Coding t o Relax Laser Linewidt h Requirements for Multichannel
CPFSK Coherent Optical Communications
Jyh-Horng Wu, Jingshown Wu
Depart.
ofElect. Eng.
National Taiwan University
Taipei,
Tel:886-2-3635251 Ext519
Abstract
A study of the multichannel coheren CPFSK commu- nication system employing Reed-Solomon codes is reported. The crosstalk between adjacent channels, the impact of the laser phase noise, and selection of the opti- mum code rate are investigated. By applying a suitable coding scheme, the laser linewidth can be greatly rela- xed, and the receiver sensitivity will be remarkably improved. A 100 Mbit/s system is used to verify the coding benefit. The results show that the impact of the laser linewidth can be largely alleviated by applying a (255, 223) Reed-Solomon code. When the linewidth is fixed (AvT = 2 %), this code can improve the receiver sensitivity by more than 15 dB.
1
Introduction
With recent great advances in coherent optical commu- nication technology, many applications for coherent systems, for example, broadband networks, are now being considered in many places
[ l l .
The niultichannel coherent optical communications which may transmit many channels simultaneously have been demonstrated [2-41. In a multichannel system, the continuous-phase frequency shift keying (CPFSK) optical heterodyne with delay demodulation is attractive because: it provides for direct modulation of laser diodes, has reasonable line- width requirements [5], and leads to close channel spa- cings [ 3 ] . Since the CPFSK delay demodulation sche- me uses signal light phase information, high receiver sen- sitivity is expected. However, the performance of coherent optical receivers is degraded significantly bythe phase noise of the semiconductor lasers [6]. Hence, the linewidth requirement is major concern in coherent optical communication applications, especially in mul- tichannel CPFSK systems [5].
Yang-Han
LeeDepart.
ofElect. Eng.
TamKang University
Tamsui,
TaipeiHsien, Republic
ofChina
Tel
:8
8 6- 2- 6 2 1 5 6 5 6 Ex t 644, Fax
:8 8
6- 2
-622 1
5
6
5
Currently to overcome this problem, one either uses the lasers with very narrow linewidth or adopts a large modulation index to avoid phase noise influence. The lasers with narrow linewidth are expensive and difficult to fabricate. For applications in local area networks, the low cost distributed feedback (DFB) lasers with typical linewidth of 50 MHz still can not be used without sig- nificant sensitivity degradation. On the other hand, with the modulation index increment, the IF spectrum is bro-
adened and the required IF bandwidth becomes large. In this case, the increase of IF noise degrades the recei- ver sensitivity.
However, i t is well known that error control codes (ECC) provides coding gain at the expense of increa- sing channel bit rate. The receiver sensitivity will be improved and the error floor can be eliminated by app- lying error control codes. In this paper, we will study the feasibility of using Reed-Solomon codes to impro- ve receiver sensitivity and to relax the laser linewidth requirements i n a multichannel CPFSK systcm with delay demodulation.
2
Receiver model and basic error rate
expression
2.1 Reciver model
Figure 1 shows a balanced delay-and-multiply CPFSK coherent receiver. The voltage a t t h e i n p u t of t h e b a n d -
pass filter (BPF) is given by
v,
(t) =s,(t>
+ " I (1) (1)where S,(t) is the signal with phase noise and n,(t) is the additive noise including shot noise, thermal noise, and crosstalk. S,(t) is given by [7]
where A=2R,/& ;
R is the detector responsitivity; PS and PLO are the powers of the signal and the local oscillator, respectively; fiF is the intermediate frequency; Fd is the frequency deviation; b(t) is a binary signal which is equal to + I or -1 corresponding to the bit “1” or “0” being transmit- ted; $“(t) is the combined phase noise of the transmit- ter and local oscillator lasers; and 8 is the random initi- al phase.
The BPF output voltage is
where S,(t) and nz(t) are the filtered versions of S,(t) and n,(t), respectively.
The output voltage of the low pass filter (LPF) is
where S3(t) is the signal and n3(t) is the noise.
The BPF is assumed to have the following transfer f u n - ction:
where BIF is the filter bandwidth.
2.2 Noise model 2.2.1 Phase noise
The phase noise $,(t) is a nonstationary Wiener process defined as
The frequency noise $(t) can be modelled as a zero-mean Gaussian process with the power spectral density (PSD) given by [8]
whereAv is the full width half maximum (FWHM) line- width at the “IF’, i. e.
where AvT and AvLo are the linewidth of the transmit- ter and local oscillator, respectively.
