Optimal Mapper for OFDM With Index Modulation: A Spectro-Computational Analysis

In this work, we present an optimal mapper for OFDM with index modulation (OFDM-IM). By optimal we mean the mapper achieves the lowest possible asymptotic computational complexity (CC) when the spectral efficiency (SE) gain over OFDM maximizes. We propose the spectro-computational (SC) analysis to capture the trade-off between CC and SE and to demonstrate that an N-subcarrier OFDM-IM mapper must run in exact Θ(N) time complexity. We show that an OFDM-IM mapper running faster than such complexity cannot reach the maximal SE whereas one running slower nullifies the mapping throughput for arbitrarily large N. We demonstrate our theoretical findings by implementing an open-source library that supports all DSP steps to map/demap an N-subcarrier complex frequency-domain OFDM-IM symbol. Our implementation supports different index selector algorithms and is the first to enable the SE maximization while preserving the same time and space asymptotic complexities of the classic OFDM mapper.