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Abstract
Evolution of next generation wireless networks brings challenges to efficiently transmit a large amount of data from a base station to a remote antenna unit. We investigate a space division multiplexing technique that employs few mode fibers (FMFs) to transmit 3 × 3 MIMO wireless signals, aiming to employ a common digital signal processing (DSP) unit to equalize both the fiber and wireless channel. We optimize system parameters and obtain above 28 dB and 23 dB signal-to-interference and noise ratio (SINR) for 3 meters wireless systems with 500 m and 2 km FMF, which correspond to the transmission capacity of 578 Mb/s and 468 Mb/s using a 20 MHz bandwidth, respectively. Moreover, we analyze that the nonlinear spectrum distortion due to the combined effect of nonlinearity in the directly modulated laser and the differential mode delay in multimode fibers and validate it by simulations.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In order to reduce the total cost of ownership and to meet stringent requirements in terms of high spectral efficiency, high energy efficiency and low latency, next generation (5G) wireless networks are evolving towards a centralized/cloud radio access network (C-RAN) architecture [1–3]. In traditional RAN, a baseband unit (BBU) and a remote radio head (RRH) are collocated at a wireless cell site and perform baseband digital signal processing and radio frequency (RF) processing functionalities, respectively. Traditional RAN has drawbacks such as difficulty to implement advanced cooperative radio technologies (e.g. coordinated multiple point transmission and reception, CoMP), high loss in RF cables connecting RRH and antennas, high operational cost due to electrical power consumption, site rent and maintenance. In the C-RAN architecture, the BBUs are centralized and the RRH is moved close to the antenna. C-RAN brings benefits in multiple aspects: (i) significant reduction in power consumption by employing low loss optical fiber link and removing cooling or air conditioning in the antenna site, (ii) improvement of radio performance as the centralized architecture enables advanced network technologies such as CoMP as well as load balancing among multiple BBUs to achieve higher spectral efficiency, (iii) simplifications in networks where the communication interface between BBUs is greatly simplified for collocated BBUs and a physically secured central office removes the requirement of a backhaul security protocol such as IPSec which reduces communication overhead.
The C-RAN network architecture introduces a new transmission link, a mobile fronthaul (MFH) that transports data between RRHs and centralized BBUs [4–7]. The requirement on multiple Gb/s capacity makes optical fiber the natural choice. Currently, most C-RAN deployments consider common public radio interface (CPRI) implementation for MFH, where sampled radio waveforms are transported [8]. The CPRI data rate is calculated by S × M × fs × N × 2 × Cw × C, which shows the capacity multiplication due to the number of antenna sectors S, the number of antennas per sector M, the sampling frequency fs, the number of sampling bits per sample N, the in-phase and quadrature data factor 2, the control word Cw, and the coding factor C. In order to maintain signal fidelity, a large number of bits are required to represent each radio waveform sample, e.g. N = 15 in long term evolution (LTE) signals. As an example, consider a three-sector LTE cell with 20 MHz bandwidth and 4 × 4 multiple-input multiple-output (MIMO), the CPRI bit rate reaches 14.7 Gb/s. For 5G and future networks, carrier aggregation is expected to enhance mobile user data rate, which increases the CPRI bit rate by a factor equal to the number of aggregated frequency bands [9]. For example, LTE-advanced allows carrier aggregation of up to five 20 MHz bands to achieve a 100 MHz bandwidth. Moreover, in massive MIMO system [10], which is an enabling technology for 5G, hundreds of antennas may be needed at an antenna site, which presents huge capacity needs on MFH. Various optical communication technologies have been proposed for MFH. A conceptually simple solution is to use two optical fibers for the uplink and downlink of each fronthaul link, however, the cost of fiber cable is high since one may need one fronthaul link (two fibers) per sector, per antenna, per radio frequency carrier, and per radio access technology (RAT). Alternatively, coarse and dense wavelength division multiplexing (CWDM and DWDM) solutions have been proposed [4]. CWDM provides a limited number of wavelength channels, e.g. 16 or 18 channels with 20 nm spacing, indicating that multiple fibers are still required for many applications. DWDM offers better spectral efficiency with typically 0.8 nm spacing, however, it brings challenges to meet the low cost transmitter requirement and the industrial temperature specifications for outdoor installations (−40 °C to + 85 °C). Moreover, WDM requires optical devices with different wavelengths for different fronthaul links, which cause complications in inventory management and cost issues.
