A Generalized Transmit and Receive Diversity Condition for Feedback-Assisted MIMO Systems: Theory and Applications in Full-Duplex Spatial Modulation

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It is widely exploited that the feedback-assisted multiple-input multiple-output (MIMO) systems, which rely on channel state information (CSI) at the transmitter not only improve the spectral efficiency but also increase the attainable diversity gains. Owing to the limited bandwidth of the feedback channel, it is impractical to feed back perfect CSI or the transmit precoding (TPC) matrix to be used by the transmitter. This issue has been studied for over a decade now and it is addressed by feeding the TPC codeword index back to the transmitter. In this paper, we derive the conditions to be satisfied by the transmit and receive codebooks (TCBs and RCBs) for achieving full transmit and receive diversity gains. Furthermore, based on the conditions derived, we propose several RCBs by exploiting the properties of circulant matrices constructed with the aid of Cyclotomic polynomials. The proposed RCBs are shown to offer several benefits when employed in full-duplex (FD) spatial modulation (SM) systems, which include: 1) reduced hardware complexity of the self-interference (SI) cancellation circuitry, 2) robustness to SI, 3) maintain the diversity gain in the face of strong line-of-sight (LoS) channels. Furthermore, we study the performance of the proposed RCBs in an emerging drone communication scenario where several drones act as FD relays. Our simulation results show that the proposed RCBs indeed do attain the diversity gains predicted by our theoretical results.