Estimated Channel Coefficients Research Articles

On the Unique Channel Identification in Ambient Backscatter Communication Systems

Channel coefficient estimation is a challenging problem in ambient backscatter communication systems. In this paper, unique identification of channel coefficients using the Expectation-Maximization (EM) method is investigated. It is proven that the EM method is not able to always yield unique solutions to channel coefficients and therefore the tag symbol estimation accuracy can be compromised. A correct derivation of the hybrid Cramer-Rao Bound (HCRB) is also provided.

Equalizer Parameters’ Adjustment Based on an Oversampled Channel Model for OFDM Modulation Systems

A physical model of a wireless transmission channel in the time domain usually consists of the main propagation path and only a few reflections. The reasonable assumptions made about the channel model can improve its parameters’ estimation by a greedy OFDM (Orthogonal Frequency Division Multiplexing) equalizer. The equalizer works flawlessly if delays between propagation paths are in the sampling grid. Otherwise, the channel impulse response loses its compressible characteristic and the number of coefficients to find increases. It is possible to get back to the simple channel model by data oversampling. The paper describes how the above idea helps the OMP (Orthogonal Matching Pursuit) algorithm estimate channel coefficients. The authors analyze the oversampling algorithm on the one hand to assess the influence of filtering function and signal resolution on the quality of the channel impulse response reconstruction. On the other hand, the abilities of the OMP algorithm are analyzed to distinguish components of the oversampled signal. Based on these analyses, we proposed modifications to the compressible channel’s impulse response reconstruction algorithm to minimize the number of transmission errors. A distinction was made between the filters used in the OMP search and channel reconstruction stages before calculating equalizer coefficients. Additionally, the results of the search stage were considered as elements within the groups.

Doubly selective channel estimation and equalization based on ICI/ISI mitigation for OQAM-FBMC systems

Over a doubly selective channel, broadband transmission systems face challenges in channel estimation and equalization. High mobility causes inter-carrier interference (ICI), while multipath transmission induces inter-symbol interference (ISI). In this paper, we present a mitigation method of ICI/ISI for the offset quadrature amplitude-modulated filter bank multi-carrier (OQAM-FBMC) system. It features low inherent imaginary interference (IMI) sensitivity and high efficiency. Specifically, a pilot indices optimization algorithm and a sparse adaptive orthogonal subspace pursuit (SAOSP) algorithm are presented based on the 2-D channel modeling scheme. The guard pilots are first added to mitigate the effect of ICI. Then the index optimization and SAOSP algorithms are applied to achieve a high-accuracy estimation of sparse channel coefficients. In addition, a threshold judgment suboptimal minimum mean square error (MMSE) equalization method is presented based on the variability of the interference power. The method uses normalized interference power thresholds to estimate the ISI dimension and reduce the equalization data, thus mitigating the effect of ISI and achieving efficient equalization. To verify the above methods, single-input-single-output (SISO) and multiple-input-multiple-output (MIMO) models are built. Simulation results indicate a 3-5 dB improvement in channel estimation accuracy. The suboptimal MMSE equalization results are close to the optimal MMSE with about four orders of magnitude reduction in complexity.

Blind block timing estimation for Alamouti STBC: An adaptive cyclostationary-based approach

Block timing synchronization, which could be data-aided or non-data-aided, is a critical part of space–time block codes (STBCs) for recovery of transmitted symbols. The data-aided schemes are not suited for some problems like bandwidth efficiency and most of the existing non-data-aided techniques rely on the received signals statistics and channel coefficients estimation increasing their complexity. In this paper, a non-data-aided cyclostationary-based approach is proposed for block timing estimation in Alamouti STBC employing frequency-shifted versions of the received signals. The method is non-statistical with low complexity and requires no knowledge of channel coefficients. Simulation results confirm the effectiveness of the method.

