Multi-Level Logarithmic Amplification-Based Fixed Threshold Circular Polarized On-Off Keying Detection for Free-Space Optical Communications

Abstract

This study investigates a multi-level logarithmic amplification (MLA)-based fixed threshold circular polarized on-off keying (CP-OOK) detection for free-space optical (FSO) communication links. OOK signal is polarized into a single circular polarization state by a linear polarizer (LP) and a quarter-wave plate (QWP). In the receiver terminal, firstly, circular polarization is transformed into linear polarization utilizing QWP without polarization coordinates alignment between transmitter and receiver. Then, the background noises are decreased by polarization filtering using LP. Then, CP-OOK signal intensity variation is eliminated by nonlinear gains from MLAs in the low gain nonlinearity condition. Finally, fixed threshold decision (FTD) is realized by optimizing cascaded LAs to reduce the extinction ratio distortion of the CP-OOK signal. The proposed CP-OOK transmission is analyzed under various strengths of turbulence channel and different configurations of MLAs. Simulation results demonstrated that the proposed CP-OOK signal was effectively detected by FTD with optimized MLAs.

1. Introduction

Compared with traditional radio communication, free-space optical (FSO) communication, which adopts a laser beam as an information carrier, has obtained substantial attention in recent decades for its higher bandwidth and lower risk of interception [1]. Generally, an intensity modulation and direct detection (IM/DD) FSO system is adopted in practical application fields due to its system simplicity [2]. Nevertheless, in FSO channel, the laser beam is vulnerable to the atmospheric turbulence which is generated by the varying temperature and pressure of atmosphere [3]. Atmospheric turbulence effect results in the variation of the received signal intensity, which leads to dramatic degradation of FSO system performance [2,3].

Large numbers of research studies were conducted to cope with the issues of decision threshold optimization, which is induced by the received signal intensity variation in FSO systems. The instantaneous signal-to-noise ratio (SNR) of the received signal was calculated to optimize the decision threshold symbol-by-symbol [4]. However, this adaptive threshold decision (ATD) method requires an accurate knowledge of channel state information (CSI) of the atmospheric turbulence channel, which is difficult in practical implementation. Pilot symbol and pilot tone were used for delivering the knowledge of CSI by sending these assistant tones and symbols [5]. However, the system complexity is increased due to the process of CSI extraction. A low-pass filter was introduced to separate the CSI components from the received signal sequence [6]. Nevertheless, the performance is limited to the lower data rate signal transmission. Fixed threshold decision (FTD) was achieved by using the information of turbulence channel model and noise power level [7]. However, a prior estimation of the channel model and noise power degree is required, which is non-attainable in practical application. An optical pre-amplifier was employed in the receiver end to optically equalize the received optical signal intensity by nonlinear gains from the saturated optical pre-amplifier [8]. However, it is difficult to control the saturation condition of the optical amplifier. Polarization shift-OOK modulation was investigated to obtain FTD by detecting the signal using a linear polarizer (LP) and logarithmic amplification [9]. However, it is difficult to have a polarization shifting on the OOK format signal and polarization coordinates alignment between transmitter and receiver. Circular polarization modulation supports polarization detection without the polarization axis matching process [10]. Therefore, it is preferable to study a single circular polarized OOK (CP-OOK) signal FTD in FSO communications.

In this paper, we propose an MLA-based fixed threshold CP-OOK detection for FSO communications. Single circular polarization is modulated into an OOK signal using an LP and a quarter-wave plate (QWP). In the receiver end, the QWP, LP, and multi-level logarithmic amplification (MLAs) are applied to detect the CP-OOK signal. The QWP is applied to convert circular polarization into linear polarization without a polarization axis matching process, and the LP is used to decrease the levels of background noises by polarization filtering. Optimized MLAs are introduced to equalize CP-OOK signal intensity fluctuation via nonlinear gains from MLAs and reduce the extinction ratio (ER) distortion of CP-OOK at peak power parts of the signal sequence by setting MLAs in the low gain nonlinearity condition. FTD is utilized to distinguish bits ‘1′ and ‘0′ of CP-OOK. The performance of the proposed CP-OOK transmission is verified under various degrees of modeled turbulence channels and different configurations of MLAs. Simulation results illustrated that the proposed CP-OOK signal was effectively detected through FTD with the assistance of optimized MLAs.

