OPTICAL code-division multiple access (OCDMA) is a

150 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 54, NO. 1, JANUARY 2006 Permuted M-Matrices for the Reduction of Phase-Induced Intensity Noise in Optical CDMA Network Jen-Fa Huang and Chao-Chin Yang Abstract Two codeword families and the corresponding encoder/decoder schemes are present for spatial/frequency optical code-division multiple-access communications. These 2-D codewords have multiple weights per row and can be encoded/decoded via compact hardware. With the proposed decoding mechanism, the intended user will reject interfering users and multiple-access interference is fully eliminated. In addition, the power of the same wavelength contributed by all interfering codewords is split and detected by distinct photodiodes in the decoder. Thus the performance degradation due to the beat noise arising in the photodetecting process is improved, as compared with the traditional 1-D coding scheme, and a larger number of active users is supported under a given bit-error rate. Index Terms Arrayed waveguide grating (AWG), maximal-area matrices (M-matrices), optical code-division multiple-access (OCDMA), phase-induced intensity noise (PIIN). I. INTRODUCTION OPTICAL code-division multiple access (OCDMA) is a promising technique for bursty traffic environments, and it provides asynchronous and secret transmissions between different individual users [1]. Among all kinds of OCDMA schemes, incoherent systems have attracted more attention than coherent ones, due to simpler realization of encoders and decoders. However, since the adopted 1-D optical code sequences are unipolar in incoherent systems, the code length should be made large to retain better auto- and cross-correlations. Therefore, 2-D codes are proposed to obtain good correlation characteristics with short code length by using other dimensions, such as wavelength, space, and so forth. Some authors generate 2-D optical codes by developing particular algorithms [2], [3], or taking advantage of the maturely developed 1-D optical codes in a combined time-spreading and frequency-hopping scheme [4], [5]. These codes have large cardinality, but the lengths of fiber delay lines used in the coding devices are quite long, and multiple-access interference (MAI) J. A. Salehi, Optical CDMA Manuscript received August 20, 2004; revised July 13, 2005. This work was supported in part by the Ministry of Education Program for Promoting Academic Excellence of Universities under Grant A-91-E-FA08-1-4, and in part by the National Science Council under Grant NSC 94-2213-E-168-005. This paper was presented in part at the International Symposium on Communications, Tao-Yuan, Taiwan, R.O.C., December 2003. J.-F. Huang is with the Department of Electrical Engineering, National Cheng Kung University, Tainan 70146, Taiwan, R.O.C. (e-mail: huajf@ee.ncku.edu.tw). C.-C. Yang is with the Department of Electronic Engineering, Kun Shan University, Tainan Hsien 710, Taiwan, R.O.C. (e-mail: ccyang@mail.ksu.edu.tw). Digital Object Identifier 10.1109/TCOMM.2005.861650 degrades the system performance seriously. When the optical beat interference is considered, the performance is worse [6]. The spectral-amplitude-coding (SAC) systems use code sequences with fixed cross-correlation and uses differential detection in the spectral domain [7] [9]. Since the codeword of each interfering user produces the same values in both photodiodes (PDs) of the balanced detector, MAI is eliminated via differential detection. Cascaded fiber Bragg gratings (FBG) are widely used as encoding/decoding devices in SAC-OCDMA systems recently. However, when the number of total users in the system is large, cascaded FBGs have impractical physical length and are hard to realize. Multiwavelength OCDMA systems suffer seriously from beat noise [6], [10], which comes from the beating between pulses of the same wavelength due to square-law detection. Codes with low cross-correlation are proposed to alleviate beat noise arising in the PDs [9]. Because of low code weight, these codes have large power loss and poor performance at low signal power. We have developed a 2-D maximal-area matrix (M-matrix) code for the SAC-OCDMA systems that can be easily coded with compact hardware [11]. Unlike traditional 2-D codes, this code does not