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hop lightwave networks in which the conventional N x N passive star coupler is replaced by fixed wavelength division multiplexed. (WDM) cross connects.
JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 10, NO. 6, JUNE 1992

A WDM Cross-Connected Star Topology for Multihop Lightwave Networks Mansour I. Irshid and Mohsen Kavehrad, Fellow, IEEE

Abstract-In this paper, we propose a star topology for multihop lightwave networks in which the conventional N x N passive star coupler is replaced by fixed wavelength division multiplexed (WDM) cross connects. The proposed topology overcomes three major limitations of the conventional star topology. First, it reduces the number of wavelengths needed in a (p, k) ShuffleNet from kpA+’wavelengths in the conventional topology to p wavelengths in the proposed one. Second, the signal power loss due to the 1/N power splitting at the star coupler no longer exists in the WDM cross connects and, therefore, the restriction on the supported number of users by the star network is alleviated. Third, it completely eliminates the need for wavelength filtering at the input to the receivers as is the case in the conventional star topology. The use of 2 x 2 WDM lapped couplers as a cheap WDM cross connect for a (2, k) ShuffleNet is investigated. We also find that a p x p star coupler followed by p fiber Fabry-Perot filters can be used as a p x p WDM cross-connect for a (p, k) ShuffleNet at the expense of using p‘ rather than p wavelengths.

I. INTRODUCTION

T

HE use of single-mode fiber with its inherent enormous bandwidth in a multi-user environment has been the subject of considerable interest in recent years. Various access techniques such as wavelength, time, space, and code division multiplexing have been proposed to tap this enormous bandwidth [ 1] - [ 3 ] . Among these techniques, the broadcastand-select wavelength division multiplexing (WDM) may, in principle, exploit the Terahertz bandwidth of the fiber. However, the required technology might not be available for some time. Multichannel-multihop lightwave networks have been proposed to overcome some of these problems and to achieve the concurrency for tapping the vast optical bandwidth with available technology [4], [ 5 ] . In this approach, user nodes are used as active repeaters with fixed-wavelength transmitters and receivers. That is, transmitting a packet from one node to another may require routing it through intermediate nodes. In a multihop network, the ShuffleNet connectivity is specifically employed to achieve efficient use of the channel bandwidth such that the capacity of the network increases monotonically with the number of users [4]. In principle, multihop lightwave networks can be implemented by a variety of physical topologies (e.g., bus, star, Manuscript received May 9, 1991; revised Nov. 11, 1991. This work was supported in part by the Telecommunication Research Institute of Ontario (Photonic Networks and Systems Thrust). R.I. I. Irshid is with the Department of Electrical Engineering, Jordan University of Science & Technology, Irbid, Jordan. This work was performed while visiting the University of Ottawa, Canada on sabbatical. hl. Kavehrad is with the Department of Electrical Engineering, University of Ottawa, Ottawa, Ontario, Ontario, K1N 6N5. IEEE Log Number 9107293.

tree, and ring). The only constraint on the topology is that it should provide a direct transmission path from each node to all the nodes one hop away, as specified by the ShuffleNet connectivity graph. The choice of a suitable topology for a specific application is based on many factors such as cost, complexity, available power budget, and availability of optical components. When multihop networks are implemented using basic topologies, as bus, star, or tree, they introduce two major problems. First, the number of different wavelengths needed in the network is very large. This number is equal to p times the number of users where 1) is the number of transceiver pairs per user. Second, although multihop networks can, in principle, support a large number of users, the network size is limited by the inherent power splitting of the required passive couplers used for interconnecting various nodes. To reduce the large number of wavelengths needed in a multihop network, several approaches have been proposed in the literature. A single-wavelength approach to multihop networks is possible by using a fully connected topology where a single fiber is dedicated to each node pair. This approach has the obvious drawback of requiring a total number of fibers which is 2p times the number of users [4]. Between these two extremes, a tradeoff between the number of wavelengths and the number of fibers is possible by using multifiber ring topologies [6]-[8]. To overcome the power splitting problem, wavelengthselective devices can be used. These devices are based on multiplexing components such as grating or birefringent elements and they have been used in many communication network architectures [9]-[ll]. A feature of such networks is that the optical power at a given wavelength is directed only to where it is required and a given wavelength can be reused in different parts of the network. This leads to a reduction in the required number of wavelengths, the number of optical filters and the power loss imposed on the individual signals. In [12], a selective-broadcast passive star coupler has been proposed to replace the conventional star coupler as a central hub of a star network. The coupler can be constructed with a prefabricated routing matrix suitable for multihop networks. This approach has the advantage of directing the optical power at a given wavelength to where it is required, and thus the network size can be increased as a consequence of the lower power loss. The difference between this approach and that of a simpler broadcast-and-select approach is that this wavelength routed method is “source determined.” That is, the receivers do not have to be tunable or wavelength selective, but that the transmitters determine the path of the signal rather than the receivers. This becomes more significant as the number

