On MIMO Detection Under Non-Gaussian Target Scattering

In this paper, we consider a multiple-input-multiple-output (MIMO) detection problem with
M
widely spaced transmit antennas and
L
widely spaced receive antennas, and we study the problem of designing the signal waveforms transmitted by each source node under non-Gaussian target scattering and temporally correlated Gaussian clutter. Two figures of merit are investigated for space-time code (STC) optimization under a semidefinite rank constraint: 1) the lower Chernoff bound (LCB) to the detection probability for fixed probability of false alarm, and 2) the mutual information (MI) between the observations available at the receive nodes and the “channel response” generated by a point-like target, assumed present tout court. Both receive and transmit power constraints are discussed. If the scattering distribution possesses some suitably defined properties of unitary invariance (see Section II-B), both MI-optimal and LCB-optimal STCs have a simple canonical structure: the same set of (clutter dependant) temporal codewords are employed at the transmit nodes, the only difference among the many solutions being the amount of power radiated by each antenna. Such a spatial power allocation critically depends upon the adopted figure of merit, the specified power constraint, and the underlying scattering model. Sufficient conditions to determine the optimal power allocation for all design criteria are provided. Asymptotic power distributions are also derived in the limit of vanishingly small and increasingly large signal-to-clutter ratios, proving that assuming Gaussian scattering at the design stage is a robust choice. A case study of relevant practical interest is examined in depth so as to compare the proposed design criteria and to assess the impact of signal non-Gaussianity on the system performances.