Investigation on repetition-coding and space-time-block-coding for indoor optical wireless communications employing beam shaping based on orbital angular momentum modes

Jianghao Li; Jianghao Li; Qi Yang; Qi Yang; Xiaoxiao Dai; Christina Lim; Ampalavanapillai Nirmalathas

doi:10.1364/OE.458691

1. Introduction

With emerging intelligent services and applications such as virtual reality (VR), augmented reality (AR), and remote tele-surgery technology, demand for high bandwidth wireless communications in indoor settings is expected to grow significantly [1–3]. Normally, networks and communications for such services and applications will require high-speed, ultra-wideband and low latency wireless connections. Furthermore, these demands will cause significant pressure on spectrum resources of radio frequency (RF) based wireless communication technologies such as Wi-Fi and millimeter-wave communications [4]. Optical wireless communications (OWC) have been evaluated as a promising technology to support ultra-high-speed and data intensive wireless connections and networks for indoor applications in the foreseeable future due to its unique advantages such as scalable unregulated bandwidth, high security and flexible networking solutions [1]. In addition, due to inherent immunity against RF interference of the transmitted optical signals, OWC systems can provide stable connections in the environment with strong RF interference [5].

Currently, the most popular realization of OWC with high-speed data rate is based on the line-of-sight (LOS) link with Gaussian-shaped profile laser beams. Such beams increase the susceptibility to performance degradation as users move away from the beam center as a result of the non-uniform received signal power within the cell that highly limits the system coverage [6]. To tackle this limitation while satisfying the regulations of laser safety simultaneously, many optical beam shaping techniques including field mapping technique using refractive and diffractive optical components [7,8] and fiber device-based beam shaping technique using long period grating (LPG) [9] and few-mode fiber Bragg gratings (FM-FBGs) [10] have been proposed and investigated. However, these methods have seldom been employed in practical OWC systems due to their inherent limitations such as low compactness, high power consumption, low flexibility and incompatibility with OWC systems. Recently, we have experimentally demonstrated and reported a novel OWC system employing few-mode based beam shaping [6,11]. However, the main drawback of indoor OWC system with the proposed few-mode based beam shaping is the performance degradation caused by inter-symbol interference (ISI) which is induced by the multipath effect [12] within different spatial modes during the transmission along the few-mode fiber (FMF). Despite the incorporation of least-mean square (LMS) based adaptive equalization for the system with few-mode based beam shaping [11] to overcome the issue, the computational and training requirements rise sharply when the transmission data rate increases [13,14]. In addition, when the channel condition changes, the equalizers need to be re-trained which is not suitable for low-latency communication networks.

In this paper, we propose a novel beam shaping based on orbital angular momentum (OAM) modes [15] for indoor OWC system for the first time, which is more attractive compared to the other beam shaping techniques because of its simpler implementation and high flexibility and reconfigurability. Most of all, as different OAM modes can be generated in free-space, the multipath induced ISI can be suppressed effectively in the system. Though the performance degradation caused by non-uniform received power can be alleviated by superposing different OAM modes with a multiple-input-single-output (MISO) configuration, the non-uniform power distribution of every single OAM mode still limits the overall system performance. Repetition coding (RC) and Alamouti-type orthogonal space-time-block-coding (STBC) schemes have been investigated and widely used in the OWC systems with multiple-input-multiple-output (MIMO) or MISO configurations to mitigate the performance fading due to channel blockages and instabilities [16 19]. Results show that the STBC scheme can provide diversity gain and resistance to channel fading compared to RC scheme in conventional RF based wireless communication systems and coherent OWC systems with both heterodyne and homodyne links. However, this is reversed in intensity modulation/direct detection (IM/DD) based OWC systems. Nevertheless, for practical indoor OWC scenarios, neither the coherent system nor IM/DD based system is the optimal choice. Coherent OWC systems are rarely implemented in indoor OWC systems due to the high cost and complexity, low compactness and limited mobility whilst IM/DD based OWC systems are mainly restricted due to the limited transmission data rate as the intensity modulation format only uses one dimension of modulation. In this paper, we adopt self-coherent OWC system with Kramers-Kronig (K-K) receiver which is preferred over coherent and IM/DD systems due to its ability to recover the optical field using direct detection with a single photodetector (PD) [20]. However, the performance of transmitter diversity techniques including both RC and STBC schemes has never been investigated in self-coherent systems. In addition, in IM/DD OWC system, the authors assume that transmitter apertures are located far enough so that the channels can be considered as independent with each other and are distinguishable by the detector [17]. However, when employing OAM mode-based beam shaping for OWC system, the transmitters need to be located as closely as possible to create the output beam with desired power distribution. Therefore, it is necessary to further investigate transmitter diversity technologies, including both RC and STBC schemes for indoor OWC systems employing OAM mode-based beam shaping with K-K receivers.

