Capacity of MIMO Systems With Mutual Coupling: Transmitter Optimization With Dual Power Constraints

This paper deals with the fundamental limit of capacity for MIMO wireless systems with antenna mutual coupling. Motivated by practical considerations, the capacity-achieving precoder is found by maximizing the capacity subject to two separate power constraints; namely, a constraint on the available power at the transmitter which is imposed on a per-amplifler basis, and a constraint on the allowable radiated power. These two separate constraints occur because MIMO antenna systems are usually unable to use a perfect conjugate multiport impedance match in practice and therefore MIMO systems with mutual coupling usually do not radiate all of the power input or available to them. Assuming that perfect channel state information is available to both the transmitter and receiver, we first derive sufficient conditions on the power constraints, in terms of the mutual coupling, under which the dual-constraint problem reduces to effectively a single-constraint problem. This greatly simplifies the optimization problem in some cases. For the more general case where both constraints are relevant, we present an efficient suboptimal algorithm by first relaxing the per-amplifier power constraint to a sum power constraint and then solving the dual-constraint problem based on dynamic water-filling and mode-dropping. Finally, we investigate the optimal precoder design at high signal to noise ratios, and provide stronger theoretical results in this regime. Numerical results are provided to demonstrate the effectiveness of our technique when dual power constraints are important to consider.