## 3 Performance Evaluation of Combinations of Modulation and Spreading Code Techniques
### Performance Evaluation of Combined Techniques
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Spreading Codes** & **OOK** & **PPM** & **DPPM** & **MPPM** & **DPIM** & **DH-PIM\({}_{2}\)** \\ \hline Block partitioning & **1:2:2**:2:2** & **1:2:2:2** & **1:2:2**:2:2** & **1:2:2:2** & **2:2:2:1** & **2:2:2:2** \\ OOC \((31,3,1)\) & 29.19 mm & 30.16 mm & 30.41 mm & 29.19 mm & 30.16 mm & 29.51 mm \\ PC \(p=5\) & 29.05 mm & 29.72 mm & 29.25 mm & 29.05 mm & 29.47 mm & 29.05 mm \\ MPC \(p=5\), \(w=4\) & 29.12 mm & 29.99 mm & 29.33 mm & 29.21 mm & 29.54 mm & 29.64 mm \\ \hline Block partitioning & **1:2:3** & **1:2**:3:3 & **1:2**:3:3 & **1:2**:3:3 & **2:3:3:1** & **2:3:3** \\ OOC \((31,3,1)\) & 29.57 mm & 30.60 mm & 31.06 mm & 29.61 mm & 30.43 mm & 29.93 mm \\ PC \(p=5\) & 28.86 mm & 29.59 mm & 30.11 mm & 29.28 mm & 29.46 mm & 29.31 mm \\ MPC \(p=5\), \(w=4\) & 29.45 mm & 29.89 mm & 30.06 mm & 29.49 mm & 30.03 mm & 29.96 mm \\ \hline Block partitioning & **1:4**:4 & **1:4**:4 & **1:4** & **1:4**:4 & **4:4**:4** & **4:4** \\ OOC \((31,3,1)\) & 29.43 mm & 30.67 mm & 32.36 mm & 29.47 mm & 30.62 mm & 30.18 mm \\ PC \(p=5\) & 29.28 mm & 29.99 mm & 30.29 mm & 29.34 mm & 30.73 mm & 29.33 mm \\ MPC \(p=5\), \(w=4\) & 29.10 mm & 30.36 mm & 30.17 mm & 29.26 mm & 30.54 mm & 29.48 mm \\ \hline Block partitioning & **1:5**:3 & **1:5**:3 & **1:5**:3 & **1:5**:3 & **5:3**:**1 & **5:3**:**1 \\ OOC \((31,3,1)\) & 29.98 mm & 31.14 mm & 31.37 mm & 30.14 mm & 31.47 mm & 30.64 mm \\ PC \(p=5\) & 29.57 mm & 30.44 mm & 30.12 mm & 29.23 mm & 30.47 mm & 30.27 mm \\ MPC \(p=5\), \(w=4\) & 29.66 mm & 30.56 mm & 30.91 mm & 29.58 mm & 30.91 mm & 29.74 mm \\ \hline Block partitioning & **1:8** & **1:8** & **1:8** & **1:8** & **8:1** & **8:1** \\ OOC \((31,3,1)\) & 29.92 mm & 32.88 mm & 32.31 mm & 30.34 mm & 32.82 mm & 31.95 mm \\ PC \(p=5\) & 29.11 mm & 30.56 mm & 31.13 mm & 29.70 mm & 30.93 mm & 30.30 mm \\ MPC \(p=5\), \(w=4\) & 29.34 mm & 31.54 mm & 31.71 mm & 29.55 mm & 31.86 mm & 31.05 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Precision as a combination of modulation and spreading code. to the modulation technique was negligible. Therefore, in the LIDAR system, it is best to use the combination with the lowest number of pulses satisfying the maximum allowable transmission time. Of the combinations we evaluated, the combination of using PPM, DPPM, or DPIM as the modulation technique and using OOC as the spreading code technique could measure the farthest distance. The relationship between maximum distance and accuracy by the combination of modulation schemes and spreading codes can be divided into two groups with similar trends. One group is indicated as OOK, MPPM, and DH-PIM, shown in Figure 4a, and Figure 4b shows the other group as PPM, DPPM, and DPIM. As the prototype LIDAR system applies the communication scheme, the system error probability by Equation (6) according to the combination of the modulation scheme and the spreading technique used for transmission is shown in Table 17. The PER \(P_{pe}\) of the modulation method by Equation (5) and Table 3 was calculated using the received energy \(E_{RX}\) by Equation (3), reflected from the object at the maximum distance \(R_{max}\) in Table 14. The bit error probability according to the spreading code \(P_{sc}\) was calculated using Table 8. Additional parameters required for the calculation were used from Tables 12-14. If the received data had an error, the measured distance for the relevant measurement point was ignored. The combination of all the modulation and spreading codes we evaluated showed a very low error rate. As long as the number of points to be measured does not exceed the cardinality of the spreading code, the current combinations can be used reliably. \[P_{sys}=P_{sc}-\left(1-P_{sc}\right)P_{pe} \tag{6}\]  
Figure 4: Relationship between the maximum distance and accuracy: (**a**) the combination of using OOK, MPPM, and DH-PIM; (**b**) the combination of using PPM, DPPM, and DPIM.