Performance of mode diversity reception of a polarization-division-multiplexed signal for free-space optical communication under atmospheric turbulence

Manabu Arikawa; Toshiharu Ito

doi:10.1364/OE.26.028263

1. Introduction

Free-space optical communication (FSO) is considered as an attractive candidate to provide high-speed wireless links including satellite-to-ground ones because it has broader available bandwidth than regulated microwaves [1,2]. Using a short optical wavelength potentially enables reduction of the size, weight, and power consumption of communication terminals as well as the risk of interference between multiple systems. There has been reported several demonstrations of optical downlinks from satellites to the ground [3–6]. A 5.625 Gb/s optical downlink from a low-Earth-orbital (LEO) satellite has been demonstrated at a high altitude ground terminal [7], and 10 Mb/s has been demonstrated at a low altitude where the effect of the atmospheric turbulence is more severe [8].

For high-speed optical communication with high sensitivity, detection of an optical beam with a small area, or fiber coupling, is generally required. Once it is achieved, we can count on using mature technologies and devices developed for fiber optical communication systems around 1.5 μm [9], which is a desirable feature for developing huge-scale systems such as downlinks from LEO satellite constellations. Single mode fiber (SMF) coupling of a received optical beam is a challenging task because the atmospheric turbulence through the optical beam propagation limits the coherence length of the wavefront of the beam [10]. Because of this limitation, a simple increase of the aperture size to collect an optical beam as much as possible does not work unless it is used together with the sophisticated wavefront compensation by adaptive optics. To mitigate the effect of the wavefront distortion, mode diversity reception with multiple propagation modes of a few-mode-fiber (FMF) has recently been proposed and demonstrated [11–13]. FMFs are also being developed for mode-division multiplexed fiber transmission systems [14,15]. A received optical beam impaired by atmospheric turbulence contains not only the fundamental mode but also components at higher order modes. In mode diversity reception, multiple signals coupled to the modes of a FMF are received and combining these signals provides diversity gain since the turbulence affects the modes differently, as well as robustness against tilt errors of coupling optics [16]. In satellite-to-ground FSO experiments so far, a single polarization signal has been conventionally used. One reason for this is to isolate the transmitted and received signals by assigning orthogonal polarizations to them. Since this isolation can be easily achieved by assigning slightly different frequencies if coherent detection is used, the use of a single polarization is no more necessary in that case. Moreover, using polarization division multiplexing in FSO enables full advantage to be taken of commercial off-the-shelf devices for fiber optical communications including conventional erbium-doped fiber amplifiers (EDFAs) and polarization diversity coherent receivers with frequency selectivity [17], as well as a high data rate. There are fewer hurdles to use polarization-division-multiplexed (PDM) transmitters than ones for a single polarization, and it has been demonstrated that the polarization state is preserved through the atmospheric propagation [18].

However, mode diversity reception of a PDM signal includes a problem that should be properly investigated. In mode diversity reception, an optical beam incident within a single aperture is coupled to a FMF and signals coupled to the modes of the FMF are independently received with conventional SMF-based receivers. The received signals are combined in the digital domain to mitigate the effect of turbulence. Mode decomposition is performed by a mode demultiplexer. Available mode demultiplexers with low insertion loss are typically based on linearly polarized (LP) modes [19, 20]. In optical propagation through a FMF, coupling between different LP modes in orthogonal polarizations occurs because LP modes are not the exact eigenmodes of a fiber [21–24]. When a single polarization signal is received, it causes the polarization state of each output of the mode demultiplexer to change in accordance with the distribution of the mode excitation at the input FMF facet, in other words, the wavefront distortion due to the atmospheric turbulence. This does not lead to a severe problem if ideal polarization controllers are used in the outputs of the mode demultiplexer. However, when a PDM signal is received, coupling between different LP modes in orthogonal polarizations causes power imbalance and loss of the orthogonality of multiplexed signals in X and Y polarizations at the transmitter within each individual LP mode at the receiver, even though the total power over modes is preserved. Therefore, the architecture of mode diversity combining affects the receiver performance. For example, selection combining (SC) can be used after signals are received and decoded individually in LP modes with a conventional digital signal processing (DSP) of polarization demultiplexing for a PDM signal, whereas power imbalance and loss of the orthogonality directly degrade the performance in this architecture.

In this study, we investigated the performance of mode diversity reception of a PDM signal with FMF coupling for high-speed free-space optical communications under atmospheric turbulence, focusing on coupling between different LP modes in orthogonal polarizations through FMF propagation. Assuming a LEO-to-ground optical downlink, we evaluated the power fluctuation coupled to each LP mode of a FMF and its dependence on the polarization state in a numerical simulation. Optical beam propagation through the atmosphere was simulated with random phase screens (RPSs), and FMF coupling and propagation were modeled with exact eigenmodes of the FMF. On the basis of the analysis of multiple-input multiple-output (MIMO) systems with minimum mean square error (MMSE) detection, we compared the performances of SC after individually decoding in LP modes and full receiver-side MIMO (Rx-MIMO) combining. We found that full Rx-MIMO combining outperformed SC by 5 dB in this case. Moreover, we experimentally evaluated this penalty and finally demonstrated three-mode diversity reception of a 128 Gb/s PDM-quadrature phase-shift keying (QPSK) with a diffuser plate as a turbulence emulator. Digital signal processing was performed for the acquired successive data bursts of 6.4 ms which were long enough to contain typical features of fading. We confirmed that full Rx-MIMO with adaptive filters could perform polarization demultiplexing and diversity combining simultaneously under severe fading of input signals and that it outperformed SC.

