# Closed-Form Performance Analysis of the Inverse Power Lomax Fading Channel Model
## 1 Introduction
Although the rigor and clarity of the presented results are praiseworthy, the practical aspects of the chosen approach can be argued. For example, the results in [37] (i.e., [26]) are delivered in terms of various bivariate confluent hypergeometric functions, which are nonstandard for most modern computer algebra systems (CASs) (although they can be easily implemented via series summation or numerical integration). In contrast, the classical univariate Meijer-G or Fox-H functions are implemented in most CASs and have the same computational complexity as the ones mentioned above. Nevertheless, [26] presented not only the statistical description but also most of the Lomax channel-performance metrics (the average bit error rate (ABER), ergodic capacity (EC), and outage probability (OP)). The model was further used for a spectrum sensing analysis [38; 39]. One of its key properties, as mentioned in [26; 39], is that it is always in the hyper-Rayleigh regime (HRR) (at least the weak HRR) and thus can describe heavy fading conditions, which are of paramount importance for modern urban wireless communications. This can be linked to the fact that the Lomax family (with its modifications) belongs to the heavy-tailed distributions [28], which tend to describe poor propagation conditions. Additionally, in the last few years, the performance of modern wireless communications has been successfully described with the help of the inverse distributions approach (e.g., inverse gamma shadowing models [40] or inverse Gaussian and inverse generalized Gaussian models [41]) and their power-transformed modifications [42; 43; 44; 45]. Hence, the inverse power Lomax model incorporates all these approaches. Although much effort has been applied to the description of the IPL model in various applications (from economics to social sciences), it has not been studied in communication theory. Thus, motivated by the problem stated above, this research studies the performance of a wireless communications system functioning in the presence of a multipath fading channel with the instantaneous signal-to-noise ratio (SNR) subjected to the inverse power Lomax distribution. The major contributions of this research can be summarized as follows:  
* An easy-to-use statistical formulation (in terms of the PDF and CDF) of the inverse power Lomax fading channel model is introduced. * A specific positioning of the IPL model among the ones most widely used in wireless communications is performed. The results help to identify its capability to handle both severe and light fading, depending on the channel parameters. * The closed-form expressions are derived for (a) the moment-generating function of the instantaneous SNR; (b) amount of fading (AoF); (c) outage probability (OP); (d) average bit error rate (ABER); and (e) ergodic channel capacity (EC). * Closed-form high-SNR asymptotic expressions for all the derived channel-performance metrics are derived. * The closed-form and numerical hyper-Rayleigh analysis of the IPL channel is performed, identifying the boundaries of weak, strong, and full hyper-Rayleigh regimes. * A thorough joint analysis of the dependence of all the assumed channel-performance metrics on the channel parameters is performed for different fading scenarios--heavy fading and light fading. * The numerical and statistical simulation results are presented, proving the correctness of the performed theoretical analysis. * The practical applicability of the proposed model was verified using a variety of datasets, including both synthetic computer-generated data and real-world experimental measurements.