Statistical analysis of Capon-Bartlett 2-D cross spectrum

An exact joint probability density function (PDF) (not approximate as in) is provided for the Capon power spectral estimate and the average output power of any other deterministic filter when based on the same data sample covariance matrix. The cross coherence/cosine (correlation coefficient) between the two filter weights determines the extent of statistical dependence. An exact PDF for a sample covariance based (SCB) estimate of this cross coherence is derived allowing complete point-level statistical characterization of the 2-D Capon-Bartlett cross spectrum introduced in. The exact bias and variance are computed for the cross spectrum showing asymptotic consistency and inviting a natural recursive refinement for reducing bias.