International Journal of Antennas and Propagation

Volume 2018, Article ID 8514705, 11 pages

https://doi.org/10.1155/2018/8514705

## Reduced-Complexity Receiver for Free-Space Optical Communication over Orbital Angular Momentum Partial-Pattern Modes

Department of Electronics and Electrical Communications Engineering (EECE), Cairo University, Cairo, Egypt

Correspondence should be addressed to Ahmed H. Mehana; gro.eeei@mahseha

Received 29 December 2017; Revised 10 April 2018; Accepted 15 April 2018; Published 22 May 2018

Academic Editor: Giancarlo C. Righini

Copyright © 2018 Alaa ElHelaly et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper explores the effect of a partial-pattern receiver for transmitted orbital angular momentum (OAM) multimodes included in the Laguerre-Gaussian beam propagating under non-Kolomogorov weak-to-moderate turbulence on the achievable capacity and the error rates with introduced controlled parameters. We deduce the necessary conditions for reducing the receiver’s area to guarantee that the modes are decoupled when the area is reduced. Furthermore, we derive the conditions at which area reduction yields a performance gain over the complete-area reception. For that, some use cases are introduced and discussed and the basic building block for multibeam MIMO receivers with a reduced area is developed and analyzed.

#### 1. Introduction

The vast majority of the research work exploring orbital angular momentum (OAM) as a mean of free-space optical (FSO) communication has been based on experimental demonstrations [1], turbulence modeling [2–4], MIMO implementations [5], detection enhancement [6], OAM generation [7, 8] and capacity derivations [3, 9]. Maximizing achievable rate by multiplexing vortex beams carrying gigabit streams is also done through space-time coding [10], vortex mode encoding [11, 12], multiple-beam processing [13] or LDPC coding [14].

However, the uniqueness of OAM has not been totally explored in terms of the distinction of the space pattern of each mode. Analogous to filters being deployed to suppress signal interference in both time and frequency domains, this paper introduces small steps in space filtering to decrease the modes interference in a multimode beam communication.

Starting with the reshaping of the basic area, we show that the receiving area can be reduced to special shapes that allow complete mode detection with minimum interference from adjacent modes. Some effort was done in this regard in [15–17] parallel to the presented work where proof of the partial-reception concept is verified. However, this was done through an experiment in only the angular direction while the analytical proof was not done in the presence of either noise or intermode interference.

The motivation behind this work is summarized as follows: First, using high-order modes enlarges the receiver size which is directly proportional to the square root of the OAM mode number [7, 18]; this constrains the maximum number of modes that can be used for a given receiver size. This suggests finding a way to reduce the receiver size upon reception. Second, the propagation of multiple modes in a turbulent medium causes intermode interference. The complexity of the optical devices, which are used to split the modes, grows proportional to the number of combined modes. This motivates spatially reshaping the receiver and finding a space-filtering rule to (1) reduce the receiver complexity and (2) to minimize the intermode power leakage. Finally, the simulation time (necessary for any design process) is also proportional to the receiver area; therefore, reducing the beam-matching area cuts down the simulation time while maintaining the same performance results.

To summarize, in this work, we derive the necessary conditions that guarantee the best distinction of the multiplexed OAM modes in a partial-pattern receiver (in both radial and angular directions). We answer the following questions: Is it possible to reduce the receiver area when detecting an OAM signal? What are the conditions that guarantee a similar performance (or better) compared to the full-area receiver? How are the main modes and the intermode leakage affected in the reduced-area receiver?

Our analysis along with Monte Carlo simulations shows that it is fairly possible to reduce the receiver area with either a controlled-performance penalty or performance gain. The system parameters that affect the receiving performance upon cutting the area are: the turbulence strength and the intermodal interference in single and multibeam operations. We also present use cases that exemplify the potential gain of the proposed partial-pattern receiver. Among these use cases, a simplified receiver is proposed with neither power splitting nor additional collimating devices.

