Mathematical Formulations of Signal Propagation in Ultra-Wideband Transceiver Systems under a UWB Channel Environment with an Extension of Frequency Offset Correction

Abstract

This paper analyzes mathematically the crucial aspects of signal processing in a Multi-Band (MB) Orthogonal Frequency Division Multiplexing (OFDM) based system considering Ultra-Wideband (UWB) channel environment. In the process of analysis, it emphasizes the significant features of UWB receiver design in comparison with ‘conventional’ narrow-band system. The analysis shows that the high dispersive nature of a frequency selective UWB channel effects the design of different signal processing blocks like pre-select filter, low noise amplifier (LNA) and analog-to-digital (A/D) converter in the receiver front end. The characteristic functions of each of these stages are now dominated by the channel characteristics and it needs to be modified accordingly. This analysis is extended further with the study of frequency offset error and its correction. The unbiased Cramer Rao Lower Bound (CRLB) of estimation error is calculated and supported by computer simulation. The performance of an MB-OFDM system with frequency offset correction in terms of Bit-Error-Rate (BER) is also reported.