Cross Coherence and Joint PDF of the Bartlett and Capon Power Spectral Estimates

The Bartlett algorithm results from a conventional (Fourier or beamforming) approach to power spectral estimation and the Capon algorithm results from an adaptive approach. Both algorithms make use of the data sample covariance matrix (SCM). The Bartlett algorithm relies directly on the SCM, while the Capon approach relies on the inverse of the SCM. Since both statistics depend on the same data, they are not independent in general. While the marginal distribution of each statistic is well-known, the joint dependence is unknown. This paper presents a complete statistical summary of the joint dependence of the Bartlett and Capon statistics, showing that the dependence is expressible via a 2 times 2 complex Wishart matrix where the coupling is determined by a single measure of coherence defined herein. Interestingly, this measure of coherence leads to a new two-dimensional algorithm capable of yielding better resolution than the Capon algorithm.