arXiv subjects

Jun Tong

Publications and source records attributed to Jun Tong.

18 recordsLinked to original sources

arXiv2026

A Unified Pulse-Shaped OFDM Framework for Chirp-Domain Waveforms: Continuous-Time Modeling and Practical I/O Analysis

A unified framework for chirp-domain waveforms, including orthogonal chirp division multiplexing (OCDM) and affine frequency division multiplexing (AFDM), is developed. Their continuous-time representations are shown to fall within the conventional Weyl-Heisenberg (WH) framework for multicarrier waveforms, with the root chirp as the prototype pulse. Since the root chirp has constant envelope and is transparent to subcarrier orthogonality, these waveforms can be further interpreted as pulse-shaped (PS) orthogonal frequency division multiplexing (OFDM) signals, whose power spectral density is derived analytically. The derived spectrum reveals that implementations based on the discrete affine Fourier transform rely on sub-Nyquist samples and exhibit frequency aliasing. We prove that the corresponding aliased chirps are only conditionally orthogonal, whereas sample-wise root-Nyquist pulse shaping of the discrete-time AFDM (DT-AFDM) sequence produces mutually orthogonal pulse-shaped chirps, resulting in the pulse-shaped AFDM (PS-AFDM) waveform. We then derive an exact waveform-level input-output (I/O) relation for PS-AFDM over delay-Doppler (DD) channels, showing that the effective channel at a practical receiver is generally not a superposition of pure path-wise DD components. Waveform simulations verify the derived relation to machine precision, while the conventional sequence-level I/O relation for DT-AFDM exhibits a substantial mismatch with waveform behavior for practical channels with continuous-valued delays.

cs.IT↗

arXiv2026

Sensing Mutual Information for Communication Signal with Deterministic Pilots and Random Data Payloads

The recent emergence of the integrated sensing and communication (ISAC) framework has sparked significant interest in quantifying the sensing capabilities inherent in communication signals. However, existing literature has mainly focused on scenarios involving either purely random or purely deterministic waveforms. This overlooks a critical reality: operational communication standards invariably utilize a hybrid structure comprising both deterministic pilots for channel estimation and random payloads for data transmission. To bridge this gap, this paper investigates the sensing mutual information (SMI) and precoding design specifically for ISAC systems employing communication signals with both pilots and data payloads. First, by utilizing random matrix theory (RMT), we derive a tractable closed-form expression for the SMI that accurately accounts for the statistical properties of the hybrid signal. Building upon this theoretical foundation, we formulate a precoding optimization problem to maximize SMI with constraints on the transmit power and communication rate, which is solved via an efficient alternating direction method of multipliers framework. Simulation results validate the accuracy of the theoretical results and demonstrate the superiority of the proposed precoding design over conventional benchmarks.

cs.IT↗

arXiv2025

Spectrum and Orthogonality of Orthogonal Delay-Doppler Division Multiplexing Modulation Waveforms

Orthogonal delay-Doppler (DD) division multiplexing (ODDM) modulation has recently emerged as a promising paradigm for ensuring reliable communications in doubly-selective channels. This work investigates the spectra and orthogonality characteristics of analog (direct) and approximate digital implementations of ODDM systems. We first determine the time and frequency domain representations of the basis functions for waveform in analog and approximate digital ODDM systems. Thereafter, we derive their power spectral densities and show that while the spectrum of analog ODDM waveforms exhibits a step-wise behavior in its transition regions, the spectrum of approximate digital ODDM waveforms is confined to that of the ODDM sub-pulse. Next, we prove the orthogonality characteristics of approximate digital ODDM waveforms and show that, unlike analog ODDM waveforms, the approximate digital ODDM waveforms satisfy orthogonality without the need of additional time domain resources. Additionally, we examine the similarities and differences that implementations of approximate digital ODDM share with the other variants of DD modulations, focusing on the domain changes the symbols undergo, the type of pulse shaping and windowing used, and the domains and the sequence in which they are performed. Finally, we present numerical results to validate our findings and draw further insights.

