A novel wavelength-correlating receiver for incoherent Optical Code Division Multiple Access (OCDMA) system is proposed and demonstrated in this paper. Enabled by the wavelength conversion based scheme, the proposed receiver can support various code types including one-dimensional optical codes and time-spreading/wavelength-hopping two dimensional codes. Also, a synchronous detection scheme with time-to- wavelength based code acquisition is proposed, by which code acquisition time can be substantially reduced. Moreover, a novel data-validation methodology based on all-optical pulse-width monitoring is introduced for the wavelength-correlating receiver. Experimental demonstration of the new proposed receiver is presented and low bit error rate data-receiving is achieved without optical hard limiting and electronic power thresholding. For the first time, a detailed theoretical performance analysis specialized for the wavelength-correlating receiver is presented. Numerical results show that the overall performance of the proposed receiver prevails over conventional OCDMA receivers.
© 2011 OSA
Optical Code Divided Multiple-Access (OCDMA) was introduced into fiber-optics for its appealing advantages of full asynchronous access, low latency, soft capacity, protocol transparency, simplified network control, convenient QoS control and network confidentiality . Meanwhile, the characteristics of fiber-optics, such as large bandwidth and fast signal processing, are quite suitable for high speed OCDMA applications. For instance, with the wide bandwidth of optical fibers, ultra-short pulses can be adopted as coding chips; optic passive devices such as fiber delay lines (FDL), Fiber Bragg Gratings (FBG) and Array Waveguide Gratings (AWG) are applicable for ultrafast all-optical en/decoding. Moreover, optical nonlinear effects in optical fibers and semiconductor devices are now considered as the most powerful tools for optical domain signal processing. Therefore, OCDMA systems assisted by optical nonlinear effects start to draw increasing attentions [2–4]. Self-Phase Modulation  and Super-continuum in dispersion-flattered-fibers  were used for autocorrelation peak discrimination and optical thresholding respectively, based on the amplitude-related nonlinear spectrum expending. Nonlinear optical loop mirror (NOLM) was reported to suppress the pedestal of the decoded pulse with low operation powers . More recently, a novel wavelength-correlating (WC) OCDMA receiver with autocorrelation peak discriminator based on four-wave mixing (FWM) is proposed for both incoherent OCDMA system utilizing two-dimensional time-spreading/wavelength-hopping (W/T 2-D) codes [5,6] and all-optical label switching system with optical code labels [7,8]. In a WC receiver, the decoded autocorrelation peak of a single-pulse-per-row (SPR) W/T 2-D code is launched into a FWM device to generate a Resulting-Pulse at certain FWM conjugate wavelengths that involve all the wavelengths contained in the autocorrelation peak, while the cross correlations from multiple access interferences (MAIs) are rejected, as illustrates in Fig. 1 . According to the principle of the WC receiver, correlating operation is conducted among the wavelengths contained in the desired 2-D code, so that the power ratio between the autocorrelation peak and cross correlations is less significant as long as the autocorrelation peak contains all the wavelengths of the desired code, and therefore no power thresholding is necessary to discriminate the autocorrelation peak. This power independent characteristic is considered as a strong strength of the WC receiver for it enables the receiver to get rid of all the challenges associated with power as in conventional OCDMA receivers, such as the power equalization,optical hard limiting, rigid power thresholding, and optical power related noises. Moreover, since that major MAIs are rejected through the wavelength correlating process, the WC receiver can support simple “bit-rate” asynchronous detection avoiding the complicated code acquisition and “chip-rate” integration . Further, it is known that the constraint on code’s out-of-phase autocorrelation value of a certain OCDMA code set is related solely to code acquisition. For WC receivers operating in asynchronous detection mode without code acquisition, this constraint on the out-of-phase autocorrelation value can be relaxed, and code cardinality can therefore be enlarged [9,10].
