## Design of dual-link (wide- and narrow-beam) LED communication systems |

Optics Express, Vol. 22, Issue 9, pp. 11107-11118 (2014)

http://dx.doi.org/10.1364/OE.22.011107

Acrobat PDF (852 KB)

### Abstract

We explore the design of an LED-based communication system comprising two free space optical links: one narrow-beam (primary) link for bulk data transmission and one wide-beam (beacon) link for alignment and support of the narrow-beam link. Such a system combines the high throughput of a highly directional link with the robust insensitivity to pointing errors of a wider-beam link. We develop a modeling framework for this dual-link configuration and then use this framework to explore system tradeoffs in power, range, and achievable rates. The proposed design presents a low-cost, compact, robust means of communication at short- to medium-ranges, and calculations show that data rates on the order of Mb/s are achievable at hundreds of meters with only a few LEDs.

© 2014 Optical Society of America

## 1. Introduction

1. F.R. Gfeller and U. Bapst, “Wireless in-house data communication via diffuse infrared radiation,” in *Proceedings of the IEEE* (IEEE, 1979), pp. 1474–1486. [CrossRef]

3. M. Wolf and D. Kreß, “Short-range wireless infrared transmission: the link budget compared to RF,” IEEE Wireless Communications **10**(2), 8–14 (2003). [CrossRef]

4. A.K. Majumdar and J.C. Ricklin, *Free-space Laser Communications: Principles and Advances* (Springer, 2008, vol. 2). [CrossRef]

8. T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Transactions on Consumer Electronics **50**(1), 100–107 (2004). [CrossRef]

21. M. Shur and R. Zukauskas, “Solid-state lighting: toward superior illumination,” in *Proceedings of the IEEE*, (IEEE, 2005), pp. 1691–1703. [CrossRef]

22. S. Pimputkar, J. Speck, S. DenBaars, and S. Nakamura, “Prospects for LED lighting,” Nature Photonics **3**, 180–182 (2009). [CrossRef]

## 2. Link model

*d*,

*ϕ*), the received optical signal power

*P*

_{Rx}is given by and the corresponding excited photocurrent is Here,

*R*[A/W] is the responsivity of the photodiode and

*A*

_{eff}[m

^{2}] is the effective area of the receiver. In general,

*A*

_{eff}is a function of the angle-of-incidence of the transmitted light at the receiver, which we define as

*ψ*(see Fig. 1). The case of

*ψ*= 0 corresponds to a receiver that is perfectly pointed at the transmitter. For a receiver that is composed of a photodiode of active area

*A*, an optical filter described by the parameter

*T*

_{s}(

*ψ*), and an optical concentrator of gain

*g*(

*ψ*), the effective area is For a given spectrum of LED emission incident on the receiver at an angle

*ψ*,

*T*

_{s}(

*ψ*) is the fraction of incident optical signal power allowed through the filter. If we assume that the concentrator is ideal, then its gain

*g*is [24

24. X. Ning, R. Winston, and J. O’Gallagher, “Dielectric totally internally reflecting concentrators,” Applied Optics **26**, 300–305 (1987). [CrossRef] [PubMed]

*n*and its half-angle field-of-view is Ψ

_{c}. Practical concentrators often approach this ideal gain relation [23

23. J. Kahn and J. Barry, “Wireless infrared communications,” in *Proceedings of the IEEE*, (IEEE, 1997), pp. 265–298. [CrossRef]

*n*= 1 (free space) and Ψ

_{c}= 90°, yielding a gain of

*g*= 1.