eess.SP↗

arXiv2025

On-Grid Equivalence of Continuous-Time Doubly Selective Channels: A Revisit of Bello's Models

Significant studies on communications over doubly selective channels have utilized on-grid DD channel models, which are previously investigated in Bello's seminar paper in 1963. The DD grid is typically specified by the bandwidth and time duration of the transmission frames. However, the physical channels are determined by the propagation environments and they are typically off-grid. Hence, there is often a gap between an actual physical channel and the on-grid model. This paper revisits the on-grid modeling of practical physical channels. We study the associated on-grid DD-domain representations for continuous-time, doubly selective channels with off-grid delay and Doppler shifts, accounting for practical time/frequency-domain windowing at the transceivers. The universal models obtained are applicable under the mild assumption that the windows have finite supports, and they extend Bello's classical results to account for more general windows. We also discuss the features and implications of the equivalent on-grid models.

eess.SP↗

arXiv2024

Performance of orthogonal delay-doppler division multiplexing modulation with imperfect channel estimation

The orthogonal delay-Doppler division multiplexing (ODDM) modulation is a recently proposed multi-carrier modulation that features a realizable pulse orthogonal with respect to the delay-Doppler (DD) plane's fine resolutions. In this paper, we investigate the performance of ODDM systems with imperfect channel estimation considering three detectors, namely the message passing algorithm (MPA) detector, iterative maximum-ratio combining (MRC) detector, and successive interference cancellation with minimum mean square error (SIC-MMSE) detector. We derive the post-equalization signal-to-interference-plus-noise ratio (SINR) for MRC and SIC-MMSE and analyze their bit error rate (BER) performance. Based on this analysis, we propose the MRC with subtractive dither (MRC-SD) and soft SIC-MMSE initialized MRC (SSMI-MRC) detector to improve the BER of iterative MRC. Our results demonstrate that soft SIC-MMSE consistently outperforms the other detectors in BER performance under perfect and imperfect CSI. While MRC exhibits a BER floor above $10^{-5}$, MRC-SD effectively lowers the BER with a negligible increase in detection complexity. SSMI-MRC achieves better BER than hard SIC-MMSE with the same detection complexity order. Additionally, we show that MPA has an error floor and is sensitive to imperfect CSI.

eess.SP↗

arXiv2023

A combinatorial model for $q$-characters of fundamental modules of type $D_{n}$

In this paper, we introduce a combinatorial path model of representation of the quantum affine algebra of type $D_n$, inspired by Mukhin and Young's combinatorial path models of representations of the quantum affine algebras of types $A_n$ and $B_n$. In particular, we give a combinatorial formula for $q$-characters of fundamental modules of type $D_{n}$ by assigning each path to a monomial or binomial. By counting our paths, a new expression on dimensions of fundamental modules of type $D_n$ is obtained.

math.QA↗

arXiv2021

Cross-Validated Tuning of Shrinkage Factors for MVDR Beamforming Based on Regularized Covariance Matrix Estimation

This paper considers the regularized estimation of covariance matrices (CM) of high-dimensional (compound) Gaussian data for minimum variance distortionless response (MVDR) beamforming. Linear shrinkage is applied to improve the accuracy and condition number of the CM estimate for low-sample-support cases. We focus on data-driven techniques that automatically choose the linear shrinkage factors for shrinkage sample covariance matrix ($\text{S}^2$CM) and shrinkage Tyler's estimator (STE) by exploiting cross validation (CV). We propose leave-one-out cross-validation (LOOCV) choices for the shrinkage factors to optimize the beamforming performance, referred to as $\text{S}^2$CM-CV and STE-CV. The (weighted) out-of-sample output power of the beamfomer is chosen as a proxy of the beamformer performance and concise expressions of the LOOCV cost function are derived to allow fast optimization. For the large system regime, asymptotic approximations of the LOOCV cost functions are derived, yielding the $\text{S}^2$CM-AE and STE-AE. In general, the proposed algorithms are able to achieve near-oracle performance in choosing the linear shrinkage factors for MVDR beamforming. Simulation results are provided for validating the proposed methods.

