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In this paper, a new signal processing framework is proposed, in which thearray time samples are represented in DOA-frequency domain through a singlestage problem. It is shown that concatenated array data is well represented ina $\mathbf{G}$ dictionary atoms space, where $\mathbf{G}$ columns correspond topixels in the DOA-frequency image. We present two approaches for the$\mathbf{G}$ formation and compare the benefits and disadvantages of them. Amutual coherence guaranteed $\mathbf{G}$ manipulation technique is alsoproposed. Furthermore, unlike most of the existing methods, the proposedproblem is reversible into the time domain, therefore, source recovery from theresulted DOA-frequency image is possible. The proposed representation inDOA-frequency domain can be simply transformed into a group sparse problem, inthe case of non-multitone sources in a given bandwidth. Therefore, it can alsobe utilized as an effective wideband DOA estimator. In the simulation part, twoscenarios of multitone sources with unknown frequency and DOA locations andnon-multitone wideband sources with assumed frequency region are examined. Inmultitone scenario, sparse solvers yield more accurate DOA-frequencyrepresentation compared to some noncoherent approaches. At the latter scenario,the proposed method with group sparse solver outperforms some existing widebandDOA estimators in low SNR regime. In addition, sources' recovery simultaneouswith DOA estimation shows significant improvement compared to the conventionaldelay and sum beamformer and without prerequisites required in sophisticatedwideband beamformers.

Single Stage DOA-Frequency Representation of the Array Data with Source Reconstruction Capability