Performance Analysis of Hybrid Optical code division and Mode division multiplexing with modified zero cross correlation codes

Abstract The suitable alternative for the optical fiber networks is Free Space Optical (FSO)

communication. This is due to its advantages over fiber optics like low maintenance cost and

deployment time. FSO is a common name which is widely used in the area of

telecommunications. It is especially used in the areas where the deployment of optical fiber is

not possible and/or in undeserved rural areas where broadband network connectivity is not

present. In this work, a system is designed which have 200Gbps data rate and combine two

techniques called mode division multiplexing (MDM) and optical code multiple access scheme

(OCDMA). Ten channels, each carrying 20Gbps data, are transported over 20 km FSO link by

using MDM of two Laguerre Gaussian modes and multi diagonal codes. Moreover, the

performance of proposed MDM– OCDMA–FSO system is also investigated under atmospheric

turbulences.

Keywords: Free space optics (FSO) Mode division multiplexing (MDM) Laguerre Gaussian

modes (LG) Multi diagonal codes

1 IntroductionIn the current period of data innovation, free space optics or FSO is considered as a cutting-edge

communication system that can be utilized for sharing any type of continuous data globally from

anywhere anytime. This transmission is very reliable and secure. FSO integrates features of the

existing optical and wireless fiber communication technologies. In the event of optical fiber

correspondence, FSO used a cost effective optical network. This FSO network incorporates a fast

transporter that quickens transmission limit (1).

Further, FSO is a proficient option to new optical fiber installations in remote and rural areas.

Moreover, FSO transmission process is a secure process because it has the feature of point-to-

point laser signals with irrelevant interference (2, 3). There are many advantages of using FSO

systems like no need of fiber optic cables, low expenses, no security upgrades, and so on (4).

Moreover, FSO system upgrades do not require RF license. The disadvantages of FSO system is

its performance can be affected by various atmospheric conditions. This happens due to the

channels of transmission is located in the troposphere region (5, 6). Since atmospheric conditions

tend to occur in this region, modulated light transmitted through FSO links is relatively affected

by various atmospheric parameters including scattering, non-selective scattering, and absorption.

Scattering is occurred due to the bigger size of raindrops and non-selective scattering whereas

atmospheric gases cause absorption (7, 8). In case of temperate regions, two major weather

conditions that affect FSO links are fog and heavy snow (9).

On the other hand, optical code division multiple access or OCDMA is one of the well-known

developments in the field of optical network systems, which integrates various types of data

traffic and increased bandwidth (10). Code division multiple access (CDMA) is used by the

wireless networks as it is secure and efficient technique. Comprised of the features of CDMA,

OCDMA can transmit data flawlessly which additionally controls and manages networks easily.

Further, FSO can integrate OCDMA to develop hybrid network for last-mile access networks

without fiber arrangement (11). FSO-OCDMA integration was first proposed and implemented

by Sasaki et al. (2008) which was utilized mostly for evaluating turbulence effects on OCDMA

using temporal or 2D encoding schemes (12, 13). However, multiple access interference (MAI)

affects the performance of OCDMA to a great extent due to more number of users (14). So to

lessening the impacts of MAI this new paper propose a technique of MDM which is mode

division multiplexing which further enhance capacity of optical networks. In this technique the

Users transmit the signal at same channel but by allocate different modes to the signals, due to

this bandwidth issues and spectrum is reduced. MDM has been utilized in FSO systems by

different researchers (15, 16), yet the area remains unexploited. The present paper aim is to

design a MDM-integrated OCDMA system for transmitting 200Gbps data over 20 km FSO

channel, which is a cost effective system without using any compensation technique which, to

the author’s best learning, was not revealed in any work. Laguerre Gaussian (LG) 01 and 02

modes are used for MDM whereas multi diagonal (MD) codes are used to design OCDMA

scheme for the proposed FSO system.

2 System descriptionsThe simulation configuration of the proposed 10x20 hybrid MDM–OCDMA–FSO sys-tem,

simulated in OptiSystemTM V-13 software, is shown in Fig. 1. It uses LG 01 and LG 02 modes—

generated by spatial laser with the power of 10dBm and multi-diagonal (MD) encoders—to

transmit ten channels each with 20Gbps non return to zero (NRZ) modulated data.

Fig.1 shown LG-01 and LG-02 modes support 10 users. First 5 users are supported by different

linearly polarized modes under LG modes. For first five users, mode users are LP11, LP12,

LP13, LP14, LP15 and for cost effectiveness, code matrix of multi diagonal codes is generated

for 5 users but it cater total 10 users. Wavelengths are same for LG01 and LG02, the later one

provide the service to another 5 users with LP modes such as LP21, LP22, LP23, LP24 and

LP25. Linearly polarized modes are basically the intensity profiles of laser source with particular

vibration of electrical field vector into one dimension.

