arXiv subjects

Chiranjib Saha

Publications and source records attributed to Chiranjib Saha.

At least 19 recordsLinked to original sources

arXiv2026

Björck Sequences: Extension to Arbitrary Lengths, Correlation Analysis, and Applications to Wireless Systems

In this paper, we propose a sequence construction framework that extends prime-length Björck sequences, a class of Constant Amplitude Zero Autocorrelation (CAZAC) sequences, to arbitrary lengths using Goldbach's conjecture for even and odd integers. The framework is generic and applies to any CAZAC family defined for prime lengths and supports extensions to both cyclically shifted sequences and sequences with different root indices. We analytically characterize the resulting correlation behavior and show that the construction preserves orthogonality among cyclic shifts while maintaining favorable zero-lag cross-correlation across different root-index sequences. We further investigate Björck sequences as candidates for reference signals in next-generation wireless systems. Using the proposed framework, we extend Björck sequences to arbitrary lengths and evaluate their time- and frequency-offset estimation performance in terrestrial (TNs) and non-terrestrial networks (NTNs). Results show performance comparable to Zadoff--Chu (ZC) sequences in low-Doppler TN environments and improved robustness in high-Doppler NTN scenarios due to superior ambiguity-function properties. We also identify an inherent Doppler-dependent behavior that can cause sequence misidentification under large Doppler shifts. To address this, we propose two mitigation strategies: (i) leveraging coarse Doppler estimates prior to detection, and (ii) selecting appropriately spaced subsets of orthogonal sequences. Ambiguity function-based analysis demonstrates the effectiveness of these approaches in improving estimation reliability. Overall, this work enables practical arbitrary-length CAZAC sequence design and establishes Björck sequences as a strong alternative for reference signal design in high-Doppler environments.

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arXiv2026

LEO-based Carrier-Phase Positioning for 6G: Design Insights and Comparison with GNSS

The integration of non-terrestrial networks (NTN) into 5G new radio (NR) enables a new class of positioning capabilities based on cellular signals transmitted by Low-Earth Orbit (LEO) satellites. In this paper, we investigate joint delay-and-carrier-phase positioning for LEO-based NR-NTN systems and provide a convergence-centric comparison with Global Navigation Satellite Systems (GNSS). We show that the rapid orbital motion of LEO satellites induces strong temporal and geometric diversity across observation epochs, thereby improving the conditioning of multi-epoch carrier-phase models and enabling significantly faster integer-ambiguity convergence. To enable robust carrier-phase tracking under intermittent positioning reference signal (PRS) transmissions, we propose a dual-waveform design that combines wideband PRS for delay estimation with a continuous narrowband carrier for phase tracking. Using a realistic simulation framework incorporating LEO orbit dynamics, we demonstrate that LEO-based joint delay-and-carrier-phase positioning achieves cm-level accuracy with convergence times on the order of a few seconds, whereas GNSS remains limited to meter-level accuracy over comparable short observation windows. These results establish LEO-based cellular positioning as a strong complement and potential alternative to GNSS for high-accuracy positioning, navigation, and timing (PNT) services in future wireless networks.

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arXiv2025

LEO-based Positioning: Foundations, Signal Design, and Receiver Enhancements for 6G NTN

The integration of non-terrestrial networks (NTN) into 5G new radio (NR) has opened up the possibility of developing a new positioning infrastructure using NR signals from Low-Earth Orbit (LEO) satellites. Compared to existing Global Navigation Satellite Systems (GNSS), LEO-based cellular positioning offers several advantages, such as a superior link budget, higher operating bandwidth, and large forthcoming constellations. Due to these factors, LEO-based positioning, navigation, and timing (PNT) is a potential enhancement for NTN in 6G cellular networks. However, extending the existing terrestrial cellular positioning methods to LEO-based NTN positioning requires key fundamental enhancements. These include creating broad positioning beams orthogonal to conventional communication beams, time-domain processing at the user equipment (UE) to resolve large delay and Doppler uncertainties, and efficiently accommodating positioning reference signals (PRS) from multiple satellites within the communication resource grid. In this paper, we present the first set of design insights by incorporating these enhancements and thoroughly evaluating LEO-based positioning, considering the constraints and capabilities of the NR-NTN physical layer. To evaluate the performance of LEO-based NTN positioning, we develop a comprehensive NR-compliant simulation framework, including LEO orbit simulation, transmission (Tx) and receiver (Rx) architectures, and a positioning engine incorporating the necessary enhancements. Our findings suggest that LEO-based NTN positioning could serve as a complementary infrastructure to GNSS and, with appropriate enhancements, may also offer a viable alternative.

