Scalability Analysis of Wave-Mixing Optical Cross-Connects

Transcription

1 Scalability Analysis of Optical Cross-Connects Abdelbaset S. Hamza Dept. of Electronics and Comm. Eng. Institute of Aviation Eng. & Technology Giza, Egypt Haitham S. Hamza Dept. of Information Technology Cairo University Giza, Egypt Kamal S. Hamza Dept. of Electronics and Comm. Eng. Arab Academy for Science and Technology Cairo, Egypt Abstract In this paper, we analyze the scalability of a class of optical cross-connects (OXCs) that uses bulk wave-mixing converters to simultaneously convert multiple distinct wavelengths. For large number of wavelengths, wave-mixing OXCs provides good scalability by reducing the number of required wavelength converters through conversion sharing. However, as the number of wavelengths increases, so does the crosstalk noise in shared converters, which may limit the scalability of the network. Thus, a fair analysis for the scalability of wave-mixing OXCs must take into consideration the benefits of conversion sharing as well as the practical limitations imposed by such sharing. This paper presents an analysis of the scalability of wave-mixing OXCs. It is shown that, for W 32 and for any number of fibers, wave-mixing OXCs have a lower conversion cost compared to the optimal OXCs that use conventional converters that converts a single channel at a time. Index Terms Optical Cross-Connects (OXCs), Converters, Wavelength Converters, Scalability, Benes Network. I. INTRODUCTION An optical cross-connect (OXC) switches an input signal on a given wavelength to the desired wavelength on the required output fiber, while keeping the signal in the optical domain. To do so, an OXC needs to perform two switching functionalities: (1) space switching, and (2) wavelength switching. Space switches are performed using optical space switches, whereas wavelength switching is implemented using wavelength converters (WCs). OXCs play an central role in the design of optical networks based on wavelength division multiplexing (WDM) technology [1] [11] [10]. Several research efforts have been devoted to the design of efficient OXCs with reduced complexity, see for example, [2] [4] [11] [10] [8] [7]. Various OXC architectures make use of different space and wavelength switching technologies; however, all architectures share the same design objective of reducing the total number of space switches and WCs without limiting the switching capability of the cross-connect. This obvious design objective becomes even more pressing for WDM networks. This is because the rapid advances in WDM technology continue to enable more and more wavelengths per fiber, making the design of an cost-efficient OXCs a real challenge. Due to their high complexity, WCs are considered as the dominate factor in the complexity, and hence the cost, of an OXC design [3] [8] [7]. As such, several attempts have been focusing on reducing the use of WCs without reducing the switching prosperities of the architecture. An obvious approach to reduce the needed WCs is to share them among several fibers or wavelength-links inside the OXC [1]. Such sharing leads to an increased cost in both switching and scheduling. Moreover, sharing may lead to blocking of some input traffic due to the unavailability of free WCs. A more effective approach to reduce WCs without introducing any blocking in the OXC is to use wave-mixing WCs [2] [4] [10]. A wave-mixing converter an convert several distinct wavelengths simultaneously [5] [10] [4]. An OXC that employs wave-mixing converters is known as wave-mixing OXC. Various wave-mixing OXCs have been introduced in the literature [2] [4] [10]. Despite the advantages of using wave-mixing WCs, a main drawback of these converters is the high crosstalk noise generated due to the simultaneous conversion of multiple wavelengths. For typical WDM networks with large number of wavelengths, crosstalk can be a fundamental factor that limits the scalability of the cross-connect in practice. Another limiting factors for the scalability of wave-mixing OXCs is the difficulty of developing converters that can simultaneously convert large number of wavelengths. A practical implementation of wave-mixing OXCs must take into consideration the tradeoff between the reduction gained by wave-mixing converters at one hand, and the increased crosstalk noise and complexity of converters that simultaneously convert large number of wavelengths on the other hand. Only then the practical scalability of wave-mixing OXCs can be fairly evaluated. Accordingly, in this paper, we attempt to study this tradeoff to understand the scalability limits of the wave-mixing OXCs. In particular, we present an analysis of the scalability of wave-mixing OXCs. It is proven that, for W > 64 and for any number of fibers, wave-mixing OXCs have a lower conversion cost compared to the optimal OXCs that use conventional converters that converts a single channel at a time. Analysis results show that for high values of W,the conversion cost of the MCWC-based design can be reduced by more than 70% of that of the SCWC-based design when both converter types convert one channel at a time. The rest of this paper is organized as follows. Section /09/$ IEEE 74

