Dynamic Spectrum Co-Access in Multicarrier-Based Cognitive Radio Using Graph Theory Through Practical Channel

Abstract

In this paper, we propose an underlay cognitive radio (CR) system that includes subscribers, termed secondary users (SUs), which are designed to coexist with the spectrum owners, termed primary users (PUs). The suggested network includes the PUs system and the SUs system. The coexistence between them is achieved by using a novel dynamic spectrum co-access multicarrier-based cognitive radio (DSCA-MC-CR) technique. The proposal uses a quadrature phase shift keying (QPSK) modulation technique within the orthogonal frequency-division multiplexing (OFDM) scheme that maximizes the system data rate and prevents data inter-symbol interference (ISI). The proposed CR transmitter station (TX) and the CR receiver node (RX) can use an advanced smart antenna system, i.e., a multiple-input and multiple-output (MIMO) system that provides high immunity against channel impairments and provides a high data rate through its different combining techniques. The proposed CR system is applicable to coexist within different existing communication applications like fifth-generation (5G) applications, emergence applications like the Internet of Things (IoT), narrow-band (NB) applications, and wide-band (WB) applications. The coexistence between the PUs system and the SUs system is based on using power donation from the SUs system to improve the quality of the PU signal-to-interference-and-noise ratios (SINRs). The green communication concept achieved in this proposal is compared with similar DSCA proposals from the literature. The simulations of the proposed technique show enhancement in the PUs system throughput and data rate along with the better performance of the SUs system.

1. Introduction

Current and next-generation networks are required to provide more services and more advanced applications, including telecommunication services like 5G, utilization of NB and WB networks, emergency applications like IoT, and applications that expect to implement an essential change in the world of smart communication technology [1,2,3,4,5,6,7,8]. Also, because the spectrum is a nonrenewable, scarce resource, and as per the above growing demand for spectral resources and the increase in communication devices, CR is becoming an important tool for enabling new wireless communication technologies to access frequency channels [9,10].

CR is an intelligent wireless communication technology that is smartly aware of its surrounding environment and the propagation radio-frequency (RF) environment. Therefore, before the CR system selects its operating mode, it must gather the information defining its radio environment. This type of information and these characteristics are known as cognitive radio capability characteristics, shown in Figure 1.

This paper presents a contribution towards achieving an efficient usage of the frequency spectrum by enabling CR industrial technology through a newly proposed technique called the dynamic spectrum co-access multicarrier-based cognitive radio (DSCA-MC-CR) technique. In addition, the proposed network aims to increase the communication system capacity, achieve an ultra-high data rate and ultra-low latency, and constitute an efficient, reliable, and secure green communication system. Thus, spectrum co-access exists between the privileged PUs system that already has legal rights over a certain band of the spectrum and the SUs system that represents the CR that desires access to the PU legal spectrum without any interference with the PU communication system. Also, the suggested proposal operates the CR system simultaneously with the privileged primary system by presenting donation power from the SU system to the PU system, without any change in the infrastructure of the privileged PU system. Furthermore, the proposed work aims to increase the primary system coverage area, capacity, and system throughput. At the same time, the SU system should achieve excellent performance and proper quality of service (QoS) by using advanced signal processing techniques within the transmission and reception process of the CR system.

The suggested proposal employs the dynamic spectrum access (DSA) technique to manage the spectrum, providing an excellent tool with which regulators can efficiently manage and improve the utilization of the spectrum [11,12,13,14,15,16,17]. In addition, to guarantee SU communication system stability, it allows the SU transmitter to act as a relay node within the proposed network to help the PU transmission data. In order to achieve this, the CR transmitter node is allowed to access the PU-RF spectrum and transmit its RF data in different models.

The MIMO smart antenna system can be employed to improve the system’s performance. The MIMO antenna system works efficiently in the complicated propagation channels and achieves improvement in system performance due to the transmission and reception antenna diversity [18,19,20]. Furthermore, advanced modulation scheme technology like the OFDM modulation technique is employed within the CR system. These techniques work efficiently in multipath fading channels and achieve a high data rate within the operating wireless systems [21,22,23,24,25].

The rest of the paper is arranged as follows: In Section 2, spectrum management and graph signal processing are described. Section 3 explains models 1 and 2 of the proposed DSCA-MC-CR system, including the system topology, system parameters, and the RF spectrum representation. The mathematical representation of the proposed DSCA-MC-CR is explained in Section 4. The SINR calculations, bit error rate (BER) estimations, data rate evaluations, and packet interarrival time analysis are presented in Section 5. The simulation results and the discussions are presented in Section 6. Finally, the paper’s conclusions are given in Section 7.

2. Spectrum Management and Graph Signal Processing

In the literature, there are different spectrum management techniques. For example, the Non-Orthogonal Multiple-Access (NOMA) technique for CR was selected for radio access in 5G mobile wireless networks, as explained in [26,27,28]. In addition, the Rate-Splitting Multiple-Access (RSMA) technique is a multiple-access technique that combines both the space-division multiple-access (SDMA) technique and the NOMA technique, as explained in [29].

The proposal uses the DSA technique, which is an essential tool in CR technology, so that it provides the CR technology with the capability to choose the most suitable free frequency bands in which the SU subscribers can work and operate at a given location over a certain available time. Thus, the DSA technique has main two keys, which are the co-access process power incentives and the co-access region area. The power donation process from the SU system to the PU system, which is called incentive, ensures that both the PU subscribers and the CR subscribers are in a win-to-win situation during system operation. Moreover, the coverage area, which is called the region of co-access, can be defined as the region area where the SU subscribers can access the frequency spectrum with the PU subscribers.

