Optical CDMA Fiber Radio Networks Using Cyclic ... - Semantic Scholar
IEEE COMMUNICATIONS LETTERS, VOL. 12, NO. 1, JANUARY 2008
41
Optical CDMA Fiber Radio Networks Using Cyclic Ternary Sequences Chao-Chin Yang Abstract— One novel method for interference elimination is proposed for the fiber radio network based on incoherent optical code-division multiple access. It is based on the orthogonality of signature sequences and thus the number of code families that can be used in the OCDMA networks is increased dramatically. Due to the characteristics of the sequences used for demonstration, the encoder in the control base station can be simple and suitable for realization. Index Terms— Fiber Radio Network, Cyclic Ternary Sequence, Spectral- Amplitude Coding (SAC), Optical CodeDivision Multiple-Access (OCDMA).
I. I NTRODUCTION ULTIPLE access interference (MAI) was the main limiting factor for the performance of incoherent optical code-division multiple access (OCDMA) systems. Spectralamplitude-coding (SAC) OCDMA schemes [1-2] have the unique talent for MAI elimination. In addition to digital systems, SAC OCDMA can also be applied in fiber radio networks for MAI elimination [3]. Though analog SAC OCDMA networks can use the codes in digital ones, they have additional opportunity of code selection due to their unique characteristics. The original unipolar codewords such as M-sequences and Hadamard codes used in the SAC OCDMA networks were mapped from the bipolar counterparts in the electrical domain [1]. However, in the incoherent optical system, the result for the coincidences of two ”0” chips in correlation process was different to the one in the electrical system due to the characteristic of optical signal. Thus MAI elimination in traditional SAC OCDMA schemes was based on condition that values of code lengths, weights and in-phase cross-correlation values for signature sequences were constant. Though the method to use the bipolar orthogonal codes in the incoherent optical system for MAI elimination was also proposed in [1], the need for code length extension effectively reduces the code cardinality. Here one novel method for applying bipolar and ternary orthogonal codes for MAI elimination in the fiber radio OCDMA networks is proposed. This encoding/decoding method maintains the code length and is suitable for all the bipolar and ternary orthogonal codes or codes with ideal autocorrelation properties. Therefore, the number of code families that can be used in the SAC OCDMA networks is increased dramatically and this helps the improvement of the ability against eavesdropping for SAC OCDMA networks[6]. In the previous fiber radio schemes [3], control base stations (CBS) should contain larger number of individual encoders
M
Manuscript received August 29, 2007. The associate editor coordinating the review of this letter and approving it for publication was M. Uysal. This work was supported by the National Science Council under Grant NSC 952221-E-168-027. C.-C. Yang is with the Department of Electronic Engineering, Kun Shan University, Tainan Hsien 710, Taiwan, R.O.C. (e-mail: [email protected]). Digital Object Identifier 10.1109/LCOMM.2008.071440.
