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This paper addresses the problem of direction-of-arrival (DOA) estimation of multiple wideband coherent chirp signals, and a new method is proposed. The new method is based on signal component analysis of the array output covariance, instead of the complicated time-frequency analysis used in previous literatures, and thus is more compact and effectively avoids possible signal energy loss during the hyper-processes. Moreover, the

Previous direction-of-arrival (DOA) estimation methods for wideband chirp signals are mostly based on the special time-frequency distribution of such signals. Ma and Goh separate the simultaneous chirp signals first according to their distinguishable auto- or cross-terms in the ambiguity function, and then use the secondary time-frequency data to estimate their directions [

This paper addresses the problem of DOA estimation of multiple wideband coherent chirp signals, which emerges due to various factors such as multi-path and echo signals [

Suppose that the chirp rate of the incident coherent signals is _{1}, _{2} and _{0}, respectively, the chirp period is _{2-}_{1}= _{1},…, _{K}_{1}(_{K}^{T}_{1},_{K}

When _{1},…,_{K}_{k,m}_{k}_{1} =0. Suppose that _{s}_{s}_{p,q}_{p,q}_{p,q}_{p,q}_{p,q}

^{2} “signal” components, including ^{2}−

As,
_{1,1}, thus we extract the 2nd to _{2,1}, …, _{M}_{,1}]^{T}_{1} can be expressed as follows:
_{1}= [ε_{2,1},…,ε_{M}_{,1}]^{T}_{1}(_{k}_{k}_{p}_{2}}_{p}_{=2,…},_{M}^{T}_{1}(_{k}_{k}_{1} is a noisy weighted sum of the atoms {_{1}(_{k}_{k}_{=1,…},_{K}_{1}, the signal directions can be determined. In this paper, we first form an overcomplete dictionary _{1=} {_{1}(_{θ}_{∈ Θ} on the possible signal direction set _{1} on _{1} under sparsity constraint to obtain the signal components. If the time delays of these multipath signals exist, we should first estimate the time delays following reference [

This sparse decomposition process can be implemented by solving the following convex optimization problem approximately [_{1} on the dictionary, and takes non-zero values of
_{1} and the observation model _{1}_{1}. The locations of the significant non-zero values in the energy distribution estimate (denoted by

In order to solve _{1}. The variance of perturbation of _{1} can be straightforwardly derived from

Thus the fitting error threshold in

In the above expression of Var(ε_{1}), _{m,m}

After calculating the fitting error threshold according to _{1}, thus estimating the source directions. Various methods can be used for the solution of

Suppose two coherent chirp signals impinge onto an 8-element ULA from directions of 10° and 20°, respectively, the central frequency of the two signals is 2.5 MHz with a bandwidth of 40% (the starting and ending frequencies are 2 MHz and 3 MHz accordingly). The initial phases of the two signals are chosen independently and uniformly between 0 and in each trial. The ULA is inter-spaced by half-wavelength of a 2.5 MHz sinusoid, and 512 snapshots are collected at 10 MHz during a chirp period.

As the two signals are completely overlapped in the time-frequency domain, the method in [

Firstly, suppose that the SNR of both signals is identical and varies from −10 dB to 20 dB, 1,000 trials are carried out at each SNR. Successful resolution is defined when the two most significant spectrum peaks are located near the true signal directions, and the biases are no larger than 3°. The resolution probabilities of the four methods at various SNR are given in

Then we fix the SNR of the first signal at 10 dB, and attenuate that of the second signal from 10 dB to 0 dB (

The technique of sparse representation to estimate the directions of simultaneous wideband coherent chirp signals is introduced in this paper. The covariance matrix, instead of the time-frequency distribution, is exploited in the new method, and the

This work was supported by the program for New Century Excellent Talents in University (NCET).

The authors declare no conflict of interest.

Resolution probabilities at varying SNR.

Resolution probabilities at varying SNR diversity.