Individual Channel Estimation Research Articles

Channel Estimation With Hybrid Reconfigurable Intelligent Metasurfaces

Reconfigurable Intelligent Surfaces (RISs) are envisioned to play a key role in future wireless communications, enabling programmable radio propagation environments. They are usually considered as almost passive planar structures that operate as adjustable reflectors, giving rise to a multitude of implementation challenges, including the inherent difficulty in estimating the underlying wireless channels. In this paper, we focus on the recently conceived concept of Hybrid Reconfigurable Intelligent Surfaces (HRISs), which do not solely reflect the impinging waveform in a controllable fashion, but are also capable of sensing and processing an adjustable portion of it. We first present implementation details for this metasurface architecture and propose a convenient mathematical model for characterizing its dual operation. As an indicative application of HRISs in wireless communications, we formulate the individual channel estimation problem for the uplink of a multi-user HRIS-empowered communication system. Considering first a noise-free setting, we theoretically quantify the advantage of HRISs in notably reducing the amount of pilots needed for channel estimation, as compared to the case of purely reflective RISs. We then present closed-form expressions for the Mean-Squared Error (MSE) performance in estimating the individual channels at the HRISs and the base station for the noisy model. Based on these derivations, we propose an automatic differentiation-based first-order optimization approach to efficiently determine the HRIS phase and power splitting configurations for minimizing the weighted sum-MSE performance. Our numerical evaluations demonstrate that HRISs do not only enable the estimation of the individual channels in HRIS-empowered communication systems, but also improve the ability to recover the cascaded channel, as compared to existing methods using passive and reflective RISs.

Individual Channel Estimation Based on Blind Interference Cancellation for Two-Way MIMO Relay Networks

In this paper, we investigate an individual channel estimation problem for multiple-input multiple-output (MIMO) two-way amplify-and-forward (AF) relay networks. To avoid self-interference during the estimation of the individual MIMO channels, a novel blind interference cancellation (BIC) approach is proposed based on an orthogonal preceding framework, where a pair of orthogonal precoding matrices is utilized at the source nodes. By designing an optimal decoding scheme, we propose to decompose the bidirectional transmission into a pair of unidirectional transmissions. Unlike most existing approaches, we make the practical assumption that the nonreciprocal MIMO channel and the mutual interference of multiple antennas are both taken into consideration. Under the precoding framework, we employ an orthogonal superimposed training strategy to obtain the individual MIMO channels. However, the AF strategy causes the noise at the terminal to be the sum of the local noise and the relay-propagated noise. To remove the relay-propagated noise during the estimation of the second-hop channel, a partial noise-nulling method is designed. We also derive a closed-form expression for the total mean square error (MSE) of the MIMO channel from which we compute the optimal power allocation. The simulation results demonstrate that the analytical and simulated curves match fully.

Interval type‐2 fuzzy Kalman filter aided individual channel estimation in MIMO relay systems

SummaryFor a multiple input multiple output relay system, the overall system performance is dependent on the effectiveness of the channel estimation technique adopted. In real time, communicating nodes have Doppler offset influences associated with them owing to high mobility that largely affects the characteristics of underlying channels. Thus, for the complete characterisation of the channel under fast time varying fading conditions, the estimation of the Doppler offset influences along with the channel coefficients becomes inevitable. However, the combined estimation of the channel and the Doppler influences renders the overall estimation problem nonlinear. In literature, majority of the channel estimation methods assume that the Doppler offset influences are already known to the receiver node or nodes are assumed to be stationary. In this paper, a novel hybrid interval type‐2 fuzzy aided Kalman filter method is proposed for the nonlinear channel estimation problem in one‐way two‐hop multiple input multiple output relay system. This channel estimation issue is represented as a nonlinear state space model, and the proposed hybrid method that combines the merits offered by the interval type‐2 fuzzy interpolation and the Kalman filter approach is applied to address the issue. For type reduction, Nie‐Tan method is adopted which is a low computational load extension of the widely used Karnik‐Mendel approach. Furthermore, a computational complexity analysis has been performed. The proposed hybrid interval type‐2 fuzzy based Kalman filter approach shows good performance‐complexity trade off under fast time varying channel conditions for one‐way two‐hop multiple input multiple output relay system.

