Doubly Dispersive Research Articles

Bifurcation analysis and soliton solutions to the doubly dispersive equation in elastic inhomogeneous Murnaghan's rod.

The doubly dispersive (DD) equation finds extensive utility across scientific and engineering domains. It stands as a significant nonlinear physical model elucidating nonlinear wave propagation within the elastic inhomogeneous Murnaghan's rod (EIMR). With this in mind, we have focused on the integration of the DD model and the modified Khater (MK) method. Through the wave transformation, this model is effectively converted into an ordinary differential equation. In this paper, the goal of our work is to explore new wave solutions to the DD model by using the MK scheme. These solutions provide extremely helpful insights into the operation of the system. The three-dimensional (3D) plot and two-dimensional (2D) combined plot via the impacts of the parameters are provided for various parameters in this manuscript. We also discussed the dynamical properties of the model, which are accomplished through the bifurcation analysis, and also found the Hamiltonian function. This research makes a substantial contribution to the area by increasing our understanding of wave solutions in the DD, introducing novel investigation tools, and carrying out an in-depth investigation of the bifurcation and stability aspects of the system. As a direct result of this research, novel openings have been uncovered for further investigation and application in the various disciplines of science and engineering.

Design of Robust Pulses to Insufficient Synchronization for OFDM/OQAM Systems in Doubly Dispersive Channels

This paper presents a pulse shaping method robust to insufficient synchronization in orthogonal frequency division multiplexing with offset quadrature amplitude modulation (OFDM/OQAM) systems over doubly dispersive (DD) channels. The proposed pulse is designed as a linear combination of several well localized Hermite functions. The coefficients optimization problem is modeled as a nonconvex constrained fractional programming problem based on the signal-to-interference ratio (SIR) maximization criterion. An efficient iterative algorithm is applied to simplify the problem to a series of quadratically constrained quadratic program (QCQP) problems which can be solved by semidefinite relaxation (SDR) method. Simulation results show that the proposed pulse is superior to traditional pulses with respect to SIR performance over DD channels in the presence of carrier frequency offset (CFO) and timing offset (TO).

On Max-SINR Receivers for HMT Systems Over a Doubly Dispersive Channel

In this paper, a novel receiver for hexagonal multicarrier transmission (HMT) systems based on a maximizing signal-to-interference-plus-noise ratio (Max-SINR) criterion is proposed. Theoretical analyses show that there is a timing offset between the prototype pulses of the proposed Max-SINR receiver and a traditional projection receiver. Meanwhile, the timing offset should be matched to the channel scattering factor of a doubly dispersive (DD) channel. The closed-form timing offset expressions of the prototype pulses for the Max-SINR HMT receiver over the DD channel with different channel scattering functions are derived. Simulation results show that the proposed Max-SINR receiver outperforms the traditional projection scheme and obtains an approximation to the theoretical upper bound SINR performance. Consistent with the SINR performance improvement, the bit error rate (BER) performance of the HMT system has been also further improved by using the proposed Max-SINR receiver. Meanwhile, the SINR performance of the proposed Max-SINR receiver is robust to the channel delay spread estimation errors.

Time and Frequency Synchronization for Multicarrier Transmission on Hexagonal Time-Frequency Lattice

In this paper, a novel synchronization acquisition approach, including preamble structure, time and frequency synchronization algorithms, is proposed for hexagonal multicarrier transmission (HMCT) system. Specifically, a novel signal acquisition scheme based on time-frequency subspace projection (TFSP) and its simplified form are proposed for reliable signal acquisition. Time and frequency synchronization is divided into three steps: 1) the coarse time offset (TO) and coarse fractional carrier frequency offset (CFO) estimation; 2) fine TO and integer CFO estimation; and 3) fine fractional CFO estimation. The closed-form Cramér-Rao lower bound of the proposed CFO estimation scheme is given. Theoretical analyses and simulation results show that the proposed preamble structure, time and frequency synchronization algorithms for HMCT system can obtain robust performance over doubly dispersive (DD) channel, and the simulation results show excellent agreement with theoretical analyses.