The DSA models in [30] are classified into three types which are called (a) interweave, (b) underlay, and (c) overlay, as shown in Figure 2.

Firstly, in the case of the interweave model, the CR node can start the transmission only if the PU slot is free and not occupied by the PU subscriber. So, the PU subscriber has strong legal rights on its own frequency spectrum. Hence, if the PU subscriber starts the transmission on his legal frequency band, then the CR is forced to be inactive on the legal band and look to another free PU band. Therefore, the interweave model in many studies is assigned to be the default model for the DSA management technique and is termed the opportunistic spectrum access (OSA) technique [9]. Thus, in the case of interweave, the CR subscribers are encouraged under strong conditions to utilize the spectrum free bands or holes, called white spaces, in the temporal domain, spatial domain, and frequency domain. Secondly, the underlay and the overlay management models, as shown in Figure 2, allow the CR subscribers to run the power transmission on the legal frequency spectrum regardless of whether the legal PU subscriber is accessing the frequency band or not. In addition, in the case of the underlay and overlay models, the transmission permission is still constrained to the condition where the total affected interference from all the SU subscribers is accepted and expected by the legal PU subscribers [30].

In the literature, several researchers discussed the different DSA management techniques that allow the CR subscribers to use and access the PU subscribers spectrum simultaneously without decreasing the PU subscriber capacity or decreasing the QoS level [9,15,31,32]. Two cases are explained below for comparison with our proposal:

• A management dynamic spectrum co-access (DSCA) technique was proposed in [10]. This technique enables the CR subscriber to access the legal frequency spectrum of the privileged PU by increasing the SNR of the privileged PU subscriber. In [10], the CR system donates a ratio of its transmission power to the privileged PU system as a power incentive that enables the CR system to co-access the legal frequency spectrum. Thus, in [10], the DSCA technique understands that the CR system recognizes the message of the PU system, and the CR system in this case uses a dirty paper coding (DPC) technique that requires a certain type of design complexity to avoid interfering with the transmitted data of the PU system. Also, the proposed technique in [10] improves the PU system SNR level but decreases the performance of the CR system.
• 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.

3. The Proposed DSCA-MC-CR Technique

The proposed network includes two systems, i.e., the privileged PU system and the CR system. In this regard, the proposed DSCA-MC-CR technique assumes no change in the infrastructure of the existing PUs privileged system that legally owns the spectrum. Thus, the proposed technique uses an underlay DSA model that has no interference effect on the PUs RF bands due to the usage of spreading orthogonal codes by the SU proposed system. In addition, the proposal includes two models, i.e., model 1 and model 2.

The SU system encoder and decoder of both models have a bit length $L=8,16$ in sequence, which encodes–decodes the SU bits by using Hadamard matrices $H_8$ and $H_{16}$, which include 8 and 16 orthogonal vectors each. The propagation channel is assumed to be Gaussian. Then, another analysis is performed through the practical fading channel (i.e., the Rayleigh channel). Finally, the proposed models use the OFDM modulation scheme so that model 1 and model 2 are applicable for one–two-way communication applications. The channel gain level of the desired signal is $\in \left\{0.7:0.95\right\}$, and the channel gain level of the interference devices is $\in \left\{0.2:0.3\right\}$.

3.1. Model 1

Model 1 assumes that the proposed SUs system (i.e., DSCA-MC-CR) has the same communication application as the existing privileged PUs system and the same modulation and demodulation schemes.

In this model topology, which is designed using OMNeT++ and shown in Figure 3a, the proposal suggests one fixed PU transmitter tower (PU-TX) and seven fixed or moving PU receivers (PU-RX) with channel gain ${\alpha }_{ui}$, where $i\in \left\{1,2\dots 7\right\}$. In addition, the proposal suggests one fixed SU transmitter (SU-TX) that is located within the coverage area (i.e., the region of co-access (ROC)) of the PU-TX for the RF learning process and seven fixed or moving SU receivers (SU-RX) with channel gain ${\alpha }_{uj}$, where $j\in \left\{1,2\dots 7\right\}$.

The representation of the model 1 spectrum is shown in Figure 3b, which indicates that the PU-RF signals, shown by the blue color, occupy the assigned legal bands. Also, the inactive PU-RF is shown in white. On the other hand, the secondary users base-band signals (i.e., ${SU}_1$ to ${SU}_7$) are shown in yellow. These signals spread in the RF mode due to the orthogonal codes within the encoder process. The SU-RF underlay signals do not affect the PU-RF signals due to the orthogonality between them.

3.2. Model 2

Model 2 assumes that the proposed SUs system has a different communication application from the existing privileged PUs system.

In this model topology, which is designed using OMNeT++ and shown in Figure 4a, the proposal suggests one fixed PU-TX tower and one fixed or moving PU-RX with channel gain ${\alpha }_{u1}$. In addition, the proposal suggests one fixed SU-TX that is located within the coverage area of the PU-TX for the learning process and seven fixed or moving SU-RXs with channel gain ${\alpha }_{uj}$, where $j\in \left\{1,2\dots ,7\right\}$.

