  The problem of optimal power allocation among the relays in a two-hop
decode-and-forward cooperative relay network with independent Rayleigh fading
channels is considered. It is assumed that only the relays that decode the
source message correctly contribute in data transmission. Moreover, only the
knowledge of statistical channel state information is available. A new simple
closed-form expression for the average symbol error probability is derived.
Based on this expression, a new power allocation method that minimizes the
average symbol error probability and takes into account the constraints on the
total average power of all the relay nodes and maximum instant power of each
relay node is developed. The corresponding optimization problem is shown to be
a convex problem that can be solved using interior point methods. However, an
approximate closed-form solution is obtained and shown to be practically more
appealing due to significant complexity reduction. The accuracy of the
approximation is discussed. Moreover, the so obtained closed-form solution
gives additional insights into the optimal power allocation problem. Simulation
results confirm the improved performance of the proposed power allocation
scheme as compared to other schemes.
