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The multimodulus algorithm (MMA) for blind equalization has good performance, but can only tolerate small carrier frequency offsets under high-order QAM. We propose a structure for joint carrier recovery (CR) and blind decision-feedback equalization (DFE), where the DFE is MMA-based. It turns out that a key point is the design and analysis of reduced-constellation phase detectors (PD) that can facilitate a wide frequency lock range and make the CR loop converge in severe intersymbol interference and noise. Based on this, we design a multistage startup procedure for joint blind DFE and CR. Simulations show that the procedure can yield fast convergence in large carrier frequency errors under high-order QAM.