Ambient backscatter communication has shown great potential in the development of future wireless networks. It enables a backscatter transmitter (BTx) to send information directly to an adjacent receiver by modulating over ambient radio frequency (RF) carriers. In this paper, we consider a cooperative ambient backscatter communication system where a multi-antenna cooperative receiver separately decodes signals from an RF source and a BTx. Upper bounds of the ergodic rates of both links are derived. The power scaling laws are accordingly characterized for both the primary cellular transmission and the cooperative backscatter. The impact of additional backscatter link is also quantitatively analyzed. Simulation results are provided to verify the derived results.