1. Introduction

Recent advances in ultraviolet (UV) light-emitting diode, filtering, and detection technology has spawned considerable research interest in UV communications (UVC). The use of deep-UV wavelengths (200–300 nm), in particular, has garnered much attention [1], owing to distinct characteristics of the atmospheric propagation of deep UV that present unique communication opportunities and challenges [2]. The significant atmospheric scattering of deep UV provides a mechanism by which transmitted radiation can be detected by a receiver without line of sight (LOS), a novelty for optical communications. Because only a small fraction of the transmitted radiation is expected to be fortuitously redirected toward a receiver by such scattering, a non-line-of-sight (NLOS) UVC system must contend with high path loss. Fortunately, ozone and other atmospheric constituents absorb nearly all deep-UV solar radiation, resulting in a virtually noiseless communication channel amenable to the use of highly sensitive photon-counting detectors, such as photomultiplier tubes (PMTs), that are capable of detecting a highly attenuated transmission.

Even with the use of photon-counting detectors, path loss is expected to limit practical UV communication distances, and for this reason, NLOS UVC is often envisioned for providing short-range (e.g., a few kilometers) low-rate (e.g., 1–100 kb/s) communication links to supplement conventional technologies by exploiting an otherwise untapped spectral resource. For example, hybrid networks comprising UV and radio-frequency (RF) links might employ UVC for local area connectivity, conserving RF bandwidth for longer range, higher rate communications. Alternatively, UVC might be used in lieu of RF systems to maintain connectivity in RF-denied environments, as might be encountered in various military applications.

Because the operation of NLOS UVC is based on the complex interaction of transmitted UV radiation with the atmosphere, modeling this propagation channel is challenging but essential to characterizing and realizing the potential of UVC systems. A common approach involves modeling the probability that a transmitted photon will traverse a particular path from the transmitter to the receiver, accounting for device characteristics and the physics of atmospheric absorption and scattering [3,4]. Summing the contribution to the received energy (or detection probability) from all such propagation paths can then yield a prediction of the expected path loss for a particular system configuration [5–7]. Additionally, by incorporating the length of each propagation path, an estimate of the temporal variation in the received energy (or detection probability) in response to, for example, a transmitted impulse can be obtained [8, 9]. Computational aspects of this modeling approach have been extensively studied, and experimental measurements have provided reasonable validation of model predictions.

The development of NLOS UVC channel models has enabled the study of system performance and design tradeoffs. For example, [10] examined the effect of system geometry (i.e., pointing angles, beamwidths, etc.) on BER performance, [11] characterized the performance of various modulation formats, and [12] compared receivers employing PMTs versus avalanche photodiodes as detectors. In addition, novel approaches to, for example, physical-layer authentication [13], full-duplex communication [14], and networking [15] have been proposed based on unique features of this communication channel. An extensive survey of UVC channel modeling and systems analysis research is given in [1].

A common model for the detection process in a photon-counting receiver assumes that impinging photons trigger detection events independently with a probability given by the quantum efficiency of the detector. In fact, due to intrinsic properties of the detector and the response times of signal processing circuitry, there is a period of time after an (ultimately detected) photon impinges on the detector during which subsequently impinging photons cannot be detected. During this so-called dead time, the receiver is essentially in a reset state and photons that otherwise would have been detected are lost, resulting in modified count statistics.

Dead time effects have been studied for decades in a variety of applications; an extensive survey of early work (up to 1981) is given in [16]. A key focus of this research has been the analysis of the statistical properties of a counting process with dead time for various underlying processes (i.e., the counting process with no dead time), including a homogeneous Poisson process [17], a heterogeneous Poisson process with a known deterministic rate function [18], and a doubly stochastic Poisson process [19, 20]. Experimental observations of dead time have been reported [21], and implications of dead time effects for system design and performance have been studied for various applications, such as image detection [22] and positron emission tomography (PET) [23]. More-recent studies of dead time include a reexamination of statistical modifications in the context of PET and single-photon emission computed tomography [24], the examination dead-time effects on Geiger-mode avalanche photodiodes [25], and the analysis of dead-time effects on non-Poisson data [26].

