# Anti-Multipath Performance Improvement of an M-ary Position Phase Shift Keying Modulation System
## 4 Simulation and Numerical Results
### Time Delay Estimation
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**SNR (dB)** & **Period of m-Sequence** & **Multipath Gain** & **Delay (s)** \\ \hline \multirow{6}{*}{\(-5\)} & \multirow{3}{*}{7} & \(0.1\) & \(-0.793\times 10^{-3}\) \\  & & \(0.5\) & \(-1.198\times 10^{-3}\) \\  & & \(0.8\) & \(-0.820\times 10^{-3}\) \\ \cline{2-4}  & & \(0.1\) & \(-0.763\times 10^{-3}\) \\  & & \(0.5\) & \(-0.736\times 10^{-3}\) \\  & & \(0.8\) & \(-0.868\times 10^{-3}\) \\ \cline{2-4}  & & \(0.1\) & \(-0.707\times 10^{-3}\) \\  & & \(0.5\) & \(-0.809\times 10^{-3}\) \\  & & \(0.8\) & \(-0.872\times 10^{-3}\) \\ \hline \multirow{6}{*}{\(-3\)} & \multirow{3}{*}{7} & \(0.1\) & \(-0.737\times 10^{-3}\) \\  & & \(0.5\) & \(-0.776\times 10^{-3}\) \\  & & \(0.8\) & \(-0.812\times 10^{-3}\) \\ \cline{2-4}  & & \(0.1\) & \(-0.718\times 10^{-3}\) \\  & & \(0.5\) & \(-0.859\times 10^{-3}\) \\  & & \(0.8\) & \(-0.877\times 10^{-3}\) \\ \cline{2-4}  & & \(0.1\) & \(-0.801\times 10^{-3}\) \\  & & \(0.5\) & \(-0.937\times 10^{-3}\) \\  & & \(0.8\) & \(-0.937\times 10^{-3}\) \\ \hline \multirow{6}{*}{\(-1\)} & \multirow{3}{*}{7} & \(0.1\) & \(-0.778\times 10^{-3}\) \\  & & \(0.5\) & \(-0.850\times 10^{-3}\) \\  & & \(0.8\) & \(-0.868\times 10^{-3}\) \\ \cline{2-4}  & & \(0.1\) & \(-0.737\times 10^{-3}\) \\  & & \(0.5\) & \(-0.851\times 10^{-3}\) \\  & & \(0.8\) & \(-0.833\times 10^{-3}\) \\ \cline{2-4}  & & \(0.1\) & \(-0.889\times 10^{-3}\) \\  & & \(0.5\) & \(-1.127\times 10^{-3}\) \\  & & \(0.8\) & \(-1.063\times 10^{-3}\) \\ \hline \multirow{6}{*}{\(1\)} & \multirow{3}{*}{7} & \(0.1\) & \(-0.831\times 10^{-3}\) \\  & & \(0.5\) & \(-0.849\times 10^{-3}\) \\  & & \(0.8\) & \(-0.886\times 10^{-3}\) \\ \cline{2-4}  & & \(0.1\) & \(-0.859\times 10^{-3}\) \\  & & \(0.5\) & \(-0.886\times 10^{-3}\) \\  & & \(0.8\) & \(-1.131\times 10^{-3}\) \\ \cline{2-4}  & & \(0.1\) & \(-0.890\times 10^{-3}\) \\  & & \(0.5\) & \(-0.849\times 10^{-3}\) \\  & & \(0.8\) & \(-0.886\times 10^{-3}\) \\ \hline \multirow{6}{*}{\(3\)} & \multirow{3}{*}{7} & \(0.1\) & \(-0.859\times 10^{-3}\) \\  & & \(0.5\) & \(-0.886\times 10^{-3}\) \\  & & \(0.8\) & \(-1.131\times 10^{-3}\) \\ \cline{2-4}  & & \(0.1\) & \(-0.890\times 10^{-3}\) \\  & & \(0.5\) & \(-1.068\times 10^{-3}\) \\  & & \(0.8\) & \(-0.941\times 10^{-3}\) \\ \hline \multirow{6}{*}{\(1\)} & \multirow{3}{*}{15} & \(0.1\) & \(-0.906\times 10^{-3}\) \\  & & \(0.5\) & \(-0.906\times 10^{-3}\) \\  & & \(0.8\) & \(-0.982\times 10^{-3}\) \\ \cline{2-4}  & & \(0.1\) & \(-0.877\times 10^{-3}\) \\ \cline{1-1}  & & \(0.5\) & \(-0.903\times 10^{-3}\) \\ \cline{1-1}  & & \(0.8\) & \(-1.017\times 10^{-3}\) \\ \cline{1-1} \cline{2-4}  & & \(0.1\) & \(-0.903\times 10^{-3}\) \\ \cline{1-1}  & & \(0.5\) & \(-0.873\times 10^{-3}\) \\ \cline{1-1}  & & \(0.8\) & \(-1.059\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Autocorrelation Scheme Delay Estimation with Multipath Gain Change. schemes mentioned above, one is to adjust the modulation parameters to separate the multipath, the other is to separate the multipath by using the correlation reception method after the spread spectrum of the signal. When the spectrum of 4 PPSK signal is spread, four quaternary symbols are corresponding to four different binary sequences, and then the binary sequence is modulated by the m-sequence, and finally the signal that needs to be transmitted is obtained by 4 PPSK modulation. The corresponding relationship is 0 corresponding to 00, 1 corresponding to 01, 2 corresponding to 11, and 3 corresponding to 10. The \(-40\) dB bandwidth of the two separated multipath schemes is shown in Table 3.  
As shown in Table 3, although both schemes can separate multipaths, the spread spectrum scheme has wider bandwidth than the modulation parameter adjustment scheme. The scheme of adjusting the modulation parameters can separate the multipath and eliminate the inter-symbol interference only by requiring appropriate modulation parameters, so the separation method is relatively simple.