Channel Estimation for Intelligent Reflecting Surface Assisted Multiuser Communications: Framework, Algorithms, and Analysis (1912.11783v4)

Abstract: In intelligent reflecting surface (IRS) assisted communication systems, the acquisition of channel state information (CSI) 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, $KMN+KM$ 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. To accurately estimate such a large number of channel coefficients within a short time interval, we propose a novel three-phase pilot-based channel estimation framework in this paper for IRS-assisted uplink multiuser communications. Under this framework, we analytically prove that a time duration consisting of $K+N+\max(K-1,\lceil (K-1)N/M \rceil)$ pilot symbols is sufficient for the BS to perfectly recover all the $KMN+KM$ channel coefficients for the case without receiver noise at the BS. In contrast to the channel estimation for conventional uplink communications without IRS where the minimum channel estimation time is independent of the number of receive antennas at the BS, our result reveals the crucial role of massive MIMO (multiple-input multiple-output) in reducing the channel estimation time for IRS-assisted communications. Further, for the case with receiver noise, the user pilot sequences, IRS reflecting coefficients, and BS linear minimum mean-squared error (LMMSE) channel estimators are characterized in closed-form, and the corresponding estimation mean-squared error (MSE) is quantified.

• The paper introduces a three-phase pilot-based framework that exploits channel redundancy to significantly reduce pilot sequence length.
• It details theoretical analysis including minimal sequence conditions and robust LMMSE estimators for both noise-free and noisy scenarios.
• The approach minimizes overhead and enables scalable, efficient IRS-assisted communications, particularly under massive MIMO configurations.

Channel Estimation for IRS-Assisted Multiuser Communications: Framework, Algorithms, and Analysis

The paper addresses a significant challenge in the implementation of Intelligent Reflecting Surface (IRS)-assisted multiuser communications: the efficient estimation of a large number of channel coefficients. The central issue arises from the need to estimate KMN + KM channel coefficients, where K represents the number of users, N the number of IRS elements, and M the number of antennas at the base station (BS). Traditional methods require considerable overhead, particularly due to the IRS's lack of RF chains for signal processing.

Proposed Framework

The authors propose a three-phase pilot-based channel estimation framework that leverages the redundancy in channel responses from IRS elements. The underlying goal is to utilize this redundancy to reduce channel estimation time:

1. Phase I: Focuses on estimating the BS-user direct channels by keeping the IRS off.
2. Phase II: Estimates the IRS-reflected channels for a typical user by turning the IRS on and allowing only this user to transmit pilot symbols.
3. Phase III: Utilizes the strong correlation between IRS-reflected channels for different users. These channels are effectively scaled versions of the ones estimated in phase II, allowing for efficient pilot-based estimation.

Theoretical Analysis and Algorithm Design

The paper provides a detailed analysis of the essential conditions required for perfect channel estimation, including:

• In a noise-free scenario, the minimal pilot sequence length is derived as $K + N + \max(K-1, \lceil(K-1)N/M\rceil)$.
• The case with M ≥ N involves a straightforward channel estimation with minimal additional complexity, given sufficient BS antenna elements.
• The case M < N presents a more involved approach, exploiting a partitioning strategy to allow orthogonal transmission of pilot symbols, which accommodates the constraints of having fewer antennas than IRS elements.

Numerical Results and Implications

Numerical simulations validate the proposed framework, showcasing significantly reduced channel estimation time compared to traditional methods. In scenarios with noise, the framework adapts using linear minimum mean-squared error (LMMSE) estimators which demonstrate robust performance across varying numbers of antennas and IRS elements.

The reduction in pilot sequence length directly correlates with the number of antennas at the BS, especially under the massive MIMO regime. This contrast with traditional multiuser systems—where estimation time generally remains constant irrespective of the number of antennas—highlights the practical feasibility of deploying IRS in real-world communications.

Practical and Theoretical Implications

This work presents a significant advancement in IRS-assisted communications by offering a detailed framework that significantly curtails overhead. The implications extend beyond efficient channel estimation, potentially enabling scalable deployment of IRS in next-generation wireless systems. By capitalizing on channel correlations, this research opens avenues for optimized beamforming strategies and enhanced spectral efficiency in IRS-assisted networks.

Future Research Directions

The paper lays a foundation for several future research opportunities:

• Exploration of further simplifications or improvements in the channel estimation process for IRS-assisted communications.
• Investigation into robust system design under varying channel conditions or imperfect CSI.
• Extension of the framework to multi-cell environments and implications of pilot contamination.
• Optimization of resource allocation to balance channel estimation length across the three phases dynamically.

The proposed work thus serves as a critical step in advancing the practical integration of IRS technology into future wireless networks, offering both a theoretical backbone and practical guidelines for implementation.