Mud pulse telemetry systems and methods may employ a downhole pulser to encode a digital telemetry data stream as pressure fluctuations in a fluid flow stream. An arrangement of spatially separated sensors acquire pressure-responsive measurements at multiple positions within the plumbing of a drill rig. A receiver collects and digitizes the measurements from the spatially separated sensors and subjects them to a principal components analysis (PCA) to determine those one or more basis vectors associated the telemetry signal. The PCA process may employ decomposition of a spatial correlation/covariance matrix or a temporal-spatial correlation/covariance tensor. The selected basis vector(s) are then used to obtain the telemetry signal for demodulation into the telemetry data stream.