Maximal Spectral Efficiency of OFDM with Index Modulation under Polynomial Space Complexity

TL;DR

This paper introduces a polynomial-time and space complexity mapper for OFDM with Index Modulation, enabling maximal spectral efficiency gains while maintaining computational feasibility.

Contribution

A novel mapper for OFDM-IM that achieves maximal spectral efficiency with polynomial computational complexity using Pascal's triangle.

Findings

The mapper performs a polynomial number of binomial coefficient calculations.

Utilizing Pascal's triangle reduces computational overhead.

Maximal spectral efficiency gain is achievable under polynomial complexity.

Abstract

In this letter, we demonstrate a mapper that enables all waveforms of OFDM with Index Modulation (OFDM-IM) while preserving polynomial time and space computational complexities. Enabling all OFDM-IM waveforms maximizes the spectral efficiency (SE) gain over the classic OFDM but, as far as we know, the computational overhead of the resulting mapper remains conjectured as prohibitive across the OFDM-IM literature. We show that the largest number of binomial coefficient calculations performed by the original OFDM-IM mapper is polynomial on the number of subcarriers, even under the setup that maximizes the SE gain over OFDM. Also, such coefficients match the entries of the so-called Pascal's triangle (PT). Thus, by assisting the OFDM-IM mapper with a PT table, we show that the maximum SE gain over OFDM can be achieved under polynomial (rather than exponential) time and space complexities.