Recently, space division multiplexing (SDM) techniques using few mode fiber (FMF) or multimode fiber (MMF) have attracted much research attention [11–15]. 3 × 10 Gb/s MIMO transmission was demonstrated using few mode fiber and mode-selective photonic lanterns [11]. Mode division multiplexing (MDM) transmission over 500 meter 4-mode MMF with direct detection was demonstrated in [12]. There are also research works investigating the transmission of MIMO signals over FMF or MMF followed by wireless signal transmission in the air. In [13], the feasibility of radio over fiber (RoF) systems based on MDM using spatial light modulator (SLM) and discrete optical components for MIMO transmission was investigated and discussed. In order to reduce system complexity and cost, it is favorable to design MDM systems using mode non-selective (de)multiplexers such as waveguide or fiber-based photonic lanterns (PLs). Ref [14] demonstrated 3 × 3 MIMO transmission of wireless signals over 200 m MMF followed by 1 m air link. Ref [15] investigated 2 × 2 MIMO transmission over 2 km elliptical-core FMF and 0.4 m air link.
In this paper, we investigate the feasibility of transmitting 3 × 3 MIMO analog signals over a few mode fiber (FMF) followed by 3 meters air link. Analog transmission saves analog-to-digital convertor (ADC) and digital-to-analog convertor (DAC) at the remote antenna site and also circumvents the inefficiency in CPRI links where sampled radio waveforms are transmitted using a large number of bits per sample. We employ MDM in the FMF to provide an extra dimension of multiplexing. We use a common digital signal processing (DSP) unit to equalize both the FMF channel and the wireless channel. To reduce system complexity, direct modulated distributed feedback (DFB) lasers and direct detection schemes as well as non-mode-selective PLs are used in the system. The experimental setup of this paper is similar to [14], but differs in the following aspects: (i) optical fibers are different; Ref [14]. showed transmission over 200 m MMF followed by 1 m air link, while this paper demonstrated transmission over 2 km FMF followed by 3 m air link. (ii) transmitter and receiver configurations are different; Ref [14]. used commercial Keysight MIMO transmitter and receivers, while this paper uses Matlab to generate and demodulate MIMO signals. Moreover, in this paper, we show experimental observations of the nonlinear spectrum distortion and provide theoretical analysis and numerical validations, which is not yet available in existing literature to our knowledge. The remaining part of the paper is organized as follows. Section 2 describes the experimental setup and the optical characteristics of the PLs. Section 3 investigates and analyzes the combined effect of the nonlinearity in direct laser modulation and the differential mode group delay (DMGD) in the FMF that results in nonlinear spectrum distortions to FMF systems but not in single mode fiber systems. The 3 × 3 MIMO transmission performance is given and discussed in Section 4. Section 5 draws the conclusions.
