Theoretical Evaluation of Spectral Efficiency and OutageProbability of TDMA Multihop Cellular Systems

Koji Yamamoto, Atsushi Kusuda, Tsuyoshi Nakano, and Susumu Yoshida

Graduate School of Informatics, Kyoto University, Kyoto, 606-8501 Japan

SUMMARY

For TDMA cellular systems that introduced multihoptransmission, the spectral efficiency and outage probabilityin a single-cell environment are formulated and evaluatednumerically. By using approximations, the numericalevaluation is also conducted in an interference-limited mul-ticell environment and compared to simulation results. Informulating these performances, the focus is on the com-mon points of multihop transmission and symbol rate con-trol, and a method similar to the performance evaluationmethod of rate-adaptive TDMA cellular systems is applied.In particular, the opposite effects of multihop transmissionon the spectral efficiency are explicitly considered. In asingle cell environment, instead of lowering the spectralefficiency somewhat by the introduction of multihop trans-mission, the cell coverage satisfying the allowable outageprobability could be clearly expanded. A multicell environ-ment could be implemented with cell reuses with a smallerallowable outage probability resulting from the introduc-tion of multihop transmission. Consequently, an improvedspectral efficiency is expected. © 2006 Wiley Periodicals,Inc. Electron Comm Jpn Pt 1, 90(4): 1–10, 2007; Publishedonline in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecja.20366

Key words: multihop; cellular system; spectral ef-ficiency; outage probability.

1. Introduction

Recently, wireless communication systems usingmultihop transmission have attracted attention. The reasonis that compared to a conventional cellular system in whichthe mobile stations and the base station communicate usingsingle-hop transmission, a reduction in the transmissionpower for constant cell coverage and an expansion in thecell coverage for a constant transmission power are ex-pected. Every year, the demand for high-speed transmissionincreases, thus a high received power is generally requiredas the transmission speed increases. However, there is amaximum transmit power of a mobile station. The introduc-tion of multihop transmission basically relaxes this con-straint. The possibility of implementing high-speedtransmission is expected even in a mobile station separatedfrom the base station.

The introduction of this multihop transmission stud-ied various systems such as the Global System for MobileCommunications (GSM) [1], Time Division Multiple Ac-cess (TDMA) cellular system [2], and HiperLAN/2 [3]. Inaddition, the Code Division Multiple Access (CDMA) cel-lular system has been widely studied in relation to theintroduction of multihop transmission because it is used inthird generation mobile communication [4–8]. In the uplinkof this CDMA cellular system, accurate transmit powercontrol is required to use the semiorthogonal channels.Many of the characteristics differ from those of an accessmethod using other orthogonal channels typified byTDMA.

On the other hand, a wireless communication systemconforming to the IEEE 802.16 [9] using TDMA is thefocus of attention, and a multihop transmission function has

© 2006 Wiley Periodicals, Inc.

Electronics and Communications in Japan, Part 1, Vol. 90, No. 4, 2007Translated from Denshi Joho Tsushin Gakkai Ronbunshi, Vol. J89-B, No. 6, June 2006, pp. 926–934

Contract grant sponsors: 21st Century COE Program (Subject No.14213201), Grant-in-Aid for Scientific Research (A) from the JapanSociety for the Promotion of Science (Subject No. 16206040), and aGrant-in-Aid for JSPS Fellows (Subject No. 16001178).

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also been introduced. Therefore, the premise for discussingthe system applied to fourth-generation mobile communi-cation is its usefulness in carefully evaluating the result ofintroducing multihop transmission to a TDMA cellularsystem. Therefore, in this paper, TDMA is assumed to bethe access method.

When the transmit power of multihop transmission isequal to that of single-hop transmission, the reasons theintroduction of multihop transmission achieves the cover-age expansion are the increase in the received Carrier-to-Interference plus Noise Ratio (CINR) accompanying theincrease in the received signal power per hop and avoidanceof the path suffering from severe shadowing. On the otherhand, even if the received CINR does not change, coverageexpansion can be implemented by a transmission technol-ogy which lowers the required received CINR such as lowsymbol rate transmission.

Therefore, we evaluated the throughput of multihoptransmission with equally spaced relaying terminals on astraight line and estimated the area spectral efficiency of theinterference-limited multihop wireless network with uni-form distributed terminals taking into account conventionaladaptive rate control [10].

