This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings
Waveguide-Grating-Routers-based Realization of Time-Spreading and
Wavelength-Group-Hopping over Fiber-to-the-Home Networks
*Yao-Tang Chang, **Jen-Fa Huang, **Li-Wei Chou and **Kuan-Ju Wang
*Department of Electro-Optical Science and Engineering,
Kao Yuan University, Taiwan, ROCVERSITY
** Department of Electrical Engineering,
National Cheng Kung University, Taiwan, ROC.
Tel: (886-6)-2757575 ext. 62370, Fax: (886-6)-2345482,
E-mail: [email protected]
Abstract—Exploiting the inherent cyclic and periodic freespectral-range (FSR) properties of arrayed-waveguide grating
(AWG) routers, the time-spreading and free-spectral-range
(FSR) group hopping code, which is embedded by maximum
length sequences (called TS/GH embedded M-sequence code) is
configured over a fiber-to-the-home (FTTH) network. For
constructing the proposed code, we use the same prime code for
generating the time code (time-spreading code) and the spectral
domain code (group hopping code). Therefore it is referred to
as a two-dimensional (2-D) optical code. Importantly, for the
proposed broadband light source (BLS), the total number of
available wavelengths is partitioned into G different groups
according to the length of the M-sequence code. Every group is
referred to as a hopping pattern and characterized by the FSR
interval of the AWG router. Improving the prime-hop code
(PHC) and the modified prime-hop code (MPHC) with
cascading one additional AWG router, the cardinality of the
proposed scheme is significantly increased by a factor of 15
under the optimum arrangement for a group hopping number
of G=7. Moreover, the correlation property and bit error rate
(BER) of proposed scheme is evaluated and the result reveals
an improvement of the BER compared to MPHC and PHC.
I.
INTRODUCTION
The two-dimensional (2-D) time spreading and
wavelength hopping (i.e., TS/WH) code implemented by
fiber Bragg’s grating (FBG) and delay line configuration has
attracted much attention in the local area network research
community [1]. We extend our previous work 1-D SACOCDMA scheme with M-sequence scheme [2,3], the
proposed scheme use a 2-D optical code-division multipleaccess network scheme by cascading one additional arrayed
waveguide grating based (AWG-based) encoder/decoder. A
better BER performance compared to conventional TS/WH
scheme (i.e. prime-hop code) [4,5] is demonstrated.
In the current study, we utilize the original binary prime
sequence (0,1) pattern in both time and spectral domain to
generate the 2-D optical CDMA. In order to increase the
number of ONUs by sharing only one additional AWG
router, the available wavelengths Δν of a broadband light
source (BLS) is partitioned into G groups based on the
wavelength number N of the M-sequence code (i.e.,
Δν=G×N). Subsequently, the free spectral range of the AWG
router is taken as the hopping interval (afterwards called
FSR group hopping). The major difference between
conventional wavelength hopping and proposed FSR group
hopping scheme is, that in the latter for one chip the
wavelengths of a whole group is changed and in the former
only one wavelength.
Moreover, since the FSR interval is occupying multiple
wavelengths, the specified M-sequence is embedded into the
above mentioned TS/GH pattern and creates the so called
TS/GH embedded M-sequence scheme.
Hence, for confidential and cardinality perspective, the
proposed schemes provide a more promising solution for
fiber-to-the-home
(FTTH)
access
networks
than
conventional TDM, WDM [6,7], and 1-D SAC-OCDMA
scheme with M-sequence [2,3].
The remainder of this paper is organized as follows. In
section II, the proposed optical TS/GH code is demonstrated
in time and spectral domain. In section III, the proposed
TS/GH code is implemented by a fine AWG router, coarse
AWG routers and a series of delay lines are configured over
a FTTH network. Furthermore, we evaluate the correlation
property of the proposed TS/GH scheme and derive the
system performance in terms of bit error rate (BER). Finally,
Section IV presents some brief conclusions and future works.
II.
DESIGN OF TS/GH EMBEDDED M-SEQUENCES
The proposed code is integrated by time and spectral
(wavelength) domain and therefore is referred to as a twodimensional (2-D) optical code. In the current study, the
popular prime code sequence is used both as time spreading
and wavelength group hopping pattern.
Firstly, in the time spreading domain, the original prime
code sequence is constructed using finite field (Galois field)
arithmetic. Elements of a prime sequence can be obtained by
multiplying each element in the Galois field GF(p) =
{0,1, …, p-1} by a preset number chosen from GF(p). Hence,
there are p prime sequences Ai = ( ai,0, ai,1, …, ai,j, …, ai,(p-1) )
constructed by the element
ai,j = (i, j)mod(p)
(1)
where (i, j) represents the product of i and j. i, j are all in
GF(p). Afterwards, we define that the number of groups G is
corresponding to the prime number p in a conventional
prime code [4,5].
