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Abstract
We investigate the self-interference characterization, achievable rate, signal detection and parameter estimation for bi-directional ultra-violet (UV) communication. We firstly characterize and experimentally demonstrate the self-interference of UV communication, which is non-negligible as the angle between the transmission and receiver directions is blow 60°. Then, we present the achievable rate and symbol detection under self-interference, which show that the offset between self-interference and desirable symbols can increase the achievable rate and decrease the symbol detection error probability. We propose the practical system design with parameter estimation under self-interference. Finally, we experimentally evaluate the receiver-side signal detection with self-interference generated by Field Programmable Gate Array, and the signal detection of a real bidirectional UV communication system. Lower symbol detection error probability can also be observed as the offset between desirable symbols and self-interference symbols increases to half-symbol length from both system-level simulation and real experiments, which further validates the theoretical results.
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1. Introduction
Ultra-violet (UV) spectrum serves as a candidate for alleviating the strong requirement of perfect alignment and no blockage of the transmitter and receiver for optical wireless communication (OWC). None-line-of-sight (NLOS) OWC system can be established [1]. Besides, weak background radiation in the UV spectrum near the ground due to strong absorption effect in the UV band allows photon-level high-sensitivity signal detection [2]. The strong attenuation of UV spectrum in the atmosphere is helpful to limit the communication in a certain area and thus can increase the communication security.
Ultra-violet communication and its channel characteristics have been demonstrated experimentally in [3–8], where Monte-Carlo approach is adopted to trace the transmission path of a photon experiencing random scattering and attenuation events. Semi-analytical modeling has also been extensively studied [9–14]. Work [15–17] evaluates photomultiplier (PMT) based receiver for short range NLOS UV communications both numerically and theoretically, and work [18] analyzes the performance of photon counting detection of PMT under maximum likelihood (ML) criterion. The Poisson channel capacity analysis can date back to [19]. The capacity of continous-time poisson channel [20,21] and discrete-time poisson channel [22,23] have been investigated, where the optimal distrbution for discrete-time Poisson channel has been investigated in [22]. Recently, the capacity of MISO poisson channel [24] and MIMO poisson channel [25] have been explored in detail. For signal detection and communication protocol, existing works focus on signal detection criterion [26–29] and communication protocol, such as the relay design [30–32] and the detection under inter-symbol interference [33,34]. These works primarily focuses on point-to-point one-way communication.
Consider a bi-directional UV communication system. In order to increase the transmission efficiency, full-duplex transmission protocol is adopted, which potentially shows a larger communication rate compared with half-duplex system. However, due to the scattering in UV spectrum, the transmitted signal may interfere the signal detection of the receiver on the same side. Moreover, since the self-interference signal also satisfies Poisson process, it cannot be perfectly cancelled even with accurate prior knowledge, which is fundementally different from radio-frequency communication. It implies that the receiver needs to operate in the existence of self-interference, which raises chanllenges on channel estimation and signal characterization.
In this paper, we focus on the modeling and performance analysis of bi-directional full-duplex UV communication. Due to weak signal intensity, OOK modulation is adopted at the transmitter and PMT is adopted at the receiver. We firstly characterize and experimentally demonstrate the self-interference, which is non-negligible as the transmission-receiving angle is blow $60^\circ$. Then, we present the achievable rate and symbol detection under self-interference, which show that offset between self-interference and desirable symbols can increase the achievable rate and decrease the symbol detection error probability. We propose the practical system design with parameter estimation under self-interference. Finally, we experimentally evaluate the receiver-side signal detection with self-interference generated by Field Programmable Gate Array, and the signal detection of a real bidirectional UV communication system. Lower symbol detection error rate can be also observed as the offset between desirable symbols and self-interference symbols increases to half-symbol length from both system-level simulation and real experiments, which further validates the theoretical results.