0733-8724/92$03.00 0 1992 IEEE

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IRSHlD AND KAVEHRAD: WDM CROSS-CONNECTED STAR TOPOLOGY

of alternate destinations for each signal increases because the same hardware can then be used to achieve a higher degree of interconnection complexity. In this paper, we propose a WDM cross-connected star topology for multihop lightwave networks. For a (p, k ) ShuffleNet, the proposed topology reduces the total required number of wavelengths in the network to p wavelengths compared to Ay"+' for a star network using a conventional star coupler. Moreover, except for the insertion loss of the WDM cross connects, there is no power splitting loss in the proposed topology. This means there is no restriction on the network size due to power constraints. For a more cost effective network, we also propose using 2 x 2 WDM lapped couplers and wavelength-independent p x p passive couplers as WDM cross connects. The main idea behind this work is spatial reuse of the wavelengths which has been studied by others as well [13]-[16]. In Section 11, we present the WDM crossconnected star topology for multihop lightwave networks. The 2 x 2 WDM lapped coupler as a WDM cross connect for a ( 2 , k ) ShuffleNet is discussed in Section 111. In Section IV, the wavelength-independent p x p passive couplers are used as WDM cross connects for the general (p, k ) ShuffleNet. Conclusions are presented in Section V. 11. A WDM CROSS-CONNECTED STAR TOPOLOGY FOR MULTIHOPNETWORKS A multichannel-multihop lightwave network is an optical fiber-based packet communication network for multi-user data transmission applications. It employs fixed wavelength transceiver pairs at each node which ought to be much smaller than the total number of nodes in the network and therefore the transmission of a packet from one node to another may require routing the packet through intermediate nodes. A (p, k ) ShuffleNet connectivity graph has N = kpk nodes ( k = 1 , 2 , 3 . . . . : p = 1 . 2 , 3 , . . .) arranged in k columns each with p k nodes where p is the number of fixed transceiver pairs per node [4]. Since each node requires p wavelengths to transmit p packets simultaneously, the total number of wavelengths needed in the network is ICpk+'. Wavelength assignment for various nodes is determined according to the ShuffleNet connectivity graph which is drawn as follows. Moving from left to right, the transmitters of the nodes in one column are connected to the receivers of the nodes in the fixed wavelengths in a fixed shuffle next column using p"' pattern with the transmitters of the last column connected to the receivers of the first column. To simplify the drawing of the ShuffleNet connectivity graph, the transmitters and the receivers of the nodes in the first column are divided into two columns with the transmitters in the left-most column and the receivers in the right-most column of the graph. This is illustrated in Fig. 1 for an 8-node 0, = 2, IC = 2) ShuffleNet. The implementation of a multihop lightwave network using star topology with a conventional passive star coupler as a central hub requires pN optical sources (laser diodes) operating at p N different wavelengths as it is shown in Fig. 2. When N is large, providing such a large number of different lasers is rather expensive with the available technology. Moreover, although

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JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 10, NO. 6, JUNE 1992

