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Abstract
Optical vortex beams (VBs) possessing helical phase-front have attracted considerable attention in multiplexing communication for their orthogonal orbital angular momentum (OAM) modes. However, the mode-crosstalk and signal jitter caused by turbulence fluctuation are two main challenges in OAM multiplexing communication. Here, we introduce an intra-symbol frequency-domain averaging technology (ISFA) for turbulence mitigation. By equalizing the distorted multiplexing signals, ISFA mitigates the amplitude and phase jitter of received signals without adding system complexity and information redundancy. The experimental results show that VBs are successfully demultiplexed, and the transmission rate reaches 48 Gbit/s. After ISFA, the bit-error-rate of QPSK-OFDM signals is reduced from 1.10 × 10−3 to 6.31 × 10−4, and the error-vector-magnitude (EVM) is reduced from 31.69% to 26.29% under the turbulence strength of $C_n^2\textrm{ = }1 \times {10^{ - 13}}{\kern 1pt} {m^{ - {2 / 3}}}$ and equivalent transmission distance of 200 m. By combining ISFA with MIMO diversity gain, the EVM can be further reduced from 46.70% to 26.70%. These indicate that ISFA is available for turbulence mitigation and compatible with MIMO technology, which may have perspective potential in improving the performance of OAM multiplexing communication.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical vortex beams (VBs) have helical phase-front and carry orthogonal orbital angular momentum (OAM) modes [1,2]. The nonuniform field distribution rewards VBs with many unique optical properties, which have been widely applied in particle manipulation, quantum information processing, super-resolution microscopic imaging, etc [3–6]. Especially in optical communication, VBs provide an additional physical dimension for signal multiplexing that increases the communication capacity density through the mutually orthogonal OAM modes [7–10]. By multiplexing 8 OAM modes, a high-speed optical communication with a transmission rate of 2.5 Tbit/s and spectral efficiency of 95.7 bit/s/Hz was achieved [11]. An ultra-high-speed communication with a transmission rate of 100.8 Tbit/s was investigated by multiplexing 12 OAM modes, 2 orthogonal polarization states and 42 wavelengths [12]. These indicate that VBs have a remarkable ability to improve information rate and spectral efficiency. However, the spatially spiral phase-front of VB is vulnerable to atmospheric turbulence in free-space transmission, resulting in severe spatial phase distortion and OAM mode crosstalk [13–16].
Various methods have been proposed to enhance the robustness of OAM multiplexing communication, which can be roughly divided into optical domain compensation and digital domain equalization schemes [17–20]. Optical compensation technologies involving adaptive optics and optical neural networks are mainly devoted to restoring distorted wave-fronts, and the communication sensitivity can be improved over 10 dB after mitigating mode crosstalk. However, the adaptive manipulation of light beams requires detecting and correcting the distorted wave-front in real time, resulting in extremely complicated optical links. The optical neural networks extract the disturbance model from the distorted VBs and compensate them in the optical domain. This method needs to obtain the prior characteristics of random channels by training neural networks [21–24]. The turbulent channel presenting dynamic random fluctuation makes the real-time compensation cumbersome. The digital equalization methods directly process the offline digital signals without correcting light beams and can be integrated into demodulation algorithms. Channel coding and multiple-input multiple-output (MIMO) technologies are two typical digital signal compensation methods. Low-density parity-check (LDPC) and Turbo coding are employed to reduce the bit-error-rate (BER) of data transmission in nasty channels [25,26], where the transmitted data is generated via an exact connection, and some erroneous data will be corrected from this correlation [27]. However, the correction matrix of channel coding algorithm normally induces non-negligible redundancy and shows limited convergence in constellations. To mitigate the mode crosstalk in OAM multiplexing communication with turbulence, a MIMO equalization scheme was investigated by finding the finite-impulse-response (FIR) tap weights of all channels [28–30]. However, turbulence fluctuation not only aggravate OAM mode crosstalk but also cause severe signal jitter, which severely deteriorates the performance of free-space OAM multiplexing communication, and an accurate channel estimation enabling signal jitter mitigation is of significance for turbulence mitigation.
