Communication-inspired sensing

Information theory, and particularly the mutual information (MI) has provided fundamental guidance for communications research. In, the MI was first applied to radar waveform design. However, the practical meaning of MI in the sensing context remains unclear. Recently, shows that under the white noise assumption, the water-filling scheme simultaneously maximizes the MI and minimizes the minimum MSE (MMSE). Such an equivalence disappears when the target parameter statistics are not perfectly known. To further the understanding of the practical meaning of MI and to establish a connection between MI and commonly adopted MSE measures for sensing, this paper takes a fresh look at the target estimation problem, by considering the general colored noise, incorporating the normalized MSE (NMSE), and establishing joint robust designs for both the transmitter (waveforms) and the receiver (estimator) under various target and noise uncertainty levels. Our results show that: i) the optimum waveform designs resulted from the MI, MMSE and NMSE criteria are all different; and ii) compared to MMSE, the NMSE-based designs share more similarities with the MI-based ones, especially when the target and noise statistics are not perfectly known.