Doubly-selective Channels Research Articles

Bit Error Probability and Capacity Bound of OFDM Systems in Deterministic Doubly-Selective Channels

Doubly-selective channels, such as those that occur when the transmitter and the receiver move relative to each other at high speeds, are a key scenario for fifth generation (5G) cellular systems, which are mostly based in the use of the orthogonal frequency-division multiplexing (OFDM) modulation. In this paper, we consider an OFDM system using quadrature amplitude modulation (QAM) symbols and we show that, when transmitting over deterministic doubly-selective channels, the inter-carrier-interference (ICI) affecting a symbol can be well approximated by a complex-valued normal distribution. Based on this, we derive a lower bound for the link capacity using the Shannon-Hartley theorem. Finally, we provide an approximation of the bit error probability (BEP) using the well-known BEP expressions for Gray-coded QAM constellations over additive white Gaussian noise (AWGN) channels, and show numerical results that confirm that the proposed BEP expression approximates accurately the bit error ratio (BER) of the OFDM system for standardized channel models. The proposed closed-form analytical expressions for the capacity and the BEP do not only allow for discarding the need of computationally-costly Monte-Carlo system simulations, but also provide a theoretical framework to optimize the system parameters directly impacting on the achievable performance.

Sparse Doubly-Selective Channel Estimation Techniques for OSTBC MIMO-OFDM Systems: A Hierarchical Bayesian Kalman Filter Based Approach

Hierarchical Bayesian Kalman filter (HBKF) based schemes are conceived for doubly-selective sparse channel estimation in orthogonal space-time block coded (OSTBC) multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) wireless systems. Initially, a pilot based multiple measurement vector (MMV) model is formulated for estimating the OSTBC MIMO-OFDM channel. This is followed by the development of a low-complexity, online pilot-based HBKF (P-HBKF) scheme for tracking the sparse time-varying frequency-selective channel. The salient advantages of the proposed P-HBKF technique are that it requires significantly lower number of pilot subcarriers, while also exploiting the inherent sparsity of the wireless channel. Subsequently, data detection is also incorporated in the proposed framework, leading to the development of a procedure for joint sparse doubly-selective channel estimation and symbol detection. Recursive Bayesian Cramér-Rao bounds and closed form expressions are also obtained for the asymptotic mean square error (MSE) based on the solution of the Riccati equation for the KF for benchmarking the performance. Simulation results are presented for validating the theoretical bounds and for comparing the performance of the proposed and existing techniques.

A low complexity iterative equalization technique for OFDMA and SC-FDMA uplink systems with Tx-Rx IQ imbalance and CFO under doubly selective channels

The next-generation wireless communication systems must address the compensation of in-phase and quadrature phase imbalance (IQI), carrier frequency offset (CFO), and doubly selective channel (DSC) to provide a high quality of service for high mobility users with low-cost radio . None of the existing works consider all these RF impairments under DSC for multi-user scenario. To address this gap, in this paper, we propose an iterative equalization technique to compensate the multi-user interference (MUI) and self inter-carrier interference (S-ICI) induced by the joint effect of transmitter IQI, receiver IQI, CFO and DSC for single carrier frequency division multiple access (SC-FDMA) and orthogonal frequency division multiple access (OFDMA) uplink systems. In each iteration of the proposed equalization technique, the extrinsic information from the decoder is used to cancel the MUI and S-ICI from the received signal. After interference cancellation, each mirror subcarriers pairs are equalized simultaneously. Additionally, unlike existing works, our proposed technique does not put any restriction on the carrier assignment scheme (CAS) used with OFDMA/SC-FDMA systems. Further, to validate the performance of the proposed compensation scheme analytically, we derive an upper bound on the bit error rate (BER) of coded OFDMA and SC-FDMA system without MUI and S-ICI. It is established that the system BER with the proposed technique satisfies the derived upper bound as the iteration converges, demonstrating the effective cancellation of MUI and S-ICI due to all the impairments.

Low Complexity Equalization of Orthogonal Chirp Division Multiplexing in Doubly-Selective Channels.