In this paper, comprehensive analysis of WC OCDMA receiver is presented and new schemes are proposed trying to make the receiving structure more versatile, efficient and reliable. Particularly, while the previously proposed WC receiver involves SRP 2-D code only, a wavelength conversion based method is introduced to enable the WC receiver to be capable for both multi-pulse-per-row (MPR) W/T 2-D code and one-dimensional code, considering that MRP W/T 2-D codes usually possess much larger code cardinality than SRP code [10,11], and one-dimensional code is appropriative for certain application scenario. Besides, although that it is quite convenient for the WC receiver to implement asynchronous detection without code acquisition, asynchronous detection does results in increased bit error probability than synchronous detection. Hence, according to the unique operation principle of the WC receiver, we propose a synchronous detection method utilizing a novel time-to-wavelength based code acquisition with substantially reduced code acquisition time and subsystem component count than previous proposals. Moreover, a novel conceptual methodology of data-validation is proposed base on pulse-width monitoring to enhance the performance of the WC receiver. Finally, an experimental demonstration of the modified WC OCDMA receiver is presented, and a detailed theoretical performance analysis specialized for the WC receiver is carried out for the first time.
2. Wavelength-conversion based scheme to support MPR 2-D and 1-D code
According to the operational principle, previously proposed WC receivers [5–7] require that the received codes should be single-pulse-per-row (SPR) 2-D W/T codes with out-of-phase autocorrelation value equal to zero, namely, each chip-pulse in the code sequence should be with a unique wavelength. This consequently results in a sharply reduced code cardinality comparing with multiple-pulse per-row (MPR) 2-D W/T codes [10,11]. Besides, in spite of the limited code cardinality, one-dimensional (1-D) optical codes are appropriative for some certain application scenarios, for example, where the overall dispersions of transmission channel are too big to support 2-D W/T code. Therefore, it is necessary to enable the WC receiver to support both MPR 2-D W/T code and 1-D code.
Actually, the WC receiver can support MPR 2-D W/T codes and 1-D codes by converting those pulses with identical wavelengths to different wavelengths, which can be conveniently implemented by FWM-based wavelength conversion. Taking the 1-D optical orthogonal code (0011000000000000010) as an example, the code weight is 3, and all 3 pulses in the code sequence are at the same wavelength, denoted by. To implement wavelength conversion, a portion of the received 1-D code at wavelengthand a continuous light wave at wavelength are launched into a FWM based wavelength converter where the 1-D code is converted to two new wavelengthsand. Then there are three copies of the 1-D code at different wavelengths: and. At the optical decoder, autocorrelation peaks containing these three wavelengths can be generated by these code copies. Following process for data receiving is identical to the case of SPR 2-D W/T codes. It is worthy to be emphasized that the signal quality should be maintained during the wavelength conversion in order to guarantee the effect of following processes in the receiver.
Moreover, note that for optical codes with code weight bigger than 3, higher order FWM is necessary for the wavelength correlating process to discriminate autocorrelation peaks. For example, second order FWM is needed for 2-D codes with weight. However, it is known that higher order FWM has quite limited efficiency, Resulting-Pulses produced by higher order FWM may be too small to be detected. To alleviate this problem, we suggest that lower order FWM conjugated wavelengths should be boosted before higher order FWM. This can effectively maintain the performance of the WC receiver but at the cost of increased operation power and system component count. Alternatively, wavelength correlating and detection can be conducted for each three marked pulses to avoid higher order FWMs, and data receiving results can be obtained by counting the number of Resulting-Pulses of each three marked pulses, similar with chip-level OCDMA receivers .