eess.SP↗

arXiv2021

Regularized Covariance Estimation for Polarization Radar Detection in Compound Gaussian Sea Clutter

This paper investigates regularized estimation of Kronecker-structured covariance matrices (CM) for polarization radar in sea clutter scenarios where the data are assumed to follow the complex, elliptically symmetric (CES) distributions with a Kronecker-structured CM. To obtain a well-conditioned estimate of the CM, we add penalty terms of Kullback-Leibler divergence to the negative log-likelihood function of the associated complex angular Gaussian (CAG) distribution. This is shown to be equivalent to regularizing Tyler's fixed-point equations by shrinkage. A sufficient condition that the solution exists is discussed. An iterative algorithm is applied to solve the resulting fixed-point iterations and its convergence is proved. In order to solve the critical problem of tuning the shrinkage factors, we then introduce two methods by exploiting oracle approximating shrinkage (OAS) and cross-validation (CV). The proposed estimator, referred to as the robust shrinkage Kronecker estimator (RSKE), is shown to achieve better performance compared with several existing methods when the training samples are limited. Simulations are conducted for validating the RSKE and demonstrating its high performance by using the IPIX 1998 real sea data.

eess.SP↗

arXiv2019

On the Performance of Massive MIMO Systems With Low-Resolution ADCs Over Rician Fading Channels

This paper considers uplink massive multiple-input multiple-output (MIMO) systems with lowresolution analog-to-digital converters (ADCs) over Rician fading channels. Maximum-ratio-combining (MRC) and zero-forcing (ZF) receivers are considered under the assumption of perfect and imperfect channel state information (CSI). Low-resolution ADCs are considered for both data detection and channel estimation, and the resulting performance is analyzed. Asymptotic approximations of the spectrum efficiency (SE) for large systems are derived based on random matrix theory. With these results, we can provide insights into the trade-offs between the SE and the ADC resolution and study the influence of the Rician K-factors on the performance. It is shown that a large value of K-factors may lead to better performance and alleviate the influence of quantization noise on channel estimation. Moreover, we investigate the power scaling laws for both receivers under imperfect CSI and it shows that when the number of base station (BS) antennas is very large, without loss of SE performance, the transmission power can be scaled by the number of BS antennas for both receivers while the overall performance is limited by the resolution of ADCs. The asymptotic analysis is validated by numerical results. Besides, it is also shown that the SE gap between the two receivers is narrowed down when the K-factor is increased. We also show that ADCs with moderate resolutions lead to better energy efficiency (EE) than that with high-resolution or extremely low-resolution ADCs and using ZF receivers achieve higher EE as compared with the MRC receivers.

eess.SP↗

arXiv2019

Gridless Variational Bayesian Channel Estimation for Antenna Array Systems with Low Resolution ADCs

Employing low-resolution analog-to-digital converters (ADCs) coupled with large antenna arrays at the receivers has drawn considerable interests in the millimeter wave (mm-wave) system. Since mm-wave channels are sparse in angular dimensions, exploiting the structure could reduce the number of measurements while achieve acceptable performance at the same time. Motivated by the variational Bayesian line spectral estimation (VALSE) algorithm which treats the angles as random parameters, in contrast with previous works which confine the estimate to the set of grid angle points and induce grid mismatch, this paper proposes the grid-less quantized variational Bayesian channel estimation (GL-QVBCE) algorithm for antenna array systems with low resolution ADCs. Compared to the traditional least squares (LS) approach, numerical results show that GL-QVBCE performs significantly better and asymptotically approaches the Cram\`{e}r Rao bound (CRB).

eess.SP↗

arXiv2019

Channel Covariance Matrix Estimation via Dimension Reduction for Hybrid MIMO MmWave Communication Systems