The first objective of this paper is to theoreticallyevaluate the characteristics in a multihop cellular systemwhere terminals have different conditions such as the dis-tance from the base station. Therefore, with the focus on thecommon points of adaptive symbol rate control and multi-hop transmission, we derive the expressions for perform-ances of the multihop cellular system while considering theexpressions of a rate-adaptive cellular system [11]. In theseexpressions, the changes in the bandwidth efficiency ac-companying the introduction of adaptive symbol rate con-trol and multihop transmission are taken into account.However, to distinguish the spectral efficiency of the sys-tem in this paper, the maximum end-to-end bit rate per unitbandwidth related to each transmission is defined as thebandwidth efficiency. The second objective is to comparethe effect of adaptive symbol rate control and that of mul-tihop transmission because these techniques are expectedto have similar effects. The evaluation criteria are the spec-tral efficiency defined as the average of the bandwidthefficiency per cell and the outage probability which isdefined as the probability that the required communicationquality is not satisfied in the cell.

Section 2 describes the system model. Based on Ref.11, Section 3 describes adaptive symbol rate control and theoutage probability and spectral efficiency of the cellularsystem using the rate control. Section 4 describes the char-acteristics of the multihop cellular system based on anevaluation method similar to that in Section 3. Section 5describes the numerical results of the single-cell environ-ment and the multicell environment using approximations,

and the computer simulation results for a multicell environ-ment, and confirms the effectiveness of the approximation.

2. System Model

2.1. Radio propagation

As shown below, for the radio propagation, propaga-tion loss with the path loss exponent α, lognormal shadow-ing, and Rayleigh fading are assumed. In this paper, thesymbol rate is determined to correspond to the local meanreceived CINR. Therefore, the Rayleigh fading affects thebit error rate (BER) with respect to the local mean receivedCINR γ. When J branch maximum ratio combining diver-sity reception was performed in Rayleigh fading, the BERβA-0(γ) is given by the following equation [11]:

The propagation loss is given by the following equa-tion as the relationship between the local mean receivedsignal powers xm(d) and xm(d0) at the distances d and d0:

When shadowing is considered, the probability densityfunction fd(x) of the local mean received signal power x isgiven by

where σx = (ln 10)σdB/10 is the standard deviation of ln x,and σdB usually assumes a value from 6 to 10 dB.

2.2. Single-cell environment

The single-cell environment is assumed to be isolatedand there is no interference from other stations as in Fig. 1.The calling mobile station and the m candidate relayingstations are assumed to be uniformly distributed within acell.

If the local mean received power is changed by themotion of the calling mobile station or the relaying stations,the characteristics change when the determined path or thesymbol rate continued to be used. However, this is a prob-lem of the tracking speed in adaptive control and is outsideof the purpose of this paper. Thus, in this paper, the callingmobile station and the relaying stations are assumed to notexperience a change in the local mean received signal powereven if they moved. The selection of the symbol rate or the

(2)

(3)

(1)

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path is based on the local mean receive carrier-to-noise ratio(CNR).

Because interference does not exist in a single-cellenvironment, the local mean received CNR γ is proportionalto the local mean received signal power x. Thus, the prob-ability density function gd(γ) of γ is given by the followingequation similar to Eq. (3):

where σγ = σx, and γm(d) is the local mean received CNR.

2.3. Multicell environment

The multicell environment is assumed to be a hexago-nal cell as shown in Fig. 2, and the co-channel interference

caused by the six neighboring co-channel cells is consid-ered. All of the interference signals are assumed to beequivalent to additive white Gaussian noise spread over theentire bandwidth (see Ref. 12 for a discussion of thisassumption). This co-channel interference dominates thethermal noise, namely, it is interference-limited. The distri-butions of the calling mobile stations and the relayingstations are the same as in the single-cell environment, anda uniform distribution is assumed in the cell.

Based on the above premise, the distributions of thereceived interference power and the received carrier-to-in-terference ratio (CIR) are determined. Each local meanreceived interference power caused by the six neighboringco-channel cells follows a lognormal distribution. Theprobability density function of the sum of lognormalizedrandom numbers can be approximated by a single lognor-mal distribution [13]. Therefore, the probability densityfunction fd1,...,d6

(y) of the sum y of the interference powersfor the propagation distances d1, . . . , d6 of each interferencesignal is approximated by the following lognormal distri-bution.

