### Novelty and Contributions  
This research set out to develop and evaluate a new prediction and compensation method for IQM in AF dual-hop upstream multiple-user SC-FDMA systems across unreliable frequency-selective wireless channels. The most notable novelties and contributions presented in this article are outlined in the following bulleted list.  
* The previously reported works of estimating and correcting IQM for SC-FDMA systems were accomplished on uncoded single-hop transmissions. This work is the first of its sort that tackles this problem for multiple users upstream SC-FDMA systems over AF dual-hop transmissions.
* We combined the consequences of IQM that take place at the users, relay, and destination terminals with the channel impulse responses that occur between the nodes to create two unknown elements that are referred to as the equivalent channel impulse response. The proposed approach contradicts the standard, which mandates a variety of techniques for monitoring channel impulse response across nodes and computing the IQM at each terminal.
* We created a novel approach that uses maximum likelihood principles to evaluate the equivalent channel impulse responses at the destination. We adopted a space-alternating generalized expectation maximization (SAGE) approach for easy implementation of the maximum likelihood algorithm that is being provided.
* We profited from the channel-decoder's outputs by computing the a posteriori expectations of the data symbols, which were then employed as training symbols. This was possible due to the widespread usage of error-control codes in a wide range of practical applications.
* We demonstrated how the decoding procedure was executed using the calculation of the unknown variables.  
Table 1 provides a summary of the contributions of previous works and the current study.  
The arrangement of the remaining sections of the work is broken down as follows. Section 2 discusses the multiple users upstream SC-FDMA system model with IQM happening at each node in the context of AF dual-hop transmissions. Section 3 describes the offered SAGE computation algorithm. Section 4 introduces crucial considerations for using the provided estimator in practice. Section 5 outlines the process of data detection using the computation of the unidentified parameters. Section 6 provides the simulation results together with a relevant analysis. Section 7 concludes the investigation by summarizing its findings.  
\begin{table}
\begin{tabular}{l l l} \hline  & **Previous Works** & **Current Study** \\ \hline  & Single user & Multiple users \\  & Uncoded & Coded \\  & Single-hop & Dual-hop \\  & IQM at either the & IQM at all nodes \\  & broadcaster & \\  & or recipient & \\ \hline  & Single user & Multiple users \\  & Uncoded & Coded \\  & Single-hop & Dault-hop \\  & IQM at all nodes & IQM at all nodes \\ \hline  & Single user & Multiple users \\  & Uncoded & Coded \\  & Single-hop & Dault-hop \\  & IQM at all nodes & IQM at all nodes \\ \hline  & Single user & Multiple users \\  & Uncoded & Coded \\  & Single-hop & Dault-hop \\  & IQM at all nodes & IQM at all nodes \\ \hline  & Multiple users & Multiple users \\  & Uncoded & Coded \\  & Single-hop & Dault-hop \\  & IQM at all nodes & IQM at all nodes \\  & Channel estimation & Channel estimation \\ \hline  & Multiple users & Multiple users \\  & Coded & Coded \\  & Single-hop & Dault-hop \\  & IQM at all nodes & IQM at all nodes \\  & Channel estimation & Channel estimation \\ \hline  & Single user & Multiple users \\  & Single carrier & Multicarrier \\  & Uncoded & Coded \\  & DF-Dault-hop & AF-Dault-hop \\  & IQM at all nodes & IQM at all nodes \\ \hline  & Single user & Multiple users \\  & OFDM & SC-FDMA \\  & Uncoded & Coded \\  & DF-Dault-hop & AF-Dault-hop \\  & IQM at all nodes & IQM at all nodes \\ \hline  & Single user & Multiple users \\  & OFDM & SC-FDMA \\  & Coded & Coded \\  & IQM at all nodes & IQM at all nodes \\ \hline \end{tabular}
\end{table}
Table 1: A summary of the contributions of previous works and the current study.