The spectrum representation of model 2 is shown in Figure 4b, which shows that the PU-RF signal occupies the assigned legal wide band, shown in blue. On the other hand, the SUs base-band signals (i.e., ${SU}_1$ to ${SU}_7$) are shown in yellow. These signals spread in the RF mode due to the orthogonal codes within the encoder process. The SU-RF underlay signals do not affect the PU-RF wide-band signal due to the orthogonality between them.

4. Mathematical Representation of the Proposed System

The technical design of the proposed SU-TX tower, which covers an area of 500 × 500 m, is shown in Figure 5. The upper part of Figure 5 within the proposed SU-TX block diagram consists of the spreading encoder with a total of seven orthogonal codes, with 8 bits each for model 1, so that the seven input message signals will spread. Then, the multiplexer rearranges the data in one line for the OFDM process. The same previous explanation is applicable for model 2 but with a spreading encoder with a total of 15 orthogonal codes, with 16 bits each. The output of the OFDM process passes through the shaping filter (S.F), whose output mixes with the assigned propagation frequency carrier. The SU-RF signal is amplified through the upper power amplifier (PA) with a gain value equal to $1-\gamma$ of the total transmission power of the SU-TX tower, where $\gamma$ is the power incentive factor.

The bottom part of Figure 5 within the proposed SU-TX block diagram consists of the RF wide-band filter, which allows the PU system RF signal to be listened to without any knowledge or changing of the PU signal structure. Also, the filtered PU-RF signal is amplified through the power amplifier (PA) with a value equal to $\gamma$ of the total SU-TX transmission power. Thus, the outputs of the two power amplifiers are summed, and the RF signal propagates from the transmitter system to cover the required coverage area.

Table 1. Parameters and functions used in the proposed DSCA-MC-CR technique mathematical representation.

Parameter	Parameter or Function Definition
$T_b$, $E_b$	Bit duration, bit energy (rectangular pulse).
$m_j\left(t\right)$	Message signal that is constant within each $T_b$ time interval.
$P_u$	User-transmitted power.
$P_p$, $P_s$	The transmitted power from the PU and SU towers.
$U_p$, $U_s$	Number of PU system subscribers and SU system subscribers.
K	The increase in PU-RX SNR due to donations from the SU system.
$\gamma$	Donation power from SU to the PU (power incentive).
$\lambda$	Min. SNR level at the SU-RX to guarantee accepted QoS.
$T_c$	Symbol (chip) duration, $T_c={\displaystyle \frac{T_b}{N_o}}$, where $N_o$ is the spreading factor.
$n\left(t\right)$	Noise function, assumed AWGN, zero mean, with $PSD={\displaystyle \frac{{\eta }_o}{2}}$.
${\tau }_u$	Random phase offset due to propagation (delay).
${\theta }_u$	Random phase, where ${\theta }_u=-{\omega }_c{\tau }_u+{\vartheta }_u$.
$E[.]$	Expectation operator.
$h_{pj}$	The channel gain from the PU-TX to the SU-RX.
$h_{si}$	The channel gain from the SU-TX to the PU-RX.
${\alpha }_u\in [0.7,0.95]$	The channel gain of the desired signal for the PU and SU subscribers.
${\alpha }_{\widehat{u}}\in [0.2,0.3]$	The channel gain of the interferers within the same system.

denotes all the parameters, functions, and concepts that will be used in the next mathematical representation sections.

The mathematical representation of the proposed model 1 and model 2 starts by defining the transmission process. In this regard, the SU-TX data messages are expressed as $m_j$, where $j\in \left\{1,2,\dots ,7\right\}$. So, the SU-TX encoder spreading codes are defined as $c_{j+1}$, where, in model 1, code $c_1$ is reserved for the PU-RF boosted signal, and codes $c_2$ up to $c_8$ are reserved for the SU transceivers within the coverage area. Hence, for simplicity, the Hadamard matrix $H_8$ of model 1, which includes eight total orthogonal codes, is defined as

$$H_8=\left[\begin{array}{c}{c}_1\\ c_2\\ ⋮\\ c_8\end{array}\right]$$

(1)

The derivations of the transmission process assume asynchronous reception at the SU-RX side due to the channel impairments, i.e., in a practical case, each carrier undergoes a shift of ${\varphi }_j$ and a delay of ${\tau }_j$. User i’s encoded message $y_i\left(t\right)$ signal can be represented as

$$y_i\left(t\right)=\sqrt{{\displaystyle \frac{2E_p}{T_p}}}{m}_i\left(t-{\tau }_i\right)c_i\left(t-{\tau }_i\right)cos({\omega }_c\left(t-{\tau }_i\right)+{\varphi }_i).$$

(2)

The overall received signal $r\left(t\right)$, which suffers from carrier shift and channel delay and assumes U users within the system coverage area, can be expressed as

$$r\left(t\right)=\sum _{u=1}^U\sqrt{{\displaystyle \frac{2E_p}{T_p}}}{m}_u(t-{\tau }_u)c_u(t-{\tau }_u)cos({\omega }_c(t-{\tau }_u)+{\varphi }_u)+n\left(t\right)=\sum _{u=1}^U{y}_u\left(t\right)+n\left(t\right),$$

(3)

where $n\left(t\right)$ is the AWGN term at the reciever. Figure 6 shows the correlator receiver of the $i^{th}$ SU. It receives $m_i$ by converting the signal from the RF band to the base-band level, then decoding it, then correlating it.

