Three-dimensional space-time shift keying with coordinate combination and joint optimisation

In this paper, the concept of three-dimensional (3-D) space-time shift keying (STSK) is introduced, which incorporates 3-D constellations into conventional STSK systems. The new 3-D STSK techniques enjoy better error resilience than their two-dimensional (2-D) counterparts. Firstly, based on different sampling rates, two three-dimensional (3-D) STSK schemes referred to as R2 3-D STSK and R3 3-D STSK, respectively, are proposed. Both schemes show improved effective spectral efficiency (ESE) than 2-D STSK at relatively low signal-to-noise ratios (SNRs). Further, the optimal combinations of the constellation coordinates for R2 3-D STSK are derived by maximising the minimal determinant of the so-called difference matrices, yielding a better system performance. In addition, a joint optimisation mechanism utilising the simplified conjugate gradient (SCG) algorithm is devised for 3-D STSK, aiming for further enhancing the achievable system performance. Finally, extensive simulation results are provided to demonstrate the benefits of the proposed schemes, exhibiting the design tradeoffs concerning date rate, link robustness and computational complexity.