The exponential rise in the number of mobile service users and the services having high bandwidth consumption such as HDTV, networking websites, video-conferencing, and cloud computing, have led to an unparalleled demand in channel bandwidth [1–3]. According to the Cisco Visual Networking Index [4], the global mobile traffic density is expected to increase tenfold from 2015 to 2020. Radio-on-free-space optics (RoFSO) transmission is a cutting-edge data transmission technology for sharing real-time data securely, effectively, and reliably, irrespective of time and geographical area [5]. In RoFSO links, the costly equipment used for different signal processing stages including data encoding and decoding, up- and down-conversion of signal frequency, channel multiplexing and de-multiplexing, and hands-off are jointly shared with the base transceiver, which minimizes the effective cost in the implementation of information transportation [6]. Other merits include last-mile access in rural and remote areas, no security upgrade requirements, no costly fiber deployments and installation on building rooftops, and so on [7]. However, factors such as signal absorption, scattering, scintillation, deep fades, and weather conditions degrade the RoFSO link performance [8]. In temperate regions, heavy rainfall is the most prominent weather condition that adversely affects the performance of RoFSO links [9]. Fog is a crucial weather phenomenon adversely affecting the RoFSO transmission because the fog particle size is comparable to the carrier-wavelength used in RoFSO transmission.

Optical orthogonal frequency-division multiplexing (OFDM) is a subset of multicarrier modulation where the high-speed information bits are transported over many low-speed sub-carriers [10, 11]. When implemented with RoFSO transmission, OFDM results in a low-power consuming and cost-effective information transmission system with enhanced performance [7]. In OFDM, a high-bit-rate information stream is divided into many low-bit-rate streams transported simultaneously. The main objective of implementing the OFDM technique is to lower the baud rate so that the system provides high tolerance to channel effects and deep fades that degrade the performance of the RoFSO transmission link. The integration of the OFDM technique with RoFSO links will explore the combined merits of both technologies to emerge as a viable solution in providing last-mile access for broadband connectivity [14]. The merits of hybrid OFDM-RoFSO technology include 1) high-speed links, 2) elimination of inter-symbol interference (ISI), 3) improvement of signal-to-noise ratio (SNR), 4) ability to cope with frequency selective fading, 5) high spectral efficiency, and 6) robustness against co-channel interference [15].

Figure 1 illustrates the conceptual schematic of the OFDM-FSO transmission. The input message bits are modulated employing M-ary schemes such as phase-shift keying (PSK) and quadrature amplitude modulation (QAM). The narrowband sub-carriers are more robust to signal fading than the high-bit-rate signal and do not require any equalization. These narrowband bit streams are then OFDM modulated using the inverse fast Fourier transformation (IFFT) algorithm, and then the cyclic prefix is added to this signal. It is then followed by digital-to-analog (D/A) conversion and parallel-to-serial (P/S) conversion. The signal is then modulated over a continuous wave laser diode and then propagated over free-space channel. At the input of receiver, a photo diode is deployed, which converts the input optical beam to electrical signal, and the reverse process is executed to recover the message signal.

Recently, investigation of OFDM-based FSO links has been reported in many works. Thus, Zhou et al. exploited OFDM-based FSO transmission using a 16-level PSK modulation scheme [16]. Further, the proposed FSO link is investigated for complex atmospheric weather phenomenon viz. sunny, rainy, snowy, and foggy states. The simulation analysis of the link demonstrates reliable high-speed transmission at 500 m FSO range with BER of 10 − 4.2 and clear constellation plots. In another work reported by Jaiswal et al. [17], an M-ary QAM based OFDM-FSO link was investigated under weak and strong turbulence conditions. The authors compared the performance of 64-level, 128-level, and 256-level QAM schemes. The results indicate that the 64-level QAM shows better performance, and the link shows reliable transportation of data at the 7000 m FSO range. Kumar et al. reported a non-line-of-sight configuration-based OFDM-FSO link using multi-hop relay [18]. Analog network coding has been incorporated to provide enhanced throughput, power efficiency, and BER performance of the link. The incorporation of coherent detection technique in an OFDM-based FSO transmission is explored in [19]. 128 and 512 sub-carrier transmissions were compared, and results indicated that the SNR performance of the link improves by 6 dB on increasing the number of sub-carriers. Further, on investigating the link for varying atmospheric turbulence, the results indicated that the received signal was more degraded for strong turbulence conditions. Dabiri et al. compared the 4-level, 16-level, and 64-level QAM transmission in an OFDM-based FSO link under varying turbulence levels and demonstrated that 4-QAM was a better choice for modulation scheme when designing a high-speed FSO link under strong turbulence conditions [20].