$s\left(t\right)$ is the desired ${SU}_i$ RF received signal. Thus, Equation (3) can be expressed as

$$\begin{array}{ccc}\hfill r\left(t\right)& =& \sqrt{{\displaystyle \frac{2E_p}{T_p}}}{m}_i\left(t-{\tau }_i\right)c_i\left(t-{\tau }_i\right)cos\left({\omega }_c(t-{\tau }_i)+{\varphi }_i\right)\hfill \\ \hfill & +& \sum _{\begin{array}{c}u=0\\ u\ne i\end{array}}^U\sqrt{{\displaystyle \frac{2E_p}{T_p}}}{m}_u\left(t-{\tau }_u\right)c_u(t-{\tau }_u)cos({\omega }_c(t-{\tau }_u)+{\varphi }_u)+n\left(t\right).\hfill \end{array}$$

(4)

So, by processing the signal down from the RF band to the base-band level for user ${SU}_1$, the correlated signal can be classified into three terms:

$$z\left(t\right)={\int }_0^{T_b}r\left(t\right)c_i(t-{\tau }_i)cos({\omega }_c(t-{\tau }_i)+{\varphi }_i)dt=v_i\left(t\right)+v_{MAI}\left(t\right)+\eta \left(t\right).$$

(5)

where $v_i\left(t\right)$ is the desired received signal term by subscriber ${SU}_i$, $v_{MAI}\left(t\right)$ is the multiple-access interference (MAI) due to $U-1$ users within the system coverage area, and $\eta \left(t\right)$ is the channel noise term. Furthermore, the derivations of $v_i\left(t\right)$, $v_{MAI}\left(t\right)$, and $\eta \left(t\right)$ are implemented using [41] in Appendix A as functions in the signal and the proposed system parameters.

The derivation of the $\gamma$ limits of the proposed DSCA-MC-CR system is obtained by using the practical asynchronous model. So, to derive the lower boundary of $\gamma$, the ${PU}_i$ receiver must have an increase of K in the SNR value due to the power donation from the SU system, which creates the following inequality:

$${\left({\alpha }_u\sqrt{P_p}+h_{si}\sqrt{\gamma P_s}\right)}^2\ge {\alpha }_u^2{P}_p\left(1+K\right),$$

(6)

After several manipulations of Equation (6), the lower boundary of $\gamma$ can be expressed as

$$\gamma \ge {\displaystyle \frac{{\alpha }_u^2{P}_p\left(K-2\sqrt{K+1}+2\right)}{h_{si}^2{P}_s}}.$$

(7)

On the other hand, to derive the upper boundary of $\gamma$, the secondary user receiver ${SU}_j$ should be guaranteed an acceptable minimum level of QoS, which creates the following inequality:

$${\displaystyle \frac{{\alpha }_u^2\frac{E_b{T}_b}{2}(1-\gamma )}{{\sum }_{\widehat{u}=1,\widehat{u}\ne u}^U\frac{T_c{E}_b}{6}{\alpha }_{\widehat{u}}^2+\frac{{\eta }_o{T}_b}{4}}}\ge \lambda ,$$

(8)

After several manipulations of Equation (8), the upper boundary of $\gamma$ can be expressed as

$$\gamma \le 1-{\displaystyle \frac{2\lambda \left({\sum }_{\widehat{u}=1,\widehat{u}\ne u}^U\frac{T_c{E}_b}{6}{\alpha }_{\widehat{u}}^2+\frac{{\eta }_o{T}_b}{4}\right)}{{\alpha }_u^2{E}_p{T}_p}}.$$

(9)

So, taking into consideration all the channel parameters, the system transmission levels, and the signal design, the boundary limits of the desired donation power level from the proposed DSCA-MC-CR system, $\gamma$, to the privileged PU system can be expressed as follows:

$${\displaystyle \frac{{\alpha }_u^2{P}_p(K+2-2\sqrt{K+1})}{{h_{si}}^2{P}_s}}\le \gamma \le 1-{\displaystyle \frac{2\lambda \left({\sum }_{\widehat{u}=1,\widehat{u}\ne u}^U\frac{T_c{E}_b}{6}{{\alpha }_{\widehat{u}}}^2+\frac{{\eta }_o{T}_b}{4}\right)}{{\alpha }_u^2{E}_p{T}_p}}.$$

(10)

5. BER and Data Rate Calculation of the Proposed Network

This section calculates the system’s SINR, BER, and data rate, and performs packet interarrival time analysis. These calculations assume practical asynchronous communication systems. In addition, the network estimations include synchronous communication systems.

5.1. The DSCA-MC-CR Asynchronous Model

The SINR term of asynchronous model 1 and model 2 at any receiver antenna is estimated as

$${SINR}_u={\displaystyle \frac{P_s}{{{\sigma }_{MAI}}^2+{{\sigma }_n}^2}},$$

(11)

Equations (A3), (A6) and (A8) from Appendix A are applied, also assuming the signal power $P_s={\displaystyle \frac{E_b{T}_b}{2}}$ and assuming the channel gain of the desired signal and interferers. Then,

$${SINR}_u={\displaystyle \frac{{{\alpha }_u}^2\frac{E_b{T}_b}{2}}{{\sum }_{\widehat{u}=1,\widehat{u}\ne u}^U\frac{T_c{E}_b}{6}{\alpha }_{\widehat{u}}^2+\frac{{\eta }_o{T}_b}{4}}}.$$

