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Abstract
With the arrival of the 5th generation mobile network, the number of user devices is increasing exponentially, and thus it is necessary to expand the capacity of transmission systems. In order to further improve the system spectral efficiency on the basis of existing mobile fronthaul devices, we propose a hybrid digital-analog fronthaul transmission system with adaptive insertion of analog bandwidth, which can dynamically change the position of inserted analog bandwidth based on the state information of free space optical (FSO) channel. We consider the effects of atmospheric attenuation and turbulence on the FSO channel and derive an analytical expression for the maximum analog signal bandwidth that can be inserted into the first null of the digital signal spectrum to meet BER requirement of 3.8 × 10−3. Through a comprehensive simulation, it is verified that the analog bandwidth is obtained by this expression can exactly represent the lower bound of the simulation results under weak turbulence condition. The obtained results show that the maximum insertable analog bandwidth beyond the spectral null of the digital signal can reach 10% of the digital signal bandwidth, even in the FSO link with a transmission distance of 0.5 km and attenuation factor of 8 dB/km.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the arrival of the 5th generation (5 G) mobile network, the traffic services of large bandwidth and high-speed, such as virtual reality and augmented reality, are thriving at an unprecedented rate. At the same time, with the opening of the era of Internet of Things (IoT), the user devices are increasing exponentially toward a larger scale, which puts forward strict requirements for the capacity of communication systems [1]. According to Shannon’s formula, there are two ways to increase system capacity: 1) increase transmission bandwidth; and 2) improve spectral efficiency (SE). However, the bandwidth of the existing 5 G low-frequency bands has almost been completely occupied, making it difficult to further explore more available bandwidth [2]. As a result, the millimeter-waves (MMW) [3], which increases the available bandwidth by tens of times to meet users’ needs, is becoming a research hotspot in recent years. Nevertheless, the wireless wave of MMW has strong directionality, making it difficult to avoid obstacles and achieve long-distance transmission. Furthermore, the generation of MMW will further increase the design cost of base stations [4]. Therefore, the large-scale deployment of MMW still requires many years of technological and economical investments. How to use existing infrastructure to improve SE has become a challenging issue worth of more attention.
Due to the significant attenuation of radio frequency (RF) wave in free space, it is not possible to achieve ultra long-distance transmission. Meanwhile, low attenuation copper-wire is expensive and bulky, and thus optical fiber becomes the best medium for long-distance transmission. Then, researchers proposed the radio over fiber (RoF) technology, which loads RF signal onto optical fiber for transmission, and fully utilizes the characteristics of low attenuation, high ductility, and low cost of optical fiber [5]. For the current 5 G centralized radio access network, which includes three parts: central unit (CU), distributed unit (DU), and radio unit (RU). The part connecting DU and RU is called mobile fronthaul, and the part connecting CU and DU is called backhaul, respectively [6]. Depending on how the RF signal is loaded onto optical fiber, we can classify RoF systems into digital RoF (D-RoF) and analog RoF (A-RoF). D-RoF can achieve high signal fidelity by using more quantization bits, however its SE is generally low [7]. Although A-RoF is susceptible to noise and inherent nonlinearity during optical transmission, it can achieve higher SE [8]. D-RoF has been mostly chosen for commercial use, also known as common public radio interface (CPRI). Therefore, the low SE issue of the existing RoF techniques attracts much more attention from industrial community, and has become an obstacle for the further promotion. Although some researchers have proposed the evolved CPRI (eCPRI) technology to improve SE as much as possible through low-layer function spilled [9] or variable quantization bits [10], it tends to cause an increase in system complexity.
