Optimization of location, power allocation and orientation for lighting lamps in a visible light communication system using the firefly algorithm

Zhengyuan Wei; Haiying Hu; Haiying Hu; Huamao Huang; Huamao Huang; Huamao Huang

doi:10.1364/OE.420773

1. Introduction

Light-emitting diode (LED) based visible light communication (VLC) is an attractive wireless communication technology, which can play an important role in high-speed communication, positioning, sensing and Internet of Things (IoT), since it can make full use of ubiquitous illumination infrastructures, enjoys low cost and has no electromagnetic radiation/interference [1]. Generally, the optical power irradiated on the receiving plane is not uniform, hence the signal-to-noise ratio (SNR) for photoelectric detectors and the illuminance for human eyes would fluctuate at different locations, which deteriorate the communication stability and the visual comfort for different users.

The most popular method to optimize the uniformity of SNR or illuminance distribution in VLC system is location design of LED lighting lamp array [2,3]. Taking 16 LED lamps as an example, the conventional typical schemes are square layout, circle layout, and square-circle layout [3,4]. Among these three typical schemes, the square-circle layout gives the most uniform SNR distribution. Based on specific location layouts, the power allocation [4] or orientation [5] can also be optimized. In these conventional optimizations, the parameter values are artificially selected. It can be inferred that the better performance can be reached if the more appropriate parameter values are selected after going through the whole value ranges. This is feasible in theory, but it cannot be realized in practice, since it leads to a huge amount of computation. In order to find the optimal values in the huge search space, intelligent optimization algorithms, such as convex optimization algorithm [6–9], evolutionary algorithm [10–16], simulated annealing algorithm [17], local search algorithm [18] and artificial fish swarm algorithm [19], are preferred to cut the computational resource. To realize fast convergence, only one degree-of-freedom (DOF), including location [15–19] or power allocation [9–12], was considered. Despite the single-degree-of-freedom (SDOF) has given significantly improved performance, the optimizations having multiple-degree-of-freedom (MDOF) could make further improvements. Combined with location, the power allocation in terms of the number of LED lamps [13] or the semi-angle at half illuminance of LED lamps [14] was adopted for two-degree-of-freedom (2DOF) optimization. In addition, a quasi 2DOF scheme, in which the location was produced by a specific stochastic function without iterative optimization, then the power allocation was determined by convex optimization algorithm, was also proposed [6,7]. Recently, taking the orientation into account, the aforementioned quasi 2DOF scheme was updated to be quasi three-degree-of-freedom (3DOF) scheme [8]. However, it is still a step-by-step optimization.

In this paper, considering location, power allocation and orientation, the SDOF, 2DOF and 3DOF schemes are investigated for the better uniformity of SNR distribution. For the sake of fast convergence in optimization, a swarm intelligent algorithm, namely, firefly algorithm, is adopted and improved. Both simultaneous and step-by-step optimizations are studied. The effects of orientation DOF is specially discussed. The schemes with and without orientation DOF are also compared at different number of LED lamps.

2. System model

In an empty room with the size of L × W × H (length × width × height), N LED lighting lamps are arranged on the ceiling. As shown in Fig. 1, the lower left corner is taken as the origin, and a Cartesian coordinate system is established along with the room edges as x, y, and z axes. For the i-th LED lamp, the location is denoted by point E (X_i, Y_i, H), where 0 ≤ X_i ≤ L and 0 ≤ Y_i ≤ W; the direct-current (DC) optical power is P_i, where P₀ − ΔP ≤ P_i≤ P₀ + ΔP, P₀ and ΔP are the median value and dimming range for each LED lamp controlled by dimming technology; the alternative-current (AC) optical power is P_i^AC=η_M · P_i · p(t), where η_M is the modulation index and p(t) is the time-domain modulated signal in on-off-keying (OOK) modulation [4,9]; the orientation is defined by the zenith angle, θ^Z_i, and azimuth angle, θ^A_i, of the normal vector in the light-emitting surface, V^E_i, where 0 ≤ θ^Z_i ≤ π / 2 and 0 ≤ θ^A_i ≤ 2 π. The receiver is placed on a moving platform, of which the moving range in x and y directions are limited by the room size. The receiving surface is parallel to the floor (i.e. the normal vector of the receiving surface, V_R, is perpendicular to the floor) and its height is H_R. Hence, the location of the receiver is denoted by point R (x, y, H_R), where 0 ≤ x ≤ L and 0 ≤ y ≤ W.

