  In this paper, we consider a cognitive radio (CR) network in which a
secondary multiantenna base station (BS) attempts to communicate with multiple
secondary users (SUs) using the radio frequency spectrum that is originally
allocated to multiple primary users (PUs). Here, we employ partially-projected
regularized zero-forcing (PP-RZF) precoding to control the amount of
interference at the PUs and to minimize inter-SUs interference. The PP-RZF
precoding partially projects the channels of the SUs into the null space of the
channels from the secondary BS to the PUs. The regularization parameter and the
projection control parameter are used to balance the transmissions to the PUs
and the SUs. However, the search for the optimal parameters, which can maximize
the ergodic sum-rate of the CR network, is a demanding process because it
involves Monte-Carlo averaging. Then, we derive a deterministic expression for
the ergodic sum-rate achieved by the PP-RZF precoding using recent advancements
in large dimensional random matrix theory. The deterministic equivalent enables
us to efficiently determine the two critical parameters in the PP-RZF precoding
because no Monte-Carlo averaging is required. Several insights are also
obtained through the analysis.
