## Abstract

We have experimentally demonstrated two novel pulse position modulation techniques, namely Double Pulse Position Modulation (2-PPM) and Differential Pulse Position Modulation (DPPM) in Time-Wavelength OCDMA systems that will operate at a higher bit rate compared to traditional OOK-OCDMA systems with the same bandwidth. With 2-PPM technique, the number of active users will be more than DPPM while their bit rate is almost the same. Both techniques provide variable quality of service in OCDMA networks.

©2007 Optical Society of America

## 1. Introduction

Promising unique features such as flexibility, high security, asynchronous nature, and plug and play functionality, optical code-division-multiple-access (OCDMA) technique has recently gained attention as a reliable structure for the physical layer of local area networks (LANs) [1]–[3]. In OCDMA systems, a unique signature code of length *F* from a set of optical orthogonal codes (OOC) is assigned to each user. These codes satisfy certain auto-correlation and cross-correlation conditions so each user at the receiver side can distinguish its own data. Each bit time, *T _{b}*, is divided into

*F*smaller chip times,

*T*, and then the user’s signature code specifies

_{c}=T_{b}/F*w*chips out of the

*F*chips to contain an optical pulse with duration of

*T*, where

_{c}*w*is the code weight [1]. If all

*w*pulses have the same wavelength, the system is one-dimensional (1-D) since the data is encoded just in time domain; otherwise, the systems is a two-dimensional (2-D) or time-wavelength OCDMA system. With an identical code length of

*F*, the cardinality of 2-D OCCs is more than 1-D case [3].

On-Off-Keying (OOK), the most common modulation format in OCDMA systems, consists of transmitting a signature code for each ‘1’ bit and nothing for a ‘0’ bit. In order to increase the bit rate, one has to decrease the bit time and consequently the chip time. Therefore, very short pulses are required which are challenging in generation, propagation, and detection.

In non-multiple-access systems, Pulse Position Modulation (PPM) provides a straightforward method for increasing the bit rate. In PPM, each signaling interval, *T _{s}*, is divided into

*M*equal slots and only one of these

*M*slots must contain a pulse. Therefore, there will be

*M*possible symbols, capable of representing log

_{2}

*M*bits, so the bit rate will be equal to (log

_{2}

*M*)/

*T*. Double-PPM (2-PPM), in which 2 out of the

_{s}*M*time slots are marked, can further increase the bit rate, approximately by a factor of 2[4]. PPM and 2-PPM symbols are shown in Fig. 1(a) and Fig. 1(b), respectively. In a 2-PPM scheme, the number of symbols will be equal to the number of ways we can choose 2 slots out of a total of M slots. Therefore, the bit rate will be equal to

Another technique to increase the bit rate in optical systems is Differential Pulse Position Modulation (DPPM). This technique has been already reported for an indoor wireless infrared application [5] and it is considered a more spectrally efficient scheme than regular PPM. In DPPM, information is encoded in the time difference between two consecutive marked time slots instead of the position of the time slot within a symbol time. This modulation format results in variable-length symbols with a duration less than or equal to the PPM symbols, thus in average, comparing to PPM, less time is required to transmit the same information (Fig. 1(c)). The average time to transmit data using DPPM is equal to (M+1)*T _{s}*/2M and the bit rate is obtained from the following equation,

The normalized bit rate of the three modulation schemes is shown in Fig. 1(d). Some theoretical studies on using PPM techniques in OCDMA systems have been reported in [6]–[8], but the suggested systems have two problems; they have to use very short pulses, or they require a cyclic code shifter in the transmitter that is difficult to implement. In [9, 10] we analytically and experimentally demonstrated a PPM-OCDMA system with a very simple structure without using extremely short pulses, i.e., the pulse width was the same as a traditional OOK-CDMA structure. Using the same idea, in this paper, the concept of 2-PPM-OCDMA and DPPM-OCDMA techniques is described and the experimental results are presented and compared with other techniques.