2. Operation Principle

Figure 1 shows the block diagram of the proposed MLA-based CP-OOK signal detection. A laser diode (LD) of 1550 nm wavelength is directly modulated with an OOK signal. A linear polarizer is deployed to obtain a polarized OOK signal, and the state of polarization (SOP) is set at $45°$ to the fast axis of QWP. The linearly polarized OOK signal is converted into right circular polarization (RCP) by QWP. Thus, the CP-OOK format signal $s\left(t\right)$ is obtained by the combination of LP and QWP. A laser beam with a CP-OOK signal suffers the turbulence effect in the FSO links. The turbulence-induced scintillation effect, which causes received signal intensity variation, is the major issue in the IM/DD FSO system [3]. In addition, the SOP of CP-OOK remains stable in the FSO links [11,12]. Thus, the scintillation effect is studied in this turbulence channel. The degree of turbulence effect is assessed by the scintillation index ${\sigma }_I^2$, which is expressed by

$${\sigma }_I^2=〈I^2〉/{〈I〉}^2-1,$$

(1)

where I is the optical intensity of the received CP-OOK signal, and ⟨.⟩ is the ensemble average [13,14]. In the receiver terminal, the RCP of CP-OOK is recovered into linear polarization by QWP without the aligning procedure of polarization coordinates between the transmitter and receiver. Linearly polarized CP-OOK passes through LP before the photodiode (PD), and the non-polarized background noises are blocked without CP-OOK signal distortion. The CP-OOK signal after LP $r_{LP}\left(t\right)$ is given by

$$r_{LP}\left(t\right)=I\left(t\right)s\left(t\right)+N_{BG}(t)/\sqrt{2},$$

(2)

where $N_{BG}(t)$ is the background noise. The PD-received signal is converted into a digital signal $r_{PD}[k]$ via an analog-to-digital conversion (ADC).

Figure 2 depicts the amplification curves of different LAs. LA has the characteristics of gain nonlinearity, and the degree of nonlinearity increases with the increase of input values and base numbers of the logarithm. The turbulence effect is reduced through the intensity variation decreasing using nonlinear gains from LA, i.e., the high and low signal intensity obtain large and small gains from LA, respectively. The received signal from a stronger turbulence channel requires a much larger degree of nonlinearity to equalize the received signal intensity variation. However, the issue of CP-OOK signal ER distortion accompanies the process of scintillation mitigation. Bit ‘1’ and bit ‘0’ also obtain different gains from LA, and it is serious in the peak power part of the signal stream in the case of LA with high gain nonlinearity, as shown in Figure 3. Besides, the ER distortion issue increases as the turbulence degree increases. Therefore, a single LA is only capable of equalizing the signal intensity variation in the case of bit ‘0’ blocking [9]. MLAs are applied in this work to cope with ER distortion issues by using cascaded LAs. Multiple stages of logarithmic amplification processes are employed to assign different gains into the intensity variated CP-OOK signal under each LA works in a low gain nonlinearity condition instead of using a single LA in a high gain nonlinearity condition. Therefore, ER degradation effect is reduced by this proposed MLAs method. The process of MLAs application is described as

$$\begin{array}{l}{r}_{LA1}[k]={\log }_a^{(r_{PD}[k]+b)}={\log }_a^{(I[k]s[k]+N_{BG}[k]/\sqrt{2}+N_{PD}[k]+b)}\\ ⋮\\ r_{LA\mathrm{n}}[k]={\log }_a^{(r_{LA(n-1)}[k]+b)},\end{array}$$

(3)

where $r_{LAN}[k]$ is the signal after log amplification, n is the levels of LA, $N_{PD}[k]$ is the PD noises. Parameters a, b, and n adjust to effectively mitigate the scintillation effect to realize an FTD without ER distortion, and this process is defined as an optimization process in this work. Consequently, the turbulence effect is effectively mitigated by the CP-OOK transmission FSO communication links.

3. Simulations and Results

We verified the proposed CP-OOK transmission in simulation. The turbulence channel was emulated by modeling the turbulence-induced scintillation effect with the features of low frequency and lognormal distribution, as shown in Figure 4, and this channel modeling is referred to in research from the National Institute of Information and Communications Technology [6,7,15,16,17]. The performance of CP-OOK detection was analyzed under various parameters of LA and different levels of cascaded LAs. Furthermore, the MLA-based fixed threshold CP-OOK detection was compared to the CP-OOK with ATD, CP-OOK with FTD, and non-polarized OOK (NP-OOK) with ATD. LA with an ideal amplitude-frequency characteristic and without noises was discussed in the simulation: i.e., the signal distortion from LA was ignored. The data rate was configured into 1 Gb/s.

