A locally optimal handoff algorithm for cellular communications

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 46, NO. 3, AUGUST 1997 603

A Locally Optimal Handoff Algorithmfor Cellular Communications

Venugopal V. Veeravalli,Member, IEEE, and Owen E. Kelly,Member, IEEE

Abstract—The design of handoff algorithms for cellular com-munication systems based on mobile signal-strength measure-ments is considered. The design problem is posed as an opti-mization to obtain the best tradeoff between theexpected num-ber of service failuresand expected number of handoffs, wherea service failure is defined to be the event that the signalstrength falls below a level required for satisfactory service tothe subscriber. Based on dynamic programming arguments, anoptimal solution is obtained, which, though impractical, can beused as a benchmark in the comparison of suboptimal schemes.A simple locally optimal handoff algorithm is derived from theoptimal solution. Like the standard hysteresis algorithm, thelocally optimal algorithm is characterized by a single threshold.A systematic method for the comparison of various handoffalgorithms that are akin to the receiver operating characteristic(ROC) curves of radar detection is presented. Simulation resultsshow that the locally optimal algorithm outperforms the hystere-sis algorithm, especially in situations where accurate predictionof signal strength is possible. A straightforward technique foradapting the locally optimal algorithm to changing environmentsis suggested. That natural adaptability is the algorithm’s principleadvantage over current approaches.

Index Terms—Handoff, handover, land mobile radio cellularsystems.

I. INTRODUCTION

A HANDOFF in cellular communication is the processwhereby amobile subscribercommunicating with one

base stationis switched to another base station during a call.The design of reliable handoff algorithms is crucial to theoperation of a cellular communication system and is especiallyimportant in microcellular systems, where the mobile maytraverse several cells during a call.

Handoff decisions can be based on measurements1 suchas the signal strength, bit error rate, and estimated distancefrom base stations. In many systems, especially microcellularsystems, signal strength may be the only reliable measurementthat can be used [2]. Some measurements such as bit errorrate are (either explicitly or implicitly) functions of the signalstrength. If location information about the mobile is available

Manuscript received May 11, 1995; revised March 11, 1996. This work waspresented in part at the 1995 International Symposium on Personal, Indoor,and Mobile Radio Communications (PIMRC).

V. V. Veeravalli was with Rice University, Houston, TX 77005 USA. Heis now with the School of Electrical Engineering, Cornell University, Ithaca,NY 14853 USA (e-mail: [email protected]).

O. E. Kelly was with Rice University, Houston, TX 77005 USA. He isnow with the Wireless Information Network laboratory, Rutgers University,Piscataway, NJ, 08855 USA (e-mail: [email protected]).

Publisher Item Identifier S 0018-9545(97)03129-0.1We restrict our attention to criteria based on degradation of the current

channel. Handoff decisions can also be based on network criteria [1].

independent from signal-strength measurements, then it canbe used to improve handoff decisions derived from signal-strength measurements.

We focus on handoff algorithms based on signal-strengthmeasurements. Consider the problem of designing an optimalhandoff algorithm for a mobile moving between neighboringcells. Many criteria for determining the efficacy of a handoffalgorithm are discussed in the literature [3]–[7] and may beused for optimal design. These include:

1) a measure of call quality, such as the received signalstrength from the operative base station;

2) the total number of handoffs on a trajectory betweenneighboring cells;

3) the number ofunnecessary handoffs, i.e., those madein situations, where the current base station would havecontinued to give satisfactory performance;

4) the number ofbad handoffs, i.e., those made to a basestation whose signal strength is below the satisfactoryperformance level;

5) the delay in making a handoff, which is sometimesdefined to be the distance of thecrossover point2 fromthe cell boundary.

Considering these criteria, we can see that limiting the num-ber of handoffs between cells [item 2)], while keeping the callquality high [item 1)] will generally eliminate those handoffsthat do not enhance call quality. In a system that balancesitems 1) and 2), separate consideration of unnecessary and badhandoffs [items 3) and 4)] is not required. Concerning delay[item 5)], it can be argued that delay in handoff is undesirableonly insofar as it impacts call quality. However, delay inhandoff can create uplink interference to other mobiles in thesystem, which results in a network cost we do not considerin our analysis. We limit our attention, therefore, to the firsttwo criteria: call quality and total number of handoffs, but,clearly, these are conflicting criteria—improved call qualitycan usually be obtained only at the expense of an increase inthe number of handoffs. Thus, a tradeoff must be made.

