No Linealidad Efecto Modulador

Optical Fiber Technology 14 (2008) 247–258

www.elsevier.com/locate/yofte

Nonlinearity effect of electro-optical modulator response in double spreadCDMA radio-over-fiber transmissions

Jen-Fa Huang, Chih-Ta Yen ∗, Tzung-Yen Li

Institute of Computer and Communications, Department of Electrical Engineering, Advanced Optoelectronic Technology Center,National Cheng Kung University, Taiwan

Received 6 September 2007; revised 2 December 2007

Available online 20 February 2008

Abstract

This study presents a double-spread code-division multiple-access (CDMA) scheme for radio-over-fiber (RoF) transmissions. The networkcoder/decoders (codecs) are implemented using arrayed-waveguide grating (AWG) routers coded with maximal-length sequence (M-sequence)codes. The effects of phase-induced intensity noise (PIIN) and multiple-access interference (MAI) on the system performance are evaluatednumerically for different values of the optical modulation index (OMI) during the nonlinear electro-optical modulator (EOM) response. At lowOMI optical device noise is dominant, but at high OMI nonlinear effect becomes significant. Numerical result shows that the system performanceis highly sensitive to the OMI. Therefore, specifying an appropriate value of the OMI is essential in optimizing the system performance. Theinfluence of the degree of polarization (DOP) in the system is also discussed. By employing the scrambler in front of the balanced photo-detector,the system performance can be enhanced. The high-performance, low-cost characteristics of the double-spread CDMA render the scheme an idealsolution for radio-CDMA wireless system cascaded with optical CDMA network.© 2007 Elsevier Inc. All rights reserved.

Keywords: Code-division multiple-access (CDMA); Radio-over-fiber (RoF); Phase-induced intensity noise (PIIN); Multiple-access interference (MAI);Degree of polarization (DOP)

1. Introduction

Satisfying the growing demand for high-quality, reliable per-sonal communication systems which allow users to exchangevoice, text, image and video data requires the realization ofbroadband distribution systems. The next generation of cellularmobile phone systems will be based on micro- and pico-cellulararchitectures. These architectures enable an effective increasein the available bandwidth, thus increasing the maximum per-missible number of simultaneous mobile units and supportingthe provision of broadband services. However, as the number ofmicro-cells in the network increases, the scale of the intercon-nection task increases accordingly. With its high transmissioncapacity and comparatively low cost, optical fiber provides anideal solution for accomplishing these interconnections.

* Corresponding author. Fax: +886 6 2345482.E-mail addresses: [email protected] (J.-F. Huang),

[email protected] (C.-T. Yen).

1068-5200/$ – see front matter © 2007 Elsevier Inc. All rights reserved.doi:10.1016/j.yofte.2007.12.007

The process of modulating RF signals onto an optical carrierfor distribution over a fiber network is referred to as “radio-over-fiber (RoF).” RoF links are designed to transfer radio sig-nals to remote stations without losing their original radio for-mat, e.g., their frequencies, modulation formats, and so on.RoF technology has a number of key advantages, including alow cost and the ability to perform RF allocation of channelswith various modulated formats at a central station (CS), thuspermitting a flexible allocation process and a rapid responseto variations in the traffic demand [1–4]. Optical fiber micro-cellular systems, in which micro-cells distributed over a widegeographic area are connected by optical fibers, and radio sig-nals are transmitted over these optical fiber links between thebase stations (BSs) and the CS, have attracted considerable at-tention. A typical BS consists of an electro-optical (E-O) modu-lator (EOM) to receive the RF signal and to send it to the CS andan opto-electronic (O-E) demodulator to receive signals fromthe CS and to transmit the corresponding RF signal. In otherwords, the BS has only two functions, namely to transmit RF

248 J.-F. Huang et al. / Optical Fiber Technology 14 (2008) 247–258

signals to the CS in an optical format and to transmit RF signalsin an electrical format. More complex tasks such as modulatingthe RF signal to an appropriate format are performed at the CS.

Optical code-division multiple-access (OCDMA) [4–12]provides a powerful solution for RoF network access schemesdesigned to allow multiple users to access the same fiber chan-nel in local area networks (LANs) asynchronously withoutdelay or the need for scheduling. Spectral-amplitude coding(SAC) scheme [4,7–12] has emerged as a powerful techniquefor OCDMA networks in recent years due to its ability toeliminate MAI by preserving orthogonality among the sys-tem users. SAC-OCDMA schemes are typically implementedusing broadband light sources (BLSs) such as light emittingdiodes (LEDs), super luminescence diodes (SLDs), or am-plified spontaneous emission (ASE) light sources and opticalgrating devices such as fiber-Bragg gratings (FBGs) or arrayed-waveguide gratings (AWGs).

SAC-OCDMA is particularly suitable for RoF access sche-me due to its asynchronous access capabilities, flexibility, secu-rity, and transparency for various radio air interfaces. However,RoF over SAC-OCDMA systems have three major drawbacks.First, they are based on intensity modulation (IM) schemes,and hence the network performance is limited by nonlineari-ties (NLs) when analog time-varying radio signals modulatedby EOM with nonlinear BLSs. The nonlinear BLS can be non-linearities in the curve for optical power output versus diodecurrent, and resulting in the intermodulation distortion and in-terference. Second, beat noise such as phase-induced intensitynoise (PIIN) [8–12] will lead to a significant reduction in thesystem performance. Third, previous AWG-based schemes suf-fered a high crosstalk beat noise [10,13] as the number of activeusers was increased. The crosstalk effect of AWG router can beimproved by employing one BLS in the coding system.