In order to combine the advantages of digital and analog signal transmission, some researchers proposed hybrid digital and analog signal transmission schemes [11–19]. This technology was first applied to the integration of fixed network and wireless network [20,21] in a series of ways to improve SE and reduce hardware cost, such as subcarrier multiplexing (SCM), and wavelength division multiplexing (WDM), etc. Reference [11] aggregated 120 long term evolution (LTE) signals for wireless analog transmission, and used nonreturn-to-zero (NRZ) signals for wired digital transmission. In view of the spectral difference between analog and digital signals, the analog signal was inserted into the spectral null of the digital signal. Band-pass filter (BPF) and low-pass filter (LPF) were used for analog and digital signals, respectively, such that they are not spectrally overlapped. Reference [12] considered several 5 G candidate waveforms based on Ref. [11]. However, the resulting performance advantages are all derived from the inherent advantages of these waveforms and have not been improved on the hybrid transmission method of digital and analog signals. Reference [13] proposed a polarization division multiplexing (PDM) method without polarization tracking to transmit digital and analog signals. The author obtained the polarized signal of the optical single sideband through an optical filter, and then separated the digital and analog signals at the receiver through an optical filter. Although the method effectively saves bandwidth, the hardware cost increases correspondingly, as the receiver requires additional optical filter. In order to reduce the hardware cost of the receiver, Ref. [14] proposed a new hybrid digital-analog transmission scheme, which achieves WDM in the optical domain by modulating the digital and analog signals to the different optical bands using two lasers. However, the digital signal in the scheme is prone to inter-signal beat interference, and thus the transmission distance is limited. Reference [15] considered the hybrid digital-analog transmission from a new perspective. Analog signal can be inserted into the non-spectral null of the digital signal, and the digital and analog signals can be separated in the time domain through a limiting amplifier at the receiver. However, the digital signal can only use the modulation format of NRZ. In addition, due to the strict requirements imposed on the power range of analog signal by limiting amplifier, it is difficult for analog signal to be transmitted through long distance optical fiber channel. Reference [16] utilized two Mach-Zehnder modulators (MZM) at the orthogonal bias point to achieve digital and analog integrated transmission. However, the receiver of such a system requires the use of a Volterra nonlinear equalizer to eliminate analog-to-digital interference, which increases the complexity and cost of the receiver. Reference [17–19] focused on time-domain hybrid digital-analog transmission system, where intensity modulation direct detection (IM/DD) transmission [17] and coherent balanced detection [18,19] were studied, respectively. However, the time-domain hybrid scheme requires strict synchronization processing at the receiver. Considering the hardware cost and the complexity of receiver demodulation, spectral null insertion may be a preferable solution to a hybrid digital-analog transmission.
Although optical fiber has many advantages, expanding or repairing optical fiber links in cities where optical fiber has already been laid not only leads to interruption of communication links, but also requires the excavation of ground that greatly increases labor costs. As a promising alternative to optical fiber when interrupted, free space optics (FSO) communication not only includes the advantages of optical fiber, but also enables wireless transmission. FSO can serve as a backup link during optical fiber maintenance, a bridge link crossing mountains or rivers, and a relay link between drones. Therefore, the system architecture of radio over FSO (RoFSO) is worth of as much attention as RoF. The hybrid analog and digital transmission in RoFSO is more challenging due to the complex atmospheric channel conditions. Although there have been many techniques such as spectral null insertion for hybrid transmission in RoF, they did not consider the characteristic of atmospheric channel, which is composed of atmospheric attenuation and turbulence and more complex than optical fiber channel. The different channel condition may impose new requirements for signal transmission and thus bring more chances for research. As for the spectral null insertion, the dynamics of atmospheric channel will make the fixed placement of analog signal hardly adapt to the changing channel states. It is necessary to design a RoFSO system structure with adaptive insertion of analog signal for the purpose of maximum spectral efficiency.
In this article, we propose a hybrid digital-analog mobile fronthaul system structure over FSO link with the channel-adaptive insertion of analog bandwidth. Instead of fixing the placement of analog signal as in most related works, the analog intermediate frequency (IF) signal will be inserted into the spectral null of digital signal with variable bandwidth according to the temporal channel states. We derive an analytical model for the maximum insertable bandwidth of the analog signal under atmospheric attenuation. Furthermore, the lower bound of the analytical model is obtained to represent the maximum insertable analog bandwidth under weak turbulence condition. The effectiveness of the lower-bound expression is verified through simulation.
The rest of the paper is organized as follows. Section 2 introduces operating principles of spectral null in digital signal. The proposed FSO communication system is described in Section 3. Section 4 introduces the atmospheric channel model, and Section 5 presents the derivation of maximum insertable analog bandwidth under different atmospheric channel conditions. Section 6 analyzes and discusses the results of the system. We finally conclude the paper in Section 7.
