## 1 Introduction
Conventionally, SUs have to periodically sense the presence/absence of PUs, so that they can use vacant bands or move to another spectrum holes [24; 25]. In [26; 27], various spectrum sensing models for CR WSNs were introduced and compared. Refs. [26; 27] also described the advantages of CR WSNs, the main difference between CR WSNs, conventional WSNs, and ad hoc CR networks. However, the transmission of SUs may be interrupted anytime due to the arrival of PUs, and this is the main disadvantage of the spectrum sensing methods. Recently, underlay CR protocols [28; 29] were proposed to guarantee the continuous operation for SUs. In this method, SUs are allowed to utilize the licensed bands simultaneously with PUs provided that the secondary transmitters must adapt transmit power to satisfy an interference constraint given by PUs. To improve the performance of the secondary networks, cooperative relaying protocols [30; 31; 32; 33] have been considered as a key technology, thanks to its capacity to increase the performances gains, i.e., coverage extension or transmission diversity, and power-saving transmission. In the literature, two proactive cooperative relaying strategies that have been widely investigated are opportunistic relay selection (ORS) [34; 31], and partial relay selection (PRS) [35; 36]. In ORS, the best relay is chosen to maximize the end-to-end (e2e) signal-to-noise ratio (SNR) between source and destination. In PRS, only the channel state information (CSI) of the source-relay links is used to select the relay for the cooperation. However, in [37], the authors proposed a new PRS scheme, where the relay is selected by using CSIs of the relay-destination links. In [37; 38; 39; 40; 41; 42], different relay selection schemes in underlay CR networks were reported. Particularly, the authors in [37; 38; 39] evaluated the performance of the PRS protocols in terms of bit error rate (BER) and outage probability (OP). In [39; 40; 41], the cooperative cognitive schemes using the ORS methods were proposed and analyzed. Naturally, the idea of EH and CR should be applied in WSNs to solve both the energy and spectrum scarcity issues. In [42], the authors considered the channel access problem utilizing Markov decision process (MDP), where SUs select a channel to access data transmission or harvest energy. Ref. [43] solved the optimization problem for the RF-EH-CR network with multiple SUs and multiple channels. Specifically, the authors proposed a system model in which SUs are able to harvest energy from a busy channel occupied by the primary user; the harvested energy is stored in the battery, and it is then used for data transmission over an idle channel. In order to tackle the energy efficiency and spectrum efficiency in CR, an EH-based DF two-way cognitive radio network (EH-TWCR) is proposed in [44]. In particular, the authors proposed two energy transfer policies, two relaying protocols, and two relay receiver structures to investigate the outage and throughput performance. In [45; 46], the authors proposed the e2e performance of underlay multi-hop CR networks, where SUs can harvest energy from the power beacon [45] or from the RF signals of the primary transmitter [46]. Next, due to the low-cost transceiver hardware, sensor nodes are suffered from several kind of impairments such as phase noise, I/Q imbalance, amplifier nonlinearities, etc. [47; 48; 49]. To compensate the performance loss, cooperative relaying protocols can again be employed. Ref. [48] investigated the impact of hardware impairments on dual-hop relaying networks operating over Nakagami-\(m\) fading channels. In [49], outage probability and ergodic channel capacity of both PRS and ORS methods were measured under joint of co-channel interference and hardware impairments. In [50], the performance of two-way relaying schemes using EH relays with hardware imperfection in underlay CR networks was studied.