2. Experimental setup
We investigate 3 × 3 MIMO signal transmission through a FMF and wireless link. Figure 1 shows the experimental setup. Two arbitrary waveform generators (AWGs) output three channels of LTE-like wireless signals. The RF carrier frequency is 2.5 GHz and the signal bandwidth is 20 MHz. The wireless signals consist of 10 orthogonal frequency division multiplexing (OFDM) training symbols followed by 100 OFDM data symbols. Due to the limited memory in the AWGs, the number of OFDM subcarriers is reduced to 120. Band pass filters (BPFs) are used to remove the out-of-band noise of the AWG output signals. The variable attenuators are used to adjust the input power to the optical transmitters, which include built-in RF amplifiers and directly modulated DFB lasers. Then, the modulated optical signals are rotated by polarization controllers (PCs) and mode multiplexed using a photonic lantern multiplexer (PL-Mux). To reduce system complexity, non-mode selective photonic lanterns are used, based on 3D laser-written waveguide technology. A FMF is used as the multi-mode link for optical signal transmission. The FMF supports LP01, LP11a and LP11b modes. The loss and dispersion coefficients for the three modes are around 0.2 dB/km and 21 ps/nm/km, respectively. The effective area of the LP01 and LP11 modes are 216 µm2 and 415 µm2, respectively. The differential mode group delay (DMGD) between LP01 and LP11 modes is 120 ps/km. After fiber transmission, a rotation controller is used before demultiplexing, which applies transverse rotation to the FMF and adjusts both the polarization status and the mode matching conditions with the photonic lantern demultiplexer (PL-Demux). The optical signals are converted into electrical signals using optical receivers, which consist of photodetectors, variable attenuators and RF amplifiers. The power of the optical receiver output signals can be adjusted by tuning the built-in variable attenuators. The RF signals at a carrier frequency of 2.5 GHz are then attenuated, amplified, filtered and transmitted via wireless antennas. The power amplifier has maximum 37 dB gain and 31 dBm output power at the 1 dB compression point. The actual gain can be adjusted by controlling the built-in variable attenuators. The transmitter antennas are arranged in a line with 1 meter separation. The wireless link is set as 3 meter. At the receiver side, the wireless signals are collected by another three antennas and then amplified by low noise amplifiers (LNAs), filtered, sampled by real-time oscilloscopes, and then passed to computers for offline MIMO processing. The LNA has 17 dB gain and 18 dBm output power at the 1 dB compression point. In the offline DSP, synchronization of the MIMO signals is realized using Schmidl and Cox’s algorithm [16]. Channel estimation is implemented based on the training sequence. Then the MIMO signal streams are demodulated using a zero-forcing algorithm.
Fig. 1 Experimental setup (AWG: arbitrary waveform generator, BPF: band pass filter, Att: attenuator, Tx: transmitter, PC: polarization controller, PL-Mux: photonic lantern multiplexer, PL-Demux: photonic lantern demultiplexer, FMF: quasi-single mode fiber, Rx: receiver, PA: power amplifier, LNA: low noise amplifier, DSP: digital signal processing).
We measure the insertion loss of the PLs by launching a CW light at 1550 nm into one of the three single mode fiber ports at a time and measure the output power at the multimode port. The insertion losses of the PL-Mux and PL-Demux are 2.3 dB, 1.8 dB, 2.4 dB and 2.0 dB, 1.8 dB, 1.6 dB for the three input ports, respectively. Figure 2 shows the beam patterns observed at the multimode port of the PLs, while launching power into one of the single mode ports. Since the PLs are not designed to be mode-selective, launching light into any of the single mode port excites a superposition of multiple modes. Figure 2 also shows the beam patterns observed at the output of FMF. By adjusting the offset and tilting between the launching light source and the FMF, we observe the fundamental and second-order field intensity of the FMF. The beam sizes in Fig. 2 are not shown to the same scale. The measured vertical and horizontal dimensions at 1/e of maximum intensity are given in Table 1. The first row in the FMF section is for the fundamental mode, while the second row is for the second-order mode. Since the commercial PLs are not optimized to match with the FMF, we observe differences in beam sizes and also a relatively high insertion loss. The end-to-end insertion loss of the cascade of PL-Mux, FMF and PL-Demux varies between 7.9 dB and 8.6 dB, when the FMF length changes from 2 m to 2 km. System transmission performance can be enhanced when the mismatch between the fiber and the PLs is reduced, which improves loss as well as mode coupling performance.
Fig. 2 Optical intensity distributions at the output port of PLs and FMF (Beam sizes are given in Table 1).
Table 1. Beam size
3. Combined effects of direct modulation and differential mode group delay (DMGD)
In this section, we discuss the combined effects of direct modulation of the signal laser and the differential mode group delay (DMGD) in a multimode fiber, which results in signal interference that are not observed in single mode fiber systems. For simplicity, we exclude the effect of wireless propagation in this Section.