Fig. 1. LOS link model.

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Since the reflected lights have negligible impacts on the system performance, only line of sight (LOS) links are considered [6–8,16,19]. For the i-th LED lamp, let ϕ_i denotes the angle between V^E_i and the LOS line, and ψ_i denotes the angle between V_R and the LOS line. The ϕ_i and ψ_i satisfy

(1)$$\left\{ \begin{array}{l} \cos ({\phi_i}) = \frac{{{{||{ER} ||}^2} + {{||{ET} ||}^2} - {{||{RT} ||}^2}}}{{2||{ER} ||\cdot ||{ET} ||}}\\ \cos ({\psi_i}) = \frac{{H - {H_R}}}{{||{ER} ||}} \end{array} \right.,$$

where the operator || || is the Euclidean length. The point T (x_i, y_i, H_R) is the intersection of V^E_i and the receiving plane. The x_i and y_i can be given as

(2)$$\left\{ \begin{array}{l} {x_i} = {X_i} + ({H - {H_R}} )\tan ({\theta_i^Z} )\cos ({\theta_i^A} )\\ {y_i} = {Y_i} + ({H - {H_R}} )\tan ({\theta_i^Z} )\sin ({\theta_i^A} )\end{array} \right..$$

Assuming that the radiation intensity of LED lamp is Lambertian pattern, the DC illuminance on the receiving surface that perceived by human eyes can be expressed as [20]

(3)$$I = \sum\limits_{i = 1}^N {\left[ {\frac{{m + 1}}{{2\pi D_i^2}}{\Phi _i}{{\cos }^m}({{\phi_i}} )\cos ({{\psi_i}} )} \right]} ,$$

where m is the order of Lambertian radiation, D_i = || ER || is the distance between the i-th LED lamp and the receiver, Φ_i = P_i / η_c is the luminous flux, η_c is the conversion factor from optical power to luminous flux [20]. The time-domain average of AC optical power in OOK modulation received by the photoelectric detector can be represented as [19,21]

(4)$$\begin{array}{cc} {{P_r} = \sum\limits_{i = 1}^N {\left[ {\frac{{m + 1}}{{2\pi D_i^2}}{\eta_M}{P_i}{{\cos }^m}({{\phi_i}} )\cos ({{\psi_i}} ){T_s}gA} \right],} }&{0 \le {\psi _i} \le {\psi _c},} \end{array}$$

where T_s and g are, respectively, the gains of optical filter and optical concentrator in the communication channel, A and ψ_c are, respectively, the receiving area and the field of view for the photoelectric detector. The noise at the photoelectric detector is mainly composed of shot noise, σ_shot, and thermal noise, σ_thermal, and hence can be written as [6,21]

(5)$${\sigma ^2} = \sigma _{shot}^2 + \sigma _{thermal}^2.$$

The parameters related to σ_shot and σ_thermal were explained in [6,21]. It was shown that σ_shot is a function of P_r. The quality factor to evaluate the uniformity of SNR in VLC system can be described as [7,8]

(6)$${F_P} = \frac{{\textrm{mean}(\varLambda )}}{{2\sqrt {{\mathop{\rm var}} (\varLambda )} }},$$

where Λ = ρ²P_r² / σ² is the electrical SNR and ρ is the photo-to-electric conversion efficiency. The operators mean(Λ) and var(Λ) are, respectively, the mean and variance of Λ, which is a matrix having the same size with the number of sampling points in the receiving plane. Therefore, to obtain the most uniform SNR, the objective function for the joint optimization of location, power allocation, and orientation can be written as

(7)$$\begin{array}{cc} {\mathop {\max }\limits_{{X_i},{Y_i},{P_i},\theta _i^Z,\theta _i^A} }&{{F_P},}\\ {s.t.}&{0 \le {X_i} \le L,}\\ {}&{0 \le {Y_i} \le W,}\\ {}&{{P_0} - \Delta P \le {P_i} \le {P_0} + \Delta P,}\\ {}&{\sum\nolimits_i {{P_i}} = N\cdot {P_0},}\\ {}&{0 \le \theta _i^Z \le {\pi / \textrm{2}},}\\ {}&{0 \le \theta _i^A \le 2\pi ,} \end{array}$$

where [X_i, Y_i, P_i, θ^Z_i, θ^A_i] are the target variables. All parameters are given in Table 1.