Individual channel estimation for amplify‐and‐forward relay networks using in‐band superimposed training

In amplify-and-forward relay networks, accurate channel estimation of individual links is essential for coherent reception and optimal design. To acquire the channel state information of individual links, a novel in-band superimposed training is proposed, where relay superimposes its own training sequence directly on top of the information-bearing received data. As a result, the training sequences from the source and relay nodes are independent of each other, thus making it more flexible and robust in relay-training design. However, the proposed training scheme induces extra data interference that degrades the estimation performance. The authors first adopted the detected symbols to mitigate the data-induced interference during channel estimation. However, the estimation performance is degraded by the symbol detection error and relay propagated noise. To resolve this problem, the interference nulling at the relay is proposed, where some special frequency components of the received data are nulled prior to training superimposition. As a result, both the data-induced interference and relay propagated noise are totally removed during channel estimation. Simulation results are provided to assess the performance of the proposed schemes.

Segment Training Based Individual Channel Estimation for Multi-pair Two-Way Relay Network with Power Allocation

In this paper, we design a segment training based individual channel estimation (STICE) scheme for the classical two-way relay network (TWRN) with multi-pair sources (MPS) and amplify-and-forward (AF). We adopt the linear minimum mean square error (LMMSE) channel estimator to minimize the mean square error (MSE) without channel estimation error, where the optimal power allocation strategy from the relay for different sources is obtained. Then the MSE gains are given with different source pairs among the proposed power allocation scheme and the existing power allocation schemes. Numerical results show that the proposed method outperforms the existing ones.

Iterative LMMSE Individual Channel Estimation Over Relay Networks With Multiple Antennas

In this paper, we investigate the individual channel estimation over the three-node one-way relay network, where all the nodes are equipped with multiple antennas. We first examine one simple but representative scenario, where the relay node is equipped with a single antenna. An iterative linear minimum mean-square-error (LMMSE) method, which has fast convergence speed, is proposed to estimate the individual channels. We derive the closed-form least square channel estimator through the matrix unitary diagonalization to provide one good initialization point for the iterative LMMSE estimator. To evaluate the performance of the proposed algorithm, we present two performance lower bounds: Bayesian Cramer lower bound and linear estimation lower bound (LELB). Then, the training block and the relay amplification factor are optimized through minimizing the LELB. After that, our studies are extended to the general case, where all the nodes are equipped with multiple antennas. Finally, numerical results are provided to corroborate our proposed studies.

Individual Channel Estimation in a Diamond Relay Network Using Relay-Assisted Training

We consider the training design and channel estimation in the amplify-and-forward (AF) diamond relay network. Our strategy is to transmit the source training in time-multiplexing (TM) mode while each relay node superimposes its own relay training over the amplified received data signal without bandwidth expansion. The principal challenge is to obtain accurate channel state information (CSI) of second-hop link due to the multiaccess interference (MAI) and cooperative data interference (CDI). To maintain the orthogonality between data and training, a modified relay-assisted training scheme is proposed to migrate the CDI, where some of the cooperative data at the relay are discarded to accommodate relay training. Meanwhile, a couple of optimal zero-correlation zone (ZCZ) relay-assisted sequences are designed to avoid MAI. At the destination node, the received signals from the two relay nodes are combined to achieve spatial diversity and enhanced data reliability. The simulation results are presented to validate the performance of the proposed schemes.

