Free-Space Optical Communication Based on Mode Diversity Reception Using a Nonmode Selective Photonic Lantern and Equal Gain Combining

This paper experimentally investigates the perform-ance of free-space optical (FSO) communication based on mode diversity reception (MDR) using nonmode selective photonic lantern (NSPL) and equal gain combining (EGC). By employing a mode demultiplexer and combining technology in the receiver, the bit error rate (BER) and outage performance of FSO communication system can be significantly improved. However, different from diversity system with multiple receive apertures, the branches in mode diversity system are non-independent fading signals, which are influenced by not only atmospheric but also the modal crosstalk of mode demultiplexer. Therefore, we take into consideration the difference of mode demultiplexer and study four schemes for FSO mode diversity reception system: 1) NSPL with equal gain combining (NSPL-EGC), 2) NSPL with maximal ratio combining (NSPL-MRC), 3) mode selective photonic lantern with equal gain combining (MSPL-EGC), and 4) mode selective photonic lantern with equal gain combining (MSPL-MRC). Experimental results show that NSPL-EGC is the most suitable scheme for MDR with low implementation complexity, and the performance difference is less than 1 dB compared with the one using MRC at BER = 3.8×10−3 under turbulence from weak to strong.

At present, the main methods which are used to overcome the influence of atmospheric turbulence are large-aperture reception, spatial diversity reception and adaptive optics (AO) [5], [6], [7], [8], [9], [10]. Among them, large aperture reception can reduce irradiance scintillation by increasing the size of the receiving aperture, but increasing the total phase fluctuation of the received beam, which limits the performance of coherent communication systems [5]. Spatial diversity receives the signals from multiple independent fading channels to reduce the probability of deep fading in an FSO system [6], [7], [8]. In essence, it does not improve the receiving capacity of a single aperture. AO is currently the most widely used turbulence compensation technology and improves the coupling efficiency of space light to a single-mode fiber (SMF) by correcting the wavefront distortion caused by turbulence [9], [10]. However, high-speed FSO communication with bandwidth on the order of GHz presents higher requirements for the accuracy and response speed of AO system, leading to slight deficiencies in the communication system reliability under strong turbulence conditions.
In recent years, mode diversity reception (MDR) has been proposed and investigated to improve the performance of highspeed FSO communication [11], [12], [13], [14]. This scheme receives optical signal using a few-mode fiber (FMF) which supports multiple orthogonal modes. Furthermore, the distorted wavefront disturbed by atmospheric turbulence can be regarded as a superposition of a fundamental mode and high-order modes. MDR receives as many high-order mode optical signals as possible, and demultiplexes them to multi-channel fundamental mode signals, and finally combines these signals to realize atmospheric turbulence compensation [11]. This was first proposed by Ozdur, who improved the signal-to-noise ratio (SNR) of LIDAR systems by 2.8 times using a photonic lantern (PL) with 19 SMF ports [12]. An FSO communication system based on 3-mode diversity reception combined with maximum ratio combining was implemented in references [13], [14], which can reduce the transmitted optical power by 5 dB under moderate to strong turbulence. A 12 spatial mode diversity reception has been realized using multi-plane light conversion technology and comes up to the performance of the system with AO under atmospheric turbulence condition [15].
The atmospheric turbulence compensation scheme based on MDR has two key technologies: the reception of different modes and the signal combination. Mode demultiplexer is an important component of a MDR system [16], [17]. In current This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ reports, mode-selective photonic lantern (MSPL) has been used as the demultiplexer for MDR. After demultiplexing, the output power distribution of each port of PL is completely affected by turbulence. There are three main methods of combining multichannel signals: selective combining (SC), equal gain combining (EGC) and maximum ratio combining (MRC). SC selects the branch with the highest SNR as the output signal and is simplest to implement, but the performance is the worst after combination, so it is rarely used. The process of EGC only needs to directly sum all the branches, so the implementation complexity is very low. The maximum output SNR can be realized by MRC that sums all the branches with weight coefficient according to the SNR of each branch signal. The current reported mode diversity FSO communication systems mainly adopt MRC which needs to monitor the SNR of each branch in real time, and the implementation complexity of the system is relatively high. As a sub-optimal combination scheme, EGC do not require complex system design in practical applications [18]. Therefore, the research and design of MDR systems with EGC whose performance is close to MRC has high practical application value. MDR based on nonmode selective photonic lantern (NSPL) and EGC has been theoretically researched with truncated multivariate Gaussian model [19]. However, the analysis only consider irradiance scintillation and ignored the influence of phase fluctuation of wavefront to coupling efficiency of fiber. There is no experimental study on the difference of MDR with different PLs.
In response to this problem, we experimentally investigated and compared the performance of different mode diversity FSO communication systems. Firstly, the output power distribution SMF ports of a mode-selective PL and nonmode selective PL are systematically studied under different turbulence strengths. Experimental results show that, the output of a NSPL is more uniform than that of MSPL in case of weak turbulence, while they are similar under moderate to strong turbulence. It means that NSPL can reduce the probability of deep fading branches due to the high model crosstalk characteristic. Therefore, the MDR combined with EGC can achieve performance close to the one based on MRC. On this basis, the MDR of 4 Gbps QPSK optical signal is realized with different PLs and combining technology. Experimental results show that the scheme based on NSPL and EGC has a performance difference of less than 1 dB compared to the one combined with MRC under turbulence strengths D/r 0 = 3.04, 9.37 and 16.6. Therefore, it is an alternative choice for mode diversity FSO communication to balance the performance and complexity, especially for high speed space optical communication.