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p nodes; 1.1 p"'? 1 2p"'. . . . 1 ( p - l)p"-' in the first column are connected to the p 2 receivers of the p nodes; pk' l , p k 2. . . . .p k + p in the second column. Likewise, the p 2 transmitters of the p nodes; 2 , 2 p"'. 2 2p"l. . . 2 + ( p - 1)pk-' in the first column are connected to the p 2 receivers of the p nodes; p" p 1.pk p 2 . . . . . p k 2 p in the second column. In general, the p 2 transmitters of the p nodes; i . i p k - ' . i 2p"-', . . . . i, ( p - l)pk-l in the first column are connected to the p 2 receivers of the p nodes; p k ( i - l ) p + 1 . ~ 1 ~( i - ~ ) p +2, . . . . p k ( i - l ) p + p in the second column with i = 1.2. . . . . p k - ' . This means that the transmitters of the p" nodes in the first column and the receivers of the p k nodes in the second column can be arranged in ilk-' groups with the members of each group connected to each other and with no connection between the members of different groups. This grouping procedure is repeated for the transmitters of each column with the receivers of the next column in the connectivity graph until the transmitters of the last column (kth column) are grouped with the receivers of the first column. The total number of transmit/receive groups in the whole network is kp"'. In each group, the p 2 transmitters of p different nodes are connected with the p 2 receivers of p different nodes in a perfect shuffle pattern. According to the above grouping procedure, the perfect shuffle connectivity graph can be redrawn with the transmitters of all the nodes in the network in one column and the receivers in another column. The transmitters and the receivers are arranged in kp"- 1 groups with p transmit/receive node pairs in each group. The p node pairs consist of p 2 transmitters and p 2 receivers. Fig. 3 shows how the 8 transmit/receive node pairs in a ($ = 2 , k = 2 ) ShuffleNet are arranged in four groups each of two transmit/receive node pairs. The arrangement of the transmitters and the receivers of the ShuffleNet in separate transmit/receive groups suggests that it is possible to implement the multihop network in a star topology using WDM cross connects as a central hub instead of the conventional N x N passive star coupler. The transmitters of p nodes and the receivers of p other nodes in each group are interconnected using a p x p WDM crossconnect. Fig. 4 shows a p x p WDM cross connect. Its operation can be explained as follows. At the transmit-side of the node, the p different wavelengths carrying p different signals from that node are wavelength multiplexed on a single fiber which runs into the central hub where it is connected to one of the inputs of the corresponding p x p WDM crossconnect. At the hub, wavelength demultiplexers separate the signals from each incoming fiber. All the signals intended for a given destination are passively arranged, remultiplexed and transmitted to the appropriate destination on a single fiber. At the receiver of each node, different signals are wavelength demultiplexed, detected, and retransmitted if necessary. Since there are p inputs and p outputs for the WDM cross connect with each input receiving p different signals, one might expect that y 2 wavelengths would be required to form a complete interconnection. It turns out, however, that it can be arranged so that with only p wavelengths, p inputs are interconnected with p outputs in a completely noninterfering way [lo]. Fig. 4 shows how the same set of p wavelengths (AI, X2, X3, . . ., A),

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Group 1

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Group 2

Group 3

Group Group 4 4

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Fig. 3. Perfect shuffle connectivity graph arranged in a cross-connected format for an 8-node (2, 2) ShuffleNet.

at the p inputs of the p x p WDM cross connect can be arranged in a noninterfering way at the p outputs of the cross connect. The superscripts on the wavelengths are used in the figure to identify to which input these wavelengths belong. At each of the cross connect outputs, p different wavelengths appear; one from each input. When the same set of wavelengths are used for other cross-connects (i.e., spatial reuse), only p wavelengths are needed in this star network as opposed to p N wavelengths in the same network with a passive star coupler as a central hub. The second advantage of using WDM cross connects is that, except for their insertion loss, there is no power loss due to power splitting. This means there is no limit on the number of users which can be supported by the new topology due to power constraints as it is the case with passive star coupler. The third advantage is that there is no need for optical filtering at the input to the receivers. This is because only the p wavelengths intended for each node appear at the input to that node. The WDM cross-connected star topology for an 8-node (2, 2) ShuffleNet is shown in Fig. 5. Four 2 x 2 WDM cross-connects are needed to implement the central hub and only two wavelengths; AI, X p , are used to carry the transmissions of different nodes in the network. For a (p, k ) ShuffleNet, a simple method is devised to identify which nodes are connected to the inputs (transmit) and to the outputs (receive) of the k . p k - l p x p WDM cross connects at the central hub. The N nodes in the network are numbered from 1 to N and the kp"'p x p WDM cross connects are

IRSHID AND KAVEHRAD: WDM CROSS-CONNECTED STAR TOPOLOGY

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Fig. 4. A schematic diagram for a p x p WDM cross-connect.

numbered from 1 to kp"'. For the ith cross connect, the p nodes connected to the input (transmit-side) and the p nodes connected to the output (receive-side) are found according to the following equations: Fig. 5. A WDM cross-connected star topology for an 8-node (2, 2) ShuffleNet.