In applying the RoF technique, it is desirable to achieve aseamless integration between the wired transport system andthe wireless radio-access system. A “double-spread CDMA”can be accomplished by using an RF-CDMA layer for the ra-dio signal and an OCDMA layer for the optical network. In thisdouble-spread CDMA scheme, RF-CDMA multiplexes the sig-nals of the individual mobile units, while OCDMA multiplexesthe signals of the individual BSs, and the concept as shown inFig. 1.

In the double-spread CDMA system proposed in this study,the RF-CDMA scheme is used to expand the spectrum of thetransmitted signals in the electrical domain. However, a nonlin-ear effect occurs in the IM process when the RF-CDMA signalsare modulated into the optical network during the nonlinearE-O process. To reflect the weak nonlinearity effect of BLSs inthe proposed system, the current analysis considers a Volterraseries comprising only a few Volterra Kernels (VKs) [14,15].Since BLSs exhibit a weak nonlinearity when the current iswell above the threshold level, the analysis considers VKs oflower orders. The nonlinearity of a BLS can be represented us-ing a third-order polynomial without memory. Various papers[3,16–19] have used RF-CDMA schemes within the electricaldomain to overcome the nonlinearity effect caused by nonlinearoptical sources in the optical domain.

Fig. 1. Concept of RoF over double-spread CDMA scheme.

Beat noise seriously impairs the network performance in theoptical domain. Since PIIN is proportional to the square of thelight intensity, simply increasing the transmitting power doesnot improve the system performance. Conventional approachesreduce the beating noise power by expanding the bandwidthin the transmitter prior to optical modulation. Kajiya et al. [3]employed the RF-CDMA scheme to suppress the interferencecaused by optical beat noise in wavelength-division multiplex-ing (WDM) systems. However, the effects of nonlinearity in adouble spread RF-CDMA/OCDMA scheme such as that con-sidered in the present study have yet to be clarified.

The remainder of this paper is organized as follows. Sec-tion 2 presents the proposed double-spread CDMA scheme forRoF transmissions. We also illustrate an example of the encod-ing/decoding process in Section 2. Section 3 develops analyticalformulations to evaluate the effect on the network performanceof nonlinearities of the optical sources and noise in the opticaldomain, respectively. Section 4 presents the numerical evalu-ation results for the proposed double spread system. Finally,Section 5 gives some brief concluding remarks.

2. Proposed RoF over double-spread CDMA configuration

Fig. 2 presents a schematic representation of the AWG-basedencoder in the double-spread system. In the proposed system,BS receives the RF-CDMA signals of M mobile units, andOCDMA signals are transmitted from the BSs to the CS withsingle-mode fiber. In the E-O IM process performed in the en-coder, the RF-CDMA signals of each BS are used to modulatea BLS whose spectrum is filtered for the one free spectral range(FSR) of the AWG router. A common ASE source can be em-ployed as BLS in the system.

The proposed OCDMA encoder and decoders employ aSAC-OCDMA scheme with quasi-orthogonal M-sequencecodes over AWG routers rather than a conventional time-division multiplexing (TDM) structure to separate the signalsfrom different BSs in order to suppress multiple-access inter-

J.-F. Huang et al. / Optical Fiber Technology 14 (2008) 247–258 249

Fig. 2. Proposed AWG encoder with BSs coded into OCDMA.

ference (MAI) in optical domain. For a total of N BSs, thesystem requires one N × N AWG router for the encoder andtwo N ×N AWG routers for the decoder. The encoder/decoders(codecs) located at the BS and CS sites are connected via anN × 1 combiner and 1 × N splitter such that all of the BSs tothe CS signals can be transmitted over a shared optical fiber.

The wavelength of the BLS light incident at the input portsof the AWG router is demultiplexed into wavelengths λ1 ∼ λN

and these wavelengths are distributed across the output ports ofthe router as a result of interference in the second slab of thewaveguide.

Let C0 = (c0,1, c0,2, . . . , c0,N ) be a unipolar M-sequencecodeword of length N assigned as the codeword of BS #0. Thecodeword of the ath user’s sequence (a = 0,2, . . . ,N − 1) canbe obtained by cyclically shifting the original sequence (i.e.,Ca = T aC0, where T is an operator which shifts vectors cycli-cally to the right by one place). Assume that the link betweenthe BLS and the ith input ports is arranged according to c0,i

(e.g., the link is connected when c0,i is 1, and disconnected,otherwise). It is found that the (i ⊕ k)th chip of Ck appears inthe ith output port (⊕ denotes modulo-N addition).

Let ck(i) denote the ith element of the kth M-sequencecodeword. The code properties can be expressed as

Rcc(k, l) =N∑

i=1

ck(i)cl(i) ={

(N + 1)/2, k = l,

(N + 1)/4, k �= l(1)

and

Rcc(k, l) =N∑

i=1

ck(i)cl(i) ={

0, k = l,

(N + 1)/4, k �= l,(2)

where N is the length of the M-sequence code.The balanced photo-detector for the desired BS #l executes

the following correlation subtractions:

Z = RCC(k, l) − RCC(k, l) ={

(N + 1)/2, k = l,

0, k �= l.(3)

Equation (3) shows that the MAI from other BSs will becompletely cancelled in theory.

