[P6] Naser Tarhuni, Timo O. Korhonen, and Mohammed Elmusrati, "State of Polarization Encoding for Optical Code Division Multiple Access Networks," Journal of ElectroMagnetic Waves and Applications JEMWA scheduled for publication, Volume 21, Number 10, Pages:1313-1321, 2007. (Journal of ElectroMagnetic Waves and Applications JEMWA, Copyright c (2007), with reprint permission from Journal of ElectroMagnetic Waves and Applications JEMWA).
J. of Electromagn. Waves and Appl., Vol. 21, No. 10, 2007 STATE-OF-POLARIZATION ENCODING FOR OPTICAL CODE-DIVISION MULTIPLE-ACCESS NETWORKS N. Tarhuni Communications Engineering Lab Helsinki University of Technology, Otakaari 5A 02150 Espoo, Finland T. Korhonen Communications Engineering Lab Helsinki University of Technology, Otakaari 5A 02150 Espoo, Finland M. Elmusrati Control Engineering Lab Helsinki University of Technology, Otaniementie 17 02150 Espoo, Finland Abstract In this paper we propose the use of the State of Polarization (SOP) encoding in order to realize an optical CDMA system. The SOP of the optical beam is alternately switched between two orthogonal SOPs according to a given codeword. Multiple users can use the network simultaneously each with a distinct codeword. Gold and Hadamard codes can be applied with minimal interference in the latter case. The optical beam power is constant in such case, therefore, self-phase and cross-phase effects can be eliminated. 1 Introduction 2 SOP-CDMA System 3 Simulation results 4 CONCLUSIONS References
2 Tarhuni 1. INTRODUCTION Capacity of optical, statistically multiplexed networks can be significantly enhanced by using optical CDMA that enables accommodation of a number of channels on a single carrier frequency, enabling soft capacity and enhanced security [1, 2]. In addition to the many advantages of optical CDMA, the use of State Of Polarization (SOP) encoding is expected to inherit several Polarization Shift Keying (PolSK) advantages such as higher immunity to laser phase noise [3], increased resistance to self-phase modulation and cross-phase modulation caused by fiber nonlinearities because of constant power [4]. Also, the use of SOP in combination with optical orthogonal codes is reported in [5]. The target was to increase the number of supported users and the SOP was switched during the Marked chip positions according to a given code word. PolSK was considered during recent years as a digital modulation candidate for the optical fiber communications [6]-[7]. It is applicability is a result of the property that an orthogonal state of polarization (SOP) pair from a monochromatic light source at the input of the single mode fiber (SMF) leads to orthogonal SOP pair at the fiber output, although the input SOP is not maintained in general. Measurements on buried SMF fibers (18, 23.7 and 13.9 km links) reported in [8] reveal that polarization fluctuations are quite slow and can vary typically between 2 o -10 o per day. Therefore, a quasi-static scenario is assumed in this paper, in which several blocks of coded data bits suffer from constant polarization offset which can be easily compensated. In this paper we propose the encoding of the SOP using a code word from a given code set to realize the SOP-CDMA approach. The paper is organized as follows: In the Section II the SOP-OCDMA system setup, SOP-encoder, and SOP signals are discussed. Section III shows the simulation results and finally conclusions are drawn at the end of the paper. 2. SOP-CDMA SYSTEM An optical signal propagating along the z-axis will have the transversal electric field components given by, } E x = a x (t) e jφ x(t) E y = a y (t) e jφ (1) y(t) where a x is the amplitude of x-component, a y is the amplitude of y- component, φ x is the phase of x-component, and φ y is the phase of
