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A Novel Bipolar Wavelength-Time Coding Scheme for Optical CDMA Systems Uri N. Griner and Shlomi Arnon, Senior Member, IEEE
Abstract—We develop a novel bipolar two-dimensional coding scheme for optical code-division multiple-access (OCDMA) communication systems. The coding scheme is based on complementary spectral amplitude coding of broad-band sources in the wavelength domain and as such enables multi-user operation and bipolar signaling. To significantly increase the number of simultaneous users a spreading sequence in the time domain is imposed on the wavelength domain coding. We analyze the performance of a LAN system based on the proposed coding scheme, and show that the coders can be realized via simple and compact hardware. Index Terms—Bipolar signaling, multi-access communications, optical code-division multiple-access (OCDMA), wavelength-time coding.
I. INTRODUCTION
I
N A LOCAL-AREA network (LAN) environment where the traffic is usually bursty, an efficient multiple access protocol that allows many users to access the network asynchronously at all times is essential. Optical code-division multiple access (OCDMA) is a very attractive multi-access technique that can be used for this purpose. Many OCDMA strategies have been proposed for one-dimensional (1-D) optical coding [1]–[3], and more recently for two-dimensional (2-D) optical coding [4]–[6]. For LAN systems, the two most important parameters are the maximum number of users that can be supported and the bit error rate (BER) in terms of multi-access interference (MAI). Due to the unipolar characteristics of optical signals, which result from the combination of intensity modulation and direct detection (IM/DD), long 1-D codes have been developed to increase the number of simultaneous users. However, the systems that adopt those coding schemes suffer from poor system capacity and BER performance. 2-D codes are a possible solution to overcome these limitations. In this letter, we present a new 2-D coding scheme for waveOCDMA systems that uses complementary length-time spectral-amplitude-coding (SAC) of broad-band sources with bipolar time spreading. The reduction in the MAI due to the 2-D coding enables many more asynchronous users to simultaneously use the system and actually enlarge the system capacity. We show that hundreds of users can be served and BER values can still be achieved. of
Manuscript received May 8, 2003; revised July 23, 2003. This work was supported by the DIP Fund (Israel-German Research Fund). The authors are with the Satellite and Wireless Communication Laboratory, Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, IL-84105 Beer-Sheva, Israel (e-mail:
[email protected];
[email protected]). Digital Object Identifier 10.1109/LPT.2003.819390
Fig. 1.
Scheme of a bipolar spectral-amplitude coding (SAC) system.
II. SPECTRAL ENCODING/DECODING SAC of broad-band sources is a well-known technique used in wavelength domain OCDMA systems. In such systems, the spectrum of the broad-band source is divided into several spectral components. Each user has his own unique code, defined by a specific combination of spectral components which should be orthogonal to all other user codes. The modulation of the spectral elements can be produced by either fiber Bragg gratings or a spatial light modulator (SLM). We consider the second option as it allows more dynamic programmable coding by using microelectrooptical mechanical systems (MEOMS). Fig. 1 shows a scheme of a compact and efficient SAC system which is suitable for the proposed coding scheme. The SAC system has two inputs that are coupled into diffraction gratings. The diffraction grating spatially decomposes the spectral components of the source. A lens collimates the spreading spectral elements from the grating and transfers each spectral element to its related mirror. The mirrors are spatially positioned in accordance with a unique code to selectively reflect the different spectral components. Hence, the spectral components of the first input are reflected from the mirrors in accordance with the spectral code to the first output, while the same spectral components of the second input are blocked by the mirrors. The complementary spectral components of the second input that are not blocked by
1041-1135/04$20.00 © 2004 IEEE
GRINER AND ARNON: A NOVEL BIPOLAR WAVELENGTH-TIME CODING SCHEME FOR OPTICAL CDMA SYSTEMS
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Fig. 2. LAN system based on the proposed coding scheme with bipolar SAC and temporal coding.
the mirrors pass between the mirrors to the first output, while the same spectral components of the first input pass to the second output. A second lens and a diffraction grating are positioned in front of each output in order to efficiently couple the optical power into the SAC system outputs. In order to implement a bipolar SAC system, each spectral code should not only be orthogonal to all other spectral codes but also to their complementary spectral codes. Therefore, we let and the spectral code sequences be any two rows in a binary N N Hadamard be the matrix (except the first row which is all ones) and binary complementary of (meaning ). The code sequences contain equal numbers of ones and zeros. Each code sequence differs from the others by exactly N/2 positions; N/4 of them are zero to one swaps and the other N/4 are one to zero swaps. Therefore, the cross-correlation of a sequence with any other sequence, or with its binary complementary is equal. The auto-and cross correlations of the code sequences are given by
(1) (2) where and are the th spectral element of the codes and , respectively. As a result, a balanced receiver that computes
(3) filters out all signals except the signal coming from one specific user and creates a positive signal if it receives the code sequence as an input, or a negative signal if it receives the complementary code sequence as an input. Hence, full orthogonality between all users is obtained whether they use their code sequence or their binary complementary code sequence. However, since the source and the optical elements do not have a flat spectral response, full orthogonality is degraded and system performance is severely damaged. For this reason, the bipolar coding of the spectral code is further augmented by temporal coding.