II. SYSTEM MODEL
In a MDR system, the free space beam is first coupled by a thin lens on plane A into a FMF in a mode diversity coherent receiver as shown in Fig. 1. The efficiency η i of the i-th mode in the FMF excited by free space beam can be expressed as [20]  where U f is the electric field distribution at the focal plane B and E i is the i-th mode distribution supported by the FMF. The total coupling efficiency of the FMF is where M is the maximum mode number supported by the FMF. M = 1 represents a SMF that only supports LP 01 mode; M = 6 repre-sents a six-mode fiber that allows the transmission of LP 01 , LP 11a/b , LP 21a/b and LP 02 . Then, the power coupled into a fiber can be represented as follows: where P f = |U f | 2 dB is the total power of focused beam upon focal plane B. It is equal to the received signal irradiance of the incident aperture because electric field distribution U A and U f are Fourier transformed to each other [21]. Then, the received optical is demultiplexed into several fundamental modes by a mode demultiplexer. Assuming that the insertion loss of all ports of the mode demultiplexer is equal, the loss coefficient is recorded as ε L ∈ [0, 1], ε L = 1 represent there is no insertion loss. The output power of PL can be represented as P P L = ε L η F P f . Defining that c i = P PL,i /P PL is the ratio of output power of i-th SMF port, P PL,i , to total output power, which satisfies the constraint condition that M i=1 c i = 1, i = 1, 2, . . . , M. Thus, the output power of i-th SMF port is The characteristics (model crosstalk) of mode demultiplexer and wavefront distortion (caused by turbulence) are the two main reasons influencing the distribution of ratio c i . It influences the output SNR of combiner using EGC algorithm. If the local oscillator (LO) power is large enough, the system noise is dominated by the shot noise of LO, and the instantaneous output SNR of MRC and EGC can be expressed as [22]: where e is the electronic charge, R and Δf are the responsivity and noise equivalent bandwidth of photodetector, respectively. In the MDR system, the SNR loss of EGC relative to MRC can be denoted as the ratio of (4) to (3) as When all c i = 1/M , the maximum value of (5) is 1, so we can obtain γ P L,EGC = γ P L,M RC . It can be seen that the performance of EGC is close to that of MRC by designing an appropriate mode demultiplexer to make the distribution of c i nearly equal.

III. EXPERIMENTAL SYSTEM
The experimental block diagram of the FSO communication system based on MDR is shown in Fig. 2. The system consists of a transmitter, atmospheric turbulence channel and receiver. At the transmitter, digital-to-analog converters (DAC) repeatedly generate two 2 Gbps pseudo-random signals with lengths of 2 11 -1, which drive the IQ modulator to generate 4 Gbps QPSK optical signals. The central wavelength of the optical carrier is 1550.14 nm, and the linewidth is less than 100 kHz. An attenuator placed after the IQ modulator is used to adjust the transmitted optical power. The polarization state of the optical signal is adjusted by a polarization controller (PC) to ensure that the polarization state of the output optical signal is parallel to the horizontal axis of the spatial light modulator (SLM). The transmitting antenna is a fiber collimator with a focal length of 25.49 mm and an output beam diameter of 4.7 mm. Then, a SLM is used to simulate the phase distortion of the transmission beam caused by atmospheric turbulence 100 times. The phase masks loaded on SLM is randomly generated according to modified Von Karman model with atmospheric coherence length r 0 = 2.14 mm, 0.69 mm and 0.39 mm. The total propagation length of the channel is 2 m.
On the receiving end, the optical beam is first coupled into a six-mode fiber with a collimator of diameter D = 6.5 mm and then demultiplexed into six single-mode beams in SMFs by the PL. In this paper, the radio D/r 0 = 3.04, 9.37 and 16.6 is used to describe turbulence strength. Each single-mode optical signal is converted into electrical signal by a coherent receiver, which is sampled by an analog-digital converter (ADC) and processed offline. The diameter of the coupling lens is 6.5 mm, and the focal length is 18.75 mm. The mode demultiplexers are NSPL and MSPL with 3.2 dB and 2.7 dB average insertion loss respectively. In offline DSP, each sampled signal is processed independently and then coherently combined. Firstly, the sampled signal is filtered by a raised cosine filter with roll-off of 0.88 and compensated for quadrature imbalance [23]. Then, clock recovery is realized by Gardner algorithm. Next, carrier-phase estimation (CPE) algorithms compensate the frequency offset and phase offset between the signal and LO lasers [24], [25]. Finally, direct sum or weighted sum is performed, which named EGC or MRC. Among them, the weighting coefficients of MRC are proportion to the estimated SNR of six branches. Hence, there are four schemes for FSO mode diversity reception system: 1) NSPL with equal gain combining (NSPL-EGC), 2) NSPL with maximal ratio combining (NSPL-MRC), 3) mode selective photonic lantern with equal gain combining (MSPL-EGC), and 4) mode selective photonic lantern with equal gain combining (MSPL-MRC). The performance of signal after coherent sum is assessed through BER analysis. In addition, to compare and evaluate the performance of MDR, FSO coherent communication system based on SMF reception is also built,as shown in Fig. 2. The performance improvement of the MDR with EGC compared to a receiver with SMF has be demonstrated in our previous report [26].