2. Simulation of mode diversity reception of a PDM signal

First, we evaluated the fluctuation of the coupled power to each LP mode of a FMF after atmospheric propagation and FMF propagation in a numerical simulation to estimate the performance of mode diversity reception of a PDM signal. A schematic diagram of the simulation model is shown in Fig. 1. An optical downlink from a LEO satellite to the ground is assumed here.

Fig. 1 Schematic diagram of simulation model for LEO-to-ground optical downlink with FMF coupling. RPSs: random phase screens, FMF: few-mode fiber, SMF: single mode fiber.

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2.1. Atmospheric propagation

The atmospheric turbulence was simulated with RPSs. 50 layers of RPSs, which were spaced densely near the ground and sparsely at high altitude reflecting the strength of the turbulence, were used to simulate the atmospheric turbulence below 50 km. The RPSs were one realization of the atmospheric turbulence, and their spatial coherence reflected the structure parameter $C_{n}^{2}$ [25,26]. Assuming the turbulence condition during daytime, the Hufnagel-Valley model was used for the vertical profile of $C_{n}^{2} (h)$ with a nominal value of $C_{n}^{2} (0)$ of 1.7 × 10⁻¹³ m^−2/3 and rms windspeed of 21 m/s. The validity of our simulation was checked with comparing the obtained scintillation index to that of the theoretical one [25]. Temporal channel variation was simulated by moving these frozen RPSs in random directions. The moving speed was adjusted so that the simulated power spectrum distribution of the aperture-incident optical power was consistent with the experimental results in LEO-to-ground optical propagation [27], while taking into account the dependence of angular velocity of the LEO satellite on elevation angles. The altitude of the LEO satellite was 400 km. The aperture diameter of the transmitter was 10 cm where the transmitted beam had an infinite radius of curvature. The ground terminal was located at sea level and the elevation angle of the satellite was 20°. In these conditions, the Fried parameter r₀ becomes about 3 cm.

2.2. FMF coupling and propagation

The optical beam incident to the receiver aperture with the diameter of 20 cm was collected and coupled to a three-mode FMF after the tip-tilt caused by the atmospheric turbulence was ideally compensated with the Zernike expansion of the beam. An optical signal coupled to the FMF propagated through it, and then the mode demultiplexer decomposed the signal to LP modes: LP₀₁, LP_11e, and LP_11o. The mode demulitiplexer was assumed to have no excess loss.

The three-mode FMF has six eigenmodes of HE_11e, HE_11o, TM₀₁, HE_21e, HE_21o, and TE₀₁. Their traverse components of the electric fields are related to those of three LP modes in two polarizations as [24],

\begin{array}{l} (E_{{HE}_{11 e}}, E_{{HE}_{11 o}}, E_{{TM}_{01}}, E_{{HE}_{21 e}}, E_{{HE}_{21 o}}, E_{{TE}_{01}}) \\ = (E_{{LP}_{01 x}}, E_{{LP}_{01 y}}, E_{{LP}_{11 ex}}, E_{{LP}_{11 oy}}, E_{{LP}_{11 ox}}, E_{{LP}_{11 ey}}) M, \\ M = (\begin{matrix} I_{2} & 0 \\ 0 & M_{1} \end{matrix}), \\ M_{1} = \frac{1}{\sqrt{2}} (\begin{matrix} 1 & - 1 & 0 & 0 \\ 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & - 1 \\ 0 & 0 & 1 & 1 \end{matrix}), \end{array}

where I₂ is the identity matrix of size 2. Although the HE mode groups are degenerate in the fiber of the ideal circular core, these eigenmodes propagate at different propagation constants β. After propagation over the length z, the electric fields are

\begin{array}{l} (E_{{HE}_{11 e}}, E_{{HE}_{11 o}}, E_{{TM}_{01}}, E_{{HE}_{21 e}}, E_{{HE}_{21 o}}, E_{{TE}_{01}}) \\ = (E_{{HE}_{11 e}}, E_{{HE}_{11 o}}, E_{{TM}_{01}}, E_{{HE}_{21 e}}, E_{{HE}_{21 o}}, E_{{TE}_{01}}) P, \\ P = (\begin{matrix} P_{0} & 0 \\ 0 & P_{1} \end{matrix}), P_{0} = (\begin{matrix} e^{i \partial β_{0} z} & 0 \\ 0 & e^{i \partial β_{0} z} \end{matrix}), \\ P_{1} = (\begin{matrix} e^{i \partial β_{M} z} & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & e^{i \partial β_{E} z} \end{matrix}) . \end{array}

where ∂β₀ = β_HE₁₁ − β_HE₂₁, ∂β_M = β_TM₀₁ − β_HE₂₁, and ∂β_E = β_TE₀₁ − β_HE₂₁. According to the perturbation results for a step-index fiber [22], the differences in the propagation constants are described in terms of a small refractive index difference