In this work, we propose an intra-symbol frequency-domain averaging (ISFA) technology to mitigate the atmospheric turbulence in free-space OAM multiplexing communication. Exploiting the random burst of turbulence noise, we reveal that ISFA can enhance the robustness of communication by equalizing the distorted multiplexing signals without increasing system complexity and information redundancy. The experimental results show that VB_+1 and VB_+4 (VB with the topological charge of +1 and +4) are successfully multiplexed and demultiplexed, and the transmission rate reaches 48 Gbit/s. With the turbulence strength of $C_n^2\textrm{ = }1 \times {10^{ - 13}}{m^{ - {2 / 3}}}$, the demodulated BER is $\textrm{1}\textrm{.1} \times {10^{ - \textrm{3}}}$, and the EVM is 36.67%. After ISFA, the BER is reduced to $\textrm{6}\textrm{.31} \times {10^{ - \textrm{4}}}$, and the EVM is 32.55%. By combining ISFA with MIMO diversity gain, the EVM can be further reduced from 46.70% to 26.70%. These indicate that ISFA provides an effective way to mitigate atmospheric turbulence and can be compatible with MIMO technology, which may have perspective potential in improving the robustness of high-speed OAM multiplexing communication.
2. Principles and methods
2.1 VB propagation in atmospheric turbulence
Laguerre-Gaussian (LG) beam is a typical VB carrying helical phase-front. Its electric field distribution at the distance of z can be expressed as [31]
In free-space transmission, the phase-front of VB will be distorted under the influence of random turbulence fluctuation. Severe crosstalk will be brought in OAM multiplexing due to the energy leakage of adjacent modes, which degrades the capacity limitation of communication [32]. The turbulence is generated by loading a turbulence phase screens on a spatial light modulator (SLM). To investigate the influence of atmospheric turbulence on OAM multiplexing communication, we introduce the Hill-Andrews spectrum model to generate atmospheric turbulence phase screens [33]. Their refractive index power spectral density can be written as [34]
After a 12 m free-space transmission, the phase distributions, intensity profiles and mode spectrums of VB_+4 under the turbulence strength of $C_n^2 = 1 \times {10^{ - 15}}{m^{ - {2 / 3}}},1 \times {10^{ - 14}}{m^{ - {2 / 3}}},1 \times {10^{ - 13}}{m^{ - {2 / 3}}}$ are shown in Fig. 1. With the increase of turbulence strength, VB shows more severe distortion in intensity distribution because the enhanced turbulence fluctuation will deteriorate the distortion of helical phase-front. From these OAM mode spectrums, more energy leaks into adjacent modes with the increase of turbulence strength, which will lead to a severe mode crosstalk in OAM multiplexing communication.
Fig. 1. Phase, intensity and mode spectrum of VB_+4 under the turbulence strength of $C_n^2 = \textrm{1} \times \textrm{1}{\textrm{0}^{\textrm{ - 15}}}{m^{ - {2 / 3}}}$, $C_n^2 = \textrm{1} \times \textrm{1}{\textrm{0}^{\textrm{ - 14}}}{m^{ - {2 / 3}}}$, $C_n^2 = \textrm{1} \times \textrm{1}{\textrm{0}^{\textrm{ - 13}}}{m^{ - {2 / 3}}}$ and a transmission distance of $\varDelta z = 12{\kern 1pt} {\kern 1pt} m$.