restrict to a single pulse per row, and each row can share a common coding/decoding device. The proposed decoding mechanism not only eliminates MAI from different users, but also suppresses the beat noise in the decoder. In this paper, we use an arrayed waveguide grating (AWG) multiplexer for coder implementation [12], and show that the decoder can be simplified without sacrificing system performance. When encoder/decoders are realized by AWG routers [13], [14], we can take advantage of the cyclic characteristics of AWG routers and M-sequence code to generate the modified version of the M-matrix code. This permuted M-matrix code produces less beat noise in the PDs, thus allows a larger number of active users to access simultaneously in the system. Low-cost broadband light sources are used for actual implementation of both code families, and spatial/frequency coding is used to demonstrate that these codewords can be easily encoded/decoded with compact hardware. The rest of this paper is organized as follows. Section II is devoted to the encoding/decoding process of the M-matrices using an AWG multiplexer. Section III is devoted to the encoding/decoding process of the permuted M-matrices using an AWG router. In Section IV, the performance of the permuted M-matrices system is evaluated in terms of various noises, and 0090-6778/$20.00 2006 IEEE

HUANG AND YANG: PERMUTED M-MATRICES FOR THE REDUCTION OF PHASE-INDUCED INTENSITY NOISE 151 Fig. 1. Spatial/frequency OCDMA network. compared with the M-matrix system. Finally, the conclusion is given in Section V. TABLE I M-MATRIX CODES GENERATED FROM X AND Y II. THE OCDMA SYSTEM USING M-MATRICES The spatial/frequency OCDMA network is shown in Fig. 1. It includes transmitters, receivers, and star couplers. The information bits of user are encoded with a 2-D codeword (, and ) by the proposed AWG-based encoder, and the resulting signals are combined with other users in the star couplers and broadcast to each user s spatial/frequency decoder. Two binary M-sequences can be used to obtain the 2-D code mentioned above. These unipolar M-sequences are easily generated by linear feedback-shift registers that are arranged according to the corresponding primitive polynomials [18]. Due to the correlation characteristics, these sequences are used in the SAC-OCDMA system for MAI elimination [7]. Let and be two M-sequence codes of length and, respectively, ( and are integers) that need not be in the same code family or the same code length. The spectral and spatial codewords for user are obtained by and, respectively, where is the operator that shifts vectors cyclically to the right by one place. The elements of M-matrix for user is constructed from the corresponding spectral and spatial codewords, as follows: (1) Equivalently, can be generated from the cyclic th row shift and the cyclic th column shift of ; therefore, in total, codewords are supported in this system. Table I shows the nine M-matrices generated from M-sequences and. The procedure to encode the information bits of each user with one M-matrix code can be implemented with AWG easily. The spatial/frequency OCDMA encoder, as shown in Fig. 2, consists of an incoherent broadband optical source, an intensity E/O modulator, a spectral encoder, and a spatial encoder. The information bits of the user is on off shift keying the broadband incoherent optical sources to fulfill the E/O modulation, then the resulting signal is encoded in the spectral and spatial domains sequentially to fulfill the 2-D encoding process. Fig. 2. Spatial/frequency encoder. The spectral encoding is realized by one AWG demultiplexer whose output ports are each connected by one optical switch. The corresponding switch of the th AWG output port is on as long as the th chip of spectral codeword is one. Thus when the information bit is one, the wavelengths from the light source that represent the spectral codeword are transmitted to the splitter. The spatial encoding is performed with the switch array positioned between the splitter and the couplers. If the th chip of spatial codeword is one, the link between the splitter and the th star coupler is on and the spectral codeword is transmitted in this spatial channel. When the th chip is zero, the link is off, and this corresponds to the transmission of all-zero spectral chips.

