This paper investigates threshold-constrained joint waveform optimization for an integrated sensing and communication (ISAC) system. Unlike existing studies, we employ mutual information (MI) and sum rate (SR) as sensing and communication metrics, respectively, and optimize the waveform under constraints to both metrics simultaneously. This provides significant flexibility in meeting system performance. We formulate three different optimization problems that constrain the radar performance only, the communication performance only, and the ISAC performance, respectively. New techniques are developed to solve the original problems, which are NP-hard and cannot be directly solved by conventional semi-definite programming (SDP) techniques. Novel gradient descent methods are developed to solve the first two problems. For the third non-convex optimization problem, we transform it into a convex problem and solve it via convex toolboxes. We also disclose the connections between three optimizations using numerical results. Finally, simulation results are provided and validate the proposed optimization solutions.
Keywords: integrated sensing and communication (ISAC); radar communications; threshold constraint; waveform optimization.