Comparison of the Bhattacharyya and Cramer-Rao lower bounds for the position estimation of an OFDM transmitter

We consider a comparison of the Bhattacharyya bound and the Cramer-Rao lower bound for the problem of mobile positioning. Since the Cramer-Rao lower bound is known to be optimistic, we investigate the improvement that may be obtained by computing the third and fifth order Bhattacharyya bounds as alternative benchmarks for performance. The analytical results derived are then applied to the problem of locating an ultrawideband OFDM transmitter in a line of sight environment. Our results show that the third order and fifth order Bhattacharyya bounds respectively offer a 1.9 dB and a 2.3 dB improvement over the CRLB over the range of SNRs that have been deemed feasible for the ultrawideband system.