2.2 Turbulence mitigation with ISFA technology
Orthogonal-frequency-division-multiplexing (OFDM) signals employing training sequence for channel estimation and pilot tones for phase shift correction possess excellent applications in mobile communication, long-haul free-space and fiber communication. In addition, OFDM signals can flexibly combine numerous digital signal processing algorithms, such as encoding and decoding algorithms [37,38], spread spectrum algorithms [39], etc. Here, we introduce the ISFA into OFDM signals for turbulence mitigation. Now we derive the implementation process of ISFA. The received training sequence of OFDM signals can be expressed as [37,40]
where ${x_p}(n)$, ${h_p}(n)$, ${r_p}(n)$ are the transmitted training sequence, channel response and random channel noise in time domain. p is the p-th subcarrier. In OAM multiplexing communication with atmospheric turbulence, ${r_p}(n)$ mainly includes the mode crosstalk and signal jitter induced by turbulence fluctuation. After $FFT$, the corresponding frequency transformation of Eq. (5) can be written as [40] where ${X_p}(n)$, ${H_P}(n)$, ${R_p}(n)$ are the frequency response of ${x_p}(n)$, ${h_p}(n)$, ${r_p}(n)$, respectively. To estimate the channel matrix, the least-squares (LS) algorithm is introduced, and its cost function can be defined as [41]To obtain the optimal solution of cost function, the derivative of J is set as zero, which can be expressed as [41]
From Eq. (8), the first derivative ${\hat{H}_P}(n) = {{{Y_P}(n)} / {{X_P}(n)}}$ is unique. The cost function monotonically increases on the interval of ($- \infty ,{{{Y_P}(n)} / {{X_P}(n)}}$) and decreases on the interval of (${{{Y_P}(n)} / {{X_P}(n)}}, + \infty$). Therefore, ${\hat{H}_P}(n)$ corresponds to the local minimum of the cost function J. ${\hat{H}_P}(n)$ is the estimated value of ${H_P}(n)$, which can be derived as
To restrain the channel noise ${R_P}(n)$ associated with turbulence fluctuation, ISFA technology is introduced to mitigate signal jitter. The ISFA can be expressed as
Figure 2 shows the ISFA based channel estimation improvements under the turbulence strength of $C_n^2 = 1 \times {10^{ - 13}}{m^{ - {2 / 3}}}$ and transmission distance of 200 m. After ISFA, the jitter of amplitude and phase of channel responses becomes weaker than before, as described in red curves of Fig. 2. Therefore, the signal jitter is restrained because the signal is recovered according to the estimated channel matrix. These indicate that ISFA provides an effective way for turbulence mitigation.
Fig. 2. Amplitude and phase of channel responses with and without ISFA under turbulence strength of $C_n^2 = \textrm{1} \times \textrm{1}{\textrm{0}^{\textrm{ - 13}}}{m^{ - {2 / 3}}}$ and transmission distance of 200 m.
3. Experimental results and analyses
Figure 3 presents the experimental schematic diagram of free-space OAM multiplexing communication. At the transmitter, two 12 GS/s QPSK-OFDM signals are generated by an arbitrary waveform generator (AWG 7122C) and modulated to the light (1550.12 nm) by using an IQ modulator (IQ-40-EVK), which is divided into two paths by an optical coupler (OC, 50%:50%). A distributed feedback laser with a line-width of 100 kHz is employed to produce signal light. After amplified by two erbium-doped fiber amplifiers (EDFAs, Amonics AEDFA-23-B-FA), the two optical signals are de-correlated via a 5 m delay fiber. In free-space channel, the Glan lens (GL) is used to convert Gaussian light to be linearly polarized and the quarter-wave plate (QWP) is employed to produce the circularly polarized light. Circularly polarized VB_+1 and VB_+4 are produced by meta-surfaces (MSs) with q=0.5 and 2, respectively. The beam-splitter (BS) is employed for light beam combination or splitting. After propagating through the GL before SLM, the circularly polarized VBs are converted to be horizontally polarized and then input an x-polarization responded SLM. The SLM is employed to load the turbulence phase screens that are computationally generated as described in Eqs. (2)–(4). The turbulence strength and equivalent transmission distances can be controlled by updating the phase screens. After spatial separation, VB_+1 and VB_+4 are restored to Gaussian-like beams by MSs with q = 0.5 and q=1, respectively. The iris is designed to filter other OAM modes. At the receiver, the signal light is inputted into an integrated coherent receiver together with local oscillator light for coherent detection. The baseband signals are sampled by oscilloscopes for offline digital signal processing (DSP).