Transmit-side = {n,

+ p"1.n + 2p'"-1,. . . , n + ( p

-

1)pk-1}

(1) are as follows:

Receive-side = { m, m

+ 1,m + 2, . . . ,m + p - 1}

(2)

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where T stands for the transmit-side and R stands for the receive-side. 111. 2 x 2 WDM

CROSS

where i = 1 , 2 . 3 , . . * , kp"1

and [XI is the floor function, i.e., the largest integer less than or equal to 5 . The node assignments for the transmit and receive-sides of the WDM cross connects in a (p, k ) ShuffleNet is shown in Fig. 6. In the above equations, for a given (p, k ) ShuffleNet, the nodes connected to the transmit and the receive-sides of a given cross connect i are found by determining n and m from (3) and (4) and substituting their values in (1) and (2). As an example, for an 18-node (JJ = 3, k = 2), there are six 3 x 3 WDM cross connects. The transmit and receive nodes connected to each cross connect

{T(2,5,8) - R(13.14,15)},

{T(1,4,7) - R(10,11,12)}, {T(3,6,9) - R(16.17,18)},

LAPPEDCOUPLERSAS WDM

CONNECTS FOR A

(2, k ) SHUFFLE NET

In general, the p x p WDM cross connect shown in Fig. 4 can be implemented in a straightforward way from p identical 1x p wavelength demultiplexers and p identical p x 1 wavelength multiplexers. The p 2 outputs of the demultiplexers are cross connected passively to the p 2 inputs of the multiplexers as discussed in Section 11. A more convenient and economical way of designing WDM cross connects is to use wavelengthselective directional couplers [171-[20]. These devices are simple and low-loss components with wavelength-selection capabilities suitable for multihop networks. For the class of multihop networks with p = 2 and k = 1 , 2 , 3 , . . . , a (2, k ) ShuffleNet requires k2"' identical 2 x 2 WDM cross connects with only two operating wavelengths. Instead of

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 10, NO. 6, JUNE 1992

2x2 WDM lapped coupler

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Fig. 6. The node assignments for the transmit and receive sides of the WDM cross-connects in a @, k ) ShuffleNet.

Fig. 7. (a) A 2 x 2 lapped coupler as a wavelength demultiplexer and its geometry. (b) A 2 x 2 lapped coupler as a wavelength multiplexer. (c) A 2 x 2 lapped coupler as a WDM cross connect for (2, k ) ShuffleNet.

using two wavelength demultiplexers and two wavelength multiplexers to implement the 2 x 2 WDM cross connect, a much cheaper 2 x 2 WDM lapped coupler can be used [19]. This will result in a great reduction in the cost and complexity of the central hub in the proposed topology. As shown in Fig. 7(a), the 2 x 2 WDM lapped coupler is a four port passive device. It is fabricated by mounting two identical monomode fibers on a holder with a certain curvature radius R and the claddings are removed by lapping down to a minimum separation d between the core axes. The lapped coupler is designed such that a complete power transfer from one fiber to another is possible at a specific wavelength called the crossover wavelength, while at the other wavelength, no power transfer can occur. The crossover wavelength is determined by the curvature radius, the spacing between the fibers and the refractive index of the matching layer between the fibers. This device can be used to wavelength multiplex, demultiplex or cross connect two widely separated wavelengths such as 1300 and 1530 nm provided that one of them is a crossover wavelength. Fig. 7(a) shows a schematic of a 2 x 2 lapped coupler and illustrates how it can be used as a wavelength demultiplexer. For this coupler, we will assume that A 2 is the crossover wavelength. When the two wavelengths AI and A 2 are simultaneously applied to either inputs of the coupler, A 2 will be completely coupled from one fiber to the other while A 1 remains on the same fiber and thus the two wavelengths are demultipiexed and directed to the