25. C. Chow, C. Yeh, Y. Liu, and P. Huang, “Mitigation of optical background noise in light-emitting diode (LED) optical wireless communication systems,” IEEE Photonics Journal **5**, 7900307 (2013). [CrossRef]

26. A.J. Moreira, R.T Valadas, and A. de Oliveira Duarte, “Optical interference produced by artificial light,” Wireless Networks **3**, 131–140, 1997. [CrossRef]

9. J. Barry, *Wireless Infrared Communications* (Springer, 1994). [CrossRef]

3. M. Wolf and D. Kreß, “Short-range wireless infrared transmission: the link budget compared to RF,” IEEE Wireless Communications **10**(2), 8–14 (2003). [CrossRef]

23. J. Kahn and J. Barry, “Wireless infrared communications,” in *Proceedings of the IEEE*, (IEEE, 1997), pp. 265–298. [CrossRef]

26. A.J. Moreira, R.T Valadas, and A. de Oliveira Duarte, “Optical interference produced by artificial light,” Wireless Networks **3**, 131–140, 1997. [CrossRef]

*P*

_{n}[W] that is received by the photodiode, an optical passband filter can be placed on the receiver. In calculating the effect of this filter on the noise level, we model it as a an ideal “boxcar” passband filter of spectral width Δ

*λ*[nm]. The filter has a transmittance

*T*

_{n}within the passband and zero outside the passband. A practical filter may have an angularly depedendent transmittance, but can be approximately modeled as a “boxcar” filter of effective passband width Δ

*λ*. We also assume that the ambient background noise incident on the receiver is “white” (constant within the pass-band), and define its spectral irradiance (power per unit photodetector area per unit spectrum) as

*p*

_{bg}[W/nm-cm

^{2}]. With an ideal optical concentrator of index of refraction

*n*, the ambient optical power incident on the photodiode is [23

23. J. Kahn and J. Barry, “Wireless infrared communications,” in *Proceedings of the IEEE*, (IEEE, 1997), pp. 265–298. [CrossRef]

^{2}] of the AWGN can be approximated by [9

9. J. Barry, *Wireless Infrared Communications* (Springer, 1994). [CrossRef]

*q*[C] is the charge of an electron,

*B*[bits/s] is the bit rate of the signal, and

*R*[A/W] is the responsivity of the photodiode.

*Q*(·) is the tail probability of the standard normal distribution [23

*Proceedings of the IEEE*, (IEEE, 1997), pp. 265–298. [CrossRef]

*B*, ambient shot noise level, average transmitted power, range, beamwidth, and BER. Combining Eq. (8)–(10) and solving for

*B*yields the rate To solve for the range, we substitute Eqs. (1) and (3) into Eq. (11), yielding

## 3. Design of wide beam/narrow-beam dual link system

### 3.1. Defining the role of the beacon link

_{c,b}as the concentrator field of view for the beacon link receiver and Ψ

_{c,p}as that for the primary link receiver. The pointing angles of the beacon and primary transmitters are

*ϕ*

_{b}and

*ϕ*

_{p}, respectively, and the pointing angles of the beacon and primary receivers are

*ψ*

_{b}and

*ψ*

_{p}, respectively. To avoid interference between the two links, there is a need to ensure orthogonality between them; this could be achieved, for instance, by using LEDs of different wavelengths for the two links or time-division multiplexing their communication.

*ϕ*

_{b}. This low rate connectivity could be used, for example, to provide positioning and alignment information for the primary link. There are many different ways this supporting link could help align the primary link; among the demonstrated uses of supporting links in FSO systems have been the transmission of GPS coordinates, inertial orientation information, and received signal strength (RSS) [7]. Regardless of the specific role chosen for the beacon link, the beamwidths we examine for both links are on the order of tens of degrees, which significantly relaxes alignment constraints relative to that of many FSO systems. By utilizing both links, the dual-link system exploits the robustness of the beacon link while maintaining the high throughput of a relatively focused primary link. This robustness makes it suitable for LED-based outdoor mobile applications, a regime that has been studied significantly less than the indoor local area network application space [8

8. T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Transactions on Consumer Electronics **50**(1), 100–107 (2004). [CrossRef]

10. Jelena Grubor, Sebastian Randel, Klaus-Dieter Langer, and Joachim W Walewski, “Broadband information broadcasting using LED-based interior lighting,” Journal of Lightwave Technology **26**, 3883–3892 (2008). [CrossRef]

