Energy Efficient MIMO Relay Transmissions via Joint Power Allocations

The energy efficient joint source-relay power allocation problem is studied for the multi-input multi-output (MIMO) amplify-and-forward two-hop relaying system, in which the objective of the optimization is the number of the bits per second per hertz per Joule with the guarantee of the minimum spectral efficiency (SE). By assuming perfect channel state information at the transmitter, the MIMO channel is divided into several single-input single-output (SISO) subchannels via singular value decomposition (SVD). The problem is first established as an optimization subject to the minimum SE constraint, in which it is observed that both of the cost function and the constraint are not convex. By employing the high signal-to-noise ratio (SNR) approximation, the problem becomes suddenly a pseudo-convex optimization problem. Yet, the difficulty comes from solving the final Lagrangian equation, which is tackled by our proposed relaxation method according to the Jensen inequality. Finally, the analytical expression is derived for the energy efficient power allocations of the multiple antennas at the source and at the relay. Simulations demonstrate the effectiveness of the proposed method.