Prior work in NLOS UVC assumes that detector dead time has a negligible effect, a reasonable assumption in many practical system configurations. For example, a system employing on-off keying (OOK) with low-power light-emitting diodes for communication at ranges and rates of less than 100 m and 10 kb/s, respectively, might require on the order of ten photons to be detected over a period of 100 μs or more. As such, the photon arrival rate can be assumed to be low enough that it is unlikely for a photon to arrive during the dead time of the receiver. However, UVC systems that are designed to communicate over longer distances (e.g., 1 km) and/or at higher rates (e.g., 10–100 kb/s) might employ, e.g., a pulsed laser to overcome increasing path loss and allow for noise gating at the receiver. As these systems are expected to deliver large bursts of energy over short intervals, it is no longer clear that losses due to dead time can be neglected.

In this paper, we build upon our preliminary work [27], studying representative UVC system scenarios to provide insight as to when dead time effects can be significant and then to characterize those effects. As in [27], we begin by extending a UVC channel model to account for dead time in the detector. Focusing on particular UVC system specifications that are consistent with a system that we previously developed, we then examine the output of the extended channel model to demonstrate the levels of dead time at which the nonideal detection behavior can result in significant loss for various system geometries. Next, for a particular dead-time specification that is consistent with our fielded system, we characterize model predictions for dead time loss, comparing these predictions with experimentally collected data. Finally, we examine how dead time can alter received photon count statistics and, thus, degrade UVC performance.

2. UVC modeling with dead time

2.1. Channel model

To study the effects of dead time given a particular system scenario, we require a model for the temporal variation in received energy in response to, e.g., a transmitted impulse as a function of system and atmospheric parameters. We employ a common modeling approach that considers the likelihood that a transmitted photon will traverse a particular path from the transmitter to the receiver. The particular model we employ is described in [9]; we provide a brief summary below.

Figure 1(a) illustrates the notation we use to describe a UVC system geometry. In particular, r is the distance from the transmitter to the receiver, θ_T and ϕ_T are, respectively, the inclination and azimuth angles defining the transmitter pointing direction, β_T is the beamwidth of the transmitter, θ_R and ϕ_R are, respectively, the inclination and azimuth angles defining the receiver pointing direction, and β_R is the angular field of view (FOV) of the receiver.

 

Fig. 1 Notation for (a) a UVC system geometry [9] and (b) a planar photon propagation path from the transmitter to the receiver [7].

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Given the parameters of the system geometry, we model the likelihood of a particular photon path comprising n atmospheric scattering events using the notation illustrated in Fig. 1(b), which, for visual clarity, depicts a planar propagation path with n = 2. The transmitter is located at v₀, the n scattering locations are given sequentially by v₁, v₂,..., v_n, the receiver is located at v_n+1, and r_i ≜ ‖v_i+1 − v_i‖, where ‖·‖ denotes the Euclidean norm. The angle between the transmitted photon direction v₁ − v₀ and the transmitter pointing direction is α₀, the deflection of the photon at the ith scattering event is α_i, and the angle between the received photon direction v_n − v_n+1 and the receiver pointing direction is α_n+1. Note that for a nonplanar propagation path, an additional angle ψ_i associated with each α_i is needed to fully describe the direction of the corresponding path segment.

