Comparison of Fiber-Optic CDMA Systems Using Different Modulation Schemes

In order to provide different data rate transmission and quality of service (QoS) for multimedia communications and networks, three common modulation techniques used for optical code-division multiple-access (O-CDMA) are multiple code (MC), multicode keying (MK) and pulse position modulation (PPM). In this paper, the performance and normalized spectral efficiency (NSE) of the O-CDMA systems using above three different modulation techniques are analyzed and compared. Moreover, the computer simulation of each O-CDMA system is performed and compared with the theoretical results to identify the validity of the performance analysis. Our numerical results show that MK scheme always has a better NSE than other two schemes (i.e., MC and PPM schemes), but PPM scheme can provide the best system performance among these three schemes at the expense of the increased bandwidth.


Introduction
Optical code-division multiple-access (O-CDMA) has been widely applied in optical communication systems and networks (1)(2)(3) , because the multiple access technique can provide many desirable features, such as dynamic bandwidth assignment, efficiency in bursty traffic, asynchronous and uncoordinated access, flexible user allocation and gradual performance degradation, compared with wavelength-division multiple-access (WDMA) and time-division multiple-access (TDMA) techniques (1)(2)(3)(4) .O-CDMA can mainly allow many simultaneous users to share the same transmission channel by assigning a unique spreading code to each user (5) .Recently, with the growing demand for high speed networks and multimedia communication services, it is expected that the future O-CDMA systems should support a larger variety of multimedia services with different data rate and quality-of-service (QoS) to accommodate the transmission requirements of the system subscribers (1,(6)(7)(8) .In addition to the multiple length and variable-weight techniques, three common modulation techniques which can support the different data rate and QoS transmission requirements for O-CDMA systems are multiple code (MC) (6) , multicode keying (MK) (7,8) and pulse position modulation (PPM) (9,10) , respectively.In this paper, not only the performance but also normalized spectral efficiency (NSE) of three schemes are also analyzed and compared to determine which scheme should be used under certain conditions (8,11) .
The remainder of the paper is organized as follows.In Section 2, the system model of MC, MK and PPM schemes are studied.Numerical examples which evaluate and investigate the system parameters how to affect the system performance, are given in Section 3. Our results show that MK scheme always has a better NSE than MC and PPM schemes, but PPM scheme can provide the best performance among these three schemes at the expense of the increased bandwidth.Conclusions are finally drawn in Section 4.

System Model
First, a brief review of two-dimensional (2-D) multilevel prime code (MPC) (12) , which is used as numerical examples in the next section, is given in this section.Moreover, the system model of O-CDMA systems using MC, MK and PPM schemes are also introduced as follows.

Pulse Position Modulation Scheme
In summary, the above-mentioned three schemes can support the multi-rate transmission requirements by simply varying the number of the transmitted code matrices at the same time (i.e., m c ) for MC scheme, the number of bits per symbol (i.e., log 2 ⎣m k ⎦) for MK scheme, and the number of PPM frames (i.e., m p ) for PPM scheme, respectively.

Numerical Examples
In this section, we mainly focus on the effect of multiple access interference (MAI) to system performance, and any physical noise, such as thermal noise, beat noise and shot noise are neglected (5,8,11,12) .It is because a practical O-CDMA system should always perform with optical power above the noise level (11) .Moreover, the use of (w × p, w, λ a =0, λ c =1) 2-D MPC briefly introduced in Section 2.1 is here assumed for the following numerical examples.

Multiple Code Scheme
The bit error probability of the MC scheme with the use of (w × p, w, 0, 1) MPC for m c multiple code transmission is given by (11) where K denotes the number of simultaneous users in the MC scheme and the effective number of interfering users is reduced to Km c -1-h and h=m c -1 due to the use of m c timeshifted copies which have λ c =0.Moreover, q j denotes the probability of getting j hits in a time slot, out of λ c =1 possible hits, j∈[0, 1], and are given by (11,12) p respectively.

