This study presents ambient backscatter communication (AmBC) network as a concept of "modulation in the air" that has drawn growing interest by both academia and industry recently. In particular, we investigate and analyze an AmBC system relying on cognitive radio, where the primary destination is equipped with multiple antennas and maximum ratio combining (MRC). A wireless powered relay is necessary to serve both primary and secondary destinations. Benefiting from the surrounding radio frequency (RF) source, the relay can support the backscattering signal. To facilitate the performance analysis of received nodes, this study presents exact closed-form expressions of the outage probability. For comparison, the outage and throughput performance of these nodes are considered in numerical simulation. Taking advantage of the AmBC technology, the impact of the backscatter ratio on system performance is carefully studied considering various other parameters. Simulation results demonstrate the exactness of the derived outage probabilities and show that the optimal throughput performance can be achieved at specific parameters.