Wavelength division multiplexing (WDM) is an important technology in which multiple data signals are transported simultaneously over the same channel using different optical beams from distinct laser source to realize a high-speed information transmission link [21, 22]. Figure 2 illustrates the conceptual block diagram of the WDM-based FSO link.

In WDM systems, multiple information signals from different transmitter sections each using a distinct laser source are combined using a WDM multiplexer (MUX), and then the multiplexed signal is transmitted through free-space channel. Independent signals at the receiver are demultiplexed by employing a WDM de-multiplexer (DEMUX) and a dedicated receiver section demodulates each signal. Shat et al. explored a 3-channel WDM-FSO transmission in which each channel transports 2.5 Gbit/s signals [25]. The transmission is investigated for light, medium, and heavy rainy conditions, and maximum achievable range is computed as 15.6, 6.1, and 3 km, respectively. Robinson et al. reported a hybrid course wavelength division multiplexed (CWDM)- and dense wavelength division multiplexed (DWDM)-based FSO link in which 4 CWDM and 12 DWDM channels, each carrying 2.5 Gbit/s information, were transported over a free-space channel [26]. The simulation results demonstrate a reliable 30 Gbit/s transmission at 2.04 km FSO range for heavy foggy and 2.64 km FSO range for heavy rainy conditions. Jain et al. reported performance comparison of return-to-zero and non-return-to-zero modulation schemes in a DWDM-based FSO link at different optical transmission bands viz. S, C, and L band [27]. The performance of the link was investigated at the 10 Gbit/s transmission rate, and non-return-to-zero at C-band was proved to be an optimal choice for implementing DWDM systems. The BER performance analysis of a 4-channel WDM-based FSO link by using the spectrum slicing technique is discussed in [28]. 4 × 1.56 Gbit/s data transmission for different climate phenomena of Vellore city in India have been discussed. The results reported reliable transmission of all channels at 3.3 km for heavy rainy and 2.7 km for heavy foggy conditions. Furthermore, Huang et al. explored a WDM-FSO transmission where 4-channels were transported over free-space at hybrid data transmission rates using a doublet lens scheme [29]. The authors report reliable transmission of 10 Gbit/s, 25 Gbit/s, 28 Gbit/s, and 32 Gbit/s data signals over the 100 m FSO range. The scheme was proposed for implementing light-based low-cost high-speed WiFi applications.

Mode division multiplexing (MDM) is a novel technique that has emerged as a cost-effective solution for providing high-speed optical communication links [30, 31]. In MDM systems, the transmission capacity is enhanced by capitalizing Eigen mode dimension of the laser beam for parallel transportation of multiple information streams. Rjeb et al. reported the development and performance investigation of MDM of orbital angular momentum (OAM) beams with the vortex of order l =   ± 2   in a few mode fiber based on inverse raised cosine function for improved performance [32]. Rusch et al. explored the transmission of three quadrature PSK modulated OAM beam with l = 0 ,   − 1 ,   a n d + 1 over the 1.4 km ring core fiber with minimum crosstalk using 2 × 2 MIMO processor [33]. Further, 4 independent 16-level QAM modulated channels using linear polarized beams are transported over 0.9 km elliptical ring core fiber. M. Hussain et al. explored the designing and investigation of a novel photonic crystal fiber that can transport up to 26 OAM beams simultaneously with low crosstalk for high-speed MDM applications [34]. The work in [35] reported 40 Gbit/s 4-OAM beam transmission under various FSO weather conditions. The works in [36, 37] report investigations on the impact of climate conditions on MDM-based FSO links. Furthermore, the application of FSO links for inter-satellite data transportation, photonic radar applications, and 5G services is reported in [41, 42].

Polarization division multiplexing (PDM) is another important technique that enhances the transmission capacity and spectral efficiency of optical links. The authors in [60] reported and investigated 640 Gbit/s hybrid PDM-WDM-based FSO transmission under adverse climate conditions of Bangladesh. A 320 Gbit/s hybrid PDM-WDM-based FSO transmission incorporating the AMI encoding scheme under adverse climate conditions was discussed in [61]. The investigations on a binary PSK RF-subcarrier FSO system using coherent detection under strong turbulence conditions has been reported in [62]. The performance comparison of on/off keying, binary, differential, quadrature, and 8-level PSK under the effect of strong atmospheric turbulent conditions is reported in [63]. The application of circular PDM with coherent detection OFDM transmission in FSO for enhanced performance was reported in [64].

