1. Introduction

The optic code division multiple access (OCDMA) technique, where different users are assigned different “signature codes”, is a promising candidate for next-generation broadband access networks. As it allows many users to share the same transmission channel, it has unique advantages inherently allowing dynamic allocation of bandwidth, protocol transparency, and a fully asynchronous operation mode with low latency that is suitable for the bursty traffic environment. It also offers robust signal security, permitting quality of service guarantees to be managed at the physical layer by assigning different weight codes to different users, and simplified management of large numbers of users by only requiring minimal network control and reconfiguration [1–7].

The coding operation in OCDMA can be roughly classified by coding dimensions into 1-dimensional (1-D) and 2-dimensional (2-D), and by working principles into coherent and incoherent schemes [6]. For incoherent 2-D (time-spreading/spectral-coding) OCDMA [7– 12], the optical source should have a relatively high speed for temporal spreading and broadband optical spectra for spectral coding, as well as a high time-bandwidth (TB) product to achieve the incoherent superposition of decoded optical pulses [3, 8]. A free-running (FR-) gain-switched Fabry-Perot laser diode (GSFP-LD) [9], an amplified spontaneous emission (ASE) plus fast electro-optic modulator (EOM) [10], a super-continuum (SC) ultra-fast light source [11], and a sequentially self-seeding (SS-) GSFP-LD [8, 12] have been used for this purpose. Compared with the others, the GSFP-LD is better suited to this application as it can simply generate short optical pulses (as short as 20 ps) with a broadband spectrum (multiple longitudinal modes spread over 10 nm), and a large TB product (in a range of 50) [3, 8].

Gain-switching is a large-signal modulation technique that may be applied to semiconductor lasers to produce short pulses, in a manner analogous to Q-switching [13, 14]. The FR-GSFP-LD has advantages of simple configuration and low cost for incoherent 2-D OCDMA applications compared to the sequential SS-GSFP-LD [8, 9]. However, its mode partition noise (MPN) results in some performance degradation. We theoretically and experimentally investigated the impact of MPN in an FR-GSFP-LD in an incoherent 2-D OCDMA system. The requirements and limitations of this scheme were evaluated as well.

2. Experiment on FR-GSFP-LD for 2-D incoherent FO-CDMA applications

Figure 1(a) outlines the setup for the incoherent 2-D OCDMA encoding/decoding experiment with the FR-GSFP-LD. The FP-LD was a commercially available index guided laser with a central wavelength of around 1550 nm and a mode spacing of about 1.28 nm. The DC bias applied to the laser here was about 4.5 mA, which was below the laser threshold current I_th (~5.2 mA). The electrical pulses from the pulse generator with a 1-GHz repetition rate and a 90-ps pulsewidth were amplified by the RF power amplifier to the +18-dBm level and applied to the FP-LD via a bias T to enable gain-switching. The FBGs in the encoder/decoder had center wavelengths positioned from 1544 nm to 1552 nm and spaced 2 nm apart. Their linewidth was about 0.5 nm and reflectivity was over 99.9%. They were 5-mm long and positioned serially along an optical fiber separated by the same distance of 8 cm (corresponding to 0.8 ns delay) from one another. The encoder corresponded to a prime/prime code C ₀ H ₁ [7, 9] that had a temporal pattern of p=5 prime code C ₀ (1000010000100001000010000) with a chip duration of T_Chip=160 ps and a spectral pattern of p=5 prime sequence H ₁ (0, 1, 2, 3, 4) with the wavelengths described above. The central wavelength of the FBGs in the encoder could be finely tuned by mechanical stretching to adjust the reflected optical power of each mode. The matched decoder had the reverse pattern of the encoder.

 

Fig. 1. Experiment on incoherent 2-D OCDMA with FR-GSFP-LD (a) Experiment setup (b) Spectra, (c) BER performance and eye diagram (inset).

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A 1-Gbit/s 2²³-1 pseudo random bit sequence (PRBS) from the pattern generator was amplified by the RF power amplifier and applied to drive the EOM. Note here that as we employed the data rate enhancement scheme [15, 16], the bit duration (1 ns) was shorter than the code duration (4 ns). The encoded signals were amplified by the erbium-doped-fiber-amplifier (EDFA) and launched into a 4-km long dispersion shifted fiber (DSF). After decoding, the spectra of decoded signals were measured with an optical spectrum analyzer (OSA), and the waveforms were detected with a photo-detector (PD) and a fast oscilloscope. Finally, the bit-error-rate (BER) performance was measured with a BER tester, while the eye diagrams were captured with the oscilloscope.

