## 2 Problem Modeling
### Effect of Interferences  
In order to be able to measure the quality of the received signal, we must take into account the interfering signals. By interfering signals, we mean those undesired signals received by different network elements that make it harder to receive the expected signal properly. In the context of this work, it is necessary to quantify the power of interfering signals both in wireless terminals (C and D) and APs. We have to take into consideration several issues for this. First, we have assumed that there are only interferences coming from other Wi-Fi devices, but not from any other wireless technologies that may be also using the 2.4-GHz frequency band. It would not be difficult to extend our interference model, but we have decided not to do so, because these interferences are unconnected to the problem that we are presenting here. Second, provided that distance also affects interference signals, those interferences coming from sources far enough from the reception point so that they fall below the receiver's sensitivity have been dismissed, according to the interference graph presented in Section 2.2. Third, it is commonly accepted that data traffic in access networks is very asymmetric, _i.e._, the downstream clearly dominates the upstream [30]. Indeed, this asymmetry has shaped the ADSL (Asymmetric Digital Subscriber Line) and cable design. For that reason, we have assumed that uplink traffic of wireless devices (D) is negligible in comparison with the traffic transmitted by APs, so they are not included in the graph. However, note that this assumption has only been made for wireless devices (D) different from cameras, as IP-based cameras' (C) data traffic will be mainly upstream.  
The quality of the received signal depends on all of the received interferences. Aside from distance (which affects signal losses; Equation (2)), interferences are also influenced by other factors: the activity index (\(\Psi\)) and the co-channel index (\(\delta\)). The purpose of the activity index is to account for the fact that different volumes of data traffic will suppose different effects on interferences. In other words, higher bandwidth flows will generate more harmful interference signals, as they will occupy the spectrum for a higher ratio of time. Note that the interferences generated by APs are mainly due to traffic sent to the other wireless devices. Finally, the co-channel index (\(\delta\)) is defined as the existing overlap between the IEEE 802.11 2.4-GHz frequency band. To model this effect, we have used the values obtained for this index in [31], where the authors provide a matrix where each value \((i,j)\) represents the interference, as seen in channel \(i\), motivated by the transmission on channel \(j\). As a summary, if a node operating in channel \(i\) is interfered by a node operating in channel \(j\), that interference power can be expressed as:  
\[I=P_{t}+G_{t}+G_{r}-L-P_{loss}+\delta(i,j)+\Psi \tag{5}\]  
where every value is expressed in dB. Once there is a model for interfering signals, the signal-to-noise ratio for terminal \(i\) (\(SINR_{i}\)) can be computed as the ratio between the received signal and the sum of the received interferences, _i.e._,  
\[SINR_{i}=\frac{P}{\sum_{j=1}^{M}I_{j}} \tag{6}\]being \(P\) the power of the desired video signal and \(M\) the number of interference signals (\(I_{j}\)) that are received.  
Note that each AP will have a \(SINR\) value for every terminal that is associated with it. In that case, we will assume that its \(SINR\) will be the minimum of all of them, which is in fact the worst case.