# Suitable Combination of Direct Intensity Modulation and Spreading Sequence for LIDAR with Pulse Coding

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Unipolar Optical Digital Modulation Schemes and Spreading Codes

#### 2.1. Unipolar Optical Digital Modulation Schemes

#### 2.2. One-Dimensional Optical Spreading Codes

## 3. Performance Evaluation of Combinations of Modulation and Spreading Code Techniques

#### 3.1. Combinations of Modulation and Spreading Code Techniques

**1**:4:4,

**1**:5:3,

**1**:6:2, and

**1**:7:1 have equal numbers of ‘1’s and different numbers of ‘0’s, and then they have very similar performance. Therefore, block partitioning

**1**:4:4 and

**1**:5:3 were selected as two representatives of four three-small-piece block partitionings. The prototype LIDAR system is a non-directional non-line of sight (NLOS) optical wireless communication system that uses Lambertian diffusion. Eye safety is a critical issue in optical wireless systems because optical signals can penetrate the human cornea and potentially cause thermal damage to the retina. Optical transmitters must comply with the class 1 of the International Electrotechnical Commission (IEC) standard. The MPE is the highest power or energy density of a light source considered safe (i.e., less likely to cause damage).

- Symbol stream;
- Block size and partitioning;
- Pulse peak power;
- Number of time slots;
- Number of pulses;
- Leading ‘$\mathbf{1}$’ or trailing ‘$\mathbf{1}$’.

#### 3.2. Performance Evaluation of Combined Techniques

- A nine-bit block was used to identify each measurement point, and the first bit was always ‘1’;
- Up to five measurement points could be measured simultaneously;
- Pulse width was fixed at 5 ns and pulse transmission was completed within 67 μs;
- The maximum output of the laser pulse was eye-safety class 1 compliant;
- The maximum desired distance: 150 $\mathrm{m}$;
- Range gate: 1 μs;
- Probability of false alarm: 0.5;
- False alarm rate: 500,000/s;
- TNR: $9.8$ dB.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

ADC | Analog-to-digital converter |

AMCW | Amplitude-modulated continuous wave |

ASPRS | American Society for Photogrammetry and Remote Sensing |

BER | Bit error rate |

CID | Column identification number |

CRC | Cyclic redundancy check |

DPIM | Digital pulse interval modulation |

DPPM | Differential pulse position modulation |

DH-PIM | Dual-header pulse interval modulation |

DPTM | Digital pulse time modulation |

DSP | Digital signal processor |

FMCW | Frequency-modulated continuous wave |

GaAs | Gallium arsenide |

GS | Guard slot |

IEC | International electrotechnical commission |

IM/DD | Intensity-modulated direct detection |

LIDAR | Light detection and ranging |

MEMS | Microelectromechanical systems |

MPE | Maximum permissible rxposure |

MPC | Modified prime code |

MPPM | Multipulse pulse position modulation |

MSB | Most significant bit |

NLOS | Non-line of sight |

NRZ | Non-return-to-zero |

OCDMA | Optical code division multiple access |

OOC | Optical orthogonal code |

OOK | On–off keying |

PC | Prime code |

PER | Packet error rate |

PIN | Positive–intrinsic–negative |

PPM | Pulse position modulation |

RID | Row identification number |

RF | Radio frequency |

RMSE | Root-mean-square-error |

RZ | Return-to-zero |

SER | Time slot error rate |

SNR | Signal-to-noise ratio |

TDMA | Time-division multiple access |

TIA | TransImpedance amplifier |

TNR | Threshold-to-noise ratio |

ToF | Time-of-flight |

WDMA | Wavelength-division multiple access |

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**Figure 1.**Overall architecture and operation flow of the proposed scanning light detection and ranging (LIDAR) system. A/D: Analog-to-digital; CRC: Cyclic redundancy check; MEMS: Microelectromechanical systems; PIN: Positive–intrinsic–negative; RX: Receiver; ToF: Time-of-flight; TX: Transmitter.

**Figure 2.**Time waveforms for on–off keying (OOK), pulse position modulation (PPM), differential PPM (DPPM), multipulse PPM (MPPM), digital pulse interval modulation (DPIM), and dual-header pulse interval modulation (DH-PIM) signals. The different symbols for the different modulation schemes shown in the figure are denoted by different colors.

**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.

Modulation | Number of Bits per Block(M) | Maximum Number of Pulses (${\mathit{N}}_{\mathit{p}}$) | Number of Possible Unique Symbols (L) | Maximum Number of Time Slots (${\mathit{L}}_{\mathit{max}}$) | Average Symbol Length ($\overline{\mathit{L}}$) | Slot Duration (${\mathit{T}}_{\mathit{s}}$) | Bandwidth Requirements (${\mathit{B}}_{\mathit{req}}$) |
---|---|---|---|---|---|---|---|

NRZ-OOK | M | M | ${2}^{M}$ | M | M | $\frac{1}{{R}_{s}}$ | ${R}_{s}$ |

PPM | M | 1 | ${2}^{M}$ | ${L}_{PPM}$ | ${L}_{PPM}$ | $\frac{1}{{R}_{s}}$ | $\frac{M{R}_{s}}{{L}_{PPM}}$ |

DPPM | M | 1 | ${2}^{M}$ | ${L}_{DPPM}$ | $\frac{{L}_{DPPM}+1}{2}$ | $\frac{1}{{R}_{s}}$ | $\frac{2M{R}_{s}}{{L}_{DPPM}+1}$ |

MPPM | $\lfloor {log}_{2}L\rfloor $ | w | $\left(\right)$ | n | n | $\frac{1}{{R}_{s}}$ | $\frac{M{R}_{s}}{n}$ |

DPIM | M | 1 | ${2}^{M}$ | ${L}_{DPIM}$ | $\frac{{L}_{DPIM}+1}{2}$ | $\frac{1}{{R}_{s}}$ | $\frac{2M{R}_{s}}{{L}_{DPIM}+1}$ |

