1. Comments

1.1 Comment 1

As illustrated in Fig. 1 of the manuscript [1], M transmit elements are evenly distributed on the transmit circle which is referred to as the uniform circular array (UCA). The authors said in the paragraph under the Fig. 1 that “with a serial-to-parallel conversion (S/P), the data stream is divided into M parallel data streams……Further, the substreams are fed into the corresponding OAM generators with different OAM modes formed in a concentric circle, which ensures that their axes of propagation coincide.” From the first half of this sentence and the UCA antenna structure, we think that each substream is associated with a specific OAM mode, and then is transmitted by a specific transmit element on the UCA. Thus, M transmit elements separately transmits M orthogonal OAM modes, achieving OAM multiplexing with the multiple radial antenna. This comprehension is identical to the authors’ presentation in Sec. 2.2, the sentence above Eq. (3), “Each signal is fed into the OAM mode generator at each transmit antenna.”, and the sentence below Eq. (3), “M transmit antennas with OAM generators are arranged in a circle. For simplicity, the mth circular array antenna is assumed to produce the OAM mode with $l_{m}=m$, where m = 1,2,3,…,M.” In this case, the centers of M optical vortices with the corresponding OAM modes are evenly distributed on the transmit circle. If we assume that the radius of the transmit radial laser array is $r_{t}$ , the center of the $m^{th}$ optical vortice is given by $(r_{t}cos\theta _{m},r_{t}sin\theta _{m})$ with $\theta _{m}$ being the azimuthal angle of the $m^{th}$ transmit laser. Obviously, the presented OAM multiplexing scheme by using the UCA structure cannot obtain the intensity profile of the concentric circle at the transmit plane. The optical axes of M optical vortices are parallel to each other and circularly symmetrical, but not coincide. So, we believe that the second half of the above-mentioned sentence (bold part) is not identical to the Fig. 1 and the authors’ presentation.

 

Fig. 1. Intensity profile of the considered system (a) UCA. (b) co-axial single aperture.

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Further, in Sec. 2.2, the authors used the Laguerre-Gaussian (LG) beam model to describe the optical vortices produced by the OAM generators. They assumed in the last sentence of the paragraph below Eq. (2) that “Without loss of generality, p is assumed to be 0 in this work.” Here p denotes the radial mode order of LG beam, and p+1 represents the number of the bright rings in the intensity profile of LG beam. The authors assumed p=0 and let the azimuthal mode order $l_{m}$ vary from 1 to M. This means that the produced optical vortices are the $TEM_{l_{m}0}$ modes, where $l_{m}=m ( m=1,2,3\cdots M )$. Since p=0, $TEM_{l_{m}0}$ has only one bright ring in its intensity profile. The small values of $l_{m}$ corresponds to the small radius of the bright ring, and vice versa. With the UCA structure, the intensity profile at the transmit plane should be shown in the following Fig. 1(a), but not the Fig. 1(b). In other words, to obtain Fig. 1(b), it requires a system that transmits multiple coaxially-propagating OAM modes through a single aperture, not the UCA structure.

1.2 Comment 2

Some concepts addressed in Fig. 1 of the manuscript [1] and the corresponding presentation are perplexing.

First, the authors explained the transmission process as “A signal stream at 1550 nm is generated and processed through a LDPC encoder firstly.” This implies that a digital data stream first modulates a 1550nm laser to produce an optical signal, and then this optical signal is sent into a LDPC encoder. To our knowledge, there do not exist the LDPC encoder that can directly process the optical signal. The LDPC encoder and decoder can only be implemented in the electrical domain, either through the FPGA hardware platform or by the software like C language. As for the LDPC-MIMO FSO system, please see [2] where illustrates that the LDPC encoder is at the front of the optical source and the LDPC decoder is at the output of the optical-to-electrical conversion.

Second, it is said that “The encoded data are then mapped to the phase shift keying (PSK) modulation formats.” According to this presentation, we think the transmission process should be described as following: the LDPC encoded data (digital electrical signal) modulates the phase of the optical carrier generated by a laser through an optical external modulator, like Mach-Zehnder Modulator (MZM), Electrical-Optical Modulator (EOM), or Fiber Modulator (FM). We plot this process in Fig. 2.

 

Fig. 2. Encoding and modulation process.

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As shown in Fig. 2, the output of the modulator is an optical signal. According to the Fig. 1 of the manuscript, this optical signal will be sent into a serial-to-parallel (S/P) converter, and then inserted by the pilot information (PI) for the channel estimation. The authors said: “Subsequently, with a serial-to-parallel conversion (S/P), the data stream is divided into M parallel data streams which are interpolated with the constant-amplitude pilot information (PI), respectively.” This implies the all-optical implementation of S/P converter and PI insertion.

