Training-based Channel Estimation Research Articles

Training-based channel estimation for massive MIMO systems using LAS algorithm

Training-based channel estimation for massive MIMO systems using LAS algorithm

Training-based channel estimation for massive MIMO systems using LAS algorithm

Training-based channel estimation for massive MIMO systems using LAS algorithm

Channel Estimation Enhancement With Generative Adversarial Networks

Improving the accuracy of channel estimation is a significant topic in the context of wireless communications. For training-based channel estimations, increasing the length of a training sequence may improve the accuracy of channel estimation but causes a higher overhead. Nevertheless, this paper shows that benefiting from generative adversarial networks (GANs), which is an emerging deep learning framework, the accuracy of channel estimation can be improved without transmitting a longer training sequence. To this end, this paper proposes a GAN-based channel estimation enhancement algorithm, where GANs are trained online with receive sequence so as to obtain a longer mimic sequence and enhance channel estimation. In order to address the problem of improving the training stability and the learning ability of GANs, this paper proposes a novel framework by integrating a conditional GAN with an improved Wasserstein GAN. Furthermore, a strategy based on a lookup table is proposed to alleviate overfitting that may occur during the training of GANs. Simulation results indicate that the proposed GAN-based channel estimation enhancement algorithm can benefit the conventional training-based channel estimation, yielding lower relative error performance, especially in the low SNR regions.

Ergodic capacity of antenna selection aided massive multi‐user MIMO systems with imperfect CSI in correlated time‐varying channels

In this study, the authors address antenna selection (AS)-aided massive multi-user multiple-input-multiple-output (MU-MIMO) system based on maximum signal-to-noise ratio, where imperfect channel state information (CSI), time-varying channel and antenna spatial correlation are considered. More explicitly, a computationally simple training-based channel estimator is firstly employed for obtaining the imperfect down-link CSI. Channel quantisation (CQ) is subsequently introduced by the feedback link which is used for feeding back so-obtained CSI to base station. Time varying coefficient is utilised to characterise channel time variety and antenna spatial correlation is modelled by Kronecker model. Furthermore, the authors derive closed-form ergodic channel capacity of the AS-aided MU-MIMO system with channel estimation error, CQ error and delay feedback, which has not yet been addressed in the state-of-the-art approaches. Simulation results are provided to demonstrate the tightness of their theoretical computations of the ergodic channel capacity.

Energy-Efficient Power Control in Cell-Free and User-Centric Massive MIMO at Millimeter Wave

In a cell-free massive MIMO architecture a very large number of distributed access points simultaneously and jointly serves a much smaller number of mobile stations; a variant of the cell-free technique is the user-centric approach, wherein each access point just serves a reduced set of mobile stations. This paper introduces and analyzes the cell-free and user-centric architectures at millimeter wave frequencies, considering a training-based channel estimation phase, and the downlink and uplink data transmission phases. First of all, a multiuser clustered millimeter wave channel model is introduced in order to account for the correlation among the channels of nearby users; second, an uplink multiuser channel estimation scheme is described along with low-complexity hybrid analog/digital beamforming architectures. Third, the non-convex problem of power allocation for downlink global energy efficiency maximization is addressed. Interestingly, in the proposed schemes no channel estimation is needed at the mobile stations, and the beamforming schemes used at the mobile stations are channel-independent and have a very simple structure. Numerical results show the benefits granted by the power control procedure, that the considered architectures are effective, and permit assessing the loss incurred by the use of the hybrid beamformers and by the channel estimation errors.

Diffusive MIMO Molecular Communications: Channel Estimation, Equalization, and Detection

In diffusion-based communication, for molecular systems, the achievable data rate depends on the stochastic nature of diffusion, which exhibits a severe inter-symbol-interference (ISI). Multiple-input multiple-output (MIMO) multiplexing improves the data rate at the expense of an inter-link interference (ILI). This paper investigates training-based channel estimation schemes for diffusive MIMO (D-MIMO) systems and corresponding equalization methods. Maximum likelihood and least-squares estimators of mean channel are derived, and the training sequence is designed to minimize the mean square error (MSE). The numerical validations in terms of MSE are compared with Cramer–Rao bound derived herein. Equalization is based on decision feedback equalizer (DFE) structure as this is effective in mitigating diffusive ISI/ILI. Zero-forcing, minimum MSE, and least-squares criteria have been paired to DFE, and their performances are evaluated in terms of bit error probability. D-MIMO time interleaving is exploited as an additional countermeasure to mitigate the ILI with remarkable performance improvements. The configuration of nano-transceivers is not static but affected by a Brownian motion. A block-type communication is proposed for D-MIMO channel estimation and equalization, and the corresponding time-varying D-MIMO MC system is numerically evaluated.

