## 4 Results
Figure 11: BER performance comparison for a single modulated band-Rx filter: third-order Bessel; \(p(t)\): raised cosine filter (changing \(\beta\)) and the matched Bessel filter (Simulations 1 and 2). The next results show the system performance in a more realistic scenario, where multiple bands may be simultaneously modulated. The considered simulation parameters were identical to the single-band scenarios. However, all the bands were modulated, and the BER was evaluated at the first and second bands. Figure 13 shows the BER performance for the first two bands (# 1 and # 2), with a third-order Bessel filter as \(g(t)\), referring to Simulations 5 and 6. For better visualization purposes, the raised cosine roll-off factor was only evaluated for \(\beta=1\), since it presented the best performance in the single-modulated band results. Figure 12: BER performance comparison for a single modulated band-Rx filter: third-order Butterworth; \(p(t)\): raised cosine filter (changing \(\beta\)) and the matched Butterworth filter (Simulations 3 and 4). Figure 13: BER performance comparison with inter-band interference-Rx filter:third-order Bessel; \(p(t)\): raised cosine filter (\(\beta=1\)) and the matched Bessel filter (Simulations 5 and 6). Comparing the performance with and without inter-band interference, there was a performance degradation when all the bands were being modulated. Although using a raised cosine filter as \(p(t)\) presented almost the same performance as before, the BER significantly degraded when the raised cosine was replaced by a matched Bessel filter. This was obviously due to the non-bandwidth limited characteristic of Bessel filters, as opposed to the raised cosine filters, which resulted in high inter-band interference. The same behavior occurred when using a matched Butterworth filter as \(g(t)\), as shown in Figure 14 (Simulations 7 and 8), however showing even worse BER performance using the matched filter. The previous results show that the Bessel filters achieved better performance when compared with Butterworth filters. Nevertheless, performance was severely degraded in scenarios where inter-band interference occurred. The results in Figure 15 consider the suppression of the even bands (Simulations 9 to 12). For visualization purposes, only \(\beta=1\) is shown for the raised cosine filter, and only the BER in the first band BER is shown. The BER curves show identical results when compared to Simulations 1 to 4, thus effectively mitigating the inter-band interference and with a remarkable performance when matched Bessel filters were considered. Although this guard band scheme degraded the spectral efficiency in half, the simplification in the receiver design can be easily achieved, allowing the desired IoT requirements for low-cost, low-power, and small-sized devices. The proposed system uses a local oscillator that may present non-ideal parameters, namely: (i) frequency shift, (ii) phase shift, and (iii) phase noise. The following analysis considered the non-ideal parameters in synchronization in the scenario of Simulation 10. Regarding frequency shift, the system was highly sensitive if the frequencies of the local oscillator, \(\omega_{LO}\), and the emitter filter sine wave, \(\omega_{c}^{m}\), did not match. Exact oscillator frequency is not feasible in real implementations due to component tolerances and thermal effects. From Equations (15) and (16), the sine and cosine terms only canceled out if both frequencies were exactly the same. In the case of a frequency shift at one of the sides, a cumulative phase delay was added; hence, the received constellation was continuously rotating (Figure 16). Without the presence of a proper carrier recover scheme in the receiver, the symbols' demodulation can not be correctly performed.