two outputs of the coupler. When it is used as a wavelength multiplexer, the two wavelengths are injected to the two inputs of the coupler as shown in Fig. 7(b). In the coupler, the crossover wavelength A2 is coupled to the other fiber and wavelength multiplexed with A l . By combining the multiplexing and demultiplexing operations shown in Fig. 7(a) and (b), the block diagram in Fig. 7(c) shows how a 2 x 2 WDM lapped coupler can be used as a 2 x 2 WDM cross-connect in a (2, k ) ShuffleNet. The two inputs of the coupler are connected via two fiber links to the transmitters of two different nodes in the network. Each input is receiving the transmission of the corresponding node via two wavelengths A 1 and A 2 (p = 2). The superscripts on the two wavelengths in Fig. 7(c) are used to identify the transmissions of the two different nodes. The two wavelengths coming from the first node and entering the upper input of the coupler are wavelength demultiplexed by coupling A: to the upper output and A i to the lower output. Likewise, due to the symmetry of the coupler, the two wavelengths coming from the second node and entering the lower input are wavelength demultiplexed by coupling A: to the lower output and A; to the upper output. Now, each output of the coupler is receiving two different wavelengths carrying signals from two different nodes. The two outputs of the coupler are connected via two fiber links to the receivers of two different nodes as specified by the ShuffleNet connectivity graph. A salient feature of the lapped coupler, besides its simplicity, is its low excess loss

IRSHID AND KAVEHRAD: WDM CROSS-CONNECTED STAR TOPOLOGY

833

(FSR) which is given by FSR = c / ( 2 n L )

Fig. 8. A wavelength-independent p x p star coupler as a WDM cross connect for a (p, k ) ShuffleNet.

compared to other WDM cross connects. A reported 2 x 2 WDM lapped coupler intended for splitting of 1300- and 1550nm wavelengths has an excess loss of less than 1 dB and an extinction ratio of 23 dB [19].

where c is the speed of light, n is the group refractive index of the transmission medium, and L is the spacing between mirrors [21]-[23]. Now, if only the p wavelengths directed to a certain output port of the coupler are located at the peaks of the transmission function of the Fabry-Perot filter introduced at that output, the wavelengths will pass through the filter, while the remaining p 2 - p wavelengths will be rejected. Since the transmission peak of a tunable Fabry-Perot filter can be scanned through one FSR by piezoelectrically tuning L through one optical half-wavelength [23], the wavelength groups directed to the other output ports can be selected in the same way provided that the transmission peaks of different Fabry-Perot filters are not overlapping. The wavelength spacing between two adjacent transmission peaks of two different filters; AA, must be large enough to prevent power leak from the undesired wavelengths. This can be done by choosing the wavelength spacing AA larger than the 3-dB passband width of the Fabry-Perot filter; f ~ given p by f

IV. WAVELENGTH-INDEPENDENT p xp PASSIVE STAR COUPLERS AS WDM CROSS CONNECTS FOR A (p, k) SHUFFLENET For a @, IC) ShuffleNet with P > 25 WaVelength-indePendent p x p passive star couplers can be used as a P X P WDM Crossconnect at the central hub, but at the expense of requiring more wavelengths and using optical filters at the receivers inputs in the network. Fig. - 8 shows how a wavelength-independent y x p passive star coupler together with p tunable fiber Fabry-Perot optical filter can be used as a p x p WDM cross connect in a @, IC) ShuffleNet. Since the passive star coupler distributes each input signal evenly among all of its outputs, using p wavelengths would result in interference between transmissions of different nodes. To avoid such interference, the y nodes connected to the same p x p star coupler must transmit on different sets of wavelengths; p wavelengths each, resulting in a total of p2 wavelengths. This same set of wavelengths can be reused for each of the ICplC-l p x p star couplers in the central hub. This number of wavelengths is still very small compared to kp"' wavelengths needed in a star topology with an N x N star coupler. Moreover, the power loss experienced by the signals due to the power splitting in the p x y star coupler is l/p compared to 1 / N for the case of an N x N star coupler. Another advantage of using a p x p passive star coupler as a WDM cross connect is that the number of 2 x 2 elementary couplers required for constructing the central hub is 1/2kpk log2(p) compared to 1/21Cpk log2(kpk)for the case of an N x N star coupler. Another very interesting feature of using the p x p star coupler as a WDM cross connect is that it is possible to use a single tunable fiber Fabry-Perot optical filter to select the desired p wavelengths from the p 2 wavelengths appearing at each output port of the coupler. This is based on the fact that the transmission function of a Fabry-Perot filter is periodic with transmission peaks spaced by the free spectral range