The remainder of this paper is organized as follows. In Section 2, we present system diagram of the UV full-duplex system. In Section 3, we theoretically analyze the achievable rate and signal processing for the bi-directional communication. In 4, we propose the estimation of background intensity, self-interference intensity, desirable signal intensity and symbol offset, and simulate the system-level transmission. Finally, experimental results of the receiver-side signal detection and real bi-directional communication are demonstrated in Section 5.
2. System model
2.1 Bi-directional full-duplex communication system
The bidirectional full-duplex UV communication system under consideration is shown in Fig. (1), where each terminal has one transmitting UV LED, and one receiving PMT suffering the self-interference from its transmitting UV LED. Assume symbol duration $T$. Random binary bits are generated and modulated via on-off keying (OOK) modulation before being transmitted.
At the receiver, the output electrical pulses of PMT are sampled by the ADC module, which quantizes the continuous pulse signal into discrete levels. The received signals are synchronized, followed by channel parameter estimation and symbol detection.
2.2 Signal model with self-interference
Due to weak UV link gain and wave-particle duality, the received signals exhibit discrete photoelectrons and can be detected via a photon counting receiver, where the number of detected photoelectrons within a certain slot satisfies Poisson distribution. The fundamental signal model for bi-directional communication is the receiver-side signal detection with self-interference, which will be addressed in this work.
The received signal consists of three parts, the desired signal, the self-interference and the background radiation. Assume that the background noise yields Poisson distribution with arrival rate $\Lambda _b$. Assume arrival rates $\Lambda _s$ and $\Lambda _i$ for the desired signal and self-interference for symbol one, respectively, and zero arrival rate for symbol zero.
The symbol offset between the desired signal and self interference signal needs to be addressed. Equation (1a) shows the probability that $N$ photoelectrons are detected within duration $T$ under arrival rate $\Lambda$, and Eq. (1b) characterizes the mixed Poisson distribution considering symbol misalignment, which can be applied to the analysis of bi-directional transmission with self interference.
Consider the senario where information symbol $S$ and self-interference symbol $I$ are perfectly aligned. For $S = i$ and $I = j$, the probability of $N$ photoelectrons detected can be expressed as follows,
Consider the scenario where $S$ and $I$ are not aligned with offset $t$, as shown in Fig. 2, where the two interference symbols of information symbol $S$ are denoted as $I_1$ and $I_2$. Let $N_1$ denote the number of detected photoelectrons in the interval of length $t$, and $N_2$ denote the number of detected photoelectrons in the interval of length $T-t$. According to Poisson arrival process, $N_1$ and $N_2$ are statistically independent. For $S = i$, $I_1 = j$ and $I_2 = k$, the probability of $N_1$ and $N_2$ photoelectrons detected within the two intervals can be written as follows,
It should be noted that symbol offset $t$ originates from unknown propagation delay of the desirable signal, which is also to be estimated. Moreover, since the self-interference symbols are known, desired symbol $S$ can be estimated from the number of detected photoelectrons and self-interference symbols.
2.3 Experimental measurement of self-interference signal
The self-interference can be measured via an one-directional point-to-point UV NLOS system, as shown in Fig. 3. The light emitting diode (LED) with optical power approximately 1 mW, whose DC bias (6 V) is provided by a DC power supply (Rigol DP832A), is modulated by OOK signals (Vpp = 3.3 V) from an arbitrary wave generator (AWG, Keysight 33600A). A photomultiplier (PMT, HAMAMATSU R-7154 module), which is connected to an oscilloscope (Keysight, 1408009S), captures the waveform and count the number of photoelectrons accordingly on the computer. The experiment is conducted on an open field, with background arrival intensity $\Lambda _b$ approximately 50000 photoelectrons per second. An UV optical filter, which passes the light signal of wavelength around 266 nm and blocks the solar background radiation on other wavelengths, is adopted to conceal the PMT in a box. Such UV filter can avoid the PMT being broken by high intensity background light.
