Expected likelihood support for deterministic maximum likelihood DOA estimation

• The ability to assess solution quality without full likelihood maximization is presented.
• This “expected likelihood” is extended from stochastic to deterministic estimation.
• Results from random matrix theory are employed to validate the performance predictions.
• Application to improvement of MUSIC direction-of-arrival performance is shown.

In this paper, a solution quality assessment method referred to as the “expected likelihood” (EL) approach, previously introduced for the stochastic (unconditional) Gaussian model, is extended over the deterministic (conditional) Gaussian model. This model is applied for arbitrary temporally correlated (narrowband) waveforms, emitted by point sources impinging upon an antenna array. Performance of direction of arrival (DOA) estimation is then examined.Unlike the stochastic model with independent training samples, the deterministic likelihood function is not always described by a scenario-invariant distribution for true DOA's (an essential requirement for expected likelihood). Modifications for deterministic likelihood functions are introduced and their utility in the EL framework is demonstrated by identifying “breakdown” in MUSIC performance.