With this notation, we can model the probability P_D,n that a transmitted photon will arrive at the receiver after n scattering events as an integral over the probability density function of the relevant paths [7]

Given P_D,n, the total probability P_D that a transmitted photon will arrive at the receiver is

2.2. Communication system model

Consider a transmitted pulse with energy E_Tx and normalized pulse shape p_Tx(t), so that, in particular, the total number of transmitted photons is given by N_Tx = E_Txλ /(h_pc), where λ is the transmitted wavelength, h_p is the Planck constant, and c is the speed of light. In the absence of dead-time effects, the expected number of detected photons from this pulse is given by

Incorporating the IRF of the channel and the transmitted pulse shape, we can describe the temporal variation in received signal counts by defining the rate function

Now, for a receiver with dead time τ, the counting process N_τ(t) of detections (assuming the same transmitted pulse as before) is no longer a Poisson process. The effect of dead time on the counting process depends on whether the dead time is nonparalyzable or paralyzable. In the former case, the receiver enters a reset state when successfully detecting an impinging photon and emerges from that reset state after the dead time expires, regardless of whether additional photons impinge on the detector during the dead-time interval. In contrast, the reset state of a paralyzable receiver is prolonged with each photon that would have been detected had the receiver not been in reset. Here, we examine the nonparalyzable case, as this is consistent with the experimental system used to collect the data that is reported in Section 5, though the approach can be modified to study paralyzable dead time as well.

Although there has been substantial work on analytically characterizing dead-time processes for both paralyzable and nonparalyzable dead time [16], we choose to statistically study realizations of the dead-time processes so as to avoid making assumptions regarding the rate functions μ(t). (For example, a common analysis approach assumes that the rate function varies slowly on the time scale of the dead time, but this is not the case in many of the scenarios considered here.) Given μ, μ[n] and τ, we generate such a realization by thinning a realization of the counting process N(t) as follows.

We first generate a realization N(∞) of the total count according to a Poisson distribution with parameter μ. Noting that the normalized (discrete time) rate function

Having generated N(t), and equivalently 𝒯, we then thin 𝒯, removing those arrival times that occur during the dead time of the receiver. The ordered set of detection times 𝒯̃ ≜ {t̃₁, t̃₂,...} for the receiver with dead time τ is constructed by setting t̃₁ = t₁ and, sequentially for i = 2, 3,..., setting t̃_i = min{t ∈ 𝒯 : t > t̃_i−1 + τ}, terminating when {t ∈ 𝒯 : t > t̃_i−1 + τ} = ∅. We then have

By generating a large number of realizations of N_τ(∞), we can obtain an estimate of the expected total count μ_τ ≜ E{N_τ(∞)}. Note that, since τ = 0 for a detector with no dead time, we have μ₀ = μ. Finally, we define the total loss of the end-to-end channel in decibels as

It should be noted that the above discussion assumed that detections due to noise are negligible. However, by considering a finite detection window, the incorporation of optical and dark noise amounts to the addition of a constant to Eq. (3) and a constant function to Eq. (4).

3. Channel rate functions

To illustrate the potential for dead time to impact practical UVC systems, we begin by examining model predictions of channel rate functions, as given by Eq. (4), parameterized by the range and transmitter and receiver elevation angles. [We assume throughout that the transmitter and receiver pointing directions are coplanar—i.e., that (ϕ_T,ϕ_R) = (−90°, 90°).] For concreteness, we consider system specifications that are consistent with the channel measurement system used to collect model validation measurements reported in Section 5. In particular, we assume that the transmitter is a 266-nm laser that emits 4-mJ Gaussian-shaped pulses with a full-width half-maximum (FWHM) pulse width of 4 ns and a FWHM beamwidth of 0.003 rad and that the receiver has a FOV of 30°, an effective sensor area of 1.77 cm², optical filtering loss of 8.86 dB, a quantum efficiency of 0.10, and a dead time of 40 ns. These specifications are assumed throughout this paper unless otherwise noted.