and waste large amount of source power in the unused chips of codewords. Though the scheme with compact encoder structure in [4] can be applied in fiber radio SAC OCDMA, the corresponding encoder required additional circulator, fiber Bragg grating and fiber connections. By using the perfect ternary (PT) codes in [5] and the corresponding cyclic shifts as signature sequences, compact encoder simpler than the one in [4] can use in CBS. II. C YCLIC T ERNARY C ODES & THE E NCODER Though all bipolar and ternary orthogonal sequences can be applied to the proposed encoding/decoding method, only the cyclic ternary (CT) codes are taken as an example here since they have additional advantage to use arrayed waveguide grating for coder implementation. In the following the generation process of the perfect ternary (PT) sequences [5] that is used to obtain CT codes is described. Let D be a Singer difference set with parameters N=
q 2l − 1 q 2l−1 − 1 q 2l+1 ,k = ,λ = , q = 2s , q−1 q−1 q−1
(1)
where l and s are integers. Let xD = [xD (0)xD (1)...xD (N − 1)] denote the characteristic vector of D, thus 1, i ∈ D; (2) xD (i) = 0, otherwise. Assume that r is the nonmultiplier of D. If xD is the characteristic vector of D’=rD, then the cross correlation function of xD and xD is θ(j) =
N −1
xD (i)xD (i ⊕ j), j = 0...N − 1
(3)
i=0
where ⊕ is the modulo-N addition. The elements of perfect ternary (PT) sequence C with length N can be obtained as[5] C(j) = (θ(j) − λ)/q l−1 ,
(4)
The number of 1, 0 and -1 in the elements of C are denoted as W+ , W0 and W− , respectively. Their values are given as follow[5]: W+ =
q l (q l + 1) q 2l − 1 q l (q l − 1) , W0 = , W− = . 2 q−1 2
(5)
Table I shows the parameters of several PT codes with length N ≤ 273, where W = W+ + W− is the number of nonzero chips in the corresponding codeword. The sequence C is called PT sequence since its in-phase periodic autocorrelation is nonzero and out-of-phase ones are zero. The property of the PT sequences mentioned above suggests that the cyclic shifts of one specific PT sequence are orthogonal to each other. Therefore, after the transformation described in the following, they can be used as signature sequences in the proposed scheme for MAI elimination. Suppose Ck is
c 2008 IEEE 1089-7798/08$25.00
42
IEEE COMMUNICATIONS LETTERS, VOL. 12, NO. 1, JANUARY 2008
TABLE I T HE PARAMETERS OF S EVERAL PT C ODES .
TABLE II S EVEN PAIRS OF CT C ODEWORDS FOR N=7.
the signature sequence of radio base station(RBS) #k (k = 0, 1, .., N − 1) , it can be obtained from Ck = T k C, where T is the operator shifting vectors cyclically to the right by one place. To adopt these codewords in the proposed network, each codeword is divided (transformed) into pair of unipolar codewords Ck+ (positive) and Ck− (negative) as follow: 1, C 1, Ck (j) = −1, (j) = 1, k Ck+ (j) = Ck− (j) = 0, otherwise. 0, otherwise. (6) These transformed codewords Ck+ ’s and Ck− ’s are named cyclic ternary (CT) code in this letter. Table II shows seven pairs of CT codewords obtained from PT sequence C = [−00 + 0 + +] using r=-1. The control base station (CBS) of the proposed fiber radio network uses the encoder shown in Fig. 1. This encoder is designed with CT codes for N =7 and contains two 7 × 7 AWG routers which can generate the positive and negative codewords of all RBSs simultaneously. The spectrum of super luminescent diode (SLD) is filtered within one free spectral range of the AWG router and the connections between SLD and upper (or lower) AWG router are determined by the positive (or negative) codeword of RBS #0. With the cyclic property of AWG routers and CT code pairs, the positive (or negative) codeword of RBS #k is generated in the output port #k of the upper (or lower) AWG router and is intensitymodulated by the signal (1+dk (t))/2 (or (1−dk (t))/2). Here dk (t) is the normalized radio signal such that max |dk (t)| = 1 and I.M. is abbreviated from intensity modulator in Fig. 1. III. D ECODING S CHEME & I MPLEMENTATION The decoding scheme of CT codes is based on the orthogonality between the cyclic shifts of PT sequences. That is, N −1 W, k = l, Ck (j)Cl (j) = (7) 0, k = l. j=0 However, since the PT sequences are not unipolar, they are transformed into the corresponding positive and negative
Fig. 1.
The shared encoder in the CBS.
Fig. 2.
