1. A method of Parallel Interference Cancellation, comprising the steps of: receiving a total received signal comprising time samples from one or more receive antennas; receiving an interference data covariance matrix representing covariance properties between samples from different time delays and/or from different antennas; calculating the root matrix of the data covariance matrix and a scalar value; and in a series of successive stages, calculating a total reconstructed signal and channel estimates based on the total received signal, root matrix, and scalar, and, except for the first stage, the total reconstructed signal and channel estimates from the prior stage; wherein each stage comprises one or more parallel modules, each operative to reconstruct an individual signal and channel estimate for a different individual signal in the total received signal, based on the demodulation and channel estimation of all received signals provided by the immediately prior stage.