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 a data covariance matrix representing covariance properties between samples from different time delays and/or from different antennas; calculating a root matrix of the data covariance matrix and a scalar value; and in a series of successive stages, calculating a total reconstructed signal and a channel estimate based on the total received signal, the root matrix, and the scalar value, and, except for a first stage of the successive stages, the total reconstructed signal, and the channel estimates from an immediate prior stage of the series of successive stages; wherein each stage comprises one or more parallel modules, each module operative to reconstruct an individual signal and a channel estimate for a different individual signal in the total reconstructed signal, based on a demodulation and the channel estimation of all received signals provided by the immediate prior stage; wherein each module comprises: a cancel function operative to cancel the reconstructed signals in a cancellation set from the total received signal to isolate a desired signal, and to adjust the root matrix of the data covariance matrix with corrections for the signals in the cancellation set to isolate a desired covariance information; a receive function operative to compute and output channel estimates for a desired signal based on the isolated desired signal and isolated covariance data information and to demodulate symbols in the desired signal; and an update function operative to output the reconstructed signal based on the demodulated symbols.