Figure 2 depicts the rate function predictions, where Figs. 2(a), 2(b), and 2(c) consider low pointing angles (θ_T, θ_R) = (80°, 80°) and ranges of 100 m, 506 m, and 2563 m, respectively, while Figs. 2(d), 2(e), and 2(f) consider elevated pointing angles of (θ_T, θ_R) = (40°, 0°) and ranges of 100 m, 506 m, and 2563 m, respectively. The extreme variability in the characteristics of the received pulse over the considered system geometries is evident, with peak rates varying by over eight orders of magnitude and pulse widths varying from around 10 ns to over 10 μs. Also, we observe that Fig. 2(f) is unique in that it exhibits two peaks. As noted in [9], such behavior can arise when the total contribution to the received energy from singly scattered radiation is comparable to that from multiply scattered radiation, as these two sources of received radiation have different temporal characteristics.

 

Fig. 2 Model predictions of rate functions for various system geometries [27]. Note the varying scales of the axes.

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In Section 4, we will precisely determine the dead time loss associated with the given rate functions by employing the dead time system model developed in Section 2.2. However, we first note that one can loosely predict whether dead time losses will be significant simply by examining the peak value of the corresponding rate function. In particular, for a receiver with dead time τ, photons arriving at a rate that is greater than 1/τ have a significant chance of arriving during the dead time of a previous detection. (More precisely, significant dead time effects can be expected when the rate function exceeds this approximate threshold for some finite period of time that depends on the magnitude of the rate function.) Hence, an approximate criterion for dead time to be a nonfactor for a particular system geometry is that the rate function not exceed approximately 1/τ. For τ = 40 ns, this implies a rate function threshold of approximately 1/τ = 2.5 × 10⁷ photons/s.

From Figs. 2(a)–2(c), we see that configurations with low pointing angles are likely to experience dead time effects, even at long ranges of 2.5 km or more. As reducing the elevation of the transmitter and receiver is one of the most effective ways to overcome the high path loss associated with long-distance NLOS UVC, it is clear that dead time can be a serious consideration in the design of such systems.

On the other hand, Figs. 2(d)–2(f) illustrate how increasing the elevation angles can reduce dead time effects. The increased path loss and pulse spreading associated with such system geometries can reduce the rate function peaks by orders of magnitude for a given range. (Of course, increased path loss and pulse spreading can be directly detrimental to communication performance as well.) Nevertheless, even for elevated geometries, we expect significant dead time effects at moderate distances of, say, less than 500 m. The peak of the rate function depicted in Figure 2(e) for a range of 506 m is on the order of 1/τ, and hence we expect that this approximate distance is a transition beyond which dead time effects may become insignificant.

4. Model predictions of dead-time loss

In this section, we quantify dead time losses associated with our representative system configuration by employing the dead time system model described in Section 2.2. Figure 3 considers the channel loss as a function of range for various receiver inclination angles with θ_T = 80° fixed. In particular, Fig. 3(a) compares the total loss TL₀ for an ideal detector (τ = 0) with the total loss TL_τ for the practical detector (τ = 40 ns), and Fig. 3(b) depicts the corresponding dead time loss TL_τ − TL₀.

 

Fig. 3 Model predictions of total loss and dead time loss for θ_T = 80°, where in (a) solid lines correspond to an ideal detector with no dead time (τ = 0) and dashed lines correspond to a practical detector with dead time τ = 40 ns [27].

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For the ideal detector, we observe the intuitive property that the total loss is monotonically increasing with range and with receiver elevation. However, the total loss for the practical detector exhibits a more complicated behavior, initially decreasing with range and then increasing as it approaches the total loss for the ideal detector. Similarly in contrast to the behavior for the ideal detector, the total loss for the practical detector decreases with receiver elevation at short range, but this trend reverses at long range.

The complicated behavior for the practical detector at short range can be understood as follows. Although the path loss associated with the atmospheric propagation channel decreases as range or receiver elevation decreases, many of the additional photons that impinge on the practical detector arrive during the dead time. Hence, the increased number of impinging photons does not have a significant effect on the total loss as a function of range, which in itself would suggest that the loss curve would initially be horizontal. However, the received pulse width also decreases with decreasing range or receiver elevation, further reducing the number of photons that can be detected by the saturated receiver. Hence, the number of detected photons can actually decrease as the range or receiver elevation decreases, as suggested by the Fig. 3(a).