A. Output Power Characteristics of Each Port of PL
The link condition is evaluated in case of different turbulence with the transmitted power at 10 dBm. The average received power of each port of NSPL and MSPL is shown as the former and latter value in Table I calculated from Figs. 3(a) and 4(a). For D/r 0 = 3.04, the received power difference of six ports of NSPL is smaller than that of MSPL, which can be find in the relatively smaller value in LP 21a and LP 02 of MSPL. When D/r 0 = 9.37 and 16.6, there is not much difference between MSPL and NSPL. Furthermore, it can be seen in Table II that the total average   received power of MSPL is slightly higher than that of NSPL, which is caused by smaller insertion loss of MSPL. Although the received power of the two photonic lanterns decreases with the increasing turbulence, it has ∼3 dB gain compared to that of SMF. Figs. 3(b) and 4(b) show the output power and power ratio c i curves fitted by discrete data of received power of NSPL and MSPL respectively. Compared with the results of NSPL in Fig. 3(b), the measuring results of MSPL in Fig. 4(b) have relatively more dispersed distribution under turbulence of D/r 0 = 3.04. The probability of power ratio c i of one port of MSPL exceeding 0.6 is 22%, while the one of NSPL is only 1%. This is because that the LP 01 mode in FMF is more likely to has the highest coupling power, while the high-order modes is extremely small under the weak turbulence. Furthermore, NSPL has high mode crosstalk and transfers the energy from one mode to multiple SMF ports, while MSPL with low mode crosstalk basically transfers the energy of a certain mode to a corresponding SMF port. There is little difference in the output power ratio distribution between NSPL and MSPL under turbulence strength of D/r 0 = 9.37 and 16.6 because the proportion of higher-order modes in the FMF increases with increasing turbulence. Then, the probability distribution function (PDF) curves of each port of NSPL and MSPL is shown in Fig. 5(a) and (b) respectively. For D/r 0 = 3.04, the port with maximum average received power of MSPL is LP 01 , and the minimum received power port is LP 21a , and the received power difference corresponding to the peak value of PDF curves of the two ports is 13 dB. However, the difference between LP 01 and LP 21a of NSPL decreases to 7 dB. Under turbulence strength of D/r 0 = 9.37 and 16.6, the differences between maximum and minimum received power ports of NSPL are 4 dB and 5.5 dB, which are 7 dB and 7.5 dB for MSPL. Under the three kinds of turbulence strengths, the output power of each port of NSPL is more balanced than that of MSPL, which make c i closer to uniform distribution.

