EUROPEAN TRANSACTIONS ON TELECOMMUNICATIONS Eur. Trans. Telecomms. 2009; 20:572–579 Published online 3 June 2008 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/ett.1310
Optical Communications Performance enhancement of spectral-amplitude coding OCDMA system using novel PPM signalling K. Cui*, M. S. Leeson and E. L. Hines School of Engineering, University of Warwick, Coventry CV4 7AL, UK
SUMMARY A spectral-amplitude coding (SAC) optical code-division multiple-access (OCDMA) system with M-ary pulse-position modulation (PPM) signalling is investigated. Novel combinatorial construction of optical signature codes is also presented, as that is applicable to both synchronous and asynchronous incoherent OCDMA. A union upper bound on the probability of error is then derived and the performance characteristics are discussed in the presence of multiple-access interference (MAI) and intensity noise. The numerical results show that the bit-error performance of the OCDMA system with proposed PPM coding outperforms that associated with on–off keying (OOK). Copyright # 2008 John Wiley & Sons, Ltd.
1. INTRODUCTION The optical code-division multiple-access (OCDMA) has become more attractive as it combines the large bandwidth of the fibre medium with the flexibility of the CDMA technique to achieve high-speed connectivity in all-optical communication networks [1]. Multiple users can then access the network asynchronously and simultaneously without strict wavelength controls and network synchronisation [1, 2]. OCDMA schemes are typically classified into two broad categories as coherent and incoherent, which differ primarily in the signal modulation and detection. Early OCDMA networks were developed based upon code sequences of incoherent pulses and intensity modulation [1, 3]. The signals are therefore unipolar with no negative components due to the incoherent nature of the system. Each user has a unique spreading sequence: coded transmission is sent to represent data bit ‘1’, and null is used for ‘0’ bit. Nevertheless, the signature codes used, that is optical orthogonal codes (OOCs), generally have much poorer correlation properties than their bipolar counterparts, and the availability is severely restricted [3, 4]. In contrast, the coherent systems often rely on the phase coding of the optical signal field and coherent detection.
The bipolar signalling is used in the form of ‘þ1’ or ‘1’, which can be obtained by manipulating the polarisation or phase of the optical coherent carrier signal [3]. The established code sets utilised in radio frequency (RF) implementations could be used directly in coherent OCDMA since the conventional spread-spectrum systems were developed with coherent reception. However, complex realisations are required due to the need to provide adequate optical phase control and polarisation. Alternative OCDMA schemes employing the spectralamplitude coding (SAC) of broadband sources are now receiving more attention since multiple-access interference (MAI) can be completely eliminated by spectral coding [2, 5]. In such systems, the data encoding is performed directly in the spectral domain, modulating the optical signal with wide spectral content. Temporal synchronisation of the code sequences is then not required, that is spectral-amplitude systems are inherently code synchronous. This proposal can avoid the limitations of unipolar codes and does not require the complexity of coherent systems [3, 4]. Unfortunately, it is eventually limited by the phase-induced intensity noise (PIIN) mainly originating from the interference between incoherent sources [3]. In this paper, a novel class of optical signature codes based on mutually orthogonal Latin squares (MOLS)
* Correspondence to: Kai Cui, School of Engineering, University of Warwick, Coventry CV4 7AL, UK. E-mail:
[email protected]
Copyright # 2008 John Wiley & Sons, Ltd.
Received 9 September 2007 Revised 28 April 2008 Accepted 5 May 2008
PERFORMANCE ENHANCEMENT OF SAC OCDMA
573
Figure 1. Ideal spectral-amplitude OCDMA system, a ¼ l=ðw lÞ [3, 4].
[6, 7] is proposed to improve the system performance beyond the interference limit. This code family can effectively suppress the noise effects upon its ideal correlation property. Furthermore, the data symbols of each active user are encoded, before multiplexing, using pulseposition modulation (PPM) technique with sufficiently large pulse-position multiplicity. In the combined optical PPM/CDMA system, higher number of simultaneous users can be accommodated than on–off keying (OOK) and no dynamic threshold is required [8, 9]. The rest of the paper is organised as follows. Section 2 introduces the basic system architecture and modelling assumptions. The code construction based on combinational designs is then given in Section 3. In Section 4, the system analysis and discussion of optical PPM-CDMA is presented. Finally, conclusions are drawn in Section 5.
