The Explicit Analytic Cramer-rao Bound On Angle Estimation

The explicit analytic Cramer-Rao bounds on angle-of-arrival estimation performance are derived for one and two sources in free space. The results are general in that the array geometry, element types, and number of snapshots, K, are arbitrary. The derivation procedure consists of two steps: 1) obtaining the Fisher information matrix, /spl Gamma/; and 2) determining the requisite part of /spl Gamma//sub -1/. The first step is facilitated by use of a notationally compact form for /spl Gamma/ derived here for a general, time-varying, nonlinear model of complex vector observations. The second step, which appears quite formidable since /spl Gamma/ is 3K+2 by 3K+2 in the single-source case and 4K+2 by 4K+2 in the two-source case, is accomplished by use of a novel partitioned-matrix approach to bound determination. The resultant bounds are shown to agree with the results obtained by others for the special cases they consider, including the closely related problem of frequency estimation of sinusoids in noise.