# Achievable Rate of NOMA-Based Cooperative Spectrum-Sharing CRN over Nakagami-\(m\) Channels
## 2 Related Work  
For a NOMA-based cognitive radio network (CRN) in an underlay spectrum-sharing scenario, a closed-form study of the average achievable sum rate and outage probability was taken into consideration in [9]. The authors took into account the peak interference restriction, which states that the secondary network's interference on the primary user's receiver must be below a specific threshold. They demonstrated that at high values of peak interference power at the PU-Rx, the CRN-NOMA outperforms the CRN with the standard OMA [9]. In contrast, the same authors proposed a system in which the secondary user's receiver and the relay both have multiple receive antennas and employ selection combining and maximal-ratio combining (MRC) to receive signals [10]. The average achievable rate and outage probabilities for the spectrum-sharing-based cooperative NOMA are determined using closed-form equations. The authors in [11] presented a scheme in which the secondary base station would send a power domain NOMA signal to the closest secondary user after detecting an idle channel. The first secondary user uses a decode-and-forward approach to send the signal meant for the second secondary user in addition to deciphering its own signal. The authors combined the design and analysis of the proposed strategy, as opposed to other publications that tackled the spectrum-sensing and transmission phases separately [11]. Analytical equations for the outage probability and the ergodic rate of the two secondary users were derived to show the performance of the latter by assuming a flat Rayleigh fading channel model. In [12], the channel condition between the primary transmitter and receiver is assumed to be weak, and a secondary transmitter is used to assist the primary transmitter while simultaneously transmitting in a full-duplex mode to a secondary receiver with strong channel conditions. Zero-forcing beamforming is implemented at the secondary transmitter to suppress self-interferences. The outage probabilities for primary and secondary networks are also derived in [12]. According to a peak interference constraint, the authors in [13] derived analytical formulas for the sum effective rate for the downlink NOMA system. They explored the way the system's performance was affected by the availability of various degrees of channel state information (instantaneous and statistical). Other important factors were taken into consideration, and their effects on the system's sum effective rate were investigated. These factors included the maximum tolerated interference level, the delay exponent, the number of antennas, and the number of users. In [5], a cooperative NOMA transmission scheme is proposed, which is based on user pairing. Therein, it is reported that when users with distinctive channel gains are paired together, then the performance gain of the cooperative NOMA scheme over the OMA scheme is large. Furthermore, the performance analysis of the cooperative NOMA scheme proposed in [5] is also presented in terms of outage probability and diversity order. In [14], the authors investigated NOMA in multicast CRNs, where the multicast secondary users function as relays to improve the performance of both primary and secondary users. Closed-form expressions for outage probability and diversity order were also derived in [14]. The performance analysis of NOMA-based CRNs was performed in [15], where closed-form expressions are derived for outage and throughput. An underlaying NOMA CRN with detect-and-forward processes was investigated in [16], where a closed-form outage probability expression for NOMA-assisted secondary users was derived. A NOMA-based cognitive hybrid satellite-terrestrial overlay network was studied in [17] using amplify-and-forward (AF) relaying mode. Therein, the authors derived closed-form outage probability expressions for primary and secondary users.