International Journal of Scientific & Engineering Research, Volume 2, Issue 4, April-2011 1

ISSN 2229-5518

Improved Performance of M-ary PPM in Different Free-Space Optical Channels due to Reed Solomon Code Using APD

Nazmi A. Mohammed, Mohammed R. Abaza and Moustafa H. Aly

**Abstract**— Atmospheric turbulence induced fading is one of the main impairments affecting the operation of free-space optical (FSO) communication systems. In this paper, the bit error rate (BER) of M-ary pulse position modulation (M-ary PPM) of direct- detection and avalanche photodiode (APD) based is analyzed. Both log-normal and negative exponential fading channels are evaluated. The investigation discusses how the BER performance is affected by the atmospheric conditions and other parameters such as the forward error correction using Reed Solomon (RS) codes and increasing Modulation level. Results strongly indicate that, RS-coded M-ary PPM are well performing for the FSO links as it reduces the average power required per bit to achieve a BER below 10-9 in both turbulence channels.

Index Terms— Free Space Optics (FSO), M-ary Pulse Position Modulation (M-ary PPM), Reed Solomon (RS) codes, Log

Normal Channel, Negative Exponential Channel, Avalanche Photodiode (APD).

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ree space optical (FSO) systems have been widely deployed for inter-satellite and deep-space communi- cations. In recent years, however, because of its nu- merous advantages over radio-frequency (RF) technology such as extremely high bandwidth, license-free and inter- ference immunity, FSO has attracted considerable atten- tion for a variety of applications, e.g. last mile connectivi- ty, optical-fiber backup and enterprise connectivity. In such kind of applications, FSO systems basically utilize atmosphere as transmission medium rather than the free space. So, the performance of FSO link is inherently af- fected by atmospheric conditions. Among these condi- tions, atmospheric turbulence has the most significant effect. It causes random fluctuations at the received signal intensity, i.e., channel fading, which leads to an increase

in the bit error rate (BER) of the optical link [1].

Current FSO communication systems employ intensi- ty modulation with direct detection (IM/DD) and use light emitting diodes (LED) or laser diodes as transmitters and PIN photodiode or avalanche photodetectors (APD) as receivers. These devices modulate and detect solely the intensity of the carrier and not its phase. Furthermore, biological safety reasons constrain the average radiated optical power, thereby constraining the average signal amplitude. The most reported modulation technique used

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for FSO is the on-off keying (OOK) which offers band- width efficiency but lacks power efficiency. Binary level signaling though is the simplest and most common mod- ulation scheme for the optical intensity channel and offers low power efficiency and high bandwidth efficiency. Power efficiency as well as the improved system perfor- mance can be achieved by adopting pulse position mod- ulation (PPM) schemes. M-ary PPM achieves high power efficiency at the expense of reduced bandwidth efficiency compared with other modulation schemes. The optimal PPM order is high, since a higher order modulation creates the higher peak power needed to overcome the weak average power. M-ary PPM has been previously suggested as a suitable modulation scheme for FSO sys- tems [2]. The IrDA specification for the 4 Mbps short dis- tance wireless infrared links specifies a 4-PPM modula- tion scheme [3].

Reed Solomon (RS) codes are a class of block codes that operate on symbols rather than bits. So, RS codes can correct both random bit errors and burst symbol errors. Moreover, their hard decoding algorithm can be easily implemented even at a high operation speed. Internation- al Telecommunication Union-Telecommunication (ITU-T) standard forward error correction (FEC) scheme based on RS (255,239) codes has been widely used in l0 Gbps prac- tical optical fiber transmission systems [4]. Kiasaleh de- rived upper bounds on the BER of M-ary PPM over log-

• *Nazmi A. Mohammed is with the Electronics and Communications Engi- *normal and exponential distributed channels, when an

neering Department, Arab Academy for Science, Technology and Maritime APD is used [5].

Transport, Egypt. naz_azz@yahoo.com.

