Time-Dependent Analysis of the Multiple-Route Packet Combining Scheme in Wireless Multihop Networks
Yasuhiro Hirayama,
1Hiraku Okada,
2Takaya Yamazato,
2and Masaaki Katayama
2In this paper, we apply the multiple-route packet combining scheme (In Proceedings of the 1st International Symposium on Wireless Communication Systems, pp. 183–187, Mauritius, 2004) to wireless multihop networks in order to support delay-sensitive applications. The performance of the system is time-dependent and is greatly affected by network-level per- formance. Therefore, it is necessary to develop an analytical framework to evaluate the per- formance of the system with taking into account its time-dependency. We use queuing theory to analyze the performance of the system. From numerical results, it is shown that the per- formance degradation of the system is mainly caused by the increase of packet delay, which is due to the increase of the traffic intensity. To prevent the increase of traffic, we propose a packet discarding scheme. We analyze the average packet error probability of the proposed system with the equilibrium point analysis (EPA). Numerical results show that the packet discarding scheme can improve the average packet error probability under heavy traffic conditions.
KEY WORDS: Wireless multihop networks; multipath routing; packet combining; queuing theory;
equilibrium point analysis.
1. INTRODUCTION
Wireless multihop networks [1,2] consist of wireless nodes that are connected with each other by a wireless link. Packets sent by a source node are forwarded toward a destination node by forwarding nodes which exist between the source node and the destination node. A routing protocol determines which nodes are selected as the forwarding nodes.
Wireless ad-hoc networks [3] and wireless sensor networks [4] are typical applications of wireless multihop networks.
In this paper, we consider a wireless multihop network which can support delay-sensitive applica-
tions such as real-time voice and real-time video. In packet communications, when a packet is received with errors, the packet is retransmitted. Packet retransmissions may cause excessive delays and large delay jitters which are undesirable for delay-sensitive applications. Therefore, packet retransmission tech- niques are generally not used. In this case, however, packet errors caused by a channel may lead to a loss of transmitted information directly. Then, it is necessary to employ a technique that can reduce the influence of packet errors.
Multipath routing [5–8] is one of the interesting and important techniques for wireless multihop networks. By using multipath routing, multiple routes can be established between a source node and a destination node. Multiple routes are used for various purposes such as maintaining alternative routes [5], load-balancing [6, 7], and diminishing the effect of frequent topological changes [8]. In [9], a multiple-route packet combining scheme is proposed to reduce bit errors on wireless channels. In this
1 Department of Electrical Engineering and Computer Science, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464–8603, Japan. E-mail: hirayama@
katayama.nuee.nagoya-u.ac.jp
2 EcoTopia Science Institute, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464–8603, Japan.
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1068-9605/05/0100-0035/0 2005 Springer Science+Business Media, Inc.
scheme, multiple copies of a packet are sent by a source node. Each copied packet is transmitted along a different route. At a destination node, the received copies are combined by a soft-output combiner. To combine multiple copies of the same packet trans- mitted along a different route provides a diversity gain. This scheme is suitable for supporting delay- sensitive applications because of the ability to reduce the influence of packet errors on quality of service without causing additional delays.
We apply the multiple-route packet combining scheme to wireless multihop networks in order to support delay-sensitive applications. To support delay-sensitive applications, a decoding and combin- ing process needs finishing within a tolerable time interval. A destination node therefore combines copies which are received before a tolerable delay bound.
Because the interarrival time between two successive packets on a node and the service time of each packet at that node are random variables, the packet delay of each route is also a random variable. Therefore, not all the copies which are sent by a source node can be received by a destination before the beginning of combining. This case is not considered in [9]. The number of combined copies increases as time elapses after the source node sends copies of a packet. Since the more copies are combined, the more the diversity gain is achieved, the packet error probability may be a function of the elapsed time.
In wireless multihop networks, the performance of an error control technique is affected by network- level performance of the system. In the case of the multiple-route packet combining scheme, the perfor- mance is greatly affected by the end-to-end packet delay. The increase of the packet delay caused by the increase of the amount of traffic may lead to decrease the number of copies received before the tolerable delay bound, that is, decrease the number of com- bined copies. Indeed, we will illustrate in Section 6 that when the number of transmitted copies increases, the performance of the proposed system improves.