The decoder in the RBS #0.
codewords. Suppose that RBS #0 is taken into consideration, the above equation is rewritten as N −1 W, k = 0, + − + − {Ck (j) − Ck (j)}{C0 (j) − C0 (j)} = 0, k = 0. j=0 (8) This equation explains the reason why the positive and negative codewords of RBS #k are transmitted simultaneously in the encoder and the amplitudes of their corresponding spectral chips are proportional to (1 + dk (t))/2 and (1 − dk (t))/2, respectively. The DC components of the encoded signals can be removed by the high pass filter (HBF) after the photodiodes of the decoder, thus these unipolar codewords can be transmitted simultaneously as if the corresponding ternary sequence is transmitted through the fiber. The decoding scheme mentioned above can be implemented via the decoder shown in Fig. 2. The connections between 1 × 7 AWG multiplexer and the photodiodes are determined by the positive and negative codewords of the RBS #0. If the j-th chip of the positive (or negative) codeword is ”1”, the output port #j of the AWG multiplexer is connected to the upper (or lower) photo-diode. Since there are AWG output ports that aren’t connected to neither photo-diode, parts of the interfering signal for other RBSs are discarded and don’t contribute to the phase-induced intensity noise(PIIN) in the photo-diodes. Suppose that C0+ = [0001011] and C0− = [1000000] are received by the decoder of RBS #0. Thus the spectral chips #3, #5 and #6 of C0+ are directed to the upper photo-diode with amplitudes proportional to (1+d0 (t))/2, and the spectral chips #0 of C0− is directed to the lower photo-diode with amplitude
YANG: OPTICAL CDMA FIBER RADIO NETWORKS USING CYCLIC TERNARY SEQUENCES
43
proportional to (1 − d0 (t))/2. Therefore, nonzero average photocurrent at the output of HBF is obtained. On the other hand, assume that C1+ = [1000101] and C1− = [0100000] are received by the decoder of RBS #0. Thus the spectral chips #6 of C0+ is directed to the upper photo-diode with amplitudes proportional to (1+d0 (t))/2, but the spectral chips #0 of C0+ is directed to the lower photo-diode with amplitude proportional to (1+d0 (t))/2. Therefore, the photocurrents produced by the two photo-diodes are canceled. Since the proposed decoding scheme may have different number of spectral chips incident to the two photo-diodes, the DC components of the received signal can’t be eliminated without the HBF connected to the differential output of the photo-diodes. IV. N ETWORK P ERFORMANCE In the following analysis, the PIIN[2], shot noise and thermal noise in the photo-diodes of one specific RBS are taken into consideration, and their powers are denoted as 2 2 >, and < Ith >, respectively. Besides, < IP2 IIN >, < Ishot the splitting loss during signal transmission is considered since it plays a more important role than the insertion loss and crosstalk of the optical components. Assume the light source in the control base station is unpolarized and has flat spectrum for encoding with bandwidth ∆ν and magnitude Ptr /∆ν, where Ptr is the effective power transmitted from the light source. The average carrier power for the balanced detector is 2 /(8W 4 N 4 ), where R is the responsivity of the Pc = R2 Ptr photodiodes. Assumed the mobile terminals use modulation with constant envelope and the radio air interface is time division multiple access (TDMA). If the CBS sends the fiber radio signals to the decoder of the RBS #k in discussion with full TDMA load, the time average amplitude < dk (t) >= 0 and time average power < dk (t)2 > =0.5. The carrier-to-noise ratio (CNR) of the decoder output can be deduced by similar methods as that in [4]: 2 2 > + < Ith >], CN R = Pc /[< IP2 IIN > + < Ishot
(9)
where 2 3 K −1 BR2 Ptr { (1 + W) 3 ∆νN W 8 N K −1 W 2 (K − 1)(K − 2) + W+ }, 2N 4N 2 Ptr K −1 2 W ). (10) > = eBR 2 (1 + < Ishot N N Here K is the number of active RBSs, B is noise-equivalent electrical bandwidth of the receiver, R is the responsivity of the photo-diodes, and e is electron’s charge. The parameters used here are B=10MHz, R=0.8 A/W, ∆ν=7.5THz, and 2 ν0 =193.1THz. The power of thermal noise is < Ith >=16 × −17 2 10 A . The relationship between CNR and K are shown in Fig. 3. Here the results for Balanced Incomplete Block Design (BIBD) codes [2] and modified Legendre sequences [4] are also shown for comparison and Ptr is assumed to be 20dBm. Note that the results for BIBD codes are obtained by assuming independent encoders in the CBS, and the results for modified Legendre (ML) codes are obtained by taking the normal and
< IP2 IIN > =
Fig. 3.