2. Preliminaries
2.1 Hybrid digital-analog fronthaul system
Figure 1 shows a system architecture for hybrid digital-analog transmission, including DU and RU. The original data information includes digital signal and analog signal, which are processed within the DU, including power combination and electro-optical (E/O) conversion. Then the hybrid digital-analog signal is sent to the RU through the optical fiber link, and is finally processed at the RU. After the optical-electro (E/O) conversion, the digital and analog signals are distributed to corresponding applications, such as digital signal to the computing devices at hospital, bank and factory, and analog signal to mobile users’ terminals. As shown in Fig. 1, the left side displays the time-domain and frequency-domain waveforms of the transmitted signals. The upper half of each slice is the corresponding time-domain waveform of the data, while the lower half is the frequency-domain waveform. The blue line in Fig. 1 is a digital signal using NRZ modulation, and the red line represents an analog signal of orthogonal frequency division multiplexing (OFDM) using 16-ary quadrature amplitude modulation (16-QAM) modulation, respectively. The pink charts in the middle show the time-domain and frequency-domain waveforms of the digital and analog signals superimposed by the power combiner, where three OFDM bands are aggregated in the spectrum.
2.2 Existing techniques for hybrid digital-analog fronthaul
Figure 2 illustrates several commonly used hybrid digital-analog transmission methods, including (a) SCM, (b) WDM, (c) PDM, (d) spectral null insertion, (e) non-spectral null insertion, and (f) time division multiplexing (TDM). SCM distinguishes digital and analog signals through different subcarriers. Analog signal is upconverted to IF, and a guard band is created between the digital and analog signals to avoid analog-to-digital interference. WDM is achieved by allocating digital and analog signals to different wavelengths, through a wavelength division multiplexer [14]. Polarization multiplexing involves modulating digital and analog signals to two different polarization planes through a polarization structure [13]. The spectral null insertion scheme inserts analog signal into the spectral null of digital signal to improve spectrum utilization [16]. Non-spectral null insertion indicates that analog signal can be inserted into any position in the digital signal spectrum [15], while TDM transmits digital and analog signals at different time slots [17–19].
Fig. 2. Multiplexing in a hybrid digital-analog system: (a) SCM, (b) WDM, (c) PDM, (d) spectral null insertion, (e) non-spectral null insertion, and (f) TDM. PSD: power spectral density; SCM: subcarrier multiplexing; WDM: wavelength division multiplexing; PDM: polarization division multiplexing; TDM: time division multiplexing.
Both SCM and WDM schemes can avoid analog-to-digital interference and require only the use of filter to separate digital and analog signals. Nevertheless, they require additional bandwidth to achieve multiplexing, which results in low spectrum utilization. Moreover, compared to SCM scheme, the expensive price of WDM also limits its use. PDM uses two different polarization planes to transmit digital and analog signals respectively, which results in very high SE and does not generate analog-to-digital interference. Unfortunately, the receiver requires complex digital signal processing (DSP), which increases hardware costs. A trade-off solution is spectral null insertion. As the analog signal is filled into the spectral null of the digital signal, the analog-to-digital interference is smaller. Furthermore, because no additional bandwidth is required, the spectral null insertion scheme also has high spectrum utilization. Finally, the receiver only needs to use a filter to separate the hybrid signal. The non-spectral null insertion scheme, which can insert analog signal into any position of the digital signal spectrum, has a high SE, but it also generates serious analog-to-digital interference. This type of analog-to-digital interference needs to be alleviated by limiting the amplitude of the analog signal, resulting in the analog signal modulated to a lower order. Finally, the hybrid digital-analog signal can be separated through a limiting amplifier. Although the TDM scheme can improve the SNR of analog signal by about 10 dB through doubling the bandwidth cost, the strict synchronization and optimization algorithms are required to ensure the signal demodulation. Taking into account the advantages and disadvantages of various schemes, in this article we choose spectral null insertion as a trade-off scheme. As shown in Table 1, we compare different digital analog hybrid transmission schemes in terms of digital analog interference, spectral efficiency, and demodulation complexity. In order to simplify the complexity of RU, we choose the simplest receiver demodulation method while avoiding excessive digital analog interference and achieving high spectral efficiency. Therefore, we choose spectrum zero filling as the hybrid digital-analog transmission scheme in this paper.
