  In this paper, power allocation is examined for the coexistence of a radar
and a communication system that employ multicarrier waveforms. We propose two
designs for the considered spectrum sharing problem by maximizing the output
signal-to-interference-plus-noise ratio (SINR) at the radar receiver while
maintaining certain communication throughput and power constraints. The first
is a joint design where the subchannel powers of both the radar and
communication systems are jointly optimized. Since the resulting problem is
highly nonconvex, we introduce a reformulation by combining the power variables
of both systems into a single stacked variable, which allows us to bypass a
conventional computationally intensive alternating optimization procedure. The
resulting problem is then solved via a quadratic transform method along with a
sequential convex programming (SCP) technique. The second is a unilateral
design which optimizes the radar transmission power with fixed communication
power. The unilateral design is suitable for cases where the communication
system pre-exists while the radar occasionally joins the channel as a secondary
user. The problem is solved by a Taylor expansion based iterative SCP
procedure. Numerical results are presented to demonstrate the effectiveness of
the proposed joint and unilateral designs in comparison with a subcarrier
allocation based method.
