## 5 Conclusions and Recommendation  
A multi-user Faster than Nyquist DCSK system, where we use transmission/reception filters below the Nyquist required limit to enable a gain in spectral efficiency as well as simultaneous access for multiple users, was presented in this paper. FTN, in combination with DCSK, enables the enhancement of the latter in terms of bandwidth usage, which is one of the main drawbacks of traditional DCSK designs. The newly proposed system enables multi-user access without the addition of complicated blocks or new procedures. Using different sampling rates in FTN is a simple yet very effective design showing promising results. Moreover, several new algorithms have been proposed for optimal FTN detection, which can be added to this conceptual system for an improved performance and may even be able to rival coherent chaos-based systems like Chaos Shift Keying (CSK). The performance analysis of the newly proposed system has shown a possible multiple-access of up to three users with good BER results even without additional transmission power or a high spreading factor. Besides, it presents the same resistance to multi-path fading as the traditional DCSK systems while going below the Nyquist rate and for multiple users. The newly designed system allows a gain in bandwidth between 10% and 200% of the DCSK reference size, assuming up to four users (\(U=4\)), and can go beyond if a better detection algorithm is introduced. One user's gain can vary depending on the sampling parameter value, from 24% at the Mazo limit up to 40% when \(\rho=0.6\). The main challenge encountered  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Modulation** & **MU-FTN-DCSK** &
\begin{tabular}{c} **CIM MC-M-DCSK** \\ **MISO-SWIPT** \\ \end{tabular} \\ \hline Blocks & matched filters & matched filters \\  & & serial to parallel \\  & & bit/symbol converter \\  & & code index modulation \\  & & Hilbert filter \\  & & code index modulation \\  & & Walsh codes \\ \hline \hline \end{tabular}
\end{table}
Table 1: Complexity comparison.  
during this study was the use of lower sampling rates, as this increases the level of ISI. Moreover, adding new users results in higher levels of IUI which restricts the number of users in the system. The limitation in the number of users or the minimum sampling rates to consider was shown here to be related to the new form of interference between chaos signals that happens to originate from the usage of the filters on non-orthogonal transmissions. Hence, future works will be directed towards improving the detection algorithm in order to eliminate interference and the possibility of applying both time and frequency FTN transmissions. In addition, MIMI-OFDM might be a possible approach in improving BER performances of the current design while keeping the design simple.  
Conceptualization, M.D. and M.H.; methodology, M.D. and M.H.; software, M.D. and M.H.; validation, M.D. and M.H.; Drafting, M.D.; proof reading and experimental analysis, M.D., M.H. and G.K. All authors have read and agreed to the published version of the manuscript  
This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.