3. Code acquisition and synchronous detection scheme for the WC receiver
3.1 A brief discussion of the necessity for synchronous detection
In conventional OCDMA receivers, the autocorrelation peak is among the autocorrelation and cross-correlation sidelobs. To fulfill correct data receiving, it is commonly necessary to determine the position where the autocorrelation peak appears within the code length. This process is called code acquisition in terms of spread spectrum communication, and the data receiving mode with code acquisition is synchronous detection, while the mode without code acquisition is asynchronous detection. In conventional OCDMA receivers, the autocorrelation peak is distinguished from correlation sidelobs by that it is supposed to have bigger power than correlation sidelobs. Hence, conventional code acquisitions are commonly based on power collecting and thresholding, which are often quite complicated, time consuming, and seriously impacted by MAIs [13–15]. For the WC receiver, however, only the Resulting-Pulse appears after decoding and wavelength correlating, major correlation sidelobs are rejected through the FWM based wavelength correlating process. Therefore, asynchronous detection without code acquisition can be implemented in the WC receiver by detecting the Resulting- Pulse all through a bit period . However, in the presence of MAIs, WC receiver operating in asynchronous detection suffers from increased bit error probability than synchronous detection due to that without knowing the position where the desired autocorrelation peak appears, any time-shift-pattern of the desired code may be recognized as the real code. In terms of interfering, during asynchronous detection the receiver exposes to interferences distributing all through the code length, while in synchronous detection mode the receiver exposes merely to interferences at each marked position of the desired code. As a kind of spectrum spread communication system, the capacity of an OCDMA system is interference limited. Since the system suffers from more interference in asynchronous detection, it possesses smaller system capacity . As derived in Appendix A, the relation between the bit error probabilities of asynchronous detection and synchronous detection under chip- synchronous assumption is:Equation (1) shows that the performance of an OCDMA system in asynchronous detection mode falls behind seriously with the increase of code length which is inevitable to enlarge the code cardinality. For example, for the carrier-hopping-prime-code (CHPC) (7, 49) with code length L = 49, which is utilized in the numerical performance analysis presented in Section 6 of this paper, the bit error probability of asynchronous detection is 49 times of the bit error probability of synchronous-detection. As it can be observed from the performance analysis in Section 6, this multiplied bit error probability results in a 20% reduction of the supported simultaneous users at bit error probability 1e-9. Actually, under the realistic chip asynchronous condition, we find that the performance of asynchronous detection is worse than that indicated by Eq. (1). This issue can be generally explained as the chip asynchronous performance of an OCDMA receiver influenced by the accuracy of code acquisition. It is a quite important problem but beyond the scope of this paper. We shall discuss this problem in a subsequence paper. In conclusion, although that it is somewhat more complicated than asynchronous detection, synchronous detection is considered worthwhile for it helps to maintain favorable system performance and capacity.
3.2 Description of the proposed code acquisition and synchronous detection scheme
In this subsection, we propose a novel code acquisition method for the WC receiver, by which code acquisition with precision of two chip time (2Tc) can be established within a bit- period (Tb). Figure 1 illustrates an example of the proposed scheme. The time-to-wavelength based code acquisition scheme is implemented by using periodic Acquisition-Sequences generated locally at the receiver. An Acquisition-Sequence comprises of a pulse chain distributing all through the code length L, with each pulse at a unique wavelength and lasting two chip time, as shown in Fig. 1. However, if the code length is too long that too many wavelengths are needed to construct an Acquisition-Sequence, each pulse in the Acquisition-Sequences is suggested to consist of a unique wavelength-set containing two wavelengths. For example, assuming that 10 wavelengths are used to construct the Acquisition-Sequence and each pulse contains 2 wavelengths, so that in total 45 different wavelength-sets are available to cover the code length L≤90.
During data receiving, burst-mode traffic with leading training-pattern that carriers a full knowledge of the transmitted code pattern first enters into the optical decoder to produce autocorrelation peaks. The decoded signal is then coupled with the locally generated Acquisition-Sequences and launched into a FWM device, where each autocorrelation peak encounters one or two pulses in the Acquisition-Sequences and generate a Resulting-Pulse at the certain FWM conjugate wavelength that involves all the wavelengths contained the autocorrelation peak and the encountered pulse in the Acquisition-Sequence. In the example shown in Fig. 1, the wavelengths contained in the autocorrelation peak are,and, the wavelengths of the encountered pulse in the Acquisition-Sequences is, so the available wavelength for the Resulting-Pulse is. Note that the wavelength of the Resulting-Pulse indicates how the autocorrelation peak encounters the Acquisition-Sequence. Namely, by detecting the wavelengths of the Resulting-Pulse, the position of autocorrelation peak within the code length is acquired and code acquisition is established. However, the wavelengths of the Acquisition-Sequences should be carefully arranged making sure that wavelengths indicating different synchronizing information do not collide with each other.