(12)

The BER calculations assume a white Gaussian channel. At the ${PU}_i$ receiver, the BER, without incentivizing the PU system by using the QPSK-OFDM scheme, can be defined as $P_e^p=Q\left(\sqrt{{\displaystyle \frac{P_p}{{\eta }_o}}}\right)$, where $Q\left(·\right)$ is the Q-function. The probability of error in incentivizing the PU system using the QPSK-OFDM modulation scheme within the OC-DSA system in [33] is defined as

$$P_{e_{OC\_DSA}}^p=Q\left(\sqrt{{\displaystyle \frac{{\left(\sqrt{P_p}+a\sqrt{\gamma P_{\widehat{s}}}\right)}^2}{{\eta }_o}}}\right),$$

(13)

The probability of error in incentivizing the PU system and using the QPSK-OFDM modulation scheme within the proposed DSCA-MC-CR system can be defined as

$$P_{e_{DSCA\_MC}}^p=Q\left(\sqrt{{\displaystyle \frac{{\alpha }_u^2\frac{E_b{T}_b}{2}\left(1+K\right)}{{\sum }_{\widehat{u}=1,\widehat{u}\ne u}^U\frac{T_c{E}_b}{6}{\alpha }_{\widehat{u}}^2+\frac{{\eta }_o{T}_b}{4}}}}\right).$$

(14)

The BER at the ${SU}_j$ receiver without incentivizing the PU system and using the QPSK-OFDM modulation scheme can be defined as $P_e^s=Q\left(\sqrt{{\displaystyle \frac{P_s}{{\eta }_o}}}\right)$. The BER calculations assume an additive white Gaussian noise channel. The probability of error in incentivizing the PU system and using the QPSK-OFDM modulation scheme within the OC-DSA system given in [33] can be defined as

$$P_{e_{OC\_DSA}}^s=Q\left(\sqrt{{\displaystyle \frac{(1-\gamma )P_{\widehat{s}}}{{\eta }_o}}}\right),$$

(15)

The probability of error in incentivizing the PU system and using the QPSK-OFDM modulation scheme within the proposed DSCA-MC-CR system can be defined as

$$P_{e_{DSCA\_MC}}^s=Q\left(\sqrt{{\displaystyle \frac{{\alpha }_u^2\frac{E_b{T}_b}{2}\left(1-\gamma \right)}{{\sum }_{\widehat{u}=1,\widehat{u}\ne u}^U\frac{T_c{E}_b}{6}{\alpha }_{\widehat{u}}^2+\frac{{\eta }_o{T}_b}{4}}}}\right).$$

(16)

The maximum data rate of the PU system and the SU system within the proposed DSCA-MC-CR technique can be formulated using the Shannon rule as

$$R_{DSCA-MC}^p={\displaystyle \frac{1}{2}}\left(1+{\displaystyle \frac{{\alpha }_u^2\frac{E_b{T}_b}{2}(1+K)}{{\sum }_{\widehat{u}=1,\widehat{u}\ne u}^U\frac{T_c{E}_b}{6}{\alpha }_{\widehat{u}}^2+\frac{{\eta }_o{T}_b}{4}}}\right),$$

(17)

$$R_{DSCA-MC}^s={\displaystyle \frac{1}{2}}\left(1+{\displaystyle \frac{{\alpha }_u^2\frac{E_b{T}_b}{2}(1-\gamma )}{{\sum }_{\widehat{u}=1,\widehat{u}\ne u}^U\frac{T_c{E}_b}{6}{\alpha }_{\widehat{u}}^2+\frac{{\eta }_o{T}_b}{4}}}\right).$$

(18)

5.2. The DSCA-MC-CR Synchronous Model

In the expression of the SINR term of the synchronous models at the subscriber receiver antenna, the MAI term vanishes due to the synchronization process. Then, the SINR becomes ${SINR}_u={\displaystyle \frac{P_s}{{\sigma }_n^2}}$. Thus,

$${SINR}_u={\displaystyle \frac{{\alpha }_u^2\frac{E_b{T}_b}{2}}{\frac{{\eta }_o{T}_b}{4}}}.$$

(19)

The probability of error in the synchronization models for both the ${PU}_i$ and the ${SU}_j$ systems, when incentivizing the PU system and using the QPSK-OFDM modulation scheme within the proposed DSCA-MC-CR system, becomes

$$P_{e_{DSCA\_MC}}^p=Q\left(\sqrt{{\displaystyle \frac{{\alpha }_u^2\frac{E_b{T}_b}{2}(1+K)}{\frac{{\eta }_o{T}_b}{4}}}}\right),$$

(20)

$$P_{e_{DSCA\_MC}}^s=Q\left(\sqrt{{\displaystyle \frac{{\alpha }_u^2\frac{E_b{T}_b}{2}(1-\gamma )}{\frac{{\eta }_o{T}_b}{4}}}}\right).$$

(21)

The maximum data rates of the synchronous PU system and the SU system within the proposed DSCA-MC-CR system are

$$R_{DSCA-MC}^p={\displaystyle \frac{1}{2}}\left(1+{\displaystyle \frac{{\alpha }_u^2\frac{E_b{T}_b}{2}(1+K)}{\frac{{\eta }_o{T}_b}{4}}}\right),$$