We then map these prime sequences to binary time
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spreading sequences and group hopping sequences to form
the prime codes. For example, the prime sequence is mapped
to the binary time spreading sequence Si = ( si,0, si,1, …,
si,k, …, si,(G2-1) ) according to
⎧1, for k =ai,k + jG, j =0, 1 ,..., G −1
si,k = ⎨ 0, otherwise
⎩
TABLE I.
TS/GH CODE PATTERN
(2)
where i = 0, 1, 2, …, G-1 and the spreading sequence length
is L = G2.
Secondly, in the spectral (wavelength) domain, for the
proposed broadband light source (BLS), the total number of
available wavelengths Δν is partitioned into G different
groups based on the M-sequence code length N (i.e.,
Δν=G×N). Every group is referred to as a hopping pattern
and characterized by the FSR interval of AWG router. Hence,
the M-sequence pattern in the spectral domain M(λ) can be
embedded (inserted) into each wavelength interval as shown
in Fig. 1. The number of groups G needs to be equal to the
prime number p. We define each hopping chip bandwidth as
Δλg. The operation g×Δλg denotes all the wavelengths in
group g which range from λ(g-1)×N +1 to λg×N.
To embed an M-sequence into a TS/GH code pattern, we
transform the TS/GH code pattern from a one-dimensional
sequence vector (i.e. as seen in Table I) into a twodimensional matrix. First, the TS/GH hybrid code vector is
represented by:
SxHgy = ( bx,y(0), bx,y(1), …, bx,y(k), …, bx,y(G2-1) )
(4)
where bx,y(k) could be either zero or g×Δλg. Here, for clear
explanation, Eq. (4) can be viewed as a two-dimensional
matrix and can be represented as SxHgy = [dx,y(i, j)]G ×G2
according to:
⎧1, for g ⋅ bx, y ( k ) occured pulse and i = g - 1, j = k (5)
d x, y (i , j ) = ⎨
⎩ 0, otherwise
where i and j denote the row and column indices of SxHgy.
Finally, the M-sequence is embedded into the g×Δλg
intervals and then the TS/GH embedded M-sequence code
matrix is written as:
Cx,y,z = SxHgy ⊗ Mz
Fig. 1. The partitioned broadband light source (BLS) for G
groups based on M-sequence length.
Using the same original prime sequence in Eq. (1), the
prime sequence is mapped to the group hopping sequence
Hgi = ( hi,0, hi,1, …, hi,j, …, hi,(G-1) ) according to
(
)
hi,j = ai ,j + 1 × Δλg
(3)
where i = 0, 1, 2, …, G-1.
In the hopping sequence, different #FSR group are
assigned to different hopping chips (multiple wavelengths).
The hopping pattern for i = 0 comprises pulses at the
same hopping chip only (Hg0), and is therefore discarded as
trivial. As a result, the number of time spreading patterns is
G. However, the numbers of hopping pattern reduce from G
to G-1. Thus G×(G-1) distinct hybrid codes (SxHgy) of
length G2 can be generated. Hence, the TS/GH code pattern
for G = 3 is shown as Table I.
(6)
where x = 0, 1, 2,…, G-1, y = 1, 2,…, G-1, z = 0, 1, 2,…, N-1,
and the symbol “ ⊗ ” denotes the Kronecker product operator.
The code matrix Cx,y,z is generated by inserting the Msequence vector, Mz into the TS/GH hybrid code vector,
SxHgy. Each element of [cx,y,z](G × N) ×G2 can be expressed as:
cx,y,z( i, j ) = dx,y(idiv G, j ) × mz(imod N)
(7)
where i div G is the quotient of dividing i into G, and i mod N
is the remainder of dividing i by N, the symbol “×” denotes
the multiplication operator, and mz denotes one element of the
M-sequence vector, Mz, respectively. For clear explanation,
the illustrative example for S0Hg1M0 and S1Hg1M0 are
created and shown as Table II.
For simplicity, we select the code family size for the
spreading and hopping sequence G = 3 and the M-sequence
code length N = 3. Hence, the proposed TS/GH embedded
M-sequence code family is created as shown in Table III. The
code family (ONU capacity) is obtained by G×(G −1)×N =
18. The corresponding cardinality of the prime-hop code
family is p×(p −1) = 6.
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TABLE II.