Orthogonal Chirp Division Multiplexing (OCDM) is a modulation scheme which outperforms the conventional Orthogonal Frequency Division Multiplexing (OFDM) under frequency selective channels by using chirp subcarriers. However, low complexity equalization algorithms for OCDM based systems under doubly selective channels have not been investigated yet. Moreover, in OCDM, the usage of different phase matrices in modulation will lead to extra storage overhead. In this paper, we investigate an OCDM based modulation scheme termed uniform phase-Orthogonal Chirp Division Multiplexing (UP-OCDM) for high-speed communication over doubly selective channels. With uniform phase matrices equipped, UP-OCDM can reduce the storage requirement of modulation. We also prove that like OCDM, the transform matrix of UP-OCDM is circulant. Based on the circulant transform matrix, we show that the channel matrices in UP-OCDM system over doubly selective channels have special structures that (1) the equivalent frequency-domain channel matrix can be approximated as a band matrix, and (2) the transform domain channel matrix in the framework of the basis expansion model (BEM) is a sum of the product of diagonal and circulant matrices. Based on these special channel structures, two low-complexity equalization algorithms are proposed for UP-OCDM in this paper. The equalization algorithms are based on block LDL factorization and iterative matrix inversion, respectively. Numerical simulations are finally proposed to show the performance of UP-OCDM and the validity of the proposed low complexity equalization algorithms. It is shown that when the channel is doubly selective, UP-OCDM and OCDM have similar BER performance, and both of them outperform OFDM. Moreover, the proposed low complexity equalizers for UP-OCDM both show better BER performance than their OFDM counterparts.

Estimating Doubly-Selective Channels for Hybrid mmWave Massive MIMO Systems: A Doubly-Sparse Approach

In mmWave massive multiple-input multiple-output (mMIMO) systems, hybrid (digital/analog) structure has been a prevalent option to balance system cost and performance. To facilitate transceiver design in hybrid mmWave mMIMO, acquiring an accurate channel state information is critical. To this end, a novel doubly-sparse approach is proposed to estimate doubly-selective mmWave channels under hybrid mMIMO. Via the judiciously designed training pattern, the well-utilized beamspace sparsity alongside the under-investigated delay-domain sparsity that mmWave channels exhibit can be jointly exploited to assist channel estimation. Thanks to our careful two-stage (random-probing and steering-probing) design, the proposed channel estimator possesses strong robustness against the double (frequency and time) selectivity whilst enjoying the benefits brought by the exploitation of double sparsity. Compared with existing alternatives, our proposed mmWave channel estimator not only works in doubly-selective channels, but also largely reduces the training overhead, storage demand as well as computational complexity.

BEM-PSP for Single-Carrier and SC-FDMA Communication Over a Doubly Selective Fading Channel

In this paper, we consider pilot-aided channel estimation and equalization for single-carrier and single-carrier frequency division multiple-access (SC-FDMA) transmission over doubly-selective channels (DSC). To reduce the channel estimation (CE) parameters, the DSC is modelled using a complex-exponential basis expansion model (CX-BEM) with non-uniform BEM frequencies. We optimize the CX-BEM basis functions using CE error minimization as the objective. As a result, the channel modelling error is greatly reduced. Next, we propose a BEM-based per-survivor processing (PSP) technique and combine it with a decision-directed channel estimator to obtain a channel-tracking equalizer at the receiver. The resultant BEM-PSP receiver significantly improves the channel estimation mean square error (MSE) and the bit error rates (BER) performance in fast fading multi-path channel, thanks to the channel tracking capability embedded within its Viterbi equalizer. Finally, we employ cross-frame channel interpolation, and power distribution between the data and pilot symbols to further improve the system performance at high fading rates. Extensive simulation results show that our BEM-PSP receiver outperforms many existing methods and approaches close to an ideal receiver with perfectly known CSI under various fading scenarios.

Signal detection algorithms for single carrier generalized spatial modulation in doubly selective channels

This paper is concerned with signal detection for zero-padded single carrier generalized spatial modulation (SC-GSM) in doubly selective channels (DSCs). Novel detection methods are proposed by expressing the DSC in terms of the basis expansion model (BEM) and considering a BEM-based maximum likelihood (BML) framework. The proposed methods, which aim at reducing the complexity of the BML detector, can be divided into two main categories. The methods in the first category, namely BEM-based partial interference cancellation (BPIC) and BPIC with successive interference cancellation (BPIC-SIC), are designed to remove the interference between the signals. Since the satisfactory performance of these methods depend on meeting a constraint on the number of transmit and receive antennas, a second category of methods is proposed, consisting of BEM-based tree search (BTS), BEM-based reduced complexity tree search (BRCTS), and BRCTS with sphere decoding (BRCTS-SD). These methods are developed to overcome the limitations of BPIC and BPIC-SIC while further reducing the detection complexity by shrinking the search space. The performance evaluation of the proposed SC-GSM methods, in terms of computational complexity and bit error rate (BER) over simulated DSCs, underlines their relative merits and clearly demonstrates their advantages over previous methods.

