Compressed Training Adaptive Equalization: Algorithms and Analysis

We propose "compressed training adaptive equalization" as a novel framework to reduce the quantity of training symbols in a communication packet. It is a semi-blind approach for communication systems employing time-domain/frequency-domain equalizers, and founded upon the idea of exploiting the magnitude boundedness of digital communication symbols. The corresponding algorithms are derived by combining the leasts-quares- cost-function measuring the training symbol reconstruction performance and the infinity-norm of the equalizer outputs as the cost for enforcing the special constellation boundedness property along the whole packet. In addition to providing a framework for developing effective adaptive equalization algorithms based on convex optimization, the proposed method establishes a direct link with compressed sensing by utilizing the duality of the l(1) and l(infinity) norms. This link enables the adaptation of recently emerged l(1)-norm-minimization-based algorithms and their analysis to the channel equalization problem. In particular, we show for noiseless/low noise scenarios, the required training length is on the order of the logarithm of the channel spread. Furthermore, we provide approximate performance analysis by invoking the recent MSE results from the sparsity-based data processing literature. Provided examples illustrate the significant training reductions by the proposed approach and demonstrate its potential for high bandwidth systems with fast mobility.