Fig. 3. Experimental schematic diagram of OAM multiplexing communication. DFB: distributed feedback laser; AWG: arbitrary waveform generator; IQ Mod.: IQ modulator; OC: optical coupler; EDFA: erbium-doped fiber amplifier; SMF: single-mode fiber; FC: fiber coupler; GL: Glan lens; QWP: quarter-wave plate; MS: meta-surface; MR: mirror; BS: beam splitter; SLM: space light modulator; PC: polarization controller; LO: local oscillator; ICR: integrated coherent receiver; Osc.: oscilloscope.
3.1 OAM multiplexing communication with atmospheric turbulence
3.1.1 Intensity distortion of the VBs influenced by atmospheric turbulence
To analyze the influence of atmospheric turbulence, we have investigated the intensity distortions of VBs influenced by the turbulence (the equivalent transmission distance is 200 m) with $C_n^2 = 0,1 \times {10^{ - 15}}{\kern 1pt} {m^{ - {2 / 3}}},1 \times {10^{ - 14}}{\kern 1pt} {m^{ - {2 / 3}}},1 \times {10^{ - 13}}{\kern 1pt} {m^{ - {2 / 3}}}$. As shown in Fig. 4, with the increase of turbulence strength, the intensity distributions of VBs are dispersed because of turbulence-induced phase distortions, and the circular symmetry in the cross-section of transmission direction is also gradually deteriorated. The spatial phase distortion can increase mode crosstalk and lead to the deterioration of communication performance.
Fig. 4. Intensity distributions of multiplexed VB_+1 and VB_+4 influenced by turbulence with different strengths.
3.1.2 OAM multiplexing communication under different turbulence strengths
The signal- and noise- powers of multiplexed VBs influenced by turbulence (200 m) with different strengths are described in Fig. 5. In the case of B2B transmission ($C_n^2 = 0$), the crosstalk corresponding to VB_+1 and VB_+4 are nearly -23.62 dB and -22.98 dB, and the crosstalk increases about 9.5 dB under the turbulence strength of $C_n^2 = 1 \times {10^{ - 13}}{m^{ - {2 / 3}}}$.
Fig. 5. Received signal- and noise- powers of VB_+1 and VB_+4 under the turbulence (200 m) strengths of $C_n^2 = 0,\textrm{1} \times \textrm{1}{\textrm{0}^{\textrm{ - 15}}}\; {m^{ - {2 / 3}}},\textrm{1} \times \textrm{1}{\textrm{0}^{\textrm{ - 14}}}\; {m^{ - {2 / 3}}},\textrm{1} \times \textrm{1}{\textrm{0}^{\textrm{ - 13}}}\; {m^{ - {2 / 3}}}$.
The corresponding EVMs of VB_+1 and VB_+4 are illustrated in Fig. 6. At the received power of -31 dBm, the EVMs of VB_+4 are 28.97% and 36.67% under the turbulence of $C_n^2 = 0$ and $C_n^2 = 1 \times {10^{ - 13}}{m^{ - {2 / 3}}}$. From Fig. 6, the communication sensitivity decreases by nearly 3 dB with the turbulence strength increases by an order of magnitude.
Fig. 6. EVMs as the function of received power under turbulence (200 m) strength of $C_n^2 = \textrm{0,1} \times \textrm{1}{\textrm{0}^{\textrm{ - 15}}}{m^{ - {2 / 3}}},\textrm{1} \times \textrm{1}{\textrm{0}^{\textrm{ - 14}}}{m^{ - {2 / 3}}},\textrm{1} \times \textrm{1}{\textrm{0}^{\textrm{ - 13}}}{m^{ - {2 / 3}}}$ corresponding to (a) VB_+1 and (b) VB_+4.