CNR versus number of active users.
complementary codewords [4] as the positive and negative codewords respectively, and using the encoder in [4] with I.M.s in place of optical switches. It is found that when N and W are relatively closer, CT codes with longer code lengths obtains better CNR. For the same code weight W =64, CT code with longer code length obtains better CNR due to the PIIN reduction. The values of CNRs for BIBD codes with N =183 and 273 remain low and nearly constant for Ptr =20dBm due to the thermal noise domination. When the code length is about N =273, the CT codes has comparable CNR as modified Legendre sequences. Therefore, the proposed coding scheme allows more code families to be used in the optical CDMA networks, and can be implemented by simple hardware with comparable CNR performances. V. C ONCLUSION One novel encoding/decoding method to adopt the bipolar and ternary orthogonal sequences in the incoherent OCDMA with MAI elimination is proposed, and, therefore, the number of code families that can be used in the SAC OCDMA networks is dramatically increased. R EFERENCES [1] 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, Sept. 1995. [2] 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. [3] B. K. Kim, S. Park, Y. Yeon, and B. W. Kim, “Radio-over-fiber system using fiber-grating-based optical CDMA with modified PN codes,” IEEE Photon. Technol. Lett., vol. 15, no. 10, pp. 1485-1487, Oct. 2003. [4] C. C. Yang, “Modified Legendre sequences for optical CDMA-based passive optical networks,” IEEE Commun. Lett., vol. 10, no. 5, pp. 393395, May 2006. [5] T. Hoholdt and J. Justesen, “Ternary sequences with perfect periodic autocorrelation,” IEEE Trans. Inf. Theory, vol. 29, no. 4, pp. 597-600, July 1983. [6] T. H. Shake, “Security performance of optical CDMA against eavesdropping,” IEEE J. Lightwave Technol., vol. 23, no. 2, pp. 655-670, Feb. 2005.
41
Optical CDMA Fiber Radio Networks Using Cyclic Ternary Sequences Chao-Chin Yang Abstract— One novel method for interference elimination is proposed for the fiber radio network based on incoherent optical code-division multiple access. It is based on the orthogonality of signature sequences and thus the number of code families that can be used in the OCDMA networks is increased dramatically. Due to the characteristics of the sequences used for demonstration, the encoder in the control base station can be simple and suitable for realization. Index Terms— Fiber Radio Network, Cyclic Ternary Sequence, Spectral- Amplitude Coding (SAC), Optical CodeDivision Multiple-Access (OCDMA).
I. I NTRODUCTION ULTIPLE access interference (MAI) was the main limiting factor for the performance of incoherent optical code-division multiple access (OCDMA) systems. Spectralamplitude-coding (SAC) OCDMA schemes [1-2] have the unique talent for MAI elimination. In addition to digital systems, SAC OCDMA can also be applied in fiber radio networks for MAI elimination [3]. Though analog SAC OCDMA networks can use the codes in digital ones, they have additional opportunity of code selection due to their unique characteristics. The original unipolar codewords such as M-sequences and Hadamard codes used in the SAC OCDMA networks were mapped from the bipolar counterparts in the electrical domain [1]. However, in the incoherent optical system, the result for the coincidences of two ”0” chips in correlation process was different to the one in the electrical system due to the characteristic of optical signal. Thus MAI elimination in traditional SAC OCDMA schemes was based on condition that values of code lengths, weights and in-phase cross-correlation values for signature sequences were constant. Though the method to use the bipolar orthogonal codes in the incoherent optical system for MAI elimination was also proposed in [1], the need for code length extension effectively reduces the code cardinality. Here one novel method for applying bipolar and ternary orthogonal codes for MAI elimination in the fiber radio OCDMA networks is proposed. This encoding/decoding method maintains the code length and is suitable for all the bipolar and ternary orthogonal codes or codes with ideal autocorrelation properties. Therefore, the number of code families that can be used in the SAC OCDMA networks is increased dramatically and this helps the improvement of the ability against eavesdropping for SAC OCDMA networks[6]. In the previous fiber radio schemes [3], control base stations (CBS) should contain larger number of individual encoders
M
Manuscript received August 29, 2007. The associate editor coordinating the review of this letter and approving it for publication was M. Uysal. This work was supported by the National Science Council under Grant NSC 952221-E-168-027. C.-C. Yang is with the Department of Electronic Engineering, Kun Shan University, Tainan Hsien 710, Taiwan, R.O.C. (e-mail: [email protected]). Digital Object Identifier 10.1109/LCOMM.2008.071440.