2. SYSTEM MODEL The functional block diagram of the proposed spectralamplitude OCDMA system [3, 4] is presented in Figure 1. For each bit of data, the broadband optical pulse is launched into the spectral encoder, which consists of a pair of lens and uniform diffraction grating. The first grating spatially decomposes the spectral components of the incoming signal with a certain resolution, where different wavelengths can be angularly dispersed and focused by the lens on the plane of the amplitude mask [2]. The second lens and grating are used to recombine the unfiltered spectral content into a single optical beam. The spectrum is encoded by a spectral distribution AðvÞ when the data bit is ‘1’; while it is encoded by the complementary spectral Copyright # 2008 John Wiley & Sons, Ltd.
distribution AðvÞ when the data bit is ‘0’ [3]. The shape of AðvÞ is a sequence of spectral pulses arranged according to the unipolar code used. The encoded optical pulses are then mixed and sent to a star coupler where all optical signals from users are superimposed. At the desired receiver, this superimposed signal is split and decoded by two complementary decoders. The original data can be recovered by using subsequent balanced detection. Spectral-amplitude OCDMA systems commonly employ code sequences with fixed in-phase cross-correlation (CC) for ideal MAI reduction [5]. Let X ¼ ðx1 ; x2 ; . . . ; xN Þ and Y ¼ ðy1 ; y2 ; . . . ; yN Þ be two different P code sequences with in-phase CC defined as XY ¼ Ni¼1 xi yi ¼ l [4, 5]. The complement of sequence X is defined by X, whose elements are obtained from X by xi ¼ 1 xi. The discrimination of interference from any user having sequence Y can then be achieved by intended receivers that compute XY ½l=ðw lÞ XY , where w denotes the code weight [5]. However, the PIIN severely degrades the overall system performance when the value of l is large and therefore, signature codes with ideal in-phase CC (i.e. l ¼ 1) are essential. To further improve the system performance, an M-ary approach adopting PPM is proposed rather than using typical OOK. In the PPM-signalling format in Figure 2, the single laser pulse is placed in one of the M adjacent time slots to represent the symbol. The entire symbol thus extends over a time frame of T ¼ M s, where is the slot width and this M-ary PPM scheme can therefore transmit log2 M bits per pulse. This results in low channel traffic and more efficiently utilisation of the laser energy [10]. Theoretical analysis in Reference [8] also shows that, under fixed average power and bit-error-rate (BER) constraints, optical PPM-CDMA is able to permit the maximum Eur. Trans. Telecomms. 2009; 20:572–579 DOI:10.1002/ett
574
K. CUI, M. S. LEESON AND E. L. HINES
Figure 2. M-ary PPM-signalling format.
number of users by increasing M whereas not all the subscribers can be accommodated in the case of OOK. Figure 3 shows the proposed optical PPM-CDMA receiver that could easily be incorporated into a typical spectralamplitude scheme. The diode pair is that from the last stage of the receiver in Figure 1. The received signal is first amplified in order to overcome the splitting and insertion loss of the coupler [11]. The optical sampler is then employed to provide a gate function and generate a very narrow optical sampling window [12]. This improves code recognition and noise reduction in detecting autocorrelation peaks. The electrical signal would be integrated at every slot interval and passed to the decision mechanism. The PPM decoder then performs the comparison between the photon counts over the M time slots; the number of the slot with the greatest count is deemed the transmitted symbol [8, 9]. 3. COMBINATIONAL CODE CONSTRUCTION An n n integer array ½Ln ði; jÞ; 14i; j4n is referred to as a Latin square (LS) if each element occurs exactly once in each row and exactly once in each column [6, 7]. Two LSs are orthogonal if all entries in the join are distinct. The set of squares L1n ; L2n ; . . . ; Lnn is mutually orthogonal, or a set of MOLS, if they are orthogonal in pairs [7].
Let dimension of squares be n ¼ pm ¼ Q (p is a prime number; m51), is a primitive element of a finite Galois field GFðQÞ, and let a1 ¼ 0; a2 ¼ 1; a3 ¼ ; . . . ; an ¼ Q2 be the elements of GFðQÞ [13]. The LS Ln is constructed by filling the ði; jÞth position by ai þ a aj (244n) [6, 13], that is 2 3 1 2 3 4 63 4 1 27 7 L14 ¼ 6 ð1Þ 44 3 2 15 2 1 4 3 and 2
1 6 4 L24 ¼ 6 42 3
2 3 1 4
3 2 4 1
3 4 17 7 35 2
ð2Þ
Each element in the MOLS is then denoted row by row from 1 to Q2 and another n n integer lattice Z formed. The initial sets of codewords are then generated by reading off the positions of integers in Z corresponding to Ln , where a one-to-one mapping C : Ln ! Z is performed. The following matrix is then obtained from Equations (1) and (2): 3 2 1 7 12 14 6 4 6 9 15 7 7 6 6 2 8 11 13 7 7 6 6 3 5 10 16 7 7 ð3Þ C¼6 6 1 8 10 15 7 7 6 6 3 6 12 13 7 7 6 4 4 5 11 14 5 2 7 9 16 Each row represents a codeword, with integers denoting the positions of optical ‘1’s in the code set. However, such unipolar codes have nonfixed in-phase CC and therefore cannot be decoded by conventional balanced detection. To achieve unity CC for entire family, the same sub-block
Figure 3. Optical PPM-CDMA receiver system. Copyright # 2008 John Wiley & Sons, Ltd.
