## 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

Since optical wireless (OW) communications was first proposed decades ago [1], there has been much exploration of its potential advantages as an alternative to traditional radio-frequency (RF) wireless technology. Unlike RF communications, OW uses spectrum that is relatively unregulated and offers large modulation bandwidths for communication [2]. Communication at these optical wavelengths can also provide high levels of security against eavesdropping and jamming, as optical links are often highly directional in nature and are typically unable to penetrate walls and other obstacles [3]. These advantages have motivated the study of OW for applications ranging from long range laser-based communications [4–7] to indoor local-area networks [8–12].

However, OW also presents its own constraints and challenges. The conversion at the receiver of intensity-modulated light to an electrical signal is fundamentally different than the conversion of an RF signal and can require a higher concentration of power incident on the receiver [2, 3]. Thus, for ranges beyond a few meters, it is often necessary for optical links to focus and precisely direct the transmitted energy onto the receiver in order to achieve desired data rates and ranges. For example, a mechanically pointed laser-based link operating at a range of 1 km can require pointing precision on the order of 10*μ*rad to 1–2 mrad [7, 13], which allows for very high data rates (e.g., on the order of 1 Gb/s) but can require bulky, specialized mechanical platforms. Such precise alignment can be also be a challenge to maintain, especially in mobile networks [2]. To address these alignment challenges, long-range links are often supported by laser-based beacons that are somewhat wider than the primary data laser have also been used to transmit positioning information and alignment feedback, but these beams are still relatively narrow (on the order of one milliradian to tens of milliradians) and assume knowledge of coarse positioning information [14], [5]. Independent RF links are often used in conjunction with laser-based FSO links, to either transmit alignment information between nodes and decrease the occurrence of complete link nonavailability or form hybrid RF/FSO networks [5, 12, 15–20].

Light-emitting diode (LED) technology is maturing into the low-cost, energy-efficient lighting source of the future [21,22], and this maturation presents an opportunity to create ubiquitous point-to-point OW links in a different regime from that of laser-based systems. Specifically, the low power consumption, compactness, low cost, reliability, and diffuse emission patterns of LEDs make them attractive candidates for use in short- to medium-range (tens to hundreds of meters) data links supporting Mb/s rates. They could be especially useful in mobile scenarios where very precise alignment can be prohibitively difficult, including some vehicle-to-vehicle or robot-to-robot communication applications. Communication in these applications has often utilized RF technology, which can sometimes suffer from external interference or generate unwanted interference in sensitive environments. LED-based communication, however, could maintain near-complete immunity to jamming interference and has much less potential to interfere with nearby electronic devices. Such technology thus has the potential to provide a wireless, robust, low-cost, secure means of communication in settings in which radio communication may cause or suffer from unwanted interference. This may include some tactical military environments and healthcare settings with sensitive electronics.

With this application space in mind, we explore the use of a directed OW communication system in which a robust, lower-data-rate, wide-beam LED-based link is used to provide acquisition and alignment support for a more tightly focused, higher-data-rate LED-based link. For both links, the beamwidths examined here are on the order of tens of degrees, which is orders of magnitude wider than what is often considered in FSO systems (10*μ*rad to 1 mrad). The relaxed alignment constraints of the proposed system make it well suited for mobile networks. To the best of the authors’ knowledge, this is the first discussion of a system that simultaneously exploits the robustness of a very wide-beam LED link and the relatively high data throughput of a more narrow-beam link.

We begin in Section 2 by describing a link model for intensity-modulation direct-detection (IM/DD) LED-based systems. In Section 3, we apply this model to investigate achievable ranges and robustness using a wide-beam link and then, based on this investigation, develop a framework for the design of a dual-link (wide- and narrow-beam) system. We illustrate this framework with calculations of achievable ranges and rates assuming one or a few LEDs, although the analysis is more generally applicable. Finally, we provide some concluding remarks in Section 4.

## 2. Link model

We consider a link model of a line-of-sight (LOS) IM/DD OW system that employs on-off keying (OOK) modulation. We assume that the transmitter has one or a few LEDs that emit light into a hemisphere and that the pattern of emission can be described by an irradiance function *I*_{s}(*d*, *ϕ*) [W/m^{2}] given by [23] as

*d*is the distance from the transmitter and

*ϕ*is the pointing angle of the transmitter, as shown in Fig. 1. The case of

*ϕ*= 0 corresponds to a transmitter that is perfectly pointed at the receiver, and thus we will sometimes refer to

*ϕ*as the “pointing error.” The average transmitted optical power is

*P*[W], and

*m*is a parameter defining the beamwidth of emission. The half-power half-beamwidth Φ

_{1/2}, which we will refer to as the “beamwidth,” is related to

*m*by

For a receiver placed at a location defined by (*d*, *ϕ*), the received optical signal power *P*_{Rx} is given by

*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]

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

_{c}. Practical concentrators often approach this ideal gain relation [23]. The case of no optical concentrator corresponds to a case of a concentrator with

*n*= 1 (free space) and Ψ

_{c}= 90°, yielding a gain of

*g*= 1.

In OW systems, there are many potential sources of noise, including thermal noise in the receiver, artificial lighting [25, 26], and shot noise from the ambient sunlight [9]. Often in OW systems, and especially for outdoor systems, the dominant noise source is shot noise from isotropic ambient light [3, 23, 26–28]. To reduce the ambient optical power *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]

This ambient light creates shot noise in the receiver, which is typically modeled as introducing zero-mean additive white Gaussian noise (AWGN) to the received photocurrent, where the variance
${\sigma}_{\text{shot}}^{2}$ [A^{2}] of the AWGN can be approximated by [9]

*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.

