*3.3. Performance Analysis*

Coverage analysis can aid in an adequate estimation of indoor and outdoor coverage in the simulated scenario. However, since coverage and capacity are linked, it is mandatory to analyze the influence of modulation in order to determine system performance. For that purpose, a ZigBee sensor network has been considered, which uses O-QPSK modulation, with a bandwidth of 3 MHz and a bit rate of 250 kbps, as well as a Bluetooth network considering V4.0 transceivers at a bit rate of 3 Mbps. As stated before, the worst-case conditions have been considered, in terms that for the different nodes density cases, one interconnecting device has been considered as the transmitter and the rest as in-band inter-system interference.

Figure 8 presents the constellation plots at two different receiver location points placed in the indoor and outdoor area of the scenario for the ZigBee system. Two different transmitter positions have been considered, which are the same ones as the previously presented results: The first one in the indoor area of the scenario (Tx 33) and the second one in the outdoor area of the scenario (Tx 5). The considered receiver spots are placed at one-meter distance of each transmitter, in the indoor and outdoor area, respectively, considering high and low-node density. It can be seen that the symbols are more disperse in the case of the transceivers placed in the indoor part of the auditorium, for both density nodes. This is explained because simulations have been made with the auditorium full of people, which causes a high number of scatterers in the area. Thus, this coupled with the assumption of the worst-case condition, where all the nodes except the transmitter are in-band inter-system interference, causes a large dispersion in the received symbols in the indoor area of the scenario. Constellations plots for the receiver location point in the outdoor area of the scenario have less symbol dispersion, achieving the ideal constellation for the low-node density case, as the interferers in this case are not placed nearby the receiver.

**Figure 8.** In Phase and Quadrature representation for two different nodes within the auditorium for offset-quadrature-phase-shift-keying (O-QPSK) modulation, (**a**) indoor node with high-node density scenario, (**b**) indoor node with low-node density scenario, (**c**) outdoor node with high-node density scenario, and (**d**) outdoor node with low-node density scenario.

To have insight into the total interference, the error vector magnitude (EVM) has been calculated for the different node-density cases. The EVM is an indicator of the modulation accuracy. To quantify the modulation error, the amplitude of the error can be calculated as:

$$Error Amplitude = \sqrt{\left(I\_i - I\_A\right)^2 + \left(Q\_i - Q\_A\right)^2} = \sqrt{\Delta I^2 + \Delta Q^2} \tag{2}$$

where *Ii* and *Qi* are the In-phase and Quadrature values of an ideal signal, while the actual location of the signal is *IA* and *QA*. The root mean square (RMS) value of the error amplitude for *N* symbols is:

$$RMS\ Error\ amplitude = \sqrt{\frac{1}{N} \left(\sum\_{k=1}^{N} \Delta l\_k^2 + \Delta Q\_k^2\right)}\tag{3}$$

If the ideal signal amplitude is *S*, the EVM is defined as:

$$EVM(\%) = \frac{RMS\ Error\ amplitude}{Ideal\ Signal\ Amplitude} = \frac{\sqrt{\frac{1}{N}\left(\sum\_{k=1}^{N}\Delta I\_k^2 + \Delta Q\_k^2\right)}}{S} \times 100\tag{4}$$

Table 2 presents the EVM (%) for the constellations' plots presented in Figure 8, including also the medium-node density case. The EVM requirement of the IEEE 802.15.4 standard must be less than 35% [38]. According to these results, the high-node density case for the indoor link is really close to the limit, so the received signal is going to be interference limited.

**Table 2.** Error vector magnitude (EVM) (%) for different nodes-density cases for the ZigBee system.


EVM analysis has also been performed in the case of considering operation of Bluetooth V4.0 transceivers within the scenario, a typical case for users or devices with high mobility. As in the previous case, variations in node density have a strong impact in EVM response, given by higher interference levels. These results are depicted in Figure 9, for the cases of node #33 and node #5, for different node densities. Table 3 presents the EVM (%) for the constellations' plots presented in Figure 9, including also the medium-node density case.

**Figure 9.** *Cont.*

**Figure 9.** In Phase and Quadrature representation for two different nodes within the auditorium for 8-DPSK modulation, (**a**) indoor node with high-node density scenario, (**b**) indoor node with low-node density scenario, (**c**) outdoor node with high-node density scenario, and (**d**) outdoor node with low-node density scenario.

**Table 3.** EVM (%) for different nodes-density cases for the Bluetooth V4.0 system.


To gain insight into the modulation error scenario characterization, the specific regions of correct operation regarding EVM for the ZigBee system have been mapped along the bi-dimensional cut planes. Although results have been obtained for the complete volume of the scenario, for the sake of clarity only the 1.2 m height has been depicted. Figure 10 presents the EVM for the different nodes-density cases and the case without interference, for a transmitter placed in the indoor area of the scenario (Tx 33) with again the worst-case conditions in terms of in-band inter-system interference. These operating regions are delimited by the configuration of the interfering network, as well as by the characteristics of the environment. It can be seen that interference levels can lead to have no service in different areas of the considered scenario, being these no-service areas bigger when high-node density is considered. It is worth noting that the low-density case considered is 19 nodes as it is presented in Figure 2c, which also implies a high interference level, as it can be seen in Figure 10c when compared with the case without interference (Figure 10d).

