proposed algorithm and reference BER value. When the signal to noise ratio is lower than 6dB, the BER
2015
Taking the formula (10) into equation (8),we can obtain approximate upper limit expression of ABER as shown in the formula (11). γ γ σ σ σ σ σ ≈ + = + + 8 ( ) 8 ( p p p p p p p ) (11) 4 OPTIMAL POWER ALLOCATION ALGORITHM The total system power is assumed to be constant. The minimum ABER is taken as the optimization criterion to decide the optimal power among source S relay R1and R2 , which is described as + + = min p p p . .p p p , 1, 2 1 2s t p (12) This optimization problem can be transformed into mathematical expression by Lagrange multiplier method. By taking its partial derivatives to p1 ,p2, and ps respectively along with the combination of the constraint, we can obtain the optimal solution which is (13) σ σ σ = + − = − − D S Sp (p p ), p p p p1 Where σ σ σ σ+A=( ) S2D 12 12 1 22 , σ σ= 2 5 SIMULATION RESULTS AND ANALYSIS Simulation conditions are as follows. Channel state information of each node is known. Assume that all channels are flat Rayleigh fading channels. The transmission power of each node is limited by the total power. Namely, + + =p p p1 2 ps . We adopt the normalized power, i.e. p=1.