Gardner plus integrate and dump approach to updates. This heavy damping achieves several things - the Gardner algorithm is statistically based, so the statistics must be smoothed; a number of samples must be fed to the equalizer buffer before the equalizer output actually responds to a step change in the sampling; we need to prevent rapid fluctuations in the sampling position, due to the optimal position being close to a boundary.
The carrier is specified as 1700Hz +- 1Hz at the transmitter, and 1700 +-7Hz at the receiver. The receive carrier would only be this inaccurate if the link includes FDM sections. These are being phased out, but the design must still allow for the worst case. Using an initial 1700Hz signal for demodulation gives a worst case rotation rate for the constellation of about one degree per symbol. Once the Gardner algorithm has been given time to lock to the symbol timing of the initial alternating pattern, the phase of the demodulated signal is recorded on two successive symbols - once for each of the constellation positions. The receiver then tracks the symbol alternations, until a large phase jump occurs. This signifies the start of the next phase of the training sequence. At this point the total phase shift between the original recorded symbol phase, and the symbol phase just before the phase jump occurred is used to provide a coarse estimation of the rotation rate of the constellation, and it current absolute angle of rotation. These are used to update the current carrier phase and phase update rate in the carrier DDS. The working data already in the pulse shaping filter and equalizer buffers is given a similar step rotation to pull it all into line. From this point on, a heavily damped integrate and dump approach, based on the angular difference between each received constellation position and its expected position, is sufficient to track the carrier, and maintain phase alignment. A fast rough approximator for the arc-tangent function is adequate for the estimation of the angular error.
The next phase of the training sequence is a scrambled sequence of two particular symbols. We train the T/2 adaptive equalizer using this sequence. The scrambling makes the signal sufficiently diverse to ensure the equalizer converges to the proper generalised solution. At the end of this sequence, the equalizer should be sufficiently well adapted that is can correctly resolve the full QAM constellation. However, the equalizer continues to adapt throughout operation of the modem, fine tuning on the more complex data patterns of the full QAM constellation.
In the last phase of the training sequence, the modem enters normal data operation, with a short defined period of all ones as data. As in most high speed modems, data in a V.29 modem passes through a scrambler, to whiten the spectrum of the signal. The transmitter should initialise its data scrambler, and pass the ones through it. At the end of the ones, real data begins to pass through the scrambler, and the transmit modem is in normal operation. The receiver tests that ones are really received, in order to verify the modem trained correctly. If all is well, the data following the ones is fed to the application, and the receive modem is up and running. Unfortunately, some transmit side of some real V.29 modems fail to initialise their scrambler before sending the ones. This means the first 23 received bits (the length of the scrambler register) cannot be trusted for the test. The receive modem, therefore, only tests that bits starting at bit 24 are really ones.