## 1 Introduction  
Multiple-input-multiple-output (MIMO) techniques have become a promising method to improve communication performances of mobile communication systems such as coverage, spectral efficiency, data rate, and reliability [1; 2; 3]. In conventional MIMO systems, multiple antennas are co-located in a single nodes, which provides diversity gain in multi-path fading channels. [PERSON] et al. investigate the performance gain through maximal ratio combining (MRC) and selective combining (SC) under Rayleigh and Nakagami-_m_ fading channels in [4; 5], respectively. However, due to the co-located nature of the conventional MIMO, the multiple single-input-single-output (SISO) links undergo the same shadowing [6; 7], which implies no macro-diversity gain can be exploited. To overcome this limitation, distributed antenna systems (DAS) were proposed to achieve spatial micro- and macro-diversity simultaneously. When it comes to cellular networks, as shown in Figure 1, DAS called remote antenna units (RAUs), which are inter-connected through high-quality wired or wireless links, are distributed in a cell [8; 9] to extend coverage and improve the spectral efficiency. Distributed antenna arrays can also be widely used in Internet-of-Things (IoT) networks with small nodes such as sensors and mobile devices [10]. Due to space and hardware limitations, multiple antennas cannot be accommodated in small devices. Instead, to mitigate fading channels, multiple nodes help another to transmit the same message, which is called cooperative transmission (CT). At the receiver of CT-based networks, multiple copies of the same message are combined at the physical layer, which provides signal-to-noise-ratio (SNR) advantage. Such SNR advantage can be used to improve throughput [11; 12], transmission range [13; 14; 15], and energy efficiency [16; 17; 18; 19]. In addition, if cooperative beamforming is applied to the DAS, sensitive message can be protected from eavesdropping [20; 21]. Also, DAS is expected to provide better connectivity in millimeter wave channel in fifth-generation (5G) cellular networks [22; 23; 24]. Because of such advantages, DAS has been extensively studied in [8; 9; 25; 26; 27; 28; 29; 30]. For example, [PERSON] et al. analyzed the outage performance of DAS assuming composite Rayleigh-lognormal environments in [25]. Similarly, [PERSON] et al. derived the downlink outage rates under composite Nakagami-\(m\) and lognormal channels [26; 27]. Also, [PERSON] et al. presented the spectral and transmit power efficiency of cooperative DASs in [8; 9]. [PERSON] et al. applied the DAS to wireless sensor networks and showed that cooperative DAS provides significant energy savings [28]. In addition, distributed MIMO multi-hop communication systems has been introduced by [PERSON] et al. in [29]. [PERSON] et al. analyzed achievable capacity of DAS in an interference-limited multi-cell environments [30]. However, most of existing studies on DAS including aforementioned ones assumed that both small and large-scale fading channels are independent for links from separated DAS antennas to a receiver. For instance, in [25; 26; 27], the outage probability is derived assuming independent log-normal shadowing for distributed antenna arrays. However, in reality, shadowing in decibels has been measured to have significant correlation in various scenarios such as outdoor channels in rural and suburban environments at 1.9 GHz [31], indoor channels measured at the University of Auckland at 1.8 GHz [32], high-speed railway environments [33], and references therein. Such correlated shadowing affects handover behavior, interference power, and macro-diversity schemes [34]. Motivated by this fact, we investigate the impact of correlated shadowing in composite Rayleigh-lognormal environments for more realistic modeling and analysis of DASs. To be specific, the main contributions of this papers are three-fold.