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arXiv2025

Determinantal Learning for Subset Selection in Wireless Networks

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.

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arXiv2025

Optimal No-Fly Zone Design for the Coexistence of Drone and Satellite Networks

Constructing a no-fly zone (NFZ) is a straightforward and effective way to facilitate the coexistence of unmanned aerial vehicles (drones) and existing systems (typically satellite systems). However, there has been little work on understanding the optimal design of such NFZs. In the absence of this design, one invariably ends up overestimating this region, hence significantly limiting the allowed airspace for the drones. To optimize the volume of the NFZ, we formulate this task as a variational problem and utilize the calculus of variations to rigorously obtain the NFZ as a function of the antenna pattern of victim receivers and the spatial distribution of drones. This approach parallels the matched filter design in the sense that the NFZ extends in directions where the antenna gain and/or the density of drones is high. Numerical simulations demonstrate the effectiveness of our optimal design compared to the known baselines in reducing the volume of the NFZ without compromising the protective performance.

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arXiv2023

NTN-based 6G Localization: Vision, Role of LEOs, and Open Problems

Since the introduction of 5G Release 18, non-terrestrial networks (NTNs) based positioning has garnered significant interest due to its numerous applications, including emergency services, lawful intercept, and charging and tariff services. This release considers single low-earth-orbit (LEO) positioning explicitly for $\textit{location verification}$ purposes, which requires a fairly coarse location estimate. To understand the future trajectory of NTN-based localization in 6G, we first provide a comprehensive overview of the evolution of 3rd Generation Partnership Project (3GPP) localization techniques, with specific emphasis on the current activities in 5G related to NTN location verification. We then delineate the suitability of LEOs for location-based services and emphasize increased interest in LEO-based positioning. In order to provide support for more accurate positioning in 6G using LEOs, we identify two NTN positioning systems that are likely study items for 6G: (i) multi-LEO positioning, and (ii) augmenting single-LEO and multi-LEO setups with Global Navigation Satellite System (GNSS), especially when an insufficient number of GNSS satellites (such as 2) are visible. We evaluate the accuracy of both systems through a 3GPP-compliant simulation study using a Cramér-Rao lower bound (CRLB) analysis. Our findings suggest that NTN technology has significant potential to provide accurate positioning of UEs in scenarios where GNSS signals may be weak or unavailable, but there are technical challenges in accommodating these solutions in 3GPP. We conclude with a discussion on the research landscape and key open problems related to NTN-based positioning.

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arXiv2021

Tensor Learning-based Precoder Codebooks for FD-MIMO Systems

This paper develops an efficient procedure for designing low-complexity codebooks for precoding in a full-dimension (FD) multiple-input multiple-output (MIMO) system with a uniform planar array (UPA) antenna at the transmitter (Tx) using tensor learning. In particular, instead of using statistical channel models, we utilize a model-free data-driven approach with foundations in machine learning to generate codebooks that adapt to the surrounding propagation conditions. We use a tensor representation of the FD-MIMO channel and exploit its properties to design quantized version of the channel precoders. We find the best representation of the optimal precoder as a function of Kronecker Product (KP) of two low-dimensional precoders, respectively corresponding to the horizontal and vertical dimensions of the UPA, obtained from the tensor decomposition of the channel. We then quantize this precoder to design product codebooks such that an average loss in mutual information due to quantization of channel state information (CSI) is minimized. The key technical contribution lies in exploiting the constraints on the precoders to reduce the product codebook design problem to an unsupervised clustering problem on a Cartesian Product Grassmann manifold (CPM), where the cluster centroids form a finite-sized precoder codebook. This codebook can be found efficiently by running a $K$-means clustering on the CPM. With a suitable induced distance metric on the CPM, we show that the construction of product codebooks is equivalent to finding the optimal set of centroids on the factor manifolds corresponding to the horizontal and vertical dimensions. Simulation results are presented to demonstrate the capability of the proposed design criterion in learning the codebooks and the attractive performance of the designed codebooks.