In this paper, we investigate two spatial diversity techniques including RC and Alamouti-type orthogonal STBC for indoor optical wireless communications employing OAM mode-based beam shaping for the first time, to the best of our knowledge. The simulation of an indoor OWC system incorporating single-sideband (SSB) 16 quadrature amplitude modulation (16-QAM) modulated signals employing OAM mode-based beam shaping is carried out with RC and STBC schemes, respectively. The performance of the two diversity schemes is systematically analyzed and compared under different beam shaping schemes with varying power ratios of different modes. It is shown that both RC and STBC can improve the system performance and effective coverage and RC outperforms STBC in all the beam shaping schemes. Moreover, to further understand the impact of the signal delays on the performance of RC and STBC schemes, the system tolerance of the two schemes to signal delays is also investigated. Our numerical results show that higher tolerance to delay interval can be achieved in STBC schemes and the advantage of STBC is more obvious when we use OAM₀ and OAM₁ based beam shaping technique.

2. Principle

The schematic block diagrams of RC and STBC schemes based 2 × 1 MISO indoor OWC systems are shown in Fig. 1, in which the SSB 16-QAM modulation is employed in both cases. In these systems, the input signals are first coded with RC or STBC format, and then the resulting signals are used to drive two respective modulators to generate the optical signals. Two transmitters (shown as Tx₁ and Tx₂) are employed to launch the modulated optical signals for free-space transmission. For RC scheme, identical signals are sent from both transmitters in each symbol interval T_i (i = 1, 2), as shown in Fig. 1(a). Assume the two channels are synchronized without any delays, the received signals at T₁ and T₂ can be expressed as [19]

(1)$${r_1} = {h_1}{S_1} + {h_2}{S_1} + {n_1},$$

(2)$${r_2} = {h_1}{S_2} + {h_2}{S_2} + {n_2},$$

respectively, where h₁ and h₂ represent channel gains of different OAM modes and n₁ and n₂ represent the additive white Gaussian noise (AWGN) which is mainly induced from the background light and the thermal and quantum noise from the PDs.

Fig. 1. The schematic block diagrams of (a) RC and (b) STBC schemes for 2 × 1 MISO indoor OWC system.

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At the receiver, the optical signals are detected by a PD with square law detection. Here we adopt K-K receiver to recover both the amplitude and phase information of the received signals. For the RC scheme, the received carriers at T₁ and T₂ can be written as

(3)$${C_{r1}} = |{{h_1}{C_1}} |+ |{{h_2}{C_1}} |+ {n_1},$$

(4)$${C_{r2}} = |{{h_1}{C_2}} |+ |{{h_2}{C_2}} |+ {n_2},$$

respectively, where C₁ and C₂ denotes the transmitted carrier from Tx₁ and Tx₂ during T₁ and T₂, respectively. Therefore, the converted photocurrent at T₁ and T₂ can be illustrated as

(5)$${I_1} = {|{{r_1} + {C_{r1}}} |^2} = r_1^2 + C_{r1}^2 + {C_{r1}}r_1^\ast{\times} {e ^{i({{\omega_{c1}} - {\omega_{s1}}} )t}} + C_{r1}^\ast {r_1} \times {e ^{i({{\omega_{s1}} - {\omega_{c1}}} )t}},$$

