  This paper investigates the combined role of transmit waveforms and (sparse)
sensor array geometries in active sensing multiple-input multiple-output (MIMO)
systems. Specifically, we consider the fundamental identifiability problem of
uniquely recovering the unknown scatterer angles and coefficients from
noiseless spatio-temporal measurements. Assuming a sparse scene,
identifiability is determined by the Kruskal rank of a highly structured
sensing matrix, which depends on both the transmitted waveforms and the array
configuration. We derive necessary and sufficient conditions that the array
geometry and transmit waveforms need to satisfy for the Kruskal rank -- and
hence identifiability -- to be maximized. Moreover, we propose waveform designs
that maximize identifiability for common array configurations. We also provide
novel insights on the interaction between the waveforms and array geometry. A
key observation is that waveforms should be matched to the pattern of redundant
transmit-receive sensor pairs. Redundant array configurations are commonly
employed to increase noise resilience, robustify against sensor failures, and
improve beamforming capabilities. Our analysis also clearly shows that a
redundant array is capable of achieving its maximum identifiability using fewer
linearly independent waveforms than transmitters. This has the benefit of
lowering hardware costs and transmission time. We illustrate our findings using
multiple examples with unit-modulus waveforms, which are often preferred in
practice.