After code acquisition is established in the WC receiver, synchronous detection can be implemented by simply remaining the pulse in the Acquisition-Sequence that encounters the autocorrelation peak, denoting by Synchronous-Pulse. Every autocorrelation peak of arriving bit “1” encounters the Synchronous-Pulse and produces a Resulting-Pulse at the confirmed wavelengths. By detecting the right wavelength of the Resulting-Pulse at bit rate, false autocorrelation peaks that are out of the Synchronous-Pulse are rejected and synchronous detection is implemented.
3.3 Discussions of the proposed code acquisition and synchronous detection scheme
Some discussions of the proposed code acquisition and synchronous detection scheme are presented here. First, the pulse-width of the pulse chain in the Acquisition-Sequences is set to be 2Tc, so that the autocorrelation peak with pulse-width equal to Tc can be easily covered by one pulse in the Acquisition-Sequence. As shown in the example in Fig. 1, the autocorrelation peak encounters one pulse in the Acquisition-Sequence. However, an autocorrelation peak may overlaps two vicinal pulses in the Acquisition-Sequences, consequently the Resulting- Pulse may contain two wavelengths that indicate uncertain synchronization information. In this case, the Acquisition-Sequences should be delayed by one chip time, and then for sure the following autocorrelation peaks will wholly encounter one single pulse in the Acquisition- Sequence. Otherwise, if the pulse-width of the pulse chain is set to be one chip-time Tc, sub chip level time shift is needed to make sure that the autocorrelation peak encounters only one pulse in the Acquisition-Sequence, this is quite difficult to realize and will lead to increased system complexity. By relaxing the precision of code acquisition to 2Tc, system can remain succinct at the cost that, as shown in section 6 of this paper, the missing of accurate synchronization information results in a slightly degenerated system performance. Second, since that one Acquisition-Sequence examines all the possible position of the autocorrelation peak with in the code length, no False-Alarm as in conventional code acquisition schemes would happen , and the code acquisition can be established within one bit period, which is a substantially reduced time comparing to former proposals [13–15]. Moreover, this proposed scheme can be implemented all optically and no continual time shift of the Acquisition-Sequences is needed. This is believed to be a favorable merit because that frequent shift of Acquisition-Sequences generally requires additional optical devices (such as optical delay lines, optical switches) and time-consuming electronic controller. Third, for a training-pattern with n bits “1”, the result of synchronization can be confirmed n times since that each bit “1” in the training-pattern can generate identical synchronization result. Hence, a code acquisition result is accepted at the condition that the wavelength indicating this result appears n times. In the presence of MAIs, the probability for MAIs to successively generate same false code acquisition result many times is negligible. Note that, aiming at enlarging the code cardinality, trade off can be made between the out-of-phase autocorrelation value of the adopted codes and the error probability of code acquisition, as long as the error probability is maintained acceptable.
4. Data-validation scheme based on pulse-width monitoring
According to the operational principle of the WC receiver, Resulting-Pulses are produce by the autocorrelation peaks and Acquisition-Sequences. Once a Resulting-Pulse is detected at the correct wavelength, a bit “1” is declared at the receiver. However, in real traffic channel with asynchronous interfering users, false Resulting-Pulses may be produced by MAIs. Figure 2 shows some sketches of false Resulting-Pulses. When a bit “0” arrives, but a false Resulting- Pulse is detected at the receiver, a bit error occurs. Therefore, in order to achieve favorable system performance, it is necessary to discriminate the real Resulting-Pulses from false ones.