3.1 Experimental observations and discussions
In this section, we replace the air link by 50 dB RF attenuators (corresponding to path loss in 3 meters propagation) in the experimental set up to exclude the impact of the wireless link on the received signal spectrum measurements. We measure signal spectrum at the optical receiver outputs so that the impact of the link components after the optical receivers are not included. The attenuators before the optical transmitters are set to zero. The power of the OFDM signal is −18 dBm at the input of the optical transmitter. FMF with different lengths are tested. Figure 3 shows the electrical signal spectrum observed at the optical receiver output. We observe that the output signals of the three optical receivers show similar spectrum shape except for differences in power levels due to power variations of mode coupling in FMF. Figure 3 shows the spectrum observed at the first optical receiver output. When the FMF is 100 m long, a normal OFDM spectrum is observed. However, as the FMF length increases to 500 m and 2 km, spectrum broadening is observed and the level of interference increases with FMF length. Figure 3 also shows the signal spectrums for the cases with two tone inputs, where all the OFDM subcarriers except for the two at the boundaries are set to zero. It clearly shows that third order and higher order intermodulation distortions (IMD) are generated, the power of which increases with FMF length. In contrast, we repeat the measurements by replacing the FMF by a 6 km long single mode fiber. It does not show the IMD components in the signal spectrum of single mode fiber systems.
Fig. 3 Signal spectrums for systems with different lengths of FMF (a ~f) and single mode fiber (g and h) (OFDM (a, b, c, and g) or two tone (d, e, f, and h) signals are used as inputs).
Considering that the IMD is observed in long FMF systems but not in single mode fiber systems, we first investigated if that it is due to nonlinear effects in the fiber. We added variable optical attenuators (VOAs) after optical transmitters to adjust the optical signal power from 8 dBm to −7 dBm, but observe that the signal spectrum at the optical receiver output remains a similar shape and only the power levels change. That is, interference component relative to the signal level in the case of OFDM signal input and the number of IMD tones in the case of two tone signal input are not dependent on the optical power. This indicates that the interference component is not due to the nonlinearity of the FMF, which is expected considering its large effective area.
Next, we investigate the impact of the power of the input RF signal to the optical transmitter on the received signal spectrum. Figure 4 shows the received signal spectrum after PD when different amount of RF attenuation is applied to the input signal to the optical transmitter. Attenuation of 0 dB, 9 dB and 18 dB corresponds to input signal power of −18 dBm, −27 dBm and −36 dBm, respectively. In order to make the interference component not buried under the noise floor when the RF attenuation is large, we switch off some variable electrical attenuators in the optical receiver to adjust its effective gain coefficient. Figure 4 shows that the interference level relative to the signal level is significantly reduced by introducing RF attenuators. For the two tone measurements, the strongest interference component is the third order intermodulation distortion (IMD3). We define a metric as signal to IMD3 power ratio (SIR). Figure 5(a) shows the SIR as a function of the input power to the optical transmitter for the system with 2 km FMF.
Fig. 4 Impact of RF attenuation on the signal spectrum. ((a~c) use OFDM signal as input, (d~f) use two tone signal as input, FMF length = 2 km).
We also investigated the MIMO transmission performance for the FMF system without air links. The performance of various RF input power conditions are measured, as shown in Fig. 5(b). The signal to interference and noise ratio (SINR) after MIMO demodulation varies with the input power in a similar manner as SIR does. In MIMO systems, signal quality is affected by noise as well as the residual interference among the MIMO channels after equalization, which is indicated by the SINR parameter. SINR decreases dramatically when the input power is larger than −27 dBm, in which region interference other than noise dominates the performance.