Fig.1 10x20Gbps hybrid MDM-OCDMA-FSO transmission system

In the code construction of multi-diagonal codes, the parameters (N, W, λc) where N is the code

length (number of total chips), W is the code weight (chips that have a value of 1), and λc is the

in-phase cross correlation are used.

The cross-correlation theorem states that cretin sets of complementary sequences have cross-

correlation functions that sum to zero by using all pair wise permutations. Here, all cross-

correlation function permutations are required in order that their sum be identically equal to zero.

For example, if the rows and columns of a (K × N) matrix are orthogonal and all the columns

except one sum to zero, then the sum of all cross-correlations between non-identical code word is

zero.

So if xij is an entry from X and yij is an entry from Y, then an entry from the product is given by

C ij¿∑k=1

n

x ik y ik

For the code sequences X= ( x1, x2, x3….xn) and Y=( y1 , y2 , y3 ,......,yn) the cross-correlation

function can be represented by:

λc=∑i=0

N

X iY i

When λc = 0, it is considered that the code possesses zero cross correlation properties. The

matrix of the MD code consists of a K×N matrix functionally depending on the value of the

number of users (K), and code weight (W). For MD code, the choice of weight value is free, but

should be more than two.

A. MD Matrix Design

The following steps explain how the MD code is constructed.

Step 1:

first of all, by using the value of the weight (W) and number of subscribers (K) create a sequence

of diagonal matrices. According to these values, the values of I, jw will be set. Where K and W

are positive integer numbers are defined by the number of rows in each matrix.

Where jw = 1, 2, 3, 4,….., W will represent the number of diagonal matrices.

Step 2: Based on the next equations the MD sequences will be computed for each diagonal matrix. (in+1-i) for jw= even number

Si, jw= (1) i for jw= odd number

1 K 2

Si,1= 3 Si,2 = 3 and so on (2) 2

K 1

Any element of Si,w matrices represent the position of one in Ti, w matrices with KxK dimensions.

Where Ti, w= Si, 1 KxK , Ti, 2= Si, 2 KxK , Ti, w= Si, w KxK

Therefore

1 0 …0 1 0 …0

Ti,1= 0 1 …0 ,…..,Ti, w 0 1 …0

⋮ ⋮⋱ ⋮ ⋮ ⋮⋱ ⋮ (3)

0 0 … 1 KxK 0 0 … 1 KxK Step3.

The total combination of diagonal matrices (3) represents the MD codes as a matrix of power

KxN.

MD= Ti,1 , Ti,2 , ……., Ti,w KxN (4)

a1,1 a1,2 … a1,n

a2,1 a2,2 …a2,n

MD = a3,1 a3,2 …a3,n (5)

⋮ ⋮ … ⋮

a in,1 a in,2 …a in,n

From the above basic matrix (5), the rows determine the number of users (K). Notice that the association between code weight (W), code length (L), and number of subscriber (K) can be expressed as:

N= KxN (6)

For example, to generate a MD code family according to the previous steps,

Let’s say K=5, and W= 4.

Therefore,

i = 1,2,3,4,5 in= 5+1=6 and Jw = 1,2,3,4

The diagonal matrices can be expressed as:

1 5 1 5

2 4 2 4

Si,1= 3 Si,2= 3 Si,3= 3 Si,4= 3 (7)

4 2 4 2

5 1 5 1

The MD codes sequence for each diagonal matrix is shown as:

1 0 0 0 0 0 0 0 0 1

0 1 0 0 0 0 0 0 1 0

Ti,1= 0 0 1 0 0 Ti,2= 0 0 1 0 0

0 0 0 1 0 0 1 0 0 0

0 0 0 0 1 1 0 0 0 0 5x5 5x5

1 0 0 0 0 0 0 0 0 1

0 1 0 0 0 0 0 0 1 0

Ti,3= 0 0 1 0 0 Ti,4= 0 0 1 0 0 (8)

0 0 0 1 0 0 1 0 0 0

0 0 0 0 1 1 0 0 0 0

5x5 5x5

The total MD code sequence will be:

1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1

0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0

MD= 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 (9)

0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0

0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 5x20

Where K=5, N=20.

So the codeword for each user according to above example is:

User 1= λ1, λ10, λ11, λ20

User 2= λ2, λ9, λ12, λ19

Codeword=

User3= λ3, λ8, λ13, λ18

User4= λ4, λ7, λ14, λ17

User5= λ5, λ6, λ15, λ16

The MD codes are proposed to SAC-OCDMA applications because of its advantage that it gives

zero cross correlation even at the increase in number of users at any weight value, while in other

several codes the cross correlation increased with the number of users increased. The MD code

design depicts that changing matrices element in the same diagonal part will result in a constant

property of zero cross correlation, and it is constructed with zero cross correlation properties,

which cancels the MAI by giving the different code for each user. The MD code presents more

flexibility in choosing the W, K parameters and with a simple design to supply a large number of

users compared with other codes like MQC, RD codes. Furthermore, there are no overlapping

chips for different users.

Generated MD code for 5 users is given in Table given below.