The gray dashed line in Fig. 1(b) represents the full measured spectra for the FR-GSFP-LD; there are over 10 longitudinal modes that can be used for spectral coding. The pulse width of the generated pulses was measured to be about 41 ps with the spectral bandwidth over 10nm, therefore the TB product was estimated to be >50. The black solid line in Fig. 1(b) represents the spectra for the encoded signal. Five longitudinal modes were used in this experiment. The encoded optical pulses spread within a 4-ns duration with widths from 60 to 80 ps, while the decoded pulse width was over 100 ps. The broadening of the decoded pulsewidth was presumably due to the convolution of the encoded signal with the decoder function, grating position deviation (GDV), dispersion in transmission [17], and distortion induced by the FBG. The eye opening in the inset of Fig. 1(c) confirms the feasibility of this scheme, while a BER floor was measured at about 5×10^-4 (Fig. 1(c)). This BER floor was due to intensity fluctuations in the modes used for coding.

3. Mode-partition-noise-induced degradation in system performance

The power fluctuations in each longitudinal mode in the FR-GSFP-LD were caused by mode competition in the laser cavity where different longitudinal modes compete for the same gain. Therefore, the energy in each mode varied while total optical power remains nearly constant [18]. These fluctuations result in MPN [19–26]. Both CW and repetitively pulsed devices exhibit MPN [21]. MPN can convert to intensity noise in several ways, and predominate over intrinsic relative intensity noise (RIN) [20, 22–26].

In our system, the encoder takes the role of an optical filter with sharp cut off to select several laser modes for 2-D coding. It has been shown that MPN arises due to the wavelength-dependent attenuation mechanism introduced by the optical filter [24, 25]. Now, we will investigate the degradation in system performance due to MPN.

The fluctuation of total laser power can be measured by RIN, which is the ratio of the mean-square amplitude of laser intensity fluctuations, ΔI, to the square of the average laser intensity, I:

As the total power emitted by a laser is stabilized by gain-saturation, RIN is generally small and was measured at low frequencies to be -125 dB/Hz and -129 dB/Hz for CW and gain-switched lasers, respectively [18, 26]. It was assumed that the total laser output power would be constant in the following analysis. Therefore, if random variable a_i denotes the normalized instantaneous power of the ith longitudinal mode, it satisfies the following relation:

where N is the number of longitudinal modes. Let us define the received waveform for the ith longitudinal mode by f(λ_i ,t) (≤1), where λ_i is the wavelength of the ith mode. Therefore, the received signal is given by the total summation of each waveform

F _en(λ_i ) represents the transmission characteristics of the encoder at wavelength λ_i . F _en(λ_i )=H(λ_i ), where H is the spectral coding pattern for the 2-D code. The variance of MPN can be expressed as the variance of r(t), evaluated at a sampling time of t=t ₀,

Following the analysis by Ogawa and Vodhanel [19], Eq. (4) can be expressed as:

where k is Ogawa’s mode partition coefficient, which is defined as:

for any i. In deriving Eq. (5), it was assumed that all modes had the same correlation in respect to one another: < a_i a_j >=(1-k ²)< a_i >< a_j > , i≠j. While such an assumption may not always strictly hold for semiconductor lasers, it allows us to estimate the MPN without knowing joint probability distribution p(a ₁, a ₂,…, a _n).

Ogawa’s factor k expresses the degree of mode partition, this value being in a range from 0 to 1. k=0 if and only if each longitudinal mode is independent (<a_i a_j >=<a_i ><a_j >). Also, if each mode represents a mutually exclusive event (<a_i a_j >=0, only one mode oscillates at a given time), k=1. Measurement, using the sampling method [19], and simulation [21] revealed that a value for k of 0.3 is appropriate for high-power modes, each contains more than 5% of the total optical power. Furthermore, k≤0.15 (we used k=0.15 in our calculation) for low-power modes.

<a_i > is the mean value of normalized ith longitudinal mode intensity, which can be obtained from the measured laser-power spectrum, normalized by the averaging power of the laser.

