performed after a low-pass filter. In the framework proposed by the present invention, the signal is sampled after a simple delay, and it can be clearly seen that the framework has relatively low hardware complexity and is easy to implement.

The specific signal model is as follows:

Suppose there are K uncorrelated far-field narrowband generalized stationary signals s(t) received by N antennas, where s(t) is expressed as: s _k (t) and Represent the complex baseband signal and carrier frequency of the kth source, respectively.

The distance d between the two antennas satisfies d<C/f _nyq , where f _nyq represents the Nyquist sampling frequency, and C is the speed of light. On the nth antenna, the signal is delayed by a preset delay factor Δ _n , where the delay of Δ _n can be set arbitrarily, as long as there are several n ₀ such that Then it is sampled by a low-speed analog-to-digital converter, and the sampling rate f _s is greater than or equal to the maximum bandwidth of the signal, that is: f _s ≥ B. Therefore, the sampling signal of the nth antenna can be expressed as:

Among them, ω _n (t) represents the additive white Gaussian noise with zero mean and variance σ2 on the nth antenna, τ ^k represents the time delay of the _kth source between two adjacent antennas and takes the value depends on its angle of arrival θ _k , and thus has the following form: This approximation holds because of the narrowband assumption for each source.

Define the indicative function δ(x) as: Therefore, the cross-correlation function between the mth and nth antennas can be expressed as: in, is the autocorrelation function of the kth source, represents the autocorrelation function of additive noise, and Because both signal and noise are broadly stationary, the autocorrelation function depends on the difference between _t1 and _t2 , each time interval being an integer multiple of the sampling period _Ts . For simplicity of expression, define:

Therefore, the cross-correlation function between the mth and nth antennas can be expressed as a discrete form: Wherein, l=-L,...,L, m=1,...,N, n=1,...,N.

For each time interval l, a cross-correlation matrix R ^x (l) can be constructed, where the m and n root elements are given by give. Likewise, it can be verified in,

Because the cross-correlation matrix Therefore, it is natural to express this cross-correlation matrix as a third-order tensor, namely: in, represents the outer product, The (l,m,n)th element is given by given, and

definition:

A joint broadband spectrum sensing and angle of arrival estimation method, the specific steps are as follows:

S1. Carry out CP decomposition, specifically:

If there are K uncorrelated far-field narrowband generalized stationary signals, that is, the number of sources is K, then:

Step A1, optimization problem in, Indicates the Frobenius norm;

Step A2, using variables replace get a new optimized in,

Step A3, solving the new optimization described in S12 by alternating least squares Alternating least squares solves this optimization problem by alternately updating one of the factor matrices while fixing the other two, namely: in, Represent tensor The n-mode expanded form of ;

If the number of sources is unknown, the order and factor matrix can be estimated simultaneously by CP decomposition technique, namely:

Step B1, in, Represents an overestimation of CP rank, μ is a regularization parameter to control low rank and data fitting error,

The optimization of step B2 and step B1 is solved using an alternating least squares process, namely:

S2. Joint estimation of wideband spectrum sensing and angle of arrival, namely:

S21. After decomposing, the autocorrelation function of the original signal is obtained and the matrix A containing the carrier frequency and angle of arrival, because there are arrangement and amplitude ambiguities in the CP decomposition, the estimated factor matrix The relationship with the matrix A of the true angle of arrival can be expressed as: Among them, {Λ ₁ , Λ ₂ , Λ ₃ } are unknown non-singular diagonal matrices satisfying Λ ₁ Λ ₂ Λ ₃ =I, Π is an unknown and negligible permutation matrix, E ₁ , E ₂ , E ₃ respectively Indicates the estimation errors of the three estimated factor matrices;

S22, because Each column of has unit norm, then the amplitude ambiguity can be estimated and eliminated, so the S21 can be written as: in, are unknown non-singular diagonal matrices whose diagonal elements lie on the unit circle;

S23. The kth column of A is characterized by the arrival angle and carrier frequency of the kth source, so the estimated with to estimate the carrier frequency and angle of arrival, The kth column of said, will written as: in, is an unknown parameter;

S24, represent the angle of complex number z with arg(z), and arg(z)∈[0,2π), therefore Among them, mod(a,b) represents the modulo operation;

S25. For For mod operation, there are: in, express The nth element of ;

