## Abstract

We consider outdoor non-line-of-sight deep ultraviolet (UV) solar blind communications at ranges up to 100 m, with different transmitter and receiver geometries. We propose an empirical channel path loss model, and fit the model based on extensive measurements. We observe range-dependent power decay with a power exponent that varies from 0.4 to 2.4 with varying geometry. We compare with the single scattering model, and show that the single scattering assumption leads to a model that is not accurate for small apex angles. Our model is then used to study fundamental communication system performance trade-offs among transmitted optical power, range, link geometry, data rate, and bit error rate. Both weak and strong solar background radiation scenarios are considered to bound detection performance. These results provide guidelines to system design.

©2009 Optical Society of America

## 1. Introduction

Ultraviolet (UV) communication systems have received increased attention due to advances in semiconductor optical sources and detectors, the unique potential for non-line-of-sight (NLOS) operation due to atmospheric scattering, and emerging needs in military and other applications [1]. A series of UV communication studies have been conducted and reported since the 1960s [2-7]. These have covered a wide variety of topics including channel modeling, characterization, system implementation, and networking. However, these early experimental communication systems were based on bulky and power-hungry flashtubes/lamps/lasers as light sources, and generally targeted long range communications. Advances in low cost, small size, low power, high reliability, and high bandwidth deep UV light emitting diodes (LEDs) [8,9] and avalanche photodiodes (APDs) [10,11] have motivated recent research in low power short-range UV communications [12-18].

We consider propagation and channel modeling in the context of NLOS deep UV communications. There are several aspects that require more attention, including UV scattering channel models, transceiver design techniques, communication performance bounds, and system and networking issues [1]. It has been shown that a popular single scattering channel model [19] reliably predicts observed propagation with 1/*r* range-dependent power decay for very short range *r* (on the order of meters) and large apex angles for the transmitter and receiver [14,20]. However, the validity of the single scattering model for other transceiver geometries remains unknown.

In this paper, we are motivated by the recent experimental work [18] to address the following questions. Is there a general power decay law that captures geometry effects? If so, what are the values of associated parameters such as path loss exponent and path loss factor, and how do they depend on the geometry? And, for an arbitrary geometry and communication range, can one predict communication performance such as bit error rate (BER) without conducting time-consuming experiments?

First we develop a path loss model built upon extensive field test results for a variety of system parameters. In our experiments we employ LEDs with divergent beams, a solar blind filter, and a photomultiplier detector, similar to [17,18]. The transmitter (Tx) and receiver (Rx) baseline separation is up to 100 meters. For this relatively short range, we neglect atmospheric absorption and turbulence effects. (Experiments for longer range and larger apex angle require sources with higher emission power than currently available LEDs.) Using a curving-fitting approach, a path loss model which depends on Tx/Rx apex angles and baseline separation is developed. We then study communication performance trade-offs as a function of the system parameters. These include transmitted power, data rate, communication range, apex angles, and the resulting BER. We also consider night and day operation, corresponding to a range of detector noise, from low (near shot noise limited), to medium and high solar noise cases. Overall our results provide guidelines for system design.

## 2. Experimental setup

Our path loss results are based on a solar blind UV path loss measurement test-bed at 260 nm wavelength, as shown in Fig. 1. The transmitter used a signal generator to feed a current driver circuit that powered an array of 7 ball-lens UV LEDs. The driving current for each LED was 30 mA, yielding an average radiated optical power of 0.3 mW. Using a beam profiler, the beam divergence angle was measured to be 17°. At the receiver, a solar blind filter was mounted on top of the circular sensing window of a Perkin-Elmer photomultiplier tube (PMT) module MP1922. (As APD devices mature and in future replace the PMT, the corresponding device parameters such as detection area, multiplication gain, quantum efficiency and dark count rate will need to be incorporated for accurate modeling [10,11].) The PMT’s output current was fed to a high speed preamplifier, whose output was further sent to a photon counter for photon detection. The LEDs, PMT and filter were attached to Tx and Rx angular control modules, respectively. Each module utilized two perpendicular rotation stages to achieve a precise angular control up to 360° in the azimuth and zenith directions. In this work, we have focused on the scenarios where the Tx beam axis and Rx FOV axis were coplanar, and only adjusted Tx and Rx apex angles. The Rx filter had full-width half-maximum (FWHM) bandwidth of 15 nm. Its in-band transmission was 8% and visible-band transmission was below 10^{-10}. The PMT sensing window had a diameter of 1.5 cm, resulting in an active detection area of π(1.5/2)^{2} = 1.77 cm^{2}. The PMT had an average of 10 dark counts per second (10 Hz), and the in-band UV detection efficiency of 13%. Combining the solar blind filter and PMT, the detector’s effective FOV was estimated to be 30° based on the shape and dimension of filter and PMT.