However, when it exceeds a certain value, the number of combined copies diminishes and the performance degrades.
In this paper, we analyze the performance of the multiple-route packet combining scheme in wireless multihop networks [10,11] with taking into account its time dependency. The performance of the system is time-dependent and is greatly affected by network- level performance. Therefore, it is necessary to develop a new analytical framework to evaluate the performance. Then, we apply queuing theory [12,13]
to analyze the time-dependent performance of the system. We derive two characteristics. One is the average packet error probability, which is obtained as a function of the elapsed time after transmission requests of copies of a packet are generated. The other is the required time for achieving a required packet error probability. The derivation is done based on queuing theory.
Moreover, we propose to apply a packet dis- carding scheme to prevent the increase of the amount of traffic. In this scheme, a packet which is received after the tolerable delay bound by a forwarding node is discarded by that node. The traffic intensity of the network is a stochastic process and depends on an underlying packet arrival process. The stochastic nature of the traffic intensity makes the analysis of the proposed system complicated one. To overcome the analytical difficulty, we apply the equilibrium point analysis (EPA) [14]. EPA assumes that the system is always at an equilibrium point. Therefore, it does not require a detailed analysis of behavior of the traffic intensity.
The rest of this paper is organized as follows.
Section 2 provides a wireless multihop network model considered in this paper. In Section 3, the multiple-route packet combining scheme is briefly described. Section 4 analyzes the system with taking into account its time dependency. Section 5 describes the principles of the proposed packet discarding scheme and analyzes its effect on the performance of the multiple-route packet combining scheme. Section 6 shows numerical results.
2. NETWORK MODEL
We consider a wireless multihop network which consists of wireless nodes which are connected with wireless links. Assume that all source-destination pairs in the network have the same number of routes that are established by a multipath routing protocol.
A network model for source–destination pairs in the network is shown in Figure 1. N mutually disjoint routes exist between the source node and the desti- nation node. Each route consists of M wireless links and M)1 forwarding nodes. The network topology is assumed not to change during packet transmissions.
Any two routes which exist between the same source–
destination pair have no common node or wireless link. On the other hand, any two routes which exist between different source–destination pairs can have common nodes or wireless links.
3. MULTIPLE-ROUTE PACKET COMBINING SCHEME
The multiple-route packet combining scheme proposed in [9] uses multiple route to reduce bit errors. In this section, we illustrate a transmitter and a receiver structure of the scheme and describe a combining and decoding technique.
A transmitter structure of a source node is shown in Figure 2. An information packet that is generated in the source node is encoded by the convolutional encoder. The coded packet is inter- leaved on a bit-by-bit basis. The output of the
interleaver is fed into the modulator. The modulated packet is sent toward the destination node.
There exist N multiple routes between the source node and the destination node. The packet sent by the source node is received by N forwarding nodes which are the first node on the routes. The decoding and reencoding process is not performed in forwarding nodes. Each forwarding node sends the received packet to the next node on the route. Therefore, N copies of the same packet are transmitted along N routes.
The multiple copies of the packet are received by a destination node. A receiver structure of the destination node is shown in Figure 3. A received copy is demodulated to a binary sequence and stored to the buffer. After some copies are received, all the stored packets are fed into the combiner simulta- neously. The combiner calculates likelihood informa- tion for each bit of the packet from its copies. A soft-output combining scheme proposed in [9] is employed. If k(1 £ k £ N) copies of the packet exist in the buffer, the likelihood information for the ith bit of the packet ^bðiÞ is calculated as
bðiÞ ¼^ 1 k
Xk
v¼1
b^vðiÞ: ð1Þ
where ^bvðiÞ represents the output of the demodulator corresponding to the ith bit of the vth copy.
Fig. 1. Model of a source–destination pair.
Fig. 2. Transmitter structure.
Fig. 3. Receiver structure.
