SER analysis and power allocation for hybrid cooperative transmission system

The symbol-error-rate(SER) and power allocation for hybrid cooperative(HC) transmission system are investigated.Closed-form SER expression is derived by using the moment generating function(MGF)-based approach.However,the resultant SER contains an MGF of the harmonic mean of two independent random variables(RVs),which is not tractable in SER analysis.We present a simple MGF expression of the harmonic mean of two independent RVs which avoids the hypergeometric functions used commonly in previous studies.Using the simple MGF,closed-form SER for HC system with M-ary phase shift keying(M-PSK) signals is provided.Further,an approximation as well as an upper bound of the SER is presented.It is shown that the SER approximation is asymptotically tight.Based on the tight SER approximation,the power allocation of the HC system is investigated.It is shown that the optimal power allocation does not depend on the fading parameters of the source-destination(SD) channel and it only depends on the source-relay(SR) and relay-destination(RD) channels.Moreover,the performance gain of the power allocation depends on the ratio of the channel quality between RD and SR.With the increase of this ratio,more performance gain can be acquired.