Phase-Aware Code-Aided EM Algorithm for Blind Channel Estimation in PSK-Modulated OFDM

TL;DR

This work tackles the challenge of fully blind phase ambiguity in EM-based channel estimation for PSK-modulated OFDM. It introduces a phase-aware, code-aided EM that leverages decoder extrinsic information and PSK symmetry to generate and select among $C$ phase candidates via model evidence, resolving phase ambiguity during initialization. The OFDM structure allows per-subcarrier EM updates, yielding low computational complexity and negligible extra cost in turbo iterations, while a phase-detection step robustly reduces convergence to suboptimal maxima. Simulation with $M=256$, $N=10$, and a rate-$1/2$ convolutional code demonstrates a dramatic reduction in failure rate from roughly $80\%$ to nearly $0\%$ for $\text{SNR} \ge 6$ dB, validating the approach for frequency-selective channels and turbo equalization.

Abstract

This paper presents a fully blind phase-aware expectation-maximization (EM) algorithm for OFDM systems with the phase-shift keying (PSK) modulation. We address the well-known local maximum problem of the EM algorithm for blind channel estimation. This is primarily caused by the unknown phase ambiguity in the channel estimates, which conventional blind EM estimators cannot resolve. To overcome this limitation, we propose to exploit the extrinsic information from the decoder as model evidence metrics. A finite set of candidate models is generated based on the inherent symmetries of PSK modulation, and the decoder selects the most likely candidate model. Simulation results demonstrate that, when combined with a simple convolutional code, the phase-aware EM algorithm reliably resolves phase ambiguity during the initialization stage and reduces the local convergence rate from 80% to nearly 0% in frequency-selective channels with a constant phase ambiguity. The algorithm is invoked only once after the EM initialization stage, resulting in negligible additional complexity during subsequent turbo iterations.

Figures (5)

• Figure 1: System block diagram of a coded bit-interleaved PSK mapper with OFDM modulation on the transmitter side. The conventional receiver includes an OFDM demodulator, an EM estimator, and a turbo decoding module.
• Figure 2: Block diagram of the phase-aware code-aided EM algorithm design for a QPSK-modulated OFDM system.
• Figure 3: One realization of constellation diagrams (crosses) of (a) the received symbols $\mathbf{Y}$ after the OFDM demodulation, and the equalizer outputs $\mathbf{Y}_{\text{eq}}$ using channel estimates obtained from (b) the conventional EM, (c) the code-aided EM, and (d) the phase-aware EM algorithms at $\text{SNR}=20$ dB. The four square markers represent the ideal symbol mapping $s_i$.
• Figure 4: Mean square error of the estimated channel frequency response from (a) conventional EM, (b) code-aided EM, and (c) the phase-aware EM. Gray lines indicate individual realizations (30 out of 5000) for an SNR of $20$ dB. The first 20 EM iterations are the initialization stage, where phase correction (red dotted line in (c)) is only performed at the 20th EM iteration. After initialization, extrinsic information from the decoder is incorporated every 5 EM iterations (red dashed lines in (b) and (c)). The mean and median of the 5000 independent simulations are represented by solid green circles and crosses, respectively, while the shaded areas indicate the 15th to 85th percentiles.
• Figure 5: Failure rate of the phase-aware EM estimator over EM iterations for SNR $=0$, $2$, $4$, $6$, and $12$ dBs.