MMSE Adaptive Waveform Design for Active Sensing With Applications to MIMO Radar

Abstract

Minimizing the expected mean squared error is one of the fundamental metrics applied to adaptive waveform design for active sensing. Previously, only cost functions corresponding to a lower bound on the expected mean squared error have been expressed for optimization. In this paper, we express an exact cost function to optimize for minimum mean squared error adaptive waveform design (MMSE-AWD). This is expressed in a general form which can be applied to nonlinear systems. Additionally, we provide a general example for how this method of MMSE-AWD can be applied to a system that estimates the state using a particle filter (PF). We make the case that there is a compelling reason to choose to use the PF (as opposed to alternatives such as the unscented Kalman filter and extended Kalman filter), as our MMSE-AWD implementation can reuse the particles and particle weightings from the PF, simplifying the overall computation. Finally, we provide a numerical example, based on a simplified multiple-input-multiple-output radar system, which demonstrates that our MMSE-AWD method outperforms a simple nonadaptive radar, whose beam-pattern has a uniform angular spread, and also an existing approximate MMSE-AWD method.