DH-PIM | M | 2 | ${2}^{M}$ | ${2}^{M-1}+\alpha $ | $\frac{{2}^{M-1}+2\alpha +1}{2}$ | $\frac{1}{{R}_{s}}$ | $\frac{2M{R}_{s}}{{2}^{M-1}+2\alpha +1}$ |

Modulation | Peak-To-Average Power Ratio of Symbol (PAPR) | Peak Current of a Symbol (${\mathit{I}}_{\mathit{p}}$) | Energy of a Symbol (${\mathit{E}}_{\mathit{s}}$) | Energy of a Bit (${\mathit{E}}_{\mathit{b}}$) |
---|---|---|---|---|

NRZ-OOK | 2 | $2{\overline{E}}_{RX\_OOK}$ | $\frac{4{\overline{E}}_{RX\_OOK}^{2}}{{R}_{s}}$ | $\frac{4{\overline{E}}_{RX\_OOK}^{2}}{{R}_{s}}$ |

PPM | ${L}_{PPM}$ | ${L}_{PPM}{\overline{E}}_{RX\_PPM}$ | $\frac{{L}_{PPM}^{2}{\overline{E}}_{RX\_PPM}^{2}}{{R}_{s}}$ | $\frac{{L}_{PPM}^{3}{\overline{E}}_{RX\_PPM}^{2}}{M{R}_{s}}$ |

DPPM | $\frac{{L}_{DPPM}+1}{2}$ | $\frac{({L}_{DPPM}+1){\overline{E}}_{RX\_DPPM}}{2}$ | $\frac{{({L}_{DPPM}+1)}^{2}{\overline{E}}_{RX\_DPPM}^{2}}{4{R}_{s}}$ | $\frac{{({L}_{DPPM}+1)}^{3}{\overline{E}}_{RX\_DPPM}^{3}}{8M{R}_{s}}$ |

MPPM | $\frac{n}{w}$ | $\frac{n{\overline{E}}_{RX\_MPPM}}{w}$ | $\frac{{n}^{2}{\overline{E}}_{RX\_MPPM}^{2}}{{w}^{2}{R}_{s}}$ | $\frac{{n}^{3}{\overline{E}}_{RX\_MPPM}^{3}}{{w}^{2}M{R}_{s}}$ |

DPIM | $\frac{{L}_{DPIM}+1}{2}$ | $\frac{({L}_{DPIM}+1)bar{E}_{RX\_DPIM}}{2}$ | $\frac{{({L}_{DPIM}+1)}^{2}{\overline{E}}_{RX\_DPIM}^{2}}{4{R}_{s}}$ | $\frac{{({L}_{DPIM}+1)}^{3}{\overline{E}}_{RX\_DPIM}^{3}}{8M{R}_{s}}$ |

DH-PIM | $\frac{2\left(\right)open="("\; close=")">{2}^{M-1}+2\alpha +1}{}$ | $\frac{2\left(\right)open="("\; close=")">{2}^{M-1}+2\alpha +1}{{\overline{E}}_{RX\_DH-PIM}}$ | $\frac{4{\left(\right)}^{{2}^{M-1}}2}{{\overline{E}}_{RX\_DH-PIM}^{2}}$ | $\frac{2{\left(\right)}^{{2}^{M-1}}3}{{\overline{E}}_{RX\_DH-PIM}^{3}}$ |

Modulation | Probability of ‘0’ (${\mathit{P}}_{0}$) | Probability of ‘1’ (${\mathit{P}}_{1}$) | Marginal Probability of ‘0’(${\mathit{P}}_{\mathit{\u03f5}0}$) | Optimum Symbol Error Probability (${\mathit{P}}_{\mathit{se}-\mathit{opt}}$) |
---|---|---|---|---|

NRZ-OOK | $\frac{1}{2}$ | $\frac{1}{2}$ | $Q\left(\right)open="("\; close=")">\frac{k{\overline{E}}_{RX\_OOK}}{\sqrt{{N}_{0}{R}_{s}}}$ | $Q\left(\right)open="("\; close=")">\frac{{\overline{E}}_{RX\_OOK}}{2\sqrt{{N}_{0}{R}_{s}}}$ |

PPM | $\frac{{L}_{PPM}-1}{{L}_{PPM}}$ | $\frac{1}{{L}_{PPM}}$ | $Q\left(\right)open="("\; close=")">\frac{k{L}_{PPM}{\overline{E}}_{RX\_PPM}}{\sqrt{{N}_{0}{R}_{s}}}$ | $Q\left(\right)open="("\; close=")">\frac{{L}_{PPM}{\overline{E}}_{RX\_PPM}}{2\sqrt{{N}_{0}{R}_{s}}}$ |

DPPM | $\frac{{L}_{DPPM}-1}{{L}_{DPPM}+1}$ | $\frac{2}{{L}_{DPPM}+1}$ | $Q\left(\right)open="("\; close=")">\frac{k\left(\right)open="("\; close=")">{L}_{LPPM}+1}{{\overline{E}}_{RX\_DPPM}}2\sqrt{{N}_{0}{R}_{s}}$ | $Q\left(\right)open="("\; close=")">\frac{\left(\right)open="("\; close=")">{L}_{DPPM}+1}{{\overline{E}}_{RX\_DPPM}}4\sqrt{{N}_{0}{R}_{s}}$ |

MPPM | $\frac{n-w}{n}$ | $\frac{w}{n}$ | $Q\left(\right)open="("\; close=")">\frac{kn{\overline{E}}_{RX\_MPPM}}{w\sqrt{{N}_{0}{R}_{s}}}$ | $Q\left(\right)open="("\; close=")">\frac{n{\overline{E}}_{RX\_MPPM}}{4w\sqrt{{N}_{0}{R}_{s}}}$ |

DPIM | $\frac{{L}_{DPIM}-1}{{L}_{DPIM}+1}$ | $\frac{2}{{L}_{DPIM}+1}$ | $Q\left(\right)open="("\; close=")">\frac{k\left(\right)open="("\; close=")">{L}_{DPIM}+1}{{\overline{E}}_{RX\_DPIM}}2\sqrt{{N}_{0}{R}_{s}}$ | $Q\left(\right)open="("\; close=")">\frac{\left(\right)open="("\; close=")">{L}_{DPIM}+1}{{\overline{E}}_{RX\_DPIM}}4\sqrt{{N}_{0}{R}_{s}}$ |

