Decision theory under “quantized filtering” -

Abstract

Convolution is an important operation in signal processing and analysis. It is a mathematical operation on two input functions which results in a third function that is typically viewed as a transformed version of one of the original functions. Convolution is used in several contexts that include probability, statistics, computer vision, image and signal processing, electrical engineering, and differential equations. In the context of communication system design, one of the initial tasks of a receiver is to detect the presence of a packet through filtering and hence convolution: The convolution is between the received signal and typically a matched filter, used to detect the presence of a training sequence or synchronizing sequence. This process is computationally intensive and usually runs for a long duration. For this reason, several methods have been proposed and implemented to alleviate this computational burden. In our work, we aim to decrease the required number of multiplications through quantizing the matched filter, without increasing the amount of input to output latency. This of course comes at the expense of ``performance''. With a view toward detection application, the selection of the quantized filter is done through applying decision theory techniques and corresponding quality measures. Cases of several stochastic noise models are studied and analyzed. The performance of the proposed scheme was measured through plotting the Operating Characteristic curve, and also through the rates of exponential decay using large deviation theory. It is found that in all studied cases, the design of the suboptimal structure was immune to Signal-to-Noise Ratio values and also typically to the various quality measures and operating points that were considered.