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arXiv2020

Meta Distribution of Downlink $\tt SIR$ in a Poisson Cluster Process-based HetNet Model

The performance analysis of heterogeneous cellular networks (HetNets), that relied mostly on the homogeneous Poisson point process (PPP) for the spatial distribution of the users and base stations (BSs), has seen a major transition with the emergence of the Poisson cluster process (PCP)-based models. With the combination of PPP and PCP, it is possible to construct a general HetNet model which can capture formation of hotspots and spatial coupling between the users and the BSs. While the downlink coverage analysis of this model in terms of the distribution of the received downlink signal-to-interference ratio ($\tt SIR$) is well understood by now, more fine grained analysis in terms of the meta distribution of ${\tt SIR}$ is an open problem. In this letter, we solve this problem by deriving the meta distribution of the downlink ${\tt SIR}$ assuming that the typical user connects to the BS providing the maximum received power.

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arXiv2020

Learning on a Grassmann Manifold: CSI Quantization for Massive MIMO Systems

This paper focuses on the design of beamforming codebooks that maximize the average normalized beamforming gain for any underlying channel distribution. While the existing techniques use statistical channel models, we utilize a model-free data-driven approach with foundations in machine learning to generate beamforming codebooks that adapt to the surrounding propagation conditions. The key technical contribution lies in reducing the codebook design problem to an unsupervised clustering problem on a Grassmann manifold where the cluster centroids form the finite-sized beamforming codebook for the channel state information (CSI), which can be efficiently solved using K-means clustering. This approach is extended to develop a remarkably efficient procedure for designing product codebooks for full-dimension (FD) multiple-input multiple-output (MIMO) systems with uniform planar array (UPA) antennas. Simulation results demonstrate the capability of the proposed design criterion in learning the codebooks, reducing the codebook size and producing noticeably higher beamforming gains compared to the existing state-of-the-art CSI quantization techniques.

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arXiv2020

Load on the Typical Poisson Voronoi Cell with Clustered User Distribution

In this letter, we characterize the distribution of the number of users associated with the typical base station (BS), termed the typical cell load, in a cellular network where the BSs are distributed as a homogeneous Poisson point process (PPP) and the users are distributed as an independent Poisson cluster process (PCP). In this setting, we derive the exact expressions for the first two moments of the typical cell load. Given the computational complexity of evaluating the higher moments, we derive easy-to-use approximations for the probability generating function (PGF) of the typical cell load, which can be inverted to obtain the probability mass function (PMF).

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arXiv2019

Millimeter Wave Integrated Access and Backhaul in 5G: Performance Analysis and Design Insights

With the emergence of integrated access and backhaul (IAB) in the fifth generation (5G) of cellular networks, backhaul is no longer just a passive capacity constraint in cellular network design. In fact, this tight integration of access and backhaul is one of the key ways in which 5G millimeter wave (mm-wave) heterogeneous cellular networks (HetNets) differ from traditional settings where the backhaul network was designed independently from the radio access network (RAN). With the goal of elucidating key design trends for this new paradigm, we develop an analytical framework for a two-tier HetNet with IAB where the macro base stations (MBSs) provide mm-wave backhaul to the small cell base stations (SBSs). For this network, we derive the downlink rate coverage probability for two types of resource allocations at the MBS: 1) integrated resource allocation (IRA): where the total bandwidth (BW) is dynamically split between access and backhaul, and 2) orthogonal resource allocation (ORA): where a static partition is defined for the access and backhaul communications. Our analysis concretely demonstrates that offloading users from the MBSs to SBSs may not provide similar rate improvements in an IAB setting as it would in a HetNet with fiber-backhauled SBS. Our analysis also shows that it is not possible to improve the user rate in an IAB setting by simply densifying the SBSs due to the bottleneck on the rate of wireless backhaul links between MBS and SBS.