As shown in Fig. 7, at the received power of -31 dBm, the BERs of VB_+4 are demodulated with $8.04 \times {10^{ - 5}}$ and $1.10 \times {10^{ - 3}}$ under the turbulence (200 m) strength of $C_n^2 = 0$ and $C_n^2 = 1 \times {10^{ - 13}}{m^{ - {2 / 3}}}$. With turbulence strength increases by an order of magnitude, the communication sensitivity also decreases by nearly 3 dB, indicating that the communication sensitivity decreases about 3 dB with the crosstalk increases from -22.98 dB to -14.18 dB.
Fig. 7. BERs as a function of received power under turbulence strength of $C_n^2 = \textrm{0,1} \times \textrm{1}{\textrm{0}^{\textrm{ - 15}}}{m^{ - {2 / 3}}},\textrm{1} \times \textrm{1}{\textrm{0}^{\textrm{ - 14}}}{m^{ - {2 / 3}}},\textrm{1} \times \textrm{1}{\textrm{0}^{\textrm{ - 13}}}{m^{ - {2 / 3}}}$ corresponding to (a) VB_+1 and (b) VB_+4.
3.1.3 OAM multiplexing communication with different turbulence distances
The signal- and noise- powers of VB_+1 and VB_+4 under turbulence ($C_n^2 = 1 \times {10^{ - 13}}{m^{ - {2 / 3}}}$) with different transmission distances (200 m, 400 m and 600 m) are described in Fig. 8. After 200 m turbulence transmission, the crosstalk corresponding to VB_+1 and VB_+4 are about -14.2 dB and -14.18 dB, and the crosstalk of VB_+1 and VB_+4 are approximately -8.91 dB and - 9.69 dB after 600 m turbulence transmission.
Fig. 8. Received signal- and crosstalk powers of VB_+1 and VB_+4 under turbulence ($C_n^2 = \textrm{1} \times \textrm{1}{\textrm{0}^{\textrm{ - 13}}}{m^{ - {2 / 3}}}$) with transmission distances of 200 m, 400 m and 600 m.
The EVMs corresponding to VB_+1 and VB_+4 under turbulence ($C_n^2 = 1 \times {10^{ - 13}}{\kern 1pt} {m^{ - {2 / 3}}}$) with different transmission distances are illustrated in Fig. 9. Under the turbulence transmission distance of 200 m and 600 m, the EVMs correspond to VB_+4 are 36.67% and 39.52% at the received power of -31 dBm. From Fig. 9, the communication sensitivity decreases about 2 dB with the transmission distance of turbulence increases from 400 m to 600 m.
Fig. 9. EVMs as a function of received power under turbulence ($C_n^2 = \textrm{1} \times \textrm{1}{\textrm{0}^{\textrm{ - 13}}}{m^{ - {2 / 3}}}$) with transmission distances of 200 m, 400 m and 600 m corresponding to (a) VB_+1 and (b) VB_+4.
The BERs of the multiplexed VBs under the turbulence ($C_n^2 = 1 \times {10^{ - 13}}{\kern 1pt} {m^{ - {2 / 3}}}$) with different transmission distances are illustrated in Fig. 10. At the received power of -31 dBm, the BERs of VB_+4 are $1.10 \times {10^{ - 3}}$ and $2.58 \times {10^{ - 3}}$ after a 200 m and 600 m turbulence transmission, indicating that the increased transmission distance will deteriorate the performance of OAM multiplexing communication.
Fig. 10. BERs as a function of received power under turbulence ($C_n^2 = \textrm{1} \times \textrm{1}{\textrm{0}^{\textrm{ - 13}}}{m^{ - {2 / 3}}}$) with transmission distances of 200 m, 400 m and 600 m corresponding to (a) VB_+1 and (b) VB_+4.