• *Mohammed R. Abaza is with the Electronics and Communications Engi-*

In this paper, Kiasaleh expressions are used to com-

neering Department, Arab Academy for Science, Technology and Maritime pare the effect of the BER of average photons per PPM bit

Transport, Egypt. OSA Student Member. rauf_abaza@hotmail.com.

with the former channels without coding and with RS

• *Mostafa H. Aly is with the Electronics and Communications Engineering *(255,207) coding. The remainder of the paper is organized

Department, Arab Academy for Science, Technology and Maritime Trans-

port, Egypt. OSA Member. drmosaly@gmail.com.

as follows. The models of FSO channels are presented in

Section 2. Based on the theory presented, a numerical

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2 International Journal of Scientific & Engineering Research, Volume 2, Issue 4, April-2011

ISSN 2229-5518

analysis of the M-ary PPM is carried out in Section 3. This

The variance, o2 , of the thermal noise in a PPM slot is

is followed by the main conclusions in Section 4.

defined by [5]

( 2 K T T

cr 2 = slot (6)

n R

A L

The log-normal channel is classified as “weak turbu- lence”, which is characterized by a scintillation index less than 0.75. In general, the scintillation index is a compli- cated function of the beam parameters, propagation dis- tance, heights of the transmitter and receiver, and the fluctuations in the index of refraction. In fact, the main

where T is the effective absolute temperature of the rceiv-

er, K is Boltzmann constant, RL is the APD load resistance and Tslot is the PPM slot duration which is related to the data rate, Rb, by [5]

T = log 2 (M ) (7)

source of scintillation is due to fluctuations (due to tem- perature variations) in the index of refraction, which is

slot

M R b

commonly known as optical turbulence. The log-normal model is also valid for propagation distances less than 100 m [5].

The bit error rate (BER) of an M-ary PPM in log-normal

channel is given by [6]

In case of coding, Rb must be multiplied by (n/k), where n is the codeword length and k is the message length.

The symbol error rate (Psymbol) can be calculated from bit error rate (Pb) as [8]

N (

M M

e2(

2cr k x i + m k )

( 2 (M - 1)

Pb :s

2

I w i Q

2cr x + m

(1)

Psymbol = Pb

(8)

n i = - N, i ;f: 0

Fe

A

k i k + K M

where M is the modulation level, wi and xi are the weight factors and the zeros of the Hermite polynomial [7].

The probability of the uncorrectable symbol error (Pues)

due to RS codes can be calculated by the formula [9, 10]

The scintillation index (o2SI) as a function of the variance

1 n ( n

i ( )n - i

of the log-normal channel (o2k) is given by [5]

Pues :s I i

Pq

1 - Pq

(9)

n i = t +1 A k

2 = ecrk - 1 (2)

The average photons per PPM slot (E{Ks}) are functions of the mean (mk) and the variance of the log-normal channel and have the form [5].

where t =((n-k)/2) is the symbol error correcting capabili- ty, Pq is the q-bit RS symbol error probability.

The BER after coding (Pbc) is given by [9]

( n + 1

( 2 P = P

(10)

crk + m

bc ues

E{K } = eA 2

k

(3)

A 2 n

s

The total noise photons per PPM slot, Kn, which results from background noise and thermal noise, is [5]

2cr2

K n = n + 2FK b (4)

(E{g}q )2

The negative exponential channel is classified as “strong turbulence”, which is characterized by a scintillation index greater than 1. The negative exponential model is valid for propagation distances more than 100 m or several kilometers [5, 8].

where Kb is the average background noise photons per PPM slot, E{g}is the average gain of the APD and q is the electron charge.

The BER of the negative exponential channel, Pb

en by [5].

M, is giv-

N ( E{K }x 2

The noise factor, F, of the APD is defined by [5]

Pb :s 2

I w i x i Q

(11

F = 2 + c E{g} (5)

i = - N ,i ;f: 0

)

F E{K

}x 2 + K

where < is the ionization factor.

To get the BER after coding (Pbc) due to negative exponen- tial channel using RS (255,207), we apply the same proce- dure of the log-normal channel coding steps, which are

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International Journal of Scientific & Engineering Research, Volume 2, Issue 4, April-2011 3

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mentioned in (7), (8), (9), (10) and use this in (11).

Based on the described model, the BER of 10-9, which is considered as a practical performance target for FSO link [11], is calculated for log-normal channel and nega- tive exponential channel and the obtained results are dis- played in Figs. 1-3. In these figures, the value of scintilla- tion index (o2SI) is taken 0.3 for weak turbulence and 1 for strong turbulence. The values of other parameters are taken as: BER=2.4 Gbps, Kb =10 photons per PPM slot, RL=50 Q, <=0.028, T=300°K, E{g}=150, n=255, k=207, t=24 symbols.

Variations of BER with the average number of pho- tons received per PPM bit (logarithmic), which are equal log10(E{Ks}/number of bits in PPM symbol), are shown in the following figures. In discussions, all results of average photons per PPM bit are in numerical values.