Table 1 Multi-diagonal code matrix for 5 users1565.2

1 0 0 0 0

1564.4

0 1 0 0 0

1563.6

0 0 1 0 0

1562.8

0 0 0 1 0

1562

0 0 0 0 1

1561.2

0 0 0 0 1

1560.40 0 0 1 0

1559.6

0 0 1 0 0

1558.8

0 1 0 0 0

1558

1 0 0 0 0

1557.2

1 0 0 0 0

1556.4

0 1 0 0 0

1555.6

0 0 1 0 01554.8

0 0 0 1 0

1554

0 0 0 0 1

1553.2

0 0 0 0 1

1552.4

0 0 0 1 0

1551.6

0 0 1 0 0

1550.8

0 1 0 0 0

1550

1 0 0 0 0

User

1 2 3 4 5

3 Results and Discussions

This section represents the discussion of results obtained from simulation of proposed 10 x

20Gbps hybrid MDM–OCDMA–FSO transmission system. Fig.2 represents the measured bit

error rate at receiver side for channel 1 and channel 10. It is shown from Fig.5.1 that the value of

BER for channel 1 is computed as 4.73e-313, 1.26e-160 and, 3.33e-051, 2.22-019, 4.49e-010

whereas for channel 10, the value of BER is noted as 5.86e-282, 1.31e-149 and 1.95e-049, 4.52e-

019, 5.95e-010 at FSO transmission link of 4, 8, 12, 16 and 20 km respectively. It is perceived

that with the increase in the transmission distance of the free space optical channel, bit error rate

of the system increases due to the effects of attenuation, dispersion and other noise factors.

Results of channel one that falls under the LG mode 01 provides better performance than the

channel 10 that operated under LG mode 02. It is suggested to use LG01 mode profiles in order

to get better performance of the system.

Fig.2 Variation of BER with transmission distance in case of channel 1 and channel 10

Fig.3 represents the Q-factor at receiver side for channel 1 and channel 10. It is shown from

simulation that the value of Q-factor for channel 1 is computed as 37.80, 26.98, 15 and8.9, 6.11

whereas for channel 10, the value of Q-factor is noted as 35.86, 26.02 and 14.73, 8.84, 6.08 at

FSO transmission link of 4, 8, 12, 16 and 20 km respectively.

Fig.3 Variation of Q-factor with distance in case of channel 1 and channel 10

It is perceived that with the increase in the transmission distance of the free space optical

channel, Q-factor of the system decreases due to the effects of attenuation, dispersion and other

noise factors. Results of channel one that falls under the LG mode 01 provides better

performance than the channel 10 that operated under LG mode 02. It is suggested to use LG01

mode profiles in order to get better performance of the system. BER is measured for proposed

system under atmospheric turbulences, then results shows that FSO prolongs to 2000m under the

influence of light fog, 1500m under the influence of medium fog and FSO prolongs to 1200m

with acceptable SNR under the influence of heavy fog. Atmospheric turbulences can be assumed

by atmospheric attenuation value with corresponding visibilities as 0.14DB/km for clear weather,

9DB/km for thin fog, 12DB/km for medium fog and 16DB/km for heavy fog. (17, 18)

The measured eye diagrams for channel 1 and channel 10 at the distance of 4 and 20 km are

shown in Fig.4and Fig.5 respectively. The measured BER and clear eye diagrams shows that

under clear weather conditions, the FSO link prolongs to 20 km with acceptable SNR. Eye

diagram analyser is decision component that provide us the values of Q-factor, BER, eye

opening, jitter etc. It depicts the amplitude of average number of logic 1s and 0s in the

transmitted sequence. A threshold value is calculated by the receiver below which all the bits are

0s and above are all 1s. Crossover value of levels of ones and zeros are referred as the jitter. It is

observed that eye opening is more in case of channel one and less in channel 10.

(a) (b)

Fig.4 eye diagram of CH1 after (a) 4km and (b) 20km FSO distance

(a) (b)

Fig.5 Eye diagram of CH10 after (a) 4km and (b) 20km FSO distance

6.1 ConclusionsIn this work, system has 10 channels, for 10 different users. First 5 users for LG 01 mode and LG

02 mode for other 5 users, further these modes are used for the mode division multiplexing. Each

channel of this system is carrying 20Gbps data and transmitted over FSO channel having a

distance of 20 km by using MDM and OCDMA technique. To utilize OCDMA technique the

MD encoder and decoders are used which also eliminate the cross correlation between the users.

The combined use of MDM and OCDMA technique also have the advantage that it allows

multiple high speed channels over single FSO link due to which huge bandwidth is saved. It is

concluded from results obtained from the simulation setup that under clear weather conditions,

FSO link prolongs to 20km with acceptable BER. When clear weather conditions changes to

light fog the FSO prolongs to only 2000m and at medium fog it prolongs to 1500m and in the

heavy fog weather conditions the FSO system prolongs to only 1250m with acceptable SNR.

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