Stochastically Modeling and Exploiting the Spatial Domain in 6G Wireless

<p dir="ltr">The move towards 6G wireless aims to integrate diverse applications into a dense, spectrally efficient, and globally accessible network. To support massive device connectivity despite the limitations of finite time and frequency resources, spatial resources are increasingly exploited through techniques such as precoding and combining. Moreover, the inclusion of 3D non-terrestrial networks (NTNs) in 6G wireless significantly expands the available spatial resources. In this dissertation, we address the growing importance of the spatial domain by exploring novel approaches to spatial filtering as well as developing new stochastic models and analyzing uplink performance in NTNs. First, we propose a novel precoded multiple-input multiple-output (MIMO) radar framework that enables independent design of the precoder and the MIMO radar waveform. We show this framework satisfies the constant modulus output requirement critical for radar applications while achieving high-resolution spatial filtering. Second, we explore a packet-level preemptive redundancy uplink technique in NTNs which mitigates volatile channel effects. Using stochastic geometry, we demonstrate this technique achieves lower latency and energy consumption when compared to traditional feedback approaches. Next, we extend our stochastic model to derive order statistics that characterize the distance from a terrestrial terminal to any node, as well as intra-nodal distances within a hierarchical NTN. These distributions enable analysis of multi-node systems while accounting for their relative spatial positions. Lastly, we propose a novel communications technique which exploits receiver motion and oversampling to synthesize a large virtual aperture. We study how the aperture enables high-resolution spatial filtering and supports spatial diversity multiple access.</p>