Training Design for Channel Estimation in Uplink Cloud Radio Access Networks

In this paper, a training design and channel estimation scheme is considered for uplink cloud radio access networks (C-RANs) consisting of multiple user equipments (UEs), remote radio heads (RRHs), and a centralized baseband unit (BBU) pool. Since most signal processing functions in C-RANs are moved from RRHs to the BBU pool, the individual channels over the links between UEs and RRHs and the links between RRHs and the BBU pool cannot be estimated directly. To address this issue, segment training based individual channel estimation for C-RANs is proposed in this paper, in which channel state information acquisition is performed through two consecutive segments. By using the Kalman filter, the sequential minimum mean-square-error (SMMSE) estimator is developed to efficiently estimate the individual channel states through prior knowledge of long-term channel correlation statistics and the latest radio channel state. A training structure design subject to a power constraint is obtained by minimizing the mean-square-error (MSE) of the SMMSE estimator. Since the MSE is insufficient to fully evaluate the overall performance of C-RANs, the uplink ergodic capacity is derived to exploit the impact of channel estimation on the data transmission by taking the estimation errors into consideration, and the tradeoff between the lengths of two segment training sequences is optimized by maximizing the corresponding spectral efficiency. Furthermore, the Cramér-Rao bound is used to evaluate the proposed SMMSE estimator's performance. Simulation results show that the SMMSE estimator and the corresponding training design can effectively decrease MSE and significantly increase the quality and efficiency of data transmission in C-RANs.

ML and MAP channel estimation for distributed one-way relay networks with orthogonal training

In this letter, we investigate the individual channel estimation for the classical distributed-space-time-coding (DSTC) based one-way relay network (OWRN) under the superimposed training framework. Without resorting to the composite channel estimation, as did in traditional work, we directly estimate the individual channels from the maximum likelihood (ML) and the maximum a posteriori (MAP) estimators. We derive the closed-form ML estimators with the orthogonal training designing. Due to the complicated structure of the MAP in-channel estimator, we design an iterative gradient descent estimation process to find the optimal solutions. Numerical results are provided to corroborate our studies.

Channel estimation for full-duplex relay transmission in cloud radio access networks

Relay in full-duplex (FD) mode can achieve higher spectrum efficiency than that in half-duplex mode, while it is crucial to suppress relay self-interference to ensure transmission quality which requires instantaneous channel state information (CSI). In this paper, the channel estimation issue in FD amplify-andforward relay networks is considered, where the training-based estimation technique is adopted. Firstly, the least square (LS) estimation is implemented to obtain composite channel coefficients of source-relay-destination (SRD) channel and relay loop-interference (LI) channel in order to assist destination in performing data detection. Secondly, both LS and maximum likelihood estimation methods are utilized to perform individual channel estimation aiming at supporting successive interference cancelation at destination. Finally, simulation results demonstrate the effectiveness of both composite and individual channel estimation, and the presented ML method can achieve lower MSEs than LS solution.

Online and Offline Bayesian Cramér–Rao Bounds for Time-Varying Channel Estimation in One-Way Relay Networks

In this paper, we examine the Bayesian Cramer–Rao lower bounds (BCRBs) for the channel estimation in an amplify-and-forward (AF) one-way relay network (OWRN) under the time-selective flat-fading scenario, where the superimposed training is adopted at the relay node in order to achieve the individual channel estimation. We formulate the nonlinear dynamic state space for the individual channels and derive the online/offline BCRBs for the fully data-aided (FDA) channel estimator and the partially data-aided (PDA) estimator. The former estimator has full knowledge about the symbols from both the source and the relay, while the latter one has imperfect statistical information about the data of the source, and possesses full information of the symbols superimposed by the relay. For the FDA scenario, we calculate the closed-form online/offline BCRBs and analyze the effect of the nodes' mobility on the BCRB performance, while for the PDA case, with the assumption of square QAM constellation set at the source, we design one framework to numerically evaluate online/offline BCRBs and analyze the asymptotic BCRBs at high SNRs particularly for the 4-QAM constellation set. Finally, numerical results are provided to corroborate the proposed studies.

