# On Multi-Hop Decode-and-Forward Cooperative Relaying for Industrial Wireless Sensor Networks
## 1 Introduction  
In recent years, technological concepts such as Industry 4.0, smart home, and smart grid are set to reshape the landscape of future industry and people's lifestyle more than we ever thought possible. The common vision of such systems is generally connected to one single concept, the Internet of Things (IoT), where through the use of wireless sensor networks (WSNs), the entire physical infrastructure is closely coupled with the achievement of intelligent monitoring and management [1, 2]. WSNs can provide great operating effectiveness through low installation and operating costs, installation flexibility, and scalability. They have be used in a broad range of scenarios such as smart home services [3], disaster detection and relief [4], and industrial automation [5, 6]. A sensor network typically consists of a number of inexpensive low-power sensor nodes, which are distributed across a large area and can perform the tasks of data sensing, simple information processing, and communication over short distances [7]. Arising from the presence of spatially distributed sensor nodes in a sensor network, cooperative diversity can be achieved by using the sensor nodes between a given source-destination pair as intermediate relay stations. This kind of communication scheme provides significant robustness against the adverse effects of shadowing and fading in wireless communications, which leads to broader coverage, enhanced mobility, and improved system performance compared to the direct transmission [8, 9, 10]. Depending on the nature and complexity of the relaying technique, the relaying strategies can be generally classified into two categories, namely decode-and-forward (DF) and amplify-and-forward (AF) [11, 12, 13]. The performance analysis of DF and AF relaying systems under different channel conditions has been the topic of a wealth of papers. In the most recent work, the analytical expressions of theend-to-end average bit error rate (BER) for DF relaying systems over Rayleigh and Nakagami-_m_ fading channels with additive white Gaussian noise (AWGN) have been derived in [14; 15], respectively. The ergodic capacities of the DF relaying systems in Rayleigh, Rician, and Nakagami-_m_ fading channels have been analyzed in [16; 17; 18], respectively. However, the analyses are made for the particular case of only two consecutive hops, which limits the use of the results. The ergodic capacity for multi-hop AF relaying systems over Rayleigh fading channels was investigated in [19]. In [20], the authors derived a tight lower bound for the error rate and the outage probability of cooperative diversity networks over independent non-identical Nakagami-m fading channels with AF relaying and maximum ratio combining (MRC) at the destination node. In [21], an upper bound for the ergodic capacity of multi-hop cooperative relaying channels over independent non-identically distributed (i.n.i.d.) Nakagami-m fading was derived assuming AF relays. From the aforementioned up-to-date reported works, it is fairly evident that the ergodic capacity for multi-hop DF relaying systems over Nakagami-_m_ fading channels is not explored from the analytical point of view. Meanwhile, the vast majority of the analyses on the performance of wireless communication systems in the open literature have been based on the assumption of interference amplitude following Gaussian distribution with flat power spectral density (i.e., AWGN) owing to its simplicity for analysis. However, the AWGN channel model does not cover the behavior of a large class of commonly occurring interference signals such as electromagnetic interference and man-made noises, which cannot be ignored in many scenarios ([22], pp. 84-90). For example, in harsh industrial environments where WSNs will play a vital role in the Industry 4.0 era, the effects of noise and interferences are significant due to the wide operating temperatures, strong vibrations and excessive electromagnetic noise caused by large motors and other equipment [23; 24; 25].