Eur. Trans. Telecomms. 2009; 20:572–579 DOI:10.1002/ett
575
PERFORMANCE ENHANCEMENT OF SAC OCDMA
Table 1. Padded-orthogonal codes for Q ¼ 4. Lattice group a2
a3
a4
0
1
Code sequence 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
00 10 01 00 00 10 01 00 00 10 01 00 11 00 00 00 00 10 01 00
0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1
0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0
00 01 10 00 01 00 00 10 10 00 00 01 00 11 00 00 00 10 01 00
1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1
of length Q þ 1 is padded into each resolvability class. These Q þ 1 sequences s0 ð#Þ are constructed as follows: 1; if # ¼ pðzÞ ð4Þ s0 ð#Þ ¼ 0 else where z is the index of code groups ðz ¼ 1; 2; . . . ; Q þ 1Þ and pðzÞ is the randomly selected chip position in each group. Note that the padding order has to be unique for the same class but different from other groups. This padding method implies increased chip rate and preserves the quasi-orthogonality between network users [5, 14]. As a result, a full set of Q2 þ Q þ 1 number sequences, termed as ‘padded-orthogonal codes’, with ideal in-phase CC is obtained as in Table 1.
4. SYSTEM ANALYSIS AND DISCUSSION 4.1. Code evaluation on noise limit When incoherent light fields are mixed and incident upon a photodetector, PIIN occurs in the photodetector output. This interference term together with shot and thermal noise are then considered and the variance of photocurrent can be expressed as [3] Copyright # 2008 John Wiley & Sons, Ltd.
0 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 0 0 0
10 00 00 01 00 01 10 00 01 00 00 10 00 00 11 00 00 10 01 00
Padded sub-block 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1
0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0
0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0
10 01 00 00 00 00 01 10 01 10 00 00 00 00 00 11 00 00 10 01
01 01 01 01 00 00 00 00 00 00 00 00 10 10 10 10 00 00 00 00
00 00 00 00 00 00 00 00 10 10 10 10 00 00 00 00 01 01 01 01
0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0
hI 2 i ffi 2PIIN þ 2shot þ 2thermal ¼ I 2 Bc þ 2eIB þ 4kB Tr B=RL
ð5Þ
where e is the electronic charge, I is average photocurrent, B is the electrical equivalent noise bandwidth of the receiver, c is coherence time of source, kB is Boltzmann’s constant, Tr is the absolute temperature of receiver noise and RL is the load resistance. The source coherence time c can be expressed in terms of its source power spectral density (PSD) GðvÞ as [15] R1 2 G ðvÞdv c ¼ R01 ð6Þ 2 G ð v Þdv 0 A term ck ðiÞ denotes the ith element of the kth paddedorthogonal codes and dk is the data bit of kth user. The PSD at photodetectors 1 and 2 of the nth receiver during 1 bit period can then be written as [3] K N X X Psr dk ck ðiÞcn ðiÞ ð1 þ aÞv k¼1 i¼1 v ðN þ 2i 2Þ u v v0 2N v u v v0 ðN þ 2iÞ 2N
G1 ðvÞ ¼
ð7Þ
Eur. Trans. Telecomms. 2009; 20:572–579 DOI:10.1002/ett
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K. CUI, M. S. LEESON AND E. L. HINES
and K N X a Psr X dk ck ðiÞcn ðiÞ ð1 þ aÞv k¼1 i¼1 v ðN þ 2i 2Þ u v v0 2N v u v v0 ðN þ 2iÞ 2N
G2 ðvÞ ¼
ð8Þ
respectively, where Psr is the effective power of a broadband source at the receiver, v is the optical source bandwidth, K is the number of active users (4Q2 þ Q), the code length is given by N ¼ Q2 þ Q þ 1 and uðvÞ is the unit step function. The photocurrent and noise variance are then given by Z 1 Z 1 I ¼I1 I2 ¼ < G1 ðvÞdv< G2 ðvÞdv 0 0 ð9Þ ðQ þ 1Þdn < Psr ¼ 2 ð Q þ Q þ 1Þ ð 1 þ aÞ and 4kB Tr B hIT2 i ¼ BI12 c1 þ BI22 c2 þ 2eBðI1 þ I2 Þ þ RL 2K 1 þ Q 4kB Tr B ffi eB
