Prior Zero Forcing for Cognitive Relaying

Relaying primary signals by cognitive base-stations (CBSs) can help the primary system and thus win CBSs a higher chance to transmit their own signals. For this purpose, conventional zero-forcing (CZF) beamforming is a straightforward solution where the primary and cognitive signals are transmitted from a multi-antenna CBS without causing interference to each other. However, with CZF, no priority is given to the primary user (PU), which is not consistent with the idea of cognitive radio. In this paper, we shall propose a prior ZF (PZF) scheme which gives priority to the PU by transmitting primary signals without considering their interference to the cognitive users (CUs), while cognitive signals are not allowed to generate interference to the PU. As a result, PZF provides a better channel for the CBS-PU link than CZF but the same channel gain for the CBS-CU links as CZF. We compare PZF and CZF by considering both the transmit power with given target rates and the outage performance with given transmit power, where closed-form conditions are derived to indicate their respective advantages. One of the important contributions of this paper is to prove that, with one CU, a target rate of 1 bit/s/Hz for the CU is the key point that differentiates PZF and CZF, which is independent of the number of CBS-antennas, the channel distributions, and the signal-to-noise power ratio (SNR).