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Relay channels have been heavily studied during the last years as a means of improving spectral efficiency, availability and coverage in combination with multiple antenna transceivers. Relaying systems can comprise many hops but the most practical approach for the time being would be a dual-hop system. In addition, the simplest method of relaying in terms of transceiver complexity is amplify and forward. In this context, we investigate the MMSE filtering performance of a dual-hop amplify-and-forward channel MIMO multiple-access channel and we propose a tight lower bound for the average MMSE based on the principles of free probability theory. The accuracy of the derived closed-form expressions and the effect of the normalized system parameters, such as first/second hop power/load, are evaluated through numerical results. It is established that the performance of MMSE receiver greatly depends on the first hop power, while increasing the second hop power marginally improves the performance. Furthermore, inequality conditions are expressed for first/second hop load in order to achieve low average MMSE.