Multicode Keying Scheme
The bit error probability of the MK scheme with the use of (w × p, w, 0, 1) MPC for m k multicode keying transmission is given by (8,11) where K denotes the number of simultaneous users in the MK scheme, and P r (w,t) represents the probability that t decoders have an output intensity level of at least w and m k -1-t decoders have an output intensity level less than w and is given by (8,11) [ ] where P r (v) denotes the probability of having a peak of v appearing at any one of m k -1 wrong decoder in the desired user and is obtained by (8,11) 1 where the hit probabilities become q 1 =w/p and q 0 =1-w/p (11) , respectively, because of continuous symbol transmission, such that the factor 1/2 is not need in MK scheme.

Pulse Position Modulation Scheme
The bit error probability of the PPM scheme using (w × p, w, 0, 1) MPC for m p PPM transmission is modified from (9,10,14) as  where K denotes the number of simultaneous users in the PPM scheme. (8,11) addition to the bit error probability, the another figure of merit, NSE, which considers the normalized data rate R b (i.e., set the basic bit transmission rate R=1), number of available wavelengths L, number of time slots N, and the number of simultaneous users K as a whole, is used to fairly compare the three schemes and is given by (8,11) LN

Normalized Spectral Efficiency
The goal is to obtain the NSE as large as possible for better spectral efficiency or utilization.In Fig. 1, the bit error probabilities P e,MC (K) of the MC Fig. 3. Bit error probability P e,PPM (K) of (5×13, 5, 0, λ c =1) MPC in PPM scheme versus the number of simultaneous users K, where m p ={4, 8, 16}.scheme with (10×43, 10, 0, λ c =1) MPC, from (2), are plotted as a function of the number of simultaneous users K, where m c ={1, 2, 4, 8}.In general, the bit error probability gets worse as K or m c increases, because there are more interfering code matrices which result in the effect of MAI, but the data bit rate of the MC scheme also increases as m c increases.That is, the MC scheme provides a trade-off between the system performance and date bit rate.Note that the dot-dashed curve with m c =1 shows the performance of the OOK scheme, which agrees to (11,eq. (12)) .Also plotted in the figure are the computer-simulation results, which match closely with the theoretical results.
Similarly, the bit error probability gets worse as K or m k increases, because there are more interfering code matrices, and there are more data bits to be decided incorrectly if a symbol detection error occurs.However, the MK scheme also can support the multi-rate transmission requirements by simply varying the number of bits per symbol (i.e., =log 2 ⎣m k ⎦).
In Fig. 3, the bit error probabilities P e,PPM (K) of the PPM scheme using (5×13, 5, 0, λ c =1) MPC, from (8), are plotted against the number of simultaneous users K, where m p ={4, 8, 16}.The bit error probability gets worse as K increases but improves with m p .It is because the hit probability will be reduced as the number of PPM frames (i.e., m p ) increases.In other words, the PPM scheme can mainly provide the better performance at the expense of the data bit rate and increased bandwidth.Again, both Figs. 2 and 3 also show the computer-simulation results, which match closely   (8,11) .with the theoretical results.
Table 2 compares the NSEs of three schemes, based on Fig. 4. From the table, we can find that the MK scheme can provide the best spectral efficiency among these three schemes.On the other hand, from Fig. 4 and Table 2, we also can know that the PPM scheme can provide the best system performance among these three schemes, but the data bit rate of the PPM scheme is lower than those of the other two schemes.In other words, the PPM scheme provides the better performance at the expense of the data bit rate and increased bandwidth.

Conclusions
In this paper, the three common modulation schemes (i.e., MC, MK and PPM schemes) which can support the different data rate and QoS transmission requirements for O-CDMA systems by simply varying the parameters of m c , m k and m p are introduced and studied.Moreover, not only the performance but also the NSE of three schemes are also analyzed and compared to determine which scheme should be used under certain conditions.Our results show that the MK scheme always has a better NSE than other two schemes, but PPM scheme can provide the best system performance at the expense of the data bit rate or the increased bandwidth.Therefore, if system performance is more important than the spectral efficiency or data bit rate, one should use the PPM scheme.If the spectral efficiency is more important, one should use the MK scheme.That is, there is a trade-off between the system performance, data bit rate and spectral efficiency.

Table 2 .
Comparison of NSE for Three Schemes under BitError Probability P e =10-9