**Figure 10.** *Cont.*

**Figure 10.** EVM (%) for the considered scenario for O-QPSK modulation when indoor node is transmitting, (**a**) high-node density scenario, (**b**) medium-node density scenario, (**c**) low-node density scenario, and (**d**) without interference.

Figure 11a presents the linear distribution line of EVM (%) for Y = 20 m along the X-axis in the considered scenario, for Tx 33 (indoor node X = 20.35 m, Y = 22 m), considering the three different node-density cases. There is only correct service in a small area around the transmitter because of the high interference levels which have been considered. Figure 11b presents the bit error rate (BER) for the same radial line for the three different node-density cases, showing that the BER is quite high in remote areas from the transmitter.

**Figure 11.** (**a**) Linear distribution line of EVM (%) for Y=20 m, X-axis in the considered scenario when indoor node is transmitting, (**b**) Linear distribution line of bit error rate for Y = 20 m, X-axis in the considered scenario when indoor node is transmitting.

A second transmitter position has been considered to perform the EVM analysis in terms of O-QPSK modulation. In this case, the transmitter is placed in an outdoor location (Tx 5) at 1.2 m height. Regions of correct operation can be seen in Figure 12 for the different node-density cases and the case without interference.

In comparison with the previous indoor transmitter case, the correct operation areas obtained are bigger in this case for all density cases, concentrating the valid area mostly in the outdoor part of the scenario. These results can be explained due to, as stated previously, operating regions are delimited by the boundaries of the scenario (i.e., walls) and the interfering network configuration. Besides, in the outdoor area of the scenario, there is less people, so the concentration of nodes is lower (see Figure 2 for reference), which increases correct operation area compared to the previous case.

**Figure 12.** EVM (%) for the considered scenario for O-QPSK modulation when outdoor node is transmitting, (**a**) high-node density scenario, (**b**) medium-node density scenario, (**c**) low-node density scenario, and (**d**) without interference.

Figure 13a presents the linear distribution line of EVM (%) for Y = 5 m along the X-axis in the considered scenario for Tx 5 (outdoor node X = 11.7 m, Y = 5.8 m) considering the three different node-density cases. It can be seen that in the vicinity area of the transmitter, correct operation for the three density cases is obtained, but as we move away from the transmitter, in the medium and high-node density cases, there is no system service due to higher interference levels. Figure 13b presents the BER of the same radial line for the three different node-density cases. As it was expected, BER is quite high in remote areas from the transmitter, and lower BER is encountered close to the transmitter.

These results can aid in a better knowledge of the network performance and are relevant in terms of interference analysis as well as on the operation of mitigation schemes, when high-node density setups are presented.

Node density distributions have a direct impact in overall system performance. This can be observed in terms of coverage/capacity estimations, which depend on wireless system operating parameters (e.g., receiver sensitivity as a function of bit rate, employed adaptive modulation, and coding scheme). Coverage/capacity values can be precisely obtained by the use of 3D-RL simulation techniques, as they provide volumetric estimations of received power levels. As an example, estimations of coverage for receiver sensitivity in Bluetooth/Bluetooth Low Energy (BT/BLE) device distributions are depicted in Figure 14, as a function of transmission power levels. Two different situations are depicted: For maximum transmit power (4 dBm) and for conventional transmission power (usually set at −12 dBm). As a function of node density, variations in received power levels exhibit average received power level variations in the order of 4.8 dB, which can lead to coverage limit conditions (e.g., location at 38 m in the linear TRX radial for the conventional −12 dBm power consideration).

**Figure 13.** (**a**) Linear distribution line of EVM (%) for Y=5 m, X-axis in the considered scenario when outdoor node is transmitting, (**b**) Linear distribution line of bit error rate for Y = 5 m, X-axis in the considered scenario when outdoor node is transmitting.

**Figure 14.** Coverage/capacity estimation for BT/BLE transceiver operation (**a**) max transmission power (4 dBm) (**b**) conventional transmission power (−12dBm).

From the previous results, performance is general degraded as node density increases. This is given by the fact that radio resource functionalities have not been considered, such as multiplexing strategies or dynamic frequency allocation. In this way, worst case operation conditions have been considered, as an initial bound in coverage/capacity analysis. Future work can be foreseen in the analysis of coverage/capacity relations as a function of radio resource functionality performance. Moreover, realistic operation conditions can present even further variations as a function of time dependent interfering sources, which depend on user behavior, which are specific of the scenario under operation [27].