Δ = (n_{1}^{2} - n_{2}^{2}) / (2 n_{1}^{2})

as,

\begin{array}{l} \partial β_{E} = 2 n_{2} k_{0} Δ^{2} {(\frac{U_{0} W_{0}}{V^{2}})}^{2} κ_{0}^{+} (W_{0}), \\ \partial β_{M} = 2 n_{2} k_{0} Δ^{2} {(\frac{U_{0} W_{0}}{V^{2}})}^{2} (κ_{0}^{+} (W_{0}) - 2 κ_{2}^{-} (W_{0})) . \end{array}

The n₁ and n₂ are the refractive indices of the core and the cladding. The k₀ is the wavenumber of light in a vacuum. The V is the normalized frequency. The U₀ and W₀ are the solution pair of

U = k_{0} a \sqrt{n_{1}^{2} - β^{2} / k_{0}^{2}}

and

W = k_{0} a \sqrt{β^{2} / k_{0}^{2} - n_{2}^{2}}

for the dispersion equation with Δ → 0. The a is the core radius, and

κ_{ν}^{\pm} = K_{ν \pm 1} / (W K_{ν})

, where K is the modified Bessel function of the second kind. In the simulation, we set n₂, V, Δ, and the wavelength to 1.5, 3, 0.002, and 1.55 μm, respectively. By using these equations, the electric fields of LP modes at the output facet of the FMF after propagation are related to those at the input facet as,

\begin{array}{l} (E_{{LP}_{01 x}}, E_{{LP}_{01 y}}, E_{{LP}_{11 ex}}, E_{{LP}_{11 oy}}, E_{{LP}_{11 ox}}, E_{{LP}_{11 ey}}) \\ = (E_{{LP}_{01 x}}, E_{{LP}_{01 y}}, E_{{LP}_{11 ex}}, E_{{LP}_{11 oy}}, E_{{LP}_{11 ox}}, E_{{LP}_{11 ey}}) M P M^{- 1}, \\ M P M^{- 1} = (\begin{matrix} P_{0} & 0 \\ 0 & {\tilde{P}}_{1} \end{matrix}), \\ {\tilde{P}}_{1} = \frac{1}{2} (\begin{matrix} e^{i \partial β_{M} z} + 1 & e^{i \partial β_{M} z} - 1 & 0 & 0 \\ e^{i \partial β_{M} z} - 1 & e^{i \partial β_{M} z} + 1 & 0 & 0 \\ 0 & 0 & e^{i \partial β_{E} z} + 1 & - e^{i \partial β_{E} z} + 1 \\ 0 & 0 & - e^{i \partial β_{E} z} + 1 & e^{i \partial β_{E} z} + 1 \end{matrix}) . \end{array}

As seen in this form, coupling between different LP modes in orthogonal polarizations occurs, for example, between LP_11ex and LP_11oy.

In collecting a received beam within the aperture to the fiber, we simply assumed that the beam is focused to the fiber facet with having only traverse components of the electric field E_r = U_r(x, y)(E_x(t)e_x + E_y(t)e_y), and the U_r corresponds to the distorted beam spatial profile obtained after simulation of atmospheric propagation with roughly scaling to match the size of the fiber mode profile. If the satellite transmits the light with a unit power in a certain polarization e_X = cos ψe_x + e^iδ sin ψe_y and the polarization state is preserved through the atmospheric propagation, (E_x, E_y)^t corresponds to (cos ψ, e^iδ sin ψ)^t. In fiber coupling, the excitation of LP modes at the input facet of the FMF is calculated by the overlap integrals as,

ρ = (\begin{matrix} \int E_{r} \cdot E_{{LP}_{01 x}}^{*} d S \\ \int E_{r} \cdot E_{{LP}_{01 y}}^{*} d S \\ \int E_{r} \cdot E_{{LP}_{11 ex}}^{*} d S \\ \int E_{r} \cdot E_{{LP}_{11 oy}}^{*} d S \\ \int E_{r} \cdot E_{{LP}_{11 ox}}^{*} d S \\ \int E_{r} \cdot E_{{LP}_{11 ey}}^{*} d S \end{matrix}) = (\begin{matrix} E_{x} \int U_{r} U_{{LP}_{01}}^{*} d S \\ E_{y} \int U_{r} U_{{LP}_{01}}^{*} d S \\ E_{x} \int U_{r} U_{{LP}_{11 e}}^{*} d S \\ E_{y} \int U_{r} U_{{LP}_{11 o}}^{*} d S \\ E_{x} \int U_{r} U_{{LP}_{11 o}}^{*} d S \\ E_{y} \int U_{r} U_{{LP}_{11 e}}^{*} d S \end{matrix}) .

After FMF propagation, the excitation becomes

\tilde{ρ} = M P M^{- 1} ρ .

According to this equation, we can calculate the coupling power to the FMF after decomposition to LP modes with the mode demultiplexer; for example the coupled power to LP_11e corresponds to |ρ̃₃|² + |ρ̃₆|².

