RNN Based Channel Estimation in Doubly Selective Environments
Abdul Karim Gizzini, Marwa Chafii
备注：
This paper has been submitted to the IEEE Transactions on Machine Learning in Communications and Networking (TMLCN). arXiv admin note: text overlap with arXiv:2305.00208
Doubly-selective channel estimation represents a key element in ensuring communication reliability in wireless systems. Due to the impact of multi-path propagation and Doppler interference in dynamic environments, doubly-selective channel estimation becomes challenging. Conventional symbol-by-symbol (SBS) and frame-by-frame (FBF) channel estimation schemes encounter performance degradation in high mobility scenarios due to the usage of limited training pilots. Recently, deep learning (DL) has been utilized for doubly-selective channel estimation, where long short-term memory (LSTM) and convolutional neural network (CNN) networks are employed in the SBS and FBF, respectively. However, their usage is not optimal, since LSTM suffers from long-term memory problem, whereas, CNN-based estimators require high complexity. For this purpose, we overcome these issues by proposing an optimized recurrent neural network (RNN)-based channel estimation schemes, where gated recurrent unit (GRU) and Bi-GRU units are used in SBS and FBF channel estimation, respectively. The proposed estimators are based on the average correlation of the channel in different mobility scenarios, where several performance-complexity trade-offs are provided. Moreover, the performance of several RNN networks is analyzed. The performance superiority of the proposed estimators against the recently proposed DL-based SBS and FBF estimators is demonstrated for different scenarios while recording a significant reduction in complexity.
The recent proposed orthogonal time frequency space (OTFS) modulation shows signifcant advantages than conventional orthogonal frequency division multiplexing (OFDM) for high mobility wireless communications. However, a challenging problem is the development of effcient receivers for practical OTFS systems with low complexity. In this paper, we propose a novel delay-Doppler reversal (DDR) technology for OTFS system with desired performance and low complexity. We present the DDR technology from a perspective of two-dimensional cascaded channel model, analyze its computational complexity and als…
The analytic expression of CRLB and the maximum likelihood estimator for the sample frequency correlation matrices in doubly selective fading channels for OFDM systems are reported in this paper. According to the analytical and numerical results, the amount of samples affects the average mean square error dominantly while the SNR and the Doppler spread do negligibly.
This paper derives the analytic expression of the sample auto-correlation matrix from the least-squared channel estimation of doubly selective fading channels for OFDM systems. According to the expression, the sample auto-correlation matrix reveals the bias property which would cause the model mismatch and therefore deteriorate the performance of channel estimation. Numerical results demonstrate the bias property and corresponding analysis.
A novel maximum Doppler spread estimation algorithm for OFDM systems with comb-type pilot pattern is presented in this paper. By tracking the drifting delay subspace of time-varying multipath channels, a Doppler dependent parameter can be accurately measured and further expanded and transformed into a non-linear high-order polynomial equation, from which the maximum Doppler spread is readily solved by resorting to the Newton's method. Its performance is demonstrated by simulations.
The analytic expression of CRLB and the maximum likelihood estimator for spatial correlation matrices in time-varying multipath fading channels for MIMO OFDM systems are reported in this paper. The analytical and numerical results reveal that the amount of samples and the order of frequency selectivity have dominant impact on the CRLB. Moreover, the number of pilot tones, SNR as well as the normalized maximum Doppler spread together influence the effective order of frequency selectivity.
