# Challenges in Wireless System Integration as Enablers for Indoor Context Aware Environments
## 4 Interference Impact as a Function of Node Density  
The number of nodes as well as their topological distribution, in relation with the surrounding environment, determine received power level distributions, which in turn determine effective signal \begin{table}
\begin{tabular}{c c c} \hline \hline
**Antenna Number (\#)** & **Mean Value (ns)** & **Standard Dev (ns)** \\ \hline
17 & 110 & 31 \\
23 & 117 & 31 \\
60 & 123 & 26 \\
65 & 120 & 35 \\
72 & 111 & 24 \\
101 & 105 & 39 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Delay Spread values at 2 m height. Figure 13: 2D Delay Spread distributions for an operating frequency of 5.8 GHz, height plane at h = 2 m for active transmitters: (**a**) TRX #17, (**b**) TRX #60, (**c**) TRX #72, (**d**) TRX #101.  
and interference levels. Adequate communication link establishment in terms of quality is provided if the following condition is met:  
\[P_{rx}(\stackrel{{\rightarrow}}{{r}},rx-hw)\geq SENS_{rx}(serv,R_{b}, mc) \tag{1}\]  
where \(P_{rx}\) is the received power for each transceiver, as a function of spatial location \(r\) and receiver parameters \(rx-hw\) (e.g., antenna gain. noise factor) and \(SENS_{rx}\) is the receiver sensitivity, determined by the required Signal to Noise Ratio (SNR) threshold (or \(\rm E_{b}/N_{o}\) in the case of digital systems), transmission bit rate \(R_{b}\) and the modulation and coding scheme \(m_{c}\). In this context, the determination of useful received power and detected interference levels provides coverage/capacity relations as a function of service requirements and density of intra-system and inter-system users within the scenario. The location of all transmitting as well as receiving elements within the scenario is a fundamental parameter, due to large variability in power distribution in the indoor environment under consideration. Once wireless channel characterization has been performed, with the aid of a scalable scenario in terms of transceiver density, as described in Section 3, interference analysis can be obtained, deriving in system coverage/capacity estimations. To this extent, based on these results, SNR volumetric estimations have been obtained, with the following rules:  
* At 2.4 GHz, typical low cost devices (such as ZigBee) uses O-QPSK modulation, and a typical low-cost detector implementation is expected to meet the 1% Packet Error Rate (PER) requirement at SNR values of 5 dB to 6 dB (following Annex E of the standard IEEE 802.15.4). The results can be extended to other modulation schemes, as a function of the employed wireless systems. * SNR minimum ZigBee (BW = 3 MHz) at 250 Kbps = \(-\)12.26 dB (following Shannon formulation). * Worst case conditions in terms SNR analysis are provided when the interconnecting device operates with in-band inter-system interference which is in principle independent from interference control mechanisms in native wireless networks of the devices under operation. Interference analysis results have been obtained by introducing a test transceiver for multiple cases, in which the initial network transceivers for node density variatons have been used as potential interference sources. In this way, results depicted in Figures 14 and 15 show bi-dimensional plots for particular heights of the SNR distribution as a function of potential location of transceivers. These plots represent, therefore, an upper bound in terms of quality degradation in terms of simultaneous operation of other transceivers. The provided SNR values can be mapped afterwards to \(\rm E_{b}/N_{o}\) ratios, where modulation scheme as well as transmission bit rate can be explicitly considered. Following the rules previously mentioned, one of the possible cases has been depicted in Figure 16, in terms of compliance/non-compliance to a specific SNR threshold, which has been set to a value of SNR \(>\)5 dB, consistent with PER \(<\)1% for O-QPSK in 802.15.4 standard. Again, results are shown for a given number of interfering nodes introduced in simultaneous operation with other devices, for example wearables.