A joint characterization of transmit/receive array geometries and transmit waveforms that minimize the single-target angle Cramér-Rao bound for a MIMO active-sensing system in white Gaussian noise. Key results: distinct array-waveform pairs can achieve the same CRB precisely because the design reduces to integer sequences with equal sums of squares (a Diophantine problem); under aperture and sensor-count constraints the CRB-minimizing receive geometry is unique while the transmit array is free; and this freedom yields a novel sparse array whose sum co-array is contiguous and nonredundant, benefiting the multi-target case.
This paper studies jointly optimal array geometry and transmit waveform design for active (MIMO radar-style) sensing, using the single-target angle Cramér-Rao lower bound (CRB) in white Gaussian nois…