In the measurement experiments, the UV LED and PMT are placed with distance $D = 20 cm$, receiving angle $\theta _1$ and emitting angle $\theta _2$. Firstly, the LED and PMT are firstly placed back to each other, with $\theta _1 = 180^{\circ }$ and $\theta _2 = 0^{\circ }$. Then, the LED and PMT are rotated, until they are parallel to each other, with $\theta _1 = \theta _2 = 90^{\circ }$. Within symbol duration $0.1ms$, the mean numbers of photons with respect to LED angle $\theta _2$ under different PMT angle $\theta _1$ are shown in Fig. 4. It is seen that for $90^{\circ }\;\leq \theta _1 \leq \; 120^{\circ }$ and $60^{\circ }\; \leq \theta _2 \leq \; 90^{\circ }$, the self-interference intensity increases significantly.
Fig. 4. The mean number of photons under different LED emitting and PMT receiving angles within duration $0.1$ ms.
3. Achievable rates and signal detection
3.1 Achievable rates under self-interference
Assume that symbol duration $T$ and symbol offset $t$, as well as known desired signal, self-interference signal and background noise intensities. Without loss of generality, assume that $t \leq 0.5T$. Since the offset model is symmetric, the case with offset $t \geq 0.5T$ can be mapped to that with offset $T - t$. Let $p_s$ and $p_i$ represent the prior probability of information symbol $S=1$ and self-interference symbol $I=1$, respectively.
Consider offset $t$ between information symbol $S$ and self-interference symbols $I_1$ and $I_2$, as shown in Fig. 2. Let $H(Y)$ denote the entropy and $H(Y|X)$ denote the conditional entropy which represents the entropy of $Y$ under fixed $X$. Mutual entropy $I(X;Y)$ is given by subtracting entropy with conditional entropy. Under known self interference $I_1$ and $I_2$, the achievable transmission rate can be expressed based on conditional entropy $I(N_1, N_2; S|I_1, I_2)$, given as follows,
Assuming $T=10^{-6} s, \ \Lambda _b=5 \times 10^4 photons/s$, we calculate the achievable rate under different offsets $t$. Set $\Lambda _i=2 \times 10^7 photons/s$, desired signal prior probability $p_s$ to 0.5, interference signal prior probability $p_i$ to 0.5 and 0.3, and $\Lambda _s$ to $10^7 photons/s$, $2 \times 10^7 photons/s$ and $5 \times 10^7 photons/s$ sequentially. The achievable rate with respect to offsets $t$ under different values of $p_i$ and $\Lambda _s$ are shown in Fig. 5. It’s shown that lower $p_i$ implies weaker self-interference and leads to higher achievable rate, and the achievable rate increases with $t$ until reaching the maximum value under $t = 0.5T$.
3.2 Signal detection under self-interference
Bayesian MAP detection is adopted to minimize the symbol detection error probability. For $I_1 = i_1$ and $I_2 = i_2$, symbol $S = 1$ is detected if and only if
Let $T_{i_1,i_2}(N_1,N_2)$ denote the corresponding indicator function, given by
Given the numbers of detected photoelectrons $N_1,N_2$ and interference symbols $i_1,i_2$, the symbol error probability $P_e^{i_1,i_2}(N_1,N_2)$ can be expressed as follows,
Assuming $T=10^{-6} s, \ \Lambda _b=5 \times 10^4 photons/s, \ \Lambda _i=2 \times 10^7 photons/s, \ p_s=0.5$, interference signal prior probability $p_i$ to 0.5 and 0.3, and $\Lambda _s$ to $10^7 photons/s$, $2 \times 10^7 photons/s$ and $5 \times 10^7 photons/s$ sequentially. The detection error probability is shown in Fig. 6. It’s seen that lower $p_i$ implies weaker self-interference and leads to lower symbol detection error probability. Moreover, larger symbol offset $t$ leads to lower detection error probability, which is consistent with higher achievable rate as shown in Fig. 5.