Fig. 2 shows the general case where the AWG router-basedencoder in the transmitter is used to encode the signals of N

Fig. 3. Illustrative example of RF-CDMA signals received in BS #l.

BSs. In this arrangement, the AWG input ports corresponding toan M-sequence code element of “1” are connected to the BLS.For example, for a codeword of “1, 1, 1, 0, 0, 1, 0,” AWG inputports #0, #1, #2, and #5 are connected to the BLS. The opticalcarriers of the same optical wavelength in AWG router incidentat different input ports are directed to different output ports bycyclic properties. The resulting optical signals of all the BSs aredirected to the corresponding output ports of the AWG router.Due to the cyclic properties of AWG routers and M-sequencecode, respectively, all of the coded chips of each BS are presentin the output ports of the AWG encoder and the mobile unitsreceived in each BS (i.e., BS #0, BS #1, . . . , BS #N − 1) canall share a single AWG encoder.

The M RF-CDMA signals transmitted to CS are collected inBS #l, as shown in Fig. 3. The j th coded binary phase shift key-ing (BPSK) signal from each mobile unit transmitted to BS #l

has the form:

Slj (t − τlj ) = dlj (t − τlj )clj (t − τlj ) cos(2πfct + φlj ), (4)

where τlj is the time asynchronism of the j th mobile unit inrelation to the other M − 1 mobile units of BS #l, fc is the RFcarrier frequency for each mobile unit, φlj is the random phaseof the j th mobile unit in BS #l, dlj (t) is the transmission data ofthe j th mobile unit in BS #l and has a value of {+1,−1} witha period Tb, and clj (t) is the RF-CDMA spreading code of thej th mobile unit in BS #l with a period Tc. The ratio of Tb to Tcrepresents the processing gain (PG) of the RF-CDMA scheme.Therefore, the output signal of BS #l is given by

Sl(t) =M∑

k=1

Slk(t − τlk). (5)

The RF-CDMA signals received in the BS #l are used tomodulate the optical signals output from the AWG router. Theideal optical power function of BS #l is expressed as

Pl(t) = PT(1 + m0Sl(t)

), (6)

where PT is the average transmitted optical power of the BLSand m0 is the optical modulation index (OMI).

Table 1 shows an example of M-sequence code of lengthN = 7. Note that for simplicity, the transmitted power for


Table 1M-sequence code of length 7 for optical spectral coding

AWG input Signature sequence BS signal Transmitted signals with wavelengths

#0 (with BLS) 1 1 1 0 0 1 0 S0(t) λ(0)1 λ

(1)2 λ

(2)3 0 0 λ

(5)6 0

#1 (with BLS) 0 1 1 1 0 0 1 S1(t) 0 λ(0)2 λ

(1)3 λ

(2)4 0 0 λ

(5)7

#2 (with BLS) 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0

#3 0 1 0 1 1 1 0 S3(t) 0 λ(5)2 0 λ

(0)4 λ

(1)5 λ

(2)6 0

#4 0 0 1 0 1 1 1 S4(t) 0 0 λ(5)3 0 λ

(0)5 λ

(1)6 λ

(2)7

#5 (with BLS) 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0

#6 1 1 0 0 1 0 1 S6(t) λ(1)1 λ

(2)2 0 0 λ

(5)5 0 λ

(0)7

Received signal S 2λ1 4λ2 3λ3 2λ4 3λ5 3λ6 3λ7

Note. Subscripts represent input port number of AWG router.

Fig. 4. Proposed AWG decoder for M-sequence code.

each BS is assumed to be unity in the current analysis. Inthis example, BS #2 and #5 do not transmit any radio signals.BS #0 signal modulates the output of output port #0 of theAWG encoder (i.e., C0 = (1,1,1,0,0,1,0) with central wave-lengths λ1, λ2, λ3, and λ6). Due to the cyclic property of theM-sequence code and the AWG router, C1 = (0,1,1,1,0,0,1)

with central wavelengths λ2, λ3, λ4, and λ7 appears at outputport #1 and is modulated by BS #1. Therefore, a total of sevenBSs can share a single AWG router in the encoder. FollowingAWG encoding, the spectral signals are combined in the com-biner and broadcast to the links connected to the decoders ofthe CS in the network. The spectrum of the received signal, S,is therefore the sum of the spectra of the individual BSs’ trans-mitted signals spectrum, i.e.,

S = (s0, s1, . . . , sN−1) =N−1∑k=0

SkCk, (7)

where Sk is the signal spectrum of BS #k. In the example shownin Table 1, the received signal spectrum S is equal to (2, 4, 3, 2,3, 3, 3).

Fig. 4 presents a schematic illustration of the proposed AWGrouter-based decoder in the CS. The splitter is connected to thedecoder’s AWG router pair, which distributes received signalsto the balanced photo-detectors of each BS to realize differen-

tial decoding. The CS use balanced photo-detectors to decodethe OCDMA signals received from the BSs and then decodedRF-CDMA signals in mobile units. Finally, the RF-CDMA sig-nals for the desired mobile unit are further extracted from thedecoded OCDMA BS signals. Similar to the connection fromthe encoder router to the star coupler, connections from the starcoupler to the upper and lower AWGs are determined by theC0 code word and its complementary code word C0, respec-tively. The balanced photo-detector of BS #l will receive SCl

from the upper AWG and SCl from the lower AWG. After cor-relation subtraction SCl −SCl is performed in the lth balancedphoto-detector, the RF-CDMA wave of BS #l is subsequentlyrecovered and other BSs’ interferences are rejected.