Table 1. Comparison of Hybrid Digital Analog Transmission Schemes
2.3 Spectral null of digital signal
For the digital signal modulated by pulse code modulation (PAM), there is a spectral null between the main lobe and the side lobe of the power spectral density (PSD) function, resulting in incomplete utilization of the spectrum. Therefore, it can be considered to fill the analog signal within the spectral null to further utilize the spectrum. The PSD of the PAM signal can be represented as [16]
As shown in Fig. 3, the position of spectral null of the PAM signal is determined by its baud rate. For example, the bit rate in Fig. 3 is set to 600 Mbit/s, corresponding to the spectral null of NRZ, PAM4, and PAM8 signals located at 600 MHz, 300 MHz, and 200 MHz, respectively. Due to the presence of spectral null, the spectral utilization of digital signal is not maximized, providing space for inserting analog signal at spectral null for hybrid transmission. In order to effectively improve the spectral utilization of digital signal, we consider inserting analog signal into only the first spectral null of the digital signal. Note that from the PSD in Fig. 3, it can be seen that as the modulation order of the digital signal increases, the concave range of the spectral null gradually gets narrow, which means that the insertable range of the analog signal also gradually decreases.
3. Proposed FSO fronthaul system
The proposed FSO fronthaul system structure includes three parts, DU, channel and RU.
Figure 4 shows the system model. In DU, the original binary data is filtered after serial to parallel conversion, inverse fast Fourier transform (IFFT), parallel to serial conversion, and adding cyclic prefix (CP) as shown in Fig. 4(b). Limiting the amplitude may reduce the peak to average power ratio (PAPR), which further introduces significant out-of-band leakage. Therefore, a raised cosine filter is used to reduce out of band leakage. Finally, the OFDM bands are aggregated through a multiplexer. Note that the number of bands for analog signal aggregation is determined by the adaptive bands allocation module. Then analog signal is converted into the required IF signal through appropriate local oscillator of RF carrier. The frequency of up conversion is set to the first spectral null of the NRZ signal. The digital signal is modulated using NRZ, and hybrid digital-analog signal can be obtained through a power combiner. Then the hybrid signal is modulated onto the optical carrier through MZM, which operates at orthogonal bias points to ensure the linearity of the device. Then the optical signal is sent to the FSO channel through the optical collimator.
Fig. 4. Schematic diagram of a hybrid digital-analog transmission system, (a) system setup; (b) generation of analog signal at the transmitter; (c) adaptive bands allocation module; (d) OFDM demodulation at the receiver. MZM: Mach-Zehnder modulator; IFFT: inverse fast Fourier transform; CP: cyclic prefix; PD: photodetector; ATT: attenuator; BPF: band-pass filter; FFT: fast Fourier transform.
As shown in Fig. 4(c), the process of adaptive bands allocation includes the following steps:
Step 1: Input parameters, including parameter settings at the transmitter, channel status information, and photodetector (PD) parameters at the receiver. The specific parameters are shown in Section 6;
Step 2: Obtain the SNR of analog signal;
Step 3: Convert SNR into EVM;
Step 4: Compare the analog signal EVM with the EVM threshold. When the analog signal EVM and EVM threshold are equal, the obtained bandwidth is the maximum insertable analog bandwidth. When the analog signal EVM is lower than the EVM threshold, the inserted analog bandwidth can be further increased, and vice versa.
Step 5: Divide the bandwidth obtained in Step 4 by the bandwidth of one OFDM band, and then floor to obtain the maximum aggregated number of bands as the output of the adaptive bands allocation module.
The detailed process of steps 2 to 5 will be introduced in Section 5.
Atmospheric turbulence and attenuation factor are usually used to describe the FSO channel state. Turbulence can be further indicated by the atmospheric refractive index structure constant $C_n^2$, which is estimated by the temperature sensor at the transmitter. The link attenuation factor depends on attenuation and geometric loss. Geometric loss can be calculated by the parameters of the transmitter, while the attenuation loss depends on weather conditions and can be obtained through the real-time update of weather forecasts or the precipitation and visibility sensors [22]. Specifically, our analytical model of maximum insertable analog bandwidth is used in the module of adaptive bands allocation at the transmitter, which can adaptively change the inserted bandwidth of analog signal based on the detected link attenuation factor and turbulence intensity at the transmitter.