(22)

$$R_{DSCA-MC}^s={\displaystyle \frac{1}{2}}\left(1+{\displaystyle \frac{{\alpha }_u^2\frac{E_b{T}_b}{2}(1-\gamma )}{\frac{{\eta }_o{T}_b}{4}}}\right).$$

(23)

5.3. The Proposed System Using an MIMO System

This section proposes to use of a smart MIMO antenna system with two antennas at the SU-TX tower and two antennas at the SU-RX node, i.e., ${MIMO}_{2\times 2}$. The MIMO system leads to a significant increase in spectral efficiency and data rates, high QoS, improved BER, a wide coverage area, and low maintenance and low operation costs [42]. Figure 7 shows a simple $M\times N$ MIMO system with channel gain matrix $H=\left[\begin{array}{cc}{h}_{11}& h_{12}\\ h_{21}& h_{22}\end{array}\right]$ that sends signals $x_s=\left\{x_{s1},x_{s2},x_{s3},\cdots \right\}$ and receives noisy signals $y_s=\left\{y_{s1},y_{s2},y_{s3},\cdots \right\}$. The BER estimation and the capacity calculations of smart MIMO systems through different channel types are suggested in different research works, i.e., [43,44,45].

The BER through the white Gaussian channel and Rayleigh fading channel is calculated as $P_{AWGN}=Q\left(\sqrt{{SINR}_u}\right)$ and $P_{Ray}=Q\left(\sqrt{{\left|H\right|}^2{SINR}_u}\right)$, respectively.

Also, the capacity derived below in Equation (24) assumes that there is no channel state information (CSI) at the SU-TX tower that represents the practical case. As the user can randomly move from one point to another point, the capacity can be expressed as

$$C_{MIMO}={log}_{2}det\left(I_M+{SINR}_u\left(H{H}^H\right)\right).$$

(24)

where $I_M$ is the identity matrix with dimension 2×2, H is the channel gain matrix, and $H^H$ is the conjugate transpose of the channel matrix, i.e., Hermitian.

5.4. The Packet Interarrival Time Analysis

Shannon’s law estimates the maximum capacity of the PU and the SU systems in bit/sec as

$$R_{PU}=B\left(1+(1+K)SIN{R}_{PU}\right),$$

(25)

$$R_{SU}=B\left(1+(1-\gamma )SIN{R}_{SU}\right).$$

(26)

where B is the operating bandwidth, K is the SINR increase of the PU system, and $\gamma$ is the power donation from the SU system to the PU system. Furthermore, the packet interarrival time analysis using the Poisson cumulative distribution function (CDF) describes the following:

• Maximum capacity of the PU system and the decrease in the data rate during the conversion of the user from an active case to an inactive case, i.e., out of service.
• Minimum rate of the SU system and the increase in the SU data rate during the conversion of the PU from an active case to an inactive case.

The Poisson distribution function is defined as

$$P\left(\beta \right)={\displaystyle \frac{q^{\beta }}{\beta !}}{e}^{-q},$$

(27)

where $\beta =0,2,3,\dots$ and q is the mean number of occurrences in the interval, i.e., the rate.

5.5. Applying the Graph Signal Processing Concepts

The different research works in the GSP field aimed to create advanced tools for data processing that are defined on different irregular graphs. Ref. [40] introduces the main ideas in the GSP field and their relation to traditional DSP analysis [40]. This includes the latest developments of the different GSP tools, i.e., the different methods of sampling, filtering, and graph learning.

The proposed network coverage area is assumed to be a cell within a total of 100 cells that cover Alexandria city. The SU-TX tower interconnection with the main control of Alexandria city is calculated by applying the modern concepts of GSP, which are simply explained in [40].

Therefore, this section aims to describe the relationship between the GSP tools and the proposed network that includes the PU system and the SU system so that the GSP delivers the best channel path that interconnects the transmission between the main control station of the city and the suggested SU system within the proposed cell, i.e., the proposed network.

The novelty of using the GSP tools is that they use singular value decomposition (SVD) mathematical analysis, which applies to the adjacency matrix which includes the relation between the 100 cells within the wide area network. The SVD elects the eigenvalues at the end, as per the details given in [40], to the best channel selection of the transmission within the Alexandria city area network.

6. Simulation

This section provides different simulations of the proposed DSCA-MC-CR system obtained using MATLAB simulator and OMNeT simulator tools. The performance evaluation is implemented using MATLAB simulator version 9.9 and its enabling toolboxes. Also, the network topology design and traffic description representation are implemented using the objective modular network (OMNeT++) simulator version 6.

6.1. The Network Evaluation Using Graph Signal Processing

This part selects a large part of Alexandria city as a coverage area with a total of $N=100$ towers in service. Each tower covers $500\times 500$ m. The main base station (BS) is responsible for the control, and also, by defining the adjacency matrix between the 100 nodes or vertices, calculating the eigenvalues $\mathrm{\Lambda }=diag[{\lambda }_0\cdots {\lambda }_{N-1}]$ and the eigenvectors $V=[v_0\cdots v_{N-1}]$ as defined in [40]. By applying filter $e^{-100v_{N-1}}$, where $N=0,1,\cdots ,99$, we obtain Figure 8. Thus, Figure 8 is the result of applying modern graph signal processing concepts using the MATLAB simulator, and Figure 8a shows the network topology with 100 nodes that use normal DSP concepts and have random interconnected paths. On the other hand, Figure 8b shows the advanced GSP tools that classify the nodes into similar closed groups interconnected with the best paths that have the highest value of the propagation channel gain.