(6)$${I_2} = {|{{r_2} + {C_{r2}}} |^2} = r_2^2 + C_{r2}^2 + {C_{r2}}r_2^\ast{\times} {e ^{i({{\omega_{c2}} - {\omega_{s2}}} )t}} + C_{r2}^\ast {r_2} \times {e ^{i({{\omega_{s2}} - {\omega_{c2}}} )t}},$$

respectively, where ω_c₁ and ω_c₂ denotes the frequency of the carrier transmitted from Tx₁ and Tx₂ respectively and ω_s₁ and ω_s₂ represents the center frequency of the modulated signals at T₁ and T₂ respectively. When employing matched filter at the receiver, the third terms in Eqs. (5) and (6) can be filtered and therefore Eqs. (5) and (6) can be rewritten as:

(7)$${I_1} = r_1^2 + C_{r1}^2 + C_{r1}^\ast {r_1} \times {e^{i({{\omega_{s1}} - {\omega_{c1}}} )t}},$$

(8)$${I_2} = r_2^2 + C_{r2}^2 + C_{r2}^\ast {r_2} \times {e^{i({{\omega_{s2}} - {\omega_{c2}}} )t}},$$

By employing K-K relationship under minimum-phase condition, the intensity and phase information of the converted electrical signals at T₁ and T₂ could be expressed as [21]

(9)$${A_i}(t )= \left[ {\sqrt {{I_i}} \exp ({i{\phi_i}} )- {C_{ri}}} \right]{e^{j\pi Bt}},$$

(10)$${\phi _i}(t )= H[{\log {I_i}(t )} ],$$

where i = 1 or 2. B denotes the signal bandwidth and H is Hilbert transform function. Finally, the BER of the recovered RC signals is performed subject to hard decision.

Assume that the two optical wireless channel gains h₁ and h₂ are known at the receiver, the conditional BER for RC can be expressed as

(11)$${P_{ e |{h}}} = Q\left( {\sqrt {SNR} } \right),$$

where Q(x) is defined as

(12)$$Q(x )= \frac{1}{{\sqrt {2\pi } }}\int_x^\infty {{e^{ - \frac{{{y^2}}}{2}}}dy} ,$$

or

(13)$$Q(x )= \frac{1}{\pi }\int_0^{\frac{\pi }{2}} {{e^{ - \frac{{{x^2}}}{{2{{\sin }^2}\theta }}}}d\theta } .$$

The signal-to-noise ratio (SNR) at the receiver for the RC scheme can be expressed as

(14)$$SN{R_{RC}} = \frac{{{{\left( {\sum\nolimits_1^2 {{I_i}} } \right)}^2}}}{{\sigma _{th}^2 + \sigma _q^2 + 2q{I_b}}},$$

where I_b denotes the average photocurrent generated by the background light and q is the charge of an electron. $\sigma _{th}^2$ and $\sigma _q^2$ represent the variance of the thermal and quantum noise, respectively.

For STBC scheme, S₁ is transmitted from Tx1 and S₂ is transmitted from Tx2 during the first bit interval T₁, and $\textrm{ - }S_2^{\ast }$ is transmitted from Tx1 and $S_1^{\ast }$ is transmitted from Tx2 during the second symbol interval T₂, as shown in Fig. 1(b), where S* represents the conjugation of S. If the two channels are well synchronized in the STBC scheme, the received signals at T₁ and T₂ can be expressed as

(15)$${r_1} = {h_1}{S_1} + {h_2}{S_2} + {n_1},$$

(16)$${r_2} = \textrm{ - }{h_1}S_2^{\ast } + {h_2}S_1^{\ast } + {n_2}.$$

Similarly, the received carriers at T₁ and T₂ can be written as

(17)$${C_{r1}} = |{{h_1}{C_1}} |+ |{{h_2}{C_2}} |+ {n_1},$$

(18)$${C_{r2}} = |{{h_1}{C_2}} |+ |{{h_2}{C_1}} |+ {n_2},$$

The converted photocurrent and the intensity and phase information of the converted electrical signals with STBC scheme at T₁ and T₂ can be obtained by using the same principle and method as deciphered for the RC scheme. Finally, unlike the hard decision decoding method employed in the RC scheme, the recovered STBC signals are decoded using maximum likelihood (ML) decision. In this case, the estimated signals at T₁ and T₂ can be expressed as