DH-PIM | $\frac{4{\overline{L}}_{DH-PIM}-3\alpha}{{\overline{L}}_{DH-PIM}}$ | $\frac{3\alpha}{{\overline{L}}_{DH-PIM}}$ | $Q\left(\right)open="("\; close=")">\frac{2k\left(\right)open="("\; close=")">{2}^{M-1}+2\alpha +1}{{\overline{E}}_{RX\_DH-PIM}}3\alpha \sqrt{{N}_{0}{R}_{s}}$ | $Q\left(\right)open="("\; close=")">\frac{\left(\right)open="("\; close=")">{2}^{M-1}+2\alpha +1}{{\overline{E}}_{RX\_DH-PIM}}3\alpha \sqrt{{N}_{0}{R}_{s}}$ |

N | Sequence Index, When $\mathit{N}\le 49$ |
---|---|

7 | $\{1,2,4\}$ |

13 | $\{1,2,5\},\{1,3,8\}$ |

19 | $\{1,2,6\},\{1,3,9\},\{1,4,11\}$ |

25 | $\{1,2,7\},\{1,3,10\},\{1,4,12\},\{1,5,14\}$ |

31 | $\{1,2,8\},\{1,3,12\},\{1,4,16\},\{1,5,15\},\{1,6,14\}$ |

37 | $\{1,2,12\},\{1,3,10\},\{1,4,18\},\{1,5,13\},\{1,6,19\},\{1,7,13\}$ |

43 | $\{1,2,20\},\{1,3,23\},\{1,4,16\},\{15,14\},\{1,6,17\},\{1,7,15\},\{1,8,19\}$ |

Index | Sequence Code |
---|---|

$\{1,2,8\}$ | $11000\phantom{\rule{3.33333pt}{0ex}}00100\phantom{\rule{3.33333pt}{0ex}}00000\phantom{\rule{3.33333pt}{0ex}}00000\phantom{\rule{3.33333pt}{0ex}}00000\phantom{\rule{3.33333pt}{0ex}}00000\phantom{\rule{3.33333pt}{0ex}}0$ |

$\{1,3,12\}$ | $10100\phantom{\rule{3.33333pt}{0ex}}00000\phantom{\rule{3.33333pt}{0ex}}01000\phantom{\rule{3.33333pt}{0ex}}00000\phantom{\rule{3.33333pt}{0ex}}00000\phantom{\rule{3.33333pt}{0ex}}00000\phantom{\rule{3.33333pt}{0ex}}0$ |

$\{1,4,16\}$ | $10010\phantom{\rule{3.33333pt}{0ex}}00000\phantom{\rule{3.33333pt}{0ex}}00000\phantom{\rule{3.33333pt}{0ex}}10000\phantom{\rule{3.33333pt}{0ex}}00000\phantom{\rule{3.33333pt}{0ex}}00000\phantom{\rule{3.33333pt}{0ex}}0$ |

$\{1,5,15\}$ | $10001\phantom{\rule{3.33333pt}{0ex}}00000\phantom{\rule{3.33333pt}{0ex}}00001\phantom{\rule{3.33333pt}{0ex}}00000\phantom{\rule{3.33333pt}{0ex}}00000\phantom{\rule{3.33333pt}{0ex}}00000\phantom{\rule{3.33333pt}{0ex}}0$ |

$\{1,6,14\}$ | $10000\phantom{\rule{3.33333pt}{0ex}}10000\phantom{\rule{3.33333pt}{0ex}}00010\phantom{\rule{3.33333pt}{0ex}}00000\phantom{\rule{3.33333pt}{0ex}}00000\phantom{\rule{3.33333pt}{0ex}}00000\phantom{\rule{3.33333pt}{0ex}}0$ |

Groups | i | PC Sequence | PC Sequence Code | ||||
---|---|---|---|---|---|---|---|

x | 0 | 1 | 2 | 3 | 4 | ||

0 | 0 | 0 | 0 | 0 | 0 | ${S}_{0}$ | ${C}_{0}=10000\phantom{\rule{3.33333pt}{0ex}}10000\phantom{\rule{3.33333pt}{0ex}}10000\phantom{\rule{3.33333pt}{0ex}}10000\phantom{\rule{3.33333pt}{0ex}}10000$ |

1 | 0 | 1 | 2 | 3 | 4 | ${S}_{1}$ | ${C}_{1}=10000\phantom{\rule{3.33333pt}{0ex}}01000\phantom{\rule{3.33333pt}{0ex}}00100\phantom{\rule{3.33333pt}{0ex}}00010\phantom{\rule{3.33333pt}{0ex}}00001$ |

2 | 0 | 2 | 4 | 1 | 3 | ${S}_{2}$ | ${C}_{2}=10000\phantom{\rule{3.33333pt}{0ex}}00100\phantom{\rule{3.33333pt}{0ex}}00001\phantom{\rule{3.33333pt}{0ex}}01000\phantom{\rule{3.33333pt}{0ex}}00010$ |

3 | 0 | 3 | 1 | 4 | 2 | ${S}_{3}$ | ${C}_{3}=10000\phantom{\rule{3.33333pt}{0ex}}00010\phantom{\rule{3.33333pt}{0ex}}01000\phantom{\rule{3.33333pt}{0ex}}00001\phantom{\rule{3.33333pt}{0ex}}00100$ |

4 | 0 | 4 | 3 | 2 | 1 | ${S}_{4}$ | ${C}_{4}=10000\phantom{\rule{3.33333pt}{0ex}}00001\phantom{\rule{3.33333pt}{0ex}}00010\phantom{\rule{3.33333pt}{0ex}}10000\phantom{\rule{3.33333pt}{0ex}}01000$ |