Table 1. The parameters for LOS link model

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3. Improved firefly algorithm

The firefly algorithm, which is a heuristic algorithm suited for multimodal functions [22], is adopted and improved to optimize the location, power allocation, and orientation for LED lamps in VLC system. In the algorithm, a firefly is a possible solution representing the status of N LED lamps; each firefly has a possibility to move towards any other fireflies with higher brightness, and the moving distance depends on their attractiveness which decreases with the increase in the distance between the two fireflies; the actual movement will make the firefly get the highest brightness among all possible movements in a single generation; finally, the firefly with the highest brightness in all generations is the best solution.

The optimization process is described briefly in Table 2. In step 1, the parameters for iteration are given in Table 3 and the brightness function is defined as F_p. These parameters should be carefully adjusted to guarantee the convergence of max(F_p). In step 2, the first generation of firefly population is established. The status of N LED lamps for a firefly can be described by a N × 5 parameter matrix, M_N_,5, in which the i-th row representing the i-th LED lamp is [X_i, Y_i, P_i, θ^Z_i, θ^A_i]. The initial status of a firefly in the first generation is produced by uniform distribution and, hence each element of M_N,₅ can be given as

(8)$$S = \textrm{unifrnd}({{S_{LB}},{S_{UB}}} ),$$

where S is X_i, Y_i, P_i, θ^Z_i, and θ^A_i; S_LB and S_UB are, respectively, the lower and upper limit of S; the function unifrnd (S_LB, S_UB) returns a random number chosen from the continuous uniform distribution on the interval from S_LB to S_UB. For each firefly, the parameter matrix M_N_,5 is passed to the function F_p to calculate the brightness.

Table 2. Optimization process using improved firefly algorithm

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Table 3. The parameters for iteration in improved firefly algorithm

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In steps 3-6, the iteration repeats between the n_iter-th and (n_iter + 1)-th generations until the maximum number of iteration is reached. In step 3, in the n_iter-th generation, a virtual firefly moves from the j-th firefly with lower brightness towards the v-th firefly with higher brightness, and the moving distance, S ^jv – S ^j, is defined as

(9)$${S^{jv}} - {S^j} = {\beta _S}\cdot ({{S^v} - {S^j}} )\cdot \textrm{unifrnd}({0,1} )+ \alpha \cdot {l_S}\cdot \textrm{unifrnd}({ - 1,1} ),$$

where the superscript jv represents the jv-th virtual firefly. The first and second term on the right-hand side are the attractive and mutative movement, which represent the global and local searching, respectively. Besides, the function unifrnd increases the diversity of firefly population. In the attractive movement, the attraction coefficient, β_S, is

(10)$${\beta _S} = \left\{ {\begin{array}{cc} {({{\beta_{UB}} - {\beta_{LB}}} ){e^{ - \gamma r_S^2}} + {\beta_{LB}},}&{if\;{\beta_S} > 0.5}\\ {0.5,}&{if\;{\beta_S} \le 0.5} \end{array}} \right.,$$

where β_LB and β_UB are, respectively, the lower and upper limits of the attraction coefficient, γ = 1/||S_UB − S_LB||² is the light absorption coefficient, and r_s= ||S ^v – S ^j|| is the distance between the j-th and v-th fireflies. In the mutative movement, α is the mutation coefficient and l_s = ||S_UB − S_LB|| is the mutation length. Note that, for a specific S, the moving distance is determined by the specific S itself. In other words, X_i, Y_i, P_i, θ^Z_i, and θ^A_i are treated separately in the iteration algorithm to avoid their interaction and mismatched magnitudes. In step 4, among all virtual fireflies originated from the j-th firefly, the one with the highest brightness become an actual firefly. The N_pop actual fireflies constitute the (n_iter + 1/2)-th generation. In step 5, the top N_pop fireflies, which have higher brightness among the 2 × N_pop fireflies in the n_iter-th and (n_iter + 1/2)-th generations, constitute the (n_iter + 1)-th generation. In step 6, the iteration repeats or be terminated according to the number of iteration.