(19)$${\hat{S}_1} = \arg \min \left( {{{\left| {{h_1}} \right|}^2} + {{\left| {{h_2}} \right|}^2} - 1} \right){\left| {{{\hat{S}}_1}} \right|^2} + {d^2}\left( {{{\tilde{S}}_1},{{\hat{S}}_1}} \right),$$

(20)$${\hat{S}_2} = \arg \min \left( {{{\left| {{h_1}} \right|}^2} + {{\left| {{h_2}} \right|}^2} - 1} \right){\left| {{{\hat{S}}_2}} \right|^2} + {d^2}\left( {{{\tilde{S}}_2},{{\hat{S}}_2}} \right),$$

respectively, where S represents the 16-QAM alphabet and ${d^2}({a - b} )= {|{a - b} |^2}$. $\mathop {{S_1}}\limits^\mathrm{\sim }$ and $\mathop {{S_2}}\limits^\mathrm{\sim }$ are expressed as

(21)$$\mathop {{S_1}}\limits^\mathrm{\sim } \textrm{ = }h_1^{\ast }{r_1}\textrm{ + }{h_2}r_2^\ast{=} ({{{|{{h_1}} |}^2} + {{|{{h_2}} |}^2}} ){S_1} + h_1^{\ast }{n_1} + {h_2}n_2^\ast ,$$

(22)$$\mathop {{S_2}}\limits^\mathrm{\sim } \textrm{ = }h_2^{\ast }{r_1} - {h_1}r_2^\ast{=} ({{{|{{h_1}} |}^2} + {{|{{h_2}} |}^2}} ){S_2} + h_2^{\ast }{n_1} + {h_1}n_2^\ast ,$$

The received SNR for STBC scheme can be written as

(23)$$SN{R_{STBC}} = \frac{{\sum\nolimits_1^2 {I_i^2} }}{{\sigma _{th}^2 + \sigma _q^2 + 2q{I_b}}},$$

Similarly, the conditional BER of STBC can be also obtained by substituting Eq. (23) into Eq. (11).

3. Simulation setup

The simulation setup of RC and STBC for indoor OWC employing OAM mode-based beam shaping is illustrated in Fig. 2. Here, the proof-of-concept of the proposed schemes are conducted via numerical simulations to overcome the device limitations for the generation and conversion of different OAM modes. RC and STBC encoded SSB 16-QAM signals are generated offline and sent to an arbitrary waveform generator (AWG) to drive two respect in-phase/quadrature (IQ) modulators (MODs) to modulate two external cavity lasers (ECLs) with wavelengths of 1549 nm and 1551 nm, respectively to provide incoherent addition of powers between different transmitted beams. The carrier-to-signal power ratio (CSPR) of the SSB signals is set as 6dB and the carrier is inserted at the lower frequency domain of the modulated signals. The sample rate of the AWG is set as 2.5 GSa/s, and the pattern length of the generated pseudo-random binary sequence (PRBS) is set as 2¹⁵-1. Two erbium-doped fiber amplifiers (EDFAs) are employed to compensate the power loss during the optical signal modulation. Next, the amplified optical signals are collimated by fiber collimators (COLs) for free-space transmission with one of them passing a combination of a polarizer (POL), a quarter-wave plate (QWP) and q-plate (QP) for the conversion to higher-order OAM mode (OAM_l with topological charge l = 1 or 2, shown as Fig. 2(a)). Next, the fundamental mode (OAM₀, shown as Fig. 2(b)) and the higher-order OAM mode are superposed concentrically by employing a 50:50 beam splitter (BS) followed by an optical lens (OL) to increase the beam size. The superposed beam is illustrated as Fig. 2(c). We define the power ratio of different OAM mode as R, which can be expressed as

(24)$$R = \frac{{{P_0}}}{{{P_l}}},$$

where P₀ and P_l are the transmitted power of OAM₀ and OAM_l mode respectively. In the simulation, we set the diameter of the superposed beam at the distance of 2m away from the transmitting OL as 50cm. It is noted that the total output power of the superposed beam is limited at 6dBm for the consideration of practical laser safety issue [22].

