[Paper Review] Message passing-based joint CFO and channel estimation in millimeter wave systems with one-bit ADCs

Nitin Jonathan Myers, Robert W. Heath|arXiv (Cornell University)|Mar 23, 2018

Millimeter-Wave Propagation and Modeling33 references3 citations

TL;DR

This paper proposes a message passing-based joint estimation algorithm for carrier frequency offset (CFO) and wideband mmWave channel in systems with one-bit ADCs. By exploiting sparsity in the angle-delay domain and compressibility of phase errors, the method uses generalized bilinear message passing to enable robust, low-complexity estimation even under phase noise and heavy quantization, achieving near-optimal performance with minimal training overhead.

ABSTRACT

Channel estimation at millimeter wave (mmWave) is challenging when large antenna arrays are used. Prior work has leveraged the sparse nature of mmWave channels via compressed sensing based algorithms for channel estimation. Most of these algorithms, though, assume perfect synchronization and are vulnerable to phase errors that arise due to carrier frequency offset (CFO) and phase noise. Recently sparsity-aware, non-coherent beamforming algorithms that are robust to phase errors were proposed for narrowband phased array systems with full resolution analog-to-digital converters (ADCs). Such energy based algorithms, however, are not robust to heavy quantization at the receiver. In this paper, we develop a joint CFO and wideband channel estimation algorithm that is scalable across different mmWave architectures. Our method exploits the sparsity of mmWave MIMO channel in the angle-delay domain, in addition to compressibility of the phase error vector. We formulate the joint estimation as a sparse bilinear optimization problem and then use message passing for recovery. We also give an efficient implementation of a generalized bilinear message passing algorithm for the joint estimation in mmWave systems with one-bit ADCs. Simulation results show that our method is able to recover the CFO and the channel compressively, even in the presence of phase noise.

Motivation & Objective

• Address the challenge of joint CFO and channel estimation in mmWave systems with one-bit ADCs, where conventional methods fail due to phase noise and quantization.
• Overcome the limitations of existing compressed sensing algorithms that assume perfect synchronization and are sensitive to CFO and phase noise.
• Develop a scalable, low-complexity algorithm that exploits sparsity in the mmWave channel and compressibility of phase errors for robust estimation.
• Enable joint estimation with structured training sequences (e.g., IID QPSK, Gaussian) while maintaining performance despite CFO propagation effects.
• Ensure robustness across practical CFO ranges and scalability to different mmWave hardware architectures.

Proposed method

• Formulate the joint CFO and channel estimation problem as a sparse bilinear optimization problem in the angle-delay and Doppler domains.
• Use generalized bilinear approximate message passing (PBiGAMP) to jointly recover the CFO and channel from one-bit quantized measurements.
• Model the phase error vector as compressible and leverage Bernoulli-Gaussian priors to enhance robustness against off-grid CFO leakage.
• Apply an Extended Kalman Filter (EKF) to estimate the CFO from the inverse DFT of the estimated synchronization vector.
• Incorporate structured training matrices (IID QPSK, Gaussian) to enable fast message passing while analyzing their identifiability trade-offs.
• Implement an efficient, scalable message passing framework that avoids high-dimensional convex optimization, suitable for wideband mmWave systems.

Experimental results

Research questions

• RQ1 Can joint CFO and channel estimation be effectively performed in wideband mmWave systems with one-bit ADCs using sparse signal models?
• RQ2 How does phase noise and CFO impact the identifiability and performance of one-bit receiver systems?
• RQ3 What is the trade-off between using structured training sequences for fast message passing and maintaining identifiability in joint estimation?
• RQ4 Can message passing-based algorithms achieve robust performance under heavy quantization and phase errors without full-resolution ADCs?
• RQ5 How does the proposed method maintain performance across different CFO values within practical system limits?

Key findings

• The proposed algorithm achieves near-optimal channel estimation performance with one-bit ADCs, even in the presence of phase noise and CFO, as shown by NMSE results.
• The NMSE for one-bit receivers saturates at high SNR due to quantization noise, but remains comparable to full-resolution systems, indicating robustness.
• The CFO estimation MSE saturates at high SNR due to phase noise, but the one-bit case performs nearly identically to the full-resolution case, confirming minimal performance loss from quantization.
• The algorithm demonstrates invariance to CFO within the practical range of ±40 ppm, with constant channel NMSE across this range, due to robust Bernoulli-Gaussian priors.
• Performance degrades significantly with shifted Zadoff-Chu training due to the CFO propagation effect, highlighting the importance of training sequence design.
• The CFO MSE decreases with increasing pilot length, and the performance gap between one-bit and full-resolution systems is negligible, confirming scalability and efficiency.