Groups | i | MPC Sequence | MPC Sequence Code | |||
---|---|---|---|---|---|---|

x | ${\mathit{a}}_{0}$ | ${\mathit{a}}_{1}$ | ${\mathit{a}}_{2}$ | ${\mathit{a}}_{3}$ | ||

0 | 0 | 0 | 0 | 0 | ${S}_{0}^{\prime}$ | ${C}_{0}^{\prime}=10000\phantom{\rule{3.33333pt}{0ex}}10000\phantom{\rule{3.33333pt}{0ex}}10000\phantom{\rule{3.33333pt}{0ex}}10000\phantom{\rule{3.33333pt}{0ex}}00000$ |

1 | 0 | 1 | 2 | 3 | ${S}_{1}^{\prime}$ | ${C}_{1}^{\prime}=10000\phantom{\rule{3.33333pt}{0ex}}01000\phantom{\rule{3.33333pt}{0ex}}00100\phantom{\rule{3.33333pt}{0ex}}00010\phantom{\rule{3.33333pt}{0ex}}00000$ |

2 | 0 | 2 | 4 | 1 | ${S}_{2}^{\prime}$ | ${C}_{2}^{\prime}=10000\phantom{\rule{3.33333pt}{0ex}}00100\phantom{\rule{3.33333pt}{0ex}}00001\phantom{\rule{3.33333pt}{0ex}}01000\phantom{\rule{3.33333pt}{0ex}}00000$ |

3 | 0 | 3 | 1 | 4 | ${S}_{3}^{\prime}$ | ${C}_{3}^{\prime}=10000\phantom{\rule{3.33333pt}{0ex}}00010\phantom{\rule{3.33333pt}{0ex}}01000\phantom{\rule{3.33333pt}{0ex}}00001\phantom{\rule{3.33333pt}{0ex}}00000$ |

4 | 0 | 4 | 3 | 2 | ${S}_{4}^{\prime}$ | ${C}_{4}^{\prime}=10000\phantom{\rule{3.33333pt}{0ex}}00001\phantom{\rule{3.33333pt}{0ex}}00010\phantom{\rule{3.33333pt}{0ex}}10000\phantom{\rule{3.33333pt}{0ex}}00000$ |

Characteristics | OOC $(\mathit{N},\mathit{w},1)$ | PC | MPC |
---|---|---|---|

Length | N | ${p}^{2}$ | ${p}^{2}$ |

Weight | w | p | w |

Peak auto-correlation | 1 | p | w |

Peak cross-correlation | 1 | 1 | 1 |

Cardinality | $\lfloor \frac{N-1}{w(w-1)}\rfloor $ | p | p |

Bit error probability (${P}_{sc}$) | $\frac{1}{2}{\displaystyle \sum _{i=0}^{w}}{(-1)}^{i}\left(\right)open="("\; close=")">\genfrac{}{}{0pt}{}{w}{i}{\left(\right)}^{1}M-1$ | $\frac{1}{2}{\displaystyle \sum _{i=0}^{p}}{(-1)}^{i}\left(\right)open="("\; close=")">\genfrac{}{}{0pt}{}{p}{i}{\left(\right)}^{1}M-1$ | $\frac{1}{2}{\displaystyle \sum _{i=0}^{\frac{w}{2}}}{(-1)}^{i}\left(\right)open="("\; close=")">\genfrac{}{}{0pt}{}{\frac{w}{2}}{i}{\left(\right)}^{1}M-1$ |

Source Symbol | OOK | 8-PPM | 8-DPPM | 2-5MPPM | 8-DPIM | 8-DH-PIM${}_{2}$ |
---|---|---|---|---|---|---|

0 | 000 | 10000000 | 1 | 10001 | 1 | 100 |

1 | 001 | 01000000 | 01 | 01100 | 10 | 1000 |

2 | 010 | 00100000 | 001 | 01001 | 100 | 10000 |

3 | 011 | 00010000 | 0001 | 10010 | 1000 | 100000 |

4 | 100 | 00001000 | 00001 | 11000 | 10000 | 110000 |

5 | 101 | 00000100 | 000001 | 00101 | 100000 | 11000 |

6 | 110 | 00000010 | 0000001 | 00011 | 1000000 | 1100 |

7 | 111 | 00000001 | 00000001 | 10100 | 10000000 | 110 |

**Table 10.**Possible modulation schemes according to the size of the bit input block. Each cell expresses the modulated results as a 2-tuple $\left(\right)$, where ${N}_{p}$ is the maximum number of pulses and ${L}_{max}$ is the maximum number of time slots.

Block Size (M) | M-OOK | M-PPM | M-DPPM | 2-nMPPM | M-DPIM | M-DH-PIM${}_{2}$ |
---|---|---|---|---|---|---|

1-bit | 1, 1 | 1, 2 | 1, 2 | 2, 3 | 1, 2 | 2, 3 |

2-bit | 2, 2 | 1, 4 | 1, 4 | 2, 4 | 1, 4 | 2, 4 |

3-bit | 3, 3 | 1, 8 | 1, 8 | 2, 5 | 1, 8 | 2, 6 |

4-bit | 4, 4 | 1, 16 | 1, 16 | 2, 6 | 1, 16 | 2, 10 |

5-bit | 5, 5 | 1, 32 | 1, 32 | 2, 9 | 1, 32 | 2, 18 |

6-bit | 6, 6 | 1, 64 | 1, 64 | 2, 12 | 1, 64 | 2, 34 |

7-bit | 7, 7 | 1, 128 | 1, 128 | 2, 17 | 1, 128 | 2, 66 |

8-bit | 8, 8 | 1, 256 | 1, 256 | 2, 24 | 1, 256 | 2, 129 |

9-bit | 9, 9 | 1, 512 | 1, 512 | 2, 33 | 1, 512 | 2, 258 |

**Table 11.**Possible block partitioning according to block partitioning and modulation techniques. A bold ‘

**1**’ shows a leading ‘1’ or a trailing ‘1’. Each cell expresses the modulated results as a 2-tuple $\left(\right)$.

Block Paritioning | OOK | PPM | DPPM | MPPM | DPIM | DH-PIM${}_{2}$ |
---|---|---|---|---|---|---|