Fig. 2. Simulation setup for RC and STBC for indoor OWC employing OAM mode based beam shaping. Insert: intensity profile of (a) OAM_l, (b) OAM₀, and (c) superposed beam of OAM₀ and OAM

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After free-space transmission, another QP with opposite topological charge sign (-l) is employed to convert the received OAM_l mode into a circularly-polarized OAM₀ mode. Next, the received optical signals are coupled into the FMF using another OL with the same size as the QP to avoid redundant OAM₀ mode being coupled into the FMF. Here we use FMF to improve the coupling efficiency as it has a larger numerical aperture compared with single mode fiber. Here we model the coupling efficiency as [23]

(25)$$\eta = \frac{{m + 1}}{{2\pi }}{\cos ^m}(\theta ),$$

where θ depicts the divergence angle of the transmitted beam and m denotes the Lambert’s mode number which can be written as [23]

(26)$$m = \frac{{ - \ln 2}}{{\ln ({\cos {\Theta _{1/2}}} )}},$$

where Θ_1/2 indicates the semi-angle at half power of the transmitted beam. The output signal of the FMF is converted into photocurrent by a PD. AWGN is added to both the carrier and the modulated signals to emulate different optical signal-to-noise ratios (OSNRs). In the following step, the converted electrical signals are fed into the digital storage oscilloscope (DSO) for offline signal processing (DSP) which mainly consists of up-sampling (4 samples per symbol), K-K relation calculation and down sampling (2 samples per symbol). Finally, BER calculation is performed subject to hard and ML decision for RC and STBC scheme respectively.

4. Results and discussion

We compare the BER performance of the OWC systems employing OAM mode-based beam shaping with RC and STBC schemes and received single OAM₀ and OAM_l(l = 1, 2) mode at different distance (d) away from the beam center which is illustrated in Fig. 3(a) and (b), respectively. In the simulation, the power ratios of OAM₀/OAM₁ and OAM₀/OAM₂ are set as 0.64 and 0.34, respectively. It can be seen that both RC and STBC schemes improve the system performance compared to single OAM₀ and OAM_l channel and RC outperforms STBC at different distances away from the beam center for both cases (OAM₀ with OAM₁ and OAM₀ with OAM₂ based beam shaping schemes). This is due to the fact that RC can provide linear addition of channel gains of both OAM₀ and OAM_l modes to the system while STBC mainly provides selective channel gain of different modes because of the ML decision employed in STBC. To clarify, when the distance is less than 4cm, the OAM₀ channel dominates the performance resulting in STBC scheme producing similar performance as that in OAM₀ channel while when the distance exceeds 12cm, the performance of STBC scheme is dominated by the higher-order OAM mode since the power of OAM₀ mode is relatively weak in this region. In addition, compared to STBC, the advantage of RC performs the most obviously when the channel condition of OAM₀ and higher-order OAM mode is similar with each other in the both OAM mode-based beam shaping schemes. This result can be attributed to the reason that the ML decision is not able to correctly distinguish the transmitters when the channel gains and transmitted power distribution are identical, which results in decoding errors in STBC scheme. In order to evaluate the effective coverage of the OWC system employing OAM mode-based beam shaping with RC and STBC schemes, we set the reference BER level as 7% hard-decision forward error correction (HD-FEC) threshold (3.8×10⁻³). It can be seen that larger effective coverage can be obtained when using RC scheme in both OAM₀ with OAM₁ and OAM₀ with OAM₂ based beam shaping schemes and the advantage of RC is more obvious in OAM₀ with OAM₂ based beam shaping scheme.

