Analysis and Design of SCMA-Based Hybrid Unicast-Multicast Relay-Assisted Networks

. 2019 Jan 15;19(2):329. doi: 10.3390/s19020329

Algorithm 2 Optimal design of cooperative transmission.

Input: transmit power P, transmit rate

I_{f}

, number of relays

N_{s}

.
Output: power allocation factor

α

, relay location factor

μ

1:
According to Equation (33), we can observe that $α$ and $μ$ are two parts that do not affect each other. Then, we can obtain the optimal values of $α$ and $μ$ separately.
2:
The calculation of the optimal value of $α$ :
3:
According to Equation (34), $α$ is optimal when $P_{s 1} P_{s 2^{†}}$ reaches the maximum value.
4:
After obtaining $\bar{N}$ (the average number of successful relays), get the expression of the average value of $P_{s 2^{†}}$ .
5:
Establish the equation $P_{s 1} P_{s 2^{†}} = 0$ .
6:
Solving the derivative of the above equation, we have $P_{s 1} \approx P / ξ$ .
7:
The optimal power allocation factor is $α = P_{s 1} ξ / (2 P) \approx 0.5$ .
8:
The calculation of the optimal value of $μ$ :
9:
Initialization $t = 0.01$ , $0 \leq μ \leq 1$ , $N_{s} = 2, 3, 4, 5, 6$ .
10:
for $N_{s} = 2 : 1 : 6$ do
11:
for $μ = 0 : t : 1$ do
12:
Calculate $Λ$ according to Equation (41).
13:
end for
14:
Search for the value of $μ$ when $Λ$ is the minimum, and this $μ$ is optimal.
15:
end for
16:
The calculation is completed.