## 2. Concept of 2-PPM and DPPM OCDMA

The block diagram of the system is shown in Fig. 2. First, the bit stream is fed into a bit to symbol converter that maps several bits to a specific symbol. In 2-PPM case, log_{2}(*M(M-1)/2)* bits are mapped to a symbol every *T _{s}* seconds, while for DPPM it tales (

*M+1)Ts/2M*seconds in average. Then, the 2-PPM or DPPM data is fed to the OCDMA encoder, while marked slots represent the autocorrelation peaks. The code length is set equal to the number of slots,

*M*=

*F*, resulting

*T*=

_{c}*T*. So the chip time will be exactly the same as an OOK-OCDMA system, which is far more than the chip time in [6] and [7]. In order to prevent implementing a cyclic code shifter, we allow each encoded symbol to spread over the next symbol. The signature codes have at most one pulse per each wavelength, so it will be guaranteed that adjacent symbols of a user do not interfere with each other [3].

_{s}/MAt the receiver point, the OCDMA decoder correlates the received chip-stream with its own signature code every T_{c} seconds. These autocorrelation peaks form the 2-PPM or DPPM symbols and finally the symbol to bit converter extracts the bits based on the position of autocorrelation peaks. In 2-PPM case, each user must be synchronous to its corresponding transmitter which can be achieved by transmitting a predefined pattern that is known by the both sides of the system. It should be emphasized that synchronization is only required for the transmitter/receiver pairs, but different users are asynchronous to each other.

## 3. Experimental Setup

The experimental setup is shown in Fig. 3. In our experiment, we used a code set with 8 wavelengths, 16 chip times (*M*=16), and weight of 6. We combined eight equally spaced lasers and modulated them at 10 Gchips/s. The encoded 2-PPM or DPPM symbols are sent to the modulator, then after an EDFA, we split the signal between a number of branches, each representing a user with a unique OCDMA encoder. We have used Fiber-Bragg-Gratings (FBGs) as encoders that separate the wavelengths and assign an appropriate time slot to each one [11]. Then, all encoded data are transmitted through different short lengths of fiber to uncorrelate the signals, and finally all the users’ signals are combined together through a coupler. At the receiving side, first we amplify the signal and then, we use another set of FBGs which are complements of the encoders, to stack the chips and decode the data. A photo-receiver detects the decoded symbols, and finally a threshold device examines the output of the photo receiver to determine if the slot is one or zero.

## 4. Results and Discussion

#### 4.1 2-PPM-OCDMA

Figure 4(a) shows the 2-PPM data after the modulator. The dashed lines show the boundaries of adjacent symbols, and the position of the two marked slots in each symbol is written on top of the intervals. The encoded symbols can leak across the other encoded symbols boundaries as shown in Fig. 4(b). It is also important to note that in the encoded stream, there are pulses with twice the amplitude of other pulses. This happens when a pulse from two adjacent encoded symbols collide; however, because our codes have at most one pulse per each wavelength, the colliding pulses have different wavelengths, and consequently they are completely separable as shown in Fig. 4(c) where the original data along with multiple access interference from four other users in the network can be observed. The BER curve as a function of the received optical power of the main user is plotted in Fig. 4(d) while there are 4 other active users in the system.

It should be noted that 2-PPM-OCDMA would suffer more from multiple-access interference (MAI) than PPM-OCDMA and OOK-OCDMA. The amount of the required extra power to switch from a PPM-OCDMA system to a 2-PPM-OCDMA system is shown in Fig. 4(e). It is important to notice that even for a single user, 2-PPM requires 3dB more power. The reason is that the average power is divided into the two pulses in 2-PPM case, therefore, in order to have the same peak power as PPM symbols, the amount of required average power is twice as much as needed in PPM symbols.

Since the amount of MAI is more in 2-PPM than in PPM (because of the two pulses per each symbol), we believe that with 2-PPM, the number of *potential* users will be approximately half of the number of *potential* users in PPM, therefore, considering the bit rate increment, the *capacity* of the system will not change significantly. Since the spectral efficiency is defined by the number of *active* users in the system [3], using 2-PPM-OCDMA in systems with a limited number of active users can significantly increase the spectral efficiency, because MAI would not be a limiting factor in such systems. In this scenario, 2-PPM-OCDMA can increase the bit rate and consequently the spectral efficiency, approximately by a factor of two compared to a PPM-OCDMA system. According to [10], the spectral efficiency of PPM-OCDMA is roughly (log_{2}(*M*))/*2* times of the spectral efficiency of OOK-OCDMA, therefore, the spectral efficiency of 2-PPM-OCDMA will be approximately log_{2}(*M*) times of the OOK-OCDMA.