2 The following is a summary of the key properties of wavemixing OXC that are used in this paper. Detailed proofs of these properties can be found in [4]. Property 1: In an FW FW wave-mixing network, channels are converted only between two consecutive switching stages i and i+1,if0 i log W 1 or log(f 2 W ) 2 i log(f 2 W 2 ) 3. Otherwise no channel is converted between the two stages. Fig wave-mixing OXC with F =2and W =4. defines notation and terminologies used throughout the paper and provides a brief overview of related works. Section 3 presents the structure and operational concept of the proposed interconnection network. Section 4 presents analysis of the conversion cost of the proposed network. Conclusions are presented in Section 5. II. PRELIMINARIES AND RELATED WORK In this section, we present few notation and definitions, and briefly review some basic concepts for wave-mixing WCs. A. Notation Let N [F, W] denote an N N OXC with F input and F output fibers each carrying W wavelengths, and N = FW. For simplicity, we assume both F and W to be powers of 2. The set of F fibers is denoted as F = {f 0,f 1,..., f F 1 } and the set of W wavelengths by W = {,,..., w W 1 }. For simplicity, all wavelengths are assumed to be equally spaced by Δw. It is assumed that the wavelengths are equally spaced and of the form w i = +iδw, where i =0,..., W 1. B. OXCs A wave-mixing OXC is a type of cross-connects in which wave-mixing WCs (also known as bulk WC) are used [4] [10]. Native forms of wave-mixing conversion uses the properties of second and third optical nonlinearity to perform wavelength conversion. Examples of such converters include second-order difference frequency generation (DFG) converters and the third-order four-wave-mixing (FWM) [4]. Existing wave-mixing OXCs are all based on the wellknown Beneš structure [4] [10]. In [4], nonnative wave-mixing conversions based on DFGs is used to provide simultaneous frequency translation for multiple wavelengths. The unique mirror-image mapping characteristics of DFGs is used to provide bulk conversion capability in the so-called Twisted Beneš network. Using wave-mixing converters has shown to greatly reduce the complexity of the OXC architecture by using a smaller number of WCs compared to that used in conventional designs. Property 2: Consider an FW FW wave-mixing network, and two consecutive stages i and i+1, where 0 i log W 1 or log(f 2 W ) 2 i log(f 2 W 2 ) 3. Define h = min(i, log(f 2 W 2 ) 3 i. Between the two stages, for d = 1,..., d 1, there are FW(2 d )/4 interstage connections that are frequencyconverted by an amount d(w/2 h+1 )Δw, and these connections are evenly distributed among W (2 d )/2 distinct wavelengths. Property 3: An FW FW wave-mixing network can be implemented with 2F log W converters. To illustrate the above properties, we show how they are applied to an 8 8 wave-mixing interconnection network shown in Figure 1 with F = 2 and W = 4. As shown in the figure, wavelength-links from each input fiber is demultiplexed, and each two similar wavelengths from the two fibers are connected to a 2 2 switching element in the first stage. Each switching element in each stage is connected to the following stage via two links: one link goes direct to the switching element with the same wavelength, and another link goes to the upper or lower subnetwork (depending on the switch position). If the second link connects to a switching element with a different wavelength, then wavelength conversion is used to shift this wavelength to the wavelength of the switching element that it connects to. For example, in Figure 1, the two output links of the first switching element in the first stage connects to the first and the third switching elements in the second stage. Only the link that connects to the third switching element would undergo wavelength conversion (from to ), which mean shifting the wavelength of the second link by +2Δw. Following the same concept, it can be seen from Figure 1 that between the first (fourth) and second (fifth) stages, two links are translated by +2Δw and two are translated by 2Δw, whereas between the second (middle) and the middle (fourth) stages, two links are translated by +Δw and two are translated by Δw. All links that require the same amount of wavelength translation can share a single wave-mixing converter as long as no two links carry the same wavelength. Thus, the 8 8 shown in Figure 1 requires 8 converts distributed as follows: Two converters between the first and the second stages, one provides +2Δw wavelength shift and that other provides 2Δw wavelength shift. Two converters between the second and the middle stages, 75