27. J. Kahn, J. Barry, M. Audeh, J. Carruthers, W. Krause, and G. Marsh, “Non-directed infrared links for high-capacity wireless LANs,” IEEE Personal Communications1, 12–25 (1994). [CrossRef]

30. D. O’Brien and M. Katz, “Optical wireless communications within fourth-generation wireless systems,” Journal of Optical Networking **4**, 312–322 (2005). [CrossRef]

_{1/2,b}, which relaxes the beacon pointing demands. In designing the exact beamwidth of the beacon transmitter, there is a tradeoff between this robustness in pointing and the transmitter-to-receiver distances (

*d*) that allow for connectivity; narrower beams can allow for longer-distance links but demand that the beacon transmitter be pointed with relative precision, whereas links with wider beams are more limited in their range but allow for more relaxed pointing demands.

_{1/2,b}by specifying a constraint on the pointing precision of the beacon transmitter. Specifically, we demand that the greatest pointing error allowed is |

*ϕ*

_{b}| =

*θ*

_{a}; in some sense, this defines an “angular range” of operation for the beacon link. In addition, we demand that for each

*ϕ*

_{b}within this permitted angular range (−

*θ*

_{a}≤

*ϕ*

_{b}≤

*θ*

_{a}), the beacon link supports a minimum data rate

*B*

_{b0}(i.e.,

*B*

_{b}≥

*B*

_{b0}). Note that this minimum rate is achievable at a different range

*d*for each of the angles

*ϕ*

_{b}within this angular span.

*d*corresponds to |

*ϕ*

_{b}| =

*θ*

_{a}, the worst case of pointing within the stated constraints. We design the beacon link beamwidth Φ

_{1/2,b}to maximize this worst case range, because we are interested in optimizing the robustness of the beacon link over a wide range of pointing angles

*ϕ*

_{b}, rather than optimizing the performance of the link for cases of perfect pointing (

*ϕ*

_{b}= 0). To do this, we set

*ϕ*

_{b}=

*θ*

_{a}and differentiate Eq. (12) with respect to

*m*. The parameter

*m*defines the beamwidth via Eq. (2). The optimal

*m*that results is with a corresponding optimal beacon beamwidth defined by Substituting this optimal

*m*=

*m*

_{b}and

*ϕ*

_{b}=

*θ*

_{a}back into Eq. (12) yields the maximized range for this worst case of pointing, and we define this range as

*d*

_{0}.

*B*

_{b}≥

*B*

_{b0}) is guaranteed to any receiver that lies

*d*

_{0}or less away from the transmitter, within the angular range −

*θ*

_{a}≤

*ϕ*

_{b}≤

*θ*

_{a}. Note that connectivity at ranges greater than

*d*

_{0}can be established for |

*ϕ*

_{b}| <

*θ*

_{a}, as well as for ranges less than

*d*

_{0}for |

*ϕ*

_{b}| >

*θ*

_{a}. A diagram that illustrates the geometry of the angular range |

*ϕ*

_{b}| ≤

*θ*

_{a}and distance

*d*

_{0}is shown in Fig. 2. In practice, a single node can employ several beacons to “cover” a wider range of azimuthal and/or elevation angle, building on angle-diversity schemes that have been explored [31, 32

32. M. Yuksel, J. Akella, S. Kalyanaraman, and P. Dutta, “Free-space-optical mobile ad hoc networks: Auto-configurable building blocks,” Wireless Networks **15**(3), 295–312 (2009). [CrossRef]

*d*

_{0}depends on many parameters [see Eq. (12)], including the required beacon rate

*B*

_{b0}; very low values of

*B*

_{b0}may be attainable at long distances, whereas higher rates may correspond to more limited ranges. The value of

*B*

_{b0}itself depends on the desired used of the beacon link. Using the beacon link for acquisition and feedback control, for example, may require

*B*

_{b0}≈ 1 kb/s. Other uses of the beacon beam, such as allowing a receiver node to detect the presence of a beacon and perhaps calculate its bearing, might require lower rates. However, while the value of

*d*

_{0}depends on

*B*

_{b0},

*ψ*

_{b}, and many other parameters, the optimal beamwidth Φ

_{1/2,b}depends only on the maximum allowed pointing error

*θ*

_{a}.