In RU, the optical signal is received through a collimator, and the hybrid digital-analog signal is detected by a PD. Then, the electrical signal is divided into two paths through a 3 dB coupler, where the analog IF signal can be filtered through a BPF. At the same time, the other hybrid signal passes through a 3 dB signal attenuator (ATT), as the power of the two signals should be kept equal to avoid most interference from the analog signal. Digital signal is obtained by subtracting analog signal from hybrid signal, which can avoid complex DSP processing. Finally, the demodulation of the OFDM signal is shown in Fig. 4(d), which is the inverse process of modulation in Fig. 4(b). The system structure in this article does not include an optical amplifier, and therefore the results obtained can be further improved if an optical amplifier is introduced. Note that the receiver can also obtain the information of the digital signal through a band-stop filter (BSF). However, the demodulation of the analog signal will be affected by the accumulated errors of the digital signal, resulting in a smaller inserted bandwidth of analog signal. In order to maximize the insertion range of analog bandwidth, we make sure the demodulation of analog signal prior to that of digital signal. Because the SNR required for digital signal demodulation is usually smaller than that is required for analog signal, the digital signal can be successfully demodulated when the SNR of analog signal is ensured, even if the involvement of accumulated digital-analog interference noise [23].
4. Atmospheric channel model
In optical communication, the optical signal is usually received through PD at the receiver, and the interference such as background noise may be introduced, due to the influence of the receiving aperture. Therefore, the optical channel can be typically expressed as [24]
where x is the transmitted symbol with average optical power, h is the channel attenuation coefficient, y is the received electrical signal, n is the photo-current noise, and ${R_0}$ is the PD responsivity. h includes two parts: atmospheric attenuation coefficient ${h_l}$ and atmospheric turbulence coefficient ${h_a}$. Assuming that these two parts independently affect the channel, the channel state can be represented as where ${h_l}$ is a deterministic function, which is mainly related to the transmission distance and attenuation factor. ${h_a}$ is a stochastic process.4.1 Atmospheric attenuation
The attenuation in atmospheric channel is mainly caused by absorption and scattering processes. As for visible and infrared wavelengths, the main atmospheric absorbents include molecules of water, carbon dioxide and ozone. The attenuation experienced by optical signal passing through the atmosphere can be quantified using optical depth. Atmospheric attenuation is usually modeled as an exponential model. Scott Bloom comprehensively considered the impact of geometric losses and attenuation loss, and proposed a more specific atmospheric attenuation model [25], as follows
4.2 Atmospheric turbulence
Atmospheric turbulence is formed by the random changes in atmospheric temperature and wind speed caused by solar radiation and various meteorological factors. The random change in atmospheric temperature causes irregular variation in atmospheric density, leading to the significant non-uniformity in atmospheric refractive index. The fluctuation of atmospheric refractive index is characterized by the random fluctuation in the optical wave parameters such as amplitude and phase. The probability density function (PDF) of turbulence-induced intensity fluctuation $I$ can be obtained by combining the space-time fading distribution [26].
5. Channel-adaptive insertion of analog bandwidth
5.1 SNR analysis for atmospheric attenuation
Since the inserted bandwidth of analog signal affects system BER, the estimation of maximum inserted analog bandwidth should make sure the required BER performance. However, for mathematical simplicity, we choose the EVM threshold instead of BER threshold as an indicator for the estimation of maximum inserted analog bandwidth. Analog signal is mainly affected by digital crosstalk ${S_D}({M,f} )$ and power attenuation of FSO link ${h_{FSO}}({l,\varepsilon ,f} )$. Therefore, the SNR of the analog signal after PD detection is:
The PAPR of OFDM signal is defined as [27]
Assuming that the OFDM signal is uniformly distributed on the spectrum with a bandwidth of B, the PSD of the analog signal can be approximated by
In fact, Eq. (11) represents the upper bound of the analog signal PSD. As there is a guard interval, the actual PSD will not be higher than Eq. (11).