Fig. 3. BER performance comparison of the OWC system employing OAM mode-based beam shaping with RC and STBC schemes and single OAM channels for power ratios of (a) OAM₀/OAM₁= 0.64 and (b) OAM₀/OAM₂= 0.34.

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The BER performance of RC and STBC schemes for different power ratios of OAM₀/OAM₁ and OAM₀/OAM₂ are shown in Fig. 4(a) and 4(b) respectively. For both OAM₀ with OAM₁ and OAM₀ with OAM₂ based beam shaping schemes, it can be seen that RC outperforms STBC regardless of the power ratios between OAM₀ and higher-order OAM modes. Furthermore, it can also be seen that the position where the maximum performance difference between RC and STBC occurs moves further away from the beam center when the power ratio increases due to the higher relative power of OAM₀ mode.

Fig. 4. BER performance of RC and STBC schemes for different power ratios of (a) OAM₀/OAM₁ and (b) OAM₀/OAM₂.

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The performance mentioned above is investigated under the assumption that the two transmission channels are synchronized without any delays. However, the use of OAM mode-based beam shaping requires QPs for mode conversion in both transmitters and receivers. This in turn introduces inevitable time delays between the two transmitted modes, violating this assumption. In order to investigate impact of time delays on the system performance, we present the BER performance of the received signals under both diversity schemes plotted as a function of the delay interval which is shown in Fig. 5(a). For fair comparison between RC and STBC schemes, in the simulation, we set the power ratio of OAM₀/0AM₁ and OAM₀/OAM₂ as 0.64 and 0.5, respectively and the receiver is located at 1cm away from the beam center. This will lead a similar BER performance for RC and STBC. We only investigated the case when the delay interval is less than one symbol as more than one symbol delay interval can be easily tracked with channel training [20]. Also shown are the constellations of the recovered signals of RC and STBC schemes employing OAM₀ with OAM₁ and OAM₀ with OAM₂ based beam shaping techniques as illustrated in Fig. 5(b) when the delay interval is 0.2 symbols. From both BER curves and the constellation diagrams, we can conclude that STBC scheme provides better tolerance to delay interval compared to RC because of the orthogonality characteristic of the transmitted STBC signals. Furthermore, we observe that less advantage of the tolerance to delay interval can be obtained in OAM₀ with OAM₂ based beam shaping scheme. This is because more power of OAM₂ mode is concentrated on the boundary of the mode field. As the receiver is located at the beam center, the interference of the time delays induced by the OAM₂ mode is relatively weaker compared with the case in OAM₀ with OAM₁ based beam shaping.

Fig. 5. (a) BER performance versus delay interval. (b) Constellations of received signals when the delay interval is 0.2 symbols.

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5. Conclusions

In conclusion, we have proposed a novel beam shaping technique based on OAM modes for OWC system. Furthermore, we have theoretically analyzed and numerically simulated a 10 Gb/s OWC system employing the new beam shaping technique integrating RC and Alamouti-type orthogonal STBC schemes. Results show that both RC and STBC can improve the system performance and effective coverage. In addition, it is also shown that RC scheme can provide more improvement on the BER performance under different beam shaping schemes with different power ratios between the fundamental and higher-order OAM modes, while STBC has higher robustness to the delay intervals between different modes especially when using OAM₀ and OAM₁ based beam shaping technique.

Funding

Australian Research Council (ARC) under Discovery Project (DP170100268).

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.

References

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Investigation on repetition-coding and space-time-block-coding for indoor optical wireless communications employing beam shaping based on orbital angular momentum modes

Abstract

1. Introduction

2. Principle

3. Simulation setup

4. Results and discussion

5. Conclusions

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (5)

Equations (26)

Optics Express

Xiaoxiao Dai	https://orcid.org/0000-0003-3408-7493
Ampalavanapillai Nirmalathas	https://orcid.org/0000-0001-7328-5359