In contrast to the total loss curve for the practical detector, we observe in Fig. 3(b) that the corresponding dead time loss is monotonically decreasing in range and receiver elevation. In particular, we note that the dead-time loss initially decreases with range at a sufficient rate to overcome the increase in atmospheric path loss, resulting in the decrease in the total loss. However, we emphasize that even though increasing the range can reduce the dead-time losses (and, hence, the total loss), the statistics of the received signal are also modified, so one cannot conclude that the reduced loss implies better communication performance. Finally, the case of θ_R = 80° confirms our prediction in Section 3 that, for this configuration, a 40-ns dead time will have a significant impact on the received signal out to 2.5 km and beyond.

Next, Figs. 4(a) and 4(b) present analogous results for various transmitter elevation angles with θ_R = 0° fixed, and similar observations can be made in this case. Of note is that for this configuration the range at which the total loss curves for the practical detector approach that for the ideal detector is significantly reduced. This corresponds to the dead time loss curves approaching 0 dB at reduced range, though we see high variability depending on θ_T. In fact, for θ_T = 80°, dead-time losses appear insignificant beyond around 200 m, while for θ_T = 80°, dead-time losses appear significant beyond around 2 km. Also, based on the rate functions presented in Section 3, we predicted that, for the case of θ_T = 40°, dead time losses would become insignificant beyond 500 m or so, and we see in Fig. 4(b) that this is indeed the case.

 

Fig. 4 Model predictions of total loss and dead time loss for θ_R = 0°, where in (a) solid lines correspond to an ideal detector with no dead time (τ = 0) and dashed lines correspond to a practical detector with dead time τ = 40 ns [27].

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5. Experimental validation

We next examine previously reported channel-measurement data [31] to validate our proposed dead-time path-loss model. This data was collected using a laser-based transmitter and a photon-counting receiver, each with specifications consistent with those assumed in this paper and synchronized using GPS clocks. (In particular, we note that the estimated receiver dead time of τ = 40 ns was based on oscilloscope measurements of the output of the receiver in saturation.) For given system geometries, laser pulses of known energy were transmitted and the number of photon counts per pulse was measured. An empirical estimate of the total loss for each geometry was then obtained as the ratio of the average measured photon count per pulse to the number of transmitted photons per pulse. We refer to [31] for further details on this experiment.

Figure 5 depicts the measured total loss and the total loss predicted for an ideal detector and a practical detector with dead time τ = 40 ns. (Note that the transmitter and receiver elevation angles are defined as 90° − θ_T and 90° − θ_R respectively.) In Fig. 5(a), we observe that the measured total loss increases as the receiver elevation decreases from 50° to 10°, a trend predicted in the previous subsection, suggesting that receiver saturation occurred at least in these cases. Indeed, the predicted total loss assuming an ideal detector significantly underestimates the total loss in all cases in Fig. 5(a), with an error of nearly 8 dB at a receiver elevation of 10°. On the other hand, model predictions assuming a dead time of τ = 40 ns capture well the general trends of the measured total loss and exhibit an error of less than approximately 2 dB in all cases.

 

Fig. 5 Comparisons of experimental results and model predictions for experimental system configurations with (a) a range of 400 m and a transmitter elevation angle of 70° and (b) a range of 758 m and a receiver elevation angle of 90°.

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Meanwhile, for the cases considered in Fig. 5(b), the predicted total loss for an ideal detector again tends to underestimate the measured total loss, while the predicted total loss for a receiver with dead time of τ = 40 ns better captures the general trends of the measurements and exhibits limited error throughout. However, the accuracy of the model with a practical detector does appear to degrade slightly at higher transmitter elevation angles, whereas the model with an ideal detector appears to quite accurately predict the measured total loss. Additional measurements are likely necessary to determine if this behavior is an indication of relative model fidelity or if it can be attributed to, e.g., measurement error.