We use this noise model to calculate the signal-to-noise ratio (SNR) at the receiver, which we define as

*Q*(·) is the tail probability of the standard normal distribution [23]. We can relate the bit rate

*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

Using the link model of Section 2, we explore the use of a wide-beamwidth LED-based link acting as a support link for a more focused, narrow-beam link. We will refer to the wide-beam link as the beacon link, and the narrow-beam link as the primary link. Throughout this discussion, subscripts b and p will be used to denote parameters relevant to the beacon link and primary link, respectively. For instance, we define Ψ_{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.

The primary link has a more focused beam than the beacon link and is expected to support a much higher data throughput than the beacon link. Operating such a relatively directional link, however, can introduce alignment challenges, especially in mobile scenarios. To address this, we propose the joint use of the supporting beacon link. The beacon link need not provide a high data rate; rather, its purpose is to provide low-data-rate connectivity for a wide range of transmitter pointing angles *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, 10, 27, 29, 30].

The beacon link provides robustness by virtue of its relatively large beamwidth Φ_{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.

We approach the design of the beacon link beamwidth Φ_{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.

The shortest of these distances *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

*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}.

With this optimal beamwidth, beacon connectivity (*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]. However, the analysis in this work will focus on the use of a single beacon per node.

In general, the value of *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

To calculate reasonable ranges and rates, we can use Eq. (11) to plot the beacon link rate as a function of the receiver position relative to the LED transmitter. Figure 3(a) shows a contour plot of the logarithm of the rates *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 _{a}*. 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

*P*

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

*p*

_{bg}= 5.8

*μ*W/nm/cm

^{2}[23]). We also assume the receiver is composed of a colored glass filter of passband width Δ

*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).

For the purposes of acquisition and feedback control, assuming a minimum beacon rate of *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.

In general, the sensitivity of *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

In designing a system that utilizes a beacon link to support a more focused link, we require that both links achieve the same range. Although the primary link may achieve useful data rates beyond the range at which the beacon link can achieve *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).

Figure 4(a) defines a pair of curves for *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.

The ranges in Fig. 4(a) are strongly dependent on 2*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.

For the beacon parameters chosen in Fig. 4(a), and for the calculated “worst-case” ranges *d*_{0}, we next examine the data rates for the primary link with the assumption that its alignment is established and maintained by exploiting a beacon link of minimum data rate *B*_{b} = 1 kb/s. Thus we assume precise pointing for the primary link (*ϕ*_{p} = *ψ*_{p} = 0), even though for the primary beamwidths we examine (10° < Φ_{1/2,p} < 20°), the primary link is not nearly as sensitive to pointing errors as typical long-range laser-based systems. To calculate the primary link data rate *B*_{p}, consider the ratio of *B*_{p} to *B*_{b} using Eq. (11). This yields

*R*, filter properties (

*T*

_{n}=

*T*

_{n,b}=

*T*

_{n,p}), concentrator indices of refraction

*n*, bit-error rates, and ambient noise level

*p*

_{bg}.

Figure 4(b) plots *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).

To calculate reasonable values of *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°.

As a design example, we see that a beacon transmitter of 2*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
${k}_{\text{p}}^{1/2}$ [see Eq. (11)]. For example, to achieve 10 Mb/s, one could boost the primary-link power such that *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.

Maintaining the primary-link bit rate (*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.

To extend the range to 500 m while maintaining the same data rate *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
${m}_{\text{p}}^{\prime}+1={k}_{\text{b}}^{2}({m}_{\text{p}}+1)$, where *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.

We have demonstrated how Fig. 4 can be used to find reasonable ranges and rates in a dual-link system given desired power levels, beamwidths, and receiver alignments. The joint consideration of two links, primary and beacon, allows for specialization in the design of each link. Because the beacon link is to be robust, its transmission beam can be wider, its optical concentrator on the receiver has lower gain and a wider field of view, its optical bandpass filter is wider but incident-angle insensitive, and its detector area can be larger (to boost signal strength) due to lower data rates. The primary link is assumed to be more precisely aligned than the beacon link, even though its pointing demands are relaxed considerably relative to those of many laser-based systems. As the more focused, higher-throughput link, its receiver is designed to have a narrower-FOV/high-gain optical concentrator, a narrower interference-based bandpass filter (for enhanced noise rejection), and a smaller detector compatible with higher data rates. The use of these two complementary links can provide an all-optical LED-based system that is low power, compact, and robust to pointing and tracking error. This robustness may make this system a suitable adjunct to RF technology in short- to medium- range mobile networks.

## 4. Conclusion

We have presented a framework for the design of an all-optical LED-based dual-link system and have illustrated this framework with achievable range and rate predictions based on the practical parameter assumptions. The calculations show that in the presence of bright skylight it is possible to achieve a data rate of 1 Mb/s at over a hundred meters with relatively low transmitter power (e.g., < 1W optical power) and excellent robustness. This dual-link approach offers the potential for a robust, portable, compact system that can provide reasonable rates with a small number of LEDs, making it a possible adjunct or alternative to RF technology in mobile applications. The framework presented here could easily be expanded to explore optical systems that exploit many channels occupying different wavelengths over the visible and infrared domains. Future work may also explore the proposed dual-link system as the basis for multi-user networks.

## Acknowledgments

Work at the University of Maryland was supported by a grant from the U.S. Army Research Office (ARO). The third author acknowledges support by ARO under grant number W911NF-13-1-0003.

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