Substituting Eq. (11) into Eq. (8), we can transform Eq. (8) in dB to the following
5.2 Analysis for turbulence effect
Due to the randomness of turbulence, the received optical power changes intensively, which affects the demodulation at the receiver. Therefore, we quantify the impact of turbulence on received optical power, and reflect the change in turbulence by measuring the fluctuation in received optical power. In the case of weak turbulence, the fluctuation of received optical power is shown in Fig. 5, where the influence of attenuation has been removed.
In Fig. 5, the x-axis represents the atmospheric attenuation factor, the y-axis represents the simulation times, and the z-axis is the fluctuation of received optical power, respectively. From the Fig. 5, it can be seen that the fluctuation range of received optical power is [-0.2, 0.2] dB. Because moderate and strong turbulence can cause severe fluctuation in the received optical power, the amplitude of the electrical signal after PD detection is disturbed significantly, resulting in a large BER. For medium or strong turbulence, optical amplification, adaptive optics [28], aperture averaging [29] and other technologies can be used to mitigate the impact of turbulence and reduce it to weak turbulence. Therefore, we choose to consider the effect of weak turbulence rather than moderate and strong turbulence.
Figure 6 shows the fluctuation pattern of received optical power through 2000 random and independent experiments. The black dashed line in the figure is a polynomial fit, while the red solid line is a Gaussian fit. It can be seen that Gaussian fitting has a good fitting effect on high amplitude data in the middle part, while polynomial fitting has a good effect on low amplitude data on both sides. However, overall, the fitted curves approximate a Gaussian distribution. It can be seen from Fig. 6 that the influence of turbulence on received optical power is approximately Gaussian distribution with a mean of zero.
Therefore, an expression can be considered to establish the relationship between turbulence and the degree of influence ${H_a}$ of turbulence on the received optical power. ${H_a}$ can be expressed as
where ${P_r}$ represents the fluctuation in optical power without atmospheric attenuation effect, and p represents the outage probability. $\max \{{|{{P_r}} |} \}$ is the maximum received optical power without atmospheric attenuation effect. Note that the unit of ${H_a}$ is dB, and we need to convert it into a dimensionless coefficient. Then, the atmospheric turbulence coefficient ${h_a}(p )$ can be expressed as5.3 Estimation of insertable analog bandwidth
Substituting Eq. (14) into Eq. (12), we can obtain
According to the relation between EVM and SNR, we can formulate EVM as [30]
In the unit of dB, Eq. (16) is converted to
Therefore, we can obtain the EVM expression $EV{M_A}({\cdot} )$ of the analog signal from Eq. (17) by substituting $SN{R_A}({\cdot} )$ in Eq. (15). For a communication system, only when $EV{M_A}({\cdot} )$ is lower than the EVM threshold $EV{M_{th}}$ corresponding to the modulation order can this error-free decoding be guaranteed. For the M-ary QAM, the EVM thresholds corresponding to the different modulation orders are shown in Table 2 [31].
Table 2. EVM Thresholds for Different Modulation Orders
Then, we define
There are three cases obtained from Eq. (18), $f(B )> 0,\textrm{ }f(B )= 0,\textrm{ }f(B )< 0$. When $f(B )> 0$, it indicates that the EVM corresponding to the analog bandwidth is less than the threshold value, which can further increase the analog bandwidth. When $f(B )= 0$, it indicates that the analog bandwidth at this time is the maximum insertable analog bandwidth. When $f(B )< 0$, it indicates that the EVM of the analog bandwidth has not reached the threshold requirement and the bandwidth needs to be reduced. The optimal insertable analog bandwidth can be obtained by the dichotomy algorithm. By adjusting the EVM threshold in Table 2, the inserted bandwidth of analog signal at different modulation orders can be obtained.