Tables 2 and 3 shows the wavelength distributions in the up-per and lower AWG routers. As shown in Table 2, wavelengthchips #1, #2, #3, and #6 of the received signal S are obtainedat output port #0 of the upper AWG router from input ports #0,#1, #2, and #5. The upper photodiode of CS decoder #0 there-fore obtains SC0 = 12 units of energy. The remaining chips ofthe received signal are obtained from input ports #3, #4, and#6 of the lower AWG router, as shown in Table 3. In this case,the lower photodiode of CS decoder #0 obtains SC0 = 8 unitsof energy. Therefore, the differential detection process yieldsa total of SC0 − SC0 = 4 units of energy. Applying the sameprocesses to CS decoder #5, the decoded energy is found tobe 0. Hence, the use of balanced photo-detectors enables theMAI arising from other BSs to be canceled.

As shown in Fig. 5, after the optical decoding process, theRF-CDMA signals are further decoded in the electrical do-main by multiplying the signals by the RF-CDMA signaturecodes for each mobile unit. Following digital demodulation,the j th mobile unit signal in the CS decoder #l is finally ex-tracted.

3. Performance analysis of double-spread CDMA RoFtransmissions

Consider the case shown in Fig. 3 where the j th RF signalcorresponding to mobile unit #j in BS #l modulates the codedwavelengths from the lth AWG output port. The form of themodulated BPSK signal of the j th mobile unit in BS #l is givenin Eq. (4). The nonlinearity optical field function can be mod-eled by a third-order polynomial without memory [16,18], i.e.,


Table 2Wavelength distribution in AWG-router based decoder. Upper AWG-decoder

Input λ Output Received signals Unit

λ1 λ2 λ3 λ4 λ5 λ6 λ7 with wavelengths power

Port #0 2 4 3 2 3 3 3 Port #0 2λ(0)1 + 4λ

(1)2 + 3λ

(2)3 + 3λ

(5)6 12

Port #1 2 4 3 2 3 3 3 Port #1 4λ(0)2 + 3λ

(1)3 + 2λ

(2)4 + 3λ

(5)7 12

Port #2 2 4 3 2 3 3 3 Port #2 2λ(5)1 + 3λ

(0)3 + 2λ

(1)4 + 3λ

(2)5 10

Port #3 0 0 0 0 0 0 0 Port #3 4λ(5)2 + 2λ

(0)4 + 3λ

(1)5 + 3λ

(2)6 12

Port #4 0 0 0 0 0 0 0 Port #4 3λ(5)3 + 3λ

(0)5 + 3λ

(1)6 + 3λ

(2)7 12

Port #5 2 4 3 2 3 3 3 Port #5 2λ(2)1 + 2λ

(5)4 + 3λ

(0)6 + 3λ

(1)7 10

Port #6 0 0 0 0 0 0 0 Port #6 2λ(1)1 + 4λ

(2)2 + 3λ

(5)5 + 3λ

(0)7 12

Table 3Wavelength distribution in AWG-router based decoder. Lower AWG-decoder

Input λ Output Received signals Unit

λ1 λ2 λ3 λ4 λ5 λ6 λ7 with wavelengths power

Port #0 0 0 0 0 0 0 0 Port #0 2λ(3)4 + 3λ

(4)5 + 3λ

(6)7 8

Port #1 0 0 0 0 0 0 0 Port #1 2λ(6)1 + 3λ

(3)5 + 3λ

(4)6 8

Port #2 0 0 0 0 0 0 0 Port #2 4λ(6)2 + 3λ

(3)6 + 3λ

(4)7 10

Port #3 2 4 3 2 3 3 3 Port #3 2λ(4)1 + 3λ

(6)3 + 3λ

(3)7 8

Port #4 2 4 3 2 3 3 3 Port #4 2λ(3)1 + 4λ

(4)2 + 2λ

(6)4 8

Port #5 0 0 0 0 0 0 0 Port #5 4λ(3)2 + 3λ

(4)3 + 3λ

(6)5 10

Port #6 2 4 3 2 3 3 3 Port #6 3λ(3)3 + 2λ

(4)4 + 3λ

(6)6 8

Fig. 5. Proposed RF-CDMA decoder for BS #l.

El(t) = [PT

(1 + m0Sl(t) + a2m

20S

2l (t) + a3m

30S

3l (t)

)]1/2

× Lel(t), (8)

where a2 and a3 are the second- and the third-order nonlin-ear coefficients, respectively, and Lel(t) is the optical sourcefunction corresponding to the filtered BLS signal at the lth out-put port of the AWG. Since the second-order inter-modulationdistortion (IMD) term generates zero frequency and a doublesignal frequency component and the third-order IMD term gen-erates a signal frequency and a triple signal frequency com-ponent as a result of the nonlinear E-O IM effect, only oneharmonic of the third-order IMD term falls in the signal fre-quency band and influences each mobile unit. At CS decoder#l, the photocurrent signal dropping by the zero-, double-, andtriple-frequency terms in (8) can be expressed by the followingequation:

il(t) = Dlj (t) +6∑

i=1

Zli(t) + n(t), (9)

where Dlj (t) is the desired mobile unit signal current from BS#l, Zli(t) is the interference signal current from the other mo-bile units in CS decoder #l, and n(t) is additive white Gaussiannoise (AWGN) with a power spectrum density (PSD) of N0/2.In the AWGN model, the noise in the fiber-optic link is definedas [16,18,19]

N0 = 4KBTabsF/RL + 2qR0P0 + PIIN, (10)

where KB is the Boltzmann constant, Tabs is the absolute tem-perature, F is the noise figure of the receiver electronics, RLis the photodiode (PD) load resistor, q is the electron charge,R0 is the responsivity for each of the PDs, and P0 is the av-erage received power of PD. The first and the second terms ofN0 represent the thermal noise and the shot noise, respectively.Meanwhile, the third term corresponds to the PIIN for the spe-cific case of SAC RoF system [11,20].