6.2. BER of the Proposed Model 1

BER calculations are implemented to estimate the performance of model 1 within the proposed DSCA-MC-CR technique by using the Gaussian channel and practical fading channel, i.e., the Rayleigh channel. Figure 9 shows the BER of the PU and the SU obtained using a QPSK-OFDM modulation scheme at $\gamma =3\%$. The following abbreviations apply:

• Excluding interference (EXC-I) is used when the PU system or the SU system works alone in the cell. This case is termed ${System}_1$.
• Including interference (INC-I) is used when the PU system and the SU system work together in the same cell. This case is termed ${System}_2$.
• Including interference and incentive (INC-(I+Incent.)) is used when the PU system works together with the SU system and obtains an incentive from the SU system too. This case is termed ${System}_3$ and represents the proposed system.

The PU system within ${System}_3$ achieves a BER of ${10}^{-3}$ at 0 dB SNR, while the PU achieved a BER of ${10}^{-3}$ at 9 dB when $\gamma =5\%$ in [33]. The SU system within ${System}_3$ achieves a BER of ${10}^{-3}$ at $2.3$ dB SNR, while the SU achieved a BER of ${10}^{-3}$ at 12 dB when $\gamma =5\%$ in [33]. In addition, Figure 10 shows the results obtained when using a practical fading channel. The PU system within ${System}_3$ achieves a BER of ${10}^{-3}$ at $5.8$ dB SNR, while the PU achieved a BER of ${10}^{-3}$ at 25 dB when $\gamma =5\%$ in [33]. Furthermore, the SU system within ${System}_3$ achieves a BER of ${10}^{-3}$ at 10 dB SNR, while the SU achieved a BER of ${10}^{-3}$ at 28 dB when $\gamma =5\%$ in [33]. Moreover, the previous results confirm that the proposal adopts the concept of green communication, which provides higher performance and achieves a wide coverage area with lower power consumption.

6.3. Error Rate of the Proposed Model 1 Using OMNeT

The evaluation of the proposed network with the use of a physical simulation environment is achieved by using the OMNeT simulator, as shown in Figure 11a. Thus, the topology of model 1 is established by using the OMNeT project with practical channel parameters. The topology consists of the PU-TX tower, seven PU-RXs, the SU-TX tower, seven SU-RXs, the radio medium module, and the physical environment module. The radio module defines the practical parameters of the propagation media so that the minimum interference level at each user is $-110$ dBm, the minimum background noise level is $-110$ dBm, the minimum reception power level is $-85$ dBm, and the carrier frequency is $2.4$ GHz. Moreover, the network description file (NED) uses the 802.11b standard with an OFDM modulation scheme. In addition, the initialization file (INI file) uses a two-ray reflection model, flat ground description, transmitted power of 10 mwatt, a message length of 56 bytes, a maximum coverage area of 500 m from the TX tower, and different application bandwidths, i.e., 6 MHz, 9 MHz, 12 MHz, 18 MHz, 24 MHz, 36 MHz, 48 MHz, and 54 MHz.

The simulation process at the ${SU}_1$ or the ${PU}_1$ without any donation leads to the results of the packet error rate (PER) versus the SINR, as shown in Figure 11b. Thus, as a sample from the different implemented results, the ${SU}_1$ of a certain application that has a bandwidth of 36 MHz achieves very closed performance when the CR system works alone and when the SU system donates $10\%$ to the PU system, as shown in Figure 12a. Therefore, the PER is $0.5\times {10}^{-8}$ for both cases.

6.4. Capacity Estimation of Model 1 Using MIMO System

In this section, the proposed CR system model 1 is equipped with $2\times 2$ MIMO antenna systems. Thus, simulations are carried out to estimate the capacity versus SINR of OSA, DSCA, OC-DSA, and DSCA-MC-CR techniques using the single-input single-output (SISO) antenna system and the proposed DSCA-MC-CR system using the MIMO smart antenna system. Also, the simulation assumes that the CSI is not available at the transmitter side, and the bandwidth is equal to 1 when applying the Shannon law given in [10,33] and applying Equations (17) and (18). In addition, the channel gain of the desired signal is assumed to be normalized, $K=0.25$, $\gamma =0.15$, and the SNR of the interferers at the desired user is equal to ${10}^{-3}$. Furthermore, the channel H matrix is a complex one, where singular value decomposition (SVD) is applied to the term $H{H}^H$ of Equation (24) to obtain the maximum eigenvalue that represents the channel gain of the desired signal at the MIMO receiver. Figure 13 shows that the MIMO systems achieve a noticeable improvement in the capacity in bits of the PU and the SU systems compared to the SISO antenna systems, i.e., when the SNR is 2 dB, the PU system achieves 1.4 bits by using OSA, 1.6 bits by using DSCA, 2.1 bits by using OC-DSA, 2.4 bits with the proposal using the SISO system, and 3.3 bits with the proposal using MIMO systems. Moreover, the SU system achieves 1.35 bits by using OSA, 1.2 bits by using DSCA, 1.2 bits by using OC-DSA, 1.9 bits with the proposal using the SISO system, and 3.4 bits with the proposal using MIMO systems.