It is convenient to come up with the idea of discriminating the real Resulting-Pulse by power thresholding, as it is the common method in conventional OCDMA receivers . However, the following issues make this idea improper for the WC receiver. First, since that the deciding variable for power thresholding is commonly the integrated photocurrent of the Resulting-Pulse , false Resulting-Pulses may also generate deciding variables that exceed the predefined threshold, as the cases sketched in Fig. 2(b), 2(c) and 2(d). For example, the false resulting pulse sketched in Fig. 2(b) is narrower but higher than the real Resulting-Pulse, which may induce higher integrated photocurrent than the real Resulting-Pulse. Optical hard limiters can be utilized to alleviate this problem, but an ideal optical hard limiter is difficult to realize and cost unfriendly . Second, due to the polarization dependence of FWM process and beating between the desired code and MAIs, severe amplitude noise may be introduced to the Resulting-Pulses and this may also make the predefined threshold invalid. In literature , Semiconductor Optical Amplifier (SOA) gain clamper is used to reduce the amplitude noise by clamping the output optical power of the Resulting-Pulse onto a certain level. However, false Resulting-Pulses can also be clamped and recognized as real ones.
Actually, besides the optical power, another parameter of the Resulting-Pulse that can be utilized as distinguishing parameter is the pulse-width. Note that the pulse-width of real Resulting-Pulses produced by correct autocorrelation peaks are no less than the chip-width Tc. For data-validation, Tc can be set as the threshold for the pulse-width of Resulting-Pulses. However, this method requires that the coding chips should be with steep edges and stable width. And decoding process should be of high time accuracy and dispersion compensation to maintain constant pulse-width of the Resulting-Pulses. In fact, pulse-width is believed to be a good distinguishing parameter for that it does not rely on the magnitude of optical power, so that the rigid optical hard limiting, electronic power integrating and thresholding is avoided. This can in return render a simple all-optical data receiving. Besides, the pulse-width of the Resulting-Pulse is immune to the noises associated with optical power, such as amplitude noise due to state of polarization fluctuation, non-ruinous beat noise introduce by MAIs , quantum shot noise and thermal noise of the photodetector, etc. Furthermore, as will be shown in Section 6, it is difficult for MAIs to produce false Resulting-Pulses with bigger pulse-width than Tc under the realistic chip asynchronous condition, so that an enhanced performance of data receiving can be achieved.
Figure 3 delineates a simple pulse-width monitoring scheme for data-validation. According to the principle of the WC receiver, the Resulting-Pulse is produced by FWM effect among the wavelengths contained in the autocorrelation peak and Synchronous-Pulse, so that several wavelengths are available for the Resulting-Pulse. To conduct pulse-width monitoring, three wavelengths available for the Resulting-Pulse,,are filtered out and launched into pulse-width monitor. At the pulse-width monitor, the pulse atexperiences no time delay, while the pulse atis delayed by Tc/2-Tc/2m, and the pulse atis delayed by Tc-Tc/m, as shown in Fig. 3, here m is an adjusting parameter. It is observed from Fig. 3 that for real Resulting-Pulses with pulse-width Tc, overlap exists between the three wavelengths and an Overlapping-Pulse at the new wavelengthcan be generated through FWM effect among these three wavelengths. Once the new wavelength is detected, a bit “1” can be declared. Note that the power of the Overlapping-Pulse at does not impact correct receiving as long as it can be detected by a following photoreceiver. Practically, the output photocurrent of the Overlapping-Pulse is compared with a low threshold, once it exceeds the threshold, a bit “1” is declared. On the other hand, when a bit “0” is transmitted, a bit error occurs when interfering users generate a false Overlapping-Pulse at the pulse-width monitor. As will be analyzed in section 6 of this paper, bit error probability of the WC receiver with data validation based on pulse-width monitoring is much smaller than receivers without data-validation. Moreover, the performance of the WC receiver with pulse-width monitor is proved to be comparable with or even better than conventional OCDMA receiver with hard limiting and rigid power thresholding. Finally, it should be emphasized again that to ensure a reliable performance of the pulse-width monitoring, the pulse width of the Resulting- Pulse should be kept stable. In this proposed pulse-width monitoring scheme, the pulse width fluctuation of the Resulting-Pulses must be no bigger than Tc /m.
