The Degrees of Freedom of MIMO Relay under Coherence Diversity

This paper studies the MIMO relay with non-identical link coherence times, a condition that is denoted coherence diversity. This can occur, e.g., when the nodes do not all have the same mobility, or the scatterers around some nodes have different mobility than others. Obviously this condition occurs in practice therefore the model is well motivated, but the performance of a relay under such conditions has not been studied to date. This paper calculates achievable degrees of freedom under this condition. Since different coherence times have a prominent impact on channel training, channel state is not made available to the decoder for free, and all channel training resources are accounted for in the calculations. A product superposition technique is employed at the source that allows a more efficient usage of degrees of freedom when the relay and the destination have different training requirements. Following the analysis of a representative example, a general analysis is provided and varying configurations of coherence times are studied. Numerical results demonstrate the gains of the proposed approach under coherence disparity.