The standard approach to effecting a tradeoff between callquality and (expected) the number of handoffs has beenthrough anad hoc algorithm based on signal-strengthhys-teresis. The implicit measure of call quality used is simplythe (average) value of the received signal strength from theoperative base station. The hysteresis algorithm is designedso that handoff is made when the (averaged) signal strength

2The crossover point is that point on the trajectory at which the probabilityof being connected to the new base station is equal to that of being connectedto the old base station [8].

0018–9545/97$10.00 1997 IEEE

604 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 46, NO. 3, AUGUST 1997

(in decibels) from the new base station exceeds that from thecurrent base station by a hysteresis level.

A drawback of signal-strength hysteresis algorithms is thatthey allow unnecessary handoffs in regions, where signalsfrom both stations are strong [8]. One approach to preventsuch handoffs has been to extend the hysteresis algorithmso that a handoff is not made in situations where the signalstrength from the current base station is adequate [9], i.e.,larger than some level needed for satisfactory performance.Our approach is to design an optimal algorithm based on ameasure of call quality that incorporates this concept of anadequate signal strength. We use a binary-valued measure ofcall quality. Call quality is good or bad, depending on whetherthe signal strength is above or below a fixed threshold. Itnot difficult to identify such a threshold above which thesubscriber will have satisfactory performance, but below whichthe distortion becomes unacceptable. This is especially true indigital systems, where the threshold level could represent thepoint at which reliable error correction is no longer possible.We refer to the event that the signal strength falls below thethreshold as aservice failure.3

Thus, in our definition, an optimal handoff algorithm is onethat gives the best tradeoff between the expected number4 ofservice failures and expected number of handoffs on a givenmobile trajectory. The tradeoff problem can be posed in twoways: a variational and Bayes formulation. We establish thatthe solutions to the variational and Bayes formulations havethe same structure (which is akin to the detection theory resultthat the Neyman–Pearson and Bayes tests are both likelihoodratio tests [10]).

The Bayes formulation of the handoff problem is amenableto dynamic programming(DP) arguments. We pose the prob-lem as a finite-horizon5 DP problem and obtain the optimalsolution through a set of recursive equations. That optimalsolution is complicated and nonstationary, and it requires priorknowledge of the mobile’s exact trajectory. However, a simple,locally optimalalgorithm can be derived from the DP solution.The locally optimal algorithm is a threshold algorithm (as isthe signal-strength hysteresis algorithm), but it is not proneto unnecessary handoffs. Furthermore, it can be designed tobe independent of the location of the mobile. We study thislocally optimal algorithm in detail.

The rest of this paper is organized as follows. In SectionII, we set up the handoff problem as an optimum tradeoffproblem. In Section III, we present the DP solution. In SectionIV, we discuss the locally optimal algorithm design. SectionV provides detailed numerical results comparing the locallyoptimal algorithm to existing algorithms. The comparisons aredone on the basis of the tradeoff between the expected numberof service failures and handoffs. A discussion on adapting thelocally optimal test to changing environments is also included.Conclusions are presented in Section VI.

3 Occurrence of service failure does not imply that the call is droppedbecause we assume that the threshold level below which a service failure isdeclared may be greater than the level below which the call is lost.

4We assume a discrete-time model for the signal-strength measurements.5This is in contrast with formulations of [11] and [12] that employ infinite-

horizon discounted-cost models.

Fig. 1. A possible mobile trajectory.

II. PRELIMINARIES

We assume that only two base stations, say and ,are involved in the handoff, i.e., we consider only that portionof the trajectory on which the signals received from basestations and are the strongest. Without loss ofgenerality, assume that the mobile is moving on a trajectorygoing from cell 1 to cell 2, moving away from andapproaching . Let denote the distance of the mobileto (see Fig. 1).

