Beam Focusing for Near-Field Integrated Sensing and Communications With Hybrid Analog/Digital Architecture

In this paper, we redesign the hybrid analog/digital precoding scheme to form focused beams at specific spatial locations for near-field <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">integrated sensing and communications</i> (ISAC) systems. Specifically, we derive the near-field <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Cramér-Rao bound</i> (CRB) for joint distance and angle sensing with arbitrary signal coherence matrices. Unlike previous optimization strategies that either maximize the communication rate or maximize the sensing performance, we aim to maximize the achievable communication rate under unit sensing error. The optimization problem is modeled to maximize the ratio of the sum rate to the CRB by jointly optimizing the analog and digital precoders. Since it is difficult to solve the problem with complicated non-convex fractional program, we first perform an equivalent reformulation to remove the fractional constraint. Then, the fully-digital precoder is obtained by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">successive convex approximation</i> (SCA). Finally, a low-complexity hybrid precoding algorithm based on alternate optimization is proposed to divide the fullydigital precoder into analog and digital precoders. Simulation results show the effectiveness of the proposed algorithm and the performance of the proposed beam focusing is superior to beam steering in the near-field.