2.2.2
Additive noiseThe additive noise n,(t) is due to the shot noise of the local oscillator, thermal noise of the receiver, and cros- stalk from adjacent channels. The single-sided PSD of n,(t) is given by [4]
S , , ( f ) = q + S , ( f ) O < f < W ( 5 ) where q is the PSD of shot noise and thermal noise, and
ScT(f) is the PSD of the crosstalk.
The value of q in a coherent system is [4]
where q is the electron charge, and i, is the thermal noise current.
2.2.3
CrosstalkCrosstalk modelling is discussed in [3]. The crosstalk
PSD can be approximated by the PSD of the signals of the adjacent channels [3], which is given by the follo- wing expression for the CPFSK modulation format
where GPN(f) is the double-sided PSD of phase noise,
SCPFSK(f) is the single-sided PSD of CPFSK modulati- on, and I*I denotes the convolution operator. The two
L
where T = R b is the bit duration, D is the electrical domain channel spacing, and S,,,,,(T (f - f1F - D)) is the normalized PSD of the CPFSK modulation scheme [4].
2.3 Error rate expression
The error rate for the delay demodulation can be expres- sed as [9]
[I,,(
:)
+
In+,(:)r
.
exp[-(2n+
l)'lcAv~]where
p
= 2m.rRb : mod dation index parameter, (1 1 )z: delay time,
R,,:
data rate,m = - 2fd : modulation index,
I,,(x): the modified Bessel function of the first kind, and signal to noise ratio, p, is given by
R b
2R
*
Ps PLOP =
q B I F
2.4
Effect of phase noise on multichannel
In a multichannel system, frequency seperation (D) must be carefully selected. If D is too small, the system per- formance will deteriorate due to crosstalk between adja- cent channels. It has been shown that the choice of modu- lation index m = 1 has the smallest sensitivity penalty,
system
and therefore, allows the smallest channel spacing [3, 41. So we assume m = 1 and BIF = 2.2 Rh in the follo- wing discussions.
Figure 2 depicts the impact of the linewidth on a mul- tichannel system; i t shows the relative penalty versus the channel spacing for several values of AvT. The rela- tive penalty is defined as the sensitivity difference in dB to achieve a given error probability IO-' for fixed
AvT, when D has a given valaue and D = CO. It is found
that as lasers with largcr linewidths are used, channel spacing must be increased i n order to maintain that the channel spacing D is equal to 2.2 Rh to keep thc rclati- ve penalty within I dB.
3
Analysis
of
coded system
3.1 Features of coded system
When coding is employed i n a multichannel system, there are several factors that influence the overall beha- vior:
1. The shorter channel bit duration reduces the impact of laser phase noise.
2. The error correcting capability makes the system more tolerable to higher channel bit error rate. 3. Coding is at the expense of increasing channel bit
rate, the required IF bandwidth becomes larger, and so does the additive noise.
4. Crosstalk is larger when channel spacing is fixed. The first two factors have benefits for the coding per- formance, but on the contrary, the last two factors deg- rade it. So the selection of code rate is important i n a multichannel system. We will determine the code rate that is suitable for multichannel application numerical- ly in the following section.
3.2 Code rate optimization
As the code length and signal power are fixed, the cope
rate, r, can be optimized such that the overall BER is
minimum. We will adopt Reed-Solomon (255, k) codes, the reasons are:
1. The (255, k) RS codes are very powerful, and have a very low misdecode rate [ 101.
2. RS codes are suitable for high speed operation [IO]. The decoded output bit error probability P, for an (n, k) RS code can be estimated from the following bound [ 1 1,
1 9 1 . I L J .
where q = the number of bits in each of the n RS code symbols in a codeword,
Psym = the RS code symbol error probability, t=- = number of symbol errors can be cor-
As an example, Fig. 3 shows the BER versus code rate
for several values of AvT, where we neglect thermal noise and use the following parameters: m = 1, Rh = 100 Mbit/s, R = 0.84 N W , z = 0.5 T, and D = 2.2 R,,. We notice that there exists an optimum code rate
n - k
2 rected in a codeword.
(r =
g)
for which the BER is minimum.Note that the curve is relatively sharp near the optimum (code rate, this indicates that the coding performance is sensitive to the code rate chosen in the multichannel
{CPFSK system.
The high rate RS code providcs additional advantages
$with practical consideration [IO]:
I . The bandwidth expansion is only 14 percent, so the
components of the receiver, for example, amplifier and BPF, could be readjusted to accomodate the slightly higher bandwidth without modification. 2. The high rate RS code is commercially available in
satellite systems, and can be easily incorporated in optical communication systems.