152 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 54, NO. 1, JANUARY 2006 The codewords in Table I are taken as example. Suppose user (0, 0), (0, 2), (1, 2), and (2, 0) transmit information bit one and other users transmit information bit zero. In the encoder of user (0,0), the switches of the AWG output ports 0 and 1 are on, and the link from the splitter to the star couplers 0 and 1 is on. Thus the wavelengths 0 and 1 are broadcast to the star couplers 0 and 1. In the encoder of user (1,2), the switches of the AWG output port 0 and 2 is on, and the link from the splitter to the star couplers 0 and 2 is on. Thus, the wavelengths 0 and 2 are broadcast to the star couplers 0 and 2. Other users encoders generate their codewords in a similar way, and one summation matrix used to represent the wavelengths broadcast to the star couplers is TABLE II CORRELATIONS BETWEEN DIFFERENT KINDS OF USERS (2) where the elements of represent the number of unit power for wavelength in star coupler. This resulting matrix is broadcast to each decoder for decoding information bits. In the following, the MAI-elimination scheme used for the decoding procedure of M-matrix is reviewed. Suppose user is the desired user, the elements of four decoding matrices are defined as (3) Fig. 3. Spatial/frequency decoder. respectively. The corresponding correlation functions with respect to the interfering codeword of user are where is the dot product of two matrices and are the elements of. The following property of M-matrices is used for MAI elimination: (4) for otherwise (5) Decoders that compute the correlation subtractions will reject the interference coming from user assigned as the associated M-matrix codeword. As compared with the desired user, there are three kinds of interfering users that can be classified: the first kind use the same spatial and different spectral codewords; the second kind use different spatial and the same spectral codewords; the third kind use different spectral and different spatial codewords. Table II shows the correlation values respectively produced by the desired users and each kind of interfering user. We find that MAI coming from all kinds of interfering users are eliminated via the proposed MAI-eliminated scheme. The structure of the decoder to realize the correlation-decoding subtractions in (5) is shown in Fig. 3. Similar to the encoder, the links from combiners to star couplers are determined by the spatial codeword of the desired user, but lower-arm links are complement to the ones in the upper arm (e.g., in the upper arm and in the lower arm). The spectral decoder consists of one AWG demultiplexer connected by one switch array. The two output ports of each switch are connected to the upper and lower PDs in the corresponding arms, respectively. If the th chip of spectral codeword is one (or zero), the corresponding switch of the th AWG output port is in the BAR (or CROSS) state, and direct the signal to the upper (or lower) PD. The switch arrays in both arms are controlled by the same spectral codeword. After passing through the spatial decoder and the spectral decoder in both arms, the signal that includes the codeword representing the desired information bit and other interfering codewords will be split into four parts. Thus, correlation subtraction in the upper arm and in the lower arm can be effectively implemented. Finally, the MAI is eliminated in the decoder output and the desired information bit is extracted. Continuing our example mentioned above, we examine the situation in the decoder of user (0,0). According to the codeword of user (0,0), the combiners are connected to star couplers 0 and 1 for the upper arm and star coupler 2 for the lower arm,

HUANG AND YANG: PERMUTED M-MATRICES FOR THE REDUCTION OF PHASE-INDUCED INTENSITY NOISE 153 respectively. The switches in the AWG output ports 0 and 1 are in the BAR state, and other switches are in the CROSS state in both arms. Thus in the upper arm, the wavelengths 0 and 1 from star couplers 0 and 1 arrive at the upper PD and 9 unit power is obtained in total. The wavelength 2 from the same star couplers arrives at the lower PD and 3 unit power is obtained. In the lower arm, the wavelengths 0 and 1 from star coupler 2 arrive at the upper PD and 3 unit power is obtained. The wavelength 2 from the same star coupler arrives at the lower PD and 1 unit power is obtained. Finally, balanced detection will result