Max-SINR Based Timing Synchronization Scheme in Hexagonal Multicarrier Transmission

In this paper, the maximizing Signal-to-Interference-plus-Noise Ratio (Max-SINR) criterion is applied in Hexagonal Multicarrier Transmission (HMT) system for timing synchronization. An iterative approach for Max-SINR timing over doubly dispersive (DD) channel with exponential power delay profile and U-shape Doppler spectrum is proposed. Theoretical analysis shows that there is an allowable SINR gap between the mean delay of DD channel and the optimal timing point. Meanwhile, a low complexity suboptimal timing approach based on instantaneous channel frequency response is proposed. Theoretical analysis and simulation results show that Max-SINR timing scheme outperforms traditional timing method about 2–15 dB in SINR and the suboptimal timing algorithm achieves a smaller Mean Square Error than 10−4 over DD channels. In addition, the Iterative Projection Sequence Detection (IPSD) receiver is proposed and the Match Filter Low Bound (MFLB) in HMT system is given. Simulation results show that the Bit Error Rate (BER) of the proposed IPSD approach based on iterative Max-SINR timing approximates to the MFLB and outperforms traditional timing scheme about 3dB at BER = 10−3.

SINR Analysis of Hexagonal Multicarrier Transmission Systems in the Presence of Insufficient Synchronization for Doubly Dispersive Channel

This paper analyzes the effect of the insufficient synchronization (carrier frequency offset, timing offset) on hexagonal multicarrier transmission (HMT) systems for doubly dispersive channel. Exact SINR and demodulated symbol expressions for HMT systems in the presence of insufficient synchronization transmission conditions over doubly dispersive channel with exponential delay power profile and U-shape Doppler power spectrum and uniform delay power profile and uniform Doppler power spectrum are derived, respectively. Theoretical analysis shows that similar degradations on symbol amplitude and phase caused by insufficient synchronization are incurred as in traditional cyclic-prefix orthogonal frequency division multiplexing (CP-OFDM) transmission. HMT systems outperform traditional OFDM systems with respect to signal to interference-plus-noise-ratio (SINR) against inter-symbol interference (ISI) and inter-carrier interference (ICI) caused by insufficient synchronization and doubly dispersive(DD) channel. The BER performance of the HMT systems using Monte Carlo simulation match with the conclusion given by the proposed exact SINR expression.

Effects of Carrier Frequency Offset, Timing Offset, and Channel Spread Factor on the Performance of Hexagonal Multicarrier Modulation Systems

Hexagonal multicarrier modulation (HMM) system is the technique of choice to overcome the impact of time-frequency dispersive transmission channel. This paper examines the effects of insufficient synchronization (carrier frequency offset, timing offset) on the amplitude and phase of the demodulated symbol by using a projection receiver in hexagonal multicarrier modulation systems. Furthermore, effects of CFO, TO, and channel spread factor on the performance of signal-to-interference-plus-noise ratio (SINR) in hexagonal multicarrier modulation systems are further discussed. The exact SINR expression versus insufficient synchronization and channel spread factor is derived. Theoretical analysis shows that similar degradation on symbol amplitude and phase caused by insufficient synchronization is incurred as in traditional cyclic prefix orthogonal frequency-division multiplexing (CP-OFDM) transmission. Our theoretical analysis is confirmed by numerical simulations in a doubly dispersive (DD) channel with exponential delay power profile and U-shape Doppler power spectrum, showing that HMM systems outperform traditional CP-OFDM systems with respect to SINR against ISI/ICI caused by insufficient synchronization and doubly dispersive channel.

Efficient Sequence Detection of Multicarrier Transmissions over Doubly Dispersive Channels

Multicarrier modulation (MCM) over a doubly dispersive (DD) channel yields complicated inter-carrier interference (ICI) and inter-symbol interference (ISI) responses. With appropriately designed MCM pulse shapes, however, ISI can be mostly suppressed, as can ICI outside a small subcarrier radius. In this case, the channel can be well described by a quasi-banded subcarrier coupling matrix. Several sequence detectors (SDs) have been proposed to leverage this quasi-banded structure, including linear, decision feedback (DF), and maximum likelihood (ML) schemes. Relative to linear and DF schemes, the ML schemes offer superior performance, but are significantly more complex, even when efficient Viterbi or sphere-detection algorithms are used. In this paper, we propose a new SD algorithm for the quasi-banded application with a frame error rate (FER) that is nearly indistinguishable from ML and an average complexity that is on par with DF SD.