Hierarchical modulated quadrature amplitude modulation with signal space diversity and maximal ratio combining reception in Nakagami-m fading channels

This study combines hierarchical modulation with signal space diversity (SSD) to present an unequal error protection scheme with improved bit-error rate (BER) performance for single as well as multiple antenna reception by employing maximal ratio combing in Nakagami-m fading channels. The optimal rotation angles for different constellation priority parameter α are derived. A theoretical BER expression in Nakagami-m fading channels using the nearest neighbour approximation approach is also derived. This is confirmed as a valid performance approximation for single and multiple antenna reception through simulations. The resultant scheme produces improved BER performance for both important and less important data without consuming any additional power than a non-SSD system at the cost of increased complexity at detection. Specifically, performance gains of up to 18 and 17 dB at a BER of 1 × 10^-5 for base and refinement bits, respectively, are observed for single receive antenna with Nakagami m = 1. A further improvement of roughly 3 dB at a BER of 1 × 10^-6 for base bits at N = 3 receiver antennas is found as hierarchy is increased. Although the gain is observed to decrease as m increases, a gain of 14 dB at 1 × 10^-6 for α = 4 is achieved even as m increases from m = 1 to m = 3.