Constant modulus constrained codebook synthesis for mmWave full-duplex ISAC devices

Self-interference (SI) is a major obstacle to the practical realization of fully full-duplex (FD) systems. This challenge becomes even more critical in FD integrated sensing and communication (ISAC) devices where the sensing signal is of several orders of magnitude weaker than the SI. In this work, we present a joint TX-RX constant modulus (CM) constrained codebook design method for SI suppression in millimeter wave (mmWave) FD ISAC terminal devices. First, we formulate a signal-to-interference-and-noise ratio (SINR) maximization problem aimed at suppressing near-field SI while maintaining the beamforming gain in a far-field sensing direction. The formulation considers the CM constraint of both the receiver (RX) and transmitter (TX) analog phase shifters, as well as a TX beamforming gain requirement in the specified communication direction. When ignoring the constraints, we derive the effective minimum variance distortionless response (MVDR) method as an upper bound of the formulated SINR maximization problem. When considering the constraints, the formulated problem is solved through an alternating optimization framework that jointly optimizes the TX and RX beams by leveraging the augmented Lagrangian method (ALM) and constant modulus-gradient descent (CM-GD). Simulations have been conducted for realistic TX/RX antenna array placements for the cellular terminal devices. The simulation results show that the proposed joint TX-RX codebook synthesis method can sufficiently exploit the mmWave phase shifters on both TX and RX sides for SI suppression, and that the resulting SINRs across all sensing directions are close to the derived effective MVDR upper bound, which is neither constrained by the CM property nor considers the communication constraint.