Consequently, the output of this combiner has k+1 levels; +1, (k)2)/k, (k ) 4)/k, . . . , )1. The k-level output of the combiner is fed into the Viterbi decoder.
If the multiple routes between the source and the destination are mutually disjoint and each route consists of independent wireless links, these routes are independent communication channels. Since the receiver combines several copies of the same packet transmitted over the independent channels, a diver- sity gain can be obtained.
4. PERFORMANCE ANALYSIS
In this section, we analyze the performance of the multiple-route with taking into account its time dependency. First, we describe assumptions and a queuing network model used in the analysis. We then analyze the average packet error probability and the required time for achieving a packet error probability.
4.1. Assumptions and Modeling
Each node can transmit and receive a packet independently. Each node is allowed to transmit and receive only one packet simultaneously. It is assumed that every packet sent from nodes is received without collisions. This assumption is valid if an optimum medium access control protocol is employed. Let us consider a set of nodes that includes all the neighboring nodes of a node, say A.
The protocol controls packet transmissions from all the nodes in the set. It is assumed that each node in the set can detect transmissions of the other nodes.
When a request for transmitting a packet to A is generated in one of the neighbors, say B, B is allowed to transmit the packet if none of the nodes in the set are not transmitting a packet to A. If one of the neighbors is transmitting a packet to A, B has to wait. When the transmission is finished, a node that has the earliest generated request is allowed to transmit the packet.
When packet transmissions are controlled as described above, a transmission request arrival pro- cess at any wireless node is modeled as a queue.
Generations of transmission requests correspond to arrivals of packets at the queue. The time between the beginning of a transmission and the end of it corresponds to the service time of the queue.
For each wireless node, the generation process of transmission requests from all its neighbors is assumed to be modeled as an independent Poisson
process with mean k)1. Then, the packet arrival process at the queue is also Poisson with mean k)1. Moreover, the length of an information packet is assumed to be exponential with mean Lb. When a convolutional encoder with rate kb/nband constraint length K is employed, the duration of a coded packet is also exponential with mean
Tc¼ nb
kbRLb ekbðK1Þ=Lb; ð2Þ where R is the transmission rate. According to the assumptions described above, each wireless link is modeled as an M/M/1 queue. The arrival process for each queue is Poisson with mean k)1. The service time distribution is exponential with mean l1¼ Tc. The time between the generation of a transmission request and the end of its transmission equals the waiting time of the queue plus the service time of that.
As described in Section 2, any two routes which exist between different source–destination pairs may have common nodes or wireless links. This means that each forwarding node on a route may also be a forwarding node on another route. Therefore, each forwarding node on a route has multiple inputs and multiple outputs. In this case, we can use the independence assumption [13]. With the assumption, the packet delay of a route which consists of M wireless links is represented by the sum of the waiting times of M M/M/1 queues.
4.2. Analysis of the Average Packet Error Probability as a Function of Elapsed Time
According to the above model, we derive the average packet error probability as a function of elapsed time after transmission requests of copies of a packet are generated. Let us consider a route of the N multiple routes. This route consists of M wireless links. When each wireless link is modeled as the M/
M/1 queue, the probability density function fw_m(t) for the packet delay wm of the mth wireless link is exponential and given by
fwmðtÞ ¼ lð1 qÞelð1qÞt; ð3Þ where q¼ k=l is the traffic intensity. Since wireless links on a route are statistically independent and have the same service time distribution, the probability density function fw(t) for the packet delay w of the route is derived by M-fold convolution of Eq. (3) and given by
fwðtÞ ¼lð1 qÞM
ðM 1Þ! tM1elð1qÞt: ð4Þ Consider N multiple copies of a packet trans- mission requests of which are generated at t=0 by the source node. The packet combining process at the destination is started when some time elapses after the transmission requests are generated. Let the time to be t. If the delay of a packet is less than t, the packet is received by the destination before the beginning of packet combining. Then, the probability p(t) that the packet transmitted along a route has already been received at the elapsed time t is given by
pðtÞ ¼Pfw tg
¼ Z t
0
fwðsÞds
¼CðMÞ CðM; lð1 qÞtÞ
ðM 1Þ! ; ð5Þ
where G(z) is the gamma function and G(a,z) is the incomplete gamma function.
