Cooperative Time Successive SSK-M-ary Modulation for Decode-and-Forward Relay Systems

Abstract

Space shift keying (SSK) is a single radio frequency (RF) chain multiple-input multiple-output (MIMO) scheme that uses the index of transmit antennas for information transmission. Time successive SSK- $ M$ -ary modulation (TSSM) and multi RF chain TSSM (MRF-TSSM) are recent MIMO techniques that achieve second order transmit diversity. We propose two cooperative relaying systems to attain distributed diversity in addition to transmit diversity of TSSM and MRF-TSSM. Cooperative-TSSM-1 (Coop-TSSM-1) uses multibranch relaying where TSSM is used in orthogonal time slots during the cooperative phase. Coop-TSSM-2 maps symbols to lower order constellations at multiple relays for simultaneous transmission of information using MRF-TSSM. We consider Decode-and-forward (DF) relaying where relays that correctly detect symbols forward it. We analyze the average number of relays that participate in cooperation, the end-to-end performance using a tight upper bound on the bit error rate (BER) and the asymptotic BER expressions to analyze diversity orders of both cooperative systems. We validate all analyzes using simulation results. From the analysis and results we show that Coop-TSSM-1 achieves better diversity order compared to Coop-TSSM-2 at the cost of higher number of time slots for completing the cooperative phase. Further in Coop-TSSM-2, results indicate that different constellation mappings used in MRF-TSSM during cooperative phase impact the BER performance. By applying spatial modulation based transmit diversity and $M$ -ary Modulation systems in the cooperative setups of Coop-TSSM schemes, performance comparison is given which highlights the significance of Coop-TSSM schemes.