This paper studies the statistical properties of the signal-to-noise ratio (SNR) of the relay link in a cooperative wireless communication system with fixed gain relay in presence of channel estimation error. The SNR expression is derived and three different analytic approaches with different approximate assumptions are used to obtain the probability distribution function of the SNR and outage probability of the relay link. The first approach is the most accurate one in many cases, however it does not have a closed-form expression. The other two approaches result in closed-form expressions for the outage probability. Therefore, the third approach has been used to find a sub-optimum power allocation scheme for the source and the relay. The numerical results compare the accuracy of the analytic approaches and simulation results for different positions of the relay between the source and the destination. It is shown that the second approach has the most accurate closed-form expression and the third one leads to the simplest closed-form result suitable for power optimization purposes.
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