## 4 Simulation Results and Discussion
It has to be noted that the MSE behavior is a direct consequence of the QoS of the network. In fact, the communication link is supposed to have the best quality in the first case (_i.e._ scenario 1), worst quality in the second case (_i.e._ scenario 2) and intermediate quality otherwise (_i.e._ scenarios 3 and 4). In other words, the degradations suffered by the  
Figure 3: Watermark MSE versus the different scenarios in the case of the video-communication between: **(a)** [PERSON] and Miss America; **(b)** [PERSON] and Foreman. watermark during the communication are proportional to the QoS (_i.e._ the BER) of the link: in fact, it can be easily seen from Figure 3 that the watermark is highly corrupted in the second scenario (corresponding to the worst BER), while it is slightly damaged in the first scenario (corresponding to the best BER). In the third and fourth scenarios, the MSE is at an intermediate level because the BER of the channel has an intermediate value between the first and second scenario. In order to characterize the performance of the proposed method to provide a quality measure of the transmission process of the multimedia content through the network, Figure 4 shows here the MSE of both the received video and the watermark, in respect to the four different operating scenarios (_i.e._ versus different BER of the transmission channel): in fact in our simulation trials, the communication link (_i.e._ the channel BER) is supposed to have the best quality in the first case (_i.e._ scenario 1), worst quality in the second case (_i.e._ scenario 2) and intermediate quality otherwise (_i.e._ scenarios 3 and 4). Once again, it can be easily seen from the figure that the watermark is highly corrupted in the second scenario (corresponding to the worst BER), while it is slightly damaged in the first scenario (corresponding to the best BER). In the third and fourth scenarios, the MSE is at an intermediate level  
Figure 4: MSE (normalized to 1) versus the different scenarios of the double boomerang watermark in the case of: **(a)** Miss America **(b)** Suzie **(c)** Carphone **(d)** Foreman video-sequences. because the BER of the channel has an intermediate value between the first and second scenario. It is not surprising that there are cases, shown in Fig. 4, where the minimum mean square error of the watermark does not closely follow the minimum mean square error of the video trace per se. This is a consequence of the particular scenario (_i.e._ the BER of the channel) under investigation. In fact, this situation happens only in the case of scenario 3 and 4 that are characterized by an intermediate quality level between the other scenarios: since the transmission errors introduced by the channel are modeled as a random Poisson process, characterized by a parametric probability of symbol error (_i.e._ proportional to the BER), operating in the scenarios 3 and 4 means to have two different quality levels for both the downlink and uplink channel. Moreover, it has to be underlined that these two scenarios are characterized by a confidence level that is greater than the one of the other two scenarios. The consequence is that the watermark degradations closely follow the ones of the video (constrained between the higher and lower performance bounds) but the minimum of the video MSE may not more correspond to the minimum of the watermark MSE, since the quality of the (uplink and downlink) channels can be different. Moreover, we can say that the first and the second scenarios represent the (upper and lower) bounds of the system performances, characterized by the same channel quality for both the uplink and downlink trajectory. It has to be underlined, as said before, that these two scenarios are characterized by a confidence level that is lower than the one of the other two scenarios.