IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 16, NO. 10, OCTOBER 2004
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A New Family of Optical Code Sequences for Spectral-Amplitude-Coding Optical CDMA Systems S. A. Aljunid, Member, IEEE, M. Ismail, Member, IEEE, A. R. Ramli, Member, IEEE, Borhanuddin M. Ali, Senior Member, IEEE, and Mohamad Khazani Abdullah, Member, IEEE
Abstract—A new code structure for spectral-amplitude-coding optical code-division multiple-access system based on doubleweight (DW) code families is proposed. The DW code has a fixed weight of two. By using a mapping technique, codes that have a larger number of weights can be developed. Modified double-weight (MDW) code is a DW code family variation that has variable weights of greater than two. The newly proposed code possesses ideal cross-correlation properties and exists for every natural number . Based on theoretical analysis and simulation, MDW code is shown here to provide a much better performance compared to Hadamard and modified frequency-hopping codes.
TABLE I COMPARISON BETWEEN MDW, MFH, OOC, HADAMARD, AND PRIME CODES = 30 FOR THE SAME NUMBER OF USERS
K
Index Terms—Cross correlation, double-weight (DW) code, modified double-weight (MDW) code, optical spectrum code-division multiple-access (OSCDMA).
I. INTRODUCTION PTICAL SPECTRUM code-division multiple-access (OSCDMA) is a multiplexing technique adapted from the successful implementation in wireless networks. In OSCDMA systems, each user is assigned with a sequence code that serves as its address. An optical code-division multiple-access (CDMA) user modulates its code (or address) with each data bit and asynchronously initiates transmission. Hence, this modifies its spectrum appearance, in a way recognizable only by the intended receiver. Otherwise, only noise-like bursts are observed [1], [2]. The advantages of OSCDMA technique over other multiplexing techniques such as time-division multiple-access and frequency-division multiple-access are numerous [3], [8]. Many codes have been proposed for OSCDMA such as optical orthogonal codes (OOCs) [4], prime codes, and modified frequency-hopping (MFH) codes [5]. However, these codes suffer from various limitations one way or another. The codes’ constructions are either complicated (e.g., OOC and MFH codes), the cross-correlation are not ideal (e.g., Hadamard and Prime codes), or the code length is too long (e.g., OOC and Prime code). Long code lengths are considered disadvantageous in its implementation since either very wide band sources or very narrow filter bandwidths are required. Table I shows the code length required by the different codes to support only 30 users. For example, if the chip width (filter bandwidth) of
O
Manuscript received January 12, 2004; revised June 8, 2004. S. A. Aljunid, A. R. Ramli, B. M. Ali, and M. K. Abdullah are with the Photonic Laboratory, Department of Computer System and Communication, Faculty of Engineering, University Putra Malaysia, 43400 UPM, Serdang, Malaysia (e-mail:
[email protected]). M. Ismail is with the Department of Electrical, Electronic and System Engineering, Faculty of Engineering, University Kebangsaan Malaysia, 43600 UKM, Bangi, Selangor Darul Ehsan, Malaysia. Digital Object Identifier 10.1109/LPT.2004.833859
0.5 nm is used, the OOC code will require a spectrum width of 182 nm and prime code will require 480.5 nm, whereas, modified double weight (MDW) only requires 45 nm. Hadamard and MFH codes show shorter code lengths than that of MDW and this will be discussed further in more detail in this letter. It will be shown that the transmission performance of MDW codes is significantly better than that of Hadamard and MFH codes. This is achieved through theoretical calculation and software simulation. II. CODE DESIGN In [5], for code sequence and , the cross-correlation is given by . A code with length , weight and can, and are two most therefore, be denoted by ( , , ). important parameters as they directly affect the overall system signal-to-noise ratio (SNR) as shown by (1) where is the noise equivalent electrical bandwidth of the receiver, is the spectral width, and is the number of simultaneous users. Therefore, for a given value of spectral width , , and , the SNR depends on only. However, for double-weight (DW)-based codes, the cross correlation is designed in such a way that at most, each chip coincides only once with the same chip from other codes. This happens when all users are transmitting at the same time. In reality when not everybody is transmitting, the cross correlation of certain codes may be zero (i.e., no overlapping weights), for example, when only Codes 1 and 3 in (3) are transmitting. Thus, the performance of DW and MDW codes depends on code weight only, which is much easier to control.