4. Results and discussion

4.1 Single-degree-of-freedom optimization

Taking 16 LED lighting lamps as an example, the SDOF optimizations are investigated in this section. In location, power and orientation SDOF schemes, the target variables are, respectively, [X_i, Y_i], [P_i] and [θ^Z_i, θ^A_i], while other parameters take default values. The default location is the typical square-circle layout [4,6–8], the default power allocation is equal power of P₀, and the default orientation is perpendicular to the receiving plane. Figures 2 and 3 show, respectively, the layout and SNR distribution after SDOF optimizations, while Table 4 lists the performance indices, e.g. F_p, average SNR and average illuminance.

Fig. 2. Layouts after SDOF optimization of 16 LED lamps. The numbers near the points in (c) and (d) are the allocated [P_i] (in watts) and [θ^Z_i, θ^A_i] (in degrees), respectively.

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Fig. 3. SNR distributions after SDOF optimization of 16 LED lamps.

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Table 4. Performance indices after SDOF optimization of 16 LED lamps

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The square-circle layout is presented at first for comparison. Its SNR distribution is uniform and the F_p is 3.8556. Using the improved firefly algorithm, the location SDOF scheme leads to a much higher F_p of 13.0172, indicating the more uniform SNR distribution, which demonstrates the algorithm is effective. The improvement can be ascribed to the optimized distribution of LED lamps in the center and near the edges. On the other hand, adopting the square-circle layout, using the improved firefly algorithm, the power and orientation SDOF schemes can also improve the uniformity of SNR distribution and increase F_p, although the improvements are not as high as the location SDOF scheme. From the perspective of F_p, it seems that the orientation SDOF scheme is better than the power SDOF scheme, since the former has a higher value of F_p than the latter. However, the former has much lower average SNR and average illuminance than the latter, especially the average illuminance of the former is much lower than the office-room standard of 300 lx [21], which are disadvantages for both illumination and communication. This can be attributed to the bad orientation settings, which cause lots of lights not to irradiate the receiving plane and decrease the SNR and illumination.

4.2 Multiple-degrees-of-freedom optimization

Considering every SDOF scheme can improve the uniformity of SNR distribution, MDOF optimizations are proposed for further improvement. For 2DOF joint optimization, two DOFs are selected from location, power allocation and orientation for simultaneous or step-by-step optimization. Taking the joint optimization of location and power allocation as an example, the differences between simultaneous and step-by-step optimizations are as follows. In the simultaneous optimization, denoted by L + P, the target variables are [X_i, Y_i, P_i], hence their search space contains both location and power domains. In the location-first step-by-step optimization, denoted by L→P, the three variables are [X_i, Y_i, P_Default] for location optimization in the first step then become [X_OPT, Y_OPT, P_i] for power optimization in the second step, where P_Default is the default power allocation and [X_OPT, Y_OPT] is the optimized location in the former step, hence the search space contains only the location domain at a specific value of power in the first step and contains only the power domain at a specific value of location in the second step. In the power-first step-by-step optimization, denoted by P→L, the three variables are [X_Default, Y_Default, P_i] for power optimization in the first step then become [X_i, Y_i, P_OPT] for location optimization in the second step, where [X_Default, Y_Default] is the default location and P_OPT is the optimized power in the former step, hence the search space contains only the power domain at a specific value of location in the first step and contains only the location domain at a specific value of power in the second step. It is shown that the search space in the simultaneous optimization is much larger than that in the step-by-step optimization.

Table 5 lists the performance indices after 2DOF optimizations. Compared to SDOF schemes, 2DOF optimizations can further improve the uniformity of SNR distribution. For example, after L→P and P→L optimizations, the F_p are, respectively, improved to be 1.14 and 2.75 times of those after location SDOF and power SDOF optimizations. Moreover, the simultaneous optimization has better performance than the step-by-step optimization, owing to the much larger search space for target variables. For example, the L + P optimization leads to higher F_p, of which the improvements are, respectively, 0.4782 and 3.4177, compared to L→P and P→L optimizations. For the three types of simultaneous optimizations, from the perspective of F_p, it seems that the L + O gives the best performance, the L + P gives the moderate performance, and the P + O gives the worst performance. However, the L + O and P + O have much lower average SNR and average illuminance than L + P, especially the average illuminances of the L + O and P + O are much lower than the office-room standard of 300 lx [21], owing to the bad orientation settings.