Dynamic Individual Channel Estimation for One-Way Relay Networks With Time-Multiplexed-Superimposed Training

In this paper, we design a time-multiplexed superimposed training (TMST) scheme to estimate the individual channels in amplify-and-forward one-way relay networks (OWRNs) under a doubly selective channel scenario, where the two-phase zero-prefixed block transmission scheme is adopted. The complex-exponential basis expansion model (CE-BEM) is utilized to approximate the channel of each individual hop and results in a coefficient vector with much smaller size, called in-BEM-CV. The channel estimation of the individual channel is then converted into the estimation of in-BEM-CVs. We develop an estimation algorithm with three steps: the standard least squares (LS) estimator, the time domain or the fast Fourier transform (FFT)-based decoupler, and the iterative LS-based refiner. We also optimize the training parameters, including the number, the position, and the power allocation of the pilot clusters by minimizing the estimation mean square error (MSE), and derive one performance lower bound for the proposed algorithm. Finally, numerical results are provided to corroborate the proposed studies.

Performance Analysis of OSTBC Relaying in AF MIMO Relay System with Imperfect CSI

In this paper, the transmission of orthogonal space–time block codes (OSTBCs) in amplify-and-forward (AF) multiple-input–multiple-output (MIMO) relay networks, with imperfect channel state information (CSI), is considered. Individual channel estimation and time-efficient cascaded (for estimating the product of channel matrices) channel estimation protocols are used for estimating the channel matrices required for decoding of OSTBC data at the destination. We derive tight approximations for the moment-generating function (m.g.f.) of the received signal-to-noise ratio at the destination node with imperfect CSI, by ignoring higher order noise terms, in Rayleigh fading. Using the derived m.g.f. expression, we obtain the analytical symbol error rate (SER) of the AF MIMO relay system for general OSTBCs with $M$ -ary phase-shift keying constellation. The diversity order of the MIMO OSTBC relay system is also derived for some special cases by using the SER expression.

Segment Training Based Individual Channel Estimation in One-Way Relay Network with Power Allocation

In this paper, we design a segment training based individual channel estimation (STICE) scheme in the classical three-node it amplify-and-forward (AF) one-way relay network (OWRN). The linear minimum mean-square-error (LMMSE) channel estimator is used to obtain a good initialization, and an iterative maximum a posteriori (MAP) channel estimator is developed to improve the estimation accuracy. We then investigate the underlying power allocation at the relay node both to minimize the mean-square-error (MSE) of the individual channel estimation and to maximize the average effective signal-to-noise ratio (AESNR) of the data detection. The closed-form Bayesian Cramér-Rao Bound (CRB) is also derived to evaluate the proposed algorithm. Finally, numerical results are provided to corroborate the proposed studies.

Study of Segment Training Based Individual Channel Estimation for Two-Way Relay Network

In this letter, we design a segment training based individual channel estimation (STICE) scheme in the classical three-node it amplify-and-forward two-way relay network (TWRN). We resort to linear minimum-mean-square-error (LMMSE) estimators to achieve the in-channel estimation without sign ambiguity through two consecutive segments. We derive the mean-square-error (MSE) of the individual channel estimation, from which the optimal training and the optimal relay's power allocation are obtained. Numerical results are provided to corroborate the provided studies.

Superimposed training design based on Bayesian optimisation for channel estimation in two-way relay networks

In this study, the superimposed training strategy is introduced into orthogonal frequency division multiplexing-modulated amplify-and-forward two-way relay network (TWRN) to perform two-hop transmission-compatible individual channel estimation. Through the superposition of an additional training vector at the relay under power allocation, the separated source–relay channel information can be directly obtained at the destination and then used to estimate the channels. The closed-form Bayesian Cramer-Rao lower bound (CRLB) is derived for the estimation of block-fading frequency-selective channels with random channel parameters, and orthogonal training vectors from the two source nodes are required to keep the Bayesian CRLB simple because of the self-interference in the TWRN. A set of optimal training vectors designed from the Bayesian CRLB are applied in an iterative linear minimum mean-square-error channel estimation algorithm, and the mean-square-error performance is provided to verify the Bayesian CRLB results.

