Linear Minimum Mean Square Error Channel Research Articles

Channel Estimation for Intelligent Reflecting Surface Assisted Multiuser Communications: Framework, Algorithms, and Analysis

In intelligent reflecting surface (IRS) assisted communication systems, the acquisition of channel state information is a crucial impediment for achieving the beamforming gain of IRS because of the considerable overhead required for channel estimation. Specifically, under the current beamforming design for IRS-assisted communications, in total KMN+KM channel coefficients should be estimated, where K, N and M denote the numbers of users, IRS reflecting elements, and antennas at the base station (BS), respectively. For the first time in the literature, this paper points out that despite the vast number of channel coefficients that should be estimated, significant redundancy exists in the user-IRS-BS reflected channels of different users arising from the fact that each IRS element reflects the signals from all the users to the BS via the same channel. To utilize this redundancy for reducing the channel estimation time, we propose a novel three-phase pilot-based channel estimation framework for IRS-assisted uplink multiuser communications, in which the userBS direct channels and the user-IRS-BS reflected channels of a typical user are estimated in Phase I and Phase II, respectively, while the user-IRS-BS reflected channels of the other users are estimated with low overhead in Phase III via leveraging their strong correlation with those of the typical user. Under this framework, we analytically prove that a time duration consisting of K + N + max(K - 1, [(K - 1)N/M]) pilot symbols is sufficient for perfectly recovering all the KMN + KM channel coefficients under the case without receiver noise at the BS. Further, under the case with receiver noise, the user pilot sequences, IRS reflecting coefficients, and BS linear minimum mean-squared error channel estimators are characterized in closed-form.

Coexistence of Direct and Relayed Transmission Users in Multi-Cell Massive MIMO Systems

In this paper, we investigate the uplink performance of a multi-cell massive MIMO relay network, where the base stations (BSs) and the relay stations (RSs) are equipped with large scale antennas and conventional number of antennas, respectively. In each cell, a portion of users communicate with the BS directly while others are aided by the RSs, which are called direct transmission users (DTUs) and relayed transmission users (RTUs), respectively. The two types of users and RSs of all cells share the same time-frequency resource and thus interfere with each other. After describing the system model, we investigate linear minimum mean-squared error channel estimation for the DTUs and RTUs and derive tractable expressions of channel estimation accuracy. With maximal ratio combining and zero-forcing detections based on the estimated channel state information (CSI), we derive the closed-form lower bound and approximation of the achievable rates for DTUs and RTUs to reveal their mutual impact, including intra- and inter-cell interference and pilot contamination. Then, we propose the power scaling law, which proves to be a simple and energy-efficient way to enable the coexistence of DTUs and RTUs in all cells. Furthermore, an optimal power allocation (OPA) scheme is designed based on the proposed power scaling law to maximize the system sum rate. Numerical results verify the accuracy of our theoretical analysis and the effectiveness of the OPA scheme to guarantee performance improvement and fairness simultaneously.

Minimum mean‐square‐error expression of LMMSE channel estimation in SISO OFDM systems

An expression of the minimum mean square error (MMSE) of the linear MMSE channel estimation is given in the case of a non-invertible channel covariance matrix, as in single-input single-output (SISO) OFDM system. A matrix expression, already proposed for a multi-input multi-output OFDM system in a previous article, is not valid in SISO. A new proof is then proposed, by deriving a scalar expression of the MMSE, which leads to solve an optimisation problem. Furthermore, we show that the proposed solution is the global minimum. Simulations validate the proposed development.

Optimal Training Signal Design for Estimation of Correlated MIMO Channels in Two-Way Amplify-and-Forward Relay Systems

In this study, we design a training signal for a correlated two-way amplify-and-forward (AF) relay channel, where the relay system consists of two sources and one relay, and each terminal is equipped with multiple antennas. In the system, given that a mean square error (MSE) exists at each source, we minimize the sum of the two MSEs. In particular, we first derive a linear minimum MSE channel estimator with an arbitrary training signal. Second, we formulate the training signal design problem to minimize the sum of the MSEs of the two sources. Finally, we present the optimal structure of the training signal. The optimal training signal is obtained numerically, and a suboptimal training signal is obtained in a closed form. The simulation results show that the MSE performance of the closed-form training signal is almost the same as that of the optimal training signal.

Conjugate-Gradient Based Doubly Selective Channel Estimation and Equalization for OFDM Systems

This paper addresses conjugate-gradient (CG) based pilot-assisted channel estimation and equalization in doubly selective channels for orthogonal frequency division multiplexing (OFDM) block transmissions. With the help of the discrete prolate spheroidal sequence, which shows flat mean-square error (MSE) curves for the reconstructed channels in the presence of Doppler frequency mismatch, a basis expansion model for a parsimonious channel representation over multiple OFDM blocks is developed, a system equation for the least square channel estimation under widely used pilot lattices, where the pilot symbols are irregularly placed in the subcarrier domain, is formulated by introducing carving matrices, and the standard CG method is applied to the system. Relying on the CG method again, the linear minimum mean-square error channel equalization is pursued without performing any matrix inversion, while elevating the convergence speed of the iterative algorithm with a simple preconditioner. Finally, we validate our schemes with numerical experiments on the integrated services digital broadcasting-terrestrial system in doubly-selective channels and determine the normalized MSE and uncoded bit error rate.

BER Analysis of Square OSTBCs with LMMSE Channel Estimation in Arbitrarily Correlated Rayleigh Fading Channels

In this paper, we examine the bit error rate (BER) performance of square orthogonal space-time block codes (OSTBCs) under arbitrarily correlated Rayleigh fading channels. We consider a mismatched maximum-likelihood receiver that obtains the channel state information through pilot-based linear minimum mean-square error channel estimation. For PAM and QAM constellations, a closed-form approximation of the BER is presented, which yields very accurate BER results over a wide range of signal-to-noise ratios.