Reverse TDD-Based Massive MIMO Systems With Underlay Spectrum Sharing

Multi-cell multi-user underlay spectrum-sharing massive multiple-input multiple-output systems operating with reverse time division duplexing (R-TDD) are investigated. By primarily aiming at fully mitigating intra-cell pilot contamination and coherent interference, in the proposed R-TDD scheme, the primary/secondary systems are allowed to operate only in the opposite transmission directions. In order to establish fundamental performance limits, the secondary transmit power constraints and achievable rates are derived in the presence of training-based channel estimation. Thereby, the joint detrimental effects of spatial correlation, beamforming uncertainty, and inter-/intra-cell coherence interference due to pilot contamination are quantified and compared against the conventional TDD (C-TDD) counterpart. A max–min optimal power control policy is designed, and thereby, the common achievable rates and power control coefficients are derived. It is shown that by invoking R-TDD, the secondary power constraints and sum rates can be made to become asymptotically independent of primary interference threshold. Thus, the secondary system can be operated with its maximum average transmit power, independent of the primary system without hindering its asymptotically achievable rates by the virtue of the inherent intra-cell coherent interference mitigation benefit of the R-TDD. By exploiting the pilot decontamination feature of R-TDD, the achievable rates of primary/secondary systems can be significantly boosted, compared to the underlay spectrum sharing with C-TDD.

Superimposed Training-Based Channel Estimation for MISO Optical-OFDM VLC

In this paper, we investigate a novel channel estimation (CE) method for multiple-input and single-output (MISO) systems in visible light communication (VLC). Direct current biased optical orthogonal frequency division multiplexing (DCO-OFDM) is commonly used in VLC where half of the available subcarriers are spent to guarantee a real-valued output after the inverse fast Fourier transform operation. Besides, dedicated subcarriers are typically used for CE, thus, many resources are wasted and the spectral efficiency is degraded. We propose a superimposed training approach for CE in MISO DCO-OFDM VLC scenarios. Analytical expressions of mean squared error (MSE) and spectral efficiency are derived when the least squares estimator is considered. This analysis is valid for outdoor and indoor scenarios. For the CE error, simulation results of MSE show a perfect match with analytical expressions. Moreover, results prove that this technique guarantees a larger spectral efficiency than previous schemes where dedicated pilots were used. Finally, the optimal data power allocation factor is also analytically derived.

Optimal Pilot Design for MIMO Broadcasting Systems Based on the Positive Definite Matrix Manifold

In the MIMO broadcasting system, channel state information (CSI) is often used for data detection at the receiver or preprocessing techniques such as the power control and user scheduling at the transmitter and hence, the study of its acquisition is important. Usually, the CSI can be obtained by the training-based channel estimation. Assuming that the users have the channels’ statistical information and adopt the minimum mean-square-error (MMSE) receivers, this paper studies how to design an optimal training sequence to minimize the total weighted mean square error (MSE) of channel estimation. Following this objective, we formulate this problem as a positive semidefinite problem (SDP) with two constraints, and further transform it into a dual problem. In the solving process of the dual problem, we model it as an optimization problem on the positive definite matrix manifold and solve it by use of the iterative geodesic equation on the matrix manifold. The convergence and correctness of the proposed method are demonstrated by computer simulation; the effects of key system parameters on the weighted MSE are also investigated. Under various system configurations, the superiority of the proposed method is shown by comparing with a few other existing schemes.

Cloud-Aided Cognitive Ambient Backscatter Wireless Sensor Networks

Cognitive ambient backscatter is a wireless communication paradigm that allows a secondary backscatter device to superimpose its information-bearing data on a primary signal, without requiring any type of power-consuming active components or other signal conditioning units. In such a network, the performance of the backscatter system can be severely degraded by channel estimation errors and co-channel direct-link interference (DLI) from the primary system. To overcome these shortcomings, we consider a cloud radio access network (C-RAN) architecture, where both the primary and secondary edge nodes are connected to a cloud processor via high-speed links. In this centralized architecture, secondary edge nodes provide network access to ambient backscatter passive and semi-passive sensors with communication capabilities, and the problem of acquiring channel state information and suppressing the DLI is managed by the cloud processor. In particular, we assess the performance of the secondary backscatter sensor transmission in a realistic system setup, which takes into account training-based channel estimation, practical modulation constraints, and imperfect DLI suppression. In addition, we formulate and solve an optimization problem aimed at maximizing the transmission rate of the secondary transmission, subject to limits on channel estimation error, average symbol error rate, power consumption, and energy storage capabilities of the backscatter sensor. The validity of our analysis and the performance of the secondary system based on the proposed designs are corroborated through the Monte Carlo simulations.

