Performance of Cooperative Spatial Modulation with AF Relaying in the Presence of Channel Estimation Error

Spatial modulation (SM) is a simple and spectrally efficient technique, which exploits transmit antenna indices to convey information. Introducing SM into a cooperative system, cooperative SM, can reduce the complexity of receiver, and also improve the spectral efficiency. In this paper, the performance of the amplify-and-forward (AF) relaying aided cooperative SM (AF-SM) system with imperfect channel estimation is analyzed, and the diversity order of the system is presented based on the performance analysis. With the maximum likelihood detection, the pairwise error probability (PEP) of the system is derived by means of moment generating functions. Using this result, the closed-form expression of average bit error rate (BER) is achieved as a union upper bound, based on which the asymptotically approximated BER expression under high SNR is derived. With the asymptotical BER, the diversity orders of the AF-SM system with N _r receive antennas for the fixed and variable estimation errors are attained as zero and N _r +1, respectively. Computer simulations show that theoretical results match the corresponding simulations well for different estimation errors, and thus the validity of the deduced theoretical expressions is validated.