Theoretical Performance of Coherent and Incoherent Detection for Zero-Forcing Receive Antenna Shift Keying

Receive antenna shift keying (RASK) is a multiple-input multiple-output transmission scheme that applies the spatial modulation concept at the receiver. Zero-forcing (ZF) precoding can be used at the transmitter side to steer the signal toward the targeted antenna. Different detection schemes can be implemented in order to detect the RASK information. Moreover, for the sake of low complexity and low power consumption, decreasing the number of RF chains by the use of switched antennas can also be implemented. In this paper, we lead a theoretical analysis of the transmission of spatial symbols in RASK, using the ZF precoding. Two detection schemes relying on maximum likelihood (ML) detection are presented and proved to be implemented as a simple single-tap detector. One, called coherent ML (CML), needs one RF chain per receive antenna and the other one, named incoherent ML (IML), is based on an envelope detector and needs only one RF chain for the entire antenna array. Theoretical expressions of the bit error rate (BER) are derived for each scheme and validated through simulation. The CML detector is demonstrated to obviously outperform the IML detector in terms of the BER but at the cost of higher complexity and power consumption. We then proposed to use switches to reduce the number of RF chains, thus trading off some performance against complexity. At some point, IML is shown to outperform CML, depending on the number of switches, RF chains, and system configuration. This turning point is analytically calculated and validated through simulations, and so can be used for further system comparison studies.