arXiv subjects

Sumit Roy

Publications and source records attributed to Sumit Roy.

At least 19 recordsLinked to original sources

arXiv2026

Joint Delay--Doppler Modeling of Multipath LEO Channels

Multipath channel models for Low-Earth-orbit (LEO) non-terrestrial network (NTN) must contend with time variability due to rapid satellite orbital motion that in turn impacts local (near terrestrial) scattering near the ground terminal (GT) receiver. While 3GPP-defined NTN channel model pipelines TR 38.811, 38.901 incorporate elevation-dependence into statistical channel generators, these are inherited largely from 2-D terrestrial propagation and are largely insufficient. Further, they do not prescribe any integrated workflow that is broadly available for generating joint delay, Doppler/phase and component multipath power profiles as a function of satellite location over a pass. This work addresses this gap by developing a geometry-based stochastic channel model driven by prescribed slant range, elevation, and azimuth over a LEO pass. A ground scene generates wall-reflected, ground-reflected, and roof-edge-diffracted components, from which joint delay-Doppler statistics and temporal channel impulse response (CIR) evolution are obtained. The resulting locally wide-sense stationary tapped-delay-line CIR enables analysis of key statistics such as the $K$-factor of the taps, multipath delay and Doppler spreads as a function of elevation and scene parameters. Depending on the scenarios (urban and rural), our model-based results show that with omnidirectional antennas, the LoS probability, delay-spread and $K$-factor trends broadly match 3GPP NTN models in TR 38.811 as a function of elevation. Beamforming instead produces a mid-elevation $K$-factor peak, which is not predicted by TR 38.811 and 6G NTN. Doppler spreads are smaller than those from our previous model and QuaDriGa because the proposed model accounts for path existence. Stationarity durations for CIR are reported and generally decrease with elevation, but with local increases at mid-elevation due to path geometry effects.

eess.SP↗

arXiv2026

Beyond TR 38.811 for 6G NTN Channel Models

As the 3rd Generation Partnership Project (3GPP) expands 6G non-terrestrial network (NTN) to S, Ku, and Ka bands for integration with existing terrestrial cellular networks, the necessary satellite channel model for link and network performance evaluation remains tied to TR 38.811, last revised in 2020. We identify issues on multiple fronts: inappropriate parameter specifications based on very limited site-specific environments considered, omission of satellite-induced Doppler spread and directional antenna effects and lack of a transparent channel model generation procedure. To address these limitations, we re-derive the channel parameters using ray tracing (RT) over urban and rural environments based on ITU-R building statistics. Our results show that TR 38.811 substantially overestimates the K-factor at low elevations and predicts a decreasing trend with elevation, which is inconsistent with RT. The Ka-band clutter loss (CL) also exceeds the RT estimates by more than 15 dB in urban cases. It also underestimates rural delay spread (DS) at low elevations and predicts an elevation trend inconsistent with RT. We further quantify the previously neglected satellite-induced Doppler spread. Finally, we demonstrate that the conventional TR 38.811 channel generator significantly underestimates the K-factor in the presence of directional antenna (beamforming), while our modified generator substantially reduces this discrepancy.

eess.SP↗

arXiv2026

Temporal vs Spectral Resolution in CSI Reporting for Wi-Fi ISAC

CSI feedback is fundamental to proposed uses of Wi-Fi sensing such as human activity recognition (HAR); but it also constitutes significant overhead as resources must be allocated away from data communications. Wi-Fi CSI extraction can be explored along two dimensions in IEEE 802.11bf: reporting intensity, i.e., temporal resolution, and number of reported subcarriers, i.e., spectral resolution. We explore periodic and IEEE 802.11bf threshold-based reporting at matched rates, and uniform decimation and block-mean grouping at matched report sizes. We further propose reporting the mean CSI accumulated since the last report. Using the 802.11bf report size as the metric, we evaluate the accuracy-cost tradeoffs on three public datasets with our proposed model, a convolutional neural network combined with a gated recurrent unit and temporal pyramid pooling. The proposed periodic reporting with mean payload and block-mean grouping improves accuracy by up to 53 percentage points at equal CSI overhead cost. Temporal resolution is generally more cost-effective than spectral resolution. With only at most 7.7% of full-CSI feedback cost, the proposed scheme achieves 96-98% of full-CSI accuracy.

