Statistical Beamforming for Multi-Set Space-Time Shift-Keying-Based Full-Duplex Millimeter Wave Communications

Full-duplex (FD) communication has been shown to provide an increased achievable rate,while millimeter wave (mmWave) communications benefit from a large available bandwidth thatfurther improves the achievable rate. On the other hand, the concept of multi-set space-time shiftkeying (MS-STSK) has been proposed to provide a flexible design trade-off between throughputand performance. Hence, in this work, we consider the design of an FD-aided MS-STSK transceiverfor millimeter wave communications. However, a major challenge is that channel reciprocity is notvalid in mmWave communications due to shorter channel coherence time. Thus, the uplink (UL)pilots cannot be utilized to estimate the downlink (DL) channel. To overcome this challenge, wepropose a beamforming technique based on channel statistics without assuming channel reciprocity.For this purpose, a closed-form expression for the outage probability of the system is derived byemploying the characterization of the ratio of the Indefinite Quadratic Form (IQF). The derivedanalytical expression is then utilized to design optimum beamforming weights using the SequentialQuadratic Programming (SQP)-based heuristic method. Moreover, an Iterative Statistical Method(ISM) of joint transmit and receive beamforming algorithm is also developed by utilizing PrincipleEigenvector (PE) and Generalized Rayleigh Quotient (G-RQ) optimization techniques. Finally, weverify our simulation results with the theoretical analysis.