6. Communications with dead time

In light of the well-known data-processing inequality [32], dead time can only degrade (or leave unchanged) communication performance (as compared to a detector with no dead time) when an optimal estimator is employed at the receiver. Furthermore, such performance degradation may be exacerbated by channel model mismatch for a suboptimal receiver that is unaware that dead time has altered the distribution of the received counts. We illustrate these notions by examining PMFs of received counts under various assumptions for representative OOK communication scenarios in which a pulse is either transmitted or not to communicate a “1” or “0” bit, respectively. In particular, we assume θ_T = 80°, θ_R = 80°, a range of either 1709 m or 3844 m, a transmitter energy per pulse of either 4 mJ or 40 mJ, and an average dark noise count rate of 10 kHz, consistent with noise measurements reported in [33].

We assume that the receiver employs noise gating, so that only photons that impinge during the time interval when a transmitted pulse might arrive at the detector are considered. We determine this gate interval by examining the Poisson rate function for the received pulse and (arbitrarily) selecting the endpoints of the interval so that approximately 0.1% of the energy arrives each before the start of the gate and after the end of the gate. For the cases considered, the resulting gate intervals are less than approximately 1 μs, resulting in an average number of dark noise counts per gate interval, denoted λ_n, of less than approximately 0.01. In the absence of a transmitted pulse, the received count for an ideal detector is therefore Poisson distributed with parameter λ₀ = λ_n. Although this distribution is theoretically altered when considering the practical detector with dead time τ = 40 ns, the small value of λ₀ makes the occurrence of more than one noise event in a single gate interval extremely unlikely, and it is even more rare for two or more noise events to be within a 40 ns dead-time interval so as to result in a missed detection. As such, the received counts for the practical detector when no pulse is transmitted are well approximated as being Poisson distributed with parameter λ₀.

Now, for an ideal detector, the signal count given a transmitted pulse is Poisson distributed with a parameter λ_s,ideal that can be estimated from the channel model. The total number of received counts (i.e., the sum of signal and noise counts) for the ideal detector is hence also Poisson distributed with parameter λ_1,ideal = λ_s,ideal +λ_n. For the practical detector, the distribution will depend on the Poisson rate function for the channel (with an additional contribution from the dark noise), and so we must employ our dead-time model to obtain an empirical estimate of the PMF.

Figure 6 depicts PMFs estimated as previously discussed. The PMFs of the received counts when a pulse is not transmitted (i.e., a “0” is communicated) are labeled “Poiss(λ₀).” Meanwhile, PMFs for received counts when a pulse is transmitted (i.e., a “1” is communicated) are labeled “τ = 0 ns” and “τ = 40 ns” for the ideal and practical photon-counting detectors, respectively. (Note that the former is often omitted for clarity of presentation.) Finally, the Poisson PMF with parameter given by the mean of the corresponding “τ = 40 ns” PMF is also depicted and labeled “Poiss(λ (40 ns)).” This PMF represents a (likely poor) model for the distribution of received counts given a transmitted pulse that might be assumed by a suboptimal estimator that is unaware that the receiver is saturated.

 

Fig. 6 PMFs of received counts for illustrative system configurations with (a) r = 1139 m and E_pulse = 4 mJ, (b) r = 1139 m and E_pulse = 40 mJ, (c) r = 3844 m and E_pulse = 4 mJ, and (d) r = 3844 m and E_pulse = 40 mJ.