We first simulated the influence of the fiber length on coupling efficiency to LP modes with certain fixed RPSs of the atmospheric turbulence. Corresponding beam intensity profile within the received aperture after atmospheric propagation is shown in the inset of Fig. 1. Figure 2 shows the simulation results of the coupling efficiency to LP modes after FMF propagation while changing the input polarization state, i.e., ψ and δ. This coupling efficiency was defined as the loss from the averaged aperture incident power in the case of the RPSs moved, which is described later, to the power of the excitation of each LP mode at the output of the mode demultiplexer. In Fig. 2, colored regions represent the range of variation with the change in the polarization state at a certain fiber length, and the solid lines correspond to the average. Coupling efficiency to LP₀₁ did not change with the input polarization state. In contrast, coupling efficiency to LP₁₁ started to change at the fiber length of about 10 cm. This corresponds to the beat length of LP₁₁ modes. The difference between the maximum and minimum coupling efficiency caused by the polarization change exceeded 20 dB.

Fig. 2 Dependence of coupling efficiency to LP modes after FMF propagation with fixed random phase patterns of the atmospheric turbulence on the fiber length: (a) LP₀₁, (b) LP_11e, and (c) LP_11o.

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Then we simulated the temporal fluctuation of coupling efficiency to LP modes. Coupling efficiency was calculated at each position of the RPSs while they were moved. The FMF length was set to 1 m. When the RPSs were moved, the loss from the transmitted power to the aperture incident power was −45 dB on average, which included the loss due to the limited receiver aperture size in collecting the optical beam that spread through free-space propagation from the satellite. The dynamic range of the fluctuation of the aperture incident power at 1% of the probability density was 9 dB. Coupling efficiency to LP modes was defined by using this averaged aperture incident power as a reference level again. Figure 3 shows an example of the simulation results of the temporal fluctuation of coupling efficiency to LP modes after FMF propagation. The histograms of the temporal fluctuation of coupling efficiency are shown in Fig. 4. Coupling efficiency to LP₀₁ was −12 dB on average over time. The histogram of the fluctuation was well fitted by the Gamma-Gamma distribution, and the dynamic range of the fluctuation at 1% of the probability density was 20 dB. The fluctuation had frequency components up to about 1 kHz. The fluctuation of coupling efficiency to LP_11e and LP_11o were similar to that of coupling efficiency to LP₀₁, except that they changed with the input polarization state. Averaged coupling efficiencies of LP_11e and LP_11o over input polarization state and time were −14 dB, and the dynamic ranges of the fluctuation were 21 and 20 dB. The range of variation between the maximum and minimum coupling efficiency caused by the polarization change differed over time, in other words, over the condition of the wavefront distortion. The difference reached 19 dB at the level of the probability density of 1%.

Fig. 3 Temporal fluctuation of coupling efficiency to LP modes after FMF propagation: (a) LP₀₁, (b) LP_11e, and (c) LP_11o. Colored regions represent the range of fluctuation with the change of the polarization state, and the solid lines correspond to the average.

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Fig. 4 Probability density function (PDF) of temporal fluctuation of coupling efficiency to LP modes after FMF propagation: (a) LP₀₁, (b) LP_11e, and (c) LP_11o. Dashed lines are regression curves by the Gamma-Gamma distribution.

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2.3. Performance of mode diversity reception

Next, we estimated the performance with mode diversity combining with coherent detection. Figure 5 shows possible architectures to perform mode diversity combining. Figure 5(a) shows SC after signals are demodulated and decoded individually. In this architecture, polarization demultiplexing is conducted in each LP mode. One of the decoded outputs of receivers with the best performance is selected in every certain time frame. This enables conventional receivers for current fiber optical communication systems to be used as much as possible, whereas the polarization problem can degrade the performance. Figure 5(b) shows full Rx-MIMO, in which polarization demultiplexing and diversity combing are performed simultaneously.

Fig. 5 Two types of architecture for mode diversity combining: (a) selection combining after signals demodulated and decoded individually, and (b) full Rx-MIMO.

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We estimate the performances of these two architectures for mode diversity combining. The MIMO system model for mode diversity reception of a PDM signal can be described by using Eq. (6) with the input polarization state of e_X = cos ψe_x + e^iδ sin ψe_y and its orthogonal one e_Y = − sin ψe_x + e^iδ cos ψe_y. The channel matrix is described as

H = ({\tilde{ρ} |}_{{(E_{x}, E_{y})}^{t} = {(cos ψ, e^{i δ} sin ψ)}^{t}}, {\tilde{ρ} |}_{{(E_{x}, E_{y})}^{t} = {(- sin ψ, e^{i δ} cos ψ)}^{t}}) .

The signal to interference-plus-noise ratio (SINR) γ of the MIMO system with MMSE detection is described in terms of the channel matrix as

γ_{j} = g_{j}^{†} h_{j} / (1 - g_{j}^{†} h_{j})

, where j = 1, 2 and g_j = (HH^† + 2IP_N/P)⁻¹h_j [28]. The h_j is the j-th column of H, and P and P_N are the transmitted signal power and the noise power, respectively. If optical amplification is used before coherent detection and the system is amplifier-noise limited, the noise power should be P_N = ħωn_spB, where n_sp is the spontaneous emission factor, and B corresponds to the symbol rate. In the case of the full Rx-MIMO approach, the SINR can be estimated by using 6 × 2 H directly. In the case of the SC approach, the channel matrix is decomposed to three 2 × 2 matrixes of

H_{{LP}_{01}} = (\begin{matrix} h_{11} & h_{12} \\ h_{21} & h_{22} \end{matrix}), H_{{LP}_{11 e}} = (\begin{matrix} h_{31} & h_{32} \\ h_{61} & h_{62} \end{matrix}), H_{{LP}_{11 o}} = (\begin{matrix} h_{51} & h_{52} \\ h_{41} & h_{42} \end{matrix}) .

