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It is advantageous from power considerations to allow suppressed-carrier coherently-detected communications. Two methods for generating a coherent reference for the demodulation of a suppressed-carrier signal, namely, the squaring loop and the mathematically equivalent Costas loop, are analyzed, including at some points the effects of VCO noise and initial frequency detuning. The steady-state phase error probability distribution is presented, as is the expected time to first loss of lock in the first-order loop. Probabilities of error in coded or uncoded telemetry systems which use a squaring loop to generate a coherent subcarrier reference are investigated, allowing appropriate values of system parameters to be chosen by system designers.