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Figure 6(a) considers a communication range of 1139 m and a transmitted energy per pulse of 4 mJ. An ideal detector counts an average of nearly 1200 photons per transmitted pulse, and the corresponding Poisson PMF (not depicted) of received counts when a pulse is transmitted is so well distinguished from the PMF when no pulse is transmitted that there is virtually a zero BER. On the other hand, the practical detector with a dead time of 40 ns counts an average of only approximately 6.25 photons per pulse. A suboptimal receiver that computes this estimate of average counts per pulse and assumes that the counts are correspondingly Poisson distributed would decide that a “0” or “1” was transmitted based on whether a received count was more consistent with the “Poiss(λ₀)” or “Poiss(λ (40 ns))” PMF, respectively. The result is a threshold test, where a “1” is decided if and only if a received count exceeds 1. Given this suboptimal bit estimator but considering the true PMF of received counts, the resulting BER would be approximately 1.4 × 10⁻³. An optimal detector, however, would base its decision criteria on the true PMF of received counts given a transmitted pulse, which deviates substantially from a Poisson distribution and exhibits a significantly reduced variance. As such, an optimal detector applies an increased decision threshold of 3 counts, and the BER is reduced by many orders of magnitude.

Now, to improve the performance of the suboptimal detector, a system might attempt to increase the transmitted power, as considered in Fig. 6(b), where the transmitted energy per pulse has been increased from 4 mJ to 40 mJ. However, because the receiver is highly saturated, the mean count given a transmitted pulse increases only to about 7 counts. This is insufficient to cause the suboptimal estimator to increase its threshold, and the BER is virtually unchanged. There is a visible change to the true PMF of photon counts for the practical detector given a transmitted pulse. In fact, with high probability, exactly 7 photons counts will be received. The resulting optimal threshold is increased and a BER of virtually 0 is obtained. However, we note that the ideal detector continues to detect orders of magnitude more photons than the practical detector. Hence, while increasing the power might slightly alter the photon count distribution and improve performance, it appears that substantial gains might be realized by reducing the detector dead time.

Figures 6(c) and 6(d) consider an analogous pair of scenarios but at a range of r = 3844 m. With an output of 4 mJ, the practical detector is only mildly saturated, with mean photon counts (given a transmitted pulse) of approximately 11.5 and 6.1 for the ideal and practical detectors, respectively. In both cases, an optimal estimator considers a decision threshold of 1 count, and the performance in both cases are similar (with BERs on the order of 1 × 10⁻⁵). Hence, in this case, reducing the receiver dead time would result in limited performance gains. Conversely, as implied by Fig. 6(d), an increase in transmitted power would have the potential to significantly improve performance. In fact, at 40 mJ, the optimal receivers with and without dead time each exhibit a BER of virtually 0. Not surprisingly, the performance of the suboptimal estimator lags significantly in both cases of 4 mJ and 40 mJ per transmitted pulse, with BERs of approximately 5.2×10⁻³ and 2.7×10⁻⁵, respectively. We conclude that modifying a UVC system to account for dead time effects can be complicated but critical to achieving reasonable performance.

7. Conclusions

In this paper, we extended a NLOS UVC channel model to account for receiver dead time, and we applied this model to statistically study the effects of dead time on UVC for a representative system configuration. Examination of model predictions of rate functions that probabilistically characterize received signals as a function of the system geometry yielded insight into when dead time might have significant impact, and these conclusions were supported by corresponding estimates of dead-time loss. In addition, the dead-time loss estimates demonstrated a complex nonmonotonic dependence on range and transmitter and receiver elevation, highlighting the nontrivial nature of dead time effects and the importance of the proposed modeling framework to understanding them. Support for the real-world validity of the framework was then given by experimentally collected data. Finally, we studied implications of dead time for communication performance with model predictions of photon-count distributions that illustrate that dead time not only introduces loss but also alters the distribution shape, thus complicating system optimization. Future research directions include the application of the proposed modeling framework to the online detection and estimation of dead time loss and to the development of dead-time compensation algorithms that optimize the system geometry, signaling, and/or receiver design for communication performance. For example, the mitigation of dead-time effects might be accomplished through the realignment (e.g., elevation) of transmitter and receiver pointing (trading off path loss for dead-time loss); the use of repetition codes with lower power, higher rate transmitted pulses; and/or by adaptive detection threshold optimization.