Keynote address I The QR decomposition and the decision feedback detectors: Applications to block data transmission systems

In this talk, we describe the relationship between the QR-decomposition of a matrix and the decision feedback detectors used in signal processing. We first introduce the QRS decomposition of a matrix and its geometric interpretation. We then examine a block-by-block communication system that employs (intra-block) decision feedback detection and develop a method for jointly designing the transmitter-receiver (transceiver) pair in such systems. We provide closed-form expressions for transmitter-receiver pairs that simultaneously minimize the arithmetic mean squared error (MSE) at the decision point (assuming perfect feedback), the geometric MSE, and the bit error rate of a uniformly bit-loaded system at moderate-to-high signal-to-noise ratios. We then examine the optimum designs of the transceivers in terms of the algebraic QRS decomposition and explains the functions of the optimum structures in the light of the component matrices. Finally we present simulation studies which indicate that the proposed transceivers perform significantly better than standard transceivers, and that they retain their performance advantages in the presence of error propagation.