SC selects the best performance of the three in every time frame.

We assume here a 128 Gb/s PDM-QPSK signal is transmitted. The bit error rate (BER) of a QPSK signal with the SNR of γ is approximately $erfc (\sqrt{η γ / 2}) / 2$ , where the η is the factor including impairment in a receiver that was set to 4.4 dB in the simulation reflecting the experimental results explained later. Now we can simulate the BER after mode diversity reception applied in the optical downlink from the satellite. We evaluated the receiver performance as the estimated forward error correction (FEC) frame error rate, which corresponds to the ratio where the BER exceeds the acceptable threshold for FEC. The FEC threshold BER was set to 1.8 × 10⁻², which corresponds to Q of 6.4 dB [29]. Figure 6 shows the simulation results of the estimated FEC frame error rate as the transmitted power changed with different receiver architecture. In Fig. 6, the performance of SMF coupling, where the receiver aperture was its optimal of 10 cm [13], is also plotted for reference. In receiving each LP mode only, the performance of receiving LP_11e and LP_11o was worse than that of receiving LP₀₁, though the averaged coupling efficiencies to them were similar as shown in Fig. 3. This was caused by power imbalance and loss of the orthogonality of multiplexed signals in each LP mode due to mode coupling. Compared with SMF coupling, the performance of LP₀₁ only was poor because the aperture diameter was larger in FMF coupling and the wavefront distortion can have relatively small structure within the aperture in this case [13]. In the case of SC, the required transmitted power was improved by 8 dB compared with LP₀₁ only at the estimated FEC frame error rate of 1%, while the performance was similar to that of SMF coupling. In the case of full Rx-MIMO, we can mitigate the required transmitted power by 5 dB compared with SC, and by 6 dB compared with SMF coupling. Therefore, full Rx-MIMO architecture should be used to obtain the maximum performance for mode diversity combining of a PDM signal. According to these simulation results, if we want to eliminate this polarization problem to use SC, FMF propagation should be less than a few cm; otherwise, a FMF with sufficiently low modal crosstalk like an elliptical core FMF [30] should be used.

Fig. 6 Simulation results of estimated FEC frame error rate, which is the ratio where BER exceed the FEC threshold against the transmitted power of a 128 Gb/s PDM-QPSK signal.

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3. Experimental demonstration with a turbulence emulator

We conducted an experiment of three mode diversity reception of a 128 Gb/s PDM-QPSK with a diffuser plate as a turbulence emulator. A schematic diagram of the experimental setup is shown in Fig. 7. The transmitted signal was a PDM-QPSK signal of the line rate of 128 Gb/s. It was generated by a fiber-based optical modulator with a laser source at the wavelength of 1550.9 nm having a linewidth of about 100 kHz and data of differentially coded pseudo random binary sequence of 2¹⁵ − 1. The modulated optical signal was emitted to free space after polarization scrambling at the rate of 10 × 2π rad/s, which emulated the polarization change in the transmitter side. A diffuser plate (Luminit: light shaping diffuser), which possessed many microscopic random lens arrays on its surface, was inserted on the beam path and acted as the turbulence emulator. The beam had its waist at the position of the diffuser plate with the diameter of about 0.2 mm. To emulate the temporal variation of the atmospheric turbulence, the diffuser plate was rotated so that the fluctuation of coupling efficiency had the speed of a few kHz. An example of the intensity profile of the beam after passing through the diffuser plate is shown in the inset of Fig. 7. The distorted beam was coupled to a FMF with a lens of the diameter of 8 mm and decomposed by the mode demultiplexer (CAILabs: PROTEUS). The length of the FMF pigtail of the mode demultiplexer was about 3 m. The mode demultiplxer and the FMF supported six LP modes (LP₀₁, LP_11e, LP_11o, LP₀₂, LP_21e, LP_21o) and relatively low modal crosstalk between different LP mode groups below about −20 dB. The average insertion loss was 2.8 dB. In this experiment, we used only the first three modes (LP₀₁, LP_11e, LP_11o). Each output of the mode demultiplexer was amplified with a conventional EDFA and then received with a polarization diversity coherent receiver. A laser source having the linewidth of about 100 kHz was used as a local oscillator (LO) commonly for three coherent receivers. The outputs of the coherent receivers were sampled with a high-speed 12-channel digital oscilloscope (Teledyne LeCroy: LabMaster) at the sampling rate of 80 GS/s with the vertical resolution of 8 bits. Successive data bursts of 6.4 ms, which corresponds to 512 MS, were acquired to perform DSP offline.

Fig. 7 Experimental setup for three-mode diversity reception of 128 Gb/s PDM-QPSK signal with turbulence emulator. EDFA: erbium-doped fiber amplifier, LO: local oscillator, OSC: oscilloscope, DSP: digital signal processing.