and waste large amount of source power in the unused chips of codewords. Though the scheme with compact encoder structure in [4] can be applied in fiber radio SAC OCDMA, the corresponding encoder required additional circulator, fiber Bragg grating and fiber connections. By using the perfect ternary (PT) codes in [5] and the corresponding cyclic shifts as signature sequences, compact encoder simpler than the one in [4] can use in CBS. II. C YCLIC T ERNARY C ODES & THE E NCODER Though all bipolar and ternary orthogonal sequences can be applied to the proposed encoding/decoding method, only the cyclic ternary (CT) codes are taken as an example here since they have additional advantage to use arrayed waveguide grating for coder implementation. In the following the generation process of the perfect ternary (PT) sequences [5] that is used to obtain CT codes is described. Let D be a Singer difference set with parameters N=
q 2l − 1 q 2l−1 − 1 q 2l+1 ,k = ,λ = , q = 2s , q−1 q−1 q−1
(1)
where l and s are integers. Let xD = [xD (0)xD (1)...xD (N − 1)] denote the characteristic vector of D, thus 1, i ∈ D; (2) xD (i) = 0, otherwise. Assume that r is the nonmultiplier of D. If xD is the characteristic vector of D’=rD, then the cross correlation function of xD and xD is θ(j) =
N −1
xD (i)xD (i ⊕ j), j = 0...N − 1
(3)
i=0
where ⊕ is the modulo-N addition. The elements of perfect ternary (PT) sequence C with length N can be obtained as[5] C(j) = (θ(j) − λ)/q l−1 ,
(4)
The number of 1, 0 and -1 in the elements of C are denoted as W+ , W0 and W− , respectively. Their values are given as follow[5]: W+ =
q l (q l + 1) q 2l − 1 q l (q l − 1) , W0 = , W− = . 2 q−1 2
(5)
Table I shows the parameters of several PT codes with length N ≤ 273, where W = W+ + W− is the number of nonzero chips in the corresponding codeword. The sequence C is called PT sequence since its in-phase periodic autocorrelation is nonzero and out-of-phase ones are zero. The property of the PT sequences mentioned above suggests that the cyclic shifts of one specific PT sequence are orthogonal to each other. Therefore, after the transformation described in the following, they can be used as signature sequences in the proposed scheme for MAI elimination. Suppose Ck is
c 2008 IEEE 1089-7798/08$25.00
42
IEEE COMMUNICATIONS LETTERS, VOL. 12, NO. 1, JANUARY 2008
TABLE I T HE PARAMETERS OF S EVERAL PT C ODES .
TABLE II S EVEN PAIRS OF CT C ODEWORDS FOR N=7.