This means ym(d1, . . . , d6) and standard deviation σy(d1, . . . , d6) are determined by numerical analysis from six distribu-tions based on the method described in Ref. 13.

As shown in Eqs. (3) and (5), both probability densityfunctions of the local mean received signal power x andthe local mean received interference power y are log-normal distributions. Therefore, the probability densityfunction hd,d1,...,d6

(γ) of the local mean received CIR γ isgiven by the following lognormal distribution:

where d is the propagation distance of the desired signal.Let the polar coordinate of the transmitting station

with each base station in the neighboring co-channel cell ias the origin be (si, φi), then the set of transmitting stationsis represented by the following subset on R2:

If a uniform independent distribution is assumed for thetransmitting stations in the neighboring co-channel cells,

Fig. 1. Model for single-cell environment. Callingmobile stations and candidates for relaying

stations are uniformly distributed in a single isolated cell with radius R.

(4)

(6)

(5)

(7)

Fig. 2. Model for multicell environment. Reuse factor L= 4.

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the probability density function gd(γ) of the local meanreceived CIR γ at position (r, θ) of the receiving station inthe same cell is given by the following equation by usingthe direct product set V = Πi=1

6 Ui and dV =ds1dφ1 ⋅ ⋅ ⋅ ds6dφ6:

As in a single-cell environment, the selection of thesymbol rate or the path is based on the local mean receivedCIR determined by the distribution as shown above. WhenCNR and CIR do not have to be distinguished, CINR iswritten.

3. Cellular System with Adaptive SymbolRate Control

3.1. Symbol rate control

One method for lowering the required CINR whenthe noise or co-channel interference is not severe is theapplication of the low symbol rate transmission with aconstant transmit power. The transmission and receptionfilters corresponding to when the symbol rate is simplychanged become necessary. On the other hand, if the samesymbol is repeatedly transmitted 2k times, where k is aninteger greater than 0 and if sampled and synchronouslycalculated at the symbol timing on the receive side, 2k

symbols are regarded as new symbols. By using new sym-bols, the symbol rate can be reduced [14]. Thus, the requiredCINR will be reduced to 1/2k. Thus, the BER βA−k(γ) of thereceived CINR γ in 1/2k-rate QPSK satisfies the followingrelationship:

The subscript “A” represents adaptive symbol rate control.The modulation method in this paper is only QPSK.

Of the symbol rates satisfying the required BER when themaximum k is K (≥ 1), the adaptive symbol rate controlwhich selects the maximum is assumed. This section usesequations to explain the evaluation method of the outageprobability and the spectral efficiency of the cellular systemthat introduced the adaptive symbol rate control, which isgiven in Ref. 11. Similar to Ref. 11, for the slot allocation,two times the slots in 1/2-rate QPSK and four times the slotsin 1/4-rate QPSK compared to full-rate QPSK are allocatedso that the throughput becomes equal even for differentsymbol rates.

3.2. Outage probability

The outage probability in a cellular system usingadaptive symbol rate control is defined as the probability

where the required BER is not satisfied even at the mini-mum symbol rate in the cell [11].

When the polar coordinates with the base station asthe origin are considered, and the calling mobile stationpositioned at geographic point (r, θ) used 1/2k-rate QPSK,the probability pA−k(r, θ) that does not satisfy the requiredBER βreq is given by

where DA−k is a subset on R given by

The outage probability PA of the cellular system thatshould be determined and uses adaptive symbol rate controlbecomes the integral of pA−K(r, θ) in the cell. The followingequation is given based on the assumption of the uniformdistribution of the calling mobile stations:

3.3. Spectral efficiency

By introducing symbol rate control, the transmis-sions have a lower bandwidth efficiency. The spectral effi-ciency which may decrease as a result is evaluated. The1/2K−1-rate is used when the required BER is not satisfiedat the 1/2K−2-rate. The following equation gives the band-width efficiency tA(r, θ) (bps/Hz) when a calling mobilestation at the (r, θ) geographic point communicates with thebase station:

where Rsmax is the symbol rate of full-rate QPSK; Feff, theframe efficiency; and Bch, the channel interval.

