Array Geometry-Invariant Space-Time Opportunistic Null-Space Communications

This work studies the impact of the array geometry on a space-time extension of a generalized class of null-space precoding format denoted as
$\pi $
-waveforms (Projection-Invariant waveforms), which exhibit subspace invariance and robustness to subspace leakage in the single-antenna case. In feedforward opportunistic communications, subspace leakage decreases the interference mitigation capability and the energy efficiency of conventional null-space precoding schemes. These effects are more notorious in multi-antenna scenarios, where miscalibrated sensors alter the array geometry. The study, which is carried out at both time-frequency non-asymptotic and asymptotic regimes, concludes that
$\pi $
-waveforms are independent of the array geometry, allowing their use in general unstructured or uncalibrated arrays. The array-geometry invariance is fundamental to enabling calibration-less coherent opportunistic communication.