Modified Nested Barker Codes for Ultra-Wideband Signal–Code Constructions

Abstract

Currently, various applications of ultra-wideband signal–code constructions are among the most vibrant technologies, being implemented in very different fields. The purpose of this research consists of analyzing Barker codes and searching for the optimal nested representations of them. We also aim to synthesize signal–code constructions based on the tenets of nesting of alternative modified Barker codes, which employ an asymmetric alphabet. The scientific merit of the paper is as follows: on the basis of new analytic expressions, modified nested codes and signal–code constructions were obtained, applicable for the establishment of the unambiguous association of the component values of the nested codes with any lobes of the normalized autocorrelation function. With these analytical expressions, we are, hence, able to determine the values of the binary asymmetrical components of the nested codes related to the side lobes of the normalized autocorrelation function. In this way, we clearly obtain better (low) levels for these lobes than by using the autocorrelation function, as established by the equivalent conventional Barker codes, including the nested constructions. Practical application of these modulated ultra-wideband signals ensures improved correlational features, high-fidelity probabilistic detection, and more precise positional detection of physical bodies depending on the range coordinate.

Keywords

• modified Barker codes
• normalized autocorrelation function
• nested codes
• side lobe level
• UWB signal–code constructions