Moreover, 2-PPM-OCDMA technique can serve as a mean for achieving variable quality of service (QoS), i.e., some users can operate in 2-PPM-OCDMA mode while the other users send their data using PPM-OCDMA or OOK-OCDMA. With M=16 and a chip rate of 10 Gchips/s, the symbol rate is equal to 1/Ts=(10Gchips/s)/16=625Msymbols/s and according to Eq. 1, the equivalent bit rate is 4.32 Gbits/s which is 6.9 times of OOK-OCDMA and 1.73 times of PPM-OCDMA. Since the total bandwidth considering the guradbands between the eight wavelengths is around 360GHz, from [3], the spectral efficiency of the whole system is 5X(4.32Gb/s)/360GHz=0.06 bits/second/Hz.

#### 4.2 DPPM-OCDMA

Fig. 5(a)–c) compares DPPM with traditional OOK and PPM. In these figures, the original bits (Fig. 5(a)) is first converted to PPM symbols ‘20594’ where each digit shows the position of the time slot (Fig. 5(b)) and then by dropping the zero slots from PPM symbols, the DPPM symbols are obtained which are shown in Fig. 5(c). It can be observed that by using DPPM, it takes 2.5 ns to transmit these five symbols while for the same 5 symbols in PPM the transmission time is 8 ns, and for OOK it takes 32 ns.

Figure 5(d) shows the encoded symbols of a single user for the aforementioned pattern. Due to the variable length of the symbols, the encoded chips have different amplitude, the reason being that each symbol leaks into the adjacent symbols and the chip times of these symbols add up together. This effect is more severe for smaller symbols such as 2, 0, and 5. However, as our OCDMA spreading codes have at most one pulse per wavelength the high amplitude pulses consist of different wavelengths, the chips can be separated in the decoder. Figure 5(e) shows the decoded autocorrelation peaks of a single user and Fig 5(f) shows the decoded data along with the MAI from two other interfering users.

The BER curves for different number of users are shown in Fig. 5(g). Using DPPM, we were able to achieve at most 3 simultaneous users, so this modulation method is considerable when the number of users is low and the MAI is not a limiting factor. Similar to 2-PPM-OCDMA, this modulation format can be used with other OCDMA schemes to provide variable QoS in the network. According to Eq. 2, the bit rate is equal to 4.71 Gbits/s which is 7.53 times of the bit rate in OOK-OCDMA and 1.88 times of PPM-OCDMA using the same codes and bandwidth. The total spectral efficiency is 3X(4.71Gb/s)/360GHz=0.04 bits/second/Hz.

## 6. Conclusion

We demonstrated 2-PPM-OCDMA and DPPM-OCDMA modulation formats to increase the operating bit rate of an OCDMA user. Theses techniques increase the bit rate approximately by a factor of 2 compared to PPM-OCDMA technique. If the number of active users is small in a system and MAI is not the limiting factor, 2-PPM and DPPM can increase the spectral efficiency; otherwise we don’t expect an increment in the spectral efficiency since the bit rate is increased while the number of active users is decreased. In order to exactly evaluate the performance of the system in terms of the capacity and spectral efficiency, further investigations are required in future.

With DPPM-OCDMA, we could achieve a slightly higher bit rate than 2-PPM-OCDMA but the MAI severely limits the performance of the system, thus the number of simultaneous active users in 2-PPM-OCDMA is more compared to DPPM-OCDMA. Both techniques provide versatility in that when there is low traffic demand in the network, for example when some users are not active in the network, a user can benefit the available bandwidth and switch to 2-PPM or DPPM scheme to operate at a higher bit rate.

## Acknowledgements

The authors wish to acknowledge the generous support of Defense Advanced Research Project Agency (DARPA), Space and Naval Warfare (SPAWAR) for this work under contract number N66001-02-1-8939.

We would also like to thank Dr. Reza Omrani and Dr. Saurabh Kumar for their comments and fruitful discussions.

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