Detection and estimation of a quantum based projected orthogonal receiver system

Abstract

An organized framework has been defined for general signal processing applications by permitting a combination of detection and estimation algorithms to achieve the best possible performance for any speech signal. Quantum signal processing (QSP) is formulated in this thesis, aimed at developing new or modifying existing signal processing algorithms by exploiting different mathematical structure of quantum mechanics such as vector algebra, analytical geometry, functional analysis and calculus of variations etc.,. It implies as bridgework between quantum measurement and signal processing algorithms leads to a new exemplar for various signal processing applications. The design of modified Projected Orthogonal Matched Filter (POMF) receiver is to represent the possible reproduction of original speech signal as transmitted with linear complexity (in data length). The probability of input signal detection and probability of error correction are considered as the performance measures for the receiver. As the primary application of the POMF receiver is greatly involved in the context of communication, the Bit Error Rate (BER) level improves the performance of the receiver system. In particular, a new viewpoint toward matched filter detection has been formulated that leads to the notion of covariance shaping least square estimator to investigate the quantum detection problem as estimation. The algorithm achieves the best performance from the class of all estimators, for all bounded Hilbert space sequences. The algorithm has been applied to Autoregressive Moving Average models (ARMA), Exponential model and Trigonometric models with various parameter values. The analysis extends to speech signal with additive white Gaussian noise and coloured noise. The main objective of wireless communication is to enhance user capacity, data rate and channel reliability. Major obstacles are channel fading, Multiple Access Interference (MAI) and frequency selective distortion.