In analyzing the performance of the current RoF system, thefollowing assumptions are made:

• Each light source is ideally unpolarized and its spectrum isflat over the bandwidth [ν0 − �ν/2, ν0 + �ν/2], where ν0is the central optical frequency and �ν is the optical sourcebandwidth.

• Each power spectrum component has an identical spectralwidth.

• Each user has an equal power at the receiver.• Each bit stream from each user is synchronized.


• The transmitted process without power attenuation, i.e.,PT = P0.

Based on these assumptions, the performance of the pro-posed system is easily evaluated using a Gaussian approxima-tion.

The instantaneous PSD of the received optical signal can bewritten as

S(t, v) = P0

�v

K−1∑k=0

[1 + m0Sk(t) + a2m

20S

2k (t) + a3m

30S

3k (t)

]

×N∑

i=1

ck(i)rect(i), (11)

where rect(i) is a rectangular function with the form:

rect(i) = u

[v − v0 − �v

2N(−N + 2i − 2)

]

− u

[v − v0 − �v

2N(−N + 2i)

](12)

in which u(v) represents a unit step function.Assuming the bit synchronism case, the instantaneous PSDs

at upper PD1 and lower PD2 of the lth decoder during one bitperiod can be written respectively as

G1(t, v) = P0

�v

K−1∑k=0

[1 + m0Sk(t) + a2m

20S

2k (t) + a3m

30S

3k (t)

]

×N∑

i=1

ck(i)cl(i){rect(i)

}(13)

and

G2(t, v) = P0

�v

K−1∑k=0

[1 + m0Sk(t) + a2m

20S

2k (t) + a3m

30S

3k (t)

]

×N∑

i=1

ck(i)cl(i){rect(i)

}. (14)

From Eqs. (13) and (14), the instantaneous power incident atthe upper PD1 and lower PD2 is given by∞∫

0

G1(t, v) dv

= P0

N

(N + 1

2

)[1 + m0Sl(t) + a2m

20S

2l (t) + a3m

30S

3l (t)

]

+ P0

N

K−1∑k=0, k �=l

(N + 1

4

)[1 + m0Sk(t) + a2m

20S

2k (t)

+ a3m30S

3k (t)

](15)

and∞∫

0

G2(t, v) dv = P0

N

K−1∑k=0, k �=l

(N + 1

4

)[1 + m0Sk(t)

+ a2m2S2(t) + a3m

3S3(t)]. (16)
0 k 0 k
The detected photocurrent in the decoder of BS #l is givenby the difference in the photodiodes’ output photocurrents, i.e.,

il(t) = i1(t) − i2(t) = R0

∞∫0

G1(t, v) dv − R0

∞∫0

G1(t, v) dv

= R0P0

N

(N + 1

2

)[1 + m0Sl(t) + a2m

20S

2l (t)

+ a3m30S

3l (t)

]. (17)

The variance of the photocurrent caused by the PIIN effectis given by

PIIN = ⟨I 2

PIIN

⟩ = E[I 2(1 + P 2)τc

], (18)

where the source coherence time, τc, is expressed as

τc =∫ ∞

0 G2(t, v) dv

[∫ ∞0 G(t, v) dv]2

(19)

and the degree of polarization (DOP), P , is defined as

P 2 = (〈s1〉2 + 〈s2〉2 + 〈s3〉2)

〈s0〉2, (20)

where s0, s1, s2, and s3 are Stoke parameters used to express thestate of polarization (SOP). The bracket 〈·〉 in Eq. (20) denotesthe average value of the parameter over wavelength, time, orspace. It is well known that the DOP is dependent on not onlythe light source, but also the distance traveled by the opticalsignal in long haul network transmissions.

In Eq. (19), G(t, v) is assumed to be the single sideband in-stantaneous PSD of the source. Since the noises at the upperand lower photodiodes are independent, the power of the noisesources in the output photocurrent can be written as (see Ap-pendix A):

⟨i2PIIN

⟩ = R20P 2

0 (1 + P 2)(N + 1)

2�v

×[

1 + M(2a2m20 + m2

0 + 2a3m40 + a2

2m40 + a2

3m60)

2

]

+ R20P 2

0 (1 + P 2)(N − 1)(N + 1)

4�v. (21)

An assumption is made that the filter is perfectly matchedto the j th mobile unit in BS #l. Without loss of generality, τlj

and φlj can be set to zero, and the matched filter output of thedesired mobile unit and the interference acting on the mobileunit output can be obtained at sampling time t = T as

Dlj =T∫

0

Dlj (t)clj (t) cos(2πfct) dt, (22)

Zli =T∫

0

Zli(t)clj (t) cos(2πfct) dt, (23)

where T is the bit period of the transmission data.


Fig. 6. CINR with number of active BSs.

