Channel Estimation for RIS-Aided mmWave MIMO Systems via Atomic Norm Minimization (2007.08158v2)

Abstract: A reconfigurable intelligent surface (RIS) can shape the radio propagation environment by virtue of changing the impinging electromagnetic waves towards any desired directions, thus, breaking the general Snell's reflection law. However, the optimal control of the RIS requires perfect channel state information (CSI) of the individual channels that link the base station (BS) and the mobile station (MS) to each other via the RIS. Thereby super-resolution channel (parameter) estimation needs to be efficiently conducted at the BS or MS with CSI feedback to the RIS controller. In this paper, we adopt a two-stage channel estimation scheme for RIS-aided millimeter wave (mmWave) MIMO systems without a direct BS-MS channel, using atomic norm minimization to sequentially estimate the channel parameters, i.e., angular parameters, angle differences, and products of propagation path gains. We evaluate the mean square error of the parameter estimates, the RIS gains, the average effective spectrum efficiency bound, and average squared distance between the designed beamforming and combining vectors and the optimal ones. The results demonstrate that the proposed scheme achieves super-resolution estimation compared to the existing benchmark schemes, thus offering promising performance in the subsequent data transmission phase.

• The paper introduces a two-stage channel estimation approach using atomic norm minimization to accurately recover angular parameters and path gains.
• It leverages sparse channel characteristics to achieve super-resolution estimates that outperform traditional methods like OMP in MSE and spectral efficiency.
• It designs adaptive beamforming and RIS phase control strategies to maximize spectral efficiency even under challenging non-LoS conditions.

Channel Estimation for RIS-Aided mmWave MIMO Systems via Atomic Norm Minimization

The paper focuses on a novel method for channel estimation in reconfigurable intelligent surface (RIS)-aided millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems, exploiting the atomic norm minimization technique. This research is driven by the challenges inherent in estimating channel state information (CSI) that is crucial for optimal control of RIS. Traditional channel estimation methodologies like orthogonal matching pursuit (OMP) are constrained by resolution issues and inadequate utilization of channel sparsity at mmWave frequencies.

Key Contributions

1. Two-Stage Channel Estimation Process:
   • The authors propose a two-stage channel estimation scheme without a direct line-of-sight (LoS) channel between the base station (BS) and the mobile station (MS). Their method decomposes the problem into smaller subproblems using atomic norm minimization to estimate channel parameters, such as angular parameters and propagation path gains.
2. Efficient Use of Sparse Channel Characteristics:
   • Utilizing atomic norm minimization allows super-resolution parameter estimation, which surpasses conventional limit approaches in resolving closely spaced paths. This strength is verified by a comparison against existing benchmarks where the proposed method demonstrates superior mean square error (MSE) performance and spectral efficiency metrics.
3. Design of Beamforming and RIS Control:
   • The design of RIS phase control and beamforming vectors at BS and MS is addressed to maximize spectral efficiency based on parameter estimates. An emphasis is placed on aligning the RIS phase control matrix with the singular vector corresponding to the highest singular value of the effective channel matrix.

Strong Numerical Results and Implications

• Super-Resolution Estimates: The work achieves super-resolution estimates of channel parameters, which are reflected in the MSE performance gains. The robustness of the scheme is further valid under non-LoS conditions and maintains efficiency across different SNR regimes.
• Spectral Efficiency: The proposed method approximates the performance of systems with perfect CSI, particularly at low SNR levels, suggesting effectiveness in environments with limited training overhead.
• Practical Implications for Future Wireless Systems: By efficiently harnessing sparsity in mmWave channels, this approach offers pathways for enhancing spectral efficiency in upcoming 5G and 6G communication systems. Additionally, it points to significant cost and complexity reductions by obviating the need for extensive data-sharing links between RIS and BS.

Speculation on Future Developments in AI for Communications

As RIS technologies evolve, incorporating AI-driven techniques could offer dynamic, adaptive channel estimation and real-time optimization solutions in response to varying channel conditions. These adaptive models can learn from the environment to perfect RIS configurations, potentially integrating with advanced MIMO transceiver designs to facilitate robust, low-latency communications in rapidly changing wireless environments.

In summary, this research charts a promising course for enhancing RIS-aided communication systems, ensuring high-resolution channel estimates while optimizing system resources. The use of atomic norm minimization in this context provides a solid foundation upon which future enhancements can be built, reflecting an ongoing move toward more intelligent and dynamic wireless communication infrastructures.