S26. Let D _p represents the difference matrix, defined as: In order to recover ω _k , the following two-stage difference operation is performed: It is easy to verify, with The elements are: The carrier frequency information ω _k is extracted, and through the delay factor {Δ _n }, the previous conditions are satisfied, so ω _k can be simply estimated: Among them, n ₀ means satisfying index of,

S27. Will Bringing back the first formula in the above formula, we can get the estimate of τ _k : get After that, bring back to get an estimate of the angle of arrival;

S28. Restoring the power spectrum: in, The power spectrum of the kth source is expressed as The Fourier transform of Denote Autocorrelation Sequence by S _k (ω) The discrete Fourier transform of According to the sampling law, and S _k (ω) have the following relationship: Since f _s ≥ B, and with prior knowledge of the carrier frequency ω _k , the power spectrum reverts to: given the estimated factor matrix autocorrelation sequence The discrete Fourier transform of can be approximated as:

The beneficial effects of the present invention are:

An easy-to-implement sub-Nyquist sampling framework is proposed. Using the sampled data under this framework, the problem is modeled as a tensor decomposition problem, and the factor matrix obtained by CP decomposition is then completed for broadband spectrum sensing and estimation. Compared with other algorithms, the structure of this scheme is simpler and easier to implement.

Description of drawings

Figure 1 is a sampling framework diagram of wideband spectrum sensing and angle of arrival joint estimation based on sub-Nyquist sampling.

Figure 2 shows the reconstruction results of the carrier frequency, angle of arrival and power spectrum of three signals with non-overlapping power spectrums.

Figure 3 shows the reconstruction results of the carrier frequency, angle of arrival and power spectrum of two power spectrum overlapping signals.

Fig. 4 is the relationship between carrier frequency and arrival angle estimation performance and the sampling number of each antenna, SNR=5dB.

Figure 5 shows the relationship between carrier frequency and arrival angle estimation performance and the sampling number of each antenna, SNR=15dB.

Fig. 6 is the relationship between carrier frequency and angle of arrival estimation performance and signal-to-noise ratio SNR.

detailed description

The present invention will be described below in conjunction with the accompanying drawings.

The present invention is implemented for joint broadband spectrum sensing and DOA estimation,

The object of the present invention is achieved through the following steps:

The first step: CP decomposition

The number K of sources is generally known or can be estimated as prior information. Therefore, the CP decomposition problem can be solved by solving the following optimization problem:

in · _F represents the Frobenius norm.

use a new variable replace This results in a new optimization: in,

This optimization can be efficiently solved by alternating least squares, which solves this optimization problem by alternately updating one of the factor matrices while fixing the other two, namely:

in, Represent tensor The n-module expanded form of .

If the number of sources is unknown, the order and factor matrix can be estimated simultaneously by a more complex CP decomposition technique. which is: in, Represents an overestimation of CP rank, μ is a regularization parameter to control low rank and data fitting error, The optimization of the above formula can also be solved by using the alternating least squares process, namely:

Step 2: Wideband Spectrum Sensing and Angle of Arrival Joint Estimation

After decomposition, the autocorrelation function of the original signal is obtained and a matrix containing carrier frequencies and angles of arrival Because of the permutation and magnitude ambiguities in the CP decomposition, the estimated factor matrix The relationship with the real factor matrix can be expressed as: Among them, {Λ ₁ , Λ ₂ , Λ ₃ } is an unknown non-singular diagonal matrix satisfying Λ ₁ Λ ₂ Λ ₃ =I, and Π is an unknown permutation matrix. E ₁ , E ₂ , E ₃ represent the estimation errors of the three estimated factor matrices respectively. The permutation matrix Π can be ignored since it is the same for the three factor matrices. because Each column of has unit norm, then the amplitude ambiguity can be estimated and eliminated, so the above formula is written as: in, are unknown nonsingular diagonal matrices whose diagonal elements lie on the unit circle.

The kth column of A is characterized by the arrival angle and carrier frequency of the kth source. Therefore, it can be estimated by with to estimate the carrier frequency and angle of arrival. The kth column of said, will written as: in, is an unknown parameter.