(5)

~

=p F S R / F

(6)

where F is the finesse of the filter. The arrangement of the transmission functions of the p Fabry-Perot filters and the locations of the p 2 wavelengths in the wavelength spectrum are shown in Fig. 9. If the p 2 wavelengths arriving at the p inputs of the coupler are numbered from 1 to p2 as shown in Fig. 8, the values of these wavelengths can be determined according to the following formula:

4-

l)p+m

=

A0

+ ( n - 1)FSR

+ ( m - l)AA,

vi,n = 1 , 2 , . . . , p

(7)

where n stands for the nth input port, m stands for the mth wavelength in the group and A 0 is the central wavelength of the left-most transmission peak of the first Fabry-Perot filter as it is shown in Fig. 9. It is obvious from (7) that the group of p wavelengths with m = 1 and n = 1 , 2 , . . . ,p , coming from p different nodes, have the following wavelength values; Ao, Ao+ FSR, A 0 2FSR, . . . , A0 ( p - 1)FSR. Therefore, a single Fabry-Perot filter having a free spectral range of FSR and with one of its transmission peaks centered at A 0 can be used to select these wavelengths from the p 2 wavelengths available at the first output port of the coupler. Likewise, the group of wavelengths with m = 2 and n = 1 , 2 , . . . ,p having the following wavelength values; A0 AA, A0 AA+ FSR, A0 AA+ 2 FSR, . . . , A0 +AA+ @ - 1) FSR can be selected from the p 2 wavelengths available at the second output port of the coupler by another Fabry-Perot filter having the same FSR but with one of its transmission peaks centered at Ao+AA. The remaining filters are chosen in a similar way provided that the wavelength spacing between two adjacent transmission peaks of two different filters is AA. Since the transmission functions of the p Fabry-Perot filters are periodic and they have the same free-spectral range, the number of transmission peaks that can fit in one FSR is determined by AA. This means, for

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+

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. IO, NO. 6, JUNE 1992

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Fig. 9. The arrangement of the transmission functions of the p Fabry-Perot filters and the locations of the p” wavelengths for the WDM cross connect shown in Fig. 8.

a (11.X) ShuffleNet, the value of p must be less than or equal to the number of wavelengths that can fit in one FSR without interference p

< FSR/AA

This replacement results in three major advantages. First, the number of wavelengths needed in a @, k ) ShuffleNet is p wavelengths as opposed to kpk++’wavelengths for the case of a star topology with an N x N star coupler. Second, since the optical power at a given wavelength is directed only to where it is required, there is no power splitting loss in the WDM cross connects. This means that there is no restriction on the number of users supported by the ShuffleNet due to power constraints. Third, the wavelength filtering needed in other topologies is completely eliminated for the proposed architecture. We also proposed using relatively cheap and low loss 2 x 2 WDM lapped couplers as WDM cross connects for a (2, k ) ShuffleNet using only two wavelengths such as 1300 and 1550 nm. Finally, for a (p, k ) ShuffleNet, wavelengthindependent p x p passive star couplers together with tunable fiber Fabry-Perot filters are used to replace the more expensive conventional p x y WDM cross connects but at the expense of using p 2 rather than p wavelengths.

(8)

REFERENCES

If the spacing AA is chosen to be six times the 3-dB passband width of the Fabry-Perot filter f ~ p by , substituting (6) in (8), we can achieve a lower bound on the finesse of a Fabry-Perot filter needed to realize a given (p, k ) ShuffleNet

F > 6p.