Table 5. Performance indices after 2DOF optimization of 16 LED lamps

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For 3DOF optimizations, all three DOFs are selected for the joint location, power allocation and orientation optimization. Table 6 lists the performance indices after 3DOF joint optimizations, including simultaneous and step-by-step optimizations. Compared to 2DOF schemes, 3DOF optimizations can further improve the uniformity of SNR distribution. For example, after L→P→O and P→L→O optimizations, the F_p are, respectively, improved to be 1.15 and 1.15 times of those after L→P and P→L optimizations. Moreover, the simultaneous optimization also has better performance than the step-by-step optimization. However, the low average illuminance is still a problem, because the orientation is involved in the optimization process. In addition, in the step-by-step optimization, the higher the priority of orientation, the lower average SNR and average illuminance, i.e. the orientation-first optimization gives the lowest average values while the orientation-last optimization gives the highest average values.

Table 6. Performance indices after 3DOF optimization of 16 LED lamps

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4.3 Multiple-degrees-of-freedom optimization with restriction of illuminance

To meet the office-room illuminance standard, the MDOF optimization should be processed with an additional restriction that the average illuminance is larger than 300 lx. Table 7 lists the performance indices after optimizations with restriction of illuminance. Here, only the MDOF simultaneous optimizations and the SDOF optimizations are discussed.

Table 7. Performance indices after MDOF optimization of 16 LED lamps with average illuminance > 300 lx

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Compared to the results shown in Tables 4, 5 and 6 without restriction of illuminance, the average SNR and average illuminance in the orientation-involved optimizations in Table 7 with restriction of illuminance are significantly improved, while the F_p is significantly decreased. On the other hand, the conclusion that the more DOF for optimization leads to the more uniformity of SNR distribution still holds true. As a result, the L + P+O optimization gives the highest F_p of 16.1188 among all the MDOF schemes, the L + P optimization gives the highest F_p of 15.3449 among all the 2DOF schemes, and the location optimization gives the highest F_p of 13.0172 among all the SDOF schemes. Compared to the typical square-circle layout, the improvements of F_p in the three schemes are, respectively, 4.18, 3.98 and 3.38 times. Compared to the highest F_p of 11.34 after quasi 2DOF optimization in [7,8], the MDOF schemes in this work show much better performance. The price of the performance improvement is the increased computing time, which represents the computational complexity of the MDOF schemes. Using our 2.7 GHz desktop computer, the computing time for the L + P+O 3DOF, L + P 2DOF, and location SDOF optimizations are, respectively, 16.57, 12.60, and 10.77 h. But the calculation for the typical square-circle layout only takes 2.84 s.

In Table 7, compared to L + P scheme, the improvement of F_p after L + P+O optimization is only 5.0%. As shown in Fig. 4, the SNR and illuminance distributions after these two optimizations are similar, although the layouts are different. The differences between these two optimizations in average SNR and average illuminance are, respectively, 0.4% and 2.1%. However, the increased computing time for L + P+O scheme is 31.5% compared to L + P scheme. In addition, the L + P+O scheme has much lower convergence speed than L + P scheme. Figure 5 presents the convergence curves of F_p in MDOF optimizations. It is shown that the more DOF leads to the lower convergence speed. Specially, with the restriction of illuminance, the F_p of L + P+O scheme is lower than that of L + P scheme before 312 iterations, then the former can surpass the latter. This can be attributed to the failed attempts of finding orientations to meet the requirement of illuminance. Without the restriction of illuminance, also shown in Fig. 5 for comparison, the former can surpass the latter after 73 iterations.

Fig. 4. Performance after MDOF optimization of 16 LED lamps with average illuminance

> 300 lx. The numbers near the points in (a) and (d) are the allocated [P_i] (in watts).

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Fig. 5. Convergence curves of F_p in MDOF optimization of 16 LED lamps with or without restriction of average illuminance > 300 lx.

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4.4 Influence of the number of LED lighting lamps

The layouts after MDOF optimization of 16 LED lamps, shown in Figs. 2(b), 4(a) and 4(d), present that most of the LED lamps are placed near the edges of the office-room and there always have two lamps standing quite close to each other. It seems that the number of LED lamps can be reduced to cut the cost of lamp array for packaging, driving, modulating, and installing, with affordable loss of F_p. Keeping the total optical power unchanged, the number of LED lamps varies from 4 to 16 and the optimization results of L + P+O and L + P schemes with restriction of illuminance are discussed in this section.

