Blind ℓ1-norm-based phase estimation for cross-QAM robust to finite precision effects

We introduce a new blind criterion for carrier phase recovery of QAM modulated data. The criterion maximizes the average of the q  -th power of the phase-compensated received data vector ℓ1ℓ1-norm. In order to improve the performance of state-of-the-art higher-order estimators for cross-QAM constellations, which are sensitive to finite precision effects, our focus is on low-order methods (q=1 and 2). Fixed-point iterations with good local convergence properties are given for these cases; different existing phase estimators can be used as initializers, depending on the operation environment and application constraints. A statistical analysis of the novel estimators is derived, which shows that they are competitive against higher-order estimators. More importantly, Monte Carlo simulations show that the novel schemes remain robust to quantization effects and finite precision implementation, and thus they constitute an attractive choice in realistic scenarios.