1 Introduction

With the exponential growth in the demand for high-speed links and channel bandwidth, free space optics (FSO) has emerged as a viable technology to manage the issue of spectrum congestion in the traditional wireless networks since it capitalizes on the underexploited and unlicensed portion of the electromagnetic spectrum. Miscellaneous FSO link merits include high-speed links, secure information transmission, low-security upgrades, large channel bandwidth, tolerance to radio frequency (RF) and electromagnetic waves interference, quick and easy deployment, low-cost, lightweight equipment, last-mile access, and low beam divergence [1,2,3]. But the quality of the received signal in FSO links is degraded due to certain factors including channel fading effects, signal absorption, scattering, scintillation, atmospheric turbulence, pointing errors, beam wandering, etc. [4]. But the most crucial parameter which limits the FSO link reach is the atmospheric attenuation for varying climate affairs which may range from 0.14 dB/km in the case of clear weather to 300 dB/km in the case of dense fog conditions. In tropical countries like India, rain weather is the most important atmospheric condition which determines the FSO link reach [5].

The current research in FSO systems is focused on maximizing the data transmission capability and bandwidth efficiency of the links. Different techniques have been reported for the development of high-capacity FSO systems. The authors in [6,7,8,9,10,11,12] propose mode division multiplexing (MDM) technique in FSO system, where multiple information signals are transmitted by capitalizing on the spatial laser modes to enhance the system capacity and further studied the impact of different climate affairs on the link performance. Further, the integration of the orthogonal frequency division multiplexing (OFDM) technique to transmit high-speed data over FSO links while mitigating inter-symbol interference and inter-carrier interference is discussed in [13,14,15]. The authors in [16] explore the incorporation of hybrid optical code division multiple access (OCDMA) and polarization division multiplexing (PDM) techniques to increase the FSO system transmission capacity. In another work [17], a PDM-coherent detection-OFDM-based FSO system is modeled and investigated for varying atmospheric turbulence conditions. The authors in [18] explore a spectral amplitude coded (SAC)-OCDMA-based FSO system with double diagonal weight (DDW) code for improved performance under adverse climate conditions. The works in [19, 20] report the incorporation of wavelength division multiplexing (WDM) in FSO system to transmit multiple information signals simultaneously through the same channel. Modulation scheme plays a pivotal role in influencing the transmission performance of a communication system. To meet the ever-rising demand for high data transmission rates, it becomes imperative to propose modulation schemes that increase the information capacity per channel and enhance the bandwidth efficiency of the system. Although different modulation schemes have been reported to maximize the data-carrying efficacy of communication links [21], orthogonal modulation scheme provides better results since it not only provides enhanced speed per channel but also increases the number of users [22]. In previous literature, different orthogonal modulation schemes such as dark-return to zero/ frequency shift keying/differential phase shift keying (DRZ/FSK/DPSK), (DPSK/DRZ), DPSK/non-return to zero (DPSK/NRZ), DPSK/code shift keying (DPSK/CSK), amplitude shift keying/FSK (ASK/FSK), and ASK/DPSK have been reported to improve the spectral efficiency and transmission speed of optical fiber links [23,24,25,26,27].

In this paper, a 3-D orthogonal modulation scheme has been proposed combining NRZ-differential quadrature phase shift keying (DQPSK)-polarization shift keying (PolSK) to transmit 120 Gb/s information over a single wavelength channel in a 32 channel WDM-based FSO system. The main motivation behind this work is to realize a high-capacity bandwidth-efficient FSO system by using a spectral-efficient orthogonal modulation scheme. After the introduction, system design is presented in Sect. 2, followed by the simulation results in Sect. 3, and the conclusions in Sect. 4.

2 Proposed WDM-FSO system design

The schematic of the 32-channel WDM-FSO system incorporating orthogonal modulation scheme is illustrated in Fig. 1a. 32 independent wavelength channels ranging from 193.1 to 196.2 THz with 0.1 THz channel spacing are multiplexed using a WDM multiplexer (MUX) and transmitted simultaneously over free space medium under different climate conditions. The system is modeled and numerically investigated using Optisystem simulation software. At the receiver end, the optical signal is amplified using a flat-gain amplifier with 20 dB gain and 4 dB noise figure. Each wavelength channel is separated by employing a WDM demultiplexer (DEMUX) and then directed toward a distinct receiver section.

