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Abstract
Vortex beams carrying orbital angular momentum (OAM) modes show superior multiplexing abilities in enhancing communication capacity. However, the signal fading induced by turbulence noise severely degrades the communication performance and even leads to communication interruption. Herein, we propose a diversity gain strategy to mitigate signal fading in OAM multiplexing communication and investigate the gain combination and channel assignment to optimize the diversity efficiency and communication capacity. Endowing signals with distinct channel matrices and superposing them with designed channel weights, we perform the diversity gain with an optimal gain efficiency, and the signal fading is mitigated by equalizing the turbulence noise. For the tradeoff between turbulence noise tolerance and communication capacity, multiplexed channels are algorithm-free assigned for diversity and multiplexing according to bit-error-rate and outage probability. As a proof of concept, we demonstrate a 6-channel multiplexing communication, where 3 OAM modes are assigned for diversity gain and 24 Gbit/s QPSK-OFDM signals are transmitted. After diversity gain, the bit-error-rate decreases from 1.41 × 10−2 to 1.63 × 10−4 at -14 dBm, and the outage probability of 86.7% is almost completely suppressed.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Vortex beams (VBs) carrying orbital angular momentum (OAM) have been extensively exploited for enhancing communication capacity via mode multiplexing [1–4]. As is independent of conventional physical dimensions involving wavelength and polarization, the OAM mode shows respectable compatibility with them to construct multidimensional multiplexing communication [5–9]. By multiplexing 12 OAM beams, 2 polarizations, and 42 wavelengths, the communication capacity reaches 100.8 Tbit/s [7]. However, the wavefront of the vortex beam is susceptible to turbulence noise in free space, which will distort the spatial phase structure and further conduce signal fading [10,11], severely degrading the communication performance and even leading to communication interruption. Hence, the exploration to mitigate signal fading is important for promoting the practical application of OAM multiplexing communication.
Abundant approaches have been investigated for mitigating channel noise, which can be mainly classified as light beam compensation [12–19] and digital signal processing [20–27]. Light beam compensation involving adaptive optics [12–14] and optical neural networks [15–19] mainly aim at restoring the distorted wavefronts, which are feasible for healing the signal fading in the optical domain but bring costly and complicated optical systems for extracting the prior characteristics of random channels. Digital signal processing strategies involving multiple-input multiple-output (MIMO) equalization [20–22] and channel coding [23–27] typically equalize the channel impairment or enhance the fault tolerance of OAM multiplexing communication but are cumbersome to heal signal fading. OAM mode transmission or reception diversity is investigated to mitigate power fading, which aims to reduce the power fluctuation by equally coupling the power of multiple OAM modes [28,29]. However, inappropriate channel weights result in a suboptimal diversity efficiency, which will be addressed in this work. In addition, few works on OAM mode diversity discuss the channel assignment, which plays a pivotal role in balancing the turbulence noise tolerance and communication capacity.
In this work, we propose a diversity gain strategy to mitigate signal fading in OAM multiplexing communication, and investigate the gain combination and channel assignment for optimizing the diversity efficiency and communication capacity. The diversity gain is performed by endowing the signals with distinct channel matrices and superposing the received signals with the channel weights obtained by searching the minimum error vector magnitude (EVM). By equalizing the turbulence noise with designed channel matrices, the signal fading will be mitigated. To perform the tradeoff between turbulence noise tolerance and communication capacity, multiplexed channels are algorithm-free assigned for multiplexing and diversity for providing diversity gain reference for turbulence with different parameters. As a proof of concept, we investigate a 6-channel multiplexing communication, where multiplexing and diversity are implemented simultaneously, and 24 Gbit/s QPSK-OFDM signals are transmitted. After diversity gain, the bit-error-rate (BER) is improved from $1.41 \times \textrm{1}{\textrm{0}^{\textrm{ - 2}}}$ to $1.63 \times \textrm{1}{\textrm{0}^{\textrm{ - 4}}}$ at the received power of -14 dBm, and the outage probability of communication decreases from 86.7% to 3.3%. As is performed by optimizing the EVM of signals, the maximal ratio combination is proven to be a gain combination scheme to obtain the optimal channel weights. The channel assignment also provides an appropriate channel deployment scheme to cope with different turbulent noises.