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arXiv2019

Machine Learning meets Stochastic Geometry: Determinantal Subset Selection for Wireless Networks

In wireless networks, many problems can be formulated as subset selection problems where the goal is to select a subset from the ground set with the objective of maximizing some objective function. These problems are typically NP-hard and hence solved through carefully constructed heuristics, which are themselves mostly NP-complete and thus not easily applicable to large networks. On the other hand, subset selection problems occur in slightly different context in machine learning (ML) where the goal is to select a subset of high quality yet diverse items from a ground set. In this paper, we introduce a novel DPP-based learning (DPPL) framework for efficiently solving subset selection problems in wireless networks. The DPPL is intended to replace the traditional optimization algorithms for subset selection by learning the quality-diversity trade-off in the optimal subsets selected by an optimization routine. As a case study, we apply DPPL to the wireless link scheduling problem, where the goal is to determine the subset of simultaneously active links which maximizes the network-wide sum-rate. We demonstrate that the proposed DPPL approaches the optimal solution with significantly lower computational complexity than the popular optimization algorithms used for this problem in the literature.

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arXiv2018

Unified Analysis of HetNets using Poisson Cluster Process under Max-Power Association

Owing to its flexibility in modeling real-world spatial configurations of users and base stations (BSs), the Poisson cluster process (PCP) has recently emerged as an appealing way to model and analyze heterogeneous cellular networks (HetNets). Despite its undisputed relevance to HetNets -- corroborated by the models used in industry -- the PCP's use in performance analysis has been limited. This is primarily because of the lack of analytical tools to characterize performance metrics such as the coverage probability of a user connected to the strongest BS. In this paper, we develop an analytical framework for the evaluation of the coverage probability, or equivalently the complementary cumulative density function (CCDF) of signal-to-interference-and-noise-ratio (SINR), of a typical user in a K-tier HetNet under a max power-based association strategy, where the BS locations of each tier follow either a Poisson point process (PPP) or a PCP. The key enabling step involves conditioning on the parent PPPs of all the PCPs which allows us to express the coverage probability as a product of sum-product and probability generating functionals (PGFLs) of the parent PPPs. In addition to several useful insights, our analysis provides a rigorous way to study the impact of the cluster size on the SINR distribution, which was not possible using existing PPP-based models.

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arXiv2018

Bandwidth Partitioning and Downlink Analysis in Millimeter Wave Integrated Access and Backhaul for 5G

With the increasing network densification, it has become exceedingly difficult to provide traditional fiber backhaul access to each cell site, which is especially true for small cell base stations (SBSs). The increasing maturity of millimeter wave (mm-wave) communication has opened up the possibility of providing high-speed wireless backhaul to such cell sites. Since mm-wave is also suitable for access links, the third generation partnership project (3GPP) is envisioning an integrated access and backhaul (IAB) architecture for the fifth generation (5G) cellular networks in which the same infrastructure and spectral resources will be used for both access and backhaul. In this paper, we develop an analytical framework for IAB-enabled cellular network using which its downlink rate coverage probability is accurately characterized. Using this framework, we study the performance of three backhaul bandwidth (BW) partition strategies: 1) equal partition: when all SBSs obtain equal share of the backhaul BW; 2) instantaneous load-based partition: when the backhaul BW share of an SBS is proportional to its instantaneous load; and 3) average load-based partition: when the backhaul BW share of an SBS is proportional to its average load. Our analysis shows that depending on the choice of the partition strategy, there exists an optimal split of access and backhaul BW for which the rate coverage is maximized. Further, there exists a critical volume of cell-load (total number of users) beyond which the gains provided by the IAB-enabled network disappear and its performance converges to that of the traditional macro-only network with no SBSs.

