Maximum achievable capacity in airborne MIMO communications with arbitrary alignments of linear transceiver antenna arrays

In this paper, the capacity of airborne multiple-input-multiple-output (MIMO) wireless communication systems with arbitrary alignments of linear transmit and receive antenna arrays is systematically analyzed and the maximum achievable capacity is determined. Based on a general three-dimensional (3D) airborne MIMO communication model, we are able to approximate the airborne MIMO capacity as a function of the transmit and receive antenna array geometry in the 3D space. The capacity approximation is asymptotically tight as the distance between the transmit and receive antenna arrays large compared to their size. Based on the asymptotically tight capacity approximation, we derive an upper bound as well as a lower bound of the airborne MIMO capacity. Interestingly, both the upper and lower bounds are achievable. We also derive a necessary and sufficient condition for airborne MIMO communication systems to achieve the capacity upper bound for any given 3D transceiver antenna array geometry. The necessary and sufficient condition allows us to properly select the system parameters and design airborne MIMO communication systems that reach the best possible performance in terms of system capacity. We prove that when the distance between the transmit and receive antenna arrays is within a certain range, there exists a set of system parameter values (e.g. antenna element separation) for which the capacity of the MIMO communication system achieves the theoretical upper bound and this capacity value is larger than the average capacity of the corresponding conventional MIMO communication system under Rayleigh fading. Finally, we prove that the airborne MIMO capacity converges to the capacity lower bound when the distance between the transmit and receive antenna arrays goes to infinity. Extensive numerical studies included in this paper illustrate and validate our theoretical developments.