Message Passing-Aided Joint Data Detection and Estimation of Nonlinear Satellite Channels

Satellite communication is capable of supporting seamless global coverage. However, owing to the reliance on limited-duration solar power, the high power amplifier (HPA) is often driven close to its saturation point, which leads to severe nonlinear distortion in satellite channels. Thus, mitigating the effect of the nonlinear distortion becomes essential for reliable communications. In this article, we propose an efficient joint channel estimation and data detection method based on message passing within the associated factor graph modelling the HPA employed in nonlinear satellite channels. Then, we develop a combined belief propagation and mean field (BP-MF) method to cope with the hard constraints and dense short loops on the factor graph. In particular, the parametric message updating expressions relying on the canonical parameters are derived in the symbol detection part. To alleviate the impact of dense loops, we reformulate the system model into a compact form within the channel estimation part and then reconstruct a loop-free subgraph associated with vector-valued nodes to guarantee convergence. Furthermore, the proposed BP-MF method is also extended to the realistic scenario of having unknown noise variance. To further reduce the computational complexity of the large-scale matrix inversion of channel estimation, the generalized approximate message passing (GAMP) algorithm is employed to decouple the vector of channel coefficient estimation into a series of scalar estimations. Simulation results show that the proposed methods outperform the state-of-the-art benchmarks both in terms of bit error rate performance and channel estimation accuracy.

Noncoherent Massive MIMO With Embedded One-Way Function Physical Layer Security

We propose a novel physical layer security scheme that exploits an optimization method as a one-way function. The proposed scheme builds on nonsquare differential multiple-input multiple-output (MIMO), which is capable of noncoherent detection even in massive MIMO scenarios and thus resilient against risky pilot insertion and pilot contamination attacks. In contrast to conventional nonsquare differential MIMO schemes, which require space-time projection matrices designed via highly complex, discrete, and combinatorial optimization, the proposed scheme utilizes projection matrices constructed via low-complexity continuous optimization designed to maximize the coding gain of the system. Furthermore, using a secret key generated from the true randomness nature of the wireless channel as an initial value, the proposed continuous optimization-based projection matrix construction method becomes a one-way function, making the proposed scheme a physical layer secure differential MIMO system. An attack algorithm to challenge the proposed scheme is also devised, which demonstrates that the security level achieved improves as the number of transmit antennas increases, even in an environment where the eavesdropper can perfectly estimate channel coefficients and experience asymptotically large signal-to-noise ratios.

Neural Network Aided Digital Self-Interference Cancellation for Full-Duplex Communication Over Time-Varying Channels

In-band full duplex communication requires precise self-interference cancellation (SIC) to successfully decode the received desired signal. The existing neural network (NN) based SIC scheme uses offline trained NN to estimate the non-linear component of received self-interference (SI) over a static SI channel without additional NN training. For the time-varying SI channel, the NN-aided SIC method needs to retrain the NN during in-band full duplex communication to adapt time-varying channels. However, NN training is not fast enough to be done during full duplex communication. Thus, the SIC performance degrades. In this paper, we propose a digital SIC scheme using channel robust NN which takes estimates of linear SI channel coefficients as an input. It was found that the NN could learn the static part of the non-linear behavior of the SI channel well. Our solution can adapt the time-varying SI channel with only the channel coefficient estimation of linear components and a pre-trained NN. The proposed scheme can successfully reduce the SI to the noise floor for both time-invariant and time-varying SI channels.

Learning-Based Channel Estimation and Phase Noise Compensation in Doubly-Selective Channels

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 novel training scheme where the training data is rotated by random phases before being fed to the network is employed. Further, using the estimated channel coefficients, a simple and effective PN estimation and compensation scheme is devised. Numerical results demonstrate that the proposed network and PN compensation scheme achieve robust OFDM performance in the presence of phase noise.

Orthogonal frequency division multiplexing system with an indexed-pilot channel estimation

In this paper, we examine an orthogonal frequency division multiplexing (OFDM) system under imperfect channel conditions and pilot-insertion- based channel estimation. However, unlike conventional pilot-insertion-based channel estimation, some inserted pilot symbols are set to zero where the index of the zero-pilot symbols is employed to transmit extra data bits. In this paper, we employ a minimum mean squared error (MMSE) to detect transmitted pilot symbols; these symbols are then used to estimate channel coefficients. Furthermore, the impact of zero-pilot symbols on the mean-squared error of channel estimation and on system error performance is examined. Our findings show that the index of zero-pilot symbols can be used to improve system throughput by carrying extra information bits without harming channel estimation accuracy or degrading system error performance. Simulation results show that, at a high signal-to-noise ratio, the bit error rate for data bits transmitted via zero-pilot symbols index selection is lower than that of data bits transmitted over data subcarriers.

