A Method for the Design of Bicomplex Orthogonal DSP Algorithms for Applications in Intelligent Radio Access Networks

Abstract

In this paper, a new method for designing orthogonal bicomplex digital signal processing (DSP) algorithms is developed. In contrast to those previously reported on, the method proposed is universal, since it is not affected by the order or the type of the real digital processing algorithm employed as a prototype. The method is based on a transformation starting with either real or complex orthogonal DSP algorithms represented in the z-domain, and transforming them into orthogonal bicomplex algorithms. The proposed new method is applied in the design of bilinear orthogonal bicomplex DSP systems with a canonical number of elements, the main advantage of which is that the order of the digital system is reduced by a factor of four. As well as being canonical, the orthogonal bicomplex digital systems are also symmetrical structures, as a result of which they offer parallelism and subsequent unification. It is experimentally shown that bicomplex orthogonal DSP algorithms acquire the properties of the initial algorithm prototype, irrespective of whether it is real or complex. Since the new design method is universally applicable, it can be used to develop bicomplex orthogonal digital algorithms of any order and type. Being simple, canonical, and symmetrical—and, thus, leading to lower equipment cost, reduced complexity, and higher energy efficiency—these structures may well be appropriate for the enhancement of the implementation of intelligent algorithms in next-generation radio access networks.