1:2:2:2:2 | 9, 9 | 5, 17 | 5, 17 | 9, 17 | ||

2:2:2:2:1 | 5, 17 | 9, 17 | ||||

1:2:3:3 | 9, 9 | 4, 21 | 4, 21 | 7, 15 | ||

2:3:3:1 | 4, 21 | 7, 17 | ||||

1:4:4 | 9, 9 | 3, 33 | 3, 33 | 5, 13 | ||

4:4:1 | 3, 33 | 5, 21 | ||||

1:5:3 | 9, 9 | 3, 41 | 3, 41 | 5, 15 | ||

5:3:1 | 3, 41 | 5, 25 | ||||

1:6:2 | 9, 9 | 3, 69 | 3, 69 | 5, 17 | ||

6:2:1 | 3, 69 | 5, 29 | ||||

1:7:1 | 9, 9 | 3, 131 | 3, 131 | 5, 21 | ||

7:1:1 | 3, 131 | 5, 70 | ||||

1:8 | 9, 9 | 2, 257 | 2, 257 | 3, 25 | ||

8:1 | 2, 257 | 3, 131 |

**Table 12.**Number of pulses ${N}_{p}$ and time slots ${L}_{max}$ as a combination of block partitioning, modulation, and spreading code. Each cell expresses the modulated and spread results as a 2-tuple $\left(\right)$.

Spreading Codes | OOK | PPM | DPPM | MPPM | DPIM | DH-PIM${}_{2}$ |
---|---|---|---|---|---|---|

Block partitioning | 1:2:2:2:2 | 1:2:2:2:2 | 1:2:2:2:2 | 1:2:2:2:2 | 2:2:2:2:1 | 2:2:2:2:1 |

OOC $(31,3,1)$ | $27,279$ | $15,527$ | $15,527$ | $27,527$ | $15,527$ | $27,527$ |

PC $p=5$ | $45,225$ | $25,425$ | $25,425$ | $45,425$ | $25,425$ | $45,425$ |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | $36,225$ | $20,425$ | $20,425$ | $36,425$ | $20,425$ | $36,425$ |

Block partitioning | 1:2:3:3 | 1:2:3:3 | 1:2:3:3 | 1:2:3:3 | 2:3:3:1 | 2:3:3:1 |

OOC $(31,3,1)$ | $27,279$ | $12,651$ | $12,651$ | $21,465$ | $12,651$ | $21,527$ |

PC $p=5$ | $45,225$ | $20,525$ | $20,525$ | $35,375$ | $20,525$ | $35,425$ |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | $36,225$ | $16,525$ | $16,525$ | $28,375$ | $16,525$ | $28,425$ |

Block partitioning | 1:4:4 | 1:4:4 | 1:4:4 | 1:4:4 | 4:4:1 | 4:4:1 |

OOC $(31,3,1)$ | $27,279$ | $9,1023$ | $9,1023$ | $15,403$ | $9,1023$ | $15,651$ |

PC $p=5$ | $45,225$ | $15,825$ | $15,825$ | $25,325$ | $15,825$ | $25,525$ |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | $36,225$ | $12,825$ | $12,825$ | $20,325$ | $12,825$ | $20,525$ |

Block partitioning | 1:5:3 | 1:5:3 | 1:5:3 | 1:5:3 | 5:3:1 | 5:3:1 |

OOC $(31,3,1)$ | $27,279$ | $9,1271$ | $9,1271$ | $15,465$ | $9,1271$ | $15,775$ |

PC $p=5$ | $45,225$ | $15,1025$ | $15,1025$ | $25,375$ | $15,1025$ | $25,625$ |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | $36,225$ | $12,1025$ | $12,1025$ | $20,375$ | $12,1025$ | $20,625$ |

Block partitioning | 1:8 | 1:8 | 1:8 | 1:8 | 8:1 | 8:1 |

OOC $(31,3,1)$ | $27,279$ | $6,7967$ | $6,7967$ | $15,775$ | $6,7967$ | $9,4061$ |

PC $p=5$ | $45,225$ | $10,6425$ | $10,6425$ | $25,625$ | $10,6425$ | $15,3275$ |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | $36,225$ | $8,6425$ | $8,6425$ | $20,625$ | $8,6425$ | $12,3275$ |

**Table 13.**Pulse peak power ${E}_{TX}$ as a combination of block partitioning, modulation, and spreading code.

Spreading Codes | OOK | PPM | DPPM | MPPM | DPIM | DH-PIM${}_{2}$ |
---|---|---|---|---|---|---|

Block partitioning | 1:2:2:2:2 | 1:2:2:2:2 | 1:2:2:2:2 | 1:2:2:2:2 | 2:2:2:2:1 | 2:2:2:2:1 |

OOC $(31,3,1)$ | $8.9143$$$$\mathrm{nJ}$ | $10.3254$$$$\mathrm{nJ}$ | $10.3254$$$$\mathrm{nJ}$ | $8.9143$$$$\mathrm{nJ}$ | $10.3254$$$$\mathrm{nJ}$ | $8.9143$$$$\mathrm{nJ}$ |

PC $p=5$ | $7.8456$$$$\mathrm{nJ}$ | $9.0895$$$$\mathrm{nJ}$ | $9.0895$$$$\mathrm{nJ}$ | $7.8456$$$$\mathrm{nJ}$ | $9.0895$$$$\mathrm{nJ}$ | $7.8456$$$$\mathrm{nJ}$ |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | $8.2957$$$$\mathrm{nJ}$ | $9.6088$$$$\mathrm{nJ}$ | $9.6088$$$$\mathrm{nJ}$ | $8.2957$$$$\mathrm{nJ}$ | $9.6088$$$$\mathrm{nJ}$ | $8.2957$$$$\mathrm{nJ}$ |