Hybrid massive MIMO structures with lower hardware complexity and power consumption have been considered as a potential candidate for millimeter wave (mmWave) communications. Channel covariance information can be used for designing transmitter precoders, receiver combiners, channel estimators, etc. However, hybrid structures allow only a lower-dimensional signal to be observed, which adds difficulties for channel covariance matrix estimation. In this paper, we formulate the channel covariance estimation as a structured low-rank matrix sensing problem via Kronecker product expansion and use a low-complexity algorithm to solve this problem. Numerical results with uniform linear arrays (ULA) and uniform squared planar arrays (USPA) are provided to demonstrate the effectiveness of our proposed method.

eess.SP↗

arXiv2019

Extreme Learning Machine Based Non-Iterative and Iterative Nonlinearity Mitigation for LED Communications

This work concerns receiver design for light emitting diode (LED) communications where the LED nonlinearity can severely degrade the performance of communications. We propose extreme learning machine (ELM) based non-iterative receivers and iterative receivers to effectively handle the LED nonlinearity and memory effects. For the iterative receiver design, we also develop a data-aided receiver, where data is used as virtual training sequence in ELM training. It is shown that the ELM based receivers significantly outperform conventional polynomial based receivers; iterative receivers can achieve huge performance gain compared to non-iterative receivers; and the data-aided receiver can reduce training overhead considerably. This work can also be extended to radio frequency communications, e.g., to deal with the nonlinearity of power amplifiers.

eess.SP↗

arXiv2018

Linear Shrinkage Estimation of Covariance Matrices Using Low-Complexity Cross-Validation

Shrinkage can effectively improve the condition number and accuracy of covariance matrix estimation, especially for low-sample-support applications with the number of training samples smaller than the dimensionality. This paper investigates parameter choice for linear shrinkage estimators. We propose data-driven, leave-one-out cross-validation (LOOCV) methods for automatically choosing the shrinkage coefficients, aiming to minimize the Frobenius norm of the estimation error. A quadratic loss is used as the prediction error for LOOCV. The resulting solutions can be found analytically or by solving optimization problems of small sizes and thus have low complexities. Our proposed methods are compared with various existing techniques. We show that the LOOCV method achieves near-oracle performance for shrinkage designs using sample covariance matrix (SCM) and several typical shrinkage targets. Furthermore, the LOOCV method provides low-complexity solutions for estimators that use general shrinkage targets, multiple targets, and/or ordinary least squares (OLS)-based covariance matrix estimation. We also show applications of our proposed techniques to several different problems in array signal processing.

cs.IT↗

arXiv2018

Matrix Completion-Based Channel Estimation for MmWave Communication Systems With Array-Inherent Impairments

Hybrid massive MIMO structures with reduced hardware complexity and power consumption have been widely studied as a potential candidate for millimeter wave (mmWave) communications. Channel estimators that require knowledge of the array response, such as those using compressive sensing (CS) methods, may suffer from performance degradation when array-inherent impairments bring unknown phase errors and gain errors to the antenna elements. In this paper, we design matrix completion (MC)-based channel estimation schemes which are robust against the array-inherent impairments. We first design an open-loop training scheme that can sample entries from the effective channel matrix randomly and is compatible with the phase shifter-based hybrid system. Leveraging the low-rank property of the effective channel matrix, we then design a channel estimator based on the generalized conditional gradient (GCG) framework and the alternating minimization (AltMin) approach. The resulting estimator is immune to array-inherent impairments and can be implemented to systems with any array shapes for its independence of the array response. In addition, we extend our design to sample a transformed channel matrix following the concept of inductive matrix completion (IMC), which can be solved efficiently using our proposed estimator and achieve similar performance with a lower requirement of the dynamic range of the transmission power per antenna. Numerical results demonstrate the advantages of our proposed MC-based channel estimators in terms of estimation performance, computational complexity and robustness against array-inherent impairments over the orthogonal matching pursuit (OMP)-based CS channel estimator.

