Differential Spatial Modulation with Gray Coded Antenna Activation Order

TL;DR

This paper introduces a gray code permutation scheme for differential spatial modulation (DSM) that improves coding gain and diversity performance, with minimal complexity increase, compared to traditional lexicographic ordering.

Contribution

It proposes a novel gray code order for antenna permutations in DSM, enhancing coding gain and diversity, and introduces the intersected gray (I-gray) code for further performance improvements.

Findings

Gray code order yields up to 1.2dB gain over lexicographic order.

I-gray code enhances diversity order with minimal bit loss.

Implementation complexity remains similar to existing methods.

Abstract

Differential spatial modulation (DSM) was recently proposed to overcome the challenge of channel estimation in spatial modulation (SM). In this letter, we propose a gray code order of antenna index permutations for DSM. To facilitate the implementation, the well-known Trotter-Johnson ranking and unranking algorithms are adopted, which results in similar computational complexity to the existing DSM that uses the lexicographic order. The coding gain achieved by the proposed gray code order over the existing lexicographic order is also analyzed and verified via simulations, which reveals a maximum of about 1.2dB for the case of four transmit antennas. Based on the gray coding framework, we further propose a diversity-enhancing scheme named intersected gray (I-gray) code order for DSM, where the permutations of active antenna indices are selected directly from the odd (even) positions of the full permutations in the gray code order. From analysis and simulations, it is shown that the I-gray code order can harvests an additional diversity order at the expense of only one information bit loss for each transmission with respect to the gray code order.