In Fig. 1, binary PPM (BPPM) is used to compare be- tween the effect of weak turbulence and strong turbu- lence without coding and with RS (255,207) coding.

Fig.1. Comparison of non-coded BPPM in weak turbulence of 0.3 scintillation index with Reed Solomon (255,207) and in strong turbu- lence of 1.0 scintillation index.

At a BER of 10-9, the value of average photons per PPM

bit in strong turbulence is found 2046 without coding and

219 with coding which gives an improvement of 9.7 dB.

While the value of average photons per PPM bit in weak turbulence is found 1462 without coding and 52 with cod-

ing which gives an improvement of 14.49 dB. It also shows that, coded strong turbulence BPPM outperforms weak turbulence BPPM without coding at a BER less than

10-3.

In Fig. 2, 8-PPM is used to show the effect of multile- vel modulation and to compare between the effect of weak turbulence and strong turbulence without coding and with RS (255,207) coding.

At a BER of 10-9, the value of average photons per PPM

bit in strong turbulence is found 728 without coding and

141 with coding giving an improvement of 11.61 dB.

While the value of average photons per PPM bit in weak turbulence is found 543 without coding and 32 with cod- ing which gives an improvement of 16.6 dB. It is shown that, coded strong turbulence 8-PPM outperforms weak turbulence 8-PPM without coding at BER less than 10-4.

Fig. 2. Comparison of non-coded 8-PPM in weak turbulence of 0.3 scintillation index with Reed Solomon (255,207) and in strong turbu- lence of 1.0 scintillation index.

In Fig. 3, 256-PPM is used for weak turbulence and strong turbulence without coding and with RS (255,207) coding.

Fig. 3. Comparison of non-coded 256-PPM in weak turbulence of 0.3 scintillation index with Reed Solomon (255,207) and in strong turbulence of 1.0 scintillation index.

At a BER of 10-9, the value of average photons per PPM

bit in strong turbulence is found 308 without coding and

80 with coding showing an improvement of 14.08 dB. While, in weak turbulence, the value of average photons

per PPM bit is found 258 without coding and 25 with cod- ing giving an improvement of 17.67 dB. It also shows that, coded strong turbulence 256-PPM outperforms weak tur- bulence 256-PPM coding less at BER less than 10-4.

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The obtained results for coded and non-coded M-ary PPM are summarized and compared in Tables 1 and 2 for strong and weak turbulence, respectively.

TABLE 1

Average number of photons per ppm bit required achiev- ing ber 10-9 in strong turbulence.

M-ary PPM | Strong turbulence | Strong turbulence with RS code | Improvement due to RS code + multilevel modulation in Strong turbulence respect to non coded BPPM | |

% | dB | |||

BPPM | 2046 | 219 | 89.3 | 9.7 |

8-PPM | 728 | 141 | 93 | 11.61 |

256-PPM | 308 | 80 | 96 | 14.08 |

TABLE 2

Average number of photons per ppm bit required achiev- ing ber 10-9 in weak turbulence.

M-ary PPM | Weak turbulence | Weak turbulence with RS code | Improvement due to RS code + multilevel modulation in Weak turbulence respect to non coded BPPM | |

% | dB | |||

BPPM | 1462 | 52 | 96.4 | 14.49 |

8-PPM | 543 | 32 | 97.8 | 16.6 |

256-PPM | 258 | 25 | 98.3 | 17.67 |

All results obtained indicate that, RS codes have low per- formance in low photons per bit range. This is because the low photons per bit causes burst erros which are beyond the correction capability of RS codes. Under these condi- tions, spreading the errors by using a code matched inter- leaver and using concatenated codes will make the cod- ing more effective [12].

In this paper, the performance of FSO system with M-ary PPM based on RS codes scheme has been numerically analyzed in weak and strong atmospheric turbulence. The results show that, the average number of photons per bit at 10-9 BER has been improved by 14.08 dB (compared with the value of BPPM without coding) in strong turbu- lence and to 17.67 dB in weak turbulence using RS (255,207) + 256-PPM.

The results also show that, coded strong turbulence out- performs the non-coded weak turbulence without coding for BPPM, 8-PPM and 256-PPM at 10-9 BER, which indi- cates a great improvement of the performance of the sys- tem tolerance for the intensity fluctuations induced by atmospheric turbulence. RS codes can be combated with matched interleaver concatenated coding to solve the problem in low photons per bit range.

Authors wish to thank Prof. Kamran Kiasaleh from Uni- versity of Texas at Dallas, USA, for his fruitful discus- sions.

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