eess.SP↗

arXiv2026

Topology of moduli of parabolic connections with fixed determinant

Let $X$ be a compact Riemann surface of genus $g \geq 2$ and $D\subset X$ be a fixed finite subset. Let $ξ$ be a line bundle of degree $d$ over $X$. Let $\mathcal{M}(α, r, ξ)$ (respectively, $\mathcal{M}_{\mathrm{conn}}(α, r, ξ)$) denote the moduli space of stable parabolic bundles (respectively, parabolic connections) of rank $r$ $(\geq 2)$, determinant $ξ$ and full flag generic parabolic weight type $α$. We show that $ π_k(\mathcal{M}_{\mathrm{conn}}(α, r, ξ)) \cong π_k(\mathcal{M}(α, r, ξ)) $ for $k \leq2(r-1)(g-1)-1$. As a consequence, we deduce that the moduli space $\mathcal{M}_{\mathrm{conn}}(α, r, ξ)$ is simply connected. We also show that the Hodge structures on the torsion-free parts of both the cohomologies $H^k(\mathcal{M}_{\mathrm{conn}}(α, r, ξ),\mathbb{Z})$ and $H^k(\mathcal{M}(α, r, ξ),\mathbb{Z})$ are isomorphic for all $k\leq 2(r-1)(g-1)+1$.

math.AG↗

arXiv2026

Quadratic one-forms on logarithmic Higgs moduli

Let $C$ be a compact Riemann surface of genus at least two, and let $G$ be a connected complex reductive group. We study quadratic one-forms associated to logarithmic $G$-Higgs bundles on a pointed curve $(C,D)$ with nilpotent residues. We use the elementary pole cancellation for invariant polynomials, where nilpotency of the residue removes the leading pole term. In degree two this places $B(Φ,Φ)$ in the cotangent space of pointed Teichmuller space, and hence gives a logarithmic quadratic one-form. We relate this one-form to the variation of the energy for tame nilpotent harmonic bundles. The energy formula is proved under a positive decay assumption near the punctures. We also write the corresponding compact formulae for classical groups and standard real forms.

math.DG↗

arXiv2026

A mathematical model to predict growth and treatment for UPS cancer

We propose a mathematical model for the growth and treatment of Undifferentiated Pleomorphic Sarcoma (UPS) using a system of nonlinear differential equations. The model combines Gompertz-type tumor growth with surface-dependent necrotic loss, surgical resection with residual disease, postoperative recovery, tumor--immune interaction, and radiation treatment scheduling. We study the mathematical properties of the model and obtain several results. The growth equation shows the existence of a threshold below which the tumor cannot survive and may disappear. The postoperative phase exhibits an early inflammatory stage followed by proliferative recovery. For the tumor-immune subsystem, equilibrium states and local stability conditions are identified. The radiation treatment problem is formulated as an optimal control problem, and the optimal strategy is shown to be of bang-bang type. The model suggests that tumor recurrence depends not only on tumor growth itself but also on residual disease, postoperative dynamics, immune response, and treatment timing.

math.OC↗

arXiv2026

Semiprojectivity and very stability in moduli of symplectic and orthogonal parabolic Higgs bundles

Let $X$ be a compact Riemann surface of genus $g \geq 2$, and let $D \subset X$ be a fixed finite subset. We prove the semiprojectivity of the moduli space of semistable symplectic or orthogonal parabolic Higgs bundles over $X$. We show that a stable symplectic parabolic bundle $E$ on $X$ is strongly very stable, meaning $E$ does not have any nonzero strongly parabolic nilpotent Higgs field, if and only if the symplectic parabolic Hitchin morphism induced on the affine space $$H^0(X,\mathrm{SPEnd}_\mathrm{Sp}(E) \otimes K(D))$$ is a proper morphism, where $\mathrm{SPEnd}_\mathrm{Sp}(E)$ denotes the set of symplectic strongly parabolic endomorphisms of $E$. We remark that the same criterion for very stability applies to the orthogonal case.

math.AG↗

arXiv2026

Semiprojectivity of the moduli of principal $G$-bundles with $λ$-connections

Let $X$ be a compact connected Riemann surface of genus $g \geq 2$ and $G$ a connected reductive affine algebraic group over $\mathbb{C}$. We prove the semiprojectivity of the moduli spaces of semistable $G$-Higgs bundles and $G$-bundles with $λ$-connections of fixed topological type $d\in π_1(G)$. As an application, in the smooth case we describe the resulting Bialynicki - Birula decomposition and derive cohomological and motivic consequences.

