Analysis of Decision-Directed Equalizer Convergence

In high-speed data transmission (4.8 or 9.6 kilobit/s) over voicegrade telephone channels, it is necessary to compensate for the linear amplitude and phase distortion to which the data signal will be subjected. This compensation is usually accomplished by passing samples of the received signal through an adaptive equalizer consisting of a tapped delay line having adjustable coefficients (tap weights). 1857 Since the distortion is initially unknown, the tap weights must be suitably adjusted. Conventionally, the equalizer tap weights are adapted by starting the transmission with a short training sequence of digital data known in advance by the receiver. The receiver then uses the difference between the equalizer output signal and the known data to adjust the tap weights. In modern data-communication environments the above method may not always be practical, and thus new training procedures which do not make use of a known data-training sequence are required. A natural suggestion is to replace the known training sequence with a sequence of data symbols estimated from the equalizer output, and treat these as if they were known data. Such procedures are often called "decision-directed" startup. However, when these decision-directed startup procedures are used the estimated data may be unreliable, so that it is not even certain that the tap weights will converge to their correct settings. For example, assume that there are N tap weights, C, c2) · · ·, Cn, to be adjusted. The collection of these numbers is to be regarded as a vector c in an abstract TV-dimensional space.