In a multicell environment with the cell reuse factorL, 1/L-th of the bandwidth is used in one cell. Therefore,the spectral efficiency is the average in the cell of thebandwidth efficiency divided by the cell reuse factor L.From the above, the spectral efficiency ηA [bps/(Hz⋅cell)]when using adaptive symbol rate control is given by

where L = 1 is set in the single-cell environment.The above outage probability PA and the spectral

efficiency ηA are a function of the cell reuse factor L in themulticell environment and a function of cell radius R in asingle-cell environment.

(11)

(10)

(12)

(9)(13)

(14)

(8)

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4. Multihop Cellular System

4.1. Multihop transmission

By introducing multihop transmission, the distancebetween stations per hop can be shortened compared tosingle-hop transmission. Therefore, if switched to multihoptransmission at a constant transmit power, an increase in thereceive power of the desired signal or a reduction in theshadowing effect becomes possible.

The objective of this paper is to compare multihoptransmission and symbol rate control. For simplicity, themodulation method is QPSK, the symbol rate is fixed atfull-rate, and the maximum number of hops is two (onerelaying station). Based on these premises, the charac-teristics are formulated similar to the evaluation method inthe previous section. Routing assumes the selection of thepath having the minimum number of hops out of the pathsin which the end-to-end BER satisfies the required value.When there are multiple paths in which the end-to-end BERsatisfies the required value in the same number of hops, therelaying station having the smallest end-to-end BER isselected. For the slot allocation, two times the number ofslots as in single-hop full-rate QPSK are allocated so thatthe throughput becomes equal. The first hop and second hopmutually communicate in each frame. The control of rout-ing and slot allocation is assumed to be carried out withoutoverhead in data transmission.

4.2. Outage probability

The probability of the end-to-end BER not satisfyingthe required value in a cell of the multihop cellular systemis defined as the outage probability.

Let (ri, θi), γn,i, and βM−n,i represent the position of thetransmitting station, received CIR, and BER of the i-th hop,for 1 ≤ i ≤ n, during n-hop transmission. The subscript “M”represents multihop transmission. When the BER per hopis small, the end-to-end BER in n-hop transmission isapproximated by the sum of the BER of each hop [10].Therefore, if the end-to-end BER during n-hop transmis-sion is set to βM−n, the following equation holds:

The subset on Rn

is used to represent the probability pM−n where the requiredBER is not satisfied during n-hop transmission and is givenby

where gn,i(γn,i) represents the probability density functionof the received CINR γn,i of the i-th hop.

As in the assumption, the limit of two hops is consid-ered. As shown in Fig. 3, the position of the calling mobilestation is (r1, θ1). The probability p1−hop(r1, θ1) where theend-to-end BER does not satisfy βreq in 1-hop transmissionbecomes

When the position of the relaying station is (r2, θ2), and thecalling mobile station positioned at (r1, θ1) performs 2-hoptransmission, the probability p2-hop(r1, θ1) of the end-to-endBER not satisfying βreq is given by

From the above, the probability p1,2-hop(r1, θ1) of the end-to-end BER not satisfying βreq at the (r1, θ1) position of thecalling mobile station is given by

Consequently, the outage probability PM of the multihopcellular system is represented by

(15)

(16)

(17)

(18)

(19)

Fig. 3. Positions of base station, calling mobile station,and relaying station. Dashed and solid arrows represent

single-hop and 2-hop transmissions, respectively.

(20)

(21)

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4.3. Spectral efficiency

When 1-hop transmission is not possible, 2-hoptransmission is assumed to be used. The bandwidth effi-ciency tM(r1, θ1) (bps/Hz) is given by

As with adaptive symbol rate control, the spectralefficiency ηM [bps/(Hz⋅cell)] of the multihop cellular sys-tem is given by

where L = 1 in the single-cell environment.

4.4. Evaluation method

In a multihop cellular system in a multicell environ-ment, the interference power given to other cells by theselected path changes. Therefore, the distribution gni

(γn,i)of the received CIR in Eq. (17) is not uniquely determined,and the numerical evaluation is difficult. Therefore, thenumerical evaluation that approximated the interferencepower performed the evaluation through computer simula-tions, then the results were compared.

In the numerical evaluation, a uniform independentdistribution is assumed for the transmitting stations in theneighboring co-channel cells. Therefore, gn,i(γn,i) is simi-larly fixed at gd(γ) in single-hop transmission. In the com-puter simulations, the approximation of the interferenceshown in Section 2.3 is not performed, and the path issequentially selected in each cell. If a path changes in theother cells, the interference is reevaluated, and the path isselected again.

