A wireless communication system in which each receiver is configured synchronize to a received waveform using only its local received signal without requiring any information about other receivers in the system. The local receiver is configured to remove frequency and/or phase error based on information encoded in the received waveform. In some examples, the local receiver uses channel probe information embedded in the received waveform to provide channel estimates for each communication channel over which the signals are received and, based on the estimates, adjusts the received signals for phase shift and amplitude scaling caused by the channel. Signal acquisition (in time and frequency), as well as partial demodulation (for channel estimation), is done independently for each channel. Signals from each channel are combined using a maximal ratio combiner.