Denote the path loss by *L*. To obtain *L*, we seek the ratio of transmitted and received power *L*=*P _{t}*/

*P*or 10log

_{r}_{10}(

*P*/

_{t}*P*) in decibels, estimated as follows. In most of the testing configurations, the received power is typically too weak to be measured via a power measurement unit. Consequently, we use the high sensitivity PMT for photon counting and then adopt the number of received photons per pulse for calculating

_{r}*L*. On the other hand, at the Tx, direct measurement of the total number of emitted photons from the LEDs by a photon counter is not possible because the reading easily overflows the counting limit. Thus, the transmitted optical power was measured using a high performance power meter and the corresponding photon count was calculated from the measured power and wavelength. Each photon carries energy

*hc*/

*λ*where

*c*is the speed of light, and

*h*is Planck’s constant. Denote the transmitted pulse duration as

*T*. Then the average number of transmitted photons per pulse is

_{p}*N*=

_{t}*P*/(

_{t}T_{p}λ*hc*). The number of photons detected per pulse is

*N*, which is a percentage of the number of photons

_{d}*N*impinging on the receiver (the solar blind filter in series with the PMT). It is given by

_{r}*N*=

_{d}*η*where

_{f}η_{r}N_{r}*η*is the filter transmission and

_{f}*η*is the PMT detection efficiency. Finally, the path loss is given by 10log

_{r}_{10}(

*N*/

_{t}*N*) dB.

_{r}We first validated our measurement system in a line-of-sight (LOS) configuration. In Fig. 2, experimental path loss is compared with an analytical square-law power decay model as a function of Tx and Rx separation distance [21], showing very good agreement. Then we used this validated test system for our NLOS link performance study, as detailed next.

## 3. Path loss measurements and modeling

Our planar communication geometry is shown in Fig. 3 [18,20]. Denote the Tx beam full-width divergence by *ϕ _{1}*, the Rx FOV by

*ϕ*, the Tx apex angle by

_{2}*θ*, Rx apex angle by

_{1}*θ*, the Tx and Rx baseline separation by

_{2}*r*, and the distances of the intersected (overlap) volume

*V*to the Tx and Rx by

*r*and

_{1}*r*, respectively.

_{2}We conducted extensive testing for path loss by varying Tx apex angle, Tx and Rx baseline separation, and Rx apex angle. Beam divergence and FOV were fixed; their effects can be investigated with additional optics to control beam width and FOV. The test distance under a full range apex angle (Tx 0~90°, Rx 0~90°) was limited to about 25 m due to the LED array transmission power. We also tested at distances of 70 m and 100 m with small apex angles (0°~45°). Longer range tests (to a few kilometers) will be conducted with a higher power laser UV source.

Experimental and analytical results in [14,18,20] show that the NLOS channel path loss in tested configurations was proportional to *r ^{α}* where

*α*varies with apex angle. For example, it was shown that Tx and Rx apex angles of 90° result in

*α*close to 1 [14,20], whereas apex angles at 30° or 45° experimentally yield

*α*in a range of 1.4~1.7 [18]. In addition to this path loss dependence on apex angles, the atmospheric attenuation renders path loss exponentially increasing with

*r*[20]. We therefore postulate the following model for NLOS path loss

where the parameters of path loss factor *ξ*, path loss exponent *α*, and attenuation factor *β* are all functions of the Tx and Rx angles. The parameter *α* takes a value of 2 for a point source in a free space LOS link as demonstrated in Fig. 2, but reduces to 1 in certain NLOS geometries [14,20]. We will show experimentally that this model better captures the path loss properties than a model based on a single scattering assumption [19].

