CRBS for the Joint Estimation of TOA and AOA in Wideband MISO and MIMO Systems: Comparison with SISO and SIMO Systems

We derive the CRBs (Cramer Rao bound) for the joint estimation of the TOA (time of arrival) and the AOA (angle of arrival) in wideband (WB) MISO (multiple input single output) and MIMO (multiple input multiple output) systems. We consider both cases of orthogonal and non-orthogonal transmitted signals. We compare the CRBs obtained in SISO (single input single output), SIMO (single input multiple output), MISO and MIMO systems under the assumption that the total transmitted energy is the same for all systems. We show that SIMO and MIMO are equivalent for TOA estimation, and MISO and SISO as well when the transmitted signals are orthogonal. For non-orthogonal signals, MIMO is better than SIMO, and MISO is better than SISO when the received signals are constructive. For AOA estimation, we show that MIMO is better than SIMO and SIMO is better than MISO when the transmitted signals are orthogonal. For non-orthogonal signals, MIMO is much better when the received signals are constructive. The CRBs obtained for non- orthogonal signals are very sensitive to the angle. Numerical results obtained in a typical scenario are provided.