Pilot Design for BEM-Based Channel Estimation in Doubly Selective Channel

This paper investigates pilot design for enhanced channel estimation in single carrier communication systems over doubly-selective channels (DSC). Our contribution is twofold: first, we propose to use Huffman sequences as pilot clusters with low peak-to-average power ratio (PAPR), yet with good channel estimation performance when periodic pilot placement is adopted; second, we propose a low-complexity pilot placement strategy based on the analysis of the complex-exponential basis expansion model (CE-BEM) of the DSC. The latter leads to improved channel estimation performance with useful insights for pilot placement.

A Doubly-Selective Channel Simulator Employing Carrier Frequency Band Sampling for Underwater Acoustic Communication Channels

A Doubly-Selective Channel Simulator Employing Carrier Frequency Band Sampling for Underwater Acoustic Communication Channels

A Speed Adaptive Joint Subcarrier and Power Allocation Technique for Downlink OFDMA Video Transmission Over Doubly Selective Channels

In this paper we propose a quality of experience (QoE) based joint subcarrier and power allocation (JSPA) technique for orthogonal frequency division multiple access (OFDMA) based downlink video transmission over doubly selective channels (DSCs), where the power allocation is made adaptive to the user velocity. Due to the doubly selective nature of wireless channels, OFDMA based wireless systems are vulnerable to inter-carrier interference (ICI). The proposed speed adaptive power allocation can combat ICI to a great extent compared to the non-adaptive power allocation schemes. Moreover, the proposed JSPA ensures a critical issue of fairness in QoE among users. By making use of space-alternating generalized expectation-maximization maximum a posteriori probability (SAGE-MAP) algorithm, this paper also studies the bit rate performance of the proposed resource allocation algorithm in the presence of perfect and imperfect channel state information (CSI).

Partial FFT Demodulation Scheme Based on Fast Convolution Structure

In systems that aim to mitigate the inter-carrier interference (ICI) caused by doubly selective (DS) channels, the partial Fast Fourier Transform (PFFT) has emerged as an interesting alternative to the conventional FFT. In this letter, we propose a novel PFFT demodulation scheme based on fast convolution (FC) structure. The proposed scheme uses the overlap-save operation of FC to further suppress the residual interference (RI) to improve performance over DS channels, including in terms of bit error rate (BER), while, at the same time, allowing for an improvement in spectral efficiency by avoiding the use of a cyclic prefix (CP). We provide a theoretical analysis of RI and numerical simulations to demonstrate the superiority of the proposed scheme in terms of BER performance.

MIMO Multicarrier Transmission Over Doubly Selective Channels With Virtual Trajectories Receiver

High mobility and multipath propagation induce Doppler and delay dispersion, respectively. When both phenomena affect the transmitted signal, the communication channel is known as a doubly selective channel (DSC). In multicarrier systems under this scenario, intersymbol interference (ISI) and intercarrier interference (ICI) are ineluctably present, severely degrading the system's performance. Therefore, much effort has been invested in researching convenient waveforms that enable the receiver self-interference cancellation, while making use of the available space, time, and frequency diversity. In this paper, a multicarrier multiple-input multiple-output (MIMO) system for communication in DSCs is presented. By using the virtual trajectory (VT) representation of the MIMO channel, direct conversion of Doppler diversity into additional virtual antennas in the receiver is achieved. This concept is developed for a coherent system with one-tap channel estimation (CE) and equalization algorithms of low complexity as well as for incoherent detection using differential space-frequency block codes (DSFBCs), where pilot signals are not used. For both systems, runtime cancellation and/or inversion of complex interference channel matrices is avoided. Diversity of the doubly selective MIMO channel is exploited without sacrificing compatibility with current multicarrier MIMO systems. The presented system offers robustness in DSCs with minimal extra complexity when compared to conventional approaches. The results demonstrate that MIMO orthogonal frequency division modulation (MIMO-OFDM) can be still implemented in extremely high Doppler scenarios if VT reception is incorporated.