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Offline DSP for mode diversity combining with full Rx-MIMO is shown in Fig. 8. The received signals were first normalized and resampled to the two-fold oversampling. Then, the relative delays among these signals were compensated. After that, full Rx-MIMO for polarization demultiplexing and diversity combining was performed with the 2 × 6 adaptive finite impulse response (FIR) filters, each of which has T/2-spaced 21 taps. The filter coefficients were controlled by the decision-directed least mean square (DDLMS) algorithm [31] using the combined outputs after carrier phase compensation with a decision-directed phase locked loop (DDPLL). The coefficients of the FIR filters were updated every eight symbol time slots while the compensation phase of the DDPLL was calculated every symbol. Since the power of the input signals fluctuates with wide dynamic range and power imbalance of multiplexed signals occurs in the case of mode diversity reception in contrast to fiber transmission, the adaptive filters are subject to the problem that they output two degenerate signals, i.e. one of the transmitted two polarization signals [32]. To ease this problem, we used pre-convergence of the filters by the data-aided LMS algorithm. If we apply SC, polarization demultiplexing and equalization are performed with three 2 × 2 FIR filters. After decoding, BER was calculated for each 3 μs (100k symbols). The evaluation results of back-to-back sensitivity without transmitting the signal to free space are shown in Fig. 9. When the signal was received with each polarization diversity coherent receiver, the required power to obtain the FEC threshold was −40.1 dBm, which corresponded to 6.0 photons per bit. Degradation from the theoretical performance was 4.4 dB, which might include quantization error in sampling of faint signals. After combining of outputs of three receivers at the same received optical power with full Rx-MIMO, the sensitivity became −45.0 dBm.

Fig. 8 Offline DSP for mode diversity combining with full Rx-MIMO. DDLMS: decision-directed least mean square, CPE: carrier phase estimation.

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Fig. 9 Evaluation results for back-to-back sensitivity.

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We first evaluated the link condition where the turbulence was emulated by the diffuser plate with continuous wave light source. Figure 10 shows the coupling efficiency to the LP mode outputs of the mode demultiplexer after passing the diffuser plate without rotating while changing the polarization state by the polarization scrambler. As expected from the simulation results, coupling efficiency to LP₁₁ modes changed with polarization scrambling. That to the LP₀₁ mode also slightly changed in the experiment, probably due to random modal crosstalk in the FMF as well as the mode dumultiplexer. Figure 11(a) shows the temporal fluctuation of coupling efficiency while rotating the diffuser plate. Figure 11(b) shows its histogram. Coupling efficiency to LP₀₁, LP_11e, and LP_11o were −12.5, −16.4, and −16.6 dB on average, respectively. The dynamic ranges at the level of the probability density of 1% were 18, 15, and 15 dB. Figure 12 shows the cumulative distribution function (CDF) of these temporal fluctuations of coupling efficiency. For reference, the evaluation result is also plotted for coupling efficiency to a SMF, instead of using the FMF and the mode demultiplexer. The summation of coupling efficiency to three modes, which determined the performance in the case of full Rx-MIMO, improved the received power by 9.6 dB at the CDF of 1% compared with SMF coupling. In this experimental setup, the dynamic range of the fluctuation of coupling efficiency in the case of SMF coupling was larger than that of LP₀₁ of the FMF, probably because the mode field diameter of LP₀₁ of the FMF, 18.2 μm, was slightly larger than that of the conventional SMF.

Fig. 10 Variation of coupling efficiency to outputs of mode demultiplexer with polarization scrambling.

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Fig. 11 (a) Temporal fluctuation of coupling efficiency to outputs of mode demultiplexer with rotating the diffuser plate, and (b) its probability density function. Dashed lines are regression curves by the Gamma-Gamma distribution.

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Fig. 12 Cumulated distribution function of temporal fluctuation of coupling efficiency.

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We finally evaluated the performance of three-mode diversity reception of a 128 Gb/s PDM-QPSK signal. Evaluation results for the BER fluctuation while rotating the diffuser plate in the case of receiving each LP mode only and after full Rx-MIMO are shown in Fig. 13(a). The transmitted power was −20 dBm. After the combining of signals received in three modes with full Rx-MIMO, the BER was much improved over that in the case of receiving each LP mode individually. Figure 13(b) shows constellations of the received signals at 5 ms. In the case of receiving each LP mode only, the signal qualities of X and Y polarizations were obviously different due to the power imbalance and loss of the orthogonality of multiplexed signals caused by modal coupling. In contrast, those after full Rx-MIMO were almost the same.

Fig. 13 Evaluation results for (a) BER fluctuation with rotating diffuser plate and (b) constellations at 5 ms. Transmitted power was −20 dBm.

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Figure 14 shows the evaluation results for the estimated FEC frame error rate, which is the ratio where the BER exceeds the threshold for FEC when the transmitted power was changed, together with the estimated ones from the results for the coupling efficiency shown in Fig. 12. In the case of receiving each LP mode individually, there were differences between the experimental results for the estimated FEC frame error rate and the results estimated from the evaluation results for coupling efficiency, due to the power imbalance of two polarizations. In the case of receiving with SMF coupling, the experimental results were close to the estimated value, as well as in the case of full Rx-MIMO. This indicates that full Rx-MIMO could appropriately perform polarization demultiplexing and diversity combining simultaneously under severe fading of input signals. At the estimated FEC frame error rate of 1%, full Rx-MIMO could mitigate the required transmitted power by 4 dB compared with SC in these experimental conditions with the turbulence emulator.