State-Of-Polarization Encoding for Optical Code-Division Multiple-Access Networks3 Coherent light in x-polarization 0' J J y-polarization 1' Set polarization to 45 o Binary input Optical Phase modulator: o 0' 0 phase shift o 1' 180 phase shift Figure 1. A schematic diagram of the polarization modulator. y-component. Then the electrical field vector is given by, E = (E x x + E y y)e jω 0t (2) where ω 0 is the optical frequency. Using the Jones representation, the field can be represented by the vector, J = [E x, E y ] T and the intensity of the beam can be normalized so that E x 2 + E y 2 = 1. Two polarization states represented by J 1 and J 2 are orthogonal if the inner product is zero, i.e., J H 1 J 2 = E1x E 2x+E1y E 2y = 0, where H is the Hermitian. Any SOP can be transformed into another by multiplying it by a Mueller matrix. Mueller matrices for ideal polarizers, rotators and retarders required for SOP processing can be found in [9]. In PolSK, the angle of one polarization component is switched relative to the other between two angles, therefore, binary data bits are mapped to two Jones vectors (Fig. 1). In Fig. 2 a schematic diagram of the proposed optical SOP-CDMA system is shown. The light source is a highly coherent laser with a fully polarized SOP. If an unpolarized source is used, then a polarizer can be inserted after the laser source. The polarized beam passes through the SOP encoder (PolM) which switches the SOP of the input beam between two orthogonal states N times per bit according to an externally supplied code (such as Hadamard, Gold, or Kassami codes). For a K-user system with the first user as the desired one, the k-th user SOP encoded signal can be written as, { J(0) if d J k (t) = k (t) c k (t) = 0 (3) J (1) if d k (t) c k (t) = 1 where d k (t) = i= d k,ip T (t it ) and c k (t) = i= c k,ip Tc (t it c ) are the data and code signals with d k,i, c k,i {0, 1} and P T (t) is a unity rectangular pulse starting at zero and of width T, and is the XOR operation. We assume for simplicity that the emitted light is initially
4 Tarhuni PN codec 1 d 1 User data Coding s1 Fiber MAI Jones Vector Polarization controller PN code c1 J Jones vector of Laser diode J 1 Desired user coded Jones Vector (a) Transmitter + Jr Jn White noise Jones Vector Electrical path Optical path Compound signal received Jones Vector + J r - Decision Variable (b) Receiver Figure 2. Optical SOP-CDMA, (a) transmitter, (b) receiver. linearly polarized at an angle of 45 o, therefore, J (0) = 1 2 [1, 1] T and J (1) = 1 2 [ 1, 1] T. Hence, the SOP encoded signal travels a distance of L [km] through a single mode fiber (SMF). Consequently, the SOP-encoded signal undergoes several impairments such as, attenuation, dispersion, polarization rotation, and fiber nonlinearity. At the receiver, the SOP rotation is compensated by applying the received SOP encoded signal to the polarization SOP control block (not shown) whose function is to insure that the received signal and the optical components at the receiver have the same SOP reference axis. Therefore, we now have the desired signal Jones vector corrupted by other users transmission
State-Of-Polarization Encoding for Optical Code-Division Multiple-Access Networks5 and by an additive Gaussian noise as, [ ] Erx K J r (t) = = J E 1 (t) + J k (t) + J n (t) (4) ry where J n = [E nx, E ny ] T is the complex Jones vector of the additive white noise. Let us now assume that this composite signal will undergo a lossless split after which the upper (lower) branch the composite signal is alternately switched according to a despreading code (code complement) which is assumed to be synchronized to the transmitter spreading code. Then the polarization transformer rotates the input polarization by 45 o in order to align the output beam polarization to the polarizer axis, which is selected here for simplicity, and without loss of generality, to be the x-polarization axis. The polarizer will pass only the optical beam matched to its axis. The upper branch and lower branch signals are denoted by the superscript ( ) (0) and ( ) (1), respectively. Therefore, the upper and lower branch Jones vectors at the output of the polarization modulators are given by, [ ] J (i) M = E rx (5) E ry exp [j (ang (E ry ) + x i π)] where i = {0, 1}, x 0 = c 1, x 1 = c 1, and ang( ) refers to the angle of the respective complex number. Next each one of these Jones vectors is applied to rotators such that, J (i) R = 1 [ ] 1 1 J (i) 2 1 1 M (6) after which the polarizers will produce only the x-polarization at their output corresponding to the first elements of the Jones vector, therefore, J (i) P = [E (i) Rx, 0]T. Using (5) and (6) the output of the polarizers is given by, Then, J (i) P k=2 = E(i) Rx = 1 2 {E rx + E ry exp [j (ang (E ry ) + x i π)]} (7) which can be written as, D (i) = E (i) Rx 2 = E (i) Rx E(i) Rx (8) D (i) = 1 2 {E rx + E ry exp [j (ang (E ry ) + x i π)]} {E rx + E ry exp [ j (ang (E ry ) + x i π)]} (9)
