We consider the time-continuous doubly-dispersive channel with additive Gaussian noise and establish a capacity formula for the case where the channel correlation operator is represented by a symbol which is periodic in time and fulfills some further integrability and smoothness conditions. The key to this result is a new Szegö formula for certain pseudo-differential operators. The formula justifies the water-filling principle along time and frequency in terms of the time--continuous time-varying transfer function (the symbol).
We consider the time-continuous doubly--dispersive channel with additive Gaussian noise and establish a capacity formula for the case where the channel operator is represented by a symbol which is periodic in time and fulfills some further integrability, smoothness and oscillation conditions. More precisely, we apply the well-known Holsinger-Gallager model for translating a time-continuous channel for a sequence of time--intervals of increasing length $α\rightarrow\infty$ to a series of equivalent sets of discrete, parallel channels, known at the transmitter. We quantify conditions when this p…
In this work, we consider the problem of detecting the presence of a new user in a direct-sequence/code-division-multiple-access (DS/CDMA) system with a doubly-dispersive fading channel, and we propose a novel blind detection strategy which only requires knowledge of the spreading code of the user to be detected, but no prior information as to the time-varying channel impulse response and the structure of the multiaccess interference. The proposed detector has a bounded constant false alarm rate (CFAR) under the design assumptions, while providing satisfactory detection performance even in the…
In this paper, a maximizing Signal-to-Interference plus-Noise Ratio (Max-SINR) receiver for Hexagonal Multicarrier Transmission (HMCT) system over non-stationary doubly dispersive (NSDD) channel is proposed. The closed-form timing offset expression of the prototype pulse for the proposed Max-SINR HMCT receiver over NSDD channel is derived. Simulation results show that the proposed Max-SINR receiver outperforms traditional projection scheme and obtains an approximation to the theoretical upper bound SINR performance within all the local stationarity regions (LSRs). Meanwhile, the SINR performan…
In this paper, a novel receiver for Hexagonal Multicarrier Transmission (HMT) system based on the maximizing Signal-to-Interference-plus-Noise Ratio (Max-SINR) criterion is proposed. Theoretical analysis shows that the prototype pulse of the proposed Max-SINR receiver should adapt to the root mean square (RMS) delay spread of the doubly dispersive (DD) channel with exponential power delay profile and U-shape Doppler spectrum. Simulation results show that the proposed Max-SINR receiver outperforms traditional projection scheme and obtains an approximation to the theoretical upper bound SINR per…
In this paper, a novel receiver for Hexagonal Multicarrier Transmission (HMT) system based on the 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 the traditional projection receiver. Meanwhile, the timing offset should be matched to the channel scattering factor of the doubly dispersive (DD) channel. The closed form timing offset expressions of the prototype pulse for Max-SINR HMT receiver over DD channel with different channel scatteri…
ENSEA（国立高等电子及应用学院）；CNRS（法国国家科学研究中心）；NYU Tandon School of Engineering（纽约大学坦登工程学院）
Wireless communications systems are impacted by multi-path fading and Doppler shift in dynamic environments, where the channel becomes doubly-dispersive and its estimation becomes an arduous task. Only a few pilots are used for channel estimation in conventional approaches to preserve high data rate transmission. Consequently, such estimators experience a significant performance degradation in high mobility scenarios. Recently, deep learning has been employed for doubly-dispersive channel estimation due to its low-complexity, robustness, and good generalization ability. Against this backdrop, …
Wireless channels generally exhibit dispersion in both time and frequency domain, known as doubly selective or doubly dispersive channels. To combat the delay spread effect, multicarrier modulation (MCM) such as orthogonal frequency division multiplexing (OFDM) and its universal filtered variant (UF-OFDM) is employed, leading to the simple per-subcarrier one tap equalization. The time-varying nature of the channel, in particular, the intra-multicarrier-symbol channel variation induces spectral broadening and thus inter-carrier interference (ICI). Existing works address both effects separately,…
