## 4 Simulation Results and Discussion
The consequence is that the watermark degradations closely follow the ones of the video, since they are transmitted over the same (uplink and downlink) noisy channels and hence, the minimum mean square error of the watermarking corresponds to the minimum mean square error of the video trace per se. To fully understand the relation between the multimedia content and the watermark, we compare the MSE of the watermark with the MSE of the video after the double boomerang trajectory. It has to be remembered that the video-sequence of every active user travels on the communication link one time as video (transparent mode), one time as watermark (hidden mode). Hence, the watermark suffers twice the degradations of the communication link, due to the boomerang path. It is worth noting that the MSE of the video-sequences _increases_ when the BER _increases_: this is in accordance with the degradation that the videos suffer at increasing BER. In addition, the quality degradation of the extracted watermark embedded into the host video has the same behaviour of the one affecting the video itself, as shown in terms of MSE in Figure 4. Comparing these experimental results, it is now possible to evaluate an empirical relationship between the MSE of the boomerang watermark and the one of the host multimedia content, as shown in Figure 5. In particular, the values of the curve have been selected considering only the cases of Fig. 4 where the watermark degradations closely follow the ones of the video. Hence, the values in Fig. 5 have been obtained exploiting the values of the four videos under investigation only in the first and second scenarios, _i.e._ considering the (_asymptotic_) performance of the system in the best and worst case, respectively. As it can be easily seen in Fig. 5, the graph shows only very large values of the MSE of the watermark and this is a consequence of the operating scenarios used in our research. In fact, considering the quality of the communication channel used in all the four scenarios, we can evaluate the relationship between the watermark MSE and the channel BER. This relationship is represented in Fig. 6, where it is clearly visible that for the minimum BER of \(10^{-4}\), the watermark MSE is characterized by a large value (equal to 0.74) while for the worst BER of more than \(10^{-3}\) the watermark MSE assumes a value that is even larger than before (almost equal to 1). Hence, these are the values of great interest for the mark MSE used in this work. Moreover, here we are interested in evaluating an _objective_ relationship between the mark and the video (_i.e._ we are using only the MSE as a quality metric) and, considered that the watermark is a narrow band low energy signal, large values of the watermark MSE are needed to appreciate alterations of the video objective quality. Future researches will be devoted to analyze subjective indicators of the video quality investigating how lower values of the watermark MSE reflect in video alterations. Figure 5: Relationship between watermark and video degradation in terms of MSE for the analyzed cases and scenarios under investigation. Figure 6: Relationship between the channel BER and the watermark MSE for the analyzed cases and scenarios under investigation. It has to be underlined that if some other videos (_i.e._, cases or scenarios) would be used, the curves in Fig. 5 and Fig. 6 would be characterized by a different behavior. Nonetheless, even if sophisticated quality metrics or cumbersome relationships could be used for quality assessment purposes in multimedia communications, the MSE between the estimated watermark and the original one is used in this contribution as a proof of concept of the objective method proposed here. This means that it would be always possible to trace the alterations endured by the data, tracing the alterations of the embedded mark, with a relationship that depends on the transmitted videos and scenarios under investigation.