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arXiv2018

Equi-coverage Contours in Cellular Networks

In this letter, we introduce a general cellular network model where i) users and BSs are distributed as two general point processes that may be coupled, ii) pathloss is assumed to follow a multi-slope power-law pathloss model, and iii) fading (power) is assumed to be independent across all wireless links. For this setup, we first obtain a set of contours representing the same meta distribution of SIR, which is the distribution of the conditional coverage probability given the point process, for different values of the parameters of the pathloss function and BS and user point processes. This general result is then specialized to 3GPP-inspired user and BS configurations obtained by combining Poisson point process (PPP) and Poisson cluster process (PCP).

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arXiv2017

Integrated mmWave Access and Backhaul in 5G: Bandwidth Partitioning and Downlink Analysis

With the increasing network densification, it has become exceedingly difficult to provide traditional fiber backhaul access to each cell site, which is especially true for small cell base stations (SBSs). The increasing maturity of millimeter wave (mmWave) communication has opened up the possibility of providing high-speed wireless backhaul to such cell sites. Since mmWave is also suitable for access links, the third generation partnership project (3GPP) is envisioning an integrated access and backhaul (IAB) architecture for the fifth generation (5G) cellular networks in which the same infrastructure and spectral resources will be used for both access and backhaul. In this paper, we develop an analytical framework for IAB-enabled cellular network using which we provide an accurate characterization of its downlink rate coverage probability. Using this, we study the performance of two backhaul bandwidth (BW) partition strategies, (i) equal partition: when all SBSs obtain equal share of the backhaul BW, and (ii) load-based partition: when the backhaul BW share of an SBS is proportional to its load. Our analysis shows that depending on the choice of the partition strategy, there exists an optimal split of access and backhaul BW for which the rate coverage is maximized. Further, there exists a critical volume of cell-load (total number of users) beyond which the gains provided by the IAB-enabled network disappear and its performance converges to that of the traditional macro-only network with no SBSs.

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arXiv2017

Nearest-Neighbor and Contact Distance Distributions for Matern Cluster Process

In this letter, we derive the cumulative density function (CDF) of the nearest neighbor and contact distance distributions of the Matern cluster process (MCP) in R2. These results will be useful in the performance analysis of many real-world wireless networks that exhibit inter-node attraction. Using these results, we concretely demonstrate that the contact distance of the MCP stochastically dominates its nearest-neighbor distance as well as the contact distance of the homogeneous Poisson point process (PPP) with the same density.

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arXiv2017

Enriched K-Tier HetNet Model to Enable the Analysis of User-Centric Small Cell Deployments

One of the principal underlying assumptions of current approaches to the analysis of heterogeneous cellular networks (HetNets) with random spatial models is the uniform distribution of users independent of the base station (BS) locations. This assumption is not quite accurate, especially for user-centric capacity-driven small cell deployments where low-power BSs are deployed in the areas of high user density, thus inducing a natural correlation in the BS and user locations. In order to capture this correlation, we enrich the existing K-tier Poisson Point Process (PPP) HetNet model by considering user locations as Poisson Cluster Process (PCP) with the BSs at the cluster centers. In particular, we provide the formal analysis of the downlink coverage probability in terms of a general density functions describing the locations of users around the BSs. The derived results are specialized for two cases of interest: (i) Thomas cluster process, where the locations of the users around BSs are Gaussian distributed, and (ii) Matérn cluster process, where the users are uniformly distributed inside a disc of a given radius. Tight closed-form bounds for the coverage probability in these two cases are also derived. Our results demonstrate that the coverage probability decreases as the size of user clusters around BSs increases, ultimately collapsing to the result obtained under the assumption of PPP distribution of users independent of the BS locations when the cluster size goes to infinity. Using these results, we also handle mixed user distributions consisting of two types of users: (i) uniformly distributed, and (ii) clustered around certain tiers.

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