In this letter, we propose a learning based channel estimation scheme for orthogonal frequency division multiplexing (OFDM) systems in the presence of phase noise in doubly-selective fading channels. Two-dimensional (2D) convolutional neural networks (CNNs) are employed for effective training and tracking of channel variation in both frequency as well as time domain. The proposed network learns and estimates the channel coefficients in the entire time-frequency (TF) grid based on pilots sparsely populated in the TF grid. In order to make the network robust to phase noise (PN) impairment, a nov…
In doubly selective channels, receiver windowing constitutes an effective technique for enhancing the banded structure of the frequency-domain channel matrix, and thus improving the effectiveness of a banded equalizer for intercarrier interference (ICI) mitigation. A common window design technique, which performs close to optimal, is based on the criterion of maximum average signal-to-interference-plus-noise ratio (SINR). The optimality of this technique has been verified for stationary channels with perfectly known statistics. However, in cases where this assumption does not hold, a near opti…
Doubly selective (DS) channel estimation in largescale multiple-input multiple-output (MIMO) systems is a challenging problem due to the requirement of unaffordable pilot overheads and prohibitive complexity. In this paper, we propose a novel distributed compressive sensing (DCS) based channel estimation scheme to solve this problem. In the scheme, we introduce the basis expansion model (BEM) to reduce the required channel coefficients and pilot overheads. And due to the common sparsity of all the transmit-receive antenna pairs in delay domain, we estimate the BEM coefficients by considering t…
Deep Learning Based Channel Estimation in High Mobility Communications Using Bi-RNN Networks
CY Cergy Paris Université（CY塞尔吉-巴黎大学）；ENSEA（法国国立高等电子及应用学院）；CNRS（法国国家科学研究中心）；New York University (NYU)（纽约大学）；NYU Tandon School of Engineering（纽约大学坦登工程学院）
In order to effetively suppress intersymbol interference (ISI) at low complexity, we propose in this paper an approximate maximum likelihood (ML) decision feedback block equalizer (A-ML-DFBE) for doubly selective (frequency-selective, time-selective) fading channels. The proposed equalizer design makes efficient use of the special time-domain representation of the multipath channels through a matched filter, a sliding window, a Gaussian approximation, and a decision feedback. The A-ML-DFBE has the following features: 1) It achieves performance close to maximum likelihood sequence estimation (M…
We consider channel estimation within pulse-shaping multicarrier multiple-input multiple-output (MIMO) systems transmitting over doubly selective MIMO channels. This setup includes MIMO orthogonal frequency-division multiplexing (MIMO-OFDM) systems as a special case. We show that the component channels tend to exhibit an approximate joint group sparsity structure in the delay-Doppler domain. We then develop a compressive channel estimator that exploits this structure for improved performance. The proposed channel estimator uses the methodology of multichannel group sparse compressed sensing, w…
Millimeter wave (mmWave) is a practical solution to provide high data rate for the vehicle-to-everything (V2X) communications. This enables the future autonomous vehicles to exchange big data with the base stations (BSs) such as the velocity and the location to improve the awareness of the advanced driving assistance system (ADAS). In this context, we consider a single-cell multiuser doubly-selective system wherein the BS simultaneously serves multiple vehicles. To accomplish this requirement, the BS is implemented in hybrid architecture to support multiple spatial streams while the vehicles h…
Recently, this journal has published a paper which dealt with basis expansion model (BEM) based least-squares (LS) channel estimation in doubly-selective orthogonal frequency-division multiplexing (DS-OFDM) systems. The least-squares channel estimator computes the pseudo-inverse of a channel estimation matrix. For the existence of the pseudo-inverse, it is necessary that the channel estimation matrix be of full column rank. In this paper, we investigate the conditions that need to be satisfied that ensures the full column-rank condition of the channel estimation matrix. In particular, we deriv…
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…
In this paper, we propose an algorithm for channel estimation, acquisition and tracking, for orthogonal frequency division multiplexing (OFDM) systems. The proposed algorithm is suitable for vehicular communications that encounter very high mobility. A preamble sequence is used to derive an initial estimate of the channel using least squares (LS). The temporal variation of the channel within one OFDM symbol is approximated by two complex exponential basis expansion models (CE-BEM). One of the Fourier-based BEMs is intended to capture the low frequencies in the channel (slow variations correspo…
