On Channel Estimation and Power Control for Multi-cell Multi-path Massive MIMO TDD System

Some more practical channels that model the networks in a real environment is the multi-path communication channels. In order to investigate these communications channels. This work addressed Channel Estimation (CE) in the Uplink (UL) phase for a multi-cell multi-user massive multipleinput multiple-output (M-MIMO) system that studies multi-path communication between each user and its serving Base Station (BS). We suppose that the network operates under Time-Division Duplex (TDD) protocol. We studied and analyzed the multi-path channels and their benefit over CE since it presents a more realistic channel that displays a real propagation circumstance. on the flip side, we evaluated the CE quality using ideal MinimumMean Square Error (MMSE). This latter relies on an impractical property that can be explicated since the MMSE estimator considers foreknowledge on Large-Scale Fading (LSF) coefficients of interfering users. Thus, the suggested estimator is introduced to overcome this issue, where the suggested estimator tackled this problem and presented result asymptotic approaches to the performance of the MMSE estimator. Besides, we considered a more real communication in which the multi-path channels are either realized using Non-Line-of-Sight (NLoS) only or using both Line-of-Sight (LoS) and NLoS path depending on the distance at which the user is located from his serving BS. Otherwise, in numerous scenarios, users at the cell edge are strongly affected by Pilot Contamination (PC). Hence, we introduced a Power Control (PoC) policy so that the users at the cell edge are less affected by the PC problem. In the simulation results segment, the analytic and simulated results are introduced to assert our theoretical study.

Particle Filters

Both the particle and Kalman filters attempt to approximate the minimum mean-square error (MMSE) estimate of the time-varying parameter. In this scenario, a prior model of the time evolution of the parameter of interest is assumed before the MMSE estimation takes place. The Kalman filter is the (optimal) MMSE estimator for a linear dynamical system with Gaussian noise. For a nonlinear system with nonGaussian noise, the particle filter approximates the mean of posterior distribution at each discrete time step with a finite number of samples or particles. For these general nonlinear systems, the particle filter approaches the MMSE estimator as the number of particles approaches infinity.

On Channel Estimation for Rician fading with the phase-shift in Cell-Free Massive MIMO system

Channel estimation (CE) is a crucial phase in wireless communication systems, especially in cell-free (CF) massive multiple input multiple output (M-MIMO) since it is a dynamic wireless network. Therefore, this work is introduced to study CE for CF M-MIMO system in the uplink phase, wherein the performance of different estimators are evaluated, discussed, and compared in various situations. We assume the scenario in which each access point has prior knowledge of the channel statistics. The phase-aware-minimum mean square error (PA-MMSE) estimator, the non-phaseaware-MMSE (NPA-MMSE) estimator, and the least-squares estimator are the three estimators which are exploited in this work. Besides, we consider the Rician fading channel in which the line-of-sight path is realized with a phase-shift that models the users’ mobility where the considered phase-shift follows a uniform distribution. On the other hand, the mean-squared error metric is employed in order to evaluate the performance of each estimator, where an analytical and simulated result is provided for the PA-MMSE estimator and the NPA-MMSE estimator in order to assert our numerical results.

Deep Residual Learning for Channel Estimation in Intelligent Reflecting Surface-Assisted Multi-User Communications

<div>Channel estimation is one of the main tasks in realizing practical intelligent reflecting surfaceassisted multi-user communication (IRS-MUC) systems. However, different from traditional communication systems, an IRS-MUC system generally involves a cascaded channel with a sophisticated statistical distribution. In this case, the optimal minimum mean square error (MMSE) estimator requires the calculation of a multidimensional integration which is intractable to be implemented in practice. To further improve the channel estimation performance, in this paper, we model the channel estimation as a denoising problem and adopt a deep residual learning (DReL) approach to implicitly learn the residual noise for recovering the channel coefficients from the noisy pilot-based observations. To this end, we first develop a versatile DReL-based channel estimation framework where a deep residual network (DRN)-based MMSE estimator is derived in terms of Bayesian philosophy. As a realization of the developed DReL framework, a convolutional neural network (CNN)-based DRN (CDRN) is then proposed for channel estimation in IRS-MUC systems, in which a CNN denoising block equipped with an element-wise subtraction structure is specifically designed to exploit both the spatial features of the noisy channel matrices and the additive nature of the noise simultaneously. In particular, an explicit expression of the proposed CDRN is derived and analyzed in terms of Bayesian estimation to characterize its properties theoretically. Finally, simulation results demonstrate that the performance of the proposed method approaches that of the optimal MMSE estimator requiring the availability of the prior probability density function of channel.</div>