When all the routes between the source and the destination are of equal hop length, the probability that the number N(t) of received packets at t equals k is given by
PfNðtÞ ¼ kg ¼ N k
pðtÞkf1 pðtÞgNk: ð6Þ Equation (6) represents the probability that the number of combined packets at the elapsed time t equals k.
Using Eq. (6), the average packet error proba- bility Qe(t) at the elapsed time t is given by
QeðtÞ ¼XN
k¼0
PeðkÞPfNðtÞ ¼ kg; ð7Þ
where Pe(k) is the packet error probability when the number of combined packets is k.
4.3. Analysis of the Required Time for Achieving a Packet Error Probability
In this section, we obtain the required time for achieving a packet error probability. To analyze the performance, we first derive the probability density function of the time required to be received k copied packets by the destination node. The probability density fw(t) of the packet delay w of a route is expressed as
fwðtÞ ¼lð1 qÞM
ðM 1Þ! tM1elð1qÞt: ð8Þ Let w(k) be defined as the time required to be re- ceived k copied packets. Then, the probability density functionfwðkÞðtÞ of w(k)is derived as
fwðkÞðtÞ ¼ N!
ðk 1Þ!ðN kÞ!Fwk1ðtÞf1 FwðtÞgNkfwðtÞ;
ð9Þ where Fw(t)is the cumulative distribution function of the packet delay of a route and obtained by
FwðtÞ ¼CðMÞ CðM; lð1 qÞtÞ
ðM 1Þ! : ð10Þ
For given k, the probability Pe(k) can be un- iquely determined. Hence, Eq. (9) represents the required time for achieving the packet error prob- ability Pe(k).
5. PACKET DISCARDING SCHEME FOR MULTIPLE-ROUTE PACKET COMBINING 5.1. Principles
In the multiple-route packet combining scheme, a diversity gain achieved by a destination depends on the number of combined packets, that is, the number of packets received before a tolerable delay bound.
When the number of combined copies increases, the achievable diversity gain becomes larger and the performance improves. If the number of transmitted copies increases, the number of combined copies may increase. However, this may increase the traffic intensity of each wireless nodes. The increase of the traffic intensity can lead to large packet delays, then the number of packets received before the tolerable delay bound may decrease. This is the main reason of the performance degradation of the multiple-route packet combining scheme. To prevent the increase of the amount of traffic, we apply a packet discarding scheme. In the multiple-route packet combining scheme, copies received after the tolerable delay bound are not combined by the destination node.
These copies do not contribute to achieving the diversity gain. Therefore, if the elapsed time after generating a transmission request of a packet is exceeds the tolerable delay bound, defined as Tmax, the copy is discarded by a forwarding node. By discarding packets, it may possible to prevent the
increase of the traffic intensity and improve the performance of the system.
5.2. Analysis of the Effect of the Packet Discarding Scheme
In this section, we analyze the effect of the packet discarding scheme on the performance of the multiple-route packet combining scheme with EPA.
We first derive an equilibrium point of the traffic intensity of the system. Then, we obtain the average packet error probability with the approach developed in Section 4.
Let us consider a route which consists of M)1 forwarding nodes. The packet delay of the mth wireless link on the route is defined by wm. Recall that the probability density of wmis derived as
fwmðtÞ ¼ lð1 qÞelð1qÞt: ð11Þ A packet is discarded by a forwarding node when the elapsed time after generating its transmission request exceeds the tolerable delay bound Tmax. The proba- bility pd(m) that the packet is discarded at the mth node is derived by
pdðmÞ ¼ Pr w½ m> Tmax ðwm1þ þ w0Þ jfwm1 Tmax ðwm2þ þ w0Þg
\ \ fw0 Tmaxg
¼flð1 qÞgm
m! Tmmaxelð1qÞTmax: ð12Þ Let q0be defined as the traffic intensity when the packet discarding scheme is not used. The value of q0
corresponds to the amount of traffic when all the copies are transmitted to the destination node. When the packet discarding scheme is applied, some amount of packets are discarded by forwarding nodes before they are received by a destination node.