III. TEMPORAL ENCODING/DECODING In temporal encoding of optical signals, the spreading sequence has only unipolar values. The sequence period, , is divided into time chips of duration , and in each chip the source is modulated to be either ON or OFF. The bipolarity of the temporal encoding/decoding scheme is made possible by the special characteristics of the spectral encoding. A LAN system coding scheme is shown in Fig. 2. The with the proposed balanced transmitter is built of two light sources, each coupled into an input of the bipolar SAC system. The two light sources are modulated ON and OFF in turn according to the temporal code. The first light source, which transmits the spectral code to the output, is modulated ON whenever the temporal spreading code is “1” and OFF whenever it is “ 1.” The second light source, which transmits the complementary spectral code to the output, is modulated ON whenever the temporal spreading code is “ 1” and OFF whenever it is “1.” At the receiver, the combination of the proposed SAC and the balanced receiver transforms the unipolar signals from the transmitter to electrical bipolar data. The bipolar data undergoes electronic correlation with the bipolar spreading sequence in the time domain. This is feasible by means of a sequence inversion keyed (SIK) switching correlator. Then the signal is integrated over the sequence period and a decision device determines if the transmitted signal is a binary “one” or “zero” in accordance with a threshold value, which is necessarily “zero.” The purpose of the temporal domain coding is to reduce the residual MAI, thus enabling many more users to use the system simultaneously. If we assume that much of the MAI is filtered in the spectral domain, bearing in mind the limited modulation rate of a LED, we can exploit the asynchronous nature of LAN transmission and allow all the users to use the same short optimal spreading sequence. The optimal spreading sequence is a sequence with maximal autocorrelation peak size to sidelobes size ratios. We considered the spreading code sequence , where . The bipolar spreading , where waveform is specified by and is a unit pulse beginning at time and ending at the chip time . Since asynchronous transmission is assumed, the relative time shift, , between user and user is a uniform random variable in the range and can be expressed as , where is an integer
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IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 16, NO. 1, JANUARY 2004
in the range , and . Unless the users are perfectly synchronized, two bits of one user necessarily overlap and to be the with one bit of a second user. If we take two overlapping bits of user that are either the code sequence for transmitted binary “one” or its complementary for transmitted binary “zero,” then, using [7], the normalized discrete periodic autocorrelation function of the spreading code can be derived as
(4) Thus, the temporal normalized autocorrelation becomes (5) In accordance with these expressions, we derived an algorithm to search for optimal sequences for any of the possible s and s{00,01,10,11}. Unexpectedly, we found that three of the optimal sequences were actually Barker codes of chip length 3, 7, and 11 [8]. By using a modified expression (5), these codes maintain their special autocorrelation property, namely for . Considering both spectral and temporal coding, the auto-and the cross correlation functions between the users are
(6) where is the coefficient which represents the power of the th spectral element of user . In our analysis, we focus on MAI, which is the dominant noise, and neglect all sources of receiver noise such as shot noise, thermal noise and dark current noise. Therefore by using the Gaussian approximation the BER can be expressed in terms of the signal-to-interference ratio (SIR):
LED, and has 512 slots. It should be noted that as the spectral code lengthens, the maximal number of users that can be supported by the system simultaneously rises, and MAI decreases. The latter is due to the reduced power difference between the spectral elements. On the other hand, at the same time that the spectral code lengthens, the requirement on the resolution of the spectral filtering is more severe and tolerance to misalignments should be greatly reduced. It is clear that when dealing with asynchronous systems, as the temporal code lengthens, the probability of user to transmit its data perfectly synchronized with user reduces, and thus MAI is reduced at the expense of the bit rate. The reduction in the bit rate may cause significant degradation to high data rate systems since the modulation rate of a LED is limited to a few hundreds of megahertz. Since we want to maintain a communication link of several tens of megahertz, a Barker code of chip-length 11 is a good compromise for achieving system performance improvement due to MAI reduction at the cost of bit rate reduction. We calculated the BER performance as derived from the Monte Carlo simulation results for the “worst” user in both the proposed system with an 11-chip long temporal Barker code and the conventional SAC system. The BER can be calculated using (7) if we assume that the receiver is perfectly synchronized in both the wavelength and time domains and that there is no dispersion. However, when using broad-band sources, dispersion could degrade performances by affecting the time-domain auto-and cross correlation characteristics and therefore should be compensated. Our results show that more than 430 users can use the proposed system simultaBER, while for the conventional SAC system, neously at for the same number of users the BER rises well above BER is achieved with just 38 simultaneous users. and In conclusion, we have proposed a 2-D optical CDMA coding scheme for OCDMA systems that uses bipolar spectral and temporal encoding. The coders can be implemented with conventional and compact hardware. We showed that a LAN system based on this coding scheme can accommodate hundreds of asynchronous users. REFERENCES
(7) and is the average variance of the sum of the cross correlation between user and the other asynchronous users , and each asynchronous user transmits a random data sequence with a random delay . where
IV. PERFORMANCE ANALYSIS AND CONCLUSION In the following analysis, we assume that all users transmit their data asynchronously, and that the light sources of the different users are identical light emitting diodes (LEDs). All the LEDs transmit at the same power and have the same spectral output, which is assumed to have a Gaussian spectral shape, , where is and is 1550 nm. The spectral code is done over the spectral range wherein the power is 50% of the overall power of the
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