Compressed channel estimation for massive MIMO-OFDM systems over doubly selective channels

Doubly selective (DS) channel estimation for the downlink massive multiple-input-multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems is a challenging problem, due to the requirements on high pilots overhead and prohibitive complexity. In this paper, by exploiting the highly correlated spatial structure of the obtained array response vectors and sparsity of the multipath signal components of the massive MIMO-OFDM channels, a modified spatial basis expansion model (modified-SBEM) is introduced. Thus, using complex exponential (CE-) modified-SBEM (i.e., modified CE-SBEM) can improve the resolution of the angles of departures (AoDs) information to represent the downlink with far fewer parameter dimensions, since the AoDs are much slower than path gains. Subsequently, we jointly design the effective pilot power and pilot placement for sparse channel estimation by means of an extended model. Our design is based on the block-coherence and sub-coherence simultaneous minimization of the measurement matrix associated with the massive MIMO-OFDM system pilot subcarriers. Furthermore, we leverage the sparse nature of the massive MIMO-OFDM system to formulate the quantized AoDs estimation into a block-sparse signal recovery problem, where the measurement matrix is designed based on the estimated virtual AoD. Thus, a new algorithm namely, generalized quasi-block simultaneous orthogonal matching pursuit (gQBSO), is introduced to solve the problem by providing sparse signal reconstruction solution. Simulation results demonstrate that the proposed scheme can effectively estimate the DS channel for massive MIMO-OFDM systems compared with other existing algorithms. For example, at SNR=20 dB for K=4 users, Doppler shift=0.093 with NT=32 antenna size, the adaptive-QBSO algorithm with G-SBEM and the proposed gQBSO with modified-SBEM can realize approximately 75.44%and 85.14% of the NMSE achieved by the oracle estimator with modified-SBEM.

Novel Adaptive Distributed Compressed Sensing Algorithm for Estimating Channels in Doubly-Selective Fading OFDM Systems

Doubly-selective (DS) fading channel is often occurred in many orthogonal frequency division multiplexing (OFDM) communication systems, such as high-speed rail communication systems and underwater acoustic (UWA) wireless networks. It is challenging to provide an accurate and fast estimation over the doubly-selective channel, due to the strong Doppler shift. This paper addresses the doubly selective channel estimation problem based on complex exponential basis expansion model (CE-BEM) in OFDM systems from the perspective of distributed compressive sensing (DCS). We propose a novel DCS-based improved sparsity adaptive matching pursuit (DCS-IMSAMP) algorithm. The advantage of the proposed algorithm is that it can exploit the joint channel sparsity information using dynamic threshold, variable step size and tailoring mechanism. Simulation results show that the proposed algorithm achieves 5dB performance gain with faster operation speed, in comparison with traditional DCS-based sparsity adaptive matching pursuit (DCS-SAMP) algorithm.

Beyond‐sparsity–based doubly selective channel estimation for high‐mobility multiuser MIMO‐OFDM systems

AbstractWireless communications in high‐mobility situations face with doubly selective (DS) fading. In addition, many practical wireless channels exhibit a sparse multipath structure. This paper investigates the DS multiuser multiple‐input–multiple‐output (MIMO) channel estimation via compressed sensing. The DS channel is characterized by a general sparse basis expansion model (BEM). This model reduces the channel estimation complexity as the channel estimation problem is reduced to estimating the BEM coefficients instead of numerous channel parameters. In addition, a pilot pattern is proposed for multiuser MIMO orthogonal frequency division multiplexing systems, which includes guard and silent pilots to reduce intercarrier interference and interuser interference, respectively. Then, two beyond‐sparsity features (ie, block and joint sparsity) of the BEM coefficients are exploited to propose a beyond‐sparsity–based channel estimation method. Moreover, a pilot design algorithm is proposed to optimize the pilot positions and enhance the estimator performance. Simulation results demonstrate that the proposed method significantly improves the estimation accuracy over the existing approaches, with a much smaller pilot overhead.

Compressed Sensing-Based Sparsity Adaptive Doubly Selective Channel Estimation for Massive MIMO Systems

By exploiting the sparsity of the channel in the delay and angle domains, compressed sensing (CS) algorithms can be used for channel estimation of massive multiple-input multiple-output (MIMO) systems to reduce pilot overhead. Due to the Doppler frequency shift, however, the intercarrier interference (ICI) and the rapid change of the channel state result in the poor estimation effect of doubly selective (DS) channel. In this paper, we propose the block sparsity adaptive matching pursuit (B-SAMP) algorithm to solve this problem. Firstly, the complex exponential basis expansion model (CE-BEM) is used to convert numerous channel tap coefficients into BEM parameter vectors and then the sparsity adaptive channel estimation scheme based on compressed sensing is proposed. Specifically, the ICI-free model is obtained by using the proposed equally placed pilot group scheme, and the B-SAMP algorithm is proposed by using the spatio-temporal common sparsity of the channel to complete the estimation of DS channel. Finally, a linear smoothing method is used to reduce the error caused by CE-BEM, thereby further improving the accuracy of the estimation. The simulation results show that the proposed method not only improves the estimation accuracy compared with the existing scheme but also requires fewer pilots.

