Abstract : This paper focuses on the constant power (CP) criterion for blind linear equalization of digital communication channels. This recently proposed criterion is specially designed for the extraction of q-ary phase shift keying (q-PSK) signals using finite impulse response equalizers. When zero-forcing equalizers exist, the CP cost function accepts exact analytic solutions that are unaffected by undesired local extrema and spare costly iterative optimization. A subspace-based method exploiting the Toeplitz-like structure of the solution space is put forward to recover the minimum-length equalizer impulse response from the overestimated- length solutions. The proposed method is more robust to the relative weights of the minimum-length equalizer taps than existing techniques. In less ideal scenarios where the analytic solutions are only approximate minimizers of the criterion, a gradient-descent algorithm is proposed to minimize the cost function. To reduce the detrimental effects of suboptimal equilibria and accelerate convergence, the iterative algorithm is initialized with the approximate closed-form solution, and an optimal step size is incorporated into its updating rule. This optimal step size, which globally minimizes the cost function along the search direction, can be computed algebraically. A semi-blind implementation, which is useful when training data are available, further reduces the impact of undesired local extrema and enhances the convergence characteristics (particularly the robustness to the equalizer initialization) of the iterative algorithm from just a few pilot symbols. All these beneficial features are demonstrated with an experimental study of the proposed CP-based methods in a variety of channels and simulation conditions.