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IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 16, NO. 10, OCTOBER 2004
A. DW Code Construction
B. MDW Code Construction
The new proposed code families are referred to as DW codes. It can be constructed using the following steps. Step 1) The DW code can be represented by using a matrix. In DW codes structures, the matrix rows columns will represent the number of user and and the minimum code length respectively. A basic DW code is given by a 2 3 matrix, as shown below
MDW is the modified version of DW code. The MDW code weight can be any even number that is greater than two. In this letter, the MDW with the weight of four is used as an example. As a family of DW code, MDW can also be represented by using matrix. The basic MDW code denoted by (9, 4, 1) the is shown below (7)
(2) Notice that has a chips combination sequence of 1,2,1 for the three columns (i.e 0 1, 1 1, 1 0). Step 2) A simple mapping technique is used to increase the number of codes as shown below
(3)
Notice that a similar structure of the basic DW code is still maintained with a slight modification, whereby, the double weight pairs are maintained in a way to allow only two overlapping chips in every column. Thus, the 1,2,1 chips combination is maintained for every three columns as in the basic DW code. . This is important to maintain The same mapping technique as for DW code is used to increase the number of user. The example shows that we can increase the number of users from four to six while the weight is still fixed at four. An MDW code with weight of four denoted ) for any given code length , which can be related by ( to the number of user through (8)
Note that as the number of user, increases, the code length, also increases. The relationship between the two parameters, and is given by for for
is even is odd.
The total spectral width governed by the code length
of DW and MDW systems is as in (9)
(4)
is the column number of the codes which Note that also represents the spectral position of the chips where is . In DW code sequence construction, the spectral for the first weight and positions of the two weights, for the second weight for the th user are given by (5) and (6) is as in (4). Notice that the spectral position of the where second weight is always the same as the minimum code is always one position length , while the first weight before. This makes the DW code construction simple. For in, the minimum code length is equivalent to stance, if six using (4), and the spectral positions and are and as obtained using (5) and (6), respectively. It is important that the weight positions are maintained in pairs, so that less filters can be used in the encoder and decoder. This way, a filter with the bandwidth twice of the chip width can be used, instead of two different filters, making the systems easier and less costly to implement.
is the chip width. Equation (9) is always valid for where number of users DW and MDW code systems because for multiplexed into a common fiber, the whole code length is spectrally covered. III. CODE EVALUATION AND COMPARISON For comparison, the properties of MDW, MFH, and Hadamard codes are listed in Table II. The table shows that MDW codes exist for any natural number while Hadamard must at codes exist only for the matrix sequence , where least be equivalent to two. On the other hand, MFH codes exist for prime number only. The number of users supported by MDW code is equivalent to . On the other hand, for Hadamard and MFH codes, the and , respectively, number of user supported depends on which in turn, alters the value of weight . This will affect both the design of the encoder–decoder and the SNR of the existing codes in use. In contrast, for MDW codes, can be fixed at any even numbers regardless of the number of users. By fixing , encoder–decoder design and the signal SNR will be maintained and will not be affected by the number of users, as shown by (1). Thus, the same quality of service can be provided for all users. The table also shows clearly that MDW codes have an ideal cross correlation while Hadamard code has increasing value of cross correlation as the number of users increase. For MFH codes, although the cross correlation is also fixed at one, the
ALJUNID et al.: NEW FAMILY OF OPTICAL CODE SEQUENCES FOR SPECTRAL-AMPLITUDE-CODING OPTICAL CDMA SYSTEMS
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TABLE II COMPARISON BETWEEN MDW, MFH, AND HADAMARD CODES
Fig. 2. using
BER versus number of users for MDW, MFH, and Hadamard code
1 = 0 8 nm, = 311 MHz at the operating wavelength of 1550 nm. F
:
B
BER for MFH was achieved for while that for MDW . For , MDW would have given better was for results as governed by (1). V. CONCLUSION Fig. 1. System architecture of the optical CDMA network under test.
