Jointly optimal array geometries and waveforms in active sensing: New insights into array design via the Cramér-Rao bound

This paper investigates jointly optimal array geometry and waveform designs for active sensing. Specifically, we focus on minimizing the Cram\'er-Rao lower bound (CRB) of the angle of a single target in white Gaussian noise. We first find that several array-waveform pairs can yield the same CRB by virtue of sequences with equal sums of squares, i.e., solutions to certain Diophantine equations. Furthermore, we show that under physical aperture and sensor number constraints, the CRB-minimizing receive array geometry is unique, whereas the transmit array can be chosen flexibly. We leverage this freedom to design a novel sparse array geometry that not only minimizes the single-target CRB given an optimal waveform, but also has a nonredundant and contiguous sum co-array, a desirable property when launching independent waveforms, with relevance also to the multi-target case.

Optimal Pilot Design for OTFS in Linear Time-Varying Channels

This paper investigates the positioning of the pilot symbols, as well as the power distribution between the pilot and the communication symbols in the OTFS modulation scheme. We analyze the pilot placements that minimize the mean squared error (MSE) in estimating the channel taps. In addition, we optimize the average channel capacity by adjusting the power balance. We show that this leads to a significant increase in average capacity. The results provide valuable guidance for designing the OTFS parameters to achieve maximum capacity. Numerical simulations are performed to validate the findings.