3.3 Model analysis under different signal intensity
Suppose background noise intensity $\Lambda _b = 5 \times 10^4 photons/s$, we evaluate the achievable rate and symbol detection error probability under different signal intensity $\Lambda _s$ and self-interference intensity $\Lambda _i$. Assume that both $\Lambda _s$ and $\Lambda _i$ take values in the range from $10^6$ to $10^8$ photons/s with step $10^6$ photons/s. For $t=0.5T$ and $p_i=0.5$, the achievable rate and minimum symbol detection error probability over $p_s$ under different $(\Lambda _i,\Lambda _s)$ are shown in Fig. 7(a) and Fig. 7(b), respectively. In general, higher $\Lambda _s$ and lower $\Lambda _i$ lead to higher achievable rate and lower symbol detection error probability. Moreover, given fixed ratio $(\Lambda _s/\Lambda _i)$, higher $\Lambda _s$ leads to higher achievable rate and lower symbol detection error probability.
Fig. 7. Achievable rate and detection error probability under different $\Lambda _s$ and $\Lambda _i$.
4. System-level design and simulation with frame transmission
In Section 3, the theoretical results are provided as the detection error probability limit, which ignores the channel parameter estimation process at the receiver side. In 4, we consider a more practical perspective for transmission, where the most crucial part lies in the synchronization and parameter estimation for both desirable and interference signals.
4.1 Transmission frame structure
Assume that the transmission rate is $1$ million symbols per second, which means the symbol duration is $10^{-6}$ s. Set that a frame consists of 1500 symbols, with $256$ synchronization symbols, $1140$ information symbols, and $104$ interval symbols, as shown in Fig. 8. During the simulation, 1000 frames are transmitted with totally $1.5$ million random symbols. It should be mentioned that all the frames are generated by the Matlab function to guarantee that the data is a pseudo-random binary sequence, while the synchronization part remains the same for each frame. We divide the transmission duration at the receiver side into chips, whose duration is given by $T_c = \frac {T_s}{M}$, where $T_s$ denotes the duration of one symbol. Since the start of an information/interference symbol is not perfectly known at the receiver, the boundary of each symbol may lie in any position within a chip, not necessarily aligned with the chip boundary. Typical values of $M$ can be set between $10$ and $20$.
In general, background noise intensity $\Lambda _b$ and self-interference siganl intensity $\Lambda _i$ are local information at each terminal and can be estimated prior to real transmission. However, information symbol intensity $\Lambda _s$ needs to be estimated along with symbol offset $t$ during the transmission.
4.2 Synchronization and parameter estimation
4.2.1 Synchronization
The synchronization is performed via creating a searching window and searching the maximum correlation peak within that window, and the chip corresponding to the correlation peak will be selected as the starting chip of a frame. In our design, based on a preset threshold, the searching window whose length is 64 symbol durations is established once the correlation value exceeds that threshold. The detailed process is the same as that in [35] and thus omitted here.
4.2.2 Parameter estimation
Background intensity $\Lambda _b$ can be estimated via turning off the UV LED on both sides, and counting the number of pulses within a long interval. For symbol duration $T$ and $[n^{(b)}_1, n^{(b)}_2,\ldots, n^{(b)}_K]$ to be the pulse numbers detected in $K$ symbol durations, e.g., $K = 256$, an estimate of $\Lambda _b$ can be given as follows,
Self-interference intensity $\Lambda _i$ can also be estimated before the transmission since it is only related to the receiver side. More specifically, it can be estimated via turning on the LED at the receiver side and counting the number of photons within a long interval, when transmitting the synchronization symbols. Let $[n^{(i)}_1, n^{(i)}_2,\ldots, n^{(i)}_K]$ be the number of pulses detected in the $K$ symbol durations, and $\textbf {Y}_I(k)$ denote the $k^{th}$ symbol in the synchronization part, the likelihood function can be written as follows,
Analytical form of $\widehat {\Lambda _i}$ can be derived by the derivation of logarithmic likelihood function. Let ${\cal S}_1 \triangleq \{k: Y_I(k) = 1\}$ denote the position of symbol one within the $K$ symbol durations. The logarithmic likelihood function can be expressed as follows,
Symbol offset $t$ can be estimated via performing synchronization of the desirable signals and self-interference signals, and finding the difference $\Delta$ between the two peaks, given by,
Desired signal intensity $\Lambda _s$ is estimated during transmission, given the estimated parameters $\widehat {\Lambda _i}$, $\widehat {\Lambda _b}$, and $\widehat {t}$. Let pseudorandom sequence $\textbf {Y}_S^1$ denote the synchronization part of $\textbf {S}$, which consists of $K/2$ ones and $K/2$ zeros, is adopted to estimate $\Lambda _s$. We adopt the following simple rule based on the convergence of mean number,
4.3 Simulation results
Consider parameters $T=10^{-6} s, \Lambda _i=2 \times 10^7 \ photons/s, \Lambda _b=5 \times 10^4 \ photons/s$. Consider desired symbol arrival intensities $\Lambda _{s1}=10^7 \ photons/s, \ \Lambda _{s2}=2 \times 10^7 \ photons/s$ and $\ \Lambda _{s3}=5 \times 10^7 \ photons/s$. Each symbol is divided into $20$ chips, with symbol offset $1 \leq t \leq 10$ chips. In the simulation, all parameters need to be estimated according to the approaches proposed in Subsection 4.2, rather than assuming to be perfectly known.