2. Principles and methods
2.1 Principles of VB generation
Pancharatnam-Berry (P-B) phased metasurfaces (PBMs) with different q-factors are employed for producing VBs in this work. The P-B phase, as one of the geometric phases related to spin-orbit interaction, enables manipulation of the phase distribution of the incident beam. The birefringence effect is introduced via the P-B phase regulation mechanism, and the PBMs are fabricated by writing nanogratings on a fused silica glass substrate. Figure 1(a) displays a photo of PBM with $q = 0.5$ (q is a constant related to the spatial rotation ratio of the optical axis), and the diameter of the active area is 5 mm. The parallel- and cross-polarized images of the PBM are presented in Figs. 1(b)-(c). Figures 1(d)-(e) illustrate the theoretical and experimental slow axis profiles of the PBM, which demonstrate that the measured results are almost consistent with the theoretical prediction.
Fig. 1. (a) Captured photo of the PBM with $q = 0.5$. (b)–(c) Measured parallel- and cross-polarized images of the PBM. Pin/Pout: Polarization states of the input/output beams. (d)–(e) Theoretical and experimental slow axis profiles of the PBM.
By measuring the power of the incident- and the output light beams of PBMs with a spatial light power meter (Newport 2936-R), we calculate the transmission efficiencies (the ratio between the transmitted power and the incident power) of PBMs with q = 0.5 and q = 1 at the wavelengths of 1540, 1550, 1560, 1570, 1580, and 1590 nm, as illustrated in Fig. 2. The transmission efficiencies remain above 87.1% all over these measured wavelengths and even reach 91.4% (q = 0.5) and 89.5% (q = 1) at 1550 nm, which owe to the transmittance type design of PBMs. The energy loss is mainly induced by material absorption and surface reflection.
Fig. 2. Measured transmission efficiencies of PBMs with q = 0.5 and q = 1 at the wavelengths of 1540, 1550, 1560, 1570, 1580 and 1590 nm.
By employing the spin-orbit interaction of the PB phase, PBM is introduced to manipulate the spatial phase front of circularly polarized light and produce VBs. The optical axis direction of the PBM can be written as
where $({r,\theta } )$ is the spatial polar coordinate. θ and φ are the azimuthal angle and initial direction of the optical axis, respectively. Set $\varphi = 0$ and the homogeneous birefringent phase retardation [30,31] as π, the corresponding Jones matrix of PBM can be written asAfter left-handed circularly polarized (LCP) or right-handed circularly polarized (RCP) light propagates through the PBM, the Jones matrix corresponding to the OAM modes of +2q or -2q (OAM_+2q or OAM_-2q) can be derived as
2.2 Theoretical analysis of diversity gain
To mitigate the signal fading caused by turbulence fluctuation, the diversity gain combination is performed in the digital domain. The received time-domain signals in form of the transient response can be expressed as the convolution operation of transmitted signals $x(t)$ with channel matrix $h(t)$, which can be written as
Suffering from the signal fading, the obtained $y\textrm{(}t\textrm{)}$ has a severe deviation from its target values. Therefore, diversity gain, implemented by transmitting multiple channels to obtain the decorrelation channel matrices and superposing the received signals with designed channel weights, is considerable for mitigating signal fading. The signal $Y\textrm{(}n\textrm{)}$ after gain combination can be derived as
where ${f_k}$ and ${h_k}$ are the channel weight and channel matrix of OAM_k, respectively, and n refers to the number of OAM modes for diversity gain. From Eq. (8), the received signals will approach the target values after diversity gain, and the signal fading is mitigated by equalizing the channel noise with the designed channel matrix. The optimal channel matrix ${f_k}{h_k}$ can be obtained by searching the minimum EVM of $Y(n)$.To optimize the diversity efficiency, gain combination technologies involving maximum ratio combination (MRC) [32] and equal gain combination (EGC) [33] are available. The MRC aims to find the appropriate channel weight ${f_k}$ by estimating the signal-to-noise ratio (SNR), which is positively correlated with the EVM of signals. The EGC setting the channel weight with ${f_k}\textrm{ = }1/n$ is straightforward to perform and is equivalent to MRC when the power gap of all diversity channels is 0, but gets a bad gain efficiency due to an inaccurate channel weight if the power gap among channels is non-negligible. Therefore, the investigation of applicable scenarios of the two gain combination methods for practical application is of importance, which will be demonstrated in this work.