Assuming the RF-CDMA code to be random code, the de-sired mobile unit strength #j in CS decoder #l and the inter-ference strength in CS decoder #l can be calculated from thefollowing equation (see Appendix B):

E(D2

lj

) = 1

2

[m0R0P0T

N

(N + 1

2

)]2

. (24)

Equation (24) above describes the desired mobile unit’s out-put signal power. Equation (25) below describes the interfer-ence noise power. The interference noise power is classifiedbased on the same phase at the matched filter output, and canbe presented as

Var(Zl1) =[

R0P0

N

(N + 1

2

)]2[m0 + a3m

30(6K − 3)

4

]2

× 9T 2

24P 3G

× 2PG2, (25a)

where K denotes the number of mobile units.

Var(Zl2) =[

R0P0

N

(N + 1

2

)]2(a3m

30

4

)2 9T 2

8

× (K − 1), (25b)

Var(Zl3) =[

R0P0

N

(N + 1

2

)]2(a3m

30

4

)2 3T 2

8P 3G

× (2PG2) × (K − 1), (25c)

Var(Zl4) =[

R0P0

N

(N + 1

2

)]2(a3m

30

4

)2 3(K − 2)T 2

8P 3G

× (2PG2) × (K − 1), (25d)

Var(Zl5) =[

R0P0

N

(N + 1

2

)]215(K − 1)(K − 2)T 2

8N3

× (2PG3), (25e)

Var(Zl6) =[

R0P0

N

(N + 1

2

)]2(a3m

30

4

)2

× 3(K − 1)(K − 2)(K − 3)T 2

80N3× 4PG4. (25f)

The carrier-to-interference-plus-noise ratio (CINR) for thej th mobile unit in BS #l is given by

CINRlj = Ei(D2lj )∑6

i=1 Var(Zli) + N0T/4. (26)

By assuming all the interference terms to be Gaussian dis-tributed, the conditional bit error rate (BER) can be calculatedfrom BPSK modulation, i.e.,

BERlj = (1/2)erfc(CINRlj )1/2. (27)

4. Numerical results

Fig. 6 shows that the system performance is degraded as thenumber of active BSs increases. In this case, the total number ofmobile units in the BS is 16 and the RF-CDMA chip length ateach BS is 511. In Fig. 6, we can find that the higher OMI (i.e.,m = 0.35) the better CINR in PIIN-limited case. The reason isthat higher OMI will contribute higher modulated signal powerin optical domain. In this case, we focus on the PIIN noise de-stroying the system performance between the BSs. When thenumber of active BSs becomes large, the system performancefalls because more wavelengths are required in the optical do-main to support a higher number of active BSs, and hence the


Fig. 7. Variation of BER with number of active mobile units.

Fig. 8. Variation of BER with RF-CDMA chip length.

PIIN increases. Fig. 7 shows that the system performance isalso degraded as the number of active mobile units’ increases.In this case, the total number of the active BSs is 16 and theRF-CDMA chip length at each BS is 511. The poorer systemperformance is a result of an increased mobile unit interferencenoise power; it will induce high MAI. The results indicate thata BS can support at least 26 mobile units when the OMI, m0, isequal to 0.35 at BER = 10−9.

Fig. 8 shows that the system performance can be improvedby increasing the chip length (i.e., increasing the PG) of theRF-CDMA code. The total number of active mobile units andBSs in this case is 16. This performance improvement arisesbecause a higher PG limits the MAI induced by the other mo-bile units in the BS. In Fig. 8, we can find the optimal OMIwhich yields the lowest BER, and this optimal OMI level isless than m = 0.35. This is because higher OMI will induce


Fig. 9. Variation of CINR with optical modulation index.

Table 4Measured DOPs of ASE light source

DOP Power Stoke parameters

s0 s1 s2 s3

ASE light source 2.1% 6.45 dB m 6.45 −0.00 −0.01 −0.01Polarized ASE light source 100% −1.34 dB m −1.33 −0.03 0.99 0.02ASE light source with polarization scrambler 0.8% 0.03 dB m 0.03 −0.00 0.00 −0.00

higher third-order IMD, hence it is important to keep opti-mal OMI.

The CINR of the double-spread CDMA system is highlysensitive to the value of the OMI, as illustrated in Fig. 9. Inthis case, the total number of the active mobile units and BSs is16 and the RF-CDMA chip length at each BS is 511. Numeri-cal results show that the CINR value improves as the OMI valueis increased from m0 = 0 to 0.29, but deteriorates as the OMIvalue is increased from m0 = 0.30 to 1.0. The maximum CINRvalue is approximately 24 dB, and is achieved at m0 = 0.29.This figure demonstrates the importance of choosing an appro-priate OMI value in optimizing the system performance.

To evaluate the DOP for a general light source, we adopt acommon ASE source (Agilent 83438A) to perform simple ex-periments with back-to-back configurations in which the ASEsource was connected to a polarization analyzer (HP 8509C).As shown in Table 4, the measured DOP is approximately 0.021at the wavelength of 1550 nm. Note that the power of the lightsource has been properly attenuated.

Subsequently, the linear polarizer of HP 8509C was selectedto polarize the ASE source. In such case, the detected DOPis approximately 1, as shown in Table 4 using linear polarizercase. It can be seen that the power is degraded by approximately8 dB compared to the un-polarized case.