We assume that the mobile measures the signal strengthfrom each base station and sends sampled values to theoperative base station. Furthermore, in our analysis, we assumethat handoff decisions are based solely on these measurements.However, the analysis is easily extended to the case, wherehandoff decisions are also based on signal-strength measure-ments made at the base stations.

The measured signal strength has three components: pathloss, which decays with distance from the base station, large-scale fluctuations (shadow fading), and small-scale fluctuations(multipath fading). We assume that the received signal ispassed through a low-pass filter to average out the small-scalefluctuations. The reason for the averaging is two-fold. First, itis impractical to design handoff algorithms that respond to thesmall-scale fluctuations. Second, these fluctuations are gener-ally compensated for by diversity combining and interleaving.

We assume that the signal strength is measured in decibelsrelative to some reference power level. (A convenient refer-ence level, used in Section V, is the minimum signal strengthrequired for satisfactory performance.) The signal strength

received from base at distance (after low-passfiltering) can be written as

dB

Parameters and account for path loss, depends ontransmitted power at the base station, andis the path-loss ex-ponent. The term is the shadow fading component, whichis accurately modeled (in decibels) as a zero-mean stationaryGaussian random process [13]. This model is referred to as thelognormal fading model. For spatial dependence, we assumea first-order autoregressive (AR) structure, which implies thatthe autocorrelation function of is given by

E

VEERAVALLI AND KELLY: LOCALLY OPTIMAL HANDOFF ALGORITHM FOR COMMUNICATIONS 605

where is thecorrelation distanceand is the variance ofthe shadow fading process.6 This AR model has been proposedby Gudmundson [14] on the basis of experimental results.The spatial correlation is assumed to beisotropic, i.e., thecorrelation of the fading process at two locations depends onlyon the distance between the two locations. Furthermore, theprocesses and are independent.

Samples of the signal-strength measurements are relayed tothe operative base station. Let the sampling time beandassume that the mobile is moving at a constant velocity.Then, with a slight abuse of notation, we get the followingdiscrete-time model for the received signal strength:

(1)

where is the distance to base station at the thsampling instant and is th sample of . The values

are, in general, not equally spaced, but due to the isotropicnature of the fading process, consecutive samples ofhavethe same correlation if speed is fixed. If speed and direction areconstant, the process is a zero-mean Gaussian discrete-time AR process with autocorrelation function

E

where is the sampling distanceand isthe correlation coefficientof the discrete-time fading process.

Suppose there are a total oftime steps onthe portion of the mobile’s trajectory that involves and

. Let denote the index of the operative base stationat time (i.e., when the mobile is communicatingwith ) and denote the other base station. A handoffdecision is made during each sampling interval. The decision

at time can be based on all signal-strength measurementsup to time . The decision variable takes on two values.If , a handoff is made resulting in . If

, no handoff is made and . Let denoteall the information available for decisionmaking at time, then

, where is the decision function at time.Handoff algorithm design involves choosing the handoff

decision functions at times . Letdenote the minimum level of signal strength required for

satisfactory service.7 Furthermore, let and denote thetotal number of service failures and number of handoffs fromtime one to , respectively. Then

E E P

and

E E P

where is the indicator function.6 Parameters�; �; d0; and� could, in general, be different for the signals

from the two base stations.7 If the interference levels for the two base stations are not the same,�

will be different for the signalsX(1) andX(2).

An optimal handoff algorithm (policy) is the set of deci-sion functions , which provides thebest tradeoff between the E and E . This optimumtradeoff problem can be posed in two ways:

1) variational formulation

E subject to E (2)

where is a control parameter;2) Bayes formulation

E E (3)

where is a tradeoff parameter.

This kind of tradeoff commonly arises in detection problems[10], [15], where the solution to the variational problem isusually also a Bayes solution for an appropriately chosentradeoff parameter. Theorem 1 of Section III shows that thesame is true for the handoff problem. Hence, we can find theoptimum tradeoff curveE E for both problems bysolving the Bayes problem for various values of. Parameter

may be interpreted as the relative cost of handoffs versusservice failures. This interpretation is especially useful foradapting the handoff algorithm to changing environments aswe shall see in Section V. We focus now on the solution tothe Bayes problem.

