# Optical Wireless Communications for Ubiquitous Computing

Fabián Seguel, Ismael Soto, Pablo Adasme, Belarmino Núñez

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Fabián Seguel, Ismael Soto, Pablo Adasme, Belarmino Núñez. Optical Wireless Communications for Ubiquitous Computing. 17th International Conference on Informatics and Semiotics in Organisations (ICISO), Aug 2016, Campinas, Brazil. pp.243-245. [hal-01646632](https://hal-inriaHal)[https://inria.hal.science/hal-01646632](https://inria.hal.science/hal-01646632)

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# Optical Wireless Communications for Ubiquitous Computing

Fabián Seguel, Ismael Soto, Pablo Adasme, and Belarmino Núñez

Department of Electrical Engineering, Universidad de Santiago de Chile,

Avenida Ecuador 3519, Estación Central, Chile

{Fabian.Seguel, Ismael.Soto, Pablo.Adasme,

Belarmino.Nunez}@usach.cl

**Abstract.** In this paper, we propose resource allocation optimization problems for indoor Optical Wireless Communications uplink. More precisely, a Binary NP-HARD optimization problem together with its relaxation are proposed. Cuckoo Search (CS) and Genetic Algorithms (GA) have been unlikely to find feasible solutions when dealing with the relaxation of the problem. For the binary model, Binary Cuckoo Search outperforms the classical GA achieving better solutions in less computational CPU time.

**Keywords:** Pervasive computing · Optical wireless communications · NP-hard

## 1 Problem Formulation and Methods

Ubiquitous Computing collects information from a variety of sources in any location and in any time. Due to the recent advances in wireless communications, integrated digital circuits, micro electro mechanical systems and the mobile technology many devices are now connected through a wireless link. In the recent years, Optical Wireless Communication (OWC) has been subject of study of many researchers. OWC provides many advantages compared to Radio Frequency (RF) making this technology suitable for new generation devices.

The proposed optimization problems referred to as OPT1 and OPT2 are defined next. OPT1 tries to increase the speed of the transmitting information by assigning each device in a pre-defined partition of the channel while OPT2 intends to maximize the bit rate of the wireless link by defining the percentage of the sub channel that will be assigned to each device. The channel link is modeled by the fundamental equations formulated in Komine & Nakagawa [1]. We use Cuckoo Search, Binary Cuckoo Search [2] and Genetic Algorithms [3].

The mathematical model can be formally written as:

$$ \max_{\{s_{u,c}, p_{u,c}\}} \sum_{u=1}^{U} R_u = \sum_{u=1}^{U} x_{u,c} (B/C) \log_2 \left( 1 + \frac{R_{PD} H_{u,c} P_{u,c}}{\sum_{\substack{j \neq u \\ j=1}}^{U} \sum_{\substack{k \neq c \\ k=1}}^{C} x_{j,k} H_{j,k} P_{j,k}^* + \sigma} \right). \quad (1) $$
The optimization problem is subject to different limitations. In OPT1 $x_{u,c} \in \{0, 1\}$ while in OPT2 $0 \le x_{u,c} \le 1$. For both $P_{u,c} \in \mathbb{R}$, $0 \le P_{u,c} \le 10$

$$ \sum_{u=1}^{U} x_{u,c} - 1 \le 0 \quad \forall c \in C, \quad 1 - \sum_{c=1}^{C} x_{u,c} \le 0, \quad \sum_{c=1}^{C} x_{u,c} P_{u,c} - 10 \le 0 \quad \forall u \in U. \quad (2) $$

## 2 Results and Conclusion

It can be seen from Table 1 that the BCS algorithm is faster to compute feasible solutions. GA overcomes BCS in 4 scenarios. Nevertheless GA also provides unfeasible (Unf) solutions in scenarios where BCS provides a feasible one.

<table><caption>**Table 1.** Objective function values for OPT1 and OPT2 by using BCS, CS and GA</caption><thead><tr><th>Devices</th><th>Channels</th><th>R<sub>OPT1</sub><br>BCS</th><th>R<sub>OPT2</sub><br>CS</th><th>R<sub>OPT1</sub><br>GA</th><th>R<sub>OPT2</sub><br>GA</th><th>BCS<br>Fitness<br>GAP (%)</th><th>GA<br>Time<br>Gap (%)</th></tr></thead><tbody><tr><td>4</td><td>32</td><td>180.74</td><td>Unf</td><td>154.15</td><td>Unf</td><td>17.24</td><td>-32.05</td></tr><tr><td>8</td><td>32</td><td>70.45</td><td>Unf</td><td>79.19</td><td>Unf</td><td>-11.03</td><td>-37.84</td></tr><tr><td>12</td><td>32</td><td>451.54</td><td>Unf</td><td>518.17</td><td>Unf</td><td>-12.85</td><td>-42.22</td></tr><tr><td>14</td><td>32</td><td>269.03</td><td>Unf</td><td>Unf</td><td>Unf</td><td>-</td><td>-</td></tr><tr><td>4</td><td>64</td><td>20.54</td><td>Unf</td><td>29.46</td><td>Unf</td><td>-30.26</td><td>-35.39</td></tr><tr><td>8</td><td>64</td><td>205.49</td><td>Unf</td><td>Unf</td><td>Unf</td><td>-</td><td>-</td></tr><tr><td>12</td><td>64</td><td>166.77</td><td>Unf</td><td>Unf</td><td>Unf</td><td>-</td><td>-</td></tr><tr><td>14</td><td>64</td><td>53.14</td><td>Unf</td><td>Unf</td><td>Unf</td><td>-</td><td>-</td></tr><tr><td></td><td>Min</td><td>70.45</td><td>-</td><td>62.70</td><td>-</td><td>-</td><td>-</td></tr><tr><td></td><td>Max</td><td>668.59</td><td>-</td><td>732.14</td><td>-</td><td>-</td><td>-</td></tr><tr><td></td><td>Average</td><td>233.68</td><td>-</td><td>155.81</td><td>-</td><td>-</td><td>-</td></tr></tbody></table>

In this case, BCS outperforms GA reaching feasible solutions in less computational time. The relaxation proposed cannot find feasible solutions in the searching space. In a future work a decomposition approach will be proposed in order to deal with the binary NP-HARD optimization problem.

**Acknowledgments.** The authors acknowledge the financial support of the “Center for Multidisciplinary Research on Signal Processing” (CONICYT/ACT1120 Project), the USACH/DICYT 061413SG and 061513VC_DAS Projects and CORFO 14IDL2-2991914.
References

1. Komine, T., Nakagawa, M.: Fundamental analysis for visible-light communication system using LED lights. IEEE Trans. Consumer Electron. **50**(1), 100–107 (2004)

2. Yang, X.S., Deb, S.: Engineering optimisation by cuckoo search. Math. Model. Numer. Optim (2015)

3. Goldberg, D.E.: Genetic Algorithms. Pearson Education (2006)