in unit power, and the decision device decides that information bit one is transmitted. In the decoder of user (0,1), the combiners are connected to star couplers 1 and 2 for the upper arm and star coupler 0 for the lower arm, respectively, and the state of switches in the AWG output ports are the same as the ones for the decoder of user (0,0). Thus, balanced detection will eliminate MAI and result in unit power, and the decision device decides that information bit zero is transmitted. Since each row in one M-matrix code is the same, each user needs only one frequency encoder to encode, and two frequency decoders to decode, the signals in each space channels. This greatly reduces the complexity of the system. In addition, the wavelengths arrived in the PD 0 (or PD 1) are different from the ones in PD 3 (or PD 2), thus, we can direct the signal arrived in PD 3 to PD 0, and direct the signal arrived in PD 2 to PD 1. Therefore, only two PDs are needed in the decoder, and the phase-induced intensity noise (PIIN) arising in the photodetection process is not increased. TABLE III PERMUTED M-MATRIX CODES GENERATED FROM X AND Y TABLE IV THE WAVELENGTH NUMBER COMMUNICATED BETWEEN INPUT/OUTPUT PORT PAIRS IN A 4 2 4 AWG ROUTER III. PERMUTED M-MATRICES The nonzero spectral codewords in each spatial channel are the same for M-matrix codes. Though this feature has the advantage that all space channels can share the same frequency encoder, the PIIN generated in the PDs is larger. To alleviate this problem, each column in M-matrix codes is permuted, and the resulting new code family named permuted M-matrix is proposed. The elements of the permuted M-matrix for user is obtained as follows: (6) where is the modulo- addition. The definitions of and are the same as the ones for M-matrix codes, and there are also in total codewords in the same family. However, the nonzero spectral codewords in each space channel is distinct when is no less than. Table III shows the nine permuted M-matrix codewords generated from and. The permuted M-matrices can be generated from AWG routers, whose operating principle is shown in Table IV. The wavelengths that are incident into the input ports of AWG routers are demultiplexed to all the output ports. However, the same wavelength signals that are incident from different input ports go to different output ports in a cyclic manner as input port no. output port no. wavelength no. (7) The encoder structure for permuted M-matrices is shown in Fig. 4. The resulting signal after E/O modulation is directed to Fig. 4. Encoder structure for permuted M-matrices. the splitter and split to the input ports of the AWG. The links between the splitter and AWG are determined by the spectral codeword of this user, and the links from AWG output ports to the star couplers are determined by the spatial codeword. Thus, AWG demultiplexes the wavelength components of signals entering from different input ports, and the codeword of permuted M-matrices is created in the output ports of AWG, as can be seen from (7). AWG routers usually have an equal number of input and output ports, therefore, the connection arrangement between the AWG router and star couplers in Fig. 4 is only valid when equals. When is smaller than, only output ports of AWG are used for spatial encoding, and the remaining output ports are left disconnected. When is larger than, the switch corresponding to the th chip of the spatial codeword is connected between star coupler and the output port of AWG. In this case, the power in each spatial channel should be carefully controlled, since the number of star couplers connected by each output port of the AWG may be different.

154 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 54, NO. 1, JANUARY 2006 The MAI-elimination scheme described in (5) can also be applied to permuted M-matrices, but the decoding matrices should be slightly modified. Suppose user is the desired user. The elements of four decoding matrices and four correlation functions are modified as (8) Fig. 5. Decoder structure for permuted M-matrices. The following property for permuted M-matrices is suitable for MAI cancellation: Case III:, (same spectral and different spatial codeword) Pf: for otherwise (9) Case IV:, (different spectral and spatial codeword) Recall that Thus, Case I:, (same spectral and spatial codeword) Case II:, (different spectral and same spatial codeword) From the above deduction, we can