This paper deals with Ergodic Capacity analysis of Amplify and Forward Wireless Relay Networks (AFWRN) with Imperfect Channel State Information (ICSI). Ergodic capacity attains prime importance as it provides a limit on the achievable rate in multipath fading channel environments for AFWRN systems. However to analyze ergodic capacity Channel State Information (CSI) is essential and it is practically not available in many scenarios. Hence, CSI needs to be estimated by estimation algorithms such as least squares (LS), minimum mean square error (MMSE) and best linear unbiased estimation (BLUE) algorithms. Here, BLUE algorithm by virtue of its advantages of non-dependence on the complete knowledge of probability density function (PDF), requiring only first and second moments of PDF, and possessing minimal variance characteristics, it is proposed to estimate the CSI of AFWRN system. Using BLUE in  AFWRN system ergodic capacity is analysed. The simulation results obtained and presented in this paper provides the tradeoff between perfect CSI and ICSI. Simulation results can be used as a bench mark for analysis of coherent detection in AFWRN systems.  
 

Index Terms—Ergodic Capacity, Amplify and Forward Wireless Relay Networks, Imperfect CSI, BLUE algorithm. (key words)