3.2 Turbulence mitigation with ISFA
3.2.1 ISFA optimization under turbulence with different strengths
To investigate the optimization effect of ISFA for turbulence with different strengths, the EVM variations of VB_+1 and VB_+4 are described in Fig. 11. At the received power of -31 dBm and turbulence strength of $C_n^2 = 1 \times {10^{ - 13}}{\kern 1pt} {m^{ - {2 / 3}}}$, the EVMs of QPSK-OFDM signals decrease from 36.67% to 32.55% after ISFA. The communication sensitivity is improved by 3 dB to 5 dB, which indicates that ISFA can effectively optimize the EVM of OAM multiplexing communication.
Figure 12 presents the BERs with and without ISFA. At the received power of -31 dBm and turbulence strength of $C_n^2 = 1 \times {10^{ - 13}}{\kern 1pt} {m^{ - {2 / 3}}}$, the BER of 48 Gbit/s QPSK-OFDM signals is reduced from $1.10 \times {10^{ - 3}}$ to $6.31 \times {10^{ - 4}}$ after ISFA. From these BERs, the communication sensitivity is improved by nearly 5 dB and the BER is closed to ${10^{ - 5}}$ at the received power of -25 dBm, manifesting that ISFA is an effective scheme for turbulence mitigation in OAM multiplexing communication.
3.2.2 ISFA optimization under turbulence with different transmission distances
The EVMs of QPSK-OFDM signals with and without ISFA are illustrated in Fig. 13. Figures 13(a) and 13(b) are corresponding to VB_+1 and VB_+4 under the turbulence ($C_n^2 = 1 \times {10^{ - 13}}{m^{ - {2 / 3}}}$) with transmission distance of 200 m, 400 m and 600 m. The communication sensitivity is improved approximately 3 dB even under the turbulence with transmission distance of 600 m.
Before and after ISFA, the BERs of VB_+1 and VB_+4 under the turbulence ($C_n^2 = 1 \times {10^{ - 13}}{m^{ - {2 / 3}}}$) with different transmission distances are illustrated in Fig. 14. At the received power of -31 dBm and turbulence transmission distance of 600 m, the BER of 48 Gbit/s QPSK-OFDM signals is reduced from $2.58 \times {10^{ - 3}}$ to $1.76 \times {10^{ - 3}}$ after ISFA. The communication sensitivity decreases about 3 dB with the transmission distance increases from 400 m to 600 m. The BER can still reach ${10^{ - 5}}$ at the received power of -18 dBm even under the turbulence with transmission distance of 600 m.
With and without ISFA, the constellations corresponding to VB_+4 under the turbulence ($C_n^2 = 1 \times {10^{ - 13}}{\kern 1pt} {m^{ - {2 / 3}}}$) with transmission distances of 200 m, 400 m and 600 m are illustrated in Fig. 15. At the received power of -28 dBm, the EVMs are 31.69%, 33.46% and 35.58%. After ISFA, the EVMs are reduced to 26.29%, 27.60% and 29.51%, respectively. The EVM is reduced by 6%∼7%, which indicated that ISFA can effectively reduce the EVM in OAM multiplexing communication.
Fig. 15. Constellations of VB_+4 (the received power is -28 dBm) with and without ISFA under the turbulence ($C_n^2 = \textrm{1} \times \textrm{1}{\textrm{0}^{\textrm{ - 13}}}{m^{ - {2 / 3}}}$) with transmission distances of 200 m, 400 m and 600 m.