the signature sequence of radio base station(RBS) #k (k = 0, 1, .., N − 1) , it can be obtained from Ck = T k C, where T is the operator shifting vectors cyclically to the right by one place. To adopt these codewords in the proposed network, each codeword is divided (transformed) into pair of unipolar codewords Ck+ (positive) and Ck− (negative) as follow: 1, C 1, Ck (j) = −1, (j) = 1, k Ck+ (j) = Ck− (j) = 0, otherwise. 0, otherwise. (6) These transformed codewords Ck+ ’s and Ck− ’s are named cyclic ternary (CT) code in this letter. Table II shows seven pairs of CT codewords obtained from PT sequence C = [−00 + 0 + +] using r=-1. The control base station (CBS) of the proposed fiber radio network uses the encoder shown in Fig. 1. This encoder is designed with CT codes for N =7 and contains two 7 × 7 AWG routers which can generate the positive and negative codewords of all RBSs simultaneously. The spectrum of super luminescent diode (SLD) is filtered within one free spectral range of the AWG router and the connections between SLD and upper (or lower) AWG router are determined by the positive (or negative) codeword of RBS #0. With the cyclic property of AWG routers and CT code pairs, the positive (or negative) codeword of RBS #k is generated in the output port #k of the upper (or lower) AWG router and is intensitymodulated by the signal (1+dk (t))/2 (or (1−dk (t))/2). Here dk (t) is the normalized radio signal such that max |dk (t)| = 1 and I.M. is abbreviated from intensity modulator in Fig. 1. III. D ECODING S CHEME & I MPLEMENTATION The decoding scheme of CT codes is based on the orthogonality between the cyclic shifts of PT sequences. That is, N −1 W, k = l, Ck (j)Cl (j) = (7) 0, k = l. j=0 However, since the PT sequences are not unipolar, they are transformed into the corresponding positive and negative
Fig. 1.
The shared encoder in the CBS.
Fig. 2.
The decoder in the RBS #0.
codewords. Suppose that RBS #0 is taken into consideration, the above equation is rewritten as N −1 W, k = 0, + − + − {Ck (j) − Ck (j)}{C0 (j) − C0 (j)} = 0, k = 0. j=0 (8) This equation explains the reason why the positive and negative codewords of RBS #k are transmitted simultaneously in the encoder and the amplitudes of their corresponding spectral chips are proportional to (1 + dk (t))/2 and (1 − dk (t))/2, respectively. The DC components of the encoded signals can be removed by the high pass filter (HBF) after the photodiodes of the decoder, thus these unipolar codewords can be transmitted simultaneously as if the corresponding ternary sequence is transmitted through the fiber. The decoding scheme mentioned above can be implemented via the decoder shown in Fig. 2. The connections between 1 × 7 AWG multiplexer and the photodiodes are determined by the positive and negative codewords of the RBS #0. If the j-th chip of the positive (or negative) codeword is ”1”, the output port #j of the AWG multiplexer is connected to the upper (or lower) photo-diode. Since there are AWG output ports that aren’t connected to neither photo-diode, parts of the interfering signal for other RBSs are discarded and don’t contribute to the phase-induced intensity noise(PIIN) in the photo-diodes. Suppose that C0+ = [0001011] and C0− = [1000000] are received by the decoder of RBS #0. Thus the spectral chips #3, #5 and #6 of C0+ are directed to the upper photo-diode with amplitudes proportional to (1+d0 (t))/2, and the spectral chips #0 of C0− is directed to the lower photo-diode with amplitude
YANG: OPTICAL CDMA FIBER RADIO NETWORKS USING CYCLIC TERNARY SEQUENCES
43
