Constrained Sensor System Resolves Closely Spaced Obscured Low-SNR Sources Using Virtual Beamforming

We present a high-resolution capability for systems constrained in the number of elements (measurements) due to size, weight, and power that operate in harsh signal-to-noise ratio (SNR) environments through virtual beamforming. The high resolution is created by applying a conventional beamformer to a virtual measurement data set. The virtual measurement data is made up of original measurements extended with vector extrapolated measurements. We derive the SNR of this new virtual system and show that, in the case of perfect extrapolation, we are within a constant of the true SNR (if we had that many sensor measurements). Simulations show the super-resolution capability of resolving the two closely spaced, equal-powered low-SNR sources, in the presence of a third closely spaced dominant source (15 dB larger signal power) with a limited number of measurements. In a second case, the virtual beamforming technique again resolves two low-SNR sources that are even closer while high-resolution techniques fall short due to the harsh environments. In both cases, the algorithm is shown to be robust in noise through Monte Carlo simulations. We provide the computational cost to achieve this high-resolution capability.