Relay channels have been heavily studied during the last decades as a means of improving spectral efficiency, availability and coverage in combination with multiple antenna transceivers. Relay channels can comprise many hops but the most practical approach at the time being would be a dual-hop system. In addition, the simplest method of relaying in terms of complexity is amplify and forward. In this direction, we investigate the ergodic capacity of a dual-hop amplify-and-forward MIMO MAC and we derive asymptotic closed-form expressions based on the principles of free probability theory. We extend the current literature by proposing a analytical model which can accommodate variance-profiled Gaussian matrices. Numerical results are utilized to verify the accuracy of the derived closed-form expressions and evaluate the effect of the channel parameters.
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