Abstract
Most non-Gaussian signals in wireless communication array systems contain temporal correlation under a high sampling rate, which can offer more accurate direction of arrival (DOA) and frequency estimates and a larger identifiability. However, in practice, the estimation performance may severely degrade in coloured noise environments. To tackle this issue, we propose real-valued joint angle and frequency estimation (JAFE) algorithms for non-Gaussian signals using fourth-order cumulants. By exploiting the temporal correlation embedded in signals, a series of augmented cumulant matrices is constructed. For independent signals, the DOA and frequency estimates can be obtained, respectively, by leveraging a dual rotational invariance property. For coherent signals, the dual rotational invariance is constructed to estimate the generalized steering vectors, which associates the coherent signals into different groups. Then, the coherent signals in each group can be resolved by performing the forward-backward spatial smoothing. The proposed schemes not only improve the estimation accuracy, but also resolve many more signals than sensors. Besides, it is computationally efficient since it performs the estimation by the polynomial rooting in the real number field. Simulation results demonstrate the superiorities of the proposed estimator to its state-of-the-art counterparts on identifiability, estimation accuracy and robustness, especially for coherent signals.
Highlights
IntroductionSensor arrays have been used in radar, sonar, wireless communications, seismology, etc
Sensor arrays have been used in radar, sonar, wireless communications, seismology, etc.Joint direction of arrival (DOA) and frequency estimation of incident signals have been attracting considerable attention due to their application to various fields
The joint angle and frequency estimation of non-Gaussian signals in coloured noise is addressed in this paper, and cumulant-based estimation algorithms are developed for independent and coherent signals, respectively
Summary
Sensor arrays have been used in radar, sonar, wireless communications, seismology, etc. Multiresolution ESPRIT, referred to as MR-ESPRIT, has been developed to handle JAFE in different geometries, such as uniform linear arrays and uniform circular arrays, by Lemma et al [6], and they subsequently presented an intensive performance analysis of the MR-ESPRIT JAFE algorithm [7] These ESPRIT-based JAFE methods can provide satisfactory estimation performance, but require an additional pairing, which may fail to work at low signal-to-noise ratios (SNRs). In addition to ESPRIT-like approaches, Zhang et al cast the JAFE problem as a trilinear model and performed trilinear decomposition to obtain angle and frequency without any eigen-decomposition to covariance matrices or singular-value decomposition to observations [8]; Liu et al proposed a unitary JAFE algorithm, termed U-JAFE, in conjunction with the frame method and the Newton iteration method, resulting in improved computational efficiency and automatic parameter pairing [9]. The symbol Z( a : b, c : d) refers to a constructed submatrix by the entries from a to the bth row and c to the dth column of Z, and the symbol Z( a, b) denotes the entry in the ath row and the bth column of Z
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