Joint Activity Detection and Channel Estimation in Cell-Free Massive MIMO Networks With Massive Connectivity

Cell-free massive MIMO is one of the key technologies for future wireless communications, in which users are simultaneously and jointly served by all access points (APs). In this paper, we investigate the minimum mean square error (MMSE) estimation of effective channel coefficients in cell-free massive MIMO systems with massive connectivity. To facilitate the theoretical analysis, only single measurement vector (SMV) based MMSE estimation is considered in this paper, i.e., the MMSE estimation is performed based on the received pilot signals at each AP separately. Inspired by the decoupling principle of replica symmetric postulated MMSE estimation of sparse signal vectors with independent and identically distributed (i.i.d.) non-zero components, we develop the corresponding decoupling principle for the SMV based MMSE estimation of sparse signal vectors with independent and non-identically distributed (i.n.i.d.) non-zero components, which plays a key role in the theoretical analysis of SMV based MMSE estimation of the effective channel coefficients in cell-free massive MIMO systems with massive connectivity. Subsequently, based on the obtained decoupling principle of MMSE estimation, likelihood ratio test and the optimal fusion rule, we perform user activity detection based on the received pilot signals at only one AP, or cooperation among the entire set of APs for centralized or distributed detection. Via theoretical analysis, we show that the error probabilities of both centralized and distributed detection tend to zero when the number of APs tends to infinity while the asymptotic ratio between the number of users and pilots is kept constant. We also investigate the asymptotic behavior of oracle estimation in cell-free massive MIMO systems with massive connectivity via random matrix theory. Moreover, in order to demonstrate the potential performance loss of SMV based MMSE estimation, which does not employ the correlation between the received pilot signals at different APs, the multiple measurement vector (MMV) based MMSE estimation, i.e., joint MMSE estimation with pilot signals from all APs, is analyzed via numerical results. Numerical analysis shows that the theoretical analyze with our decoupling principle for the SMV based MMSE estimation of sparse signal vectors with i.n.i.d. non-zero components matches well with the numerical results.

Adaptive Turbo Equalization for Nonlinearity Compensation in WDM Systems

In this paper, the performance of adaptive turbo equalization for nonlinearity compensation (NLC) is investigated. A turbo equalization scheme is proposed where a recursive least-squares (RLS) algorithm is used as an adaptive channel estimator to track the time-varying intersymbol interference (ISI) coefficients associated with inter-channel nonlinear interference (NLI) model. The estimated channel coefficients are used by a MIMO $2\times 2$ soft-input soft-output (SISO) linear minimum mean square error (LMMSE) equalizer to compensate for the time-varying ISI. The SISO LMMSE equalizer and the SISO forward error correction (FEC) decoder exchange extrinsic information in every turbo iteration, allowing the receiver to improve the performance of the channel estimation and the equalization, achieving lower bit-error-rate (BER) values. The proposed scheme is investigated for polarization multiplexed 64QAM and 256QAM, although it applies to any proper modulation format. Extensive numerical results are presented. It is shown that the scheme allows up to 0.7 dB extra gain in effectively received signal-to-noise ratio (SNR) and up to 0.2 bits/symbol/pol in generalized mutual information (GMI), on top of the gain provided by single-channel digital backpropagation.

Wireless channel estimation and beamforming by using block sparse adaptive filtering

Channel estimation normally provides information about indoor and outdoor fading channel statistics. The adaptive channel estimation models play an important role to generate the required channel state information (CSI) using the estimated channel coefficient vector. The CSI can be utilized to generate an angle vector that controls the steering mechanism of a beamformer. The beamformer provides better directive gain for linear antenna array and helps to improve the signal to noise ratio of the wireless receiver. The proposed estimation model process the transmitted quadrature amplitude modulation (QAM) data samples in the frequency domain. The adaptive design incorporates norm-based sparsity through block recursive least square (BRLS) algorithm to develop a computationally efficient model. The proposed sparse-FBRLS (Fast BRLS) model has simultaneously addressed the problems of channel estimation and beamforming in case of indoor and outdoor communication. The performance of the model is tested by different performance measures under practical mobility conditions.