The detection error rates with respect to preset symbol offset $t$ under different signal intensities are shown in Fig. 9. The theoretical detection error probability assuming perfectly known parameters are also plotted for comparison. It is seen that both theoretical and simulated detection error rates decrease as offset $t$ increases from $0$ chip to $10$ chips, which validates the theoretical results.
The detection error rates of simulation are around one order of magnitude higher than the theoretical ones for detection error rate approximately higher than $10^{-3}$. This can be justified by inaccurate synchronization and estimation of signal and interference intensity, which leads to accuracy loss of binary detection. Notice that the performance gap between theoretical analysis and simulation increases for the detection error rate lower than $10^{-5}$, since inaccurate channel estimation will have larger influence on the accuracy of binary detection under better channel conditions.
5. Experimental system
Based on the system-level signal processing in 4, real experiments including optical transmission will be conducted in this Section. To further verify the observation that larger symbol offset decreases the detection error probability, the experiment under varying symbol offsets will be conducted. After that, we will establish a real bi-directional ultraviolet communication system and test the detection error probabilities. Notice that the transmission symbol rate is still $1$ million symbols per second.
5.1 Receiver-side signal detection under different symbol offsets
An experimental system is established to prove that larger symbol offsets leads to lower detection error probability. The block diagram is shown in Fig. 10, along with the main device and equipments. Field Programmable Gate Array (FPGA, Xilinx AX7021) is adopted to generate the desirable and interference signals with different preset symbol offsets, with the same frame structure as that shown in Fig. 8. Two different synchronization sequences are adopted for desired signal and self-interference signal. The OOK baseband signals for desired signal and self interference signal are generated by maximum length sequence method (MLS method). Specifically, two pseudo-random binary sequences, both with length $120000$, are generated for desirable and self-interference sequences. The generated binary sequences are transmitted $13$ times to guarantee approximately the same length with that adopted in the simulation.
Fig. 10. The system block diagram of experimental system with prefixed symbol offset generated by FPGA.
One UV-LED (266 nm, 6 V) is adopted to transmit the desired signal and the other is adoted to generate the self-interference signal. A PMT (HAMAMATSU, R-7154 module), which is concealed with an UV optical filter, is adopted to detect the UV photons. The PMT output waveform from both desirable and interference signals is captured by the oscilloscope (Keysight, 1408009S), where the data is processed in an offline manner on the computer using the system-level simulation code for frame synchronization, channel parameter estimation and binary detection to get the output OOK symbol stream. The detection error rate is obtained by comparing the estimated symbols with the original symbols.
