###### Abstract  
This paper improves energy efficiency and communications reliability for wireless transmission under \(\kappa\)-\(\mu\) shadowed fading (i.e., integrating all channel impairments including path loss, shadowing, fading) and hardware impairment by employing a nonlinear energy harvester and multi-antenna power transmitter. To this end, this paper provides explicit formulas for outage probability. Numerous results corroborate these formulas and expose that energy-harvesting nonlinearity, hardware impairment, and channel conditions drastically deteriorate system performance. Notwithstanding, energy-harvesting nonlinearity influences system performance more severely than hardware impairment. In addition, desired system performance is accomplished flexibly and possibly by choosing a cluster of specifications. Remarkably, the proposed communications scheme obtains the optimal performance with the appropriate selection of the time-splitting factor. multiple antennas; energy-harvesting nonlinearity; hardware impairment; \(\kappa\)-\(\mu\) shadowed fading; performance analysis +
Footnote †: journal:  
In practice, hardware impairment (HWi), which may originate from an imperfect design process (viz. in-quadrature-phase imbalances and phase noises) or imperfect hardware elements (viz., amplifier nonlinearities), is present in transceivers [20; 21; 22]. HWi plays a role as an interference source and therefore, in degrading system performance significantly [23]. Accordingly, it is mandatory to analyze and evaluate it elaborately in the system configuration process before implementation. Moreover, wireless communications are challenging due to propagation conditions, which include shadowing, fading, and path loss. These conditions happen concurrently and dramatically influence its performance. For WCwEH investigated in our work, propagation conditions also affect the quantity of harvested energy, eventually affecting communications reliability. For performance analysis practically, propagation conditions need to be featured appropriately to match field measurements. The \(\kappa\)-\(\mu\) shadowed fading paradigm is extensively avouched in characterizing properly simultaneous influences of shadowing, fading, and path loss [24; 25]. Remarkably, by varying a parameter group \((\kappa,\mu,\chi,\delta)\) representing such a paradigm, divergent impairment degrees of shadowing, fading, and path loss can be set straightforwardly. The parameter \(\delta\) indicates channel power including path loss, \(\kappa\) signifies the Rician-\(K\) element that represents the Line of sight effect, \(\chi\) stands for the shadowing effect, and \(\mu\) denotes a sum of multi-path sets. As a result, this paradigm features a plurality of general-and-practical propagation conditions, including well-acknowledged fading distributions, viz., Rayleigh, one-sided Gaussian, Rice, Hoyt, Nakagami-\(m\), etc. [25]. A few works [26; 27; 28; 29] have studied wireless communications under concurrent consideration of energy-harvesting nonlinearity (EHNL) and hardware impairment. Nonetheless, these works have revealed several limitations. To be more specific, the authors in ref. [26] considered transmission from S to D under the aid of the reconfigurable intelligent surface operated as a relay. Although the authors in [26] analyzed rate-energy tradeoff, it investigated simple Rayleigh fading channels without accounting for shadowing, and missed the throughput (TP) and the outage probability (OP) analyses. Suffering from the same limitations as [26], the authors in [27] designed beamformers to obtain power efficiency and information security for direct transmission from S to multiple destinations. Nevertheless, ref. [27] studied Rician fading for the channel from T to S. Similar to [26; 27] in which no analysis of the TP and the OP was presented, the authors in ref. [28] assessed  
Figure 1: Wireless communications with energy harvesting.