## 1 Introduction
However, we notice that the work in [19] was limited in the sense of practical deployment, due to the following reasons: DF was used at the relay instead of more general AF; a direct path between the satellite and destination was present (which is uncommon in urban canyons and indoor environments); and Rayleigh fading was used instead of generalized Nakagami-\(m\) fading. A more recent and practically oriented study was conducted in [20], where exact performance analysis of AF-based HSTS with co-channel interference was presented, considering multiple independent interferers and the effects of different channel parameters in a network. However, we note that the cumbersome performance analysis framework of [20] can be simplified with reasonable system model simplifications without any loss in practical insight, e.g., by considering single dominant co-channel interferer. Furthermore, extensions to other digital modulation techniques are possible in addition to M-ary phase shift keying (M-PSK) studied therein, such as commonly-used M-ary pulse amplitude modulation (M-PAM) and M-ary quadrature amplitude modulation (M-QAM). For M-QAM with chunk-based resource allocation in orthogonal frequency-division multiple access (OFDMA) systems, the papers [3; 4] have given its performance in Rayleigh fading. Furthermore, the mathematical expressions for a simple, yet accurate high signal-to-noise ratio (SNR) approximation (asymptotic SER) of the exact SER, not provided in [20], could also be provided. As multiple co-channel-independent interferers were considered in [20], therefore, the resulting performance analysis developed was too cumbersome and tedious for the purpose of system-level analysis and simulations. Specifically, we point out that computationally-simple and holistic performance characterization of three node AF-based HSTS for generalized fading channels, with noise and CCI at the relay, is not reported in the open literature despite the presence of some loosely-related studies. Therefore, in this work, we deal with the many open problems/issues (explained in the last paragraph) regarding the performance analyses of HSTS and develop the holistic and computationally-tractable performance analysis framework, which also addresses all of the shortcomings in [19; 20] explained previously. As a result, the novelty and main contributions of this work for HSTS can be listed as follows: (1) We analyze the average SER of a digitally-modulated dual-hop fixed gain AF-based relay network with interference and noise at the relay, while the destination only experiences noise. We derive the average SER for the following constellations: M-PSK, M-QAM and M-PAM; (2) We consider a network where a direct connection between source node (satellite) and destination node (terrestrial receiver) is absent, so a terrestrial relay forwards the source symbol to the destination; (3) We assume generalized fading channels where the source-relay link follows the shadowed Rice LMS model [21]; and the channels of the relay-destination and interferer-relay links follow the Nakagami-\(m\) model; (4) Using the moment generating function (MGF)-based approach [22], the exact MGF of the proposed HSTS is derived, based on the derived MGF, the average SER of the considered network is given; (5) Finally, and importantly, we develop a simple (in terms of computational complexity), yet appropriately accurate high SNR approximation (asymptotic SER) for the exact SER, which provides important insight in the high SNR regime. Extensive numerical results in terms of the average SER and the asymptotic SER of the considered system model are provided in this paper. According to the authors' best knowledge, this practically significant performance characterization of HSTS with CCI over generalized fading channels, which is analytically holistic while being of low computational complexity, shows the novelty of the presented work.