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The Canadian RD-3 digital radio system will utilize duobinary encoded, offset QPSK modulated signals. This complex signal structure is such that a conventional fourth order nonlinearity and phase-locked loop cannot be used for carrier recovery. In this paper, a decision-directed phase-lock loop is proposed for carrier recovery and demodulation of these signals. The equations describing loop operation are obtained, and the effective phase-detector characteristic is examined. Fokker-Planck techniques are then employed to approximately find the steady-state probability density function of the phase error, and this is used to find an upper bound on the average probability of error.