Third, for a typical OAM multiplexing system, the first step in the reception process is to do the OAM demultiplexing [3–5]. Each of N receive apertures regardless of their arrangement (circular, rectangular, or linear) can receive M OAM modes, ${{\{l_{m}\}}_{m=1\cdots M}}$ . Then, for each receive branch, the OAM beams tends to the Gaussian beams, i.e., ${l_m} \to {l_0}$, by use of M optical devices (like spatial light modulator or spiral phase plate) with the inverse phase of M OAM generator. The second step is to do the heterodyne detection which uses the local oscillator and the photodetector to perform the optical-to-electrical conversion. The third step is to do the digital signal processing in the electrical domain, including demodulation, equalization, channel estimation and decisions. However, the authors explained the receiving process as “After transmission through the atmospheric turbulence simulated by several turbulence phase screens, the signals will be distorted and received by the N antennas placed in a circular array at the receiver, where the constant-amplitude pilot information is first extracted to obtain the CSI and the superposed signals are then sent to the equalizer which implements the ZF and MMSE algorithms to discard the interference from other signals. Finally, after a parallel-to serial conversation (P/S), the desired signals will be retrieved by further signal processing including demodulation and LDPC decoding” They do not show the details of how the OAM demultiplexing and optical-to-electrical conversion are performed. It is essential for the analysis of the performance of the receiver. In addition, all the reception process plotted in Fig. 1 seems to be done in the electrical domain. However, the PI removing, P/S converter, and demodulator are the reverse process of the PI insertion, S/P converter, and modulator which are performed in the optical domain at the transmit end. We think the authors should give more details about the reception process.

1.3 Comment 3

In Sec. 2.2, the authors presented “Each signal is fed into the OAM mode generator at each transmit antenna and the transmitted signal of the $m^{th}$ transmit antenna at time t can be represented as

We think there are three problems with Eq. (1) (i.e., Eq. (3) of the manuscript). First, according to our comment 1, the center of each LG beam should be $(r_{t}cos\theta _{m},r_{t}sin\theta _{m})$ , not $(0,0)$. So, $A_{m}(r,z)$ in Eq. (1) should be rewritten as $A_{m}(x-r_{t}cos\theta _{m},y-r_{t}sin\theta _{m},z)$ with $\theta _{m}=l_{m}\theta$ . Second, Eq. (1) is the transmitted optical field at the distance $z=0$ . So $z=0$ should be reflected in Eq. (1). Third, $x_{m}(t)$ is the MPSK signal which modulates the phase of the optical carrier. It should appear inside the exponential function. Now it directly multiplies with the amplitude of the optical field $A_{m}(r,z)$ which seems that the authors perform the amplitude shifting keying (ASK) modulation. Further, the authors do the channel state information estimation symbol-by-symbol. In this case, the channel is assumed to be unchanged during one symbol, and thus t can be omitted in $x_{m}(t)$ . The same problems exist in Eq. (4) of the manuscript.

1.4 Comment 4

Also in Sec. 2.2, the authors presented “After the LG beam propagates through the atmospheric turbulence, the sampled signal at $n^{th}$ receive antenna in the receiver end, where $1\leq n\leq N$ , can be given by

According to the scalar diffraction theory, the optical field at the arbitrary location $(r,\theta _{n},z)$ of the observation plane after propagating through free space or atmospheric turbulence should be obtained by using the Huygens-Fresnel integral [6]. Specifically, the optical field of at the arbitrary location $(r,\theta _{n},z)$ of the observation plane is equal to the convolution of the decentered $m^{th}$ LG beam at the source plane $A_{m}(x-r_{t}\cos m\theta ,y-r_{t}\sin m\theta ,0)exp(im\theta )$ and the Fresnel impulse response $h\left ({x,y}\right )=\frac {{{e^{jkz}}}}{{j\lambda z}}\exp \left [{ \frac {{jk}}{{2z}}\left ({{x^2}+{y^2}} \right )}\right ]$. It is not clear that whether Eq. (2) corresponding to the Eq. (6) of the manuscript is derived from the Huygens-Fresnel integral or not. If they do not use the Huygens-Fresnel integral, they should give the convincing derivation process. Additionally, the phase distortion induced by atmospheric turbulence is related to the radial distance $r$ as well as the propagation distance $z$. So, it is better to express it as $\psi (r,z)$. As mentioned before, the accurate form of Eq. (2) with Huygens-Fresnel integral should be written as

1.5 Comment 5

We cast doubt on the accuracy of Eq. (4), i.e., Eq. (7) of the manuscript “

As we discussed in Comment 2, the authors did not give the details of the receiver. Did they perform the heterodyne detection? Does Eq. (4) denote an optical signal or an electrical signal? Commonly, the noise induced in the optical-to-electrical conversion process can be model by the AWGN. It includes the thermal noise produced by the receive circuit at the output of the optical detector, the shot noise and dark current noise created by the optical detector (then convert to the electrical noise with the optical-electrical conversion). In other words, AWGN is usually used to model the electrical noise. However, the first term on the right side of Eq. (4) is the receiving optical field at the nth receive aperture, while the second term is an AWGN $w_{n}$ . An reasonable explanation can be that $w_{n}$ is an optical noise. In this context, the authors should give the details how they get Eq. (4) and some reference which use the AWGN to model the optical noise in their considered reception process.

1.6 Comment 6

As discussed in Comment 4, we think the channel gain expressed in Eq. (8) of the manuscript does not follow the scalar diffraction theory.

1.7 Comment 7

The authors applied the LS algorithm to realize the channel estimation. To our best of knowledge, this can only be achieved in the electrical domain. However, in Eq. (14), they show that they estimate the term $A_{m}(r,z)exp(il_{m}\theta )$ which is an optical field. We think the authors should explain how they complete such an CSI estimation.

1.8 Comment 8

In Sec. 3. Para 1, the authors presented “this OAM system is equipped with four transmit and receive antennas formed in a circle.” However, for Fig. 4, they said “when the SNR is equal to 24 dB, in this system with four, five and six receive antennas.” These descriptions should be identical.