Fig. 14 Experimental results for estimated FEC frame error rate against transmitted power and its estimated value from results for coupling efficiency shown in Fig. 12.

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4. Conclusion

We investigated the performance of mode diversity reception of a PDM signal with FMF coupling for high-speed free-space optical communications under atmospheric turbulence. Assuming a LEO-to-ground optical downlink, we simulated coupling efficiency to each LP mode of a FMF while considering the eigenmodes of FMF after atmospheric propagation and FMF propagation. On the basis of the analysis of MIMO systems with MMSE detection, we found that full Rx-MIMO combining in three-mode diversity reception outperformed SC by 5 dB because of power imbalance and loss of the orthogonality of multiplexed signals within each LP mode, and that it mitigated the required transmitted power by 6 dB compared with reception with SMF coupling. If we want to eliminate this polarization problem to use SC, the FMF propagation should be less than a few cm or a FMF with sufficiently low modal crosstalk should be used. We also experimentally verified this penalty and demonstrated three-mode diversity reception of a 128 Gb/s PDM-QPSK with a diffuser plate as a turbulence emulator. We confirmed that full Rx-MIMO with adaptive filters could perform polarization demultiplexing and diversity combining simultaneously under severe fading of input signals and that it outperformed SC by 4 dB in this case.

Funding

National Institute of Information and Communications Technology (NICT), Japan (1860101).

References

1. V. W. S. Chan, “Free-space optical communications,” J. Light. Technol. 24(12), 4750–4762 (2006). [CrossRef]

2. M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” IEEE Communication Survey & Tutorials 16(4), 2231–2258 (2014). [CrossRef]

3. M. Reyes, S. Chueca, A. Alonso, T. Viera, and Z. Sodnik, “Analysis of the preliminary optical links between ARTEMIS and the optical ground station,” Proc. SPIE 4821, 33–43 (2002). [CrossRef]

4. T. Jono, Y. Takayama, K. Shiratama, I. Mase, B. Demelenne, Z. Sodnik, A. Bird, M. Toyoshima, H. Kunimori, D. Giggenbach, N. Perlot, M. Knapek, and K. Arai, “Overview of the inter-orbit and orbit-to-ground laser communication demonstration by OICETS,” Proc. SPIE 6457, 645702 (2007). [CrossRef]

5. D. M. Boroson, B. S. Robinson, D. V. Murphy, D. A. Burianek, F. Khatri, J. M. Kovalik, Z. Sodnik, and D. M. Cornwell, “Overview and results of the lunar laser communication demonstration,” Proc. SPIE 8971, 89710S (2014). [CrossRef]

6. A. Biswas, B. V. Oaida, K. S. Andrews, J. M. Kovalik, M. J. Abrahamson, and W. Wright, “Optical payload for lasercomm science (OPALS) link validation during operation from the ISS,” Proc. SPIE 9354, 93540F (2015). [CrossRef]

7. R. A. Fields, D. A. Kozlowski, H. T. Yura, R. L. Wong, J. M. Wicker, C. T. Lunde, M. Gregory, B. K. Wandermoth, F. F. Heine, and J. J. Luna, “5.625 Gbps bidirectional laser communications measurements between the NFIRE satellite and an optical ground station,” Proc. SPIE 8184, 81840D (2011). [CrossRef]

8. H. Takenaka, Y. Koyama, D. Kolev, M. Akioka, N. Iwakiri, H. Kunimori, A. Carrasco-Casado, Y. Munemasa, E. Okamoto, and M. Toyoshima, “In-orbit verification of small optical transponder (SOTA) –Evaluation of satellite-to-ground laser communication links–,” Proc. SPIE 9739, 973903 (2016). [CrossRef]

9. R. Zhang, J. Wang, G. Zhao, and J. Lv, “Fiber-based free-space optical coherent receiver with vibration compensation mechanism,” Opt. Express 21(15), 18435–18441 (2013).

10. Y. Dikmelik and F. M. Davidson, “Fiber-coupling efficiency for free-space optical communication through atmospheric turbulence,” Appl. Opt. 44(23), 4946–4952 (2005). [CrossRef] [PubMed]

11. M. Arikawa, T. Ishikawa, K. Hosokawa, S. Takahashi, Y. Ono, and T. Ito, “Demonstration of turbulence-tolerant free-space optical communication receiver using few-mode-fiber coupling and digital combining,” in Proceedings of IEEE Photonics Society Summer Topical Meeting Series (2016), paper TuC3.4.

12. D. J. Geisler, T. M. Yarnall, G. Lund, C. M. Schieler, M. L. Stevens, N. K. Fontaine, B. S. Robinson, and S. A. Hamilton, “Experimental comparison of 3-mode and single-mode coupling over a 1.6-km free-space link,” Proc. SPIE 10524, 105240H (2018).

13. M. Arikawa, Y. Ono, and T. Ito, “Mode diversity coherent receiver with few-mode fiber-coupling for high-speed free-space optical communication under atmospheric turbulence,” Proc. SPIE 10524, 1052412 (2018).

