Compact Cramer-Rao bound expressions on directional covariance for DF of sources with unknown constant polarizations

The Cramer-Rao Bound B_C on directional covariance routinely is used as a yardstick for assessing the performance of candidate direction-finding (DF) algorithms. Stoica and Nehorai (1989, 1990) and Yau and Bresler (see ibid., vol.40, no.5,p.1226, 1992) introduced compact formulae for B_C applicable to DF scenarios in which sources transmit signals having known polarizations. These formulae have proven quite useful in that they facilitate identification of performance limitations that otherwise would be difficult or impossible to obtain. This article presents compact formulae for B_C for DF scenarios in which n uncorrelated sources transmit signals having constant but unknown polarizations. Also it is shown that these formulae elucidate achievable DF performance for scenarios involving partially correlated sources