Here, we present the designing of the 80 Gbit/s-160 GHz RoFSO link using hybrid WDM-MDM-OFDM techniques with enhanced detection and investigate the proposed link for heavy rainy and foggy weather. Section 2 elucidates link schematic, results are discussed in Section 3 followed by the concluding remarks in Section 4.

The schematic of WDM-MDM-OFDM-RoFSO link is elucidated Figure 3. Opti-System and MATLAB tools were used to implement this work.

At 193.1 THz central frequency, HG01 transports channel 1 data, and HG03 transports channel 2 data. Likewise, at 193.2 THz, LG02 transports channel 3 data and LG03 transports channel 4 data. A multiplexer combines both frequency channels. Figure 4 elucidates the spectrum of the transmitted signal. Figure 5 shows the excited profiles of HG and LG modes at the transmitter terminal.

The HG and LG modes are mathematically described using Eqs. 1, 2 respectively as [36]: φ m , n ( x ,  y ) =  H m ( 2 x ω 0 , x ) exp ( − x 2 ω ox 2 ) exp ( j πx 2 λR ox )   ×  H n ( 2 y w o , y ) exp ( − y 2 w oy 2 ) ( j πy 2 λR oy ) , (1) φ m , n ( r ,   ∅ ) = ( 2 r 2 w o 2 ) | n / 2 | L m n ( 2 r 2 w 0 2 ) exp ( r 2 w 0 2 )   × exp ( j πr 2 λR 0 ) { s i n ( | n | ∅ ) ,   n ≥ 0 c o s ( | n | ∅ ) ,   n < 0 } , (2) where the X -polarization axis modal dependency is denoted by m , the Y -polarization axis modal dependency is denoted by n , the Laguerre polynomial is denoted by L m n , and the Hermite polynomials are denoted by H m  and  H n , and the radius of beam and spot size are denoted by R and w 0   , respectively. 20 Gbit/s 4-level QAM signals having 2-bits per symbol are OFDM modulated using 32 prefix points, 512 sub-carriers, and 1024 IFFT points. This signal is mixed with the 7.5 GHz quadrature modulator (QM) at 40 GHz and then transmitted into the free-space channel modeled as [36]: P Received =  P Transmitted  ( d R 2 ( d T +  θZ ) 2 ) 10 − σZ / 10 , (3) where the optical power at the photodetector surface is denoted by P Received , transmitted optical power is denoted by P Transmitted  , the diameter of receiver and transmitter antenna is represented by d R and d T , respectively, range is represented by Z , and weather attenuation by σ . The simulation parameters have been considered as per practical RoFSO links reported in [36–40]. Optical amplifier with 12 dB gain has been deployed for enhancing the link range. Different modes at the receiver side are separated using mode selector and the spatial modes are converted to electrical signal using photodiode. A square root module (SRm) is used after the photo diode to compensate for its nonlinear response. The transmitted message is recovered using the QAM demodulator preceding OFDM and QM decoders. Attenuation for varying levels of rainy weather can be calculated using the equation [65]: β rain = 1.076 R 0.67 , (4) where R is the rainfall rate in mm/hr. The attenuation because of rainy weather in RoFSO links can be reasonably approximated by having information about the visibility range, V (km) (Table 1) as: σ rain  =   2.8 V , (5) β f o g   ( λ ) =   3.91 V   ( λ 550 ) − p , (6) where λ   ( n m ) is the optical beam wavelength, and p is the scattering coefficient, which is expressed using Kim’s model as [68]: p = { 1.6 V   > 50 1.3 6   < V   < 50 0.16   V   + 0.34 1   < V   < 6 V − 0.5   0.5   < V   <   1 0 V   < 0.5 , (7)

Based on the above equations, the attenuation for heavy rainy and foggy weather is approximated to be 19.28 and 22 dB/km, respectively [68]. Another factor is geometric loss ( A Geo ) that degrades the RoFSO link performance and is expressed as [69]: A Geo = 10 log 10 [ 4 A RX π ( θZ ) 2 ] ⋅ d B , (8) where the area of the surface of receiver antenna is expressed as A RX , the size of laser beam is expressed as θ , and the range is expressed as Z . Figure 6 reports the geometric loss for the 1000–3500 m FSO range.