find that each kind of interfering signal in permuted M-matrix systems produces the same set of correlation values in the PDs as the one in the M-matrix systems. In spite of this, these correlation values are no longer made up of only the spectral codeword signals of each user, and the wavelengths of each user s signal in each spatial channel are distributed more uniformly in four PDs. Fig. 5 shows the structure of the decoder for permuted M-matrices. The states of switches connected between star couplers and the input ports of upper (or lower) AWG are determined by (or ) of the desired user, and similar modification is needed when and are not the same. The way that the spectral codeword controls the transmission of wavelengths from the AWG output ports is also the same as in the encoder. It can be validated from (7) that the MAI-elimination scheme in (9) is realized in the decoder output. Note that the wavelengths that are combined in the PD 0 (or PD 1) may be the same as the ones in PD 3 (or PD 2), thus PDs cannot be shared without increasing PIIN. IV. PERFORMANCE ANALYSIS MAI is the main factor that affects the system performance in some OCDMA systems. In a SAC-OCDMA system using light sources with a nonideal power spectrum, this imperfect phenomenon also affects the system performance. However, with 2-D coding, the code length in the spectral domain can be reduced, and the relatively flat spectrum may be chosen for spectral coding, thus the impact of MAI is no longer serious. The

HUANG AND YANG: PERMUTED M-MATRICES FOR THE REDUCTION OF PHASE-INDUCED INTENSITY NOISE 155 number of total users supported in the system can be maintained by increasing the code length in the spatial domain. When the nonideal power spectrum of light sources is equalized and the signal power is high, the PIIN is the dominant noise source in the SAC-OCDMA systems, and it determines the ultimate supportable capacity of the system [10]. PIIN is the beating between pulses at the same wavelength, which is due to the square-law detection of PDs. The shot noise is proportional to the number of active users, and thus limits the scalability of the total system. When the signal power is low, the thermal noise will dominate the other two noises. Thus we consider these noises in each PD, and their power is denoted as,, and, respectively. In the following analysis, each user in the system is assigned one permuted M-matrix as his signature sequence, and each light source is assumed to be unpolarized and ideal flat with magnitude, where is the effective power from a single source at the receiver, and is the optical source bandwidth in Hertz. Because the probability of sending bit one at any time for each user is 1/2, the total power of noise sources that exist in the photocurrent can be written as [9] The number of active users is denoted as and not more than. For discussion, we divide into two variables and, and we divide into and, where is the floor of the real value. Thus the PSD at four PDs of the receiver (0,0) during one bit period can be written as (10) where ; ; ; electron s charge; noise-equivalent electrical bandwidth of the receiver; Boltzmann s constant; absolute receiver noise temperature; receiver load resistor; responsivity of the PDs; single sideband power spectral density (PSD) of the source received by PD ; photocurrent outputs from PD ; coherent time of the source received by PD [15]. It is given by So the photocurrent of desired signal is and the variance of shot noise is (15) (16) (11) The PSD of the received optical signals from the th star coupler can be written as where is the information bit of the th active user and (12) (17) Here, the worse case where each active user sends bit one is assumed. By using (15), we obtain (18), shown at the bottom of the next page. From the above equations, the variance of PIIN in (10) is obtained. To compute the signal-to-noise ratio (SNR) in the permuted M-matrix systems, we can apply (10), (17), (18), and (16) to the following: is the unit step function defined as (13) (14) SNR (19) The SNR in the M-matrix systems can be obtained by similar methodology, and the results have been proposed in [11]. The relation between the SNR and the number of active users is shown in Fig. 6. This is the case when the number of total users is nearly equal to 255. Because only a certain length of M-sequence exists, the numbers of total users in 1-D and 2-D