An un-polarized ASE source is used in the current double-spread CDMA system because the scheme considers only thesource power, but not phase or polarization. The results in Ta-ble 4 with scrambler case confirm the small DOP effect ofthe ASE light source, which can be neglected. However, onthe long-haul transmissions over RoF network the DOP effectmust be addressed. In this study, CINR is improved by posi-tioning a scrambler in front of balanced photo-detector to elim-inate the polarization-dependent effect of the detector. Hence,the average values of s1, s2, and s3 in Eq. (20) approach zeroas shown in Table 4 and the DOP is significantly decreased.In other words, the scrambler theoretically removes the polar-ization sensitivity of the photodetector in the proposed RoFscheme. In a previous study, Lutz [21] also configured a de-polarizer in front of the balanced photo-detector and achieveda DOP of 0.03 (i.e., P = 0.03). In order to analyze the BERperformance with and without the scrambler, respectively, theaverage DOP value of 0.5 (i.e., the DOP varies in the range 0to 1) was assumed to represent the general case of zero depo-larization compensation following long haul transmission.

As shown in Fig. 10, the BER performance of the proposeddouble-spread CDMA scheme is characterized by an upperbound of P = 1 for the worst case and a lower bound of P = 0for the ideal case with the same assumption at OMI = 0.25


Fig. 10. BER performance with degree of polarization, DOP.

as Fig. 7. Significantly, by placing a scrambler (FIBERPROPS-155-A) in front of the balanced photo-detector to achievea DOP of P = 0.008, it is observed that the curve of P = 0.008virtually overlaps that of the proposed RoF scheme with M-sequence code in the ideal case (i.e., P = 0). Compared to theaverage DOP of 0.5, the maximum permissible number of ac-tive mobile units is improved by approximately 3% for a 10−9

error probability.

5. Conclusions

Radio-over-fiber system has prompted the development ofpassive optical networks. The double-spread CDMA schemefor RoF transmissions presented in this study performs SACmethod of a BLS in the wavelength domain and only requiresa single optical source connected to (N + 1)/2 input ports ofan AWG router to accomplish encoder of N BSs. By exploitingthe cyclic properties of M-sequence codes and AWG devices,respectively, the proposed scheme requires just three AWG de-vices to implement the coders/decoders. Furthermore, the useof balanced photo-detectors in the decoders of the proposedsystem cancels MAI between BSs in the optical domain, al-though MAI may increase between mobile units following theE-O nonlinear process.

The analytical results have shown that the PIIN increaseswith an increasing number of active BSs since more wave-lengths are required in the optical domain and depend on thevalue of DOP. By introducing a scrambler in front of the bal-anced photo-detector, the PIIN effect can be decreased. Further-more, due to the nonlinearity of the optical source, the systemperformance is reduced as a result of MAI when the numberof active mobile units in an BS increases. However, the system

performance can be improved by increasing the chip length ofthe RF-CDMA code. Finally, the results have shown that theperformance of the proposed double-spread CDMA system ishighly sensitive to the value of the OMI. Therefore, for a givennumber of users, an appropriate choice of the OMI value isessential to ensure that the optimal system performance is ob-tained.

Appendix A. Derivation of Eq. (18) for PIIN power

According to the instantaneous PSDs given in Eqs. (13)and (14), it can be shown that∞∫

0

G21(t, v) dv = P 2

0

N�v

N∑i=1

[K−1∑k=0

[1 + m0Sk(t) + a2m

20S

2k (t)

+ a3m30S

3k (t)

]ck(i)

][K−1∑s=0

[1 + m0Ss(t)

+ a2m20S

2s (t) + a3m

30S

3s (t)

]cs(i)

]cl(i) (A.1)

and∞∫

0

G22(t, v) dv = P 2

0

N�v

N∑i=1

[K−1∑k=0

[1 + m0Sk(t) + a2m

20S

2k (t)

+ a3m30S

3k (t)

]ck(i)

][K−1∑s=0

[1 + m0Ss(t)

+ a2m20S

2s (t) + a3m

30S

3s (t)

]cs(i)

]cl(i). (A.2)


Applying the expectation operation to Eqs. (A.1) and (A.2)and assuming the worst-case scenario in which all of the mobileunits in BSs simultaneously transmit the signals, will yield:

E

[( ∞∫0

G21(t, v) dv +

∞∫0

G22(t, v) dv

)]

= P 20

N�vE

{N∑

i=1

[K−1∑k=0

[1 + m0Sk(t)

+ a2m20S

2k (t) + a3m

30S

3k (t)

]ck(i)

]

×[

K−1∑s=0

[1 + m0Ss(t) + a2m

20S

2s (t) + a3m

30S

3s (t)

]cs(i)

]}

= P 20

N�v

N∑i=1

E

{[K−1∑k=0

[1 + m0Sk(t)

+ a2m20S

2k (t) + a3m

30S

3k (t)

]ck(i)

]

×[

K−1∑s=0

[1 + m0Ss(t) + a2m

20S

2s (t) + a3m

30S

3s (t)

]cs(i)

]}

= P 20

N�v

N∑i=1

K−1∑k=0

K−1∑s=0

E{[

1 + m0Sk(t)

+ a2m20S

2k (t) + a3m

30S

3k (t)

]× [

1 + m0Ss(t) + a2m20S

2s (t) + a3m

30S

3s (t)

]}cs(i)ck(i)

= P 20

N�v

K−1∑k=0

K−1∑s=0

E{[

1 + m0Sk(t)

+ a2m20S

2k (t) + a3m

30S

3k (t)

