On the performance of dual-hop space shift keying with single amplify-and-forward relay

In this paper, single amplify and forward (AF) relay is placed between the source and the destination in space shift keying (SSK) multiple-input single output (MISO) system. In SSK, transmit-antenna indices form a spatial constellation diagram where each group of base two logarithm of the input data bits are mapped to one spatial constellation point. Hence, at each time instant, only single transmit antenna is active, which transmits certain energy that contains no data symbol, and all other antennas are off. The receiver, with single receive antenna, decodes the received signal from the single antenna AF relay and estimates the index of the active transmit-antenna to retrieve the transmitted information bits. Closed-form bit error ratio (BER) is derived for the considered system in correlated and uncorrelated channels assuming a transmitter with two transmit antennas. The analytical framework is generalized for an arbitrary number of transmit antennas and a tight upper bound on the BER performance is derived. Additionally, asymptotic analysis are carried out to investigate the effect of the different system parameters on the overall system performance. The analytical results are validated through Monte-Carlo simulation results.