  To broaden the application scenario and reduce energy consumption, we propose
an energy-efficient fixed-gain (FG) amplify-and-forward (AF) relay assisted
orthogonal frequency-division multiplexing with index modulation (OFDM-IM)
scheme in this letter. The proposed system needs neither instantaneous channel
state information (CSI) nor complicated processing at the relay node. It
operates based on the power allocation scheme that minimizes the sum of
transmit power at both source and relay node, given an outage probability
constraint. Through a series of problem transformation and simplification, we
convert the original power allocation problem to its relaxed version and solve
it using convex programming techniques. To reveal the computing efficiency of
the proposed power allocation scheme, we analyze its computational complexity.
Numerical simulations substantiate that the proposed optimization scheme has a
neglectable loss compared with the brute force search, but the computational
complexity can be considerably reduced.