math.AG↗

arXiv2026

On some topological equivalences for moduli spaces of $G$-bundles

Let $X$ be a smooth projective curve of genus $g \geq 3$, and let $G$ be a nontrivial connected reductive affine algebraic group over $\mathbb{C}$. Examining the moduli spaces of regularly stable $G$-Higgs bundles and holomorphic $G$-connections with a fixed topological type $d\in π_1(G)$ over $X$, we establish that the $k$-th homotopy groups of these two moduli spaces are isomorphic for $k \leq 2g-4$. We also prove that the mixed Hodge structures on the rational cohomology groups of these two moduli spaces are pure and isomorphic. Lastly, we explicitly describe the homotopy groups of the moduli space of $\mathrm{SL}(n,\mathbb{C})$-connections over $X$.

math.AG↗

arXiv2025

LEO Downlink Channel Model Revisited: Scattering Geometry-Inspired Derivation

This paper presents a new derivation of LEO-to-ground receiver channel model to address a clear gap in the prior art: the lack of an appropriate geometry aware characterization of non LOS (NLOS) link model represented by the power spectral density (PSD). Specifically, the main contribution is a coherent derivation of the PSD from 1st principles that is able to reproduce results in prior art and explain the causal relationship of main PSD features to the propagation geometry parameters.

eess.SP↗

arXiv2024

Static Background Removal in Vehicular Radar: Filtering in Azimuth-Elevation-Doppler Domain

Anti-collision assistance, integral to the current drive towards increased vehicular autonomy, relies heavily on precise detection and localization of moving targets in the vehicle's vicinity. A crucial step towards achieving this is the removal of static objects from the scene, thereby enhancing the detection and localization of dynamic targets - a pivotal aspect in augmenting overall system performance. In this paper, we propose a static background removal algorithm tailored for automotive scenarios, designed for common frequency-modulated continuous wave (FMCW) radars. This algorithm effectively eliminates reflections corresponding to static backgrounds from radar images through a two-step process: 4-dimensional (4D) radar imaging and filtering in the azimuth-elevation-Doppler domain. Our proposed approach is underpinned by a model customized for FMCW radar signals, incorporating a time-division multiplexing-based multiple-input multiple-output scheme on the non-uniform radar array. Furthermore, our filtering process requires knowledge of the 3-dimensional (3D) radar ego-motion velocity, typically obtained from an external sensor. To address scenarios where such sensors are unavailable, we introduce a self-contained 3D ego-motion estimation approach. Finally, we evaluate the performance of our algorithm using both simulated and real-world data, analyzing its sensitivity and time complexity in comparison to established baselines.

eess.SP↗

arXiv2024

Revisiting Multi-User Downlink in IEEE 802.11ax: A Designers Guide to MU-MIMO

Downlink (DL) Multi-User (MU) Multiple Input Multiple Output (MU-MIMO) is a key technology that allows multiple concurrent data transmissions from an Access Point (AP) to a selected sub-set of clients for higher network efficiency in IEEE 802.11ax. However, DL MU-MIMO feature is typically turned off as the default setting in AP vendors' products, that is, turning on the DL MU-MIMO may not help increase the network efficiency, which is counter-intuitive. In this article, we provide a sufficiently deep understanding of the interplay between the various underlying factors, i.e., CSI overhead and spatial correlation, which result in negative results when turning on the DL MU-MIMO. Furthermore, we provide a fundamental guideline as a function of operational scenarios to address the fundamental question "when the DL MU-MIMO should be turned on/off".

cs.NI↗

arXiv2024

IEEE 802.11be Network Throughput Optimization with Multi-Link Operation and AP Coordination

IEEE 802.11be (Wi-Fi 7) introduces a new concept called multi-link operation (MLO), which allows multiple Wi-Fi interfaces in different bands (2.4, 5, and 6 GHz) to work together to increase network throughput, reduce latency, and improve spectrum reuse efficiency in dense overlapping networks. To make the most of MLO, this paper proposes a new data-driven resource allocation algorithm for the 11be network with the aid of an access point (AP) controller. To maximize network throughput, a network topology optimization problem is formulated for 11be network, which is solved by exploiting the totally unimodular property of the bipartite graph formed by the connection between AP and station (STA) in Wi-Fi networks. Subsequently, a proportional fairness algorithm is applied for radio link allocation, network throughput optimization considering the channel condition, and the fairness of the multi-link device (MLD) data rate. The performance of the proposed algorithm on two main MLO implementations - multi-link multi-radio (MLMR) with simultaneous transmission and reception (STR), and the interplay between multiple nodes employing them are evaluated through cross-layer (PHY-MAC) data rate simulation with PHY abstraction.

