## 2 Unipolar Optical Digital Modulation Schemes and Spreading Codes
### Unipolar Optical Digital Modulation Schemes
The value of empty slots \(d_{n}\in\big{\{}0,1,\ldots,2^{M-1}-1\big{\}}\) is the decimal value of the input block if the symbol starts with \(H_{1}\). If the symbol starts with \(H_{2}\), it is the decimal value of the 1's complement of the input code word. The header pulses play the dual role of symbol initiation and time reference for the preceding and succeeding symbols, resulting in built-in symbol synchronization. In other words, DH-PIM creates a symbol to enable built-in symbol synchronization. Thus, like the DPPM symbol, the DH-PIM removes the extra time slot after the pulse and increases the average symbol length compared with PIM, thus increasing data throughput. Comparisons of modulation techniques with fixed pulse width are based on various parameters, such as bandwidth occupancy, distortion, SNR, suitability for transmission channels, and error probability. No scheme yields optimal performance and negotiates all signals. For optical transmission, DPTMs are preferred because of their high pulse peak power and low average power characteristics. They require higher bandwidth than OOK, and provide a higher SNR. If \(M\)-bits are needed to present a symbol, OOK requires \(M\) time slots and maximum \(M\) pulses, but DPTM requires \(2^{M}\) time slots and one or two pulses. In the case of LIDAR, since the laser pulse reflected from the object is received, as shown in Equation (3), the higher the pulse peak power used for transmission, the longer the distance that can be measured. The pulse peak power is limited by the MPE, so the smaller the number of pulses, the higher the pulse peak power that can be used. Therefore, LIDAR can measure a longer distance by adopting a method such as DPTM, in which the number of pulses necessary for symbol representation is small. The disadvantage of DPTM is that it requires symbol synchronization and, therefore, more circuitry and complexity than other approaches, which are outside of the scope of this paper. Tables 1 and 2 [31; 40; 41; 42; 43; 44; 45; 50; 51] summarize the characteristics of \(M\)-bit input blocks when they are converted into symbols by OOK, PPM, DPPM, MPPM, DPIM, and DH-PIM, where \(R_{s}\) is the time slot rate and \(N_{0}\) is the energy of noise. In the case of optical communication, the influence of path loss can be ignored. The maximum transmitted energy is calculated using the received average energy. The received energy per bit, received energy per symbol, and power efficiency are calculated using the maximum transmitted energy. By contrast, in the case of LIDAR, the maximum energy to be emitted is fixed, and the reflected signal from the object is received. Thus, the influence of path loss must be reflected in the received energy. Therefore, in this paper, energy \(E_{TX}\) emitted from LIDAR is reflected off the surface of an object at a distance \(R\) away, and the received energy \(E_{RX}\) is calculated by Equation (3). \(\tau_{o}\) is the optics transmission; \(\tau_{a}\) is the atmospheric transmission; \(D_{R}\) is the receiver aperture diameter; \(\rho_{T}\) is the target surface reflectivity; and \(\theta_{R}\) is the target surface angular dispersion. The received energy per bit \(E_{b}\) and received energy per symbol \(E_{s}\) are calculated by Table 2. Table 3 [31; 40; 43; 44; 45; 50; 51; 53; 54; 55] summarizes the error probability of the digital pulse modulation techniques. The symbol error rate (SER) \(P_{se}\) is calculated by Equation (4) and Table 3, and the packet error rate (PER) \(P_{pe}\) by Equation (5) and Table 3 using \(E_{RX}\), which is the received energy according to each modulation technique. \(P_{0}\) is the probability of '0', \(P_{1}\) is the probability of '1', \(P_{e0}\) is the marginal probability of '0', \(P_{e1}\) is the marginal probability of '1', Q-function \(Q(x)\) is the probability that a standard Gaussian random variable takes a value larger than \(x\), \(M\) is the size of the bit block, \(N_{pkt}\) is the number of bits in a packet, and \(\bar{L}\) is the average symbol length.