14. S. Randel, R. Ryf, A. Sierra, P. J. Winzer, A. H. Gnauck, C. A. Bolle, R.-J. Essiambre, D. W. Peckham, A. McCurdy, and R. Lingle Jr., “6×56-Gb/s mode-division multiplexed transmission over 33-km few-mode fiber enabled by 6×6 MIMO equalization,” Opt. Express 19(17), 16697–16707 (2011). [CrossRef] [PubMed]

15. P. Sillard, M. Bigot-Astruc, and D. Molin, “Few-mode fibers for mode-division-multiplexed systems,” J. Light. Technol. 32(16), 2824–2829 (2014). [CrossRef]

16. T. M. Yarnall, D. J. Geisler, C. M. Schieler, and R. Yip, “Analysis of free-space coupling to photonic lanterns in the presence of tilt errors,” in Proceedings of IEEE Photonics Conference (2017), paper ThH1.5.

17. R. Maher, D. S. Millar, S. J. Savory, and B. C. Thomsen, “Widely tunable burst mode digital coherent receiver with fast reconfiguration time for 112 Gb/s DP-QPSK WDM networks,” J. Light. Technol. 30(24), 3924–3930 (2012). [CrossRef]

18. M. Toyoshima, H. Takenaka, Y. Shoji, Y. Takayama, Y. Koyama, and H. Kunimori, “Polarization measurements through space-to-ground atmospheric propagation paths by using a highly polarized laser source in space,” Opt. Express 17(25), 22333–22340 (2009). [CrossRef]

19. J.-F. Morizur, P. Jian, B. Denolle, O. Pinel, N. Barré, and G. Labroille, “Efficient and mode-selective spatial multiplexer based on multi-plane light conversion,” in Optical Fiber Communication Conference (2015), paper W1A.4. [CrossRef]

20. S. G. Leon-Saval, A. Argyros, and J. Bland-Hawthorn., “Photonic lanterns: a study of light propagation in multimode to single-mode converters,” Opt. Express 18(8), 8430–8439 (2010). [CrossRef] [PubMed]

21. D. Gloge, “Weakly guiding fibers,” Appl. Opt. 10(10), 2252–2258 (1971). [CrossRef] [PubMed]

22. H. Kogelnik and P. J. Winzer, “Modal birefringence in weakly guiding fibers,” J. Light. Technol. 30(14), 2240–2245 (2012). [CrossRef]

23. Y. Kokubun, T. Watanabe, S. Miura, and R. Kawata, “What is a mode in few mode fibers?: Proposal of MIMO-free mode division multiplexing using true eigenmodes,” IEICE Electron. Express 13(18), 1–12 (2016). [CrossRef]

24. S. Miura, T. Watanabe, and Y. Kokubun, “Accurate analysis of crosstalk between LP₁₁ quasi-degenerate modes due to offset connection using true eigenmodes,” IEEE Photonics J. 10(1), 7900811 (2018). [CrossRef]

25. L. C. Andrews and R. L. Phillips, Laser beam propagation through random media2nd ed. (SPIE Press, 2005). [CrossRef]

26. J. D. Schmidt, Numerical simulation of optical wave propagation with examples in MATLAB, (SPIE Press, 2010). [CrossRef]

27. M. Toyoshima, H. Takenaka, Y. Shoji, and Y. Takayama, “Frequency characteristics of atmospheric turbulence in space-to-ground laser links,” Proc. SPIE 7685, 76850G (2010). [CrossRef]

28. N. Kim and H. Park, “Performance analysis of MIMO system with linear MMSE receiver,” IEEE Transaction on Wirel. Commun. 7(11), 4474–4478 (2008). [CrossRef]

29. Y. Miyata, K. Sugihara, W. Matsumoto, K. Onohara, T. Sugihara, K. Kubo, H. Yoshida, and T. Mizuoch, “A triple-concatenated FEC using soft-decision decoding for 100 Gb/s optical transmission,” in Optical Fiber Communication Conference (2010), paper OThL.3. [CrossRef]

30. E. Ip, G. Milione, M.-J. Li, N. Cvijetic, K. Kanonakis, J. Stone, G. Peng, X. Prieto, C. Montero, V. Moreno, and J. Liñares, “SDM transmission of real-time 10GbE traffic using commercial SFP+ transceivers over 0.5km elliptical-core few-mode fiber,” Opt. Express 23(13), 17120–17126 (2015). [CrossRef] [PubMed]

31. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008). [CrossRef] [PubMed]

32. L. Liu, Z. Tao, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “Initial tap setup of constant modulus algorithm for polarization de-multiplexing in optical coherent receivers,” in Optical Fiber Communication Conference (2009), paper OMT.2.

Performance of mode diversity reception of a polarization-division-multiplexed signal for free-space optical communication under atmospheric turbulence

Abstract

1. Introduction

2. Simulation of mode diversity reception of a PDM signal

2.1. Atmospheric propagation

2.2. FMF coupling and propagation

2.3. Performance of mode diversity reception

3. Experimental demonstration with a turbulence emulator

4. Conclusion

Funding

References

Cited By

Figures (14)

Equations (8)

Optics Express