Lower bounds of correlation measure for time hopping codes in UWB communication systems

Abstract

Correlation measure is an important indicator of the performance any code sequence family used for communication system. Frequency Hopping (FH) codes are similar in construction of Time Hopping (TH) codes used in Ultra Wide Band (UWB) communication systems. Since the development of TH codes is not yet fully established, in this paper an effort has been made to utilize FH code families as TH codes as the former are widely available in large numbers and have been dealt with in literature. This paper investigates the similarity between correlation properties of FH and TH codes. Lower bounds of auto correlation and cross correlation functions of TH codes have been derived and compared those with FH codes. It is found that the values of correlation functions for TH codes are higher than those for FH codes. This conclusion has been established through a case study using three well-established FH code sequence families.