Outage probability is also a crucial index to evaluate the performance of OAM mode diversity. Due to the channel impulse responses are statistically independent, the overall outage probability corresponding to the EGC case can be written as [33,34]
3. Experimental results and analysis
3.1 OAM multiplexing communication under atmospheric turbulence
To investigate the influence of signal fading on OAM multiplexing communication system, we demonstrate a 4-channel OAM communication with turbulence of different strengths or transmission lengths (see Supplement 1, Section S2.), as illustrated in Fig. 3. The intensity-modulation QPSK-OFDM signals (the number of subcarriers and pilots is 256 and 8, respectively) with a sampling rate of 12 Gbit/s are separately carried by 4 OAM modes and demodulated by the method of direct detection. The turbulence is experimentally performed by loading a phase screen on a spatial light modulator, and the phase screen is computationally generated based on the Hill-Andrews spectrum model [35]. Please refer to the Supplementary materials for a detailed description of the experimental setup.
Fig. 3. Schematic diagram of the 4-channel OAM multiplexing communication with turbulence. LD: laser diode; OC: optical coupler; IM: intensity modulator; AWG: arbitrary waveform generator; EDFA: erbium-doped fiber amplifier; SMF: single mode fiber; Col.: collimator; GL: Glan lens; QWP: quarter-wave-plate; PBM: PB phase based metasurface; BS: beam splitter; Mir.: mirror; PC: polarization controller; VOA: variable optical attenuator; PD: photo detector; DSO: digital signal oscilloscope.
To study the OAM mode distortion induced by turbulence noise, we experimentally capture the intensity maps of OAM_+2, OAM_+1, OAM_-1 and OAM_-2 under 400 m turbulence with $\textrm{C}_\textrm{n}^\textrm{2}\textrm{ = 0, 1} \times \textrm{1}{\textrm{0}^{\textrm{ - 14}}}\textrm{, 1} \times \textrm{1}{\textrm{0}^{\textrm{ - 13}}}\textrm{ }{\textrm{m}^{\textrm{ - 2/3}}}$, as illustrated in Fig. 4. Columns 1-3 show the intensity distributions corresponding to the turbulence strength with $\textrm{C}_\textrm{n}^\textrm{2}\textrm{ = 0, 1} \times \textrm{1}{\textrm{0}^{\textrm{ - 14}}},\textrm{ }\textrm{ 1} \times \textrm{1}{\textrm{0}^{\textrm{ - 13}}}{\textrm{m}^{\textrm{ - 2/3}}}$, which show that the distortion becomes more severe with increasing turbulence strength. Column 4 describes the cylindrical lens (C-Lens) detection results, where the white dashed lines follow the direction of dark stripes, and the OAM mode can be identified according to the number of dark stripes. After being demultiplexed and focused by the lens, the Gaussian-like beam profiles are presented at the center of light beam which are shown as Column 5. Column 6 shows the beam line profiles of the demultiplexed OAM_+2, OAM_+1, OAM_-1 and OAM_-2 in the longitudinal direction (follow the direction of green dotted lines in Column 5). From the normalized distribution of energy values, the demultiplexed beams present Gaussian-like distribution. These indicate that 4-channel OAM multiplexing is successfully implemented.
Fig. 4. Intensity profiles, C-lens detection results, restored Gaussian beams under turbulence with $\textrm{C}_\textrm{n}^\textrm{2}\textrm{ = 0}$, $\textrm{ 1} \times \textrm{1}{\textrm{0}^{\textrm{ - 14}}}$, $\textrm{1} \times \textrm{1}{\textrm{0}^{\textrm{ - 13}}}\textrm{ }{\textrm{m}^{\textrm{ - 2/3}}}$.