Figure 5 depicts the bit error rate (BER) performance of CP-OOK detection by FTD with a single LA at ${\sigma }_I^2$ of 0.05 and 0.25. A single LA with a base of 2 was used to evaluate the turbulence effect mitigation, and CP-OOK signal ER distortion under different b values. In Figure 5a, initially, the turbulence effect was effectively compensated by nonlinear gains from the LA with low b values. An LA with a larger b value has a higher gain nonlinearity, which can more effectively mitigate the turbulence effect. However, BERs were decreased with the increase of b values due to a serious side effect of CP-OOK signal ER distortion under a high gain nonlinearity of LA. In addition, a single LA with various b values is ineffective as a turbulence channel at ${\sigma }_I^2$ of 0.25, as shown in Figure 5a. This is because the compensation of a higher level turbulence effect requires a high gain in the nonlinearity of the LA, and this high gain nonlinearity causes a significant ER degradation of the CP-OOK signal. Therefore, the b value of LA is set to a low value in order to reduce the ER distortion issue from the high gain nonlinearity of LA during the turbulence effect compensation.

Figure 6 shows the BER performance of CP-OOK detection using FTD with a single LA under various values of a. The b value of LA was set to 1.1 for the sake of the ER distortion reduction. The LA with a base of e (natural logarithm) and 10 (common logarithm) were compared to the LA with a base of 2. In Figure 6a, a similar performance was observed for CP-OOK detection using a single LA with FTD under various base values of the LA at ${\sigma }_I^2$ of 0.05 due to the low intensity variation of turbulence channel. In addition, it has a better BER performance compared to CP-OOK detection with FTD under various average SNRs by reason of the turbulence effect reduction with nonlinear gains from the LA. However, a poor BER performance was obtained compared with CP-OOK detection with ATD due to the ER distortion from the LA. Besides, initially, it performs better than NP-OOK detection with ATD at the lower SNR conditions because of the non-polarized background noise reduction. Nonetheless, a poorer BER is obtained at the higher SNR conditions due to the ER distortion effect. CP-OOK detection with ATD has an improved BER performance compared to NP-OOK detection with ATD due to the filtering of non-polarized background noise. Figure 6b shows the CP-OOK detection using a single LA with FTD at ${\sigma }_I^2$ of 0.25. The FTD method is ineffective with the assistance of a single LA under a higher turbulence effect due to a serious ER distortion of CP-OOK from the LA. Therefore, multi-level LAs are required to improve the performance of CP-OOK detection.

Figure 7 shows the BER performance of CP-OOK detection using FTD under different levels of MLAs at ${\sigma }_I^2$ of 0.05. Figure 7a illustrates MLAs-based CP-OOK FTD detection under LA with a base of 2. Initially, BERs were improved with the growth of MLAs levels due to a more effective turbulence effect mitigation, and it has a better BER performance than CP-OOK with ATD in the case of four and six levels of MLAs on account of turbulence effect reduction. However, BERs were decreased as to adopting eight and ten levels of MLAs due to the ER degradation of CP-OOK signal from excessive nonlinear gains. With regard to MLAs with a base of e, BERs were enhanced with the increasing of MLAs levels, as shown in Figure 7b. Besides, four, six, eight, and ten levels of MLAs with a base of e-based CP-OOK detection have better BER performance compared to that of MLAs with a base of two because of a more effective turbulence effect compensation. In Figure 7c, a poor BER performance was observed for four, six, eight, and ten levels of MLAs with a base of ten-based CP-OOK detection due to high nonlinearity-induced ER degradation issues. Thus, the CP-OOK signal was effectively detected by MLAs with a of two, and e and n of four and six under ${\sigma }_I^2$ of 0.05. In Figure 8, the proposed technique was discussed in case of a stronger turbulence effect under ${\sigma }_I^2$ of 0.25. The performance of MLAs-based CP-OOK detection was evaluated under different values of a, b, and n as well. Figure 8 shows that the CP-OOK signal was effectively detected by MLAs with a of two and n of six under ${\sigma }_I^2$ of 0.25 since a larger intensity variation can cause a serious ER distortion from MLAs. Therefore, a stronger turbulence effect can be compensated by the MLAs-based CP-OOK detection with lower values of a. Therefore, the turbulence effect was effectively compensated via MLAs-based CP-OOK detection in the case of MLAs optimization. In this work, the proposed technique was evaluated under an ideal LA. However, the signal distortion from bandwidth limitation and amplified noises will limit the available levels of logarithmic amplification. Furthermore, as the parameters of MLAs are determined by the degree of intensity fluctuation, the average power of the received signal, and the gain curve of the LA, comprehensive training is required to determine the parameters of MLA in practical implementations.

4. Conclusions

In summary, an MLA-based fixed threshold CP-OOK detection technique was proposed for the FSO communication system. CP-OOK signal modulation and detection were investigated in the transmitter and receiver ends. Furthermore, MLAs-based fixed threshold CP-OOK detection was analyzed under various parameters of MLAs. The BER performance of the proposed CP-OOK transmission was evaluated in simulation. The simulation results illustrated that the CP-OOK signal was effectively detected using MLA-based FTD under various turbulence channel circumstances. Therefore, it would be a useful technique for IM/DD FSO links.