For short range communications upon which our measurements rely, the effect of *β* is negligible with the value of the attenuation coefficient on the order of (1~10) km^{-1} [4]. However, we note that its effect may become appreciable when the distance is longer than 1 km. Thus, for the short range case in this paper, we model path loss using

where path loss exponent *α* and path loss factor *ξ* are functions of the apex angles.

#### 3.1 Path loss exponent

We conducted many measurements at distances of 8 m, 15 m and 25 m, for a large range of Tx/Rx apex angles. At each distance, we varied both the Tx apex angle *θ _{1}* and the Rx apex angle

*θ*from 0° to 90° with a step size of 10°. We recorded the received number of photons and obtained the path loss

_{2}*L*for each distance and geometry as described above. Using these measurements, we applied a curve-fitting technique to estimate the path loss exponent

*α*and path loss factor

*ξ*. For example, to find

*α*for any fixed pair of Tx and Rx apex angles, we utilized all path loss measurements at different distances and obtained the ratios

*L*/

_{i}*L*=(

_{j}*r*/

_{i}*r*)

_{j}^{α}, for

*i, j*=1,2,3,

*i*≠

*j*. Notice that

*α*is not a function of distance. Then

*α*was estimated from the average of log

_{10}(

*L*/

_{i}*L*)/log

_{j}_{10}(

*r*/

_{i}*r*). For small apex angles, we improved the estimation accuracy by obtaining additional data points at the longer distances of 75 m and 100 m.

_{j}Figure 4 shows the path loss exponent *α* for different Tx and Rx apex angles. The exponent *α* varies from 0.45 to 2.4. For Rx apex angle less than 20°, *α* is close to 2. In this case, path loss is very sensitive to distance. For Rx apex angle larger than 70°, *α* is either close to 1 or less than 1, leading to low sensitivity with distance. For both Tx and Rx angles close to 90°, *α* is around 1, which agrees with results reported in [14].

Although correspondence of the path loss exponent to apex angles is numerically demonstrated by this figure, a closed-form analytical expression for the path loss exponent as a function of apex angles is difficult to obtain due to complexity of their relations. The same situation also applies to the path loss factor to be discussed next.

#### 3.2 Path loss factor

The small path loss exponent a corresponding to large Tx and Rx apex angles does not mean that the total path loss is smaller for a larger apex angle since it also depends on the path loss factor *ξ*. In fact, *ξ* becomes dominant in the overall path loss as angles increase, as seen from Fig. 5. This was obtained as an average of all *L _{i}*/

*r*according to Eq. (2) and estimated path loss exponent

_{i}^{α}*α*as above. The path loss factor changes by several orders of magnitude for varying Rx angles at any given Tx angle. The path loss dynamic range with a small Tx angle varies considerably more than with a large Tx angle. For example, we observe two orders of magnitude change with a 90° Tx angle, while this increases to five orders of magnitude with a 10° Tx angle. On the other hand, for a fixed Rx angle, the difference is about three orders of magnitude when the Rx angle is small, and less than one order of magnitude when the Rx angle is large.

#### 3.3 Path loss model validation

For given Tx/Rx apex angles and baseline distance within tens of meters, the path loss exponent is obtained from Fig. 4 and the path loss factor from Fig. 5. Then, the path loss may be calculated from Eq. (2). These results for short range links can be used to predict path loss for medium communication range, say up to a few hundred meters, so long as the attenuation can be safely ignored.

As a means of validation, we used the above results to predict path loss for Tx and Rx apex angles up to 40° with a baseline separation of 100 m. (Recall that at this range we are restricted to smaller apex angles to achieve sufficient signal-to-noise ratio at the receiver.) Figure 6 compares prediction and measurement, depicting reasonably good agreement between predicted and tested results. The prediction errors for each Tx apex angle are within a few decibels over the specified range of the Rx apex angle.

Next we compare with the single scattering channel impulse response model for NLOS UV communication [19], which has been adopted to predict path loss at various distances [14,20]. Figure 7 shows the comparison for different Tx and Rx apex angles. For large apex angles, the difference between the two models is very small. Also, from the slopes of the path loss lines, the large angle path loss exponent *α* is found to be 1. This has also been verified experimentally [14,20].

