The coexistence between radar and communications systems has received considerable attention from the research community in the past years. In this paper, a radar waveform design method for target parameter estimation is proposed. Target time delay parameter is used as an example. The case where the two systems are not co-located is considered. Radar waveform optimization is performed using statistical criteria associated with estimation performance, namely Fisher Information (FI) and Cramer-Rao Bound (CRB). Expressions for FI and CRB are analytically derived. Optimization of waveforms is performed by imposing constraints on the total transmitted radar power, constraints on the interference caused to the communications system, as well as co...