  Radar sensing will be integrated into the 6G communication system to support
various applications. In this integrated sensing and communication system, a
radar target may also be a communication channel scatterer. In this case, the
radar and communication channels exhibit certain joint burst sparsity. We
propose a two-stage joint pilot optimization, target detection and channel
estimation scheme to exploit such joint burst sparsity and pilot beamforming
gain to enhance detection/estimation performance. In Stage 1, the base station
(BS) sends downlink pilots (DP) for initial target search, and the user sends
uplink pilots (UP) for channel estimation. Then the BS performs joint target
detection and channel estimation based on the reflected DP and received UP
signals. In Stage 2, the BS exploits the prior information obtained in Stage 1
to optimize the DP signal to achieve beamforming gain and further refine the
performance. A Turbo Sparse Bayesian inference algorithm is proposed for joint
target detection and channel estimation in both stages. The pilot optimization
problem in Stage 2 is a semi-definite programming with rank-1 constraints. By
replacing the rank-1 constraint with a tight and smooth approximation, we
propose an efficient pilot optimization algorithm based on the
majorization-minimization method. Simulations verify the advantages of the
proposed scheme.