proportional to (1 − d0 (t))/2. Therefore, nonzero average photocurrent at the output of HBF is obtained. On the other hand, assume that C1+ = [1000101] and C1− = [0100000] are received by the decoder of RBS #0. Thus the spectral chips #6 of C0+ is directed to the upper photo-diode with amplitudes proportional to (1+d0 (t))/2, but the spectral chips #0 of C0+ is directed to the lower photo-diode with amplitude proportional to (1+d0 (t))/2. Therefore, the photocurrents produced by the two photo-diodes are canceled. Since the proposed decoding scheme may have different number of spectral chips incident to the two photo-diodes, the DC components of the received signal can’t be eliminated without the HBF connected to the differential output of the photo-diodes. IV. N ETWORK P ERFORMANCE In the following analysis, the PIIN[2], shot noise and thermal noise in the photo-diodes of one specific RBS are taken into consideration, and their powers are denoted as 2 2 >, and < Ith >, respectively. Besides, < IP2 IIN >, < Ishot the splitting loss during signal transmission is considered since it plays a more important role than the insertion loss and crosstalk of the optical components. Assume the light source in the control base station is unpolarized and has flat spectrum for encoding with bandwidth ∆ν and magnitude Ptr /∆ν, where Ptr is the effective power transmitted from the light source. The average carrier power for the balanced detector is 2 /(8W 4 N 4 ), where R is the responsivity of the Pc = R2 Ptr photodiodes. Assumed the mobile terminals use modulation with constant envelope and the radio air interface is time division multiple access (TDMA). If the CBS sends the fiber radio signals to the decoder of the RBS #k in discussion with full TDMA load, the time average amplitude < dk (t) >= 0 and time average power < dk (t)2 > =0.5. The carrier-to-noise ratio (CNR) of the decoder output can be deduced by similar methods as that in [4]: 2 2 > + < Ith >], CN R = Pc /[< IP2 IIN > + < Ishot
(9)
where 2 3 K −1 BR2 Ptr { (1 + W) 3 ∆νN W 8 N K −1 W 2 (K − 1)(K − 2) + W+ }, 2N 4N 2 Ptr K −1 2 W ). (10) > = eBR 2 (1 + < Ishot N N Here K is the number of active RBSs, B is noise-equivalent electrical bandwidth of the receiver, R is the responsivity of the photo-diodes, and e is electron’s charge. The parameters used here are B=10MHz, R=0.8 A/W, ∆ν=7.5THz, and 2 ν0 =193.1THz. The power of thermal noise is < Ith >=16 × −17 2 10 A . The relationship between CNR and K are shown in Fig. 3. Here the results for Balanced Incomplete Block Design (BIBD) codes [2] and modified Legendre sequences [4] are also shown for comparison and Ptr is assumed to be 20dBm. Note that the results for BIBD codes are obtained by assuming independent encoders in the CBS, and the results for modified Legendre (ML) codes are obtained by taking the normal and
< IP2 IIN > =
Fig. 3.
CNR versus number of active users.
complementary codewords [4] as the positive and negative codewords respectively, and using the encoder in [4] with I.M.s in place of optical switches. It is found that when N and W are relatively closer, CT codes with longer code lengths obtains better CNR. For the same code weight W =64, CT code with longer code length obtains better CNR due to the PIIN reduction. The values of CNRs for BIBD codes with N =183 and 273 remain low and nearly constant for Ptr =20dBm due to the thermal noise domination. When the code length is about N =273, the CT codes has comparable CNR as modified Legendre sequences. Therefore, the proposed coding scheme allows more code families to be used in the optical CDMA networks, and can be implemented by simple hardware with comparable CNR performances. V. C ONCLUSION One novel encoding/decoding method to adopt the bipolar and ternary orthogonal sequences in the incoherent OCDMA with MAI elimination is proposed, and, therefore, the number of code families that can be used in the SAC OCDMA networks is dramatically increased. R EFERENCES [1] 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, Sept. 1995. [2] 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. [3] B. K. Kim, S. Park, Y. Yeon, and B. W. Kim, “Radio-over-fiber system using fiber-grating-based optical CDMA with modified PN codes,” IEEE Photon. Technol. Lett., vol. 15, no. 10, pp. 1485-1487, Oct. 2003. [4] C. C. Yang, “Modified Legendre sequences for optical CDMA-based passive optical networks,” IEEE Commun. Lett., vol. 10, no. 5, pp. 393395, May 2006. [5] T. Hoholdt and J. Justesen, “Ternary sequences with perfect periodic autocorrelation,” IEEE Trans. Inf. Theory, vol. 29, no. 4, pp. 597-600, July 1983. [6] T. H. Shake, “Security performance of optical CDMA against eavesdropping,” IEEE J. Lightwave Technol., vol. 23, no. 2, pp. 655-670, Feb. 2005.
