# Energy and Spectrally Efficient Modulation Scheme for IoT Applications
## 4 Simulation Results
### ABER Performance  
Figure 3 depicts the analytical ABER of the proposed OSP-MSK over AWGN in Equation (27) compared to the numerical simulation results for the uncoded and coded scenarios. As shown in Figure 3, the simulation results manifest a close match to the analytical formula over a wide range of SNR values. Figure 4 depicts the analytical ABER of the OSP-MSK modulation over the Rayleigh fading channel in Equation (39) and over the Nakagami-m fading channel in Equation (45) (e.g., \(m=\) two and \(m=\) four) compared to the numerical simulation results for the uncoded scenario. Furthermore, Figure 5 considers the coded scenario, where the convolutional encoder rate is set to \(\frac{1}{2}\). As depicted in Figures 4 and 5, again, the simulation results are very akin to the analytical results for a wide range of SNR values. The high consistency between the analytical formulas and the simulation results dates primarily to the absence of any mathematical assumptions in deriving the ABER of the OSP-MSK modulation. This, without a doubt, evinces the potency of the mathematical analysis conducted throughout this paper. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline ADC sampling rate & 16 fs \\ Number of bits/packets & Eight bits \\ MLSE equalizer size & 256 states \\ Band pass filter (BPF) & Six-order Butterworth BPF \\ BPF bandwidth (BW) & BW = 0.6 \\ ADC resolution & One-bit ADC \\ Channel encoder & Convolutional Encoder \\ Channel encoder’s constraint length & Constrain length = seven \\ Channel encoder’s rate & rate = \(\frac{1}{2}\) \\ Channel encoder’s polynomials & g\({}_{0}=\) x\({}^{7}+\) x\({}^{2}+\) x\({}^{1}\) \\  & and g\({}_{1}=\) x\({}^{7}\). \\ Channel decoder & Hard decision Viterbi decoder \\ Number of transmit antennas & Two antennas \\ Number of receive antennas & Two antennas \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation Parameters. ADC: analog to digital converter, MLSE: maximum-likelihood sequence estimation. Figure 3: The analytical and the simulated average bit error rate (ABER) performance of the OSP-MSK modulation over additive white Gaussian noise (AWGN) for the uncoded and coded scenarios. Figure 6 depicts the ABER performance of the single-input single-output orthogonal shaping pulses minimum shift keying (SISO-OSP-MSK) modulation compared to the ABER performance of the SISO-CEM system by using GMSK and QMGMSK modulation schemes [32; 33]. As depicted in Figure 6, the proposed SISO-OSP-MSK captures the same ABER performance of the conventional SISO-CEM with GMSK modulation, while the ABER performance of the SISO-CEM system is degraded by about four dB of SNR value when the QMGMSK modulation is utilized. Figure 7 depicts the ABER performance of the MIMO-OSP-MSK modulation compared to the ABER performance of the MIMO-CEM system with the GMSK and QMGMSK modulation schemes, where a 2 \(\times\) 2 transmit and receive antenna configuration is utilized to achieve a multiplexing gain for both of the considered schemes. As depicted in Figure 7, a comparable result is obtained in the MIMO scenario. Again, the proposed MIMO-OSP-MSK captures the same ABER performance of the conventional MIMO-CEM with GMSK modulation, while the ABER performance of the MIMO-CEM system is degraded by about five dB of SNR value when the QMGMSK modulation is utilized. In Figure 8, the ABER performance of the MIMO-OSP-MSK modulation is evaluated and compared to the ABER performance of the conventional MIMO-CEM system in the presence of  
Figure 4: The analytical and the simulated ABER performance of the OSP-MSK modulation over the Raleigh fading channel and Nakagami-m fading channel for the uncoded scenario. Figure 5: The analytical and the simulated ABER performance of the OSP-MSK modulation over the Raleigh fading channel and Nakagami-m fading channel for the coded scenario.