Denote by arg(z) the angle of the complex number z, and arg(z)∈[0,2π), Therefore, there are Among them, mod(a,b) represents the modulo operation, and returns the remainder of a divided by b.

for For mod operation, there are in, express The nth element of .

let D _p represents the difference matrix, defined as:

In order to recover ω _k , the following two-stage difference operation is performed:

It is easy to verify, with The elements are:

From the second formula of the above formula, it can be seen that after two stages of differential operations, the carrier frequency information ω _k is extracted. By properly designing the delay factor {Δ _n }, the previous required conditions are satisfied, so ω _k can be simply estimated as: Among them, n ₀ means satisfying index of.

Will Bringing back the first formula in the above formula, we can get the estimate of τ _k : get After that, bring back to An estimate of the angle of arrival can be obtained.

Now discuss the restoration of the power spectrum: in, Can be any real number. The power spectrum of the kth source can be expressed as The Fourier transform of

Denote Autocorrelation Sequence by S _k (ω) The discrete Fourier transform of

According to the sampling law, and S _k (ω) have the following relationship Since f _s ≥ B, and with prior knowledge of the carrier frequency ω _k , the power spectrum can be perfectly reverted to:

given the estimated factor matrix autocorrelation sequence The discrete Fourier transform of can be approximated as:

After the above steps, the estimation of the signal carrier frequency, angle of arrival and power spectrum is completed.

The following will verify the performance of the algorithm through a series of experiments.

Mean square errors (mean square errors, MSEs for short) and normalized mean square errors (NMSE for short) are used as the measurement indexes of the angle of arrival and the performance of the estimated carrier frequency. The MSE and NMSE in the simulation are defined as:

In the experiment, set f _nyq =1 GHz. The distance d between the two antennas is fixed at d=0.8×C/f _nyq . For simplicity, the delay setting of the receiving antenna is: The signal-to-noise ratio is defined as:

Experiment 1: Three uncorrelated, generalized stationary signals, the carrier frequencies are

f ₁ ＝152MHz, f ₂ ＝323MHz, f ₃ ＝432MHz, the bandwidths are

B ₁ =20MHz, B ₂ =20MHz, B ₃ =15MHz, and the arrival angles are θ ₁ =2.051, θ ₂ =1.447, θ ₃ =0.361. The number of antennas N=8. The sampling number of each antenna is N _s =10 ⁵ . Signal-to-noise ratio SNR=5dB. The sampling frequency is 28MHz.

Figure 2(a) is the comparison between the estimated carrier frequency and angle of arrival and the real carrier frequency and angle of arrival. Figure 2(b) is the power spectrum of the original signal, and Figure 2(c) is the reconstructed power spectrum. From Figure 2(c), the bandwidth occupied by the signal can be clearly seen. From Fig. 2 we can see that even though the signal-to-noise ratio is very low and a very low sampling frequency (slightly greater than the maximum bandwidth) is used, the invention can still accurately estimate the carrier frequency, angle of arrival and power spectrum of the original signal.

Experiment 2: Two irrelevant, generalized stationary signals, the carrier frequencies are f ₁ =151.36MHz, f ₂ =161.36MHz, the bandwidths are B ₁ =20MHz, B ₂ =10MHz, and the arrival angles are θ ₁ =2.064 , θ ₂ =0.968. The number of antennas N=8. The sampling number of each antenna is N _s =10 ⁵ . The signal-to-noise ratio SNR=20dB, and the sampling frequency is f _s =28MHz. (a) and (c) in Fig. 3 show the effect of carrier frequency, DOA and spectrum reconstruction with partially overlapping spectrum. This experiment illustrates that our invention can be used not only for wideband spectrum sensing, but also for blind separation of power spectra of signals with partially overlapping power spectra.

Experiment 3: Two irrelevant, generalized stationary signals, the carrier frequencies are f ₁ =152MHz, f ₂ =437MHz, the bandwidths are B ₁ =126KHz, B ₂ =63KHz, and the arrival angles are θ ₁ =π/4 , θ ₂ =π/3. In the experiments shown in Fig. 4 and Fig. 5, the number of antennas is set to N=8, and the signal-to-noise ratio (SNR) is 5dB and 15dB respectively, and then the relationship between the restoration effect and the sampling number N _s of each antenna is investigated. It can be seen that even with very few samples, the carrier frequency and angle of arrival can be accurately estimated, which means that the requirements for the number of data sampling points and response time can be further reduced. In the experiment shown in Figure 6, the number of antennas is set to N=8, the number of samples per antenna is N _s =300, and then the restoration effect is investigated under different SNR conditions. It can be seen that the SNR=15dB When , the parameters of the signal can be accurately estimated, which makes the invention have strong practicability.