Block partitioning | 1:2:3:3 | 1:2:3:3 | 1:2:3:3 | 1:2:3:3 | 2:3:3:1 | 2:3:3:1 |

OOC $(31,3,1)$ | $8.9143$$$$\mathrm{nJ}$ | $10.9178$$$$\mathrm{nJ}$ | $10.9178$$$$\mathrm{nJ}$ | $9.4923$$$$\mathrm{nJ}$ | $10.9178$$$$\mathrm{nJ}$ | $9.4923$$$$\mathrm{nJ}$ |

PC $p=5$ | $7.8456$$$$\mathrm{nJ}$ | $9.6088$$$$\mathrm{nJ}$ | $9.6088$$$$\mathrm{nJ}$ | $8.4543$$$$\mathrm{nJ}$ | $9.6088$$$$\mathrm{nJ}$ | $8.4543$$$$\mathrm{nJ}$ |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | $8.2957$$$$\mathrm{nJ}$ | $10.1601$$$$\mathrm{nJ}$ | $10.1601$$$$\mathrm{nJ}$ | $8.8336$$$$\mathrm{nJ}$ | $10.1601$$$$\mathrm{nJ}$ | $8.8336$$$$\mathrm{nJ}$ |

Block partitioning | 1:4:4 | 1:4:4 | 1:4:4 | 1:4:4 | 4:4:1 | 4:4:1 |

OOC $(31,3,1)$ | $8.9143$$$$\mathrm{nJ}$ | $11.7319$$$$\mathrm{nJ}$ | $11.7319$$$$\mathrm{nJ}$ | $10.3254$$$$\mathrm{nJ}$ | $11.7319$$$$\mathrm{nJ}$ | $10.3254$$$$\mathrm{nJ}$ |

PC $p=5$ | $7.8456$$$$\mathrm{nJ}$ | $10.3254$$$$\mathrm{nJ}$ | $10.3254$$$$\mathrm{nJ}$ | $9.0895$$$$\mathrm{nJ}$ | $10.3254$$$$\mathrm{nJ}$ | $9.0895$$$$\mathrm{nJ}$ |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | $8.2957$$$$\mathrm{nJ}$ | $10.9178$$$$\mathrm{nJ}$ | $10.9178$$$$\mathrm{nJ}$ | $9.6088$$$$\mathrm{nJ}$ | $10.9178$$$$\mathrm{nJ}$ | $9.6088$$$$\mathrm{nJ}$ |

Block partitioning | 1:5:3 | 1:5:3 | 1:5:3 | 1:5:3 | 5:3:1 | 5:3:1 |

OOC $(31,3,1)$ | $8.9143$$$$\mathrm{nJ}$ | $11.7319$$$$\mathrm{nJ}$ | $11.7319$$$$\mathrm{nJ}$ | $10.3254$$$$\mathrm{nJ}$ | $11.7319$$$$\mathrm{nJ}$ | $10.3254$$$$\mathrm{nJ}$ |

PC $p=5$ | $7.8456$$$$\mathrm{nJ}$ | $10.3254$$$$\mathrm{nJ}$ | $10.3254$$$$\mathrm{nJ}$ | $9.0895$$$$\mathrm{nJ}$ | $10.3254$$$$\mathrm{nJ}$ | $9.0895$$$$\mathrm{nJ}$ |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | $8.2957$$$$\mathrm{nJ}$ | $10.9178$$$$\mathrm{nJ}$ | $10.9178$$$$\mathrm{nJ}$ | $9.6088$$$$\mathrm{nJ}$ | $10.9178$$$$\mathrm{nJ}$ | $9.6088$$$$\mathrm{nJ}$ |

Block partitioning | 1:8 | 1:8 | 1:8 | 1:8 | 8:1 | 8:1 |

OOC $(31,3,1)$ | $8.9143$$$$\mathrm{nJ}$ | $12.9835$$$$\mathrm{nJ}$ | $12.9835$$$$\mathrm{nJ}$ | $10.3254$$$$\mathrm{nJ}$ | $12.9835$$$$\mathrm{nJ}$ | $11.7319$$$$\mathrm{nJ}$ |

PC $p=5$ | $7.8456$$$$\mathrm{nJ}$ | $11.4269$$$$\mathrm{nJ}$ | $11.4269$$$$\mathrm{nJ}$ | $9.0895$$$$\mathrm{nJ}$ | $11.4269$$$$\mathrm{nJ}$ | $10.3254$$$$\mathrm{nJ}$ |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | $8.2957$$$$\mathrm{nJ}$ | $12.0825$$$$\mathrm{nJ}$ | $12.0825$$$$\mathrm{nJ}$ | $9.6088$$$$\mathrm{nJ}$ | $12.0825$$$$\mathrm{nJ}$ | $10.9178$$$$\mathrm{nJ}$ |

Spreading Codes | OOK | PPM | DPPM | MPPM | DPIM | DH-PIM ${}_{2}$ |
---|---|---|---|---|---|---|

Block partitioning | 1:2:2:2:2 | 1:2:2:2:2 | 1:2:2:2:2 | 1:2:2:2:2 | 2:2:2:2:1 | 2:2:2:2:1 |

OOC $(31,3,1)$ | 95 $\mathrm{m}$ | 102 $\mathrm{m}$ | 102 $\mathrm{m}$ | 95 $\mathrm{m}$ | 102 $\mathrm{m}$ | 95 $\mathrm{m}$ |

PC $p=5$ | 89 $\mathrm{m}$ | 96 $\mathrm{m}$ | 96 $\mathrm{m}$ | 89 $\mathrm{m}$ | 96 $\mathrm{m}$ | 89 $\mathrm{m}$ |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | 91 $\mathrm{m}$ | 98 $\mathrm{m}$ | 98 $\mathrm{m}$ | 91 $\mathrm{m}$ | 98 $\mathrm{m}$ | 91 $\mathrm{m}$ |

Block partitioning | 1:2:3:3 | 1:2:3:3 | 1:2:3:3 | 1:2:3:3 | 2:3:3:1 | 2:3:3:1 |

OOC $(31,3,1)$ | 95 $\mathrm{m}$ | 105 $\mathrm{m}$ | 105 $\mathrm{m}$ | 98 $\mathrm{m}$ | 105 $\mathrm{m}$ | 98 $\mathrm{m}$ |