### 3.2. Exploring reasonable beacon rates and ranges

*B*

_{b}over space, assuming that the receiver is pointed perfectly at the beacon transmitter (i.e.,

*ψ*

_{b}= 0). Here, we choose to assume that the maximum allowed pointing error for the beacon is

*θ*

_{a}= 45°, and the beamwidth is optimized according to Eqs. (13) and (14) for this

*θ*. The beacon transmitter is located at (X,Y) = (0,0) and is pointed in the positive Y-direction. In these calculations, we assume that the link uses a single high-power LED (beacon transmitting power

_{a}*P*

_{b}= 0.3 W) in bright daytime skylight noise (

*p*

_{bg}= 5.8

*μ*W/nm/cm

^{2}[23

*Proceedings of the IEEE*, (IEEE, 1997), pp. 265–298. [CrossRef]

*λ*

_{b}= 100 nm and

*T*

_{s,b}=

*T*

_{n,b}= 0.8, a silicon

*p*-

*i*-

*n*photodiode of responsivity

*R*= 0.6 A/W and active area

*A*

_{b}= 1 cm

^{2}, and a glass optical concentrator (

*n*= 1.5). Figure 3(b) assumes identical parameters, except that here the receiver is assumed to be poorly aligned. Specifically, it is misaligned by an amount equal to the transmitter maximum pointing error (

*ψ*

_{b}=

*θ*

_{a}= 45°). In both figures, we have a chosen receiver (and concentrator) field of view equal to the transmitter maximum pointing error (Ψ

_{c,b}=

*θ*

_{a}= 45°). In practice, field of view varies among receivers, and there is no absolutely optimal field of view; rather, there is a tradeoff between field of view and gain, as seen in Eq. (6).

*B*

_{b0}= 1 kb/s is reasonable. The calculations in Fig. 3(a) show that for an aligned receiver (

*ψ*

_{b}= 0), this required rate is achievable at

*d*

_{0}≈ 85 m. If both the the transmitter and receiver are pointed perfectly (i.e., the receiver lies along the line X = 0, where

*ϕ*

_{b}= 0), then

*B*

_{b}= 1 kb/s is achievable at

*d*≈ 133 m. In the case of poor receiver alignment (

*ψ*

_{b}=

*θ*

_{a}= 45°), shown in Fig. 3(b),

*d*

_{0}is roughly 71 m.

*d*

_{0}to the receiver pointing angle

*ψ*

_{b}depends on the optical concentrator gain [

*g*

_{b}(

*ψ*

_{b})], optical filter [

*T*

_{s,b}(

*ψ*

_{b})], and a geometrical factor cos(

*ψ*

_{b}) [see Eqs. (5) and (12)]. Specifically,

*d*

_{0}is proportional to the square root of these factors. In the calculations presented in Fig. 3, the concentrator gain

*g*is considered constant within its field of view defined by

*ψ*

_{b}< Ψ

_{c,b}=

*θ*

_{a}. We also assume that

*T*

_{s,b}(

*ψ*

_{b}) is invariant in

*ψ*

_{b}for the beacon link, which is consistent with the behavior of an absorptive colored filter. Thus, in these calculations, the only dependence of

*d*

_{0}on the receiver misalignment

*ψ*

_{b}is the geometrical factor (cos

*ψ*

_{b})

^{1/2}. For the two receiver alignments examined here, [cos(

*ψ*

_{b})]

^{1/2}= 1 for the well-aligned receiver [Fig. 3(a)], and [cos(

*ψ*

_{b})]

^{1/2}≈ 0.84 for the poorly aligned case [Fig. 3(b)]. Thus the ratio of the values of

*d*

_{0}in Fig. 3(a) and Fig. 3(b) is (71 m)/(85 m) ≈ 0.84.