156 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 54, NO. 1, JANUARY 2006 Fig. 6. SNR versus number of active users. Fig. 7. PIIN produced in both arms of decoder. systems are not exactly the same. We can find that 2-D codewords outperform traditional 1-D counterparts. This is because the power of the same wavelength contributed by all interfering M-matrices codewords is split into two and detected by two distinct PDs in the double-balanced detector, while in the 1-D case, one certain wavelength of all active users is detected by the same PD. For permuted M-matrices, each wavelength may distribute among four PDs, thus the PIIN is further decreased. Fig. 7 shows the PIIN produced in the upper and lower arms of the decoder for M-matrices. By using Gaussion approximation, bit-error rate (BER) can be obtained by BER SNR. Fig. 8 shows the relation between BER and the number of active users of the codes compared in Fig. 6. The number of active users to achieve for M-matrix ( and ), permuted M-matrix ( and ), and ( and ) are 33, 37, and 46, respectively. The number of simultaneous users among them is increased at most 84% as compared with traditional 1-D systems, whose performance is hardly changed with respect to the code length. When the number of total users is fixed, there exists an optimal value of that maximizes Fig. 8. BER versus number of active users when Psr = 010 dbm. under a given, which can be seen from Fig. 9. If the number of total users is 255, the optimal value of is 3 and 15 for (18)

HUANG AND YANG: PERMUTED M-MATRICES FOR THE REDUCTION OF PHASE-INDUCED INTENSITY NOISE 157 with low cross-correlation can be used as the spatial or spectral codeword of permuted M-matrices while maintaining the number of simultaneous users. V. CONCLUSIONS Fig. 9. BER versus M when number of total users is 255. We propose a 2-D OCDMA system which uses code families with a multiple-weight-per-row property and the MAI can be eliminated theoretically. This system can accommodate a large number of users with the help of an additional dimension, and the encoding/decoding process is realized by low cost and compact structures. Due to the power distribution of each wavelength signal in each PD of the decoder, PIIN arising in photodetecting process is suppressed. When M-matrices are used as signature sequences, only AWG multiplexers are adopted as frequency encoding/decoding devices, and each user needs only one and two AWG multiplexers to encode and decode the signals in each space channels, respectively. To achieve better performance, permuted M-matrices coding is needed, and AWG routers are used to distribute/collect signal with different sets of wavelength to/from each spatial channel. Such a coding scheme is also suitable for any code family for SNR improvement, as long as these code families can be used as the signature sequences of 1-D SAC-OCDMA systems. Both schemes use few additional spatial channels and reduce the number of frequency filters. REFERENCES Fig. 10. BER versus K when M is fixed. M-matrix and permuted M-matrix, respectively. This phenomenon can be explained as follows. Interfering users of the second kind induce the most serious PIIN among the three kinds of interfering users. When the number of total users is fixed, the number of these interfering users decreases as increases. Thus, M-matrices obtain lower BERs for larger. For permuted M-matrix, the PIIN induced by interfering users of the second kind is less, due to the permutation of spectral codewords, thus the influence of interfering users of the first kind becomes more obvious, whose number of users is less, as is smaller. However, as is smaller than, the permutation of spectral codewords does not produce totally different spectral codewords in each spatial channel, and PIIN is increased. Thus, has the optimal value for BER minimization. Fig. 10 shows the effect of when is fixed. Though the system performance is better as is increased, the increment becomes slower as is larger. The main reason is that the large cross-correlation of M-sequences [16] results in more PIIN in the PDs. Therefore, if the power of light sources is large, codes [1] A. Stok and E. H. Sargent, The role of optical CDMA in access networks, IEEE Commun. Mag., vol. 40, no. 9, pp. 83 87, Sep. 2002. [2] K. Kitayama, Novel spatial spread spectrum based fiber optic CDMA networks for image transmission, IEEE J. Sel. Areas Commun., vol. 12, no. 5, pp. 762 772, May 1994. [3] W. C. Kwong and G.