ML-Based Channel Estimations for Non-Regenerative Relay Networks with Multiple Transmit and Receive Antennas

This paper investigates the channel estimations in a relay network with multiple transmit and receive antennas, including the estimation of the end-to-end channel matrix and the individual estimation of the transmitter-relay channels and the relay-receiver channels. For the end-to-end channel estimation, instead of directly estimating entries of the channel matrix, we use singular value decomposition (SVD) and estimate its largest singular value and singular vectors, which are then combined to form an estimation of the channel matrix. An approximate maximum-likelihood (ML) estimation is proposed, which is shown to become the exact ML estimation when the time duration of each training step equals the number of antennas at the transmitter. Simulation on the mean square error (MSE) shows that the SVD-based approximate ML estimation performs about the same as the exact ML estimation and is superior to entry-based estimations. For the individual channel estimation, we decompose each channel vector into the product of its length and direction, and find the ML estimation of each. By using an approximation on the probability density function (PDF) of the observations during training, an analytical ML estimation is derived. The ML estimation with the exact PDF is also investigated and a solution is obtained numerically. Simulation on the MSE shows that the two have similar performance. Compared with cascade channel estimations, its performance is superior for the relay-receiver channel estimation and comparable for the transmitter-relay channel estimation. Extension to the general multiple-antenna multiple-relay network is also provided.

Optimal Training Design for Individual Channel Estimation in Two-Way Relay Networks

This correspondence considers the optimal training design in a classical three-node amplify-and-forward two-way relay network (TWRN) that targets at estimating the individual channel between each source node and the relay node. The transmission environment is assumed to be frequency selective and the orthogonal-frequency-division multiplexing (OFDM) modulation is adopted. We derive the Bayesian Cramer-Rao bound (CRB) for the individual channel estimation, from which the optimal training is obtained. Extensive numerical results are provided to corroborate the proposed studies.

Superimposed Training-Based Channel Estimation for MIMO Relay Networks

We introduce the superimposed training strategy into the multiple-input multiple-output (MIMO) amplify-and-forward (AF) one-way relay network (OWRN) to perform the individual channel estimation at the destination. Through the superposition of a group of additional training vectors at the relay subject to power allocation, the separated estimates of the source-relay and relay-destination channels can be obtained directly at the destination, and the accordance with the two-hop AF strategy can be guaranteed at the same time. The closed-form Bayesian Cramér-Rao lower bound (CRLB) is derived for the estimation of two sets of flat-fading MIMO channel under random channel parameters and further exploited to design the optimal training vectors. A specific suboptimal channel estimation algorithm is applied in the MIMO AF OWRN using the optimal training sequences, and the normalized mean square error performance for the estimation is provided to verify the Bayesian CRLB results.

Time-Frequency Based Channel Estimation for High-Mobility OFDM Systems—Part II: Cooperative Relaying Case

We consider the estimation of time-varying channels for Cooperative Orthogonal Frequency Division Multiplexing (CO-OFDM) systems. In the next generation mobile wireless communication systems, significant Doppler frequency shifts are expected the channel frequency response to vary in time. A time-invariant channel is assumed during the transmission of a symbol in the previous studies on CO-OFDM systems, which is not valid in high mobility cases. Estimation of channel parameters is required at the receiver to improve the performance of the system. We estimate the model parameters of the channel from a time-frequency representation of the received signal. We present two approaches for the CO-OFDM channel estimation problem where in the first approach, individual channels are estimated at the relay and destination whereas in the second one, the cascaded source-relay-destination channel is estimated at the destination. Simulation results show that the individual channel estimation approach has better performance in terms of MSE and BER; however it has higher computational cost compared to the cascaded approach.