Methods and apparatus are described that provide efficient detection of the carrier-phase difference (CPD) between communicating devices over the entire signal bandwidth. The CPD detection utilizes the linear structure of the CPD, which eliminates most of the feedback overhead. Both feedback mechanisms, compact digitized feedback, and feedback via fast signaling protocols, are described. The CPD can be decomposed into a fixed/slow-changing portion and a fast-varying portion, with the former being pre-calibrated and communicated prior to communications sessions, thus further reducing the feedback overhead and improving the CPD detection accuracy. The nonlinearity in the TX/RX chains can also be pre-calibrated, allowing CPDs with more general structures to be detected by methods that detect CPDs with linear structures. Applications of the described methods and apparatus include wireless multipoint broadcast systems, also known as coordinated multipoint transmission, or CoMP, in LTE-A (long-term evolution, advanced) systems, and frequency and phase synchronization of a cluster of base stations.