THE ILLUSTRATIVE EXAMPLE FOR S0Hg1M0 AND S1Hg1M0 CODE
A. M-sequence implemented by the fine AWG router
The fine AWG is used to create M-sequence code
patterns in accordance with the FSR interval. Since the
AWG is characterized by an inherent cyclic property, the
fine AWG is shared by different M-sequence code patterns
while the input ports of the fine AWG router are activated
according to a M-sequence. As shown in Fig. 4, the output
spectrums of the fine AWG appear in M0, M1 and M2
including the different FSR intervals at output port #1, 2 and
3, respectively while the input ports of the fine AWG router
are activated according to the M-sequence (1, 0, 1).
TABLE
III.
PROPOSED TS/GH CODE FAMILY. (G = 3, AND M-SEQUENCE CODE LENGTH N
= 3)
Fig. 4. M-sequence implemented by the fine AWG router
B. TS/WH implemented by coarse AWGs and delay lines
III. THE PROPOSED AWG ENCODER/DECODER
In previous papers, 1-D M-sequence AWG-based codecs
were used in FTTH network [2,3]. In current design, the
transmitter of the TS/GH embedded M-sequence scheme
shown in Fig. 2 consist of a fine AWG router, coarse AWG
routers, and a series of delay lines.
Here, as a simple example, we consider a network with
G=3 for the spreading/hopping sequence and N=3 for the Msequence code length. The proposed code family shown in
Table III is configured as shown in the following paragraphs.
Fig. 2. The implementation of proposed encoder.
Coarse AWG routers and a series of delay lines are
connected to the output of the fine AWG router to implement
a 2-D OCDMA function.
In our proposed scheme, coarse AWG routers separate
the different wavelength groups in the spectral domain to
provide the different FSR group of BLS broadband light
source with a M-sequence code pattern.
A series of delay lines are designed as a prime-code
pattern to implement a time-spreading (TS) pattern in time
domain. Hence, in a properly wired arrangement between the
output ports of the coarse AWG and the input ports of the
delay line, the 2-D TS/WH code family is generated.
As shown in Fig. 5, three 1×3 coarse AWG are used to
select the multiple wavelengths following the characteristics
of the FSR. Here, the FSR #1 which includes M0 to M2
appear in the output port #1 of each coarse AWG. In the
same way, FSR #2 and FSR #3 which include M0 to M2
appear in the output ports #2 and #3 of each coarse AWG,
respectively. That is, one coarse AWG router can be shared
by G×(G-1) ONUs.
Subsequently, a series of delay lines generates the primecode pattern S0 = (1, 0, 0, 1, 0, 0, 1, 0, 0) shown in the first
row of Table III. Hence, the proposed TS/GH code family
(S0Hg1M0) is created as ( M10 , 0, 0, M 02 , 0, 0, M30 , 0, 0) while
the different wavelength groups of the light source are
properly wired and then impinge into a series of S0. Hence,
the code family SxHgyMz of G×(G-1)×N ONUs is composed
by the time-spreading pattern Sx, the wavelength hopping
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pattern Hgy and the M-sequence pattern Mz, as shown in
Table III.
A. BER evaluation
In this system, a wavelength hit (i.e., collision) takes
place only when a pulse of a particular ONU overlaps with a
pulse of the desired user and the wavelengths of both pulses
are the same. Therefore, the probability q that a pulse of a
particular user hits one of the pulses of the desired user is
given by
q=
Fig. 5. TS/GH implemented by coarse AWGs and delay
lines
Finally, the SxHgyMz code is modulated by an E-O
modulator using on-off keying modulation for ONU #0 to
ONU #17 and as shown in Fig. 2.
As seen in Fig. 6, at the desired ONU #(Sx, Hgy, M0), a
pair of 3×3 AWG routers (i.e., original and complementary
AWG-based decoder), which have pre-written M-sequence
codes is used to implement the optical correlation process
for M0. Behind every output port of the AWG, a 1×3 coarse
AWG router and complementary delay lines (to synchronize
the different wavelength arrival) are implemented to match
the hopping patterns and the time spreading patterns,
respectively. The desired data bit of an individual ONU is
then recovered via a balanced photo-detector. Similarly,
ONU #(S1, Hg1, M0) to #(S2, Hg2, M2) is obtained.
1
G
⋅
2 2G 2 − 1
(9)
where the first factor, 1/2 represents that the data bit of zero
or one is sent with equal probability, and the second factor,
G/(2G2 – 1) denotes the probability that cross-correlation
peak values will appear in the period of correlation since the
period of correlation equals 2G2 – 1.