Figures 7 and 8 report the SNR and power plots at the photo diode for varying range under heavy rainy weather. It is observed from Figure 7 that the SNR for channel 1 (HG01 mode) is 60.00, 47.69, and 12.14 dB at the 1000, 2250, and 3500 m range, respectively, whereas the SNR for channel 2 (HG03 mode) is 59.98, 45.35, and 7.61 dB at the 1000, 2250, and 3500 m range, respectively. Likewise, the SNR for channel 3 (LG02 mode) is 58.66, 47.30, and 12.04 dB and for channel 4 (LG03 mode) is 58.65, 43.86, and 5.66 dB at the 1000, 2250, and 3500 m range, respectively. The results show that channel 1 (HG01 mode) having the highest SNR at the receiver terminal is most robust against fading followed by channel 3 (LG02 mode), channel 2 (HG03 mode), and channel 4 (LG03 mode). In addition, all the channels are transported reliably at the 3000 m range with acceptable SNR at the receiver ( ∼ 20 dB). Alternatively, it is observed from Figure 8 that total power for channel 1 is −10.29, −39.98, and −74.19 dBm; for channel 2 is −12.91, −42.64, and −77.69 dBm; for channel 3 is −10.55, −40.24, and −74.81 dBm; and for channel 4 is −13.76, −43.50, and −78.31 dBm at 1000, 2250, and 3500 m, respectively. The highest power at the receiver terminal is observed for channel 1. Thus, channel 4 (LG03 mode) is most affected by fading, and channel 1 (HG01 mode) is most robust against it.

Figures 9 and 10 present the constellation graph and RF power for all channels at the 3000 m range. The clear constellation graph for all the channels in Figure 9 indicates a reliable 80 Gbit/s-160 GHz transmission at 3000 m under heavy rainy weather. The results presented in Figure 10 show that the highest RF power at the receiver terminal is collected by channel 1, which further demonstrates that channel 1 is least susceptible to channel fading.

Furthermore, the link was investigated for heavy foggy weather, as illustrated in Figures 11 and 12. The SNR for channel 1 is 51.84, 45.74, and 19.04 dB; for channel 2 is 51.82, 43.03, and 14.01 dB; for channel 3 is 51.82, 43.34, and 14.57 dB; and for channel 4 is 51.77, 40.15, and 8.64 dB at the 1000, 2000, and 3000 m range, respectively. The total power for channel 1 is −11.23, −37.68, and −65.33 dBm; for channel 2 is −14.46, −40.92, and −70.12 dBm; for channel 3 is −14.11, −40.57, and −69.59 dBm; and for channel 4 is −17.57, −44.07, and −74.69 dBm at the 1000, 2000, and 3000 m range, respectively. The results show reliable transmission of all channels up to the 2700 m range under heavy foggy conditions with acceptable SNR.

Figure 13 shows the power-coupling coefficients of different LP modes decomposed at the receiver terminal. For channel 1, most power is coupled into mode LP [1] followed by LP [1, 2], LP [1, 3], and LP [2, 3]. For channel 2, most power is coupled into LP [1, 2] followed by LP [1, 3], LP [1, 3], LP [2, 3], and LP [1, 5]. For channel 3, most power is coupled into the LP [1, 3] mode followed by LP [2, 3], LP [1, 2], and LP [1, 3]. For channel 4, most power is coupled into the LP [1, 2] mode, followed by LP [2], LP [2, 3], and LP [2, 4]. Further, the comparison of the system performance with conventional techniques reported in literature is listed in Table 2.

The present work reports the designing and investigation of a high-speed RoFSO link incorporating hybrid WDM-MDM-OFDM techniques under heavy rainy and foggy conditions. Four channels each carrying the 20 Gbit/s-40 GHz information are successfully transmitted using distinct spatial modes (HG01, HG03, LG02, and LG03) over the 3000 and 2700 m range under heavy rain and foggy weather, respectively, with acceptable performance using an enhanced detection technique involving the use of SRm at the receiver terminal. The proposed 4 × 20 Gbit/s-40 GHz-based RoFSO link provides a useful platform for future long-reach high-capacity RoFSO transmission links. In future works, the performance of the proposed link will be further improved by incorporating optical code-division multiple access transmission along with adaptive optics and digital signal processing techniques at the receiver.