Biological Optical-to-Chemical Signal Conversion Interface: A Small-Scale Modulator for Molecular Communications

Although many exciting applications of molecular communication (MC) systems are envisioned to be at microscale, the MC testbeds reported in the literature so far are mostly at macroscale. This may partially be due to the fact that controlling an MC system at microscale is challenging. To link the macroworld to the microworld, we propose and demonstrate a biological signal conversion interface that can also be seen as a microscale modulator. In particular, the proposed interface transduces an optical signal, which is controlled using a light-emitting diode, into a chemical signal by changing the pH of the environment. The modulator is realized using Escherichia coli bacteria as microscale entity expressing the light-driven proton pump gloeorhodopsin from Gloeobacter violaceus. Upon inducing external light stimuli, these bacteria locally change their surrounding pH level by exporting protons into the environment. To verify the effectiveness of the proposed optical-to-chemical signal converter, we analyze the pH signal measured by a pH sensor, which serves as a receiver. We develop an analytical parametric model for the induced chemical signal as a function of the applied optical signal. Using this model, we derive a training-based channel estimator that estimates the parameters of the proposed model to fit the measurement data based on a least square error approach. We further derive the optimal maximum likelihood detector and a suboptimal low-complexity detector to recover the transmitted data from the measured received signal. It is shown that the proposed parametric model is in good agreement with the measurement data. Moreover, for an example scenario, we show that the proposed setup is able to successfully convert an optical signal representing a sequence of binary symbols into a chemical signal with a bit rate of 1 bit/min and recover the transmitted data from the chemical signal using the proposed estimation and detection schemes. The proposed modulator may form the basis for future MC testbeds and applications at microscale.

Training Based Channel Estimation in OFDM Systems

Training Based Channel Estimation in OFDM Systems

Locally Orthogonal Training Design for Cloud-RANs Based on Graph Coloring

We consider training-based channel estimation for a cloud radio access network (CRAN), in which a large amount of remote radio heads (RRHs) and users are randomly scattered over the service area. In this model, assigning orthogonal training sequences to all users will incur a substantial overhead to the overall network, and is even impossible when the number of users is large. Therefore, in this paper, we introduce the notion of local orthogonality, under which the training sequence of a user is orthogonal to those of the other users in its neighborhood. We model the design of locally orthogonal training sequences as a graph coloring problem. Then, based on the theory of random geometric graph, we show that the minimum training length scales in the order of $\ln K$, where $K$ is the number of users covered by a CRAN. This indicates that the proposed training design yields a scalable solution to sustain the need of large-scale cooperation in CRANs. Numerical results show that the proposed scheme outperforms other reference schemes.

Performance analysis of non-coherent MIMO MRC scheme with training using finite-SNR diversity and multiplexing tradeoff

The inherent tradeoff between the twin benefits offered by multiple antenna systems, namely, the diversity gain and the multiplexing gain is captured as the diversity multiplexing tradeoff (DMT). The DMT at asymptotically high signal-to-noise ratio (SNR) is optimistic, whereas at finite SNR, it is practical. In this paper, point-to-point multiple input multiple output (MIMO) systems are considered under the assumption of coherent and non-coherent communication implying, respectively, whether perfect channel state information is available at the receiver (CSIR) or not. The literature mainly addresses non-coherent communication with training at asymptotically high SNR, whereas the finite-SNR analysis is more relevant in practice. We address the performance analysis of a MIMO maximal ratio combining scheme by deriving closed-form expressions of the DMT at finite SNR under non-coherent communication with training. At a fixed multiplexing gain and finite SNR, a reduction in the diversity gain is observed when coherent communication is replaced by non-coherent communication with training. We also show that for a high multiplexing gain, the reduction in diversity gain is much more pronounced as compared to that at a low multiplexing gain. A training-based channel estimation scheme discussed in the literature is used in two modes of power allocation, namely, the capacity optimal power allocation and equal power allocation (EPA). In both modes, at a fixed average SNR and with equal duration of training, we observe that the power allocation mode does not make a significant impact on the finite-SNR DMT of the MIMO scheme. We also observe that in the EPA mode, the diversity gain reduces with increase in training duration.

Training Based Channel Estimation for Multitaper GFDM System

Recent activities in the cellular network world clearly show the need to design new physical layer waveforms in order to meet future wireless requirements. Generalized Frequency Division Multiplexing (GFDM) is one of the leading candidates for 5G and one of its key features is the usage of circular pulse shaping of subcarriers to remove prototype filter transients. Due to the nonorthogonal nature of the conventional GFDM system, inherent interference will affect adversely channel estimation. With Discrete Prolate Spheroidal Sequences (DPSSs) or multitapers as prototype filters an improved orthogonal GFDM system can be developed. In this work, we investigate channel estimation methods for multitaper GFDM (MGFDM) systems with and without Discrete Fourier Transform (DFT). The simulation results are presented using Least Squares (LS) and Minimum Mean Square Error (MMSE) channel estimation (CE) methods. DFT based CE methods provide better estimates of the channel but with an additional computational cost.

