Chiranjib Saha

In this paper, we investigate the use of Björck sequences, a class of constant amplitude zero autocorrelation (CAZAC) sequences, as a potential candidate for the design of positioning reference signals (PRS) in Low Earth Orbit (LEO)-based positioning, navigation, and timing (PNT) systems. Unlike legacy systems such as Global Navigation Satellite Systems (GNSS) or terrestrial networks (TNs), LEO-based systems experience large Doppler shifts and delay spreads, where traditional orthogonalization methods become ineffective. Compared to commonly used sequences such as Gold and Zadoff-Chu (ZC), Björck sequences offer improved ambiguity function behavior, nearly ideal autocorrelation, greater resilience to interference, and accurate delay estimation in high Doppler environments. We further propose a novel sequence construction method to extend Björck sequences to non-prime lengths while minimizing cyclic autocorrelation. Focusing on LEO-based non-terrestrial network (NTN) localization, we evaluate positioning accuracy under various interference conditions, comparing the performance of Björck sequences against Gold sequences, which are traditionally used for PRS generation. While Björck sequences demonstrate strong performance in Doppler-rich environments, we identify an inherent Doppler-dependent behavior that may lead to sequence misidentification. To mitigate this, we propose two strategies: 1) leveraging the availability of a coarse Doppler estimate and 2) employing sequence subset selection to ensure sufficient separation between sequences to account for maximum Doppler uncertainty. Finally, we present scalable sequence reuse strategies for large LEO constellations.

Subset selection is central to many wireless communication problems, including link scheduling, power allocation, and spectrum management. However, these problems are often NP-complete, because of which heuristic algorithms applied to solve these problems struggle with scalability in large-scale settings. To address this, we propose a determinantal point process-based learning (DPPL) framework for efficiently solving general subset selection problems in massive networks. The key idea is to model the optimal subset as a realization of a determinantal point process (DPP), which balances the trade-off between quality (signal strength) and similarity (mutual interference) by enforcing negative correlation in the selection of {\em similar} links (those that create significant mutual interference). However, conventional methods for constructing similarity matrices in DPP impose decomposability and symmetry constraints that often do not hold in practice. To overcome this, we introduce a new method based on the Gershgorin Circle Theorem for constructing valid similarity matrices. The effectiveness of the proposed approach is demonstrated by applying it to two canonical wireless network settings: an ad hoc network in 2D and a cellular network serving drones in 3D. Simulation results show that DPPL selects near-optimal subsets that maximize network sum-rate while significantly reducing computational complexity compared to traditional optimization methods, demonstrating its scalability for large-scale networks.