-C. Yang, Image transmission in multicore-fiber code-division multiple-access network, IEEE Commun. Lett., vol. 2, no. 10, pp. 285 287, Oct. 1998. [4] L. Tancevski and I. Andonovic, Hybrid wavelength hopping/time spreading schemes for use in massive optical networks with increased security, J. Lightw. Technol., vol. 14, no. 12, pp. 2636 2647, Dec. 1996. [5] G.-C. Yang and W. C. Kwong, Performance comparison of multiwavelength CDMA and WDMA + CDMA for fiber-optic networks, IEEE Trans. Commun., vol. 45, no. 11, pp. 1426 1434, Nov. 1997. [6] L. Tancevski and L. A. Rusch, Impact of the beat noise on the performance of 2-D optical CDMA systems, IEEE Commun. Lett., vol. 4, no. 8, pp. 264 266, Aug. 2000. [7] D. Zaccarin and M. Kavehrad, An optical CDMA system based on spectral encoding of LED, IEEE Photon. Technol. Lett., vol. 4, no. 4, pp. 479 482, Apr. 1993. [8] J. F. Huang and D. Z. Hsu, Fiber-grating-based optical CDMA spectral coding with nearly orthogonal M-sequence codes, IEEE Photon. Technol. Lett., vol. 12, no. 9, pp. 1252 1254, Sep. 2000. [9] Z. Wei, H. M. H. Shalaby, and H. Ghafouri-Shiraz, Modified quadratic congruence codes for fiber Bragg-grating-based spectral-amplitude-coding optical CDMA systems, J. Lightw. Technol., vol. 19, no. 9, pp. 1274 1281, Sep. 2001. [10] E. D. J. Smith, R. J. Blaikie, and D. P. Taylor, Performance enhancement of spectral-amplitude-coding optical CDMA using pulse-position modulation, IEEE Trans. Commun., vol. 46, no. 9, pp. 1176 1185, Sep. 1998. [11] C.-C. Yang and J.-F. Huang, Two-dimensional M-matrices coding in spatial/frequency optical CDMA networks, IEEE Photon. Technol. Lett., vol. 15, no. 1, pp. 168 170, Jan. 2003. [12] C. F. Lam, D. T. K. Tong, M. C. Wu, and E. Yablonovitch, Experimental demonstration of bipolar optical CDMA system using a balanced transmitter and complementary spectral encoding, IEEE Photon. Technol. Lett., vol. 10, no. 10, pp. 1504 1506, Oct. 1998.

158 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 54, NO. 1, JANUARY 2006 [13] H. Takahashi, K. Oda, H. Toba, and Y. Inoue, Transmission characters of arrayed waveguide N 2 N wavelength multiplexer, J. Lightw. Technol., vol. 13, no. 3, pp. 447 455, Mar. 1995. [14] S. Kim, Cyclic optical encoders/decoders for compact optical CDMA network, IEEE Photon. Technol. Lett., vol. 12, no. 4, pp. 428 430, Apr. 2000. [15] J. W. Goodman, Statistical Optics. New York: Wiley, 1985. [16] X. Zhou, H. M. H. Shalaby, C. Lu, and T. Cheng, Code for spectral amplitude coding optical CDMA systems, Electron. Lett., vol. 36, pp. 728 729, Apr. 2000. [17] J. F. Huang, C. C. Yang, and H. P. Tseng, Complementary Walsh Hadamard-coded optical CDMA coder/decoders structured over arrayed-waveguide-grating routers, Opt. Commun., vol. 229, no. 1 6, pp. 241 248, Jan. 2004. [18] E. H. Dinan and B. Jabbari, Spreading codes for direct sequence CDMA and wideband CDMA cellular networks, IEEE Commun. Mag., no. 9, pp. 48 54, Sep. 1998. Chao-Chin Yang was born in Tainan, Taiwan, R.O.C., in 1972. He received the B.S. degree in communication engineering from National Chiao Tung University, Hsinchu, Taiwan, R.O.C., and the Ph.D. degree in electrical engineering from National Cheng Kung University, Tainan, Taiwan, R.O.C., in 1996 and 2004, respectively. In August 2004, he joined the faculty of Kun Shan University, Tainan, Taiwan, R.O.C., where he is now an Assistant Professor in the Department of Electronic Engineering. His major interests are in multiuser optical communications and in the DWDM data communication network. Jen-Fa Huang received the B.Sc. degree in electrical engineering from National Cheng Kung University (NCKU), Tainan, Taiwan, R.O.C., in 1969, and the M.A.Sc. and Ph.D. degrees, both in electrical engineering, from the University of Ottawa, Ottawa, ON, Canada, in 1981 and 1985, respectively. Since 1991, he has been with the Department of Electrical Engineering, NCKU, where he is currently an adjunct Professor of the Institute of Computer and Communication Engineering and the Institute of Electro-Optical Science and Engineering. Previous to 1991, he was with MPB Technologies, Montreal, QC, Canada, in the Optical Communication Laboratories working on the TAT-9 transatlantic undersea lightwave transmission project. His research interests are mainly in the areas of optical fiber communications, all-optical data networking, and in active/passive optical devices.