Recent results have pointed out the importance of inducing cyclostationarity at the transmitter for blind identification and equalization of communication channels. This paper addresses blind channel identification and equalization relying on the modulation induced cyclostationarity, without introducing redundancy at the transmitter. It is shown that single-input singleoutput channels can be identified uniquely from output secondorder cyclic statistics, irrespective of the location of channel zeros, color of additive stationary noise, or channel order overestimation errors, provided that the period of modulation-induced cyclostationarity is greater than half the channel length. Linear, closed-form, nonlinear correlation matching, and subspace-based approaches are developed for channel estimation and are tested using simulations. Necessary and sufficient blind channel identifiability conditions are presented. A Wiener cyclic equalizer is also proposed.