cs.NI↗

arXiv2024

On motives of parabolic Higgs bundles and parabolic connections

Let $X$ be a compact Riemann surface of genus $g \geq 2$ and let $D\subset X$ be a fixed finite subset. We considered the moduli spaces of parabolic Higgs bundles and of parabolic connections over $X$ with the parabolic structure over $D$. For generic weights, we showed that these two moduli spaces have equal Grothendieck motivic classes and their $E$-polynomials are the same. We also show that the Voevodsky and Chow motives of these two moduli spaces are also equal. We showed that the Grothendieck motivic classes and the $E$-polynomials of parabolic Higgs moduli and of parabolic Hodge moduli are closely related. Finally, we considered the moduli spaces with fixed determinants and showed that the above results also hold for the fixed determinant case.

math.AG↗

arXiv2023

On torsion-freeness of Kähler differential sheaves

Let $X$ be a normal algebraic variety over an algebraically closed field $k$ of characteristic zero. We prove that the Kähler differential sheaf of $X$ is torsion-free if and only if any regular section of the ideal sheaf of the first order deformation of $X$ inside $X\times_k X$, defined outside the singular locus of $X \times_k X$, extends regularly to the singular locus.

math.AG↗

arXiv2023

Mutual Interference Mitigation for MIMO-FMCW Automotive Radar

This paper considers mutual interference mitigation among automotive radars using frequency-modulated continuous wave (FMCW) signal and multiple-input multiple-output (MIMO) virtual arrays. For the first time, we derive a general interference signal model that fully accounts for not only the time-frequency incoherence, e.g., different FMCW configuration parameters and time offsets, but also the slow-time code MIMO incoherence and array configuration differences between the victim and interfering radars. Along with a standard MIMO-FMCW object signal model, we turn the interference mitigation into a spatial-domain object detection under incoherent MIMO-FMCW interference described by the explicit interference signal model, and propose a constant false alarm rate (CFAR) detector. More specifically, the proposed detector exploits the structural property of the derived interference model at both \emph{transmit} and \emph{receive} steering vector space. We also derive analytical closed-form expressions for probabilities of detection and false alarm. Performance evaluation using both synthetic-level and phased array system-level simulation confirms the effectiveness of our proposed detector over selected baseline methods.

eess.SP↗

arXiv2023

Perception Through 2D-MIMO FMCW Automotive Radar Under Adverse Weather

Millimeter-wave (mmWave) radars are being increasingly integrated in commercial vehicles to support new Adaptive Driver Assisted Systems (ADAS) features that require accurate location and Doppler velocity estimates of objects, independent of environmental conditions. To explore radar-based ADAS applications, we have updated our test-bed with Texas Instrument's 4-chip cascaded FMCW radar (TIDEP-01012) that forms a non-uniform 2D MIMO virtual array. In this paper, we develop the necessary received signal models for applying different direction of arrival (DoA) estimation algorithms and experimentally validating their performance on formed virtual array under controlled scenarios. To test the robustness of mmWave radars under adverse weather conditions, we collected raw radar dataset (I-Q samples post demodulated) for various objects by a driven vehicle-mounted platform, specifically for snowy and foggy situations where cameras are largely ineffective. Initial results from radar imaging algorithms to this dataset are presented.

eess.SP↗

arXiv2022

Optimal Beam Training for mmWave Massive MIMO using 802.11ay

Beam training of 802.11 ad is a technology that helps accelerate the analog weighting vector (AWV) selection process under the constraint of the existing code-book for AWV. However, 5G milli-meter wave (mmWave) multiple-input-multiple-output (MIMO) system brings challenges to this new technology due to the higher order of complexity of antennae. Hence, the existing codebook of 11ad is unlikely to even include the near-optimal AWV and the data rate will degrade severely. To cope with this situation, this paper proposed a new beam training protocol combined with the state-of-the-art compressed sensing channel estimation in order to find the AWV to maximize the optimal data-rate. Simulation is implemented to show the data-rate of AWV achieved by 11 ad is worse than the proposed protocol.

cs.IT↗