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 It is undeniable that in the last two decades wireless devices have become extremely ubiquitous, and are no longer employed under carefully chosen conditions.
 
-Nowadays, smart phones, internet of things (IoT) devices and many other wireless applications are omnipresent and have to work in environments that are very far from ideal. Furthermore, in addition to the already large class of networked appliances, next generation wireless devices in urban environments will include the new category of vehicles \cite{AntonescuTB17}, where reliability of inter-vehicular communication directly translates into safety. While at the same time in rural regions, developing countries as well as in other low-user density areas, wireless transmission links using mesh networks have become a practical alternative to wired broadband \cite{Macmillan2019tidal,Subramanian2006rethinking,Flickenger2007wireless}.
+Nowadays smart phones, internet of things (IoT) devices and many other wireless applications are omnipresent and have to work in environments that are very far from ideal. Furthermore, in addition to the already large class of networked appliances, next generation wireless devices in urban environments will include the new category of vehicles \cite{AntonescuTB17}, where reliability of inter-vehicular communication directly translates into safety. While at the same time in rural regions, developing countries as well as in other low-user density areas, wireless transmission links using mesh networks have become a practical alternative to wired broadband \cite{Macmillan2019tidal,Subramanian2006rethinking,Flickenger2007wireless}.
 
-Thus today the study of problems concerning wireless devices is a very relevant topic. In particular, a common issue observed in the previously mentioned use cases is the so called \emph{multipath fading effect}, that degrades the reliability of a wireless transmission links \cite{Mathis, Gallager}. The problem of fading was actually foreseen \cite{Frederiksen2002overview,Maddocks1993introduction} and today most modern transmission schemes implement measures to reduce the effects fading \cite{Mathis,Hsu}.
+Thus today the study of problems concerning wireless devices is a very relevant topic. In particular, a common issue observed in the previously mentioned use cases is the so called \emph{multipath fading effect}, that degrades the reliability of a wireless transmission link \cite{Mathis, Gallager}. The problem of fading was actually foreseen \cite{Frederiksen2002overview,Maddocks1993introduction} and today most modern transmission schemes implement measures to reduce the effects fading \cite{Mathis,Hsu}.
 
 This work studies the multipath fading effect, and how it affects modern digital transmission systems that use quadrature amplitude (QAM) and phase shift keying (PSK) modulation.