III. D YNAMIC PROGRAMMING SOLUTION

Dynamic programming allows optimization of the total costalong a state trajectory of a discrete-time dynamical systemthat has a stepwise additive-cost criterion and, conditioned onthe state, stepwise independent-noise statistics (see [16], p.10). Here, we cast the handoff problem in that form.

For the handoff problem, the state at time consistsof the triple . From (1) and the definition of

, we get the following update equation for :

where is the change in the fading

process and . The update equationconstitutes a discrete-time dynamical

model for our system (with exogenous input and controlinput ).

Given the first-order AR model for processes and, the noise variables have the required independence

structure. In particular, it is easy to show that is

independent of , given .Finally, the cost criterion as defined in (3) is additive over

time. In particular, if we define

(4)


and

then a Bayes optimal handoff algorithm minimizes

E E

Remark 1: The cost structure in (4) does not take intoaccount the possibility that the call may be terminated atsome time between one and . If is the termination(hangup) probability [11] for each time step and if a geometricdistribution is assumed for the call duration, then each costterm should be multiplied by . Thus, if a goodestimate of is available, it can easily be incorporated into thecost structure without any fundamental changes in the analysis.

The DP solution is obtained recursively as follows. Letthe expected cost-to-go at time (due to all the decisionsup to time ) be denoted by . Due to the conditionallyindependent noise statistics, is a function only of the state

. The expected cost of the Bayes optimal handoff policyover the entire trajectory is simply , and optimal handoffdecision functions are obtained by solving the following setof recursive equations (see [16] for an explanation of the DPtechnique):

(5)

E

P

P (6)

and for

E

E

E (7)

Note that for each , the optimum decision functiondepends only on the state and not on any past signal-strength measurements. These optimum decision functions aredescribed by

P

P (8)

and for

E

E (9)

The decision functions described in (8)and (9) constitute a Bayes optimal handoff algorithmfortradeoff parameter. The following theorem, whose proof isgiven in the Appendix, addresses the solution to the variationalformulation of (2).

Theorem 1: An optimal handoff algorithm for the varia-tional formulation is a Bayes solution for an appropriatelychosen value of the tradeoff parameter.

The DP equations can be solved numerically to obtain theoptimum handoff policy , however, the solution can be quitecomplex and nonstationary. Furthermore, the computation of

relies on prior knowledge of the trajectory of the mobile.These considerations imply that the DP solution is impractical.The tradeoff curve for the DP solution can, however, be used asa theoretical benchmark in the comparison of other suboptimalalgorithms. In the next section, we discuss the design of asimple stationary locally optimal handoff algorithm that isbased on the DP solution.

IV. L OCALLY OPTIMAL ALGORITHM

Solutions (8) and (9) correctly indicate that the globallyoptimal strategy at a particular location depends on the futuretrajectory. That unreasonable requirement suggests that theproblem should be reformulated specifically to ignore thefuture trajectory. A locally optimal solution to the Bayesproblem may be obtained by restricting the trajectory underconsideration to the points and . That is, we ignore theconsequences of a handoff decision at timeat times beyond

and base the decision on all available information up totime . Restricting (8) and (9) to yields decision rules

that select the best tradeoff between the cost of a handoffand the probability that falls below , given theinformation . Hence, the locally optimal decision function

at time has the structure

P P (10)

The local criterion gives rise to a solution that uses only localinformation.

Remark 2: Suppose we account for possible call termina-tion in the design of the locally optimal test by multiplyingeach cost function by the discount factor . Theonly modification that results in the locally optimal decisionfunction is that the parameter is replaced by .The structure of remains unchanged. Furthermore, ifissmall, is virtually unaffected by the discount factor.

For the lognormal fading model that we have assumed,the conditional distribution of given is Gaussian,hence, the probabilities in (10) are entirely determined by theconditional means and variances

E (11)

Var (12)


Fig. 2. Decision regions based on the predicted signal strength^X(B) of the current station and the other station^X(B ), respectively, for three different

handoff strategies. Decision in favor of handoff is made when the signal strengths lie inside the shaded area.