Robust Faster-Than-Nyquist PDM-mQAM Systems With Tomlinson–Harashima Precoding

A training-based channel estimation algorithm is proposed for the faster-than-Nyquist PDM-mQAM (m = 4, 16, 64) systems with Tomlinson-Harashima precoding (THP). This is robust to the convergence failure phenomenon suffered by the existing algorithm, yet remaining format-transparent. Simulation results show that the proposed algorithm requires a reduced optical signal-to-noise ratio (OSNR) to achieve a certain bit error rate (BER) in the presence of first-order polarization mode dispersion and phase noise introduced by the laser linewidth.

Performance evaluation of DFT-based channel estimation in MIMO-OFDM system

Multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) is an emerging multiplexing technique used in modern mobile communication systems. A main challenge to MIMO-OFDM is retrieval of the channel state information (CSI) accurately and synchronisation between the transmitter and receiver. The CSI is retrieved with the help of channel estimation algorithms such as training-based, blind and semi-blind channel estimation by various researchers. The mean square error (MSE) of existing training-based least square (LS) and minimum mean square error (MMSE) estimation are usually high. In order to minimise MSE, discrete Fourier transform (DFT)-based channel estimation is proposed. This paper deals with MIMO-OFDM system and simulation of training-based LS and MMSE channel estimation, performance evaluation of DFT-based channel estimation. The simulation results clearly indicate the drastic minimisation of MSE by the implementation of DFT channel estimation with LS and MMSE estimation.

Joint Design of Iterative Training-Based Channel Estimation and Cluster Formation in Cloud-Radio Access Networks

A dilemma in cloud radio access networks (C-RANs) is how to keep a balance between the performance and the efficiency of centralized processing. To solve this problem, the joint design of training-based channel estimation and cluster formation are studied in this paper. To provide efficient cooperation strategies in C-RANs, individual C-RAN clusters are formed by the remote radio heads (RRHs), and a data-assisted channel estimation scheme is studied, which can reduce the redundant cost of training sequences. To ensure the performance of channel estimation and data transmissions, the cluster formation and the channel estimation are optimized jointly. In particular, an iterative training-based channel estimation scheme is designed by using convex optimization and the Broyden-Fletcher-Goldfarb-Shanno algorithm jointly. Moreover, a utility function of cluster formation can be established based on the estimates and the mean squared error of our proposed channel estimation algorithm, and the cluster formation of RRHs can be formulated as a coalitional formation game. Furthermore, a sub-optimal algorithm is also proposed to reduce the computational complexity. Finally, the simulation results are shown to evaluate the performance of our proposed algorithms.

Training-Based Channel Estimation Algorithms for Dual Hop MIMO OFDM Relay Systems

In this paper, we consider minimum-mean-square error (MMSE) training-based channel estimation for two-hop multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) relaying systems. The channel estimation process is divided into two main phases. The relay-destination channel is estimated in the first phase and can be obtained using well-known point-to-point MIMO OFDM estimation methods. In the second phase, the source-relay channel is estimated at the destination with the use of a known training sequence that is transmitted from the source and forwarded to the destination by a nonregenerative relay. To obtain an estimate of the source-relay channel, the source training sequence, relay precoder, and destination processor, require to be optimized. To solve this problem, we first derive an iterative algorithm that involves sequentially solving a number of convex optimization problems to update the source, relay, and destination design variables. Since the iterative algorithm may be too computationally expensive for practical implementation, we then derive simplified solutions that have reduced computational complexity. Simulation results demonstrate the effectiveness of the proposed algorithms.

Superimposed Training Based Channel Estimation for Uplink Multiple Access Relay Networks

In this paper, the channel estimation in uplink multiple access relay networks (MARNs) with analog network coding protocol has been researched. We apply the superimposed training (ST) scheme where each relay puts a separate training sequence on the top of the received one before forwarding to destination, and design a maximum likelihood based channel estimation algorithm for the composite source-relay-destination and individual relay-destination links. The optimal training sequences as well as the superimposed training power are also derived in closed forms. To make our study more complete, the channel estimation in the time-selective fading environment is further considered, and a correlation-based channel estimation (CBCE) algorithm is developed by taking advantage of time-domain channel autocorrelation nature. Simulation results show that the presented ST scheme can effectively improve the performance of multi-user detection in MARNs, and the proposed CBCE algorithm significantly outperforms the existing channel estimation methods.