Joint Antenna Selection and Covariance Matrix Optimization for ISAC Systems

Abstract

We consider an integrated sensing and communication (ISAC) system with a\nsingle communication user and multiple targets. For the communication\nfunctionality, the achievable rate is employed as the performance metric, while\nfor sensing, we focus on minimizing the mean squared error (MSE) between the\ndesigned beampattern and a desired one for tracking the targets. Towards this,\nand by assuming that there are fewer radiofrequency (RF) chains than antenna\nelements at the transmitter (Tx), we focus on the joint antenna selection (AS)\nand covariance matrix (CM) optimization at the Tx. This is a mixed-integer\noptimization problem, yet we demonstrate that it can be efficiently solved, in\npolynomial time, by combining convex optimization tools with dynamic\nprogramming (DP). By introducing an adjustable trade-off parameter, we\nformulate a joint objective function that captures both the communication and\nsensing metric. In this way, different ISAC solutions can be obtained,\nconsidering the trade-off among the two functionalities. It is shown that\nselecting the active antennas with our proposed method is superior than\nassuming a uniform Tx array with fixed antenna positions. Notably, by\nindividually considering the optimization of either the sensing or the\ncommunication system alone, our proposed algorithm outperforms the literature\nproposals, by incurring only a small increase in complexity.\n