Note that the conditional variance does not depend on locationinformation. Furthermore, if the sampling rate is high, theargument of the log function in (11) is close to one, whichimplies the conditional mean is also approximately indepen-dent of location information. However, with andunknown, we are, in practice, forced to use the best avail-able estimate of (11), denoted , based on the availableinformation . The resulting test is described by

(13)

where . The correlationparameter is speed dependent and, inpractice, it can be determined from velocity estimates. Severalauthors treat the problem of estimating statistics of the fadingenvironment [17]–[20], and the algorithm suggested by (13)can clearly accommodate on-line estimates of and .This adaptation is discussed further in Section V.

Fig. 2 shows the decision regions of the conventionalhysteresis algorithm, locally optimum test, and hysteresis-threshold algorithm presented by Zhang and Holtzman [9].Comparing the hysteresis test and the locally optimum test, wesee the locally optimum test can avoid unnecessary handoffsin situations where both signal strengths are above. Insystems designed to produce very few service failures, i.e.,those with large fade margins, this could result in a significantsaving in the number of handoffs. The locally optimum testalso avoids bad handoffs when both signals are below.However, in systems with large fade margins, that situationoccurs very rarely.

An ad hocscheme that emulates the behavior of the locallyoptimum test is the hysteresis-threshold algorithm [9], which

performs the usual hysteresis test , but onlyafter first verifying that with a suitably chosenthreshold. In Section V, we see that the performance of alocally optimum test can be closely approximated by thehysteresis-threshold test, but the advantage in doing so is notclear. Unlike the locally optimum test, the hysteresis-thresholdtest requires two design parameters and is not easily adaptedto changing environments.

V. NUMERICAL RESULTS

We simulate a scenario in which the mobile traverses theline leading a distance from station 1 to station 2. The

specific simulation parameters were:

m station distance;station strength;path-loss exponent;fading process variance;

and m sampling distances;m correlation distance;

dB threshold of service failure.

These values are consistent with [9] and [14] and togetheryield a median signal strength of 15 dB (with respect to)at the midpoint between stations. At a sampling period of

s, the sampling distances of 2, 5, and 10 m correspondto speeds of 14.4, 36, and 72 km/h.

50 000 realizations were used to estimate the performanceof each strategy at each parameter setting. The same signal-strength predictor was used in comparingdecision strategies. The Bayes optimal solution was con-structed by quantizing the decision regions (akin to Fig. 2) for

and calculating the expectations in (5)–(7) by numericalintegration.

Fig. 3 compares the performance of the locally optimumhandoff algorithm with that of straightforward hysteresis andhysteresis-threshold tests in terms of the tradeoff betweenthe number of handoffs and service failures. Compared tothe simple hysteresis test, the locally optimum and thresholdstrategies consistently achieve fewer service failures for thesame number of handoffs. The locally optimum test has,effectively, the same performance as the best of thresholdtests. More precisely, the number of service failures for thelocally optimum test can slightly exceed that of the hysteresis-threshold test, but, by varying a single parameter, thelocally optimum performance curve appears to trace closeto the minimum E of all threshold tests. Wehave no strategy to construct the best performance curve forall hysteresis-threshold tests. However, experimentation showsthat the best hysteresis-threshold tests employ small hysteresisvalues (such as 0, 1, and 2 dB used in the figure) to whichtheir performance is somewhat insensitive.

Fig. 4 compares performance of the locally optimum deci-sion rule at three sampling distances corresponding to differentspeeds. Due to spatial correlation, short-sampling distancesallow better signal-strength prediction and, thus, better handoffdecisions and fewer service failures. Dashed lines show howthe operating point changes if the tradeoff parameter remains


Fig. 3. Performance comparison. We compare the tradeoff between handoffsand service failures for three strategies to each other and to the best achievable(dynamic programming solution). Each curve is parameterized by the variablein parenthesis. With a single parameter, the locally optimum test follows thebest performance that is achievable using two parameter hysteresis-thresholdtests.