Consequently, the traffic intensity may decrease from q0to a certain value. Let this value be defined as ^q.
The traffic intensity of the network is a stochastic process and depends on an underlying packet arrival process. Moreover, the traffic intensity also depends on the packet delay distribution. The stochastic nature of the traffic intensity and the relationship between the traffic intensity and the packet delay distribution make the analysis of the proposed system complicated one. To overcome the analytical diffi- culty, we apply equilibrium point analysis (EPA) [14].
EPA assumes that the system is always at an equilibrium point. Therefore it does not require a
detailed analysis of stochastic properties of the traffic intensity.
The relationship between q and q0 may be expressed as
^q¼ q0 1M2X
m¼0
M m 1 M pdðmÞ
( )
: ð13Þ
The traffic intensity at an equilibrium point can be derived as a root of (13). The value is defined by qe. It is assumed that the traffic intensity of the system is always at the equilibrium point. Then, the probability density of the packet delay of the route is derived as
fwðtÞ ¼
flð1qeÞgm
ðm1Þ! tm1elð1qeÞt; t Tmax
0; otherwise
: ð14Þ Then, the probability that the packet transmitted along the route has already been received at the elapsed time t is given by
pðtÞ ¼
CðMÞCðM;lð1qeÞtÞ
ðM1Þ! ; t Tmax CðMÞCðM;lð1qeÞTmaxÞ
ðM1Þ! ; otherwise (
: ð15Þ
By substituting Eq. (15) into Eq. (6), the probability that the number of received packets at t equals k can be derived. Then, the average packet error probabil- ity of the system can be obtained by Eq. (7).
6. NUMERICAL RESULTS
In this section, we evaluate the performance of the proposed system. First, we show the performance of the multiple-route packet combining scheme without the packet discarding scheme. Then, we show the effect of the packet discarding scheme on the performance of the multiple-route packet combining scheme.
It is assumed that the information packet length is exponential with mean Lb=500 bits. A convolu- tional encoder with kb/nb=1/2, K=7 is employed.
Binary phase shift keying (BPSK) is used as the modulation method. All the multiple routes are of equal length and assumed to be 5 hops. Wireless links are assumed to be statistically independent and identical Rayleigh fading channel. All packets are assumed to be received with equal power.
In order to evaluate Eqs. (7) and (9) numerically, we first obtain the packet error probability Pe(k) by computer simulation. Then, the average packet error probability and the required time for achieving a packet error probability are evaluated. To consider
the effect of the increase in transmitted packets on the amount of traffic, it is assumed that the traffic intensity for each wireless link is proportional to the number of multiple routes and defined by q=0.1N.
Moreover, the Eb/N0is assumed to be 9 dB, where Eb
is the energy per bit and N0/2 is the two-sided spectral density of the additive white Gaussian noise process.
The results for several values of k are illustrated as a function of Eb/N0in Figure 4. It is shown in this figure that the packet error probability at a specific Eb/N0decreases as the number of combined packets increases.
6.1. Average Packet Error Probability as a Function of Elapsed Time
Figure 5 represents the average packet error probabilities for several numbers of transmitted copies as a function of the elapsed time. The time
axis is normalized by the mean duration of the coded packet Tc. It is observed that for all N, the average packet error probability decreases and approaches a constant value as the time elapses. This is because the probability that all the copies sent by the source node are received at the destination node tends to 1 as the time elapses. Indeed, the minimum achievable value for each N equals Pe(N), which is the packet error probability when all the transmitted copies are combined.
At a small elapsed time, the average packet error probability does not decrease when N exceeds a certain value. For example, at t=Tc = 30, the achievable value decreases as the number of the multiple routes increases from N = 1 to N = 7.
However, when N increases from N = 7 to N = 9, the achievable value increases. The packet delay of each route increases as the number of transmitted copies increases. When the packet delay of each route increases, the number of received and combined packets at a specific elapsed time decreases. As shown in Figure 4, the packet error probability increases as the number of combined packets decreases. There- fore, if N exceeds the certain value, the average packet error probability at a specific time increases.