Integrated Swarming Computing Paradigm for Efficient Estimation of Channel Parameters in MIMO System

In this study, optimum channel estimation in MIMO network is investigated by an integrated computing paradigm using Particle Swarm Optimization (PSO) and Nelder Mead Method (NMM). The efficacy of global optimization is exploited through PSO while for fine-tuning of channel coefficients, the strength of NMM as an efficient local optimization technique is utilized. Hybrid swarm intelligence framework is applied for square channel matrix having identical array elements at both transmitter and receiver end. Different signal–noise ratios are applied for analyzing the response of complex received signal from flat fading Additive White Gaussian Noise channel. Numerical simulations are done for evaluating Mean Square Error among true and estimated channel coefficients. Performance analysis is conducted not only for a single run of proposed hybrid swarm intelligence but also on extensive simulations on multiple independent trials to prove the worth of the scheme.

On the relaxed maximum-likelihood blind MIMO channel estimation for orthogonal space-time block codes

This paper concerns the maximum-likelihood channel estimation for MIMO systems with orthogonal space-time block codes when the finite alphabet constraint of the signal constellation is relaxed. We study the channel coefficients estimation subspace generated by this method. We provide an algebraic characterisation of this subspace which turns the optimization problem into a purely algebraic one and more importantly, leads to several interesting analytical proofs. We prove that with probability one, the dimension of the estimation subspace for the channel coefficients is deterministic and it decreases by increasing the number of receive antennas up to a certain critical number of receive antennas, after which the dimension remains constant. In fact, we show that beyond this critical number of receive antennas, the estimation subspace for the channel coefficients is isometric to a fixed deterministic invariant space which can be easily computed for every specific OSTB code.

Real-Time Cooperative Adaptive Robust Relay Beamforming Based on Kalman Filtering Channel Estimation

In this paper, an adaptive channel estimation algorithm is proposed for the multi-user robust relay beamforming problem. We propose a norm-bounded channel uncertainty model for all of the channels. We employ the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF) for joint estimation of channel coefficients and beamforming weights, and propose a Markov model for source-relay and relay-destination channels as well as the beamforming weights in the relays. The channel coefficients and bemforming weights are shown to be well-estimated in order to minimize the total relays power transmission subject to worst-case signal to interference and noise ratio (SINR) criterion at each receiver. As the main contribution of this paper, we propose an adaptive method for simultaneous estimation of the beamforming weights and channel states information, and solving the associated optimization problem by estimation tools. Furthermore, we show that our algorithm outperforms the interior point based methods for non-linear optimization. In comparison to our recent work, a sub-optimal solution to the non-convex robust relay beamforming problem was provided, the proposed method has superior performance and lower complexity.

Differential-Detection Aided Large-Scale Generalized Spatial Modulation is Capable of Operating in High-Mobility Millimeter-Wave Channels

A large-scale differential-detection aided generalized spatial modulation (GSM) system is proposed, which relies on a novel Gram–Schmidt basis set and an adaptive low-complexity detector, and is evidently suitable for high-mobility millimeter-wave (mmWave) channels. We consider nonstationary time-varying mmWave channels and assume that the beam-angles remain relatively fixed, while the channel coefficients vary rapidly. In this scenario, it is a challenging task to find the accurate estimates of channel coefficients for digital beamforming, which becomes an even more severe problem, as the numbers of subarrays and subcarriers increase. Our analog-beamforming-aided nonsquare differentially detected scheme achieves a higher transmission rate than the conventional coherent multiple-input multiple-output schemes because the pilot overhead and the complex-valued feedback are eliminated. Our simulation results following the IEEE 802.11ad specifications show that the performance of our proposed nonsquare differential GSM improved upon increasing the number of subarrays, where the maximum transmission rate of 16 b/s/Hz was considered.