For investigating the power fading induced by the turbulence in OAM multiplexing communication, we measure the received powers of these 4 OAM modes under the 400 m turbulence with $\textrm{C}_\textrm n^2 = 1 \times {10^{ - 14}},1 \times {10^{ - 13}}{\textrm m^{ - 2/3}}$, and 600 m, 800 m turbulence with $\textrm{C}_n^2 = 1 \times {10^{ - 13}}{\textrm m^{ - 2/3}}$, as shown in Fig. 5. The horizontal axis represents the 40 samples that is captured under the influence of 40 computationally generated phase patterns with the same turbulence parameter. These received powers are sampled by switching different turbulence phase screens. From the figure, the magnitudes of power variation increase with the enhancement of turbulence strength or transmission length, which ranges from 0.73 dB to 0.88 dB and 2.40 dB to 2.66 dB corresponding to the 400 m turbulence with $\textrm{C}_n^2 = 1 \times {10^{ - 14}}{\textrm m^{ - 2/3}}$ and 800 m turbulence with $\textrm{C}_n^2 = 1 \times {10^{ - 13}}{\textrm m^{ - 2/3}}$, respectively. These show that severe power fading is induced by turbulence noise, which will eventually manifest as signal fading.
Fig. 5. Measured received powers of (a) OAM_+2, (b) OAM_-2, (c) OAM_+1, and (d) OAM_-1 under turbulence with $\textrm{C}_\textrm{n}^2 = 1 \times {10^{ - 14}},1 \times {10^{ - 13}}{\textrm m^{ - 2/3}}.$
By employing these 40 turbulence phase screens, we further measure the average values of signal- and noise powers corresponding to 4 OAM modes under 400 m turbulence with $\textrm{C}_n^2 = 1 \times {10^{ - 14}}{\textrm m^{ - 2/3}}$ and 800 m turbulence with $\textrm{C}_n^2 = 1 \times {10^{ - 13}}{\textrm m^{ - 2/3}}$ turbulence, as shown in Fig. 6. From the Fig. 6(a), the signal powers of OAM_+2, OAM_+1, OAM_-1 and OAM_-2 are -13.05 dBm, -12.86 dBm, -12.77 dBm and -13.13 dBm, respectively, and the corresponding noise powers coupled from other OAM modes are -29.43 dBm, -30.28 dBm, -30.43 dBm and -29.87 dBm, which is mainly caused by the phase front distortion of OAM beams. From the Fig. 6(b), compared with the case of 400 m turbulence with $\textrm{C}_n^2 = 1 \times {10^{ - 14}}{\textrm m^{ - 2/3}}$, the signal powers corresponding to 800 m turbulence with $\textrm{C}_n^2 = 1 \times {10^{ - 13}}{\textrm m^{ - 2/3}}$ decrease approximately 5 dB, which is mainly induced by the light beam drift and mode dispersion under the influence of a stronger turbulence noise [36].
Fig. 6. Measured signal- and noise powers corresponding to OAM_±1 and OAM_±2 under the (a) 400 m turbulence $\textrm{C}_n^2 = 1 \times {10^{ - 14}}{\textrm m^{ - 2/3}}$ and (b) 800 m turbulence $\textrm{C}_n^2 = 1 \times {10^{ - 13}}{\textrm m^{ - 2/3}}$.
Figure 7 presents the BERs of 4 OAM modes versus the received power under turbulence. With the transmission length of turbulence increasing from 400 m to 800 m, the communication sensitivity decreases by approximately 4 dB. Compared with the 400 m turbulence with $\textrm{C}_n^2 = 1 \times {10^{ - 14}}{\textrm m^{ - 2/3}}$, the communication sensitivity corresponding to the 400 m turbulence with $\textrm{C}_n^2 = 1 \times {10^{ - 13}}{\textrm m^{ - 2/3}}$ decreases by approximately 2 dB. These results show that the communication sensitivity will be degraded with increasing turbulence strength or transmission length, which is associated with power fading.
The outage probabilities of communication are further investigated, which are calculated by evaluating the BERs of sampled signals, as described in Fig. 8. The duration of a single BER calculation is about 5.8 seconds, and the average BER of 120 samples is employed for evaluating the outage probability of communication. Communication interruption is defined as the BER exceeding the threshold ($3.8 \times {10^{ - 3}}$) of hard decision forward error correction. From Fig. 8, the outage probabilities increase with the enhancement of turbulence strength or transmission length, which even reach 100% at the received power of -18 dBm. Based on the abovementioned analysis, communication interruption is caused by turbulence-induced signal fading. Therefore, the exploration to mitigate signal fading is crucial for promoting OAM multiplexing communication.