Fig.1
figure 1

a Schematic of the proposed 32 channel WDM-FSO transmission system. b Schematic of single-channel orthogonal modulation transmitter. c Schematic of single-channel orthogonal modulation receiver

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The link equation can be expressed as [28]:

$$ S_{{{\text{Received}}}} = S_{{\text{Transmitted }}} \left( {\frac{{d_{R}^{2} }}{{\left( {d_{T} + \theta R} \right)^{2} }}} \right)10^{ - \sigma R/10} $$
(1)

where \(S_{{{\text{Received}}}}\) is the optical power at the receiver aperture; \(S_{{\text{Transmitted }}}\) is the input power of laser beam (0 dBm); \(R\) is the link range; \(\theta\) is the angle of beam divergence (0.25 mrad); \(d_{T}\) is the transmitter antenna aperture diameter (10 cm); \(d_{R}\) is the receiver antenna aperture diameter (10 cm); and \(\sigma\) is the attenuation constant.

In each orthogonal modulation transmitter section, three independent 40 Gb/s data signals are modulated over intensity, phase, and state of polarization of a single laser beam to generate a 120 Gb/s orthogonal modulated signal as illustrated in Fig. 1b. The laser beam from a continuous wave (CW) laser is directed toward a dual-electrode Mach Zehnder Modulator (De-MZM) with 30 dB extinction ratio which modulates 40 Gb/s Data 1 to generate an NRZ-encoded signal (Fig. 2a). At the output of De-MZM, we have an NRZ-encoded signal which is directed toward the input of phase modulator 1 (PM 1). 40 Gb/s Data 2 is divided into two parallel streams using a serial-to-parallel converter, and each stream is directed toward a distinct phase modulator (PM 1 and PM 2). PM 1 and PM 2 modulate the phase of the optical carrier to generate DQPSK-encoded signal according to Data 2. PM 1 modulates the phase of the optical carrier signal to 180° and PM 2 adds a 90° phase shift to it. At the output of PM 2, we have an NRZ-DQPSK-encoded signal (Fig. 2b). This signal is linear polarized at 45° using a polarization controller (PC) for PolSK modulation. A third phase modulator (PM 3) placed between the horizontal ports of the polarization beam splitter (PBS) and polarization beam combiner (PBC) modulates 40 Gb/s Data 3 to generate a PolSK-encoded signal. At the output of PBC, we have a 120 Gb/s 3-D NRZ-DQPSK-PolSK modulated signal (Fig. 2c). 32 such orthogonal modulated signals from each transmitter section are multiplexed to realize a 3.84 Tb/s FSO system. Figure 3a and b illustrates the optical spectrum of the signal at the output of WDM MUX and the input of WDM DEMUX, respectively.

Fig. 2
figure 2

Optical spectrum of information signal for channel 1 (193.1 THz) at a output of De-MZM b output of PM2 c output of PBC

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Fig. 3
figure 3

Optical spectrum of the WDM signal at a output of MUX b input of DEMUX

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In each orthogonal modulation receiver section, dedicated paths are used for retrieving independent information signals as shown in Fig. 1c. The intensity-modulated Data 1 is retrieved using PIN photodiode with 0.9 A/W responsivity and 1e−022 W/Hz thermal noise power density followed by a Bessel low pass filter (LPF) to remove high-frequency noise. The phase-modulated Data 2 is retrieved using two Mach Zehnder Interferometers (MZI) with a delay of 2 s followed by a balanced detector. Data 3 is retrieved using a PBS followed by a balanced detector and a subtractor.

In this paper, we also analyze the proposed system performance for different levels of rain conditions. The attenuation due to rain in FSO links can be reasonably approximated and given by [29]:

$$ \sigma_{{{\text{rain}}}} = \frac{2.8}{V} $$
(2)

where \(V\) denotes visibility in km and its value depending on the rainfall rate is presented in Table 1.

Table 1 Visibility and attenuation coefficient depending on rainfall rate [29, 30]
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3 Results and discussion

Here, we report the numerical simulative investigation of the proposed system for varying climate conditions. First, we investigate the proposed link performance under clear weather by computing the Quality Factor (Q Factor), bit error rate (BER) and eye diagram of the received signals for increasing link range and to determine the maximum range. In the proposed work, while performing numerical simulations, all the 32 WDM channels are transmitted simultaneously to realize a net transmission of 3.84 Tb/s information. But for the sake of convenience, we have reported Q Factor and log(BER) versus link range plots in Fig. 4 for wavelength channel 1 (193.1 THz central frequency) only since all the other channels perform similarly.