5. Proof- of-conception experimental demonstration
In this section, an experimental demonstration of the modified WC receiver with data-validation is presented. Setup of the experiment is shown in Fig. 4 . An OCDMA user, which operates at 1.25Gbits/s is encoded into 2-D W/T optical code OC1 [(1, 1562.5); (2, 1560.9nm); (4, 1554.5nm)] with code length 6, chip rate Rc = 8.75Gchip/s and correspondingly the chip width Tc≈130ps. MAIs are created with pulse at wavelength contained in OC1. At the WC receiver for users1, traffic signal containing both OC1 and MAIs first enters decoder1 where OC1 generates an autocorrelation peak, as shown in Fig. 5(a) . The decoded signals are then launched into a FWM device of 500m HNL fiber with nonlinear coefficient of 10 W−1km−1 and zero-dispersion wavelength at 1556nm. In the HNL fiber, two Resulting-Pulses at wavelengths 1552.9nm and 1556.1nm are produced by OC1’s autocorrelation peak, the waveform and spectrum are shown in Fig. 5(b), 5(c) and 5(e). Note that Acquisition-Sequence can be added before the HNL and Synchronizing detection can be conducted before FWM. These processes are not included in the experiment due to the equipment limitation. Even though, the proposed code acquisition and synchronous detection method can also be verified by this experiment to some extent since that any pulse in the autocorrelation peak can be deemed as a Synchronous-pulse. During the receiving of payload data for user1, these two confirmed wavelengths of Resulting-Pulse are filtered out for pulse-width monitoring. Optical boosting amplifier and polarization controller are arranged for Resulting-Pulses to guarantee the FWM effect of the following pulse-width monitoring. The pulse-width monitor is constructed with filters, FDL set and HNL fiber, similar to the decoder and wavelength correlator. With the FDL set, the Resulting-Pulse at 1552.9nm is delayed by S after the pulse at 1556.1nm as expressed in Fig. 3, with m≈3, 4, 5. Then overlaps among the two Resulting- Pulses appear, as shown in Fig. 5(d). The overlapped pulses are then sent into the HNL fiber where an Overlapping-Pulse at the wavelength 1559.3nm is produced through FWM effect when a bit “1” is received, with the spectrum shown in Fig. 5(g). After that, the Overlapping-Pulse is filtered out by an optical bandpass filter, amplified and gain-clamped by a SOA (CIP SOA-S-OEC), and detected by a 15GHz low-speed photoreceiver. The waveforms of Overlapping-Pulses are shown in Fig. 5(e). Bit error rate measured form the obtained electronic signals are represented in Fig. 6 .
It is observed from Fig. 5 that good waveforms are obtained at key spots of the experimental setup. It can be observed that amplitude noise exists in the Resulting-Pulse due to polarization fluctuation and beat noise between user1 and the MAIs. However, as a proof of concept experimental demonstration, no ruinous beat noise that can collapse the data receiving is introduced to user1. In real traffic channel, ruinous beat noise is possible, but, as can be deduced, it will be with small probability. As shown in Fig. 6, low bit-error-rate data receiving is achieved in the experimental demonstration. Note that for the case without date-validation, only the first FWM process is needed to produce the Resulting-Pulse. As expected, the BER performance for such case is better than the cases with pulse-width monitor since additional noises and distortions may be added to the overlapping-pulses during the second FWM process for width monitoring. However, pulse-width monitor is considered worthwhile since that it improves the performance system by eliminating impact from MAIs in realistic OCDMA networks, and the attainable improvement will be illustrated clearly in the theoretical analysis in Section 6. High operation power of FWM is the disadvantage of the receiving structure. However, advanced material like bismuth-oxide fibers with ultra-large nonlinear coefficient can alleviate this problem and also render a more compacted system .