]× [

1 + m0Ss(t) + a2m20S

2s (t) + a3m

30S

3s (t)

]}×

N∑i=1

ck(i)cs(i)

= P 20

N�v

(N + 1

2

)N

×[

1 + M(2a2m20 + m2

0 + 2a3m40 + a2

2m40 + a2

3m60)

2

]

+ P 20

N�v

(N + 1

4

)N(N − 1). (A.3)

By substituting Eq. (A.3) into Eq. (18), the PIIN can be ex-pressed as⟨i2PIIN

⟩ = E[I 2(1 + P 2)τc

] = E[(

I 21 (t) + I 2

2 (t))(1 + P 2)τc

]= E

[( ∞∫0

G21(t, v) dv +

∞∫0

G22(t, v) dv

)](1 + P 2)R2

0

= R20P 2

0 (1 + P 2)(N + 1)

2�v

×[

1 + M(2a2m20 + m2

0 + 2a3m40 + a2

2m40 + a2

3m60)

2

]

+ R20P 2

0 (1 + P 2)(N − 1)(N + 1)

4�v. (A.4)

Appendix B. Desired signal and interference currents

The current of the desired mobile unit signal output is givenby

Dlj (t) = R0P0

N

(N + 1

2

)[m0 + a3m

30(6K − 3)

4

]× dlj (t − τlj )clj (t − τlj ) cos(2πfct + φlj ). (B.1)

The interference signal currents can be presented as

Zl1(t) = R0P0

N

(N + 1

2

)[m0 + a3m

30(6K − 3)

4

]

×K∑

k=1k �=j

dlk(t − τlk)clk(t − τlk)

× cos(2πfct + φlk), (B.2a)

Zl2(t) = R0P0

N

(N + 1

2

)(a3m

30

4

)

×K∑

k=1k �=j

dlj (t − τlj )clj (t − τlj )

× cos(2πfct + 2φlk − φlj ), (B.2b)

Zl3(t) = R0P0

N

(N + 1

2

)(3a3m

30

4

)

×K∑

k=1k �=j


× cos(2πfct + 2φlj − φlk), (B.2c)

Zl4(t) = R0P0

N

(N + 1

2

)(3a3m

30

4

)

×K∑

n=1n�=j

K∑k=1

k �=j,n


× cos(2πfct + 2φln − φlk), (B.2d)

Zl5(t) = R0P0

N

(N + 1

2

)(3a3m

30

4

)

×K∑

n=1n�=j

K∑k=1

k �=j,n

dlj (t − τlj )dln(t − τln)dlk(t − τlk)

× clj (t − τlj )cln(t − τln)clk(t − τlk)

× [cos(2πfct + φlj + φln − φlk)

+ cos(2πfct + φlj − φln + φlk)

+ cos(2πfct − φlj + φln + φlk)], (B.2e)


Zl6(t) = R0P0

N

(N + 1

2

)(3a3m

30

4

)

×K∑

i=1i �=n,k,j

K∑n=1n�=j

K∑k=1

k �=j,n

di(t − τi)dn(t − τn)dk(t − τk)

× ci(t − τi)cn(t − τn)ck(t − τk)

× [cos(2πfct + φli + φln − φlk)

+ cos(2πfct + φli − φln + φlk)

+ cos(2πfct − φli + φln + φlk)]. (B.2f)

References

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[8] B.D. Ivan, B. Vasic, Combinatorial constructions of optical orthogonalcodes for OCDMA systems, IEEE Comm. Lett. 8 (6) (2004) 391–393.

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[13] H. Takahashi, K. Oda, H. Toba, Impact of crosstalk in an arrayed-waveguide multiplexer on N × N optical interconnection, IEEE J. Light-wave Technol. 14 (6) (1996) 1097–1105.

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Jen-Fa Huang received the M.A.Sc. and Ph.D.degrees from the Department of Electrical Engi-neering at the University of Ottawa, ON, Canada,in 1981 and 1985, respectively. Since 1991, he hasbeen with the Department of Electrical Engineeringat the National Cheng Kung University (NCKU),Taiwan, where he is currently an adjunct Profes-

sor of the Institute of Computer and Communication Engineering andthe Institute of Electro-Optical Science and Engineering. Previous to1991, he was with MPB technologies, Montreal, PQ, Canada, in theOptical Communication Laboratories working on the TAT-9 transat-lantic undersea lightwave transmission project. His research interestsare mainly in the areas of optical communications, all-optical data net-working, and in passive optical devices.

Chih-Ta Yen was born in Taipei, Taiwan, onJanuary 1974. He received the B.S. degree fromthe Department of Electrical Engineering at theTamkang University, Taiwan, in 1996, the M.S. de-gree from the Department of Electrical Engineer-ing, National Taiwan Ocean University, Taiwan, in2002. He is currently working toward the Ph.D.

degree in the area of fiber-optic communications at the Departmentof Electrical Engineering, National Cheng Kung University, Taiwan.His major interests are in multi-user optical communications, wirelesscommunication systems, and satellite communication.

Tzung-Yen Li was born in Taipei, Taiwan, onDecember 1981. He received the B.S. degree fromthe Department of Electrical Engineering at the Na-tional Dong Hwa University in 2004, the M.S. de-gree from the Institute of Computer and Communi-cation Engineering, National Cheng Kung Univer-sity, Taiwan, in 2006. His major interests are fiber

communication system and radio over fiber system.

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