### 3.3. Jointly designing the beacon and primary link

*B*

_{b}=

*B*

_{b0}, we assume use of the primary link is contingent on successful operation of the beacon link. To meet this requirement of joint operation, it is necessary to consider the design space of the two links together. Figure 4 illustrates a representative example of this joint design space, where Fig. 4(a) describes the beacon link and Fig. 4(b) describes the primary link. The parameters assumed are the same as those of Fig. 3, except for

*θ*

_{a}and the beacon power

*P*

_{b}, parameters that are varied in Fig. 4(a).

*d*

_{0}as a function of beacon power

*P*

_{b}, one for

*ψ*

_{b}= 0 (well-aligned receiver, greater

*d*

_{0}) and one for

*ψ*

_{b}=

*θ*

_{a}(misaligned receiver, shorter

*d*

_{0}); this pair of curves is presented for three values of 2

*θ*

_{a}. Thus, for a given power

*P*

_{b},

*θ*

_{a}, and receiver alignment

*ψ*

_{b}, the plot defines a range

*d*

_{0}. This is the distance from the transmitter at which a data rate of

*B*

_{b}= 1 kb/s can be guaranteed within the angular range −

*θ*

_{a}≤

*ϕ*

_{b}≤

*θ*

_{a}. Taken alone, Fig. 4(a) is a design space only for the beacon link.

*θ*

_{a}, but relatively weakly dependent on the receiver alignment. At all three ranges of 2

*θ*

_{a}, the

*ψ*

_{b}= 0 (well-aligned receiver) case corresponds to only a slightly greater range

*d*

_{0}than the poorly aligned case of

*ψ*

_{b}=

*θ*

_{a}. This weak dependence on

*ψ*

_{b}is a consequence of the choice of an incident-angle-insensitive filter and concentrator at the beacon receiver, as discussed at the end of the previous subsection. Note that this assumed misalignment

*θ*

_{a}changes for each value of 2

*θ*

_{a}examined; for 2

*θ*

_{a}= 40°, the misalignment considered is only

*ψ*

_{b}= 20°. Thus for this narrowest allowed angular range examined, the separation between the curves is small compared to that of the other two pairs.

*B*

_{p}as a function of

*P*

_{p}/

*P*

_{b}. For each of the values of

*θ*

_{a}examined in Fig. 4(a), Fig. 4(b) plots a pair of curves of primary-link data rates corresponding to two primary-link beamwidths (Φ

_{1/2,p}= 10° and Φ

_{1/2,p}= 20°), where rates corresponding to intermediate beamwidths lie between the paired curves. A common color-coding scheme is applied to Fig. 4(a) and Fig. 4(b), so that, for example, the two blue solid-line curves in Fig. 4(b) correspond to the case of 2

*θ*

_{a}= 90° in Fig. 4(a).

*B*

_{p}, we assume different parameters for the primary link from those of the beacon link, including a smaller detector suited for higher modulation rates (

*A*

_{p}= 1 mm

^{2}vs.

*A*

_{b}= 1 cm

^{2}) and a narrower bandpass filter (Δ

*λ*

_{p}= 30 nm vs. Δ

*λ*

_{b}= 100 nm) that can more effectively filter ambient noise. The other parameters in Eq. (15) assume values determined by Fig. 4(a), as the two plots are linked. For example, the transmitter pointing angle

*ψ*

_{b}and receiver field-of-view Ψ

_{b,c}are dictated by the value of 2

*θ*

_{a}chosen in Fig. 4(a) and the previous assumptions that

*ψ*

_{b}=

*θ*

_{a}and Ψ

_{b,c}=

*θ*

_{a}. The beamwidth parameter

*m*

_{b}is determined by

*θ*

_{a}and Eq. (13). The beacon receiver is assumed to be either perfectly aligned (

*ψ*

_{b}= 0) or misaligned (

*ψ*

_{b}=

*θ*

_{a}) depending on the choice assumed in Fig. 4(a). We also assume that

*T*

_{s,b}(

*ψ*

_{b}) =

*T*

_{s,p}(

*ψ*

_{b}) = 0.8 and Ψ

_{p,c}= 5°.