Figure 6 presents the layouts after optimization of different numbers of LED lamps. It seems that the optimal layout has a certain degree of symmetry, which can be attributed to the symmetric office-room model. This implies that a more effective algorithm can be established by considering the symmetry of the VLC system. Moreover, for the L + P+O scheme, most of the LED lamps are placed near the edges of the office-room, except that only one lamp is placed in the middle when N ≥ 8. For the L + P scheme, when N ≥ 9, similar to the former scheme, most of the LED lamps are placed near the edges and only one lamp is placed in the middle. This invariable type of multiple-edge-one-middle layout implies there would be plenty of LED lamps, which would suppress the rate of change in performance if N keeps increasing, and, thus, an optimal N can be found considering the cost-performance ratio.

Fig. 6. Layouts after optimization of different numbers of LED lamps with average illuminance > 300 lx.

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Figure 7 illustrates the performance indices after optimization of different numbers of LED lamps. With the increase of N, the F_p increases monotonously. In the range from N = 4 to 9, the F_p increases quickly, especially a significant increase occurs when N varies from 8 to 9; in the range from N = 9 to 16, the F_p increases slowly, which is consistent with the invariable type of multiple-edge-one-middle layout. As for the average SNR and average illuminance, those after the L + P+O optimization change slightly due to the restriction of illuminance. For the L + P scheme, the average SNR and average illuminance decrease quickly in the range from N = 4 to 8 and change slightly when N ≥ 9. Hence, considering the uniformity of SNR distribution, the larger N induces the better performance; considering the cost-performance ratio, N = 9 could be an optimal number of LED lamps.

Fig. 7. Performance indices after optimization of different numbers of LED lamps with average illuminance > 300 lx.

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Compared to the L + P scheme, the L + P+O scheme with restriction of illuminance can get higher F_p but lower average SNR and average illuminance, regardless of the number of LED lamps. When N = 4, the differences between the two schemes in F_p, average SNR and average illuminance are, respectively, 29.5%, 6.2% and 32.2%, demonstrating the significant impacts of the orientation DOF. However, with the increase of N in the range from 4 to 8, the differences decrease quickly. When N ≥ 8, the maximum differences between the two schemes in F_p, average SNR and average illuminance are, respectively, 7.1%, 1.0% and 4.5%, indicating the unnecessity of the orientation DOF. Hence, considering the uniformity of SNR distribution, the L + P+O scheme induces the better performance; considering the ease of implementation, the L + P scheme may be a preferred choice if N ≥ 8.

5. Conclusion

Considering a LOS VLC model, to optimize the uniformity of SNR distribution, the firefly algorithm is improved for joint optimization of location, power allocation and orientation. Taking 16 LED lamps arranged in a 5 × 5 × 3 m³ empty office-room as an example, the SDOF, 2DOF and 3DOF optimization are investigated. It is shown that the more DOF in optimization leads to the more uniformity of SNR distribution, and the simultaneous optimization has better performance than the step-by-step one. The orientation-involved optimizations significantly decrease the average SNR and average illuminance. In our case, on condition that the average illuminance is larger than 300 lx, the 3DOF optimization gives an improvement of 4.18 times in SNR uniformity, compared to the typical square-circle layout. Besides, with this restriction of illuminance, the differences between the L + P and L + P+O schemes in F_p, average SNR and average illuminance are small. These two schemes are further compared at different N. Considering the cost-performance ratio, the optimal N is 9; considering the ease of implementation, the L + P scheme may be a preferred choice if N ≥ 8.

Funding

Natural Science Foundation of Guangdong Province (2018A030310373).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Parameter	Symbol	Value
Room size (m³)	L × W × H	5 × 5 × 3
Height of receiving plane (m)	H_R	0.85
Number of LED lamps	N	4 ∼ 16
Median value of DC optical power for each LED lamp (W)	P ₀	98 / N
Dimming range of DC optical power for each LED lamp (W)	ΔP	23.5 / N
Modulation index for transmit signal in on-off-keying modulation	η_M	1
Conversion factor from optical power to luminous flux (mW/lm)	η_c	4.2
Order of Lambertian radiation for each LED lamp	m	1
Gain of optical filter in communication channel	T_s	1
Gain of optical concentrator in communication channel	g	2.32
Receiving area of the photoelectric detector (cm²)	A	1
Field of view of the photoelectric detector (degree)	ψ_c	80
Photo-to-electric conversion efficiency of the photoelectric detector (A/W)	ρ	0.53