PC $p=5$ | 89 $\mathrm{m}$ | 98 $\mathrm{m}$ | 98 $\mathrm{m}$ | 92 $\mathrm{m}$ | 98 $\mathrm{m}$ | 92 $\mathrm{m}$ |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | 91 $\mathrm{m}$ | 101 $\mathrm{m}$ | 101 $\mathrm{m}$ | 94 $\mathrm{m}$ | 101 $\mathrm{m}$ | 94 $\mathrm{m}$ |

Block partitioning | 1:4:4 | 1:4:4 | 1:4:4 | 1:4:4 | 4:4:1 | 4:4:1 |

OOC $(31,3,1)$ | 95 $\mathrm{m}$ | 109 $\mathrm{m}$ | 109 $\mathrm{m}$ | 102 $\mathrm{m}$ | 109 $\mathrm{m}$ | 102 $\mathrm{m}$ |

PC $p=5$ | 89 $\mathrm{m}$ | 102 $\mathrm{m}$ | 102 $\mathrm{m}$ | 96 $\mathrm{m}$ | 102 $\mathrm{m}$ | 96 $\mathrm{m}$ |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | 91 $\mathrm{m}$ | 105 $\mathrm{m}$ | 105 $\mathrm{m}$ | 98 $\mathrm{m}$ | 105 $\mathrm{m}$ | 98 $\mathrm{m}$ |

Block partitioning | 1:5:3 | 1:5:3 | 1:5:3 | 1:5:3 | 5:3:1 | 5:3:1 |

OOC $(31,3,1)$ | 95 $\mathrm{m}$ | 109 $\mathrm{m}$ | 109 $\mathrm{m}$ | 102 $\mathrm{m}$ | 109 $\mathrm{m}$ | 102 $\mathrm{m}$ |

PC $p=5$ | 89 $\mathrm{m}$ | 102 $\mathrm{m}$ | 102 $\mathrm{m}$ | 96 $\mathrm{m}$ | 102 $\mathrm{m}$ | 96 $\mathrm{m}$ |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | 91 $\mathrm{m}$ | 105 $\mathrm{m}$ | 105 $\mathrm{m}$ | 98 $\mathrm{m}$ | 105 $\mathrm{m}$ | 98 $\mathrm{m}$ |

Block partitioning | 1:8 | 1:8 | 1:8 | 1:8 | 8:1 | 8:1 |

OOC $(31,3,1)$ | 95 $\mathrm{m}$ | 114 $\mathrm{m}$ | 114 $\mathrm{m}$ | 102 $\mathrm{m}$ | 114 $\mathrm{m}$ | 109 $\mathrm{m}$ |

PC $p=5$ | 89 $\mathrm{m}$ | 107 $\mathrm{m}$ | 107 $\mathrm{m}$ | 96 $\mathrm{m}$ | 107 $\mathrm{m}$ | 102 $\mathrm{m}$ |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | 91 $\mathrm{m}$ | 110 $\mathrm{m}$ | 110 $\mathrm{m}$ | 98 $\mathrm{m}$ | 110 $\mathrm{m}$ | 105 $\mathrm{m}$ |

Spreading Codes | OOK | PPM | DPPM | MPPM | DPIM | DH-PIM${}_{2}$ |
---|---|---|---|---|---|---|

Block partitioning | 1:2:2:2:2 | 1:2:2:2:2 | 1:2:2:2:2 | 1:2:2:2:2 | 2:2:2:2:1 | 2:2:2:2:1 |

OOC $(31,3,1)$ | $29.19$ | $30.16$ 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 $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ mm | $29.12$ mm | $29.99$ mm | $29.33$ mm | $29.21$ mm | $29.54$ mm | $29.64$ mm |

Block partitioning | 1:2:3:3 | 1:2:3:3 | 1:2:3:3 | 1:2:3:3 | 2:3:3:1 | 2:3:3:1 |

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 $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | $29.45$ mm | $29.89$ mm | $30.06$ mm | $29.49$ mm | $30.03$ mm | $29.96$ mm |

Block partitioning | 1:4:4 | 1:4:4 | 1:4:4 | 1:4:4 | 4:4:1 | 4:4:1 |

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 $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | $29.10$ mm | $30.36$ mm | $30.17$ mm | $29.26$ mm | $30.54$ mm | $29.48$ mm |

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 $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | $29.66$ mm | $30.56$ mm | $30.91$ mm | $29.58$ mm | $30.91$ mm | $29.74$ mm |

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 $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | $29.34$ mm | $31.54$ mm | $31.71$ mm | $29.55$ mm | $31.86$ mm | $31.05$ mm |

Spreading Codes | OOK | PPM | DPPM | MPPM | DPIM | DH-PIM${}_{2}$ |
---|---|---|---|---|---|---|

Block partitioning | 1:2:2:2:2 | 1:2:2:2:2 | 1:2:2:2:2 | 1:2:2:2:2 | 2:2:2:2:1 | 2:2:2:2:1 |

OOC $(31,3,1)$ | $3.74$ mm | $4.86$ mm | $4.85$ mm | $3.74$ mm | $4.91$ mm | $3.60$ mm |

PC $p=5$ | $2.89$ mm | $3.93$ mm | $3.69$ mm | $2.89$ mm | $3.78$ mm | $2.87$ mm |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | $3.12$ mm | $4.14$ mm | $4.03$ mm | $3.12$ mm | $4.41$ mm | $3.24$ mm |

Block partitioning | 1:2:3:3 | 1:2:3:3 | 1:2:3:3 | 1:2:3:3 | 2:3:3:1 | 2:3:3:1 |

OOC $(31,3,1)$ | $3.69$ mm | $5.52$ mm | $5.52$ mm | $4.06$ mm | $5.58$ mm | $4.29$ mm |