Therefore, the number N of analog bands can be defined as:
where ${B_0}$ represents the bandwidth of a single OFDM band, and $\lfloor\cdot \rfloor $ represents floor operator.6. Results and discussion
The parameter settings for OFDM signal are as follows. The subcarrier bandwidth of OFDM signal is 15 kHz and the number of subcarriers in each band is 600, resulting in an effective bandwidth of 9 MHz. There is a guard interval of 1 MHz to avoid interference between bands, and therefore the total bandwidth of one band is 10 MHz. To simplify the analysis, only the spectral null of the first main lobe of the NRZ signal is considered at 600 MHz, which is also the frequency at which the baseband analog signal is upconverted. Note that the maximum amplitudes ${A_a}$ and ${A_d}$ of both analog and digital signals are normalized. The laser frequency is 193.1 THz and the output power is 0 dBm. The PD responsivity is 1 A/W. The roll-off coefficient of the bandpass raised cosine filter is 0.2, and the center frequency is 600 MHz. Thanks for your valuable comment. The software simulation we used OptiSystem 15, and the calculation and analysis results were conducted using Matlab. The turbulence model in the simulation software is the Gamma-Gamma distribution, the specific parameter settings are shown in Table 3.
Table 3. Simulation Parameters
Figure 7 shows the impact of changing digital signal frequency on EVM of analog signal under different OSNR. The attenuation factor is 10 dB/km, and the FSO link length is 0.5 km. We determine the selection of OSNR for different modulation orders in Eq. (17) by setting a fixed inserted analog bandwidth value. The inserted analog bandwidth in Fig. 7 is preset to 50 MHz. The frequency range is [300, 1300] MHz, and the horizontal line in Fig. 7 represents the threshold of EVM under different modulation methods. The black solid line in Fig. 7 represents the situation without noise interference, which is the theoretical upper bound when OSNR approaches infinity. Within this frequency band, two points with zero EVM value can be found, namely 600 and 1200 MHz, which correspond precisely to the spectral null of the NRZ signal. We can observe that as the OSNR increases, the degree of concavity in the curve gradually increases at 600 MHz. As the frequency increases, it ultimately approximates as a straight line. Specifically, the intersection range of analog bandwidth refers to the frequency scope meeting the EVM threshold. For example, when OSNR = 30 dB, the analog bandwidth that can be inserted for 4-QAM is 50 MHz, and OSNR needs to be increased to 33 dB for 16-QAM. Because 4-QAM is used as an example in subsequent simulations, we set the OSNR in the analytical expression to 30 dB.
Figure 8 shows the comparison of the analog signal bandwidth that can be inserted in different link lengths ([400, 1000] m) with a fixed atmospheric attenuation of 10 dB/km. The horizontal axis represents the FSO link length, and the vertical axis represents the maximum insertable bandwidth of analog signal. The black solid line in Fig. 8 is the result of software simulation, while the red line is the result of theoretical analysis. The red dashed line in Fig. 8 represents the floor result in Eq. (19), while the black dashed line represents the floor result in simulation. The floor result is the maximum number of bands that can be aggregated for the analog signal. Note that only when the value of the red dashed line is less than or equal to the value of the black dashed line, the inserted analog bandwidth can meet the BER requirement of $3.8 \times {10^{ - 3}}$. From the curve in Fig. 8, there is a negative exponential relationship between the FSO link length and the maximum insertable analog bandwidth. As the transmission distance increases, the insertable analog bandwidth will decrease. When the link length exceeds 650 m, the decreasing trend gradually becomes flat. We find that the results obtained from the analytical expression deviate significantly from the simulation results when the transmission distance is greater than 650 m. Because the received optical power at this time is already very small, it is difficult for the receiver to demodulate the analog signal. Then, the analytical expression results are no longer applicable.
Figure 9 shows the effect of different atmospheric attenuation factors on the insertable bandwidth of analog signal at a fixed transmission distance of 0.5 km. The horizontal axis represents the atmospheric attenuation factor, while the vertical axis represents the maximum insertable analog bandwidth. It can be observed that the atmospheric attenuation factor is approximately linearly related to the insertable analog bandwidth. We expected result is that the number of maximum insertable analog bandwidth obtained by analyzing the expression after floor is always less than or equal to the number of maximum insertable analog bandwidth obtained by the simulation results. This ensures that after inserted the hybrid signal with analog bandwidth through the channel according to the analysis expression, it will not cause demodulation failure of the hybrid signal. Therefore, corresponding to the same abscissa conditions in Fig. 8 and Fig. 9, we hope that the value of the analytical expression is always less than or equal to the value simulated by the software. In Fig. 8 or Fig. 9, there is a hysteresis phenomenon between the red dashed line and the black dashed line. Compared with Fig. 8 and Fig. 9, the hysteresis phenomenon in Fig. 9 is more obvious, and its corresponding link attenuation range is sufficiently large. Therefore, comparing the results in Fig. 8 and Fig. 9, it can be seen that the analytical expression has a better fitting effect on the variation of atmospheric attenuation compared to the transmission link distance. For practical scenarios, the distance between the transmitter and receiver is basically fixed and unchanged. Therefore, the derived analytical expression is feasible as a guideline for practical system optimization.