The number of users that interfere with the desired user
has a binomial distribution with the parameters K and q. K is
the number of simultaneous active ONUs and q the hit
probability, where K ≤ G×(G - 1)-1. Here, K is smaller than
the total number of users of the groups in SxHgy, which is
G×(G - 1), and the “ -1” term denotes the exclusion of the
ONU itself. If PI(I= i) denotes the probability of i interfering
users, we have
PI(I = i) = CiK q i ⋅ (1 − q) K −i , i = 0, 1, …, K.
(10)
The exact probability of bit error, Pe, at the receivers is
defined as
Pe = P(b =0)P(i ≥ Th | b=0) + P(b=1)P(i < Th | b=1)
(11)
where P(b = j) denotes the probability that the transmitting
bit equals j.
The probability of the transmitting bit 0 conditioned on
the occurrence of the transmitting bit 1 equals 0 (i.e., P(i <
Th | b = 1) = 0). Hence, the evaluation of the probability of
error associated with the MAI become:
K
P(i ≥ Th | b = 0) =
∑ P ( I = i)
I
(12)
i =G
Fig.6.The implementation of proposed decoder for SxHgyM0
IV.
SYSTEM PERFORMANCE EVALUATION
In evaluating the performance of the proposed TS/GH
scheme, the present study adopts a similar analysis method
as in [8]. The following evaluations assume that each light
source is unpolarized and that the optical source has an ideal
flat spectrum. Also, the effects of thermal noise and shot
noise in the photodetection process are neglected.
Substituting Eq. (10) into Eq. (12) and rearranging the
Eq. (11), the exact probability of bit error, Pe, namely the bit
error rate (BER), is written as:
K
Pe =
G
G
1
1
1
) i ⋅ (1 − ⋅
) K −i .
⋅ CiK ( ⋅
2 i =G
2 2G 2 − 1
2 2G 2 − 1
∑
(13)
Depicted in Fig. 8, we have represented the system BER
by changing the prime number p (i.e., corresponding to G),
and the period N of the M-sequence. For a fixed N=3, it
reveals that a lower BER is achieved as G is increased. Note
that the M-sequence code length N is increased as the group
hopping number G is decreased (i.e., Δν= G×N). In the
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current study, it is a trade off problem between cardinality
and data bit rate. That is, a greater group hopping number G
achieves a greater cardinality (i.e., G×(G −1)×N ) but a
lower date bit rate (a longer code length of G2).
spectral-range (FSR) properties of arrayed-waveguidegrating (AWG) routers, an improved prime-hop code (PHC)
and a modified prime-hop code (MPHC) with cascading one
additional AWG router is presented. The proposed scheme,
which integrates time and spectral (wavelength) domain, is
referred to as an alternative 2-D optical CDMA code scheme
over fiber-to-the-home networks.
Furthermore, the correlation property and bit error rate
(BER) of the proposed scheme is evaluated. The results show
that the BER performance of the proposed scheme is much
better than of a modified prime-hop code (MPHC) and a
prime-hop code (PHC) using the prime number, p = 7.
In our future work, the optical filters need to be improved
by optical switch arrays to decrease the system complexity.
ACKNOWLEDGMENT
Fig. 8. BER calculations for our proposed scheme for
various M-sequence code lengths, N and group hopping
numbers, G.
This work was supported in part by the Kao Yuan
University, under a project grant from the National Science
Council, NSC 97-2218-E-244-003, and in part by the
Advanced Optoelectronic Technology Center, National
Cheng Kung University, under a project grants from the
Ministry of Education and the National Science Council of
Taiwan, NSC 97-2221-E-006-149-.
REFERENCES
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Fig. 9. BER comparison for different M-sequence code
lengths, N and group hopping numbers, G.
In practical applications, considering the limitation of
the processing time (i.e., 40Gbps) of the electrical/optical
modulator (EOM), the optimum group hopping number is
G=7, because the data chip rate is approximately 49 Gbps
(i.e., with a code length G2=49 chip/bit) for a typical data bit
rate of 1 Gbps over FTTH networks. Hence, the cardinality
of the proposed scheme is significantly increased by a factor
of 15 compared to a conventional prime-hop scheme.
Comparing the prime-hop code (PHC) and the modified
prime-hop code (MPHC) scheme [4,5], the BER of our
proposed scheme for different G values are shown in Fig. 9.
As seen in Fig. 9, the result show that the BER
performance of our proposed scheme is much better then
MPHC and PHC with p = 7, and also for p = 5 with a shorter
code length (i.e., higher bit rate), the BER of proposed
scheme is still better than MPHC and PHC when the active
user is increased (i.e., namely the heavy loading traffic).
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CONCLUSIONS
By exploiting the inherent cyclic and periodic free-
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