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.

Mathematics is the wide-ranging solid foundation of the engineering sciences which ensures their progress by providing them with its unique toolkit of rules, methods, algorithms and numerical systems. In this paper, an overview of the numerical systems that have currently found an application in engineering science and practice is offered, while also mentioning those systems that still await full and comprehensive applicability, recognition, and acknowledgment. Two possible approaches for representing hypercomplex numbers are proposed—based on real numbers and based on complex numbers. This makes it possible to justify the creation and introduction of numerical systems specifically suited to digital signal processing (DSP), which is the basis of all modern technical sciences ensuring the technological progress of mankind. Understanding the specifics, peculiarities, and properties of the large and diverse family of hypercomplex numbers is the first step towards their more comprehensive and thorough study, and hence their use in a number of high-tech intelligent applications in various engineering and scientific fields, such as information and communication technologies (ICT), communication and neural networks, cybersecurity and national security, artificial intelligence (АI), space and military technologies, industrial engineering and machine learning, astronomy, applied mathematics, quantum physics, etc. The issues discussed in this paper are, however, far from exhausting the scientific topics related to both hypercomplex numbers in general and those relevant to DSP. This is a promising scientific area, the potential of which has not yet been fully explored, but research already shows the enhanced computational efficiency and intelligent performance of hypercomplex DSP.

Thanks to their potentials in providing reliable communications for a large number of devices, 5G non-orthogonal multiple access (NOMA) techniques have recently been the subject of considerable research interest. Accordingly, research of Physical Layer Security approaches in NOMA is essential. A primary purpose and challenge for security at the physical level of NOMA-based systems is to protect the information transmitted against both external and internal eavesdropping attacks. To this end, it is necessary to develop PLS schemes which allow each user to decode the signals transmitted by other users, thus guaranteeing normal operation of the successive interference cancellation, while also providing privacy of the information exchange. In this paper, different types of eavesdropping are studied and a summary of existing approaches to improve security at the physical layer in 5G NOMA networks is provided.

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