Deep Residual Learning for Channel Estimation in Intelligent Reflecting Surface-Assisted Multi-User Communications

<div>Channel estimation is one of the main tasks in realizing practical intelligent reflecting surfaceassisted multi-user communication (IRS-MUC) systems. However, different from traditional communication systems, an IRS-MUC system generally involves a cascaded channel with a sophisticated statistical distribution. In this case, the optimal minimum mean square error (MMSE) estimator requires the calculation of a multidimensional integration which is intractable to be implemented in practice. To further improve the channel estimation performance, in this paper, we model the channel estimation as a denoising problem and adopt a deep residual learning (DReL) approach to implicitly learn the residual noise for recovering the channel coefficients from the noisy pilot-based observations. To this end, we first develop a versatile DReL-based channel estimation framework where a deep residual network (DRN)-based MMSE estimator is derived in terms of Bayesian philosophy. As a realization of the developed DReL framework, a convolutional neural network (CNN)-based DRN (CDRN) is then proposed for channel estimation in IRS-MUC systems, in which a CNN denoising block equipped with an element-wise subtraction structure is specifically designed to exploit both the spatial features of the noisy channel matrices and the additive nature of the noise simultaneously. In particular, an explicit expression of the proposed CDRN is derived and analyzed in terms of Bayesian estimation to characterize its properties theoretically. Finally, simulation results demonstrate that the performance of the proposed method approaches that of the optimal MMSE estimator requiring the availability of the prior probability density function of channel.</div>

Improved Performance in the Detection of ACO-OFDM Modulated Signals Using Deep Learning Modules

Free space optical communication (FSO) is widely deployed to transmit high data rates for rapid communication traffic increase. Asymmetrically clipped optical orthogonal frequency division multiplexing (ACO-OFDM) modulation is a very efficient FSO communication technique in terms of transmitted optical power. However, its performance is limited by atmospheric turbulence. When the channel includes strong turbulence or is non-deterministic, the bit error rate (BER) increases. To reach optimal performance, the ACO-OFDM decoder needs to know accurate channel state information (CSI). We propose novel detection using different deep learning (DL) algorithms. Our DL models are compared with minimum mean square error (MMSE) detection methods in different turbulent channels and improve performance especially for non-stationary and non-deterministic channels. Our models yield performance very close to that of the MMSE estimator when the channel is characterized by weak or strong turbulence and is stationary. However, when the channel is non-stationary and variable, our DL model succeeds in improving the performance of the system and decreasing the signal to noise ratio (SNR) by more than 8 dB compared to that of the MMSE estimator, and it succeeds in recovering the received data without needing to know accurate CSI. Our DL decoders also show notable speed and energy efficiency improvement.

On the Distribution of an Effective Channel Estimator for Multi-Cell Massive MIMO

Accurate channel estimation is of utmost importance for massive MIMO systems to provide significant improvements in spectral and energy efficiency. In this work, we present a study on the distribution of a simple but yet effective and practical channel estimator for multi-cell massive MIMO systems suffering from pilot-contamination. The proposed channel estimator performs well under moderate to aggressive pilot contamination scenarios without previous knowledge of the inter-cell large-scale channel coefficients and noise power, asymptotically approximating the performance of the linear MMSE estimator as the number of antennas increases. We prove that the distribution of the proposed channel estimator can be accurately approximated by the circularly-symmetric complex normal distribution, when the number of antennas, M, deployed at the base station is greater than 10.

Applying Compressive Sensing to the Massive MIMO Channel Estimation Problem

This paper proposes the use of compressive sensing to tackle the Massive MIMO channel estimation problem. As our results show compressive sensing-based estimators perform as well as the optimum MMSE estimator.