## 1 Introduction  
Propagation in mobile radio environments is characterized by waves that interact with the surfaces of the objects they encounter. These waves react through phenomena such as diffraction, reflection, refraction, scattering, and absorption, causing the signal to fade rapidly. This is referred to as short-term fading [1]. The amplitudes and phases of the propagation waves vary in accordance with the physical properties of the surfaces they encounter. Various distributions can describe these variations. Among them is the \(\eta\)-\(\mu\) distribution [2] and the so-called \(\eta\)-\(\mu\) fading, which influences mobile networks. The \(\eta\)-\(\mu\) fading model observes a signal consisting of clusters of multipath waves that propagate in an inhomogeneous environment. Within any cluster, the phases of the scattered waves are random and have similar delay times, but there is a relatively large spread in the delay times of different clusters [2]. The \(\eta\)-\(\mu\) distribution is a general fading distribution used to faithfully represent the small-scale variation of the fading signal, provided there is no line-of-sight [3]. Because of its generality, the impact of this fading on wireless systems has been extensively discussed in the literature. Various aspects of wireless systems' performance under the influence of fading effects have been evaluated for different purposes. In [4; 5; 6; 7; 8], the first-order system performance in the presence of \(\eta\)-\(\mu\) fading was derived. In [4], the moment generating function (MGF) of the generalized \(\eta\)-\(\mu\) distribution was derived and used to evaluate the average bit error rate (ABER) in \(\eta\)-\(\mu\) fading channels in terms of elementary functions. An exact closed-form expression for the outage probability (OP) in \(\eta\)-\(\mu\) fading channels was derived in [5]. Reference [6] investigated the ABER and OP of binary coherent, and non-coherent modulation schemes were obtained for an \(L\)-branch maximal ratio combining (MRC) diversity receiver over exponentially correlated \(\eta\)-\(\mu\) fading channels. In [7], expressions for the rate and OP were developed for the MRC receiver in scenarios involving \(\eta\)-\(\mu\) fading and interferers with unequal power. Reference [8] provided exact closed-form expressions for the OP of MRC in \(\eta\)-\(\mu\) fading channels with antenna correlation and Rayleigh co-channel interference (CCI) with arbitrary powers. The second-order performance of wireless systems in the presence of \(\eta\)-\(\mu\) fading was considered in [9; 10]. The formula for the level crossing rate (LCR) was derived in [9] for the selection combining (SC) receiver in mobile systems under the influence of \(\eta\)-\(\mu\) fading and \(\eta\)-\(\mu\) CCI. The LCR, the average fade duration (AFD), and the phase crossing rate (PCR) were derived in [10] for \(\eta\)-\(\mu\) fading channels. The channel capacity (CC) is one of the most important performance metrics of the first order. Increasing the CC of mobile networks is one of the main demands in today's wireless services. Analyses of the channel capacity can be found in the existing literature [11; 12; 13]. This is why we have chosen to investigate this performance metric in our paper. In addition to small-scale fading, CCI is also present in wireless systems. It can be a consequence of different influences, including the weather conditions, administrative factors, or design issues. References [8; 9; 10] took into account the impact of CCI, in addition to the \(\eta\)-\(\mu\) fading. CCI can also be modeled with different distributions. The standard approach to mitigating the impact of fading and CCI is through diversity combining [1]. Some of the most common diversity-combining techniques are maximal ratio combining (MRC) [6; 7; 8], equal gain combining (EGC) [14], and selection combining (SC) [9; 13; 15]. While all of these techniques improve system performance, MRC is considered the most effective.