These results show that there is an optimum number of transmitted copies that minimizes the average packet error probability at the tolerable delay bound.
6.2. Required Time for Achieving a Packet Error Probability
Figures 6–9 illustrate the complimentary cumu- lative distributions of fwðkÞðtÞ. These figures represent
Fig. 4. Packet error probability Pe(k) versus Eb/N0(M = 5).
Fig. 5. Average packet error probability Qe(t) (M = 5, Eb/ N0= 9dB).
Fig. 6. Complementary cumulative distribution of required time for achieving a packet error probability (k = 1, Pe(1) = 9.9· 10)1).
the required time for achieving the packet error probabilities Peð1Þ ¼ 9:9 101, Peð5Þ ¼ 5:7 102, Peð6Þ ¼ 6:0 103 and Peð7Þ ¼ 7:0 104, respec- tively. In the figures, the time axis is normalized by Tc.
We evaluate the time required to achieve Pe(k) with probability 0.99. In Fig. 6, the required time decreases as the number of routes increases from N=1 to N=3. The minimum value is attained at N=3. However, when N increases from N=3 to N=9, the required time increases. Such property can also be seen in Figures 7 and 8. However, in these figures, the amount of the reduction is small com- pared to Figure 6. Besides, in Figure 9, the required time does not reduce at all. These results represent that there is an optimum number of transmitted copies that minimizes the required time to achieve a given packet error probability. However, the reduc- tion is limited to the small values of k.
6.3. The Effect of the Packet Discarding Scheme Table I shows the values of the traffic intensity at an equilibrium point qe for each offered traffic intensity q0when Tmax= 30 Tc and 40 Tc.
From this table, it is found that the packet discarding scheme can suppress the increase of the traffic intensity when the number of transmitted copies is large. On the contrary, when the number of transmitted copies is relatively small, the scheme can hardly suppress the increase of the traffic intensity.
This is because almost all the transmitted copies can be received by a destination node before the tolerable delay bound and the copies are barely discarded by forwarding nodes when the offered traffic intensity is small. Moreover, it is observed that the amount of the reduction in the traffic intensity for Tmax = 30 Tc is larger than that for Tmax¼ 40Tc.
Fig. 7. Complementary cumulative distribution of required time for achieving a packet error probability (k = 5, Pe(5) = 5.7· 10)2).
Fig. 8. Complementary cumulative distribution of required time for achieving a packet error probability (k = 6, Pe(6) = 6.0· 10)3).
Fig. 9. Complementary cumulative distribution of required time for achieving a packet error probability (k = 7, Pe(7) = 7.0· 10)4).
Table I. Traffic Intensity at the Equilibrium Point
N q0 qeTmax= 30Tc qeTmax=40Tc
1 0.10 0.10 0.10
2 0.20 0.20 0.20
3 0.30 0.30 0.30
4 0.40 0.40 0.40
5 0.50 0.50 0.50
6 0.60 0.60 0.60
7 0.70 0.70 0.70
8 0.80 0.78 0.79
9 0.90 0.83 0.85
Figures 10 and 11 show the average packet error probability as a function of the elapsed time. We evaluate the average packet error probability which can be achieved at Tmax. In these figures, the solid lines plot the performance in the case where the proposed packet discarding scheme is applied while the dotted line plot the performance in the case where the scheme is not applied. From these figures, it is found that the achievable average packet error probability increases when the number of transmitted copies exceeds 7 for both the cases. However, when the packet discarding scheme is applied, the system can prevent the degradation of the achievable average packet error probability.
From these results, the packet discarding scheme can prevent the increase of the traffic intensity and improve the average packet error probability under
the heavy traffic conditions. However, it can hardly decrease the minimum average packet error before a tolerable delay bound.
7. CONCLUSIONS
In this paper, we have applied the multiple-route packet combining scheme to wireless multihop networks in order to support delay-sensitive applica- tions. The performance of the system is time- dependent and is greatly affected by network-level performance. We then use queuing theory to analyze the time-dependent performance of the system.