Under a Gaussian assumption, the system BER can be estimated by:

where Q is the well known Q-function, P_s is the received optical power, and σ is the standard deviation for total noise, which is given by:

where, ${{\mathrm{\sigma }}_{\text{sh}}}^2$=2BeP_sR, ${{\mathrm{\sigma }}_{\text{dk}}}^2$=2Bei _dk, and ${{\mathrm{\sigma }}_{\text{th}}}^2$=2BN _th are the variances of shot noise, dark current noise, and thermal noise, respectively. Here, B=10 GHz is system bandwidth, e is electron charge, R=0.8 is photodiode responsivity, i _dk=2 nA is dark current, and N _th=1pA²Hz^-1 is thermal current power spectral density (PSD).

A comparative experimental and theoretical study was carried out with four different FR-GSFP-LD longitudinal mode selections: 1. all laser modes, 2. selected by WDM band filter, 3. selected by WDM and FBG filter, and 4. selected by FBG 2-D encoder alone. Figure 2 shows the measured spectra (linear scale) and their eye diagrams. It is obvious that the more laser modes that are selected, the clearer the eye diagram is.

 

Fig. 2. Measured spectra (upper) and eye diagrams (lower) of (a) FR-GSFP-LD, (b) filtered by WDM band filter, (c) filtered by WDM and FBG filter, and (d) filtered by FBG encoder

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The measured BER vs. received optical power are plotted in Fig. 3 together with the theoretical predictions. BER-free (BER<10^-9) transmission was achieved where laser power was used entirely. If only part of the modes was selected for use, a BER floor due to MPN appeared. For the 2-D encoding/decoding scheme with 5 wavelengths and transmission rate of 1 Gbit/s, the BER floor was measured at about 5×10^-4. The theoretical predictions agreed reasonably well with the experimental results. The differences between measurements and theory in the low optical power regime of the filtered cases are probably due to the measuring system bandwidth limitation [6].

 

Fig. 3. Measured BER vs. received optical power (symbols) and theoretical predictions (solid lines)

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Figure 4 plots the relationship between system performance and Nm, which is the number of modes used for coding. The calculations were based on the laser spectrum in Fig. 2 (a-1). The longitudinal modes were first selected from the central wavelength (1544 nm) then alternately picked from the two sides. Fig. 4(a) plots the BER vs. received optical power for different Nm. With an increase in Nm, the BER floor due to MPN decreases. Therefore, the 2-D OCDMA scheme with FR-GSFP-LD should operate with sufficient large Nm to enable error-free transmission. Fig. 4(b) plots the power penalty (at BER=10^-9) vs. Nm. At least 9 high-power longitudinal modes (Nm>9) should be used for 2-D coding with this laser. As the consequence, the incorporated 2-D code set should have code weight greater than 9. Generally, increase of Nm will result in a longer code with better correlation property and larger code set size. For instance, the prime-hop sequence has the code length (or the time-spreading factor) of Nm ² with the auto-correlation peak of Nm and code size of Nm×(Nm-1) [7]. The high time-spreading factor means longer code duration, which will lower the transmission data rate if the bit duration equals to the code duration. However, the better correlation property of the code sets enables higher data rate enhancement ratio, which can mitigate this problem [15]. Regarding the spectral efficiency compared with other OCDMA schemes that employ the full set of modes of FR-GSFP-LD [27], suppose prime-hop sequence is used, the number of users to the number of wavelengths ratio is Nm-1 (users/wavelength) in this scheme, therefore one benefit of using larger Nm is the higher spectral efficiency.

However, the MPN limits the application of FR-GSFP-LD in the 2-D OCDMA by requiring sufficient large Nm to be used. Sequentially SS-GSFP-LD, which exhibits to be free of the MPN [8], could be more flexible in terms of code selection.

 

Fig. 4. Relationship between system performance and Nm (a) BER vs. received optical power for different Nm (b) Power penalty vs. Nm

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4. Conclusion

FR-GSFP-LD is an appropriate incoherent broadband optical source for incoherent 2-D OCDMA compared with other sources. However, the MPN due to mode selection will seriously degrade system performance. The BER expression was derived in the presence of MPN. Only the power spectra of the laser were needed for calculation. The theoretical and experimental results revealed that there was a power penalty and a BER floor due to the MPN in the laser. The theoretical predictions agreed reasonably well with the experimental results. Increasing Nm could reduce the power penalty and the level of the BER floor. For the laser that was investigated in this work, at least 9 high-power longitudinal modes should be used for coding to achieve error-free (BER<10^-9) transmission at 1 Gbit/s.