B. Comparison of the Performance of MRC and EGC Based on NSPL and MSPL
There are four MDR schemes: NSPL-MRC, NSPL-EGC, MSPL-MRC and MSPL-EGC. The average BER of the four schemes versus transmitted optical power are shown in Fig. 6. As a comparison, the result of coherent reception with SMF is represented by a black solid line. Compared with MSPL-EGC, NSPL-EGC scheme reduces the transmitted power by approximately 1.7 dB at BER = 3.8×10 −3 under D/r 0 = 3.04, as shown in the illustration of Fig. 6(a). This is also reduced by approximately 3.6 dB compared to SMF coherent reception. Furthermore, compared to NSPL-MRC and MSPL-MRC, the transmitted power of NSPL-EGC increases by less than 0.5 dB. As shown in Fig. 6(b), under turbulence strength of D/r 0 = 9.36, the transmitted power of proposed NSPL-EGC is the same as the one of MSPL-EGC and is reduced by 4.4 dB compared to that of SMF coherent reception. Compared to NSPL-MRC and MSPL-MRC, the transmitted power of NSPL-EGC increases by 0.4 dB and 0.7 dB, respectively. For D/r 0 = 16.6, the required transmitted power of NSPL-EGC is also basically similar to that of MSPL-EGC and is reduced by 4 dB compared to that of SMF coherent reception, as shown in Fig. 6(c). The required transmitted power of NSPL-EGC increases by approximately 0.9 dB and 1 dB compared to that of NSPL-MRC and MSPL-MRC. It can be seen from the above experimental results that under the condition of weak turbulence, the performance of NSPL-EGC is obviously better than the one of MSPL-EGC and is similar to the one of MRC; under the condition of medium and strong turbulence, there is little difference in the performance of NSPL-EGC, NSPL-MRC, MSPL-EGC and MSPL-MRC.
Interruption probability (IP) is an important index used to measure the reliability of an FSO communication system. The IP (BER>3.8 × 10 −3 ) curves of the four cases versus transmitted  Fig. 7(b) that NSPL-EGC relaxes the required transmitted power by 4.2 dB compared to SMF coherent reception and increases by less than 1.1 dB compared to MSPL-EGC, NSPL-MRC and MSPL-MRC. For D/r 0 = 16.6, shown in Fig. 7(c), the required transmitted power of NSPL-EGC increases to −-18 dBm, which is reduced by 3.2 dB compared to SMF coherent reception and increases by less than 1.5 dB compared to MSPL-EGC, NSPL-MRC and MSPL-MRC. From the measurement results of IP, it can be seen that under the condition of weak turbulence, the performance of NSPL-EGC is also better than that of MSPL-EGC; under the condition of medium and strong turbulence, there is little difference in the performance between the four schemes. Under the three turbulent conditions, the performance of the proposed NSPL-EGC can always be close to that of MRC. Therefore, the MDR based on a NSPL and EGC can approach the performance of that with MRC and has the characteristic of simple realization, so it is an ideal scheme for MDR communication systems.

V. ANALYSIS OF EXPERIMETAL RESULTS
It can be seen from (5) that output power distribution of each port of mode demultiplexer affects the performance of MDR with EGC. Defining ideal distribution state d = [d 1 , d 2 , …, d 1 ], d i = 1/M, then τ MRC,EGC = 1, the performance of EGC will equal MRC. The greater the dispersion degree of actual distribution stats c, the greater the performance loss of EGC, and vice versa. To quantitatively measure the dispersion between the output power distribution c of each port of PL and ideal distribution d, we calculate their cosine similarity, which is defined as: Because 0 < c i , d i < 1, the value of cosine similarity is 0 to 1. If c equals d, we can obtain that ρ = 1; the greater the difference between c and d, the smaller ρ is. Fig. 8 shows the average cosine similarity between NSPL and MSPL under D/r 0 = 3.04, 9.37 and 16.6. In the case of D/r 0 = 3.04, theρ of the output power distribution of NSPL is 0.81, which is 0.1 larger than that of MSPL. This means that the distribution state of NSPL is closer to d than that of MSPL, so that NSPL-EGC has a performance close to that of MRC in terms of BER and IP, while MSPL-EGC has a great performance loss compared with the one with MRC. When the turbulence strength increases to D/r 0 = 9.37 and 16.6, the valueρ of NSPL is still greater than 0.81 and fluctuates very little, while theρ of MSPL increases with the strength of turbulence and is gradually similar to that of NSPL. This means that the difference in the distribution state between NSPL and MSPL is reduced, which is why the performance of NSPL-EGC and MSPL-EGC in Fig. 4(b) and (c) and Fig. 5(b) and (c) is close to the ones of MRC.

V. CONCLUSION
In this paper, a FSO communication based on mode diversity using NSPL and EGC is proposed, and the performance of the system under different turbulence strengths is verified experimentally. First, the output power distributions of NSPL and MSPL are measured under different turbulence strengths. The experimental results show that the output power distribution of each port of NSPL always has a greaterρ than that of MSPL. Then, the performance of NSPL-EGC, NSPL-MRC, MSPL-EGC and MSPL-MRC is studied experimentally, and the results show that under weak-to-strong turbulence strength, NSPL-EGC has a BER and IP performance close to that of MRC, while MSPL-EGC has a great performance loss at weak turbulence. Furthermore, the primary advantage of EGC is the simplicity to implement, so MSPL-EGC is the best choice for MDR communication systems.