4. Discussion
Optical OAM multiplexing provides an additional dimension to enlarge the capacity density of optical communication. However, the mode crosstalk and signal jitter induced by turbulence fluctuation severely deteriorate the performance of free-space OAM multiplexing communication. To mitigate mode crosstalk, the schemes involving light beam quality compensation and MIMO equalization have been proposed successively. Light beam quality compensation schemes, such as adaptive optics method and neural network based beam pre-distortion technology, are mainly designed for turbulence mitigation in optical domain. MIMO equalization focuses on eliminating the noise components by finding the tap weight of FIR filter. To address the signal jitter that brings severe channel estimation error, ISFA enabling the equalization of signal jitters is proposed. OAM multiplexing employing neighboring modes typically has more severe crosstalk than non-neighboring modes, because more energy is diffused into neighboring OAM modes. By equalizing signal jitter, ISFA enables the similar quality of communication even for neighboring OAM modes.
In order to realize the optimization of communication performance, the combination of multiple signal processing algorithms is crucial for random channels. By equalizing the estimated FIR taps of channels, ISFA can be combined with MIMO equalization to mitigate mode crosstalk and equalize signal jitter. By allotting two or more channels to transmit the same data information, MIMO diversity gain [42,43] is also feasible for turbulence mitigation in OAM multiplexing communication. In MIMO diversity gain scheme, the signals characterized by different channels are received as multiple outputs, which are further superimposed with appropriate weights. The optimal weights for sub-channels can be obtained by estimating the EVMs of received signals, which relates to SNR in general. Figure 16 describes the relation of EVM variation versus the weight of one sub-channel in a 2×2 MIMO communication. The optimal gain weights of two sub-channels are approximately 54% and 46%.
After MIMO diversity gain (the optimal weights are 54% and 46% for two sub-channels) combining with ISFA, the constellations of QPSK-OFDM signals are shown in Fig. 17, where the signals are captured under turbulence strength with $C_n^2 = \textrm{1} \times \textrm{1}{\textrm{0}^{\textrm{ - 13}}}{m^{ - {2 / 3}}}$ and transmission distance of 600 m. The EVM is improved by 12.39% and 20% for sub-channel-1 and sub-channel-2. Similar to MIMO equalization, MIMO diversity gain possessing more channels enables a better optimization. The combination of MIMO equalization, MIMO diversity gain and ISFA is available to further mitigate the mode crosstalk and signal jitter brought by turbulence fluctuation, which may have potential applications in high-speed acoustic [44], microwave [32] and optical OAM communications [28–30].
Fig. 17. Constellations of QPSK-OFDM signals corresponding to sub-channel 1, sub-channel 2 and the case combining ISFA with MIMO diversity gain.
5. Conclusion
In conclusion, we propose and experimentally investigate an ISFA method to mitigate the atmospheric turbulence in OAM multiplexing communication. The experimental results show that two VBs carrying 48 Gbit/s QPSK-OFDM signals were successfully multiplexed and demultiplexed even under the turbulence strength of $C_n^2 = 1 \times {10^{ - 13}}{m^{ - {2 / 3}}}$ and a transmission distance of 200 m. After ISFA, the BER reduced from $1.10 \times {10^{ - 3}}$ to $6.31 \times {10^{ - 4}}$, and the EVM was optimized for about 5.4%. By combining ISFA with MIMO diversity gain, the EVM can be further reduced from 46.70% to 26.70%. These indicate that ISFA is available for turbulence mitigation and compatible with MIMO technology, which may provide an efficient way for the performance improvement of OAM multiplexing communication.
Funding
National Natural Science Foundation of China (12047539, 61805149); Guangdong Basic and Applied Basic Research Foundation (2019A1515111153, 2020A1515011392, 2020A1515110572, 2021A1515011762); Shenzhen Fundamental Research Program (JCYJ20180507182035270, JCYJ20200109144001800); Science and Technology Project of Shenzhen (GJHZ20180928160407303); Shenzhen Universities Stabilization Support Program (SZWD2021013); Shenzhen Excellent Scientific and Technological Innovative Talent Training Program (RCBS20200714114818094); China Postdoctoral Science Foundation (2020M682867).
Disclosures
The authors declare no conflicts of interest.
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