Study of Optical MIMO Transmission Systems Using the MGDM Multiplexing Technique

In current local area networks, multimode fibers (MMFs), mainly graded index (GI) MMFs, are the main types of fibers used for data communications. Because of their high bandwidth, they are considered the main method of transmission that allows to offer multiservice broadband services using optical multiplexing techniques. The MGDM (ModeGroup Division Multiplexing) is a Multiplexing technique, which aims to improve the performance of the multimode optical fiber by spatially multiplexing the data streams to be transmitted. In this work, we study optical MIMO (multi-input multi-output) transmission systems on an MMF optical fiber, specifically the adaptation of the architecture of MIMO transmission systems. In this context, we have studied the mode group multiplexing technique (MDGM), to evaluate the transmission capacity. In fact, the latter depends on the injection conditions and the state of the optical fiber.


Introduction
Multimode fiber (MMF), is a very interesting method of transmission due to its low cost compared to single mode fiber (SMF), in indoor broadband networks (Koonen, 2006).
The main objectives are the optimization of these networks for the transport of a particular set of services (voice telephony, Internet, etc.) to the end user and the integration of new broadband services.Because of its broad bandwidth, MMF is the only medium capable of offering a multi-service broadband in office and indoor networks, using multiplexing techniques.To simultaneously transport different types of services (having different bandwidths, specific signal formats, various requirements in terms of quality of service (QoS)), such multiplexing technique must respect a high efficiency/cost ratio.
In the following we will focus on the mode group diversity multiplexing (MGDM) technique, which is a developed version of a wireless transmission chain known as the BLAST (Basic Local Alignment Search Tool) (Kuchta et al., 2004).
The MGDM multiplexing technique is based on the spatial detection and launching of subgroups to create a number of independent communication channels on a single MMF fiber, which increases the transmission capacity (Baklouti and Attia, 2013).
In principle, the MGDM technique is similar to the MIMO (multiple input -multiple output) system in radio communications.Where, (*) is the conjugate transpose, M is the number of modes of the MMF fiber and B is the bandwidth of the fiber.

Excitation Condition in the MGDM System
For an MGDM system, the incident field at the input side of the optical fiber is considered a Gaussian characterized by three parameters that determine the state of excitation of MMF, these parameters are (Raddatz et al., 1998) : Radial offset (F) Spot size (w) angular offset (θ) These parameters affect the capacity and transmission quality in the fiber by MGDM.In the following we study the choice of these parameters.

The Choice of Radial Offset (F) and Spot Size (w)
The distribution of the intensity of the luminous flux at the output of the fiber depends on the number of modes excited at the entrance of the fiber.
So the relation between radial offset F and spot size w is expressed as follows (Calzavara et al., 1984.): And the choice of the radial offset is related to the optimization of the injection conditions in order to minimize the interferences between the channels

The Choice of Angular Offset
It is possible to reduce the crosstalk between the channels by introducing the injection of the luminous flux with an angular offset compatible with the launching of helical rays.For a helical radius, there exists a unique angle (θ) as a result for each radial offset (F), the relation between θ and F is given by (Calzavara et al., 1984.): Where," a" is the diameter of the optical fiber, n is the refractive index.

Simulation of the Capacity of the MGDM System4.1 Transmission Capacity
Figure 4 shows the effect of transmission and reception conditions on the change of the capacity of the system.As shown in the figure, the capacity of the (2 × 2) system is significantly reduced compared to (3 × 3) channels, (reduced by22 bits/s/Hz at 17 bits/sec/Hz for SNR = 30 dB).The transmission conditions of the MGDM channels depend on the excitation conditions F, w and θ. mas.ccsenet

Simula
In this par d = 62.5μm optical sig  We simulated the transmission system (2 * 2) MGDM by setting the injection parameters (offset, spot size and angular offset), and by changing the length of the optical fiber.
We have drawn the eye diagram for a length L = 100m and we found a good opening (Figure 5), for the length L2 = 400m, we have a fairly open eye (Figure 6), then for the length L3 = 4Km we found a bad opening (Figure 7).

Conclusion
In this paper, we have studied and analyzed the performance of the MGDM system, by studying the optimization of the injection, detection and length parameters of the MMF fiber using the Optisystem software in order to simulate the transmission capacity of the MGDM system O-MIMO via Matlab.
Figure 1.Block f N transmitter e output signal Figure 4 sh

Figure 7 .
Figure 7. Eye-diagram for an optical fiber of length L3 = 4Km