Signal subspace sphericity and inter-signal coherence-MUSIC induces inter-signal coherence

The role and importance of signal subspace sphericity are discussed. Using signal subspace arguments with the true correlation matrix, it is shown that MUSIC effectively induces intersignal coherence due to its requirement for subspace sphericity. It is also shown in the finite data case that some commonly used direction finding methods yield results identical to those of MUSIC if subspace sphericity is induced. It is demonstrated that sphericity induced coherence can be desirable. This is accomplished with an infinitely averaged example using spatial smoothing to reduce the coherence. However, reducing the sphericity induced coherence has a detrimental effect on resolution