Leveraging the Restricted Isometry Property: Improved Low-Rank Subspace Decomposition for Hybrid Millimeter-Wave Systems

TL;DR

This paper introduces a non-adaptive channel estimation method for millimeter wave MIMO systems that leverages the restricted isometry property, resulting in improved accuracy and reduced overhead compared to prior adaptive techniques.

Contribution

It proposes a simple open-loop channel estimation framework based on RIP-compliant random sampling signals, with an iterative algorithm for low-rank subspace decomposition, outperforming previous methods.

Findings

Estimation error is bounded and decreases with tighter RIP conditions.

Required channel uses scale linearly with channel degrees of freedom.

Proposed method outperforms prior adaptive techniques in accuracy and overhead.

Abstract

Communication at millimeter wave frequencies will be one of the essential new technologies in 5G. Acquiring an accurate channel estimate is the key to facilitate advanced millimeter wave hybrid multiple-input multiple-output (MIMO) precoding techniques. Millimeter wave MIMO channel estimation, however, suffers from a considerably increased channel use overhead. This happens due to the limited number of radio frequency (RF) chains that prevent the digital baseband from directly accessing the signal at each antenna. To address this issue, recent research has focused on adaptive closed-loop and two-way channel estimation techniques. In this paper, unlike the prior approaches, we study a non-adaptive, hence rather simple, open-loop millimeter wave MIMO channel estimation technique. We present a simple random design of channel subspace sampling signals and show that they obey the restricted isometry property (RIP) with high probability. We then formulate the channel estimation as a low-rank subspace decomposition problem and, based on the RIP, show that the proposed framework reveals resilience to a low signal-to-noise ratio. It is revealed that the required number of channel uses ensuring a bounded estimation error is linearly proportional to the degrees of freedom of the channel, whereas it converges to a constant value if the number of RF chains can grow proportionally to the channel dimension while keeping the channel rank fixed. In particular, we show that the tighter the RIP characterization the lower the channel estimation error is. We also devise an iterative technique that effectively finds a suboptimal but stationary solution to the formulated problem. The proposed technique is shown to have improved channel estimation accuracy with a low channel use overhead as compared to that of previous closed-loop and two-way adaptation techniques.