Trade-Off Between Positioning and Communication for Millimeter Wave Systems With Ziv-Zakai Bound

In this paper, we investigate the trade-off between positioning and communication for an integrated positioning and communication (IPAC) millimeter wave system. First, in terms of the positioning in the IPAC system, the Cramér-Rao bound (CRB) is commonly used as a performance metric. Unfortunately, the CRB is only tight in a certain region for the high signal-to-noise ratio (SNR). To compensate for this deficiency, we derive the Ziv-Zakai bound (ZZB) for the IPAC system by exploiting the a priori delay information extracted from both the time delay parameter and the channel amplitude attenuation. Further, we derive the expected CRB (ECRB) and the weighted CRB (WCRB) of the system for comparisons. Second, we analyze the trade-off between positioning and communication for this IPAC system based on the derived ZZB. Specifically, we aim to optimize the power allocation to maximize the achievable data rate subject to the ZZB and total transmit power constraints. Numerical results show that the ZZB provides a tighter and more reasonable bound for the minimum mean square error (MMSE) estimator over the wide range of SNRs compared to the ECRB and WCRB. Moreover, the trade-off between positioning and communication is revealed via changing critical parameters by simulations.