cs.IT↗

arXiv2016

Low-Complexity and Basis-Free Channel Estimation for Switch-Based mmWave MIMO Systems via Matrix Completion

Recently, a switch-based hybrid massive MIMO structure that aims to reduce the hardware complexity and power consumption has been proposed as a potential candidate for millimeter wave (mmWave) communications. Exploiting the sparse nature of the mmWave channel, compressive sensing (CS)-based channel estimators have been proposed. When applied to real mmWave channels, the CS-based channel estimators may encounter heavy computational burden due to the high dimensionality of the basis. Meanwhile, knowledge about the response of the antenna array, which is needed for constructing the basis of the CS estimators, may not be perfect due to array uncertainties such as phase mismatch among array elements. This can result in the loss of sparse representation and hence the degraded performance of the CS estimator. In this paper, we propose a novel matrix completion (MC)-based low-complexity channel estimator. The proposed scheme is compatible with switch-based hybrid structures, does not need to specify a basis, and can avoid the basis mismatch issue. Compared with the existing CS-based estimator, the proposed basis-free scheme is immune to array response mismatch and exhibits a significantly lower complexity.

cs.IT↗

arXiv2014

Possible spin frustration in Nd$_2$Ti$_2$O$_7$ probed by muon spin relaxation

Muon spin relaxation on Nd$_2$Ti$_2$O$_7$ (NTO) and NdLaTi$_2$O$_7$ (NLTO) compounds are presented. The time spectra for both compounds are as expected for the paramagnetic state at high temperatures, but deviate from the exponential function below about 100 K. The muon spin relaxation rate increases with decreasing temperature firstly, and then levels off below about 10 K, which is reminiscent of the frustrated systems. An enhancement of the relaxation rate by a longitudinal field in the paramagnetic state is observed for NTO, and eliminated by a magnetic dilution for the NLTO sample. This suggests that the spectral density is modified by a magnetic dilution and thus indicates that the spins behave cooperatively rather than individually. Zero-field measurement at 0.3 K indicates that the magnetic ground state for NTO is ferromagnetic.

cond-mat.str-el↗

arXiv2010

Suppression of $T_c$ by Zn impurity in the electron-type LaFe$_{0.925-y}$Co$_{0.075}$Zn$_y$AsO system

The effect of non-magnetic Zn impurity on superconductivity in electron-type pnictide superconductor LaFe$_{0.925-y}$Co$_{0.075}$Zn$_y$AsO is studied systematically. The optimally doped LaFe$_{0.925}$Co$_{0.075}$AsO without Zn impurity exhibits superconductivity at $T_c^{mid}$ of 13.2 K, where $T_c^{mid}$ is defiend as the mid-point in the resistive transition. In the presence of Zn impurity, the superconducting transition temperature, $T_c^{mid}$, is severely suppressed. The result is consistent with the theoretic prediction on the effect of non-magnetic impurity in the scenario of $s_{\pm}$ pairing, but it is in sharp contrast to the previous report on the effect of Zn impurity in the F-doped systems. The possible interpretation of the different effects of Zn impurity on superconductivity in different systems is discussed.

cond-mat.supr-con↗

arXiv2010

Effect of a Zn impurity on T_c and its implication to pairing symmetry in LaFeAsO$_{1-x}$F$_x$

The effect of non-magnetic Zn impurity on superconductivity in LaFe$_{1-y}$Zn$_y$AsO$_{1-x}$F$_x$ system is studied systematically. In the presence of Zn impurity, the superconducting transition temperature increases in the under-doped regime, remains unchanged in the optimally doped regime, and is severely suppressed in the over-doped regime. Our results suggest a switch of the symmetry of the superconducting order parameters from a $s$-wave to $s_{\pm}$ or $d$-wave states as the charge carrier doping increases in FeAs-based superconductors.

cond-mat.supr-con↗