Timing and Frequency Synchronization and Doubly Selective Channel Estimation for OFDMA Uplink

In this brief, a novel algorithm is proposed for timing and frequency synchronization and doubly selective channel (DSC) estimation in the uplink of orthogonal frequency division multiple access systems. By using a basis expansion model (BEM) to represent a DSC, a maximum likelihood approach is proposed to jointly estimate the timing and carrier frequency offsets of different users as well as the BEM coefficients of the time-varying channels. A space-alternating generalized expectation-maximization algorithm is then employed to transform the maximization problem for all users into several simpler maximization problems for a single user. Implementation issues are investigated and, the computational complexity and mean square error of the proposed scheme are evaluated. Performance assessment of the new scheme shows a significant improvement as compared with previous methods.

Low-Complexity Equalization of Orthogonal Signal-Division Multiplexing in Doubly-Selective Channels

Orthogonal signal-division multiplexing (OSDM) is a generalized modulation scheme to bridge the gap between orthogonal frequency-division multiplexing (OFDM) and single-carrier frequency-domain equalization. It allows significantly more flexibility in system design; however, over doubly-selective channels, it suffers from a special signal distortion structure, namely inter-vector interference, which is analogous to inter-carrier interference in conventional OFDM. To analyze its effect, in this paper, the complex exponential basis expansion model (CE-BEM) is used to approximate the doubly-selective channel. We show that the composite channel matrix of OSDM systems is cyclically block banded in this case, and the blocks in its main band can be further diagonalized. By exploiting this unique matrix structure, low-complexity block and serial OSDM equalization algorithms are then proposed. These two equalization algorithms are based on block LDLH factorization and block iterative matrix inversion, respectively, both of which are implemented in a transformed domain to avoid direct inversion of large matrices. In addition, a CE-BEM channel estimation method is designed for OSDM systems, which uses frequency-shifted Chu sequences as pilots to ease the computation. Numerical simulations are finally provided to justify the validity of our channel equalization and estimation algorithms.

Spectrum-Efficient Distributed Compressed Sensing Based Channel Estimation for OFDM Systems Over Doubly Selective Channels

In this paper, we deal with channel estimation (CE) for high-mobility orthogonal frequency division multiplexing (OFDM) systems. To make the numerous (unknown) estimation for the high-mobility OFDM systems practicable, the channels are assumed to be time- and frequency-selective–or doubly selective (DS) and approximated by a basis expansion model (BEM). As the DS channel requires the distributed acquisition of multiple correlated signals in the delay-Doppler channel domain, we proceed to estimate jointly sparse BEM coefficient vectors over a DS channel as against numerous channel coefficients. On account of channel time-variation, the resulting channel matrix in the frequency domain exhibits (approximately banded) pseudo-circular structure, which gives rise to a diagonally dominant yet full matrix rather than a diagonal matrix and thus induces inter-channel interference (ICI). On the premise of this observation, we propose a new pilot design scheme that identifies the optimal pilot placement and values for each pilot cluster to combat ICI. Furthermore, to obtain a channel estimator consistent with the jointly sparse delay-Doppler [i.e., two dimensional (2D)] channel model, an algorithm namely, distributed compressed sensing (DCS)-based stage determined matching pursuit (DCS-SdMP), is proposed. Our claims are supported by simulation results, which are obtained considering Jakes’ channels with fairly high Doppler spreads, which show the superiority of the proposed schemes over other different methods of CE.

A Compressed Sensing Estimation Technique for Doubly Selective Channel in OFDM Systems

In this work, an estimation algorithm based on the compressive sensing (CS) technique is proposed for an orthogonal frequency division multiplexing (OFDM) system applied to multi-path time-varying channels. A fitting polynomial is used to approximate each channel path, and full-band training symbols are adopted. The variation of the channel response can then be evaluated according to the observation on the inter-carrier interference (ICI) from the determinate signals. The CS-based technique is introduced to explore the sparsity of the double-selective channel and the usage of high-order fitting polynomials is allowed. The orthogonal matching pursuit (OMP) algorithm is designed to cooperate with the fitting polynomial model, and more accurate channel estimation results can be provided compared to those provided by conventional least-square (LS) algorithms. When multiple transmission antennas are required, the advantage of the proposed polynomial-fitting OMP (PF-OMP) algorithm is more obvious as more transmission antennas are used.