The paper is organized as follows. Section 2 provides the communication model. Section 3 presents a partial-pattern receiving concept and derives operational rules. Section 4 derives the signal-to-interference plus noise power ratio for both full- and reduced-plane receivers and derives operational rules. Section 5 discusses cases of single- and multiple-beam-configuration uses. Section 6 combines multipartial patterns and proposes a novel simple-receiver structure. The conclusion is provided in Section 7.

#### 2. System Model

Consider a Laguerre-Gaussian (LG) beam carrying a single mode that has the parameters defined in [19, 20] with a zero-order Laguerre function carrying the OAM mode “” affected by the turbulence which has a model defined in [21]. Assume that the beam is carrying the data signal denoted by over this single mode “.” The noise-free-received waveform (denoted by ) for a single mode is written as

When this single beam carries multiple modes, the received signal is where we use , after dropping the time variable “” for simplicity. is the curvature radius and is the beam width at the transmitter, whereas at the receiver we have . is the Rayleigh range, is the Gouy phase, , and is the beam wavelength. is the symbol’s average energy for data carried on mode “” and is the power of mode “” (we assume all the modes have equal power). Using the above format, each mode’s power equals to unity . is the actual number of the utilized modes .

The exponential term represents the first-order Rytov approximation for the turbulence induced by the channel. It is generally a complex random variable that is approximated by the lognormal distribution in weak to moderate turbulence [2, 20]. The term represents the orbital momentum for mode “*m*” and this is the term that makes the waveforms for different mutually orthogonal [4, 18].

At the receiver side, the beam is power divided into branches, where is the actual number of used modes . Each branch is then matched with a one-beam mode [1, 22, 23]. Ideally, in a turbulence-free environment, only the target mode is received. However, in the presence of the turbulence, all the receiver mode branches output nonzero power; these outputs represent the leakage power from the target transmit mode to all other modes. The matching output power for the target mode relative to the leaked power from other modes is reduced as the turbulence strength increases. The channel estimation is performed by sending a pilot single-mode beam and correlating with [18] (for every mode *n*) followed by an integration process over the receiver area [4].

Let and be the shot and thermal noise with variances and , respectively, as described in [24]. Let and be the corresponding noise terms for the receiver branch “*.*” The output of the mode “” correlator for the transmit mode “” is

is the leaked power from the transmit mode *m* to mode *n*. The matrix with coefficients is the channel efficiency matrix as described in [4]. The overall received signal at branch denoted by () and the data estimation are, respectively, given by

The aggregate capacity of the multimode beam is hence given by [9]

A superscript “” is added to to indicate that we are using a multimode beam with “” number of modes.

#### 3. Receiver Pattern Area Reduction

We begin this section by briefly explaining the design process, and then we proceed with the detailed analysis.

In order to design the reduced-pattern receiver, we use (3) with modified integration limits to derive the output of matching the incident beam carrying mode “” with a partial pattern of mode “.” This output is then compared to the output of matching the same beam with a full pattern of mode “.” Evaluating the integration in (3) for the partial pattern is analytically intractable in its general form as will be shown.

Alternatively, we provide a bounding technique that allows for a simplified, yet accurate form for the matched filtering output range. This enables a direct comparison between the partial-pattern and the full-pattern matching receivers for both the desired () and undesired () modes.

We then proceed with the design rules for the reduced-area receiver as follows. We first deduce the necessary conditions in order to obtain the best performance when using a reduced matching area in the absence of the noise and the interference using the derived matching output bounds. This gives good insights of the system parameters and some of the key performance indicators. Finally, we deduce the necessary conditions in the presence of multimode interference and noise. We also provide use cases that show the performance gain and the complexity reduction in single and multibeam operations.

We have a wide range of options while choosing the partial pattern to analyze. Figure 1 shows seven different scenarios: half, quarter, section, and so on. We can even use a hybrid of configurations in a single matching irregular pattern. Our goal is to study how to reduce the receiver area while keeping a controlled impact on the end performance.