Affine Frequency Division Multiplexing (AFDM), which is based on discrete affine Fourier transform (DAFT), has recently been proposed for reliable communication in high-mobility scenarios. Two low complexity detectors for AFDM are introduced here. Approximating the channel matrix as a band matrix via placing null symbols in the AFDM frame in the DAFT domain, a low complexity MMSE detection is proposed by means of the $\rm{LDL}$ factorization. Furthermore, exploiting the sparsity of the channel matrix, we propose a low complexity iterative decision feedback equalizer (DFE) based on weighted max…
In this work we consider the problem of identification and reconstruction of doubly-dispersive channel operators which are given by finite linear combinations of time-frequency shifts. Such operators arise as time-varying linear systems for example in radar and wireless communications. In particular, for information transmission in highly non-stationary environments the channel needs to be estimated quickly with identification signals of short duration and for vehicular application simultaneous high-resolution radar is desired as well. We consider the time-continuous setting and prove an exact…
Orthogonal time frequency space (OTFS) is a 2-dimensional (2D) modulation technique designed in the delay-Doppler domain. A key premise behind OTFS is the transformation of a time varying multipath channel into an almost non-fading 2D channel in delay-Doppler domain such that all symbols in a transmission frame experience the same channel gain. It has been suggested in the recent literature that OTFS can extract full diversity in the delay-Doppler domain, where full diversity refers to the number of multipath components separable in either the delay or Doppler dimension, but without a formal a…
Extensive work has demonstrated the excellent performance of orthogonal time frequency space (OTFS) modulation in high-mobility scenarios. Time-variant wideband channel estimation serves as one of the key compositions of OTFS receivers since the data detection requires accurate channel state information (CSI). In practical wideband OTFS systems, the Doppler shift brought by the high mobility is frequency-dependent, which is referred to as the Doppler Squint Effect (DSE). Unfortunately, DSE was ignored in overall prior estimation schemes employed in OTFS systems, which leads to severe performan…
We consider the application of compressed sensing (CS) to the estimation of doubly selective channels within pulse-shaping multicarrier systems (which include OFDM systems as a special case). By exploiting sparsity in the delay-Doppler domain, CS-based channel estimation allows for an increase in spectral efficiency through a reduction of the number of pilot symbols. For combating leakage effects that limit the delay-Doppler sparsity, we propose a sparsity-enhancing basis expansion and a method for optimizing the basis with or without prior statistical information about the channel. We also pr…
Orthogonal time frequency space (OTFS) modulation can effectively convert a doubly dispersive channel into an almost non-fading channel in the delay-Doppler domain. However, one critical issue for OTFS is the very high complexity of equalizers. In this letter, we first reveal the doubly block circulant feature of OTFS channel represented in the delay-Doppler domain. By exploiting this unique feature, we further propose zero-forcing (ZF) and minimum mean squared error (MMSE) equalizers that can be efficiently implemented with the two-dimensional fast Fourier transform. The complexity of our pro…
We study the recovery of operators with bandlimited Kohn-Nirenberg symbol from the action of such operators on a weighted impulse train, a procedure we refer to as operator sampling. Kailath, and later Kozek and the authors have shown that operator sampling is possible if the symbol of the operator is bandlimited to a set with area less than one. In this paper we develop explicit reconstruction formulas for operator sampling that generalize reconstruction formulas for bandlimited functions. We give necessary and sufficient conditions on the sampling rate that depend on size and geometry of the…
Orthogonal time frequency space (OTFS) modulation has recently emerged as an effective waveform to tackle the linear time-varying channels. In OTFS literature, approximately constant channel gains for every group of samples within each OTFS block are assumed. This leads to limitations for OTFS on the maximum Doppler frequency that it can tolerate. Additionally, presence of cyclic prefix (CP) in OTFS signal limits the flexibility in adjusting its parameters to improve its robustness against channel time variations. Therefore, in this paper, we study the possibility of removing the CP overhead f…