Fig. 7. BERs corresponding to (a) OAM_+2, (b) OAM_-2, (c) OAM_+1, and (d) OAM_-1 versus the received power under turbulence with $\textrm{C}_\textrm{n}^2 = 1 \times {10^{ - 14}},\textrm{ }1 \times {10^{ - 13}}{\textrm m^{ - 2/3}}$.
Fig. 8. Outage probabilities of communication versus the received powers corresponding to (a) OAM_+2, (b) OAM_-2, (c) OAM_+1, and (d) OAM_-1.
3.2 Signal fading mitigation with OAM mode diversity gain
To mitigate signal fading induced by turbulence, we investigate a mode diversity gain in OAM multiplexing communication. By assigning the conjugate OAM modes (OAM_±1 or OAM_±2) for diversity gain, the schematic diagram of 2-channel diversity gain and 2-channel multiplexing communication is illustrated in Fig. 9. As carried by different OAM modes that suffer from phase front distortion of varying degrees, the signals feature low channel correlation, which possess natural superiority for diversity gain.
Fig. 9. Schematic diagram of 2-channel diversity gain in 4-channel OAM multiplexing communication. Div.: diversity; MUX: multiplexing; AT: atmospheric turbulence; DEMUX: demultiplexing; Com.: combination.
The investigation of diversity gain combination technologies involving EGC and MRC are crucial for optimizing the receiving performance of OAM multiplexing communication and algorithm complexity. In OAM multiplexing communication, a power gap of 0∼4 dB among the multiplexed channels is universal due to the channel selective fading [5–7,30]. Hence, we choose the channel power gaps of 0 and 2 dB to investigate the diversity gain efficiencies of EGC and MRC, where the “2 dB” corresponds to one of the cases that a nonzero power gap exists in OAM multiplexed channels. There are 60 sampled signals are employed for performing the above investigation, where 15 groups samples (30 signals in total) have a power gap of 0 and the power gap of the other 15 groups samples is 2 dB. The BERs corresponding to the EGC and MRC with power gaps of 0 and 2 dB are illustrated in Fig. 10. From the figure, the gain efficiency of EGC is almost equivalent with MRC when the power gap among channels is 0, but it will get worse than MRC if the power gap is non-negligible (such as 2 dB). Actually, the gain efficiency decrease of EGC is caused by an inaccurate channel weight for gain combination, and MRC is an optimal diversity gain scheme for random channel power gap, which calculates the channel weight by searching the minimum EVM of signals, as described in Fig. 11. By calculating the EVMs of signals corresponding to the channel weight of channel 1 (channel 2) ranging from 0 to 100%, the optimal channel weight for 3-channel diversity gain will be searched. In addition, this scheme for calculating channel weight is also available for the 2-channel diversity gain after setting one of the channel weights (channel 1 or channel 2) as zero.
Fig. 10. Measured BERs after EGC and MRC corresponding to the channel power gaps of (a) 0 dB, and (b) 2 dB.
Fig. 11. EVMs corresponding to different channel weights after 2-channel and 3-channel diversity gain.
By employing the MRC scheme, we investigate 2-channel diversity and 2-channel in 4-channel OAM multiplexing communication under 600 m or 800 m turbulence with $\textrm{C}_n^2 = 1 \times {10^{ - 13}}{\textrm m^{ - 2/3}}$. The BERs and outage probabilities with and without diversity gain are described in Fig. 12. Under 600 m turbulence with $\textrm{C}_n^2 = 1 \times {10^{ - 13}}{\textrm m^{ - 2/3}}$, the optimal channel weights are 56% and 44% for the gain combination of OAM_+2 and OAM_-2, the communication sensitivity of which increases by approximately 3 dB, and the outage probability decreases from 22.5% to 0% and BER decreases form $2.02 \times \textrm{1}{\textrm{0}^{\textrm{ - 3}}}$ to $2.93 \times \textrm{1}{\textrm{0}^{\textrm{ - 4}}}$ at the received power of -14 dBm. Assign OAM_+2 and OAM_+1 for diversity gain, the corresponding BER decreases form $1.75 \times \textrm{1}{\textrm{0}^{\textrm{ - 3}}}$ to $2.60 \times \textrm{1}{\textrm{0}^{\textrm{ - 4}}}$ with channel weights of 42% and 58%, and the outage probability decreases from 18.33% to 0%. Therefore, the noise tolerance of 2-channel diversity gain system is sufficient for mitigating signal fading induced by 600 m turbulence with $\textrm{C}_n^2 = 1 \times {10^{ - 13}}{\textrm m^{ - 2/3}}$ or a weaker turbulence. Under the 800 m turbulence with $\textrm{C}_n^2 = 1 \times {10^{ - 13}}{\textrm m^{ - 2/3}}$, the communication sensitivity is also improved by approximately 4 dB, and the BER can reach $8.14 \times \textrm{1}{\textrm{0}^{\textrm{ - 4}}}$ at the received power of -14 dBm, but the BER is hard to reach the order of magnitude of $\textrm{1}{\textrm{0}^{\textrm{ - 5}}}$ even at the received power of -10 dBm, where the error floor nearly appears. In addition, the outage probabilities are about 10% and 7.5% corresponding to the diversity gain of OAM_+2 with OAM_-2 and OAM_+2 with OAM_+1, which exceeds the outage probability target of 5% [29], as illustrated in Figs. 12(c)-(d). These indicate that 2-channel OAM mode diversity gain scheme is cumbersome for mitigating the signal fading induced by 800 m turbulence with $\textrm{C}_n^2 = 1 \times {10^{ - 13}}{\textrm m^{ - 2/3}}$ or stronger turbulence.