To sum up, in the present invention, a new sub-Nyquist sampling framework is first proposed, and then a joint broadband spectrum sensing and DOA estimation method is proposed under this framework. By autocorrelating the data sampled between different antennas and constructing a tensor, and then performing CP decomposition on the tensor, a factor matrix with autocorrelation function, carrier frequency and DOA as parameters can be obtained, so as to realize wideband Spectrum sensing of the signal simultaneously estimates the DOA. At the same time, the architecture implemented by the algorithm is simple, and the requirements for delay are very broad, which can greatly reduce the hardware cost. In addition, the accurate estimation of signal parameters can also be realized under extremely low sampling frequency, low signal-to-noise ratio and few sampling samples, which shows the real-time and practicability of the algorithm.

Claims (1)

1. A method for combined broadband spectrum sensing and arrival angle estimation is characterized by comprising the following specific steps:

s1, performing CP decomposition, specifically:

if there are K uncorrelated far-field narrow-band generalized stationary signals, i.e., the number of sources is K, then:

step A1, optimization problemWherein,||·||_Frepresents the Frobenius norm;

step A2, utilizing variablesInstead of the formerObtain a new optimizationWherein,

step A3, solving the New optimization of S12 by alternating least squaresThe alternating least squares method solves this optimization problem by alternately updating one of the factor matrices while fixing the other two factor matrices, namely:wherein,tensor of representationN-mode expanded form of (a);

if the number of the information sources is unknown, estimating the order and the factor matrix simultaneously by a CP decomposition technology, namely:

step B1,Wherein,representing an over-estimation of CP rank, μ is a regularization parameter to control low rank and data fitting errors,

the optimization of step B2, step B1 is solved by an alternating least squares process, namely:

s2, jointly estimating the broadband spectrum sensing and the arrival angle, namely:

s21, obtaining the autocorrelation function of the original signal after decompositionAnd a matrix A containing carrier frequency and arrival angle, because of permutation and amplitude ambiguity in CP decomposition, the estimated factor matrixThe relationship to the matrix a of true angles of arrival can be expressed as:wherein, Λ₁,Λ₂,Λ₃The non-singular diagonal matrix, which is unknown, satisfies Λ₁Λ₂Λ₃I, n is an unknown, negligible permutation matrix, E₁,E₂,E₃Respectively representing the estimation errors of the three estimation factor matrixes;

s22 becauseHas a unit norm, the amplitude ambiguity can be estimated and eliminated, and the result is S21Can be written as:wherein,are unknown nonsingular diagonal matrices whose diagonal elements lie on a unit circle;

the kth column of S23, A is characterized by the angle of arrival and carrier frequency of the kth source, and thus can be estimatedAndto estimate the carrier frequency and the angle of arrival,for the k-th column ofShow thatWriting into:wherein,is an unknown parameter;

s24, representing the angle of complex number z by arg (z)Degrees, and arg (z) ∈ [0,2 π),thus, it is possible to provideWherein mod (a, b) represents a modulo operation;

s25, forThe mod operation is performed with:

wherein,to representThe nth element of (1);

s26, letD_pRepresents a difference matrix defined as:to recover omega_kThe following two differential operations are performed:it is easy to verify that the information is stored in the memory,andthe elements of (A) are respectively:carrier frequency information omega_kIs extracted by a delay factor [ delta ]_nThe previously required condition is satisfied, thus ω_kCan be simply estimated:wherein n is₀Represents satisfactionThe index of (a) is determined,

s27, mixingBack into the first of the above equations, the pair τ is obtained_kEstimation of (2):to obtainThen brought back toObtaining an estimate of the angle of arrival;

s28, restoring the power spectrum:wherein,the power spectrum of the kth source is represented asFourier transform of, i.e.With S_k(ω) denotes the autocorrelation sequenceDiscrete Fourier transform of, i.e.According to the law of sampling,and S_k(ω) has the following relationship:because f is_sNot less than B and carrier frequency omega_kA priori knowledge of (a) power spectrumThe recovery is:given an estimated factor matrixAuto-correlation sequenceThe discrete fourier transform of (a) can be approximated as: