Maximum Capacity and Relay Designs for Airborne MIMO Relay Communication Systems
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Multiple-Input-Multiple-Output (MIMO) relay communication has drawn significant attention since it can extend communication coverage, overcome obstacle shadowing, and increase communication capacity. When considering MIMO relay communication in airborne or free-space environment, there experiences Line-of- Sight (LoS) communication without scattering and reflection. One challenging issue is how to design and deploy relay potentially equipped with multiple antennas in order to achieve maximum capacity. Although the relay may use various relaying strategies, Naive Amplify-and-Forward (NAF) has the least complexity and it is easy to implement since it just scales the received signal and forwards it to the destination. In this work, we intend to investigate and find optimal MIMO relay designs in order to achieve maximum capacity with the NAF relaying scheme for any given power allocation at source and relay, alignment of source and destination antenna arrays in airborne MIMO communication environment. More specifically, first we analyze the capacity of airborne MIMO relay communication systems with arbitrary alignments of source, relay and destination antenna arrays. We consider a three-dimension (3D) Cartesian coordinate system and derive a closed-form expression for the capacity of airborne MIMO relay communication systems in terms of the antenna geometry and approximation of distance. When the distances between source and relay, relay and destination antenna arrays are large compared to the sizes of the antenna arrays, the capacity analysis is asymptotically tight. Based on the capacity analysis, we derive a capacity upper bound for any given relay location. Interestingly, the capacity upper bound is achievable by adjusting relay parameters (e.g. antenna spacing and angles). We derive a necessary and sufficient condition for MIMO relay communication system to achieve the capacity upper bound in airborne communication environment for two system architectures : i) there are multiple antennas at the source and the destination and only one antenna at the relay, and ii) there are multiple antennas at the relay and one antenna at the source and at the destination. We then derive a maximum capacity with the best relay location. It implies that there exists a set of relay parameters (e.g. antenna spacing, angles and location) allowing the airborne MIMO relay communication system to achieve the maximum capacity. We also extend the analysis for a general scenario with multiple antennas at the source, the relay and the destination to properly design and determine the best location of MIMO relay for any given power allocation at source and relay, alignment of source and destination antenna arrays in airborne communication environment. Extensive numerical studies have been conducted to validate our theoretical developments.