Fig. 12. BERs and outage probabilities after the 2-channel diversity gain under (a), (c) 600 m and (b), (d) 800 m turbulence with $\textrm{C}_n^2 = 1 \times {10^{ - 13}}{\textrm m^{ - 2/3}}$.
To address the signal fading induced by 800 m turbulence with $\textrm{C}_n^2 = 1 \times {10^{ - 13}}{\textrm m^{ - 2/3}}$, 3 OAM modes are assigned for diversity gain. By introducing 2 wavelengths (1550 nm, 1551 nm) and 3 OAM modes (OAM_+2, OAM_-2, and OAM_+1), a 6-channel communication link is designed, where 2 wavelengths are assigned for multiplexing, and the corresponding schematic diagram is described in Fig. 13.
Fig. 13. Schematic diagram of 3-channel diversity (OAM mode) and 2-chanenl (wavelength) multiplexing communication with under 800 m turbulence with $\textrm{C}_n^2 = 1 \times {10^{ - 13}}{\textrm m^{ - 2/3}}$. Div.: diversity; MUX: multiplexing; AT: atmospheric turbulence; DEMUX: demultiplexing; Com.: combination.
Figure 14 shows the BERs and outage probabilities corresponding to 2-channel and 3-channel diversity gain in a 6-channel diversity and multiplexing communication under 800 m turbulence with $\textrm{C}_n^2 = 1 \times {10^{ - 13}}{\textrm m^{ - 2/3}}$. From the Fig. 14(a), the BER increases from $8.14 \times \textrm{1}{\textrm{0}^{\textrm{ - 4}}}$ to $1.4 \times \textrm{1}{\textrm{0}^{\textrm{ - 3}}}$ (-14 dBm) after introducing the physical dimension of wavelength, because the crosstalk induced by wavelength-dimension-multiplexing will decrease the system sensitivity. The outage probabilities after 2-channel diversity gain are 20.83% and 10% corresponding to the wavelength of 1551 nm and 1550 nm, which also increase compared with the case before introducing the wavelength-dimension-multiplexing. After 3-channel OAM mode diversity gain, the communication sensitivity is improved by approximately 6 dB, and the BERs decrease from $7.70 \times \textrm{1}{\textrm{0}^{\textrm{ - 3}}}\sim \textrm{1}\textrm{.41} \times \textrm{1}{\textrm{0}^{\textrm{ - 2}}}$ to $\textrm{1}\textrm{.3} \times \textrm{1}{\textrm{0}^{\textrm{ - 4}}}\mathrm{\sim }1.63 \times \textrm{1}{\textrm{0}^{\textrm{ - 4}}}$. The outage probabilities after 3-channel diversity gain reduces from 60%∼86.67% to 2.5%∼3.3%, which shows that the communication interruption is nearly suppressed.
Fig. 14. Measured (a) BERs and (b) outage probabilities after 2-channel diversity gain, and (c) BERs and (d) outage probabilities after 3-channel diversity gain under 800 m turbulence with $\textrm{C}_n^2 = 1 \times {10^{ - 13}}{\textrm m^{ - 2/3}}$.