To sum up, the measured signal spectrum at the optical receiver output shows nonlinear interference components in FMF systems, but not in single mode fiber systems. The nonlinear interference level is dependent on the power of the RF modulating signal, but not on the power of the optical signal after direct modulation. Moreover, the interference level increases with the FMF length. The experimental observations can be explained by the combined effects of the nonlinearity in direct modulation of laser and the DMGD in the FMF. In direct modulation, the optical signal intensity is
where P0 is the DC optical power, m indicates the modulation depth, and u(t) is the modulating signal. The optical field iswhere . The square root operation in direct modulation introduces nonlinearity and generates harmonics and inter-modulation products, especially when the modulation depth is not small enough. At the optical receiver, a photodetector (PD) is a square-law device, which recovers the electrical signal by taking the square of Eq. (2).where K = RP0. Equation (3) shows that a PD recovers the electrical modulating signal even if the modulation depth is not small. This implies that harmonics and inter-modulation products generated by the square root operation do not show up in the received signal spectrum of a PD. This agrees with the measured spectrum of single mode fiber systems even without any RF attenuation. However, in FMF systems, each input signal stream excites the three modes in the FMF. And the received optical signal is a superposition of the three modes with various delays. The PD square-law operation on the mixed signals cannot undo the square root operation that was performed on each single signal stream separately. In the case of insufficiently small modulation depth, second order harmonics and high order IMD are generated in the direct modulation of laser, which appear as interference in the received signal spectrum since the PD cannot remove them from a mixture of variously delayed signals. The amount of accumulated differential delay is proportional to the FMF length. Therefore, the interference level increases with FMF length, as shown in Fig. 3 and Fig. 5.3.2 Modeling and simulations
In this Section, we develop a numerical model to simulate the propagation of multiple signal streams in a multimode fiber. First, three channels of baseband OFDM signals are generated first in the same way as in experiments, which are then upconverted to the intermediate frequency (IF) band at 2.5 GHz carrier frequency. Optical signals are generated by direct modulation of the three IF signals. Without detailed information on mode launching condition at the PL-Mux, we assume that each IF signal stream excites all of the three modes with equal power for simplicity. In addition, we assume that both X and Y polarizations are excited with equal power. The total optical signal after PL-Mux consists of a vector of six signal streams. This optical signal propagates in a FMF fiber using the following linear propagation model where the fiber nonlinearity is ignored. After that, the power of both X and Y polarizations of each signal stream is detected using a PD.
The output optical field after propagating in a multimode fiber is [17,18]
where is the input signal, is the signal field of the mth mode in the p polarization, M is the total number of modes. The multimode fiber is modeled as multiple cascaded short segments and the total linear propagation operator is defined aswhere K is the total number of segments. The operator of the kth segment includes a polarization rotation operator and a linear propagation operatorwhere Here, IM × M is a unit matrix, θ and φ are uniformly distributed random phase angles representing the random polarization rotation and polarization phase delay, respectively. The propagation operators ΓX and ΓY are M × M matrices, of which the diagonal elements are given in Eq. (9) and Eq. (10). α, β1,pm, β2,pm and ∆τpm are the loss, inverse group velocity, dispersion coefficient and differential mode delay of the mth mode at p polarization. ∆z is the length of the kth fiber segment. The elements of the mode coupling matrix C is given in Eq. (11) [17]. k0 and β0 are the wave number and propagation constant, respectively. Fm and Im are the mth order mode field and its normalized power. nr0 and nr are the unperturbed and perturbed refractive index of the kth fiber segment. The mode coupling coefficients are determined by introducing perturbations on the fiber core radiusThe random variables a1, a2, ϕ1, ϕ2 controls variations of fiber core size, core position and ellipticity. In simulations, a1 and a2 are zero-mean Gaussian random variables with standard deviation of 0.5 μm and 1 μm, respectively. ϕ1 and ϕ2 are uniformly distributed within [0, 2π].We perform system simulations using the above model and calculate the signal spectrum after PD. Figure 6 shows the received signal spectrum for the two tone input signal for the cases of 100 m and 2 km FMF, which confirms that nonlinear interference becomes strong at long FMF systems and agrees qualitatively with experimental results. Figure 7 shows that the SIR obtained by simulations shows a similar dependence trend with FMF length as in the experimental results. The carrier to sideband ratio (CSR) represents the ratio of the optical carrier power to the power of the signal band after direct modulation. A larger CSR represents a lower modulation depth. Due to the lack of detailed information in experiments such as modulation depth, mode coupling in PL-Mux and PL-Demux as well as in FMF, index variation in FMF, we do not expect the numerical model to exactly reproduce the experimental results, but the purpose is to validate the trend.
