A parallel interference cancellation (PIC) receiver incrementally removes interference from signals in parallel modules in successive stages. For each desired signal, as interfering signals are removed, corresponding updates to a data covariance matrix are modeled as computationally tractable rank-one updates to a root matrix of the covariance matrix. Processing of signals and/or covariance information may be initiated, continued, and/or halted at various stages, e.g., in response to signal or data quality. The PIC receiver using root matrix updates is applicable to a variety of demodulation techniques.