## 2 Spectrum Management and Graph Signal Processing
Also, the proposed technique in [10] improves the PU system SNR level but decreases the performance of the CR system. 2. In [33], an orthogonal codes-based dynamic spectrum access (OC-DSA) technique was proposed. The proposed OC-DSA management technique provides the the CR system with the capability to co-access the legal PU frequency spectrum band simultaneously by providing power incentives from the CR system to the PU system. Thus, the proposed technique in [33] is based on employing orthogonal sequence codes at the TX side of the SU system. Furthermore, these codes can cancel the signal interference caused by the CR subscribers so that the performance of the PU system can be enhanced. In addition, due to employing the orthogonal codes at the SU-TX, in [33], the donated power percentage decreases and the data rate increases to the levels of the proposal in [10]. The main novelty of the paper is the extension of the concept of orthogonal codes-based dynamic spectrum access presented in [33] to multi-PUs and multi-SUs (not only one PU and one SU as in [33]) with full analysis. That is, the power incentive parameter lower and upper bounds are derived. Also, a BER analysis for the extended system is presented. Also, extensive Monte Carlo simulations are carried out to show that the simulation results almost coincide with the analytical results. The proposed technique within this paper adopts and applies the concepts of the current developments in graph theory regarding the transmission from the main base station (BS) to the main SU-TX of the proposed CR system. In addition, graph theory developments and research are essential tools in the emergence of current modern data sources like large-scale sensor networks and social networks. These networks provide huge underlying physical, social, and geographic structures that require a novel tool to establish statistical inference, which then leads to data processing proceedings on the different graphs, within a new field of graph signal processing (GSP) [34; 35; 36; 37; 38; 39]. Hence, GSP research leads to the development of advanced tools to process the different data that are defined on the domains of different irregular graphs. Thus, the DSCA-MC-CR proposal adopts the main ideas and concepts of GSP and their derivations from conventional digital signal processing. Moreover, a summary of the recent developments of the basic GSP tools, including the different methods for sampling, filtering, and graph learning, is given in [40]. It states that classical signal processing signals and filters use Fourier transform in the current state of the art of GSP, and analyzes the definition of frequency, graph learning, and sampling representation. The research in [40] introduces the basic GSP concepts. Also, the signal model is introduced in Algebraic Signal Processing (ASP) based on spectral graph theory, where the proposal chooses a more suitable presentation by reviewing the idea of the shift in digital signal processing (DSP) to create interconnection between the DSP analysis and the GSP analysis. In addition, ref. [40] develops a corresponding tool for the shift for GSP analysis, which performs according to the definition of the different frequencies for the graph signals and their interpretation. Therefore, this paper adopts and focuses on the tools that are derived from the adjacency operator matrix or Laplacian matrix of the proposed designed graph.