The system is tested under three different conditions from experiments and the BER results are compared with those from system-level simulations and theoretical results. In the system-level simulation, we set the background radiation intensity, desirable signal intensity and interference signal intensity as those estimated from the real signal, and run the signal detection with parameter estimation. In the theoretical results, we set the background radiation intensity, desirable signal intensity and interference signal intensity as those estimated from the real signal, and calculate the detection error rate assuming perfect channel estimation. The comparisons are shown in Fig. 11(a), Fig. 11(b) and Fig. 11(c), for the three scenarios of desirable signal intensity $\Lambda _s$ and interference signal intensity $\Lambda _i$. It is seen that larger symbol offset leads to lower detection BER, and the detection error rates from real experiments are generally within three times of degradation of those from the system-level simulations. It should be noted that symbol offset leads to lower detection error probability.
5.2 Real bi-directional communication syetem tests
A bi-directional full-duplex communication system with two terminals is established, as shown in Fig. 12. The OOK baseband signals for both sides are generated by FPGA (Xilinx AX7021). The synchronization sequences are known to both sides, while the desirable information symbol needs to be detected with known self-interference. Two pseudo-random binary sequences with lengths $120000$ are generated at both transmitters, which are sent $13$ times to guarantee approximately the same length as that adopted in the simulation.
Firstly, both LEDs are turned off to estimate the background radiation intensity on both terminals. Then, one LED is turned off while the other is turned on to estimate the self-interference intensity for both terminals. Finally, both LEDs are turned on for approximately 5 seconds with unknown offsets that need to be estimated. The same frame structure as that shown in Fig. 8 is adopted. The PMT (HAMAMATSU, R-7154 module) output waveforms are captured by the oscilloscope (Keysight, 1408009S) and sent to the computer for offline processing. In the offline processing, the system-level simulation code is adopted to perform frame synchronization, channel estimation and symbol detection, which is then compared with the original symbols to calculate the detection error rate.
We consider three settings of transmitters and receivers, denoted as groups $1$, $2$ and $3$ (G1, G2 and G3). The parameter estimation results at both terminals (T1 and T2) are shown in Table 1, where ’$GxTy$’ means the $y$th terminal of the $x$th group.
Table 1. Parameter estimation of the bi-directional transmission system.
Based on the estimated parameters, we calculate the theoretical detection error probability. Moreover, we perform system-level simulation based on those parameters and obtain the detection error rate. The detection error rates from real experiments are compared with the theoretical results and those from system-level simulations, as shown in Table 2.
Table 2. The detection error rate from theoretical calculations, system-level simulations and real experiments.
5.3 Comparison with system-level simulation results
It is seen that the detection error probabilities from real experiments are higher than those from theoretical calculation and system-level simulation. The core reason falls in imperfect photon counting. The arrival of photoelectrons getting too close to each other leads to pulse signals aliasing, and finally lower number of real detected photoelectrons under limited sampling rate and imperfect threshold for detection. In this way, the performance of both channel estimation and frame synchronization will be degraded. Moreover, the pulse number of each information symbol will be inaccurate, which further degrades the symbol detection performance.
To conclude, inaccurate pulse counting for photoelectron detection and the related parameter estimation inaccuracy lead to higher detection error rate in the real experiments compared that in system-level simulation. However, lower detection error probability at the offset of half symbol duration can still be observed.
6. Conclusion
We have characterized and experimentally demonstrated the self-interference under bi-directional UV communication, which is non-negligible as the transmission-receiving angle is blow $60^\circ$. We have presented the achievable rate and symbol detection under self-interference, where the achievable rate increases and symbol detection error probability decreases as the offset between self-interference and desirable symbols increase to half-symbol duration. We have also proposed the practical system design with parameter estimation under self-interference, and experimentally demonstrated the receiver-side signal detection with self-interference, and the signal detection of a real bidirectional UV communication system. It is also observed from both system-level simulation and experiments that lower symbol detection error probability can be also observed as the offset between desirable symbols and self-interference symbols increases to half-symbol length, which further validates the theoretical results.
Funding
National Key Research and Development Program of China (2018YFB1801904); National Natural Science Foundation of China (61631018); Key Research Program of Frontier Sciences of CAS under Grant (QYZDY-SSW-JSC003); National Natural Science Foundation of China under Grant (62171428).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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