Step 1	Set the parameters for iteration (e.g. population size, N_pop, maximum number of iteration, N_iter, mutation coefficient, α, and its damping ratio, α_damp) and build the brightness function (i.e. the quality factor, F_p).
Step 2	Set the parameter matrix, M_N_,5, for each firefly and calculate its brightness, F_p (j), where j is 1, 2, …, N_pop. Set the number of iteration as n_iter = 1.
Step 3	For the j-th and v-th fireflies in the n_iter-th generation, if F_p (j) < F_p (v), a virtual firefly, denoted as the jv-th firefly, moves from the j-th point towards the v-th point, where v is 1, 2, …, N_pop. Calculate F_p (jv).
Step 4	For the j-th firefly, find the v corresponding to the maximum of F_p (jv) and denote it as v_max. An actual firefly, denoted as the k-th firefly, moves from the j-th point towards the v_max-th point. Save M_N_,5 for the k-th firefly and set F_p (k) = F_p (jv_max). Denote all the k-th fireflies as the (n_iter + 1/2)-th generation.
Step 5	Rank all the 2 × N_pop fireflies in the n_iter-th and (n_iter + 1/2)-th generations. The top N_pop fireflies having higher brightness constitute the (n_iter + 1)-th generation. Save M_N_,5 and F_p for the firefly in the (n_iter + 1)-th generation.
Step 6	If (n_iter + 1) < N_iter, go to step 3 and set n_iter = (n_iter + 1) and α = (α × α_damp). Otherwise, stop the iteration and output the best results in the N_iter-th generation.

Parameter	Symbol	Value	Parameter	Symbol	Value
Population size	N_pop	25	Upper limit of attraction coefficient	β_UB	2
Maximum number of iteration	N_iter	500	Lower limit of attraction coefficient	β_LB	0.2
Mutation coefficient	α	0.01	Damping ratio of mutation coefficient	α_damp	0.98

Optimization scheme	F_p	Average SNR (dB)	Average illuminance (lx)
Square-circle	3.8556	40.9407	357.4481
Location optimization	13.0172	39.6742	309.2384
Power optimization	4.3427	40.6692	346.4147
Orientation optimization	6.9860	32.2068	130.3012

Optimization scheme		F_p	Average SNR (dB)	Average illuminance (lx)
Joint location (L) and power allocation (P)	L + P	15.3449	39.5969	306.4942
	L→P	14.8667	39.5620	305.2559
	P→L	11.9272	39.6207	307.3155
Joint location (L) and orientation (O)	L + O	18.2234	36.8212	222.2401
	L→O	15.7038	37.7551	247.6039
	O→L	12.9278	32.7792	139.2700
Joint power allocation (P) and orientation (O)	P + O	7.8645	33.8345	157.2764
	P→O	7.2027	34.3753	167.4032
	O→P	7.2516	32.3506	132.4891

Optimization of location, power allocation and orientation for lighting lamps in a visible light communication system using the firefly algorithm

Abstract

1. Introduction

2. System model

3. Improved firefly algorithm

4. Results and discussion

4.1 Single-degree-of-freedom optimization

4.2 Multiple-degrees-of-freedom optimization

4.3 Multiple-degrees-of-freedom optimization with restriction of illuminance

4.4 Influence of the number of LED lighting lamps

5. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (7)

Tables (7)

Equations (10)

Optics Express

Optimization scheme	F_p	Average SNR (dB)	Average illuminance (lx)
L + P+O	26.5886	35.9984	202.0708
L→P→O	17.1169	37.9041	251.9169
L→O→P	16.4152	37.7770	248.2342
P→L→O	13.7154	37.8821	251.2617
P→O→L	14.0323	34.2833	165.7057
O→L→P	13.4880	32.6178	136.7002
O→P→L	9.1395	31.8581	125.1938

Optimization scheme	F_p	Average SNR (dB)	Average illuminance (lx)	Computing time (h)
L + P+O	16.1188	39.4123	300.0096	16.57
L + P	15.3449	39.5969	306.4942	12.60
L + O	13.8996	39.4129	300.0166	12.91
P + O	4.9180	39.4227	300.0079	11.88
Location	13.0172	39.6742	309.2384	10.77
Power	4.3427	40.6692	346.4147	7.73
Orientation	4.1086	39.4275	300.0007	11.31