SNR is smaller than that of MDW. MFH needs a higher number to increase SNR. of or IV. PERFORMANCE ANALYSIS The performance of MDW, MFH, and Hadamard codes was simulated by using simulation software, OptiSystem Version 3.0. A simple schematic block diagram consists of two users, as illustrated in Fig. 1. Each chip has a spectral width of 0.7 nm. The tests were carried out at the rate of 10 Gb/s for 70-km distance with the ITU-T G.652 standard single-mode optical fiber. All the attenuation (i.e., 0.25 dB/km), dispersion (i.e., 18 ps/nm km), and nonlinear effects were activated and specified according to the typical industry values to simulate the real environment as close as possible. The performances of the system were characterized by referring to the bit-error rate (BER). At the receiver side of the system, the incoming signal splits into two parts, one to the decoder that has an identical filter structure with the encoder and the other to the decoder that has the complementary filter structure. A subtractor is then used to subtract the overlapping data from the intended code. A similar approach has been used in a previous report [7]. The corresponding simulated BER for MDW, Hadamard, and MFH codes , , and , respectively. The results systems were are consistent with the calculated BER for all the codes as shown in Fig. 2. Note that Fig. 2 shows a significantly better performance (smaller BER) than the software simulated results. This is due to the more practical approach of the simulation. Nevertheless, both the simulated and calculated results show the superior performance of MDW codes. Note also that the calculated
In this letter, we have proposed a new family of optical code structure for amplitude-spectral encoding optical CDMA system. It has been shown that the MDW code performs better than the system encoded with Hadamard and MFH codes. The advantages of the proposed code are numerous, including easy and efficient code construction, simple encoder–decoder design, existence for every natural number , ideal cross-corre, and high SNR. The simulated result of one of the lation four MDW coded carriers running at 10 Gb/s over a communication-standard fiber shows a good quality transmission at the . BER of REFERENCES [1] M. B. Pearce and B. Aazhang, “Multiuser detection for optical code division multiple access systems,” IEEE Trans. Commun., vol. 42, pp. 1801–1810, Feb./Mar./Apr. 1994. [2] X. Zhang, Y. Ji, and X. Chen, Code Routing Technique in Optical Network. Beijing, China: Beijing Univ. Posts & Telecommunications, pp. 416–419. [3] S. V. Maric, Z. I. Kostic, and E. L. Titlebaum, “A new family of optical code sequences for use in spread-spectrum fiber-optic local area networks,” IEEE Trans. Commun., vol. 41, pp. 1217–1221, Aug. 1993. [4] J. A. Salehi, “Code division multiple access techniques in optical fiber network—part I: Fundamental principles,” IEEE Trans. Commun., vol. 37, pp. 824–833, Aug. 1989. [5] Z. Wei and H. Ghafouri-Shiraz, “Codes for spectral-amplitude-coding optical CDMA systems,” J. Ligtwave Technol., vol. 50, pp. 1209–1212, Aug. 2002. [6] 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, pp. 1176–1185, Sept. 1998. [7] M. Kavehrad and D. Zaccarin, “Optical code-division-multiplexed systems based on spectral encoding of noncoherent sources,” J. Lightwave Technol., vol. 13, pp. 534–545, Mar. 1995. [8] P. Prucnal, M. Santoro, and F. Ting, “Spread spectrum fiber-optic local area network using optical processing,” J. Lightwave Technol., vol. LT-4, pp. 547–554, May 1986.