Our model and the single scattering model differ for small apex angles. In this case, the single scattering model maintains *α* = 1, predicting a 1/*r* power decay profile irrespective of apex angles. However, *α* is expected to approach 2 as both Tx and Rx angles approach 0°, such as in the LOS case [21]. From Figure 7, our proposed model yields *α* = 1.88 under the Tx angle of 20° and the Rx angle of 30°, close to *α* = 2 and consistent with Fig. 4. Therefore, the proposed path loss model predicts link loss more reliably than the single scattering model over a large range of apex angles. The poor prediction performance of the single scattering model under small apex angles also suggests that a more realistic multiple scattering
analytical channel impulse response model is necessary to characterize NLOS link performance with a variety of pointing conditions.

Next, we apply our model to predict communication performance and study system tradeoffs in power, distance, data rate and BER.

## 4. Predicted communication bit-error performance

The BER for a communication system depends on several parameters, including modulation format, detector type, transmitted power, path loss (as a function of angles and distance), data rate, and noise. We restrict our attention to on-off keying (OOK) and direct detection (e.g., see [21]) and analyze BER performance of the corresponding UV system. Analysis for other cases can be similarly carried out.

The BER expression may take different forms depending on the noise level and distribution. For photon counting with a very low dark count rate PMT detector, we assume the primary noise stems from solar radiation, and the noise level varies from day to night. With a 200 μs pulse width, we found that low, medium and high noise conditions gave rise to measured (0.03, 0.95, 2.9) photon counts per pulse, equivalent to the noise count rates of (0.15, 4.75, 14.5) kHz respectively. For a medium or high noise scenario, such as daytime operation or with longer pulses, the noise is assumed Gaussian distributed. Then, the BER may be calculated as a function of signal to noise ratio (SNR) using the *Q*-function [21]

Following our discussion in Section 2, the SNR is calculated from the ratio of the number of detected signal photons *N _{d}* and noise photons

*N*by

_{n}*SNR*=

*N*/

_{d}*N*, where

_{n}*N*is given by

_{d}*N*=

_{d}*η*=

_{f}η_{r}N_{r}*η*/

_{f}η_{r}N_{t}*L*=

*η*/(

_{f}η_{r}P_{t}λ*hcRL*) and

*R*is the data rate. For the low noise case, such as at night time or with shorter pulses, we adopt a shot-noise-limited BER formula assuming both signal and noise follow Poisson distributions [21]

where *m _{T}* is the optimum threshold given by an integer floor operation of a continuous variable

*a*

Note that *N _{d}* is a function of multiple system parameters.

Next we use our results to predict the effects of path loss, communication range, Tx/Rx apex angles (embedded in path loss), transmitted optical power, and data rate on communication performance in terms of BER. This will be based on our path loss model and either Eq. (3) or Eq. (4). Subsequent BER curves corresponding to the low noise case are based on Eq. (4), while BER curves corresponding to the medium noise and high noise cases are based on Eq. (3). Note that pulse duration is related to data rate *R* by *T _{p}*=1/

*R*for an OOK modulation system.

#### 4.1 BER versus path loss

Path loss directly impacts BER performance since it affects *N _{d}*. Their correspondence is demonstrated in Fig. 8 for the high, medium and low noise cases. Here the Tx optical power is 10 mW and data rate is 5 kbps. BER varies rapidly at low path loss, and converges to 0.5 as path loss increases to infinity. The slightly non-smooth curve in the low noise case is due to discrete-valued formula (4). A roughly 9 dB path loss difference is observed at BER of 10

^{-3}between the low and high noise cases.

#### 4.2 BER versus distance

As an example with realistic system parameters, let UV LEDs emit 10 mW optical power, the Tx and Rx apex angles be 30°, and a data rate of 5 kbps. Figure 9 shows BER performance against distance for the high, medium, and low noise cases. According to Fig. 4 and Fig. 5, the path loss exponent at these apex angles is 1.72 and path loss factor is 8.54×10^{6}. These numbers translate into path loss as a function of distance using Eq. (2). For example, for *r* = (10, 20, 30) m, the path loss is calculated to be (86.5, 91.7, 94.7) dB. Then for the high noise case, the corresponding BERs (4.5×10^{-5}, 1.6×10^{-2}, 6.4×10^{-2}) in this figure are consistent with those three points in Fig. 8. Similarly one can find correspondence for the medium and low noise cases. BERs are sensitive to distance when the distance is small, and converge to 0.5 at a large baseline separation. Note that in this scenario, for a given noise level, the BER changes by a few orders of magnitude when *r* increases from 10 m to 20 m.