6. Theoretical performance analysis of the proposed WC receiver with data validation
6.1 Theoretical analysis of bit error probability under chip asynchronous assumption
In this section, a specified theoretical analysis of the modified WC receiver is presented. The receiver is assumed to work in synchronous detection mode with synchronization precision equals to 2Tc (utilizing the scheme discussed in section 3), and the analysis is carried out under the realistic chip asynchronous assumption. We consider the case that the adopted code set has ideal cross correlation value for easy calculation. During the analysis, we concentrate on multiple users’ interferences only, neglecting the power-related noises introduced during four-wave mixing and photo detection. Note that ruinous destructive beating between the desired code and MAIs may harm the receiving of bit “1”. However, the detailed discuss about this question is beyond the scope of this paper. In the following theoretical analysis, we assume that the probability for ruinous destructive beating is negligible since that the WC receiver possesses excellent tolerance for beat noise, then no bit error occurs when “1” is received.
Unlike most performance analysis carried out for conventional OCDMA receivers where only the number of hits between the desired code and interfering codes is concerned, the performance analysis for the WC receiver with pulse-width monitoring needs to consider both the number of hits and the manner how hits happen. Here we assume that the bandwidth of the photodetector is bigger than the Overlapping-Pulses. According to the pulse-width monitoring scheme described in Section 4, a bit error occurs when MAIs generate a false Resulting-Pulse that satisfies one of the following two conditions:
- a. the false Resulting-Pulse is no narrower than;
- b. the false Resulting-Pulse contains two narrow portions and overlaps exist between the two portions after being delayed in the pulse-width monitor. Namely, at least one of the two portions should be no narrower than.
Based on the definition above, the bit error probability of the WC receiver with pulse- width monitoring based data-validation can be expressed as:Eq. (5), the factor 1/2 comes from the assumption that bit “1” and bit “0” is transmitted with equal probability and no bit error would happen when bit “1” is transmitted. is the set of all possible interfering pattern vectors κ that satisfyEq. (6) represents the probability that there arehits at the ith marked position which meet condition a or b. According to Fig. 3 we obtainEq. (9) and (10), the factor m is the adjusting parameter for pulse-width monitoring.
6.2 Numerical results
Some numerical results of the performance analysis are presented in this subsection. We take 2-D carrier-hopping prime codes (CHPC) with cross correlation valueas examples to calculate the bit error probabilities of the WC receiver with data-validation. For CHPC (5,25) with code weight, wavelengths number L = p1 = p2 = 5, and code length N = p1p2 = 25, we have the discrete hit probability p1,0 = 0.0833 and p1,1 = 0.0167, here p1 and p2 are two prime numbers. Also we have p1,0 = 0.0625 and p1,1 = 0.089 for CHPC (7, 49) with, L = p1 = p2 = 7, and N = p1p2 = 49 ,
We first calculate the influence of phenomenological coefficientαto the BER, Fig. 7 shows the calculated BER under different values of αfor both CHPC (5,25) and CHPC (7, 49). When α is set to be 0, it indicates that no double-hit contributes to the BER and represents the upper bounder of the BER values; and when α is set to be 1, it indicates that every double-hit contributes to the BER and represents the lower bounder of the BER values. Actually, it is observed from Fig. 7 that the value of αinfluences the results in a slight way because p1,0 is commonly much bigger than p1,1. In the following analysis, we adopt the lower bound of BER by setting α = 1.