Design of Nature Inspired Computing Approach for Estimation of Channel Coefficients in MIMO Networks

In this study, nature inspired computing (NIC) techniques are designed for estimation of channel co-efficients in multi-inputs multi-output (MIMO) networks. NIC methods based on recently introduced variants of swarm intelligence are exploited as optimization mechanism for MIMO channel co-efficients estimation. In MIMO systems there is m input matrix s multiplied with channel matrix H and there is some addition of noise ν and this whole is equivalent to output matrix r. In this research work, the goal is to achieve an optimized channel co-efficient matrix of different orders with the help of various NIC based optimization techniques. Such that MIMO networks give output exactly matching with the information sent by the transmitter. Comparative studies for the parameter estimation of MIMO networks against the true values of the parameters is evaluated by taking different cases, based on variations in the order of channel matrix and SNRs values. Performance analysis of the proposed NIC variants is conducted for single preferred run. NIC computing is done for equal number of antennas on transmitter and receiver end making a square channel matrix H. Four cases are taken in this research work for checking the trend of received signal for noisy channel like rayleigh fading channel. In each case channel estimation is developed by taking channel matrix of orders 2 × 2, 3 × 3, 4 × 4 and 8 × 8. In each case there are five sub cases which are without noise and for different values of SNR such as 70 db, 60 db, 50 db and 40 db.

Pilot contamination mitigation based on antenna subset transmission for mmWave massive MIMO

SummaryThis paper tackles the problem of pilot contamination (PC) in mmWave Massive MIMO cellular systems. We propose an analog precoder based on antenna subset transmission technique to mitigate the PC. This technique ensures the interfering signal to become noise‐like signal thus helping a more efficient estimation of channel coefficients. Also, this strategy is low cost and introduces no complexity load. The result shows the effectiveness of the proposed precoder to mitigate PC issue.

A Scalable and Statistically Robust Beam Alignment Technique for Millimeter-Wave Systems

Millimeter-wave (mm-wave) frequency bands provide an opportunity for much wider channel bandwidth compared with the traditional sub-6-GHz band. Communication at mm-waves is, however, quite challenging due to the severe propagation pathloss incurred by conventional isotropic antennas. To cope with this problem, directional beamforming both at the base station (BS) side and at the user equipment (UE) side is necessary in order to establish a strong path conveying enough signal power. Finding such beamforming directions is referred to as beam alignment (BA). This paper presents a new scheme for efficient BA. Our scheme finds a strong propagation path identified by an angle-of-arrival (AoA) and angle-of-departure (AoD) pair, by exploring the AoA–AoD domain through pseudo-random multi-finger beam patterns and constructing an estimate of the resulting second-order statistics (namely, the average received power for each pseudo-random beam configuration). The resulting under-determined system of equations is efficiently solved using non-negative constrained least-squares, yielding naturally a sparse non-negative vector solution whose maximum component identifies the optimal path. As a result, our scheme is highly robust to variations of the channel time dynamics compared with alternative concurrent approaches based on the estimation of the instantaneous channel coefficients, rather than of their second-order statistics. In the proposed scheme, the BS probes the channel in the downlink and trains simultaneously an arbitrarily large number of UEs. Thus, “beam refinement,” with multiple interactive rounds of downlink/uplink transmissions, is not needed. This results in a scalable BA protocol, where the protocol overhead is virtually independent of the number of UEs, since all the UEs run the BA procedure at the same time. Extensive simulation results illustrate that our approach is superior to the state-of-the-art BA schemes proposed in the literature in terms of training overhead in multi-user scenarios and robustness to variations in the channel dynamics.

Non-stationary Channel Estimation with Diffusion Adaptation Strategies Over Distributed Networks

In this paper we address non-stationary channel estimation problem with diffusion least mean square algorithm in distributed adaptive wireless sensor networks. Here we estimate channel coefficients or taps that are produced with Rayleigh fading models. All detailed explanations regarding to this fading channel type are presented and it is explained that how we can extend channel estimation with sensor networks to other newly presented channel types. We use the tracking performance analysis of diffusion cooperation over adaptive sensor networks to investigate the reliability of used algorithms and show the link between channel estimation problem and tracking a time varying entity. Theoretical analyzes are performed and the results are compared with simulation performance diagrams. It is proven that there is a reasonable match between these two outcomes. We present our results with the mean square deviation criteria.