## 4 Discussion  
The performance of RP-MPSK can be discussed in three contexts: data rate, link reliability, and energy efficiency. With the proposed RP-MPSK modulation for RPW, a data rate of up to 2 Mbps is realizable for \(M=16\). This is comparable to the data rate of LTE-M. With RP-QPSK, a data rate higher than NB-IoT can be achieved [24]. With the lowest order of modulation, i.e., RP-BPSK, the data rate of 125 kbps is higher than most of the existing LPWANs. The high data rate also translates to the spectral efficiency because the same bandwidth is made capable to transmit higher data rate using RP-MPSK. The context of reliability can be more clearly stated in terms of diversity gain. Figure 6 exhibits a large diversity gain of RP-BPSK over simple BPSK that exploits second-order diversity. According to Figure 7, RP-16-PSK with \(N_{p}=3\) attains significant diversity gain over 8-PSK and 16-QAM without diversity. Since LPWANs do not employ spatial diversity, it is not considered for this comparison. Another interesting aspect of the reliability of RP-MPSK is its flexibility to achieve desired BER with any value of \(M\). Generally higher order PSK modulations degrade the error performance of a communication system. But in RP-MPSK the value of \(N_{p}\) can be increased to fetch the required BER. However, this is limited by hardware specification of the receiver. The last and the most important context is the energy efficiency of RP-MPSK. This can be better explained from two aspects. In the simplest way, the energy efficiency of RP-MPSK modulation comes from the gain in \(\alpha=E_{b}/N_{o}\) as shown in Figures 6 and 7. The desired BER can be achieved at a much lower value of \(\alpha\) compared with other modulation methods and the most reliable BPSK modulation with second order diversity is not an exception. Secondly, based on our argument in Section 1, use of RP-MPSK encapsulates more amount of data by the same amount of energy without an increase in the symbol duration. Since a communication system consumes highest energy while it is transmitting and most of the power is consumed by the power amplifier, an improvement of as low as 5 dB in \(\alpha\) for every bit transmitted using RP-MPSK makes a significant contribution to cut down overall power consumption of RPW nodes. Improvement in \(\alpha\) can also be viewed as improvement in SNR of the transmitted signal. With RP-MPSK, the required BER can be achieved at a substantially lower SNR as compared to other modulations considered  
Figure 9: Performance of RP-MPSK under multipath and Interference for \(N_{p}=7\). in this article. Therefore, the sensitivity of the receiver is also improved offering more fade margin. We now summarize the error performance of RPW with the proposed MPSK modulation. In terms of BER, RPW performs better than other LPWAN modulation schemes. The receiver sensitivity and BER rate can be controlled at RP-MPSK receiver by adjusting the sampling rate according to the design requirements of the system. RPW has a huge potential to grow and mature as a leading LPWAN with the proposed modulation scheme. The data rate obtained by RP-MPSK is sufficient for most of the M2M applications. However, Rotating Polarization MQAM (RP-MQAM) can be proposed and employed for further increment in data rate. RP-MPSK can also be made to compete WiFi-HaLow if RP-MPSK and RP-MQAM modulations exploit orthogonal frequency division multiplexing (OFDM). Maximal Ratio Combining (MRC) can be considered in addition to SC and EGC using classical model of PD. Error correction codes can be implemented to achieve ultra-high reliability. The results indicate that RP-MPSK offers higher sensitivity. Therefore, link budget analysis of RPW system should be investigated for comparison with other LPWANs to estimate the achievable range [28]. Experiments should be performed in real industrial environment for performance evaluation of RP-MPSK. Limitation on maximum sampling rate should be investigated by prototyping and SDR based implementation.