Analysis of a Gradient Algorithm for Simultaneous Passband Equalization and Carrier Phase Recovery

The combination of adaptive equalization and decision-directed estimation of a fixed carrier phase offset in suppressed-carrier PAM modems by means of a gradient algorithm has been suggested by Chang1 and by Kobayashi,2 the latter also including adaptive timing recovery. The receivers contemplated in those papers demodulated the received data signal prior to equalization and carrier phase estimation. Reference 3 describes an alternative receiver configuration for twodimensional modulated data transmission systems, combining equalization and carrier recovery. This receiver's distinction is that it employs a passband equalizer4 whose reference signal consists of receiver decisions amplitude-modulating a carrier whose phase shift is the receiver's estimate of the channel phase shift. Following the passband equalizer is a demodulator which compensates for the channel's phase shift (which may be time-varying as a result of frequency offset or phase jitter). The receiver's estimation of the carrier phase shift is based on a decision-directed gradient algorithm for estimating a fixed phase shift, as proposed in Refs. 1, 2, 5, and 6. An advantage of the demodulator following the equalizer is that the demodulator's phase reference is delayed relative to the actual channel phase shift by only one symbol interval instead of by the entire equalizer delay as in the traditional "baseband" receiver configuration. This fact, plus the provision of a sufficiently large gain coefficient in the phase-tracking gradient algorithm, makes possible tracking and compensation of typical conditions of frequency offset and phase jitter that may occur on voiceband telephone channels.