Figure 8 shows the chip asynchronous bit error probability for CHPC (5, 25) and CHPC (7,49) with different pulse-width monitoring adjusting parameter m versus the number of simultaneous users. We can see that the error probability of the WC receiver gets worse as K increases. As expected, the error probability of CHPC (7,49) is 4 or 5 orders of magnitude smaller than that of CHPC(5,25). Moreover, better performance is achieved with bigger m, especially for smaller K. Particularly, the calculated bit error probability with m = 1, which represents a receiver without the pulse-width monitoring based data-validation, is much worse than receivers with pulse-width monitoring and consequently has smaller system capacity at certain bit error probability. Figure 9 draws the capacity for both CHPC (5, 25) and CHPC (7, 49) versus the value of m. It can be observed that system capacity increased rapidly with m in the region m<5. When m becomes bigger than 10, the system capacity grows with flat slope. This suggests that a small m, for example m = 5, should be adopted since it provides good performance as well as maintains desirable system simplicity.
In Fig. 10 , the calculated chip-asynchronous performance of the WC receiver with data-validation was compared with the performance of conventional OCDMA receiver with hard limiting (OHLCR) obtained in reference . It is observed that, for both CHPC (7, 49) and CHPC (5, 25), the performance of a WC receiver with data-validation (m = 10) is slightly inferior to the performance of OHLCR with rigid threshold equal to the code weight. More precisely, Fig. 11 illustrates the comparison between the performance of the WC receiver and OHLCR with different threshold. For CHPC (7, 49), the performance of the WC receiver is slightly inferior to that of OHLCR with rigid threshold Th = 7, and better than receivers with Th<7. For instance, the bit error probability of a WC receiver with m = 10 is 1 orders smaller than that of a OHLCR with Th = 6 for CHPC(7, 49) and 3 orders smaller than OHLCR with Th = 5. For realistic OHLCRs, it is usually necessary to set the threshold at half weight to compromise noises , so it can be observed from Fig. 10 that the proposed receiver has great strength compared to OHLCR.
Figure 10 and 11 confirm that WC receiver with pulse-width monitoring based data- validation is a promising receiving structure since it possesses reduced system complexity as well as excellent system performance. Moreover, the performance analysis here does not consider noises other than MAIs. It is believed that the system performance of the WC receiver under various noises would be also quite admirable since that WC receiver possesses excellent noise tolerance.
In this paper, we propose and demonstrate a modified WC receiver with new functions. A method based on wavelength conversion is introduced to enable the WC receiver to support MPR 2-D code and 1-D optical code. Besides, we introduce a time-to-wavelength based all-optical code acquisition scheme for the WC receiver with the code acquisition time being substantially reduced. A novel conceptual methodology for data-validation is proposed base on pulse-width monitoring. The proposed scheme does not rely on rigid power thresholding, and is immune to most noise associated with optical power. This power independent property is believed to be a great merit for the practical application of incoherent OCDMA system. Experimental demonstration of the modified WC receiver with data-validation is presented; low BER receiving of OCDMA traffic is achieved without hard limiting and electronic power thresholding. Finally, a theoretical performance analysis specialized for the WC receivers are carried out under realistic chip asynchronous condition. Numerical results show that the overall performance of the proposed WC receiver with data-validation scheme prevails over conventional OCDMA receiver with hard limiting and rigid power thresholding.
Appendix: Derivation of bit-error-probabilities comparison between synchronous and asynchronous-detection
First we denote the chip synchronous bit-error-probability of an OCDMA receiver as:
Pr(p=i) represents the probability that an error happened due to that MAIs construct a false autocorrelation peak at the ith chip position in a code sequence, Lrepresents the code length. Then the bit error probability in asynchronous detectioncan be expressed as
Under the reasonable approximation that:
This work is supported in part by the National Basic Research Program of China (973 Program) under Contract No. 2011CB301703 and the Science Foundation of China under Contract No. 60807028. The authors would like to thank Mr. Weihua Xu of Tektronix, Inc. for providing the CDR module. Acknowledgment is also conveyed to Dr. Yun Ling and Dr. Bo Xu from UESTC for their inspiring discussions.
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