PC $p=5$ | $2.83$ mm | $4.21$ mm | $4.30$ mm | $3.19$ mm | $4.27$ mm | $3.11$ mm |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | $3.14$ mm | $4.85$ mm | $4.87$ mm | $3.42$ mm | $4.78$ mm | $3.69$ mm |

Block partitioning | 1:4:4 | 1:4:4 | 1:4:4 | 1:4:4 | 4:4:1 | 4:4:1 |

OOC $(31,3,1)$ | $3.68$ mm | $6.24$ mm | $6.55$ mm | $5.05$ mm | $6.40$ mm | $5.03$ mm |

PC $p=5$ | $2.85$ mm | $5.03$ mm | $5.03$ mm | $3.76$ mm | $4.88$ mm | $3.80$ mm |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | $3.25$ mm | $5.35$ mm | $5.49$ mm | $4.31$ mm | $5.62$ mm | $4.17$ mm |

Block partitioning | 1:5:3 | 1:5:3 | 1:5:3 | 1:5:3 | 5:3:1 | 5:3:1 |

OOC $(31,3,1)$ | $3.68$ mm | $6.22$ mm | $6.39$ mm | $4.99$ mm | $6.13$ mm | $4.96$ mm |

PC $p=5$ | $2.81$ mm | $5.20$ mm | $4.97$ mm | $3.85$ mm | $5.25$ mm | $3.96$ mm |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | $3.33$ mm | $5.52$ mm | $5.53$ mm | $4.24$ mm | $5.66$ mm | $4.32$ mm |

Block partitioning | 1:8 | 1:8 | 1:8 | 1:8 | 8:1 | 8:1 |

OOC $(31,3,1)$ | $3.83$ mm | $7.82$ mm | $7.68$ mm | $4.92$ mm | $7.81$ mm | $6.51$ mm |

PC $p=5$ | $2.81$ mm | $6.05$ mm | $5.95$ mm | $3.86$ mm | $5.82$ mm | $5.04$ mm |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | $3.23$ mm | $6.91$ mm | $6.77$ mm | $4.09$ mm | $6.97$ mm | $5.61$ mm |

**Table 17.**Error rate at maximum distance ${R}_{max}$ as a combination of modulation and spreading code.

Spreading Codes | OOK | PPM | DPPM | MPPM | DPIM | DH-PIM${}_{2}$ |
---|---|---|---|---|---|---|

Block partitioning | 1:2:2:2:2 | 1:2:2:2:2 | 1:2:2:2:2 | 1:2:2:2:2 | 2:2:2:2:1 | 2:2:2:2:1 |

OOC $(31,3,1)$ | 0.006 19 | 0.000 08 | 0.000 08 | 0.000 68 | 0.000 08 | 0.000 68 |

PC $p=5$ | 0.025 04 | 0.000 53 | 0.000 53 | 0.002 80 | 0.000 53 | 0.002 80 |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | 0.014 15 | 0.000 26 | 0.000 26 | 0.001 58 | 0.000 26 | 0.001 58 |

Block partitioning | 1:2:3:3 | 1:2:3:3 | 1:2:3:3 | 1:2:3:3 | 2:3:3:1 | 2:3:3:1 |

OOC $(31,3,1)$ | 0.006 19 | 0.000 03 | 0.000 03 | 0.000 30 | 0.000 03 | 0.000 30 |

PC $p=5$ | 0.025 04 | 0.000 26 | 0.000 26 | 0.001 45 | 0.000 26 | 0.001 45 |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | 0.014 15 | 0.000 11 | 0.000 11 | 0.000 75 | 0.000 11 | 0.000 75 |

Block partitioning | 1:4:4 | 1:4:4 | 1:4:4 | 1:4:4 | 4:4:1 | 4:4:1 |

OOC $(31,3,1)$ | 0.006 19 | 0.000 01 | 0.000 01 | 0.000 08 | 0.000 01 | 0.000 08 |

PC $p=5$ | 0.025 04 | 0.000 08 | 0.000 08 | 0.000 53 | 0.000 08 | 0.000 53 |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | 0.014 15 | 0.000 03 | 0.000 03 | 0.000 26 | 0.000 03 | 0.000 26 |

Block partitioning | 1:5:3 | 1:5:3 | 1:5:3 | 1:5:3 | 5:3:1 | 5:3:1 |

OOC $(31,3,1)$ | 0.006 19 | 0.000 01 | 0.000 01 | 0.000 08 | 0.000 01 | 0.000 08 |

PC $p=5$ | 0.025 04 | 0.000 08 | 0.000 08 | 0.000 53 | 0.000 08 | 0.000 53 |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | 0.014 15 | 0.000 03 | 0.000 03 | 0.000 26 | 0.000 03 | 0.000 26 |

Block partitioning | 1:8 | 1:8 | 1:8 | 1:8 | 8:1 | 8:1 |

OOC $(31,3,1)$ | 0.006 19 | 0.000 00 | 0.000 00 | 0.000 08 | 0.000 00 | 0.000 01 |

PC $p=5$ | 0.025 04 | 0.000 01 | 0.000 01 | 0.000 53 | 0.000 01 | 0.000 08 |

MPC $p=5,\phantom{\rule{3.33333pt}{0ex}}w=4$ | 0.014 15 | 0.000 00 | 0.000 00 | 0.000 26 | 0.000 00 | 0.000 03 |

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**MDPI and ACS Style**

Kim, G.; Park, Y.
Suitable Combination of Direct Intensity Modulation and Spreading Sequence for LIDAR with Pulse Coding. *Sensors* **2018**, *18*, 4201.
https://doi.org/10.3390/s18124201

**AMA Style**

Kim G, Park Y.
Suitable Combination of Direct Intensity Modulation and Spreading Sequence for LIDAR with Pulse Coding. *Sensors*. 2018; 18(12):4201.
https://doi.org/10.3390/s18124201

**Chicago/Turabian Style**

Kim, Gunzung, and Yongwan Park.
2018. "Suitable Combination of Direct Intensity Modulation and Spreading Sequence for LIDAR with Pulse Coding" *Sensors* 18, no. 12: 4201.
https://doi.org/10.3390/s18124201