5. Evaluation Results

The parameters in Table 1 were used to evaluate theoutage probability and the spectral efficiency. The requiredCINR is shown in Fig. 4 and was determined from the BERcharacteristic [J = 2 in Eqs. (1) and (9)] of 2-branch maxi-mum ratio combining diversity reception. The transmitpowers and antenna gains of all of the stations were constantregardless of the symbol rate and number of hops, and anomnidirectional antenna was assumed.

The evaluation methods and results of the single-cellenvironment and multicell environment are described be-low.

5.1. Single-cell environment

In the single-cell environment, the outage probability(12), (21) and the spectral efficiency (14), (23) were nu-merically evaluated for the cell radius R. The evaluationresults are shown in Figs. 5 and 6. In addition to the full-ratein adaptive symbol rate control, the characteristics areshown when the 1/2-rate is used (K = 2) and when the1/4-rate is used (K = 3). In multihop transmission, thecharacteristics were shown when the number m of candidaterelaying stations changed. In this paper, the cell radiuswhere a given allowed outage probability is satisfied iscalled the coverage in a single-cell environment. In particu-lar, the coverage is set to R0 when the allowed outageprobability was set to 10% in a single-hop cellular systemusing full-rate QPSK. This value is used to normalize thecell radius R.

From Fig. 5, the coverage expands along with therange of available symbol rates. Accompanying the intro-

(22)

(23)

Table 1. Parameters used in evaluations

Fig. 4. BER for 1/2k-rate QPSK.

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duction of multihop transmission and the increase in thecandidate relaying stations, the coverage is similarly ex-panded.

This coverage expansion can be easily predicted. Theimportant point is to evaluate the changes in the spectralefficiency accompanying the expansion of the coverage. Asis seen from Fig. 6, the spectral efficiency of the systemdecreases because the low-rate users increase with theexpansion of the coverage. From Fig. 5, the coverage ofeach equation was determined when the allowed outageprobability was set to 1% and 10%. Figure 7 shows thespectral efficiency corresponding to the coverage togetherwith that determined from Fig. 6. For each allowed outage

probability, the coverage can be expanded with some sac-rifice as the spectral efficiency. Thus, multihop transmis-sion has the same effect as the adaptive symbol rate control.In addition to this, as the number m of candidate relayingstations becomes large, multihop transmission has higherspectral efficiency for the same coverage than symbol ratecontrol.

5.2. Multicell environment

Figure 8 shows the outage probability for the cellreuse factor L and the spectral efficiency determined for the

Fig. 5. Outage probability in single-cell environments.

Fig. 7. Spectral efficiency as a function of coverage.

Fig. 8. Effects of introducing rate adaptation on outageprobability and spectral efficiency.Fig. 6. Spectral efficiency in single-cell environments.

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cellular system with adaptive symbol rate control. Figure 9shows these characteristics for the multihop cellular sys-tem. Notice that the cell reuse factor only becomes L = 3,4, 7, 9, 12, . . . because a hexagonal cell is not sectored.Because the cell reuse factor L is discontinuous, the deter-mined value from equations corresponds to the point on theupper left of the step characteristics in Figs. 8 and 9. Thecharacteristic does not depend on the cell radius R becausethe distance variation model is inversely proportional to thepower of the distance under interference-limited situation.

From Figs. 8 and 9, accompanying the introductionof the symbol rate control and multihop transmission, if theoutage probability is less than 0.2, the spectral efficiencyincreases. On the other hand, the spectral efficiency de-creases when the outage probability is higher than 0.35. Thereason why these inconsistent results are obtained is thatthe introduction of the low symbol rate transmission andmultihop transmission leads to the following two effects:the acceptance of a calling mobile station with a low band-width efficiency and the decrease in the cell reuse factorsatisfying the allowed outage probability. The contraryeffects are that the former lowers the spectral efficiency, andthe latter increases it. The cell reuse factor affects theefficiency of all communication as shown in Eqs. (14) and(23) because the number of channels per cell is dependenton the cell reuse factor. Similar to the single-cell environ-ment, there are many calling mobile stations incapable ofsingle-hop transmission. In other words, as the outageprobability increases, the number of accepted calling mo-bile stations with a low bandwidth efficiency becomeslarge, and the spectral efficiency decreases as the average.This is represented in Eqs. (13) and (22). The above resultsare when the outage probability is above 0.35, the decrease

in the spectral efficiency caused by reception by a callingmobile station having a low bandwidth efficiency becomeslarger than the increase in the spectral efficiency caused bythe decrease in the cell reuse factor.