The goal of this paper is to obtain a better knowledge of the achievable data rate over noncoherent Rician fading channel with time and frequency memory. We assume that the average-power as well as the peak-power of the input signal are finite and the peak-power limitation is applied in the time domain. Expression for this rate is based on a lower bound on mutual information that assume independent and identically distributed input data symbols. The lower bound is expressed as a difference of two terms. The first term is the information rate of the coherent channel with a weighted signal-to-no…
Ultra-reliable wireless communication links require the utilization of all diversity sources of a wireless communication channel. Hadani et al. propose a two dimensional discrete symplectic Fourier transform (DSFT) as orthogonal pre-coder for a time-frequency modulation scheme. In this paper we explore \emph{general} orthogonal precoding (OP) and its performance in time- and frequency-selective channels. We show that iterative parallel interference cancellation (PIC) and iterative channel estimation methods can be used for the detection of OP. A scalar signal model for OP transmission is obtai…
To detect spatially-modulated signals, a receiver needs the channel state information (CSI) of each transmit- receive antenna pair. Although the CSI is never perfect and varies in time, most studies on spatial modulation (SM) systems assume perfectly known CSI and time-invariant channel. The spatial correlations among multiple spatial subchannels, which have to be considered when CSI is imperfect, are also often neglected. In this paper, we release the above assumptions and take the CSI uncertainty along with the spatial-temporal selectivities into account. We derive the channel estimation err…
Most methodologies for modeling Transmission Line (TL) based channels define the input-output relationship in the frequency domain (FD) and handle the TL resorting to a two-port network (2PN) formalism. These techniques have not yet been formally mapped into a discrete-time (DT) block model, which is useful to simulate and estimate the channel response as well as to design optimal precoding strategies. TL methods also fall short when they are applied to Time Varying (TV) systems, such as the power line channel. The objective of this paper is to establish if and how one can introduce a DT block…
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,…
This paper develops a low-complexity channel estimation (CE) scheme based on compressive sensing (CS) for time-domain synchronous (TDS) orthogonal frequency-division multiplexing (OFDM) to overcome the performance loss under doubly selective fading channels. Specifically, an overlap-add method of the time-domain training sequence is first proposed to obtain the coarse estimates of the channel length, path delays and path gains of the wireless channel, by exploiting the channel's temporal correlation to improve the robustness of the coarse CE under the severe fading channel with long delay spre…
Orthogonal time-frequency space (OTFS) scheme, which transforms a time and frequency selective channel into an almost non-selective channel in the delay-Doppler domain, establishes reliable wireless communication for high-speed moving devices. This work designs and analyzes low-complexity zero-forcing (LZ) and minimum mean square error (LM) receivers for multiple-input multiple-output (MIMO)-OTFS systems with perfect and imperfect receive channel state information (CSI). The proposed receivers provide exactly the same solution as that of the conventional counterparts, and reduce the complexity…
In this paper, we derive an asymptotic closed--form expression for the error bound on extrapolation of doubly selective mobile MIMO wireless channels. The bound shows the relationship between the prediction error and system design parameters such as bandwidth, number of antenna elements, and number of frequency and temporal pilots, thereby providing useful insights into the effects of these parameters on prediction performance. Numerical simulations show that the asymptotic bound provides a good approximation to previously derived bounds while eliminating the need for repeated computation and …
Department of Electrical and Computer Engineering, New York University (NYU), Abu Dhabi（纽约大学（阿布扎比）电气与计算机工程系）
IEEE 802.11p standard defines wireless technology protocols that enable vehicular transportation and manage traffic efficiency. A major challenge in the development of this technology is ensuring communication reliability in highly dynamic vehicular environments, where the wireless communication channels are doubly selective, thus making channel estimation and tracking a relevant problem to investigate. In this paper, a novel deep learning (DL)-based weighted interpolation estimator is proposed to accurately estimate vehicular channels especially in high mobility scenarios. The proposed estima…
In this paper, channel estimation and data detection for multihop relaying orthogonal frequency division multiplexing (OFDM) system is investigated under time-varying channel. Different from previous works, which highly depend on the statistical information of the doubly-selective channel (DSC) and noise to deliver accurate channel estimation and data detection results, we focus on more practical scenarios with unknown channel orders and Doppler frequencies. Firstly, we integrate the multilink, multihop channel matrices into one composite channel matrix. Then, we formulate the unknown channel …