6.5. BER Estimation of the Proposed Model 2

BER simulations are implemented to estimate the performance of model 2 within the proposed DSCA-MC-CR technique by using a Gaussian channel and practical fading channel, i.e., the Rayleigh channel. Figure 14 shows the BER of the PU and the SU obtained by using QPSK-OFDM modulation at $\gamma =3\%$. Figure 14a,b show the theoretical and simulation results. Moreover, when using the Gaussian channel, the PU system within ${System}_3$ achieves a BER of ${10}^{-3}$ at $-3$ dB SNR, while the PU achieved a BER of ${10}^{-3}$ at 9 dB for $\gamma =5\%$ in [33]. Furthermore, the SU system within ${System}_3$ achieves a BER of ${10}^{-3}$ at $-0.5$ dB SNR, while the SU achieved a BER of ${10}^{-3}$ at 12 dB for $\gamma =5\%$ in [33]. In addition, Figure 15 shows the results when using the fading channel, where the PU system within ${System}_3$ achieves a BER of ${10}^{-3}$ at 2 dB SNR, and the PU achieved a BER of ${10}^{-3}$ at 25 dB for $\gamma =5\%$ in [33]. Also, the SU system within ${System}_3$ achieves a BER of ${10}^{-3}$ at 5 dB SNR, while the SU achieved a BER of ${10}^{-3}$ at 28 dB for $\gamma =5\%$ in [33].

6.6. The Packet Interarrival Analysis

The packet interarrival analysis is implemented for the proposed DSCA-MC-CR technique by using the parameters of the LTE and 5G systems shown in

Table 2. Parameters for packet interarrival analysis through LTE and 5G networks.

Parameters	Description
LTE networks	Channel bandwidth = 20 MHz; minimum bandwidth = 14 MHz;
	downlink speed up to 1 Gbps; uplink speed up to 500 Mbps.
5G networks	Channel bandwidth = 300 MHz:1 GHz.
TX packets; SNR	500; 4.6 dB.
$P_p$; $P_s$	500 mwatt; 500 mwatt.
$\gamma$, K	$0.2$, $0.3$.
Used techniques	OSA [10], DSCA [10], OC-DSA [33], the proposed DSCA-MC-CR.

. The calculations using the LTE system shown in Figure 16 indicate that the SU system within the OSA technique is not capable of accessing the PU system spectrum when the PU subscriber is active on its spectrum at a rate of 8 Mbps. In addition, the SU starts accessing the PU system spectrum when it senses that the PU power of a certain subscriber decreases and then the PU becomes inactive. Moreover, the DSCA technique achieves a maximum rate of 10 Mbps for the PU and a guaranteed minimum rate of 5 Mbps for the SU system. Furthermore, the OC-DSA technique achieves a maximum rate of 15 Mbps for the PU and a guaranteed minimum rate of $6.5$ Mbps for the SU system. Thus, the proposed DSCA-MC-CR succeeds in achieving a maximum rate of 43 Mbps for the PU and a guaranteed minimum rate of 33 Mbps for the SU. The previous results indicate that the proposed system succeeds in achieving and guaranteeing higher rates than the other techniques in the literature.

The calculations using the 5G system shown in Figure 17 indicate that the SU system within the OSA technique also cannot access the PU system spectrum when the PU subscriber is active at a rate 11 Mbps, as with the LTE system. In addition, the DSCA technique achieves a maximum rate of 15 Mbps for the PU and a guaranteed minimum rate of 8 Mbps for the SU system. The OC-DSA technique achieves a maximum rate of 22 Mbps for the PU and guaranteed minimum rate of 10 Mbps for the SU system. Just as importantly, the proposed DSCA-MC-CR system succeeds in achieving a maximum rate of 65 Mbps for the PU system and guarantees a minimum rate level of 50 Mbps for the SU system. Finally, the previous results indicate that the proposed system succeeds in achieving and guaranteeing higher rates than the other techniques in the literature too.

7. Conclusions

In conclusion, this paper introduces a new dynamic spectrum co-access multicarrier-based cognitive radio (DSCA-MC-CR) technique through the practical propagation channel, which employs multicarrier codes between the PU subscribers and the SU subscribers where the power donated by the CR system to the PU system has already incentivized the PU system by using an underlay management model. The proposed DSCA-MC-CR technique allows the CR system to access the frequency spectrum with the PU privileged system due to the CR donating power. The power donated by the CR system achieves a noticeable improvement in the received signal strength and a higher data rate at the PU receiver, and provides an excellent QoS at the SU receiver. The use of the MIMO antenna system achieves higher capacity than the SISO antenna system and other techniques in the literature. The privileged PU system enhancement is achieved within the proposal without any changes to the existing implemented PU system infrastructure. Employing the orthogonal code sequences in the proposed DSCA-MC-CR technique releases any interference that might be caused by the SU subscribers. Then, the donated power to the PU system is reduced.

The proposed technique is estimated by using MATLAB and OMNeT simulators, and the results show a better performance than that achieved by other similar techniques in the literature when using 3% donated power from the SUs system to the PUs system. In addition, the proposed technique achieves the concept of green communication because the SUs system can coexist with the PUs system on the same spectrum while keeping the SUs at an excellent QoS level and maximizing the performance of the PUs system within the same coverage area with low power consumption at the SU-TX tower.

The proposed network applies to existing wide-band technologies like LTE cellular systems and 5G cellular systems. In addition, the proposed network applies to applications that have a bandwidth range from 6MHz to 54MHz, as indicated in Section 6.3. Future work will involve utilizing graph theory advanced tools to create a CR topology by using a CDMA modulation scheme.