Set Partition Modulation

Abstract

In this paper, a novel modulation scheme called set partition modulation (SPM) is proposed. In this scheme, set partitioning and ordered subsets in the set partitions are used to form codewords. We define different SPM variants and depict a practical model for using SPM with orthogonal frequency division multiplexing (OFDM). For the OFDM-SPM schemes, different constellations are used to distinguish between different subsets in a set partition. To achieve good distance properties as well as better error performance for the OFDM-SPM codewords, we define a codebook selection problem and formulate such a problem as a clique problem in graph theory. In this regard, we propose a fast and efficient codebook selection algorithm. We analyze error and achievable rate performance of the proposed schemes and provide asymptotic results for the performance. It is shown that the proposed SPM variants are general schemes, which encompass multi-mode OFDM with index modulation (MM-OFDM-IM) and dual-mode OFDM with index modulation (DM-OFDM-IM) as special cases. It is also shown that OFDM-SPM schemes are capable of exhibiting better error performance and improved achievable rate than conventional OFDM, OFDM-IM, DM-OFDM-IM, and MM-OFDM-IM.

Q-Ary Multi-Mode OFDM With Index Modulation

“…SEs for uncoded Q-MM-OFDM-IM (4, 4, 2); Q-MM-OFDM-IM (8, 4, 1) and OFDM-OFSPM (4, 2); MM-OFDM-IM (4, 2), OFDM-IM (4, 3, 4) and OFDM (QPSK) are 2.5 bps, 2.25 bps and 2 bps, respectively. In the uncoded case, the Q-MM-OFDM-IM (8, 4, 1) scheme is capable of achieving the same SE as OFDM-OFSPM (4, 2) by employing only index 7 In Fig. 1, BER curves of the uncoded schemes are obtained by employing the optimum ML detector, whereas the coded schemes perform hard-decision decoding based on the optimum ML detector.…”

“…Specifically, when IM is applied to orthogonal frequency division multiplexing (OFDM) technique, a better error performance and improved data rate compared to conventional OFDM are shown to be possible [1]- [6]. Moreover, an application of a recent IM scheme, called set partition modulation (SPM), to OFDM brings about a marginal enhancement in error rate at high signal-to-noise ratio (SNR) values and a substantial improvement in data rate when compared to other OFDM-IM benchmarks [7].…”

“…the combinations of active subcarriers, thus the total power is distributed across all subcarriers. Moreover, dual-mode OFDM-IM (DM-OFDM-IM) [3], [4], multi-mode OFDM-IM (MM-OFDM-IM) [5], [6] and OFDM-SPM [7] use disjoint constellations on all subcarriers. The presence of the index codewords makes these schemes capable of achieving the same spectral efficiency (SE) as that of conventional OFDM by employing lower order modulation.…”

“…The presence of the index codewords makes these schemes capable of achieving the same spectral efficiency (SE) as that of conventional OFDM by employing lower order modulation. On the other hand, the potential of index domain is exploited more by the studies that increase the number of index symbols with combinatorial tools such as permutation and set partitioning [5]- [7]. However, it is not obvious whether the existing OFDM-IM schemes can achieve the full potential of the index domain by producing the largest number of possible index symbols.…”