Analysing the effects of constraints and inter-signal coherence on the MUSIC algorithm

We perform an analysis of constrained and unconstrained MUSIC demonstrating that (asymptotically) improved subspace estimates always result from the use of constraints, and (asymptotically) the variance of constrained MUSIC is less than that of unconstrained MUSIC under either high coherence, large numbers of sensors, or high SNR conditions. As part of this analysis, we study the effects of coherence on MUSIC and derive best/worst case coherences in terms of the variance of MUSIC. We also demonstrate that those conditions where the variance of MUSIC is predicted to be less than that of constrained MUSIC generally correspond to conditions where MUSIC is in breakdown (and constrained MUSIC is not). So, unconstrained MUSIC does not achieve its predicted advantage in those cases