3.3 Discussions
Figure 4 depicts the BER versus the receiver sensitivi- ty of both coded and uncoded cases for AvT = 0, I %,
and 2 %. We define the coding gain as the ratio o f t h e sensitivity without coding to the sensitivity with coding under the same data rate and at BER = IO". As shown
in Fig. 4, when the laser linewidth increases, the coding gain increases. It indicates that coding can be used to effectively combat the phase noise.
Figure 5 shows the impact of the phase noise on thc BER pcrformance in a niultichannel system with and with- out coding for AvT = I % and various values of D. As thc channel spacing becomes smaller, the uncoded system will lcad to an additional dctcrioration. But in a coded system, the deterioration can be compcnsatcd by the code.
The coding gain at BER = versus AvT for several channel spacings is shown in Fig. 6. For a fixed chan- nel spacing, the coding gain increases dramatically as AvT increases; on the other hand, for a fixed value of AvT, coding gain also enhances as channel spacing decreases. So coding is an effective way to combat both phase noise and adjacent channel crosstalk in a mul- tichannel system. As shown in Fig. 6, the coding gain can be larger than 15 dB when AvT = 2 96 and
D
= 2.2Rb.
Fig.7 shows the linewidth relaxing factor versus AUT a t D=2.2Rb. The relaxing factor is defined as
follows : A v T = l % (uncoded) and AUT =2 % (coded)
have the sensitivity a t B E R = lo-', then the relaxing factor is 2 for AUT = 1 %. We see that the relaxing factor may be larger than 10 (AUT =0.5 %) and de- creases as AvT increases.
4
Conclusions
In this paper, we illustrate the possibility of relax- ing the laser linewidth requirement and improving the receiver sensitivity by using Reed-Solomon codes on a
multichannel coherent optical CPFSK delay demodu- lation system. It is found that the (255,223) RS code is
a suitable coding scheme for this channel, and can ef- fectively combat both phase noise and adjacent chan- nel crosstalk.
Taking advan1,age of the commercially available elec- tronics in satellite system, the high rate (r=0.875) RS code can be easily incorporated in optical communi- cation system. By employing this coding scheme, the receiver sensitivity can be remarkably improved, and the laser linewidth requirement can be greatly relaxed. An improvement of more than 15dB a t AvT = 2 % and relaxing factor of more than 10 a t AUT = 0.5 % are estimated.
In a multicha~mnel system, adjacent channel crosstalk degrades system performance seriously. In this paper it is shown that the coding gain increases as chan- nel spacing decreases, and compensate the sensitivity penalty due to adjacent channel crosstalk.
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1. AvT = 0 2. AvT = 0.5 % 3. AvT = 1.0 K 4. AvT
-
1.5 K 20 18. 16 14 2 1 2 - a 1 0 - Y " 2 I -z
I - 4 . 2 - 0 , 0 1 4 1 1 I I I I I I 1 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 Code RateFig. 3: The BER versus (255, k) RS codes under several values of AvT with D = 2.2 Rb and P, = -64 dBm
- -
Data Rate = lOOMbitls D = 1.8, 2.0, 2.2
1. D = 2.2 Rb
3.D=1.8Rb
2. D = 2.0 flb
Sensitivity in dBm, CPFSK 100MbiVs
Fig. 5 : BER versus receiver sensitivity for both coded and uncoded case under several values of D with AvT = I %
R&dvsd
W-Lzq.
3dB" oelecw2
Fig. I : A balanced delay-and-multiply CPFSK coherent optical recei- ver 3.0 2.5
-
2.0 1.5-
E - a 1. AvT = 0 3.AvT=1.0% 4.AvT=1.5% 0.5 - 0 I I I I I I ' I ' 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 Channel Spacinflata Rate .-Fig, 2: Relative penalty versus normalized electrical domain channel spacing for AvT = 0, 0.5 8, 1 %, and 1.5 '%
Data Rate I lOOMbiUs
1.AvT-0 2.AvT-1% 3. AvT= 2 36
Sensitivity In dBm, CPFSK 100MbiUs
Fig. 4: BER versus receiver sensitivity for both coded and uncoded case under several values of AvT with D = 2.2 R b
l 4
-
1.D=2.0Rb1 2 3 4
0.004 0.008 0.012 0.016 0.020
l , l l l ' l l l , J
Unewidth-Data Rate Ratio AvT
O O
Fig. 6: Coding gain versus linewidk-datr rate ratio for several &an- ne1 spacings at BER = 10'