These figures show the results of the numerical evalu-ations and simulations described in Section 4.4. The char-acteristics in the trend explained earlier are also shown. Theincrease in the spectral efficiency caused by the symbol ratecontrol or multihop transmission can be verified throughnumerical evaluation. The differences between the numeri-cal evaluation and the simulation result produced duringsingle-hop transmission show the accuracy of the approxi-mation described in Section 2.3. On the other hand, thereason for the appearance of the larger difference duringmultihop transmission is considered below. The introduc-tion of multihop transmission brings about an increase inthe desired signal power and a reduction in interferencefrom the other cells. The reason for this reduction in inter-ference is the distribution of the transmitting station movestoward the cell center nonuniformly because of the newtransmission of the relaying station in addition to callingmobile station. In the numerical evaluation, the transmittingstations were assumed to be uniform. Therefore, moreinterference than in practice is estimated. As a result, theevaluation result having a low outage probability is believedto be obtained for the same cell reuse factor L compared tothe simulation.

From Fig. 9, a high spectral efficiency is obtained forthe same outage probability accompanying the increase inthe number m of candidate relaying stations. The reasonsare the increase in the probability of a path satisfying therequired CINR and the lower outage probability accompa-nying the increase in the number m of candidate relayingstations for the same cell reuse factor. Because the numberof hops does not change, the spectral efficiency does notdecrease in a high outage probability state.

6. Conclusion

Similar to the evaluation method for a TDMA cellularsystem with adaptive symbol rate control, the outage prob-ability and the spectral efficiency of a TDMA multihopcellular system were derived. From a numerical evaluationin a single-cell environment, the ability to expand the cellcoverage in contrast to the drop in the spectral efficiencywas demonstrated. This result can be easily surmised fromthe fact that each multihop transmission can expand thecommunication range at the loss of bandwidth efficiencysimilar to symbol rate control. In addition, from the numeri-cal evaluation or computer simulation, the increase in thespectral efficiency was demonstrated also in an interferencelimited multicell environment because of the ability toachieve the allowed outage probability with a smaller cell

Fig. 9. Effects of introducing multihop transmission onoutage probability and spectral efficiency.

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reuse factor. Each effect in multihop transmission wasequivalent to symbol rate control. The effects were shownto increase with the number of candidate relaying stations.

Acknowledgments. We thank Mr. Atsushi Fuji-hara for his important comments. A portion of this researchwas supported by a grant from the 21st Century COEProgram (Subject No. 14213201), Grant-in-Aid for Scien-tific Research (A) from the Japan Society for the Promotionof Science (Subject No. 16206040), and a Grant-in-Aid forJSPS Fellows (Subject No. 16001178).

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AUTHORS

Koji Yamamoto (member) received a B.E. degree in electrical and electronic engineering and M.E. degree in informaticsfrom Kyoto University in 2002 and 2004 and became a research fellow of the Japan Society for the Promotion of Science. In2005, he received a doctorate from Kyoto University and became a research associate in the Graduate School of Informatics.His research interests include next-generation mobile communication systems and wireless ad hoc networks. In 2004, hereceived the PIMRC Best Student Paper Award.

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AUTHORS (continued) (from left to right)

Atsushi Kusuda (member) received a B.E. degree in engineering science and M.E. degree in informatics from KyotoUniversity in 2003 and 2006 and joined KDDI Corporation. His research interest is mobile communication systems.

Tsuyoshi Nakano (student member) received a B.E. degree in electrical and electronic engineering from Kyoto Universityin 2005 and is now in the M.E. degree program of the Graduate School of Management.

Susumu Yoshida (fellow) received a B.E. degree in electronic engineering and M.E. degree from Kyoto University in1971 and 1973 and became a research associate on the Faculty of Engineering, an associate professor in 1979, and a professorin 1992. He has been a professor in the Graduate School of Informatics since 1998. His research interests include transmissioncodes, digital mobile communications, and ad hoc networks. He received the 1978 IEICE Young Researcher’s Award, the 1988Telecom System Technology Award from the Technology Advancement Foundation, and the 1992 IEICE Achievement Award.

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