  Joint communication and radar sensing (JCAS) integrates communication and
radar/radio sensing into one system, sharing one transmitted signal. In this
paper, we investigate JCAS waveform optimization underlying communication
signals, where a base station detects radar targets and communicates with
mobile users simultaneously. We first develop individual novel waveform
optimization problems for communications and sensing, respectively. For
communications, we propose a novel lower bound of sum rate by integrating
multi-user interference and effective channel gain into one metric that
simplifies the optimization of the sum rate. For radar sensing, we consider
optimizing one of two metrics, the mutual information or the Cramer-Rao bound.
Then, we formulate the JCAS problem by optimizing the communication metric
under different constraints of the radar metric, and we obtain both closed-form
solutions and iterative solutions to the non-convex JCAS optimization problem.
Numerical results are provided and verify the proposed optimization solutions.