Fig. 4
figure 4

a Q Factor b log(BER) versus FSO link range under clear weather

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Figure 4 illustrates that for channel 1 (193.1 THz central frequency), the Q Factor under clear weather is computed as [17.36 dB, 17.46 dB, 17.44 dB] at 20 km link range, [12.12 dB, 12.27 dB, 10.94 dB] at 30 km link range, and [8.40 dB, 8.55 dB, 6.53 dB] at 40 km link range for DQPSK, PolSK, and NRZ encoded data streams, respectively. Alternatively, log(BER) of the received signal for channel 1 is computed as [− 67.27, − 68.03, − 67.84] at 20 km link range, [− 33.55, − 34.39, − 27.50] at 30 km link range, and [− 16.82, − 17.39, − 10.51] at 40 km link range for DQPSK, PolSK, and NRZ encoded data streams, respectively. Here, it can be noted that for all data streams, the signal quality degrades as the range is increased which can be attributed to the signal power loss due to atmospheric attenuation. Also, it can be noted that all three data streams have an acceptable Q Factor (\(\sim\) 6 dB) and log(BER) (\(\sim\) − 9) at 40 km link range. The clear eye diagrams at 40 km for DQPSK, PolSK, and NRZ encoded data streams for channel 1 as illustrated in Fig. 5 demonstrate faithful transmission at 40 km under clear weather conditions. For better reader clarity, we have reported the Q Factor and log(BER) for all 32 WDM channels at 40 km in Fig. 6 which shows that all the channels demonstrate faithful transmission to realize a 3.84 Tb/s FSO transmission system.

Fig. 5
figure 5

Eye diagram at 40 km link range for channel 1 (193.1 THz) a DQPSK-encoded data b PolSK encoded data c NRZ encoded data under clear weather

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Fig. 6
figure 6

a Q Factor b log(BER) for all WDM channels (193.1–196.2 THz) at 40 km link range under clear weather

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Furthermore, we have investigated the proposed FSO transmission system performance under varying level of rain weather conditions using numerical simulations as illustrated in Figs. 7 and 8. Here also, all 32 WDM channels are transmitted simultaneously but for the sake of convenience, the performance of channel 1 (193.1 THz central frequency) is only reported since other wavelength channels perform similarly. From the results illustrated in Figs. 7 and 8, two main observations are: (1) For all rain conditions, with increasing range, the Q Factor of the information signal decreases and log(BER) increases which is because of the increasing signal power loss due to atmospheric attenuation as the optical signal propagates through free space medium and (2) As the climate conditions move from light rain to heavy rain, the achievable range decreases which can be attributed to the fact that with increasing rainfall rate, the atmospheric attenuation increases as illustrated in Table 1. The Q Factor for channel 1 under light rain conditions at 4000 m is computed as 8.21 dB, 8.36 dB, and 6.31 dB; under moderate rain at 2800 m is computed as 8.96 dB, 9.11 dB, and 7.15 dB; and under heavy rain at 1600 m is computed as 8.65 dB, 8.80 dB, and 6.80 dB for DQPSK, PolSK, and NRZ encoded data streams, respectively. Alternatively, the log(BER) for channel 1 under light rain conditions at 4000 m is computed as − 16.12, − 16.67, and − 9.91; under moderate rain at 2800 m is computed as − 18.95, − 19.58, and − 12.42; and under heavy rain at 1600 m is computed as − 17.75, − 18.34, and − 11.33 for DQPSK, PolSK, and NRZ encoded data streams, respectively. The reported simulation results in Figs. 7 and 8 demonstrate a faithful transmission at a link distance of 4000 m under light rain, 2800 m under moderate rain, and 1600 m under heavy rain with acceptable performance.

Fig. 7
figure 7

Q Factor versus link range under a light rain b moderate rain c heavy rain

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Fig. 8
figure 8

log(BER) versus link range under a light rain b moderate rain c heavy rain

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Also, we have compared the proposed FSO system performance with other reported systems in previous works as illustrated in Table 2 to highlight the performance enhancement using the proposed technique. Here, it can be noted that the proposed FSO system achieves the highest transmission capacity of the link as compared to the other reported systems. The higher achieved link range in the case of Ref. [19] and [20] is because the authors have used high power laser with an input power of 30 dBm and 25 dBm, respectively, as compared to low-power laser with 0 dBm input power used in this work.

Table 2 Performance comparison of the proposed FSO system with other reported systems
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4 Conclusion

A novel high-capacity bandwidth-efficient NRZ-DQPSK-PolSK modulation scheme has been proposed to transmit simultaneously three independent 40 Gb/s data signals on a single optical carrier beam to realize 120 Gb/s transmission capacity per channel. The proposed modulation scheme is incorporated in a 32 channel WDM-FSO system with 0.1 THz channel spacing. Using numerical simulations, we investigate the transmission performance of the proposed 3.84 Tb/s WDM-FSO system for clear and varying rainfall conditions. The numerical results demonstrate faithful transmission at 40 km under clear conditions whereas the maximum link range limits to 4 km, 2.8 km, and 1.6 km under light, moderate, and heavy rain conditions, respectively. The proposed work can be implemented to realize a high-capacity FSO transmission system under adverse climate affairs.