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This paper addresses the ergodic capacity of multiple input multiple output (MIMO) amplify and forward (AF) wireless relay networks (WRN) with imperfect channel state information (ICSI) between the source node to relay node links and relay node to destination node links using best linear unbiased estimation (BLUE) algorithm. Ergodic capacity is derived by linear processing at the relay node and by using eigenvalues of the channel coefficients between source node to relay node and relay node to destination node. Unfortunately, in practical scenarios, the estimated channel coefficients are imperfect. The imperfect CSI obtained via traditional estimation methods like least squares (LS) and minimum mean square error (MMSE) does not reduce estimation errors to a significant extent thereby leading to severe degradation in system performance. This paper advocates, best linear unbiased estimation algorithm for estimating the channel coefficients between the relay node and destination nodes of MIMO-AF-WRN to analyze ergodic capacity. Eventhough, it is an existing algorithm BLUE algorithm is still largely unexplored and it produces minimal estimation errors in comparison to other estimators due to its minimum variance attribute inherent within it. Moreover, BLUE algorithm posses the minimal variance among all the unbiased estimators. Simulation results using BLUE algorithm shows that the ergodic capacity decreases as the variance of the channel estimation error increases. Further, it is also inferred that the mutual information grows very slowly or shrinks when the number of source antennas are more than the destination antennas when a large number of relay antennas are used. The simulation results are validated by deriving the analytical expressions for ergodic capacity with ICSI.