(9)

Since for a practical ShuffleNet p is usually a small number; less than 10, a finesse of utmost 60 is needed. Fabry-Perot filters with such low values of finesse have already been realized with 1-dB excess loss [23]. It is noteworthy to mention that in such approach when used for star topology with an AVx N star coupler, the required finesse is 6N which is very difficult to realize for large values of N. The proposed design overcomes three of the star-based multihop [16] disadvantages: 1. Large number of wavelengths required. 2. Limited number of users due to power splitting and the resulting signal attentuation. 3. Cost of hardware. The second disadvantage may also be overcome by using fiber amplifiers [24]. It is also fair to say, the reduced number of wavelengths and the associated cost reduction is at the expense of introducing additional hardware, e.g., the WDM cross connects. However, the added hardware is still worth the cost that otherwise had to be paid. The proposed approach in this work does not seem to readily extend to other regular connection diagrams as de Bruijn or Manhattan street networks. However, by rearranging the interconnection according to a new @, k ) ShuffleNet connectivity graph with a larger user number, it is possible to accommodate more users in this type of network architecture. V. CONCLUSIONS

In this paper, we proposed a new star topology suitable for multihop lightwave networks. This is done by replacing a hub passive star coup1er as a in the star topology by kp”’ p x p WDM cross connects.

I41 [5 I

(61 [71 [81 [9] [lo] (111 [12] [13] [14] [15]

[16]

(171 [18] [19] [20]

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IRSHID AND KAVEHRAD: WDM CROSS-CONNECTEDSTAR TOPOLOGY

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Mansour I. Irshid was born in Amman, Jordan on 1952. He received the BSc. degree from King Saud University, Saudi Arabia in 1974 and the M.S. and Ph.D. degrees from University of WisconsinMadison, in 1978 and 1982, all in electrical engineering. From 1982 to 1986 he was an Assistant Professor in the Electrical Engineering Department at Yarmouk University, Jordan. In 1986, he joined the Electrical Engineering Department, Jordan University of Science and Technology, Jordan where he is currently the head of the Department. In 1990 he was a visiting professor at the University of Ottawa, Canada, doing research in the field of fiberoptic communication systems. His current research interests are in fiber-optic devices and systems, digital communications, and digital electronics.

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Mohsen Kavehrad (S’75-M’78-SM’86-F’92) was born in Tehran, Iran, on Jan. 1, 1951. He received the B.S. degree from Tehran Polytechnic Institute, Iran, in 1973, the M.S. degree from Worcester Polytechnic Institute, Worcester, MA in 1975, and the Ph.D. degree from Polytechnic lnstitute of New York (now: Polytechnic University), Brooklyn, NY, in Nov. 1977, all in electrical engineering. He worked for Fairchild Industries (Space Communications Group) and then joined GTE. He worked for GTE Satellite Corp. and GTE Laboratories in Waltham, MA. In Dec. 1981 he joined AT&T Bell Laboratories where he worked in Research, Development, and Systems Engineering areas as a member of technical staff. In March 1989 he joined the Department of Electrical Engineering at University of Ottawa, as a Full Professor. He is the Leader of Photonic Networks and Systems Thrust and a Project Leader in the Telecommunications Research Institute of Ontario (TRIO). Also, he is a project leader in the Canadian Institute for Telecommunications Research (CITR). In summer of 1991, he was a visiting researcher at N l T Laboratories in Japan. Also, in summer of 1972 he worked at ORTF, in Paris, France. He has worked on satellite communications, point-to-point microwave radio communications, portable and mobile radios communications, atmospheric laser communications and on optical fiber communications and networking. He has also worked on multiple access networks, routing and flow control problems in packet switched networks. He has published over 90 papers and has several patents issued or pending in these fields. He has been a technical consultant to BNR in Ottawa, N l T Labs in Japan, and a number of other industries. Dr. Kavehrad is on the Editorial Board of the IEEE MAGAZINE SYSTEMS. He is a former Technical LIGHTWAVE TELECOMMUNICATION Editor for the IEEE TRANSAmIONS ON COMMUNICATIONS and the IEEE COMMUNICATIONS MAGAZINE. He has organized and chaired sessions at a number of IEEE Communications Society international conferences and is on conference program committee for the Optical Society of America.