We further investigate the EVM improvement of QPSK-OFDM signals after 2-channel and 3-channel diversity gain, as described in Fig. 15. Figures (c1)-(d1) and Figures (d2)-(e2) present the diversity gain combination of “OAM_+2, OAM_-2”, and “OAM_+2, OAM_-2, OAM_-1” corresponding to MRC and EGC, respectively. Besides, the EVM optimizations after 2-channel and 3-channel are calculated as about 10% and 16%, indicating 3-channel diversity possesses a better turbulence noise tolerance than 2-channel diversity in processing signal fading.
Fig. 15. Constellations of (a1)/(a2) OAM_+2, (b1)/(b2) OAM_-2, (c2) OAM_+1, (c1)-(d1) MRC and EGC of OAM_+2 and OAM_-2, and (d2)-(e2) MRC and EGC of OAM_+2, OAM_-2 and OAM_+1.
4. Discussion
A mode diversity gain strategy is proposed to address the signal fading induced by turbulence. Previous works employing OAM modes for transmitting or receiving diversity pay few attentions to calculate the optimal channel weight, which decreases the diversity gain efficiency because of an imprecise channel weight. To address this problem, we perform the gain combination offline in the digital domain, and the optimal channel weight is calculated by evaluating the EVM of the signal. Actually, this process for searching the optimal channel weight is similar with the decision-feedback-estimation, which will add the algorithm complexity for obtaining the target channel matrices. As the gain combination is offline performed after sampling the diversity signal disturbed by turbulence, this scheme for channel weight search is still available even though the atmospheric turbulence fluctuates randomly in real-time. Compared with optical diversity gain, signal synchronization can be conveniently implemented in the digital domain, which is crucial for diversity gain and may act as an auxiliary to capture the time delay for the gain combination in the optical domain. An optical fiber delay line can be introduced for synchronizing the diversity signal according to the calculated delay time, which will be addressed in our future work.
The tradeoff for multiplexing and diversity is also important for OAM multiplexing communication. For turbulence with varying strengths and transmission distances, assigning appropriate channel number for diversity can maintain a system performance of high quality as well as a large communication capacity density. In addition, multiplexing and diversity communication make the diversity gain compatible with the other MIMO algorithms, by which the signal fading and crosstalk will both be eliminated.
5. Conclusion
In summary, we have proposed a mode diversity gain strategy in OAM multiplexing communication to mitigate signal fading induced by turbulence, and investigated the gain combination and channel assignment technologies for improving the diversity gain efficiency and communication capacity. After 2-channel diversity gain, the BER (-14 dBm) of 12 Gbit/s QPSK-OFDM signals decreases from $2.02 \times \textrm{1}{\textrm{0}^{\textrm{ - 3}}}$ to $2.93 \times \textrm{1}{\textrm{0}^{\textrm{ - 4}}}$, and the outage probability of 22.5% is almost completely suppressed under the 600 m turbulence with $\textrm{C}_n^2 = 1 \times {10^{ - 13}}{\textrm m^{ - 2/3}}$. The gain combination technologies comprising MRC and EGC are experimentally demonstrated, which confirms that MRC finding the channel weight by evaluating the EVM of signals obtains an EVM of 0.43% smaller than that of EGC. To cope with the 800 m turbulence with $\textrm{C}_n^2 = 1 \times {10^{ - 13}}{\textrm m^{ - 2/3}}$, 3 OAM modes are assigned for diversity gain, of which the communication sensitivity is optimized by 3 dB compared with the 2 OAM modes diversity gain.
Funding
Shenzhen Peacock Plan Project (20180521645C, 20180921273B); China Postdoctoral Science Foundation (2020M682867); Shenzhen Excellent Scientific and Technological Innovative Talent Training Program (RCBS20200714114818094); Shenzhen Universities Stabilization Support Program (SZWD2021013); Shenzhen Fundamental Research Program (JCYJ20200109144001800, JCYJ20210324095610027, JCYJ20210324095611030); Basic and Applied Basic Research Foundation of Guangdong Province (2019A1515111153, 2020A1515011392, 2020A1515110572, 2021A1515011762); National Natural Science Foundation of China (12047539, 61805149, 62101334).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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