  This paper studies an integrated sensing and communication (ISAC) system
where a multi-antenna base station (BS) aims to communicate with a
single-antenna user in the downlink and sense the unknown and random angle
parameter of a target via exploiting its prior distribution information. We
consider a general transmit beamforming structure where the BS sends one
communication beam and potentially one or multiple dedicated sensing beam(s).
Firstly, motivated by the periodic feature of the angle parameter, we derive
the periodic posterior Cram\'{e}r-Rao bound (PCRB) for quantifying a lower
bound of the mean-cyclic error (MCE), which is more accurate than the
conventional PCRB for bounding the mean-squared error (MSE). Then, note that
more sensing beams enable higher flexibility in enhancing the sensing
performance, while also generating extra interference to the communication
user. To resolve this trade-off, we formulate the transmit beamforming
optimization problem to minimize the periodic PCRB subject to a communication
rate requirement for the user. Despite the non-convexity of this problem, we
derive the optimal solution by leveraging the semi-definite relaxation (SDR)
technique and Lagrange duality theory. Moreover, we analytically prove that at
most one dedicated sensing beam is needed. Numerical results validate our
analysis and the advantage of having a dedicated sensing beam.