3 one provides +Δw wavelength shift and that other provides Δw wavelength shift. Two converters between the middle and the fourth stages, one provides +Δw wavelength shift and that other provides Δw wavelength shift. Two converters between the fourth and the fifth stages, one provides +2Δw wavelength shift and that other provides 2Δw wavelength shift. III. SCALABILITY ANALYSIS OF WAVE-MIXING OXCS In this section, we analyze the scalability of wave-mixing OXCs. In particular, the trade-off between the total number of simultaneously converted channels and the conversion cost is analyzed. A. OXC with Conventional WCs The hardware complexity of an OXC, and hence its cost, is proportional to the switching and conversion complexity of the cross-connect. Switching complexity can be computed by the total number of switching elements (e.g., 2 2 switches). Conversion complexity indicates the overall complexity of the wavelength conversion processes in the cross-connect. Conversion complexity is proportional to the total number of WCs used and the conversion range of each WC (i.e., the number of input and output wavelengths to be converted) [9] [7] [8]. It is worth noting that, WCs with wide conversion ranges are not only expensive, but also can be technologically infeasible to build. One of the simplest approaches to construct an OXC with the minimum conversion complexity is to use an array of fixed conventional WCs (i.e. signal-channel) at the input ports to convert various wavelengths to a specific wavelength (w i ), and then use another array of fixed WCs at the output ports to convert w i to the desired output wavelength. Note that in such a design, no WCs for wavelength w i are needed in input and output wavelength conversion arrays. It can be shown that such a design has a conversion complexity of 2F (W 1). B. OXCs with Limited Simultaneously Converted Channels From Property 3 above, it is shown that an N [F, W] wavemixing OXC architecture with F 2 and W 2 requires 2F log W wave-mixing converters. However, it should be noted that this result is obtained under the assumption that each converter can simultaneously convert up to W 2 channels. As discussed before, this assumption may limit the scalability of the cross-connect when W is large, as it may be technologically and/or economically infeasible to build wavemixing converters that convert large number of wavelengths simultaneously. Moreover, if even feasible, the crosstalk noise generated in such devices may be above the acceptable levels. Thus, in order to study the scalability of the wave-mixing OXCs, we need to generalize the above result for the case in which the number of simultaneously converted channels TABLE I SUMMARY OF CONVERSION COST FOR W =32. C Conventional OXC OXC Reduction % TABLE II SUMMARY OF CONVERSION COST FOR W =64. C Conventional OXC OXC Reduction % per wave-mixing converter is W 2. The following theorem establishes this result. Theorem 1: Let C be the total number of channels that can be simultaneously converted in a wave-mixing converter, such that: C = W/2 c, where c is an integer c =1, 2,..., log W. Thus, for F 2 and W 2, ann [F, W] wave-mixing OXC, each capable of simultaneously converting C channels, requires the following number of wave-mixing converters: Number of Converters =2F log W log W C (1) Proof: By limiting the number of simultaneously converted signals in each MCWC to C = W/2 c,wemustuse c F MCWCs between any pair of consecutive stages where interstage connections are converted. Thus, from Theorem 1, the total number of MCWCs is 4F. Since c = log(w/c), then it is straightforward to show that the total number of MCWCs is 2F log W log W C. It is easy to validate the generalized result of Theorem 1 by instantiating the typical case for c =1(i.e., C = W/2 which means that each converter can convert up to W/2 channels at a time). 2F log W log W C =2F log W log 2) = 2F log W. As discussed earlier in the paper, the conversion complexity of an interconnect depends on the total number of used WCs and the conversion range of each converter. In the case of wave-mixing converters, the total number of converters used represents the conversion complexity of the design. This can be achieved by building a wave-mixing converter in which the number of distinct nonlinear waveguides does depend on the number of channels that can be simultaneously converted [4]. C. Scalability Analysis Although the conversion complexity of an OXC based on wave-mixing converter is O(F log W ), which is less than the 76