*θ*

_{a}= 90° with a range

*d*

_{0}= 117 m can be achieved at a power

*P*

_{b}= 0.57 W (roughly 1–2 high-power LEDs) for a misaligned receiver (

*ψ*

_{b}=

*θ*

_{a}= 45°). At this point in the design space, and at this range

*d*

_{0}, Fig. 4(b) shows that a primary link of beamwidth Φ

_{1/2,p}= 10° using 0.24 times the beacon transmitter power (

*P*

_{p}/

*P*

_{b}= 0.24,

*P*

_{p}= 0.14W) can achieve a data rate of about 1 Mb/s. Note the sensitivity of the data rate to beamwidth, as increasing Φ

_{1/2,p}to 20° drops

*B*

_{p}to about 4.5 kb/s. To instead increase the primary-link data rate

*B*

_{p}by a factor

*k*

_{p}, one could increase the power

*P*

_{p}by a factor of

*P*

_{p}/

*P*

_{b}increases by a factor of [(10 Mb/s)/(1 Mb/s)]

^{1/2}, so that

*P*

_{p}/

*P*

_{b}= 0.77 and

*P*

_{p}= 0.44 W.

*B*

_{p}= 1 Mb/s) but instead extending the range (

*d*

_{0}) of the dual-link system from 117 m to 500 m would require adjustments to both the beacon and primary links. At a beacon power of

*P*

_{b}= 0.57 W, a range of

*d*

_{0}= 500 m could be achieved by narrowing 2

*θ*

_{a}from 90° to 40°, as seen in Fig. 4(a). This adjustment would demand greater pointing precision for the beacon transmitter and receiver. Alternatively, this greater range could be reached by maintaining 2

*θ*

_{a}= 90° and increasing the power

*P*

_{b}by a factor of [(500m)/(117m)]

^{2}, as computed from Eq. (11). This power increase would require

*P*

_{b}= 10.4 W, a significant increase in the number of necessary LEDs. For reference, in the visible regime this might be on the order of two car headlights in terms of perceived brightness.

*B*

_{p}= 1 Mb/s, the primary link would also have to be adjusted. One way to extend the primary-link range is to similarly increase the primary link power by a factor of [(500 m)/(117 m)]

^{2}. An alternative is to narrow the beamwidth Φ

_{1/2,p}[and thus increase the corresponding

*m*

_{p}, defined by Eq. (2), according to Eq. (12)]. Specifically, adjusting the beamwidth from Φ

_{1/2,p}= 10° (

*m*

_{p}= 45.28) to a narrower Φ′

_{1/2,p}(and larger

*m′*

_{p}) requires following the relation

*k*

_{b}= (500 m)/(117 m) in this example. Thus the beamwidth would be narrowed to Φ′

_{1/2,p}= 3 (

*m′*

_{p}= 478.77) to support a rate of 1 Mb/s at a range of 500m.

## 4. Conclusion

## Acknowledgments

## References and links

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**OCIS Codes**

(060.4510) Fiber optics and optical communications : Optical communications

(230.3670) Optical devices : Light-emitting diodes

(060.2605) Fiber optics and optical communications : Free-space optical communication

**ToC Category:**

Optical Communications

**History**

Original Manuscript: February 20, 2014

Revised Manuscript: April 5, 2014

Manuscript Accepted: April 8, 2014

Published: May 1, 2014

**Citation**

Thomas C. Shen, Robert J. Drost, Christopher C. Davis, and Brian M. Sadler, "Design of dual-link (wide- and narrow-beam) LED communication systems," Opt. Express **22**, 11107-11118 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-9-11107

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