Figure 10 shows the effect of different atmospheric attenuation factors on BER under weak turbulence and a transmission distance of 0.5 km. The colored bands in Fig. 10 represent our proposed adaptive bands insertion, while the black reference sidebands represent the six fixed bands inserted. The bandwidth of each band in the figure is 10 MHz. By comparing the color band with the black band, we can verify whether the results of our derived analysis expressions meet the actual requirements. The parameter settings here are the same as the previous simulation results, with the range of inserted analog bandwidth being [300, 900] Hz, and the spectrum null of the digital signal being at 600 Hz. The BER changes of each of the six bands are shown with respect to the atmospheric attenuation factor. The six colored bands represent the BER variation for each band from a changed number of aggregated bands by the adaptive bands allocation module, while the six black bands referenced represent the BER variation of fixed six bands that are all used to carry analog signal under different channel conditions. When the link attenuation is greater than 10 dB/km, the analog bandwidth that can be inserted cannot exceed 60 MHz in Fig. 10. Since the sixth band no longer meets the error correction threshold of forward error correction (FEC), it is necessary to change the inserted analog bandwidth range based on the attenuation of the link. Note that the interval of the neighboring analog bands in our simulation is 10 MHz, which has a larger granularity. As the bandwidth of the transmitted digital signal increases, the granularity of the inserted analog bandwidth will also decrease accordingly, thus obtaining a more accurate number of insertable analog bands.
Figure 11 shows the effect of different attenuation factors on the insertable analog bandwidth under weak turbulence condition, and the simulation conditions are the same as Fig. 10. The x-axis in the Fig. 11 represents the atmospheric attenuation factor, the y-axis represents the insertable simulation bandwidth, and (a) (b) (c) (d) (e) and (f) represent the situations from different simulation times. These simulations are conducted as random and independent experiments under the same conditions. From Fig. 11, it can be seen that with the introduction of turbulence, the insertable analog bandwidth fluctuates randomly. Although Eq. (12) has a good fitting effect in the absence of turbulence, the blue dashed line in Fig. 11 mostly overlaps with the red line in (a) at atmospheric attenuation factors of 10-11 dB/km and in (d) at atmospheric attenuation factors of 12-14 dB/km. Thus Eq. (12) cannot be applied to the link situations with turbulence effect. Based on Eq. (13), we set the outage probability to 0.05, as shown by the black solid line in Fig. 11. The black solid line is the lower bound of the inserted analog bandwidth obtained through Eq. (15), which indicates that the black solid line is the basic requirement of the red line to ensure that the system will not outage due to excessive transmission of analog bands.
Fig. 11. The effect of different attenuation factors on the insertable analog bandwidth under weak turbulence; (a) (b) (c) (d) (e) and (f) represent the situations from different simulation times (LB: lower bound).
7. Conclusion
This article focused on the hybrid digital-analog transmission of RoFSO system and proposed a channel-adaptive insertion of analog bandwidth into digital signal spectrum. By inserting analog IF signal into the spectral null of digital signal, the utilization of the spectrum can be improved. Based on the proposed system structure, we derived an analytical expression for the insertable analog bandwidth in the FSO link to achieve adaptive transmission of hybrid digital-analog signal. We estimated the insertable analog bandwidth by establishing an equation between the SNR of analog signal and the EVM threshold, which can be extended to higher-order QAM modulation methods. Finally, through software simulation, it was verified that the bandwidth derived from the analytical expression approximates the simulation results under weak turbulence condition.
Funding
National Natural Science Foundation of China (62025105, U21B2005); Chongqing Science and Technology Commission (cstc2021ycjh-bgzxm0329, CSTB2022NSCQ-LZX0070); Chongqing Municipal Education Commission Foundation (KJZD-M202300606, CXQT21019).
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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