4 TABLE III SUMMARY OF CONVERSION COST FOR W = 128. C Conventional OXC OXC Reduction % O(FW) complexity of the OXCs with conventional WCs; however, a practical concern with wave-mixing converters is the high impact of in-band crosstalk generated due to the simultaneous conversion of multiple wavelengths [4]. The number of first-order in-band crosstalk terms generated in converters in an OXC with shared wave-mixing converters is proportional to O(W log W ) [4]. Conventional WCs, on the other hand, have a smaller in-band crosstalk as each converter deals with a single wavelength at a time. It is therefore important to investigate the impact of crosstalk on the practicality and scalability and efficiency of wave-mixing OXCs. In particular, we need to answer the following key question: When it would be practical to implement scalable OXCs with wave-mixing converters? The following theorem answers this question by establishing the following result Fig. 2. Comparison of Conversion complexity for N [4, 8] OXCs based on 140 Theorem 2: For F 2 and W 2, ann [F, W] OXC with wave-mixing converters, each capable of simultaneously converting C = W/2 c the conversion complexity of the OXC is strictly less than that of best conventional OXC design (Section III) when: C W 2 W 1 log W Proof: The result follows directly from Lemma 1 and Theorem In order to study the scalability of the wave-mixing OXCs we investigate its conversion complexity under various constraints on the number of simultaneously converted channels (C). Figure 2 compares the conversion complexity of the OXCs with conventional single-channel converters and wave-mixing converters with W = 32. As shown in the figure, wavemixing converters reduces the conversion complexity only when the number of simultaneously converted channels per each converter is at least two. If the number of channels is less than two, the conversion complexity of conventional WCs is smaller. The conversion complexity of the wave-mixing OXCs decreases as the number of simultaneously converted channels per converter increases. The best reduction in conversion Fig. 3. Comparison of Conversion complexity for N [4, 16] OXCs based on complexity is obtained when each wave-mixing convert can covert up to 4 (= W/2) simultaneously. The same trends discussed above hold for W = 16. Figure 3 compares the conversion complexity of OXCs with conventional and wave-mixing converters for W =16. As can be seen from the figures, the complexity of OXCs with wave- 77

5 Fig. 4. Comparison of Conversion complexity for N [4, 32] OXCs based on Fig. 6. Comparison of Conversion complexity for N [4, 128] OXCs based on Fig. 5. Comparison of Conversion complexity for N [4, 64] OXCs based on mixing converters is less when the number of simultaneously converted channel per each converter is two or more (i.e., C 2). When C =8, wave-mixing converters yield around 73 % reduction in the conversion complexity as compared to conventional WCs. Figure 4 compares the conversion complexity of OXCs with conventional and wave-mixing converters for W =32. As shown in the figure, wave-mixing OXCs always have a smaller conversion complexity as compared to OXCs that use conventional WCs. Table I gives the conversion complexity of both designs for F =4. The table also shows the reduction percentage in the conversion complexity obtained by the use of wave-mixing converters. These trends hold for W =64and 138 as shown in Figures 5 and 6. The effective scalability of wave-mixing OXCs is demonstrated by the considerable reductions in the conversion complexity as compared to conventional WCs (see Tables II and III). From the above results, for interconnection networks with large number of wavelengths per fiber, wave-mixing OXCs provide better scalability as compared to OXCs with convention single-channel WCs. IV. CONCLUSIONS In this paper, we study the scalability of wave-mixing OXCs by analyzing the trade-off between the reduction gained by wave-mixing converters at one hand, and the increased crosstalk noise and complexity of converters that simultaneously convert large number of wavelengths on the other hand. It is shown that, for W 32 and for any number of fibers, wave-mixing OXCs have a lower conversion cost compared to the optimal OXCs that use conventional converters that converts a single channel at a time. Analysis results show that for high values of W, the conversion cost of wave-mixing OXCs can be reduced by more than 90% of that of OXCs with conventional single-channel wavelength converters. 78

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