Abstract: This paper discusses transmission performance and power allocation strategies in an underlay cognitive radio (CR) network that contains relay and massive multi-input multi-output (MIMO). The downlink transmission performance of a relay-aided massive MIMO network without CR is derived. By using the power distribution criteria, the k^th user’s asymptotic signal to interference and noise ratio (SINR) is independent of fast fading. When the ratio between the base station (BS) antennas and the relay antennas becomes large enough, the transmission performance of the whole system is independent of BS-to-relay channel parameters and relates only to the relay-to-users stage. Then cognitive transmission performances of primary users (PUs) and secondary users (SUs) in an underlay CR network with massive MIMO are derived under perfect and imperfect channel state information (CSI), including the end-to-end SINR and achievable sum rate. When the numbers of primary base station (PBS) antennas, secondary base station (SBS) antennas, and relay antennas become infinite, the asymptotic SINR of the k^th PU and SU is independent of fast fading. The interference between the primary network and secondary network can be canceled asymptotically. Transmission performance does not include the interference temperature. The secondary network can use its peak power to transmit signals without causing any interference to the primary network. Interestingly, when the antenna ratio becomes large enough, the asymptotic sum rate equals half of the rate of a single-hop single-antenna K-user system without fast fading. Next, the PUs’ utility function is defined. The optimal relay power is derived to maximize the utility function. The numerical results verify our analysis. The relationships between the transmission rate and the antenna number, relay power, and antenna ratio are simulated. We show that the massive MIMO with linear pre-coding can mitigate asymptotically the interference in a multi-user underlay CR network. The primary and secondary networks can operate independently.

Key words: Massive multi-input multi-output, Cognitive radio, Relay network, Transmission rate, Power analysis

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