#### 4.3 BER versus Tx/Rx apex angles

We next predict BER performance as a function of different Tx/Rx geometry in the case of medium noise (0.95 counts per pulse). By varying Tx/Rx apex angles, the path loss exponent and path loss factor are obtained from Fig. 4 and Fig. 5. Then at a given distance, path loss is calculated from Eq. (2). Consequently the BER can be calculated via Eq. (3).

Assume an LED array with power 10 mW, communication distance 25 m, and data rate of 5 kbps. Figure 10 depicts the resulting BERs. Large BER variations can be observed for different geometry choices. In addition, the slopes of the plotted BER versus Rx apex angle curves are different for different Tx apex angles. A small Tx apex angle leads to sharp degradation of BER as the Rx apex angle increases. In general, when the Rx angle is smaller than 40°, BER degrades very fast with increased Rx angle. For example, when the Tx angle is 60°, the BER increases from 3×10^{-5} to 10^{-1} when the Rx angle changes from 20° to 40°. For a fixed Rx angle less than 30°, the BER is very sensitive to the Tx angle. This angle dependence may be attributed to angular dependent scattering, as represented by the scattering phase function [4,20].

#### 4.4 BER versus Tx optical power

Transmitted optical power has an effect on BER that is similar to that from the inverse of path loss. In Figure 11, we vary the Tx optical power *P _{t}* from 1 mW to 300 mW and show BER versus

*P*for different distances. Assume the Tx and Rx apex angles are fixed at 30° (giving path loss exponent 1.72), data rate of 5 kbps and a medium noise environment. If we increase the distance by a factor of four, such as from 25 m to 100 m, while maintaining a constant detected signal power (equivalently constant BER),

_{t}*P*has to increase by a factor of 4

_{t}^{1.72}≈ 10.86 according to Eq. (2). This can be observed in Figure 11.

#### 4.5 BER versus data rate

BER performance and communication data rate also provide a trade-off with the other parameters fixed: the lower the data rate, the lower the BER. Here we consider one pulse per bit and vary the data rate from 100 bps to 1 Mbps by varying pulse width *T _{P}* from 10 ms to 1 μs. The Tx and Rx angles are fixed at 30° and Tx power at 10 mW, and we consider the low noise case. Figure 12 depicts BER versus data rate for different distances. For a given distance, the BER typically changes by five orders of magnitude when the data rate changes by only one order. For a fixed BER, the data rate decreases by a factor of

*x*when the distance increases by

*x*

^{1.72}times, as predicted by Eq. (2) and SNR expressions. For example, from 20 m to 100 m at a BER of 10

^{-3}, the data rate decreases from 5.74 kbps to 360 bps, about a 15.9 times decrease, which is consistent with a predicted value of 5

^{1.72}. The high sensitivity of BER to distance is due to the high sensitivity of path loss over some ranges, as in Fig. 8.

## 5. Conclusions and future work

This paper presented a path loss model for short range NLOS UV links based on extensive field measurements. The path loss exponent and path loss factor were obtained as a function of transmit and receive apex angles, respectively. The proposed model can predict UV NLOS link loss reliably for a large range of apex angles and separation distance (whereas results based on a single scattering model are generally only accurate for large apex angles; e.g., see [20]). Using this model, various analytically predicted BER results were demonstrated, and system performance trade-offs were studied in detail, including transmitted optical power, communication range, apex angles, and data rate. These experimental and analytical results are valuable for the design of a practical NLOS UV communication system.

Further study is needed to develop an analytical NLOS UV channel impulse response model from which path loss can be found. The model should incorporate different
meteorological conditions, the effects of beam divergence angle and FOV. This enables study of NLOS UV channel capacity [22], as well as achievable rate for particular system choices. Incorporating the attenuation factor *β* in the channel model is also a topic of interest, enabling analysis for longer ranges. This can be explored experimentally by employing a high power UV source.

## Acknowledgments

The authors would like to thank Qunfeng He for his invaluable help with experiments. This work was supported in part by the Army Research Office under Grants W911NF-06-1-0364, W911NF-08-1-0163, and W911NF-06-1-0173, and the Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0011.

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