The CRB-Rate Trade-off for JCAS: A Low-Complexity Beamforming Design

Joint communication and sensing (JCAS) systems aim to perform communication and radar duties simultaneously, through a single unified transmit waveform. They are expected to exploit mutually beneficial information between the JCAS functionalities through sharing hardware, spectrum and other network resources. In this paper, we consider a JCAS base station (BS) serving a single multi-antenna communication user with perfect channel state information (CSI), while simultaneously sensing an extended target without any prior knowledge. We formulate a beamforming optimisation problem to jointly max-imise the sum-rate at the communication user and the inverse Cramer-Rao bound (CRB) on the sensing target response matrix at the JCAS receiver under a total transmit power constraint. We are able to characterize the optimal beamforming direction in closed form, while the remaining scalar power allocation is solved numerically. We present a generalised low-complexity convex formulation of the JCAS beamforming optimisation and discuss it's validity for both, full rank and rank deficient beamformers. Numerical results indicate a performance gain of upto 37% in sum-rate at the same CRB with optimal antenna selection for the JCAS design compared to random selection. Further, the results illustrate JCAS functionality trade-offs and demonstrate flexibility in joint design for choosing the optimal CRB-rate pairs as a function of a CRB trade-off parameter.