6 Tarhuni (a) Gold (b) Hadamard Figure 3. Eye Diagram for 3-user SOP-CDMA using (a) Gold (b) Hadamard; codes after 20 km SMF. After expanding and some algebra we get, D (i) = E rx 2 + E ry 2 2 + E rx E ry cos (Φ + x i π) (10) where Φ = ang (E ry ) ang (E r ). The decision variable is the difference between the upper and lower branch outputs which is formulated as follows, D = T 0 E (1) Rx 2 dt T 0 E (0) Rx 2 dt = And the decision is made according to the following rule, T 0 (D (1) D (0) )dt (11) ˆd 1 = { 0 if D < 0 1 if D 0 (12) 3. SIMULATION RESULTS A numerical simulation of the proposed SOP-CDMA system is performed using the VPIphotonics T M VPItransmissionMaker T M WDM simulator. A test with a 20 km SMF fiber having a correlation length of 100 m [10] is performed. Attenuation coefficient of both the fast and slow polarization axis
State-Of-Polarization Encoding for Optical Code-Division Multiple-Access Networks7 are set to 0.2 db/km and a dispersion coefficient of 16 ps/nm/km is assumed. Polarization mode dispersion of 1 ps/ km is applied, which gives rise to 10 ps mean Differential Group Delay (DGD) over 100 Km. For the applied bit rate of 100 Mbit/sec, the DGD is is about 1.4% of the chip period, and therefore it can be neglected. Two type of codes were tested, namely Gold (zero padded) and Hadamard codes with length of 32. Fig. 3 shows the Eye pattern for both codes for 3 simultaneous users. Due to the higher crosscorrelation values of Gold codes, the Eye is severely degraded as compared to the Hadamard case. Synchronous operation is assumed for both cases. The Q factor is depicted in Fig. 4 which shows that Hadamard coded SOP- CDMA will outperform the Gold based system. The main drawback of using Hadamard based system is the requirement of synchronization subsystems. Finally the effect of laser linewidth on the Q factor of a 3-user Hadamard coded SOP-CDMA system is shown in Fig. 5. The Q factor decreases gradually as the linewidth is increased. When the linewidth < 20 KHz the longer code performs better due to higher processing gain. On the other hand, for higher linewidths the longer code is much affected by the fiber dispersion resulting in reduced Q factor. The SOP-CDMA is performance is superior to the conventional optical orthogonal code (OOC) based system [11] in terms of number of supported users and BER performance. An OOC of length N and weight W can support K (N 1)/W (W 1), where x means the integer part of x. Therefore, for an OOC with N = 32 and W = 3 the number of users that can be supported is K = 5 with BER performance (back-to-back system, no fiber link) of 5 10 3. The considered SOP- CDMA with code length of 32 can support 31 users (neglecting the all ones code) and from Fig. 4 the BER of the Hadamard based system with 5 users can be estimated by relating the Q factor with BER as BER = 1 2 erfc( Q 2 ) and this gives a BER 10 15. On the other hand, the OOC based system is less complex and designed to work in asynchronous mode. 4. CONCLUSIONS In this paper we proposed the use of SOP coding to realize an optical CDMA network. The SOP-CDMA network is suggested by assigning to each user a specific code. The polarization of the optical beam is switched according to the supplied code. We demonstrated that multiple users can access the network simultaneously with SOPencoding. Hadamard and Gold codes were tested with the first outperforms the second.
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