Advanced equalization of digital television signals using the conjugate gradient algorithm

Terrestrial-broadcast digital television channels are characterized by long multipath impulse responses. Therefore, standard time-domain equalizers tend to be long. In the United States, the broadcast digital television standard (8-VSB) specifies a training sequence which is transmitted relatively infrequently; in addition, the length of the training sequence is on the order of the length of the longest channel impulse responses. Under these conditions, previous work on equalization of 8-VSB has rightly focused on blind or semi-blind techniques. However, conventional blind techniques generally take a long time to converge and, in some cases, may converge to a local minimum. This research examines alternative methods for equalization of the 8-VSB signal to improve convergence time and track channel changes between training sequences with manageable complexity. First, direct adaptive implementations of the decision feedback equalizer are presented. The equalizers use the conjugate gradient algorithm and their performance is compared to implementations using the recursive least squares and least mean squares algorithms. Using the training sequence, a channel estimate is obtained and used to initialize the equalizers, significantly improving the convergence rate. The conjugate gradient algorithm is particularly amenable to initialization and, when fully initialized, performs the best. The computational complexity of the conjugate gradient algorithm is controlled by using the FFT to calculate the matrix-vector product. Indirect adaptation is then introduced, which relies on the ability to obtain and periodically update an estimate of the channel. Error propagation in the decision feedback equalizer is reduced by placing a constraint on the feedback filter vector. The constrained equalizers are analyzed and their performance is simulated. Three practical algorithms are then introduced for implementing the 2-norm constrained equalizer using indirect adaptation: the Pegasus iteration, a modified secant iteration, and a nonlinear fit. The nonlinear fit converges the fastest by exploiting knowledge of the shape of the iteration function.