From the numerical results, it has been shown that for a tolerable delay bound, there exists an optimum number of transmitted copies that mini- mizes the achievable average packet error probabil- ity. Moreover, if the number of transmitted copies is selected appropriately, the required time for achiev- ing a required packet error probability can be minimized.
In the multiple-route packet combining scheme, the performance degradation is mainly caused by the increase of the traffic intensity. To prevent the increase of traffic, we have applied the packet discarding scheme. We have analyzed the average packet error probability of the proposed system with EPA. The numerical results have shown that the packet discard- ing scheme can improve the average packet error probability under the heavy traffic conditions.
ACKNOWLEDGMENTS
This work is supported in part by the Ministry of Education, Culture, Sports, Science and Technology in Japan and the Ministry of Internal Affairs and Communications in Japan.
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Yasuhiro Hirayama was born in Nagoya, Japan in 1978. He received the B.S. and M.S degrees in from Nagoya University, Japan in 2001 and 2003, respectively. His current research interests include packet radio communications, wireless multihop networks and multimedia traffic. He is currently working toward Ph.D.
degree at Nagoya University. Mr. Hirayama is a student member of IEEE and IEICE.
Hiraku Okada was born in Nagoya, Japan in 1972. He received the B.S., M.S. and Ph.D. degrees in Information Electronics Engineering from Nagoya University, Japan in 1995, 1997 and 1999, respectively. From 1997 to 2000, he was a research fellow of the Japan Society for the Promotion of Science. Since 2000, he has been an Assistant Professor of the Center for Information Media Studies at Nagoya University, Japan. His current research interests include the packet radio communications, multimedia traffic, wireless multihop/multicell networks, and CDMA technologies. He received the Inose Science Award in 1996, and the IEICE Young Engineer Award in 1998. Dr. Okada is a member of IEEE, IEICE and SITA. Takaya Yamazato was born in Okinawa, Japan in 1964. He received the B.S. and M.S. degrees from Shinshu University, Nagano, Japan, in 1988 and 1990, respectively, and received the Ph.D. degree from Keio University, Yokohama, Japan, in 1993, all in Electrical Engineering. He is now an Associate Professor of the EcoTopia Science Institute at Nagoya University, Japan. His research interests include sensor networks, satellite and mobile communication systems, CDMA, joint source- channel coding and e-Learning. Dr. Yamazato received the IEICE Young Engineer Award in 1995. He is a member of IEEE, IEICE and SITA.
Takaya Yamazato was born in Okinawa, Japan in 1964. He received the B.S. and M.S. degrees from Shinshu University, Nagano, Japan, in 1988 and 1990, respectively, and received the Ph.D. degree from Keio University, Yokohama, Japan, in 1993, all in Electrical Engineering. He is now an Associate Professor of the EcoTopia Science Institute at Nagoya University, Japan. His research interests include sensor networks, satellite and mobile communication systems, CDMA, joint source-channel coding and e-Learning. Dr. Yamazato received the IEICE Young Engineer Award in 1995. He is a member of IEEE, IEICE and SITA.
Masaaki Katayama was born in Kyoto, Japan in 1959. He received the B.S., M.S. and Ph.D. degrees from Osaka University, Japan in 1981, 1983, and 1986, respectively, all in Communication Engineering. He was an Assistant Professor at Toyohashi University of Technology from 1986 to 1989, and a Lecturer at Osaka University from 1989 to 1992. In 1992, he joined Nagoya University as an associate professor, and has been a professor since July 2001. He is now a professor and head of Division of Information and Communication Sciences at EcoTopia Science Institute of Nagoya University. He had been working at the
College of Engineering of the University of Michigan from 1995 to 1996 as a visiting scholar. His current research interests are on the physical and media-access layers of radio communication systems.
His current research projects include, Software Defined Radio systems, Reliable Robust Radio Control Systems with multi- dimensional coding and signal processing, Power-Line Commu- nication Systems, and Satellite Communication systems. He received the IEICE(was IECE) Shinohara Memorial Young Engineer Award in 1986. Dr. Katayama is a member of IEICE of Japan, SITA, and IEEE.
