Abstmct-In this paper a new method for obtaining a quantitative estimate of an acoustic field consisting of a set of discrete sources and background noise is described. The method is based on the L1 (least absolute values) norm solution to an underdetermined system of linear equations defining the Fourier transform of the signal series. Implementations of the method with either equality or inequality constraints are presented and discussed. The much faster and more compact equality constraint version with a provision for modeling the noise field is recommended in practice. Experience with real data has shown the necessity of correcting for an observed Gaussian decay on the covariances. A simple means of estimating this effect and taking it into account in the signal estimation procedure is discussed, and the implications of this effect in high-resolution beamforming are considered. The effectiveness and versatility of the L1 method indicate that it has a useful role in high-resolution signal estimation.

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Previous communications systems research has demonstrated that the Spectrally Modulated, Spectrally Encoded (SMSE) framework is well suited to SDR platforms and operation in both contiguous and non-contiguous spectrum given its ability to generate a wide variety of multicarrier waveforms such as OFDM, NC-OFDM, MC-CDMA, NC-MC-CDMA, CI/MC-CDMA, NCCI/MC-CDMA, and TDCS. In this paper, SMSE waveforms are extended for use in sparse frequency radar systems. Sparse frequency radar can be capable of dynamically sensing available spectrum, and tailoring the transmitted waveforms to suit the instantaneous RF environment conditions, simultaneously transmitting energy in multiple noncontiguous spectrum bands. Conventional radar performance metrics are reviewed, and a new metric is introduced which specifically addresses performance of noncontiguous spectrum waveforms through comparison to contiguous spectrum waveforms. Through simulation, various examples are shown to illustrate and characterize the impairments that are introduced in processing these classes of non-contiguous spectrum waveform returns, specifically the generation of large range sidelobes.I.