4. 3 × 3 MIMO transmission performance
In this section, we investigate the 3 × 3 MIMO transmission performance for systems with 2 km FMF and/or 3 m wireless link. We compare the performance for three different system configurations: (i) the system without FMF but with 3 m air link, and the optical receivers are directly connected with optical transmitters using short single mode fibers. (ii) the system with 2 km FMF but without air link, and the air link is replaced by 50 dB RF attenuators. (iii) the system with 2 km FMF and 3 m air link. For all three system configurations, the input power to the optical transmitter is maintained at −33 dBm, which is the optimal input power considering the trade-off between noise and nonlinear interference for 2 km FMF as shown in Fig. 5. Also, the input power to the power amplifiers and the low noise amplifiers are kept at −25 dBm and −42 dBm for all the three system configurations. The polarization controllers before the PL-Mux and the rotation controller before the PL-Demux are adjusted in order to obtain the lowest mode crosstalk. Figure 8(a) shows the cumulative distribution function (CDF) curves for condition number of the MIMO channels and the SINR after MIMO demodulation. The FMF channel has a relatively steeper CDF curve than the wireless channel. In the presence of wireless link, the condition number fluctuates dramatically with the OFDM subcarriers due to the frequency dependent fading. Moreover, it shows that the combined FMF and wireless channel has a much higher condition number than the other two cases. The same MIMO demodulation code is applied for the three cases, which estimates the channel matrix based on the training sequence and then utilizes it to demodulate the data sequence. Figure 8(b) compares the CDF curves of the SINR. It shows that case (i) outperforms case (ii) by about 6.1 dB, which is mainly attributed to the fact that the FMF channel varies faster than the wireless channel and the training sequence based channel estimation cannot track the fast channel variation that happens within the data sequence time period [19]. In addition, optical losses due to the FMF, connectors, and the photonic lanterns reduces SNR. Figure 8 also shows that case (iii) is about 6.3 dB worse than case (ii), which is related to the significant increase in the condition number for the combined FMF and wireless channel.
Figure 9 shows the transmission performance for different FMF lengths, where the air link is kept at 3 meters. Figure 9(a) shows the median SINR value, obtained at 50% of the CDF curves. The input power to the optical transmitter is optimized at each FMF length, as shown in Fig. 9(b). For all cases, the input power to the power amplifier is kept constant at −25 dBm by adjusting the variable attenuators. The SINR decreases with FMF length due to two factors: (i) the input power to the optical transmitter is decreased to combat nonlinear interference at a longer FMF length; (ii) mode coupling is proportional to FMF length which introduces fast channel variation. The median SINR values are above 28 dB and 23 dB for the systems with 500 m and 2 km FMF, respectively. The transmission capacity is estimated using the Shannon theoretical formula , where B = 20 MHz is the signal bandwidth. As shown in Fig. 9(b), the total transmission capacity of the three channels are 578 Mb/s and 468 Mb/s for 500 m and 2 km FMF systems, respectively.
Fig. 9 (a) SINR vs. FMF length, (b) optimal RF input signal power and capacity vs. FMF length (air link = 3 m).
5. Conclusions
We investigated the transmission of 3 × 3 MIMO wireless signals through space division multiplexing in few mode fibers followed by a 3 meters wireless link and employed digital signal process to demodulate the mixed fiber and wireless channel simultaneously. We experimentally observed nonlinear interference in the received signal in systems using FMF, but not in systems using single mode fibers. We analyzed that the combined effects of the nonlinearity of the square root operation in the direct modulation of laser and the differential mode delay in the FMF generate nonlinear interference, which is qualitatively validated through numerical simulation of MIMO signal propagation through FMFs. We showed that introducing 2 km FMF in the system resulted in about 12.4 dB SINR degradation as compared with the wireless system without FMF, which is due to faster variation in the FMF channel than the wireless channel and the noises in the optical links. We optimized system parameters and operation conditions and obtained greater than 28 dB and 23 dB SINR for 3 meters wireless systems with 500 m and 2 km FMF, which correspond to transmission capacity of 578 Mb/s and 468 Mb/s using a 20 MHz bandwidth, respectively.
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