Fig. 4. Tradeoff curve parametrization. Performance of the locally optimumtest is shown at sampling distances corresponding to mobile speeds 14.4,36, and 72 km/h (assumingts = 0:5 s). Dashed lines connect points of theequal tradeoff parameter. Unlabeled tradeoff values are spaced logarithmicallybetween indicated values.

fixed, while the cellular environment (e.g., speed) changes. Inmaking (13) adaptive, we may clearly use on-line estimates ofthe shadow fading variance and signal-strength correlation, butis it also necessary to adapt the tradeoff parameter? Fig. 4shows that if the tradeoff parameter remains fixed, then the“knee” of the operating curve at slow speeds transforms nearlyto the knee of the curve at high speeds. Thus, an acceptabletest can be had by choosing a fixed value for the tradeoff pa-rameter. This compares favorably with approaches to adaptivehysteresis tests that require separate analysis at each speed inorder to determine the optimal hysteresis value [17].

Fig. 5 shows performance curves of the simple hysteresistest as a function of sampling distance. Note, in comparison

Fig. 5. The hysteresis algorithm does not adapt to speed. Performance ofthe hysteresis test is shown at sampling distances corresponding to mobilespeeds 14.4, 36, and 72 km/h (assumingts = 0:5 s). Compared with thelocally optimal test (Fig. 4), the achievable performance of hysteresis tests isrelatively unchanged at different mobile speeds.

to Fig. 4, that hysteresis performance curves are relativelyunchanged at different sampling distances. A speed-adaptiverule could ideally move the operating point to any point onthe particular curve specified by the current mobile speed. Buteven with such a rule, hysteresis tests cannot reach the samepoints in the E E plane as the locally optimal testcan. Hysteresis tests cannot take advantage of the increasedpredictability of the signal strength at slow speeds.

VI. CONCLUSIONS

We introduced a new call-quality criterion to balance againstthe number of handoffs in designing an optimal handoff strat-egy and showed that the Bayes and variational formulations ofthe resulting optimization are equivalent. The optimal decisionrules may be found by dynamic programming, but are toocostly to implement and depend on prior knowledge of thetrajectory of the mobile.

A locally optimal solution gives rise to a hysteresis test thatcompares probabilities rather than signal strengths. This locallyoptimal test naturally has the property of preventing handoffswhen the signal from the operative base station is strongand allowing handoffs when that signal is weak. The locallyoptimum test compares favorably in performance with simplehysteresis tests and is competitive with hysteresis-thresholdtests. For the locally optimum strategy, it is immediately clearhow to incorporate on-line parameter estimates to obtain analgorithm that responds to changes in the propagation envi-ronment. This natural adaptability is the principle advantageof the locally optimal handoff test over current approaches.

APPENDIX

Proof of Theorem 1:Let denote the Bayes costfor a handoff policy , i.e.,

E E


where E and E are written explicitly as functionsof . The Bayes optimal solution has a cost that isgiven by

The following lemma gives an important property of .Lemma 1: is a concave continuous function ofon

.Proof: The Bayes optimal solution is obtained recur-

sively from (5) to (9). In particular, . Inthe following, we write the cost-to-go functions explicitly asfunctions of , i.e., .

The function is trivially a concave function of. Now, suppose is a concave function of.

Then, from (6), it follows that is a concave functionof as well since is expressed as the sum of aconstant and the minimum of two concave functions of.Thus, by induction, is also a concave(hence continuous) function of on .

Now, for any fixed policy , the Bayes cost isa straight line as a function of with slope andintercept . Furthermore, this line must lie above theconcave curve . The line corresponding to the variationalsolution is one that has an intercept less than or equal to

and the minimum possible slope. It is clear that such a linemust pass through a point (or points) on curve . Let theordinate of one such point be . Then, the Bayes solution for

is a solution to the variational problem.

ACKNOWLEDGMENT

The authors thank R. Vijayan for helpful discussions andR. Rezaiifar for providing an early copy of [11] that gives thecall-termination interpretation for the discounted cost structure.

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Venugopal V. Veeravalli (S’84–M’93) received theB.Tech. degree (Silver Medal Honors) in 1985 fromthe Indian Institute of Technology, Bombay, India,the M.S. degree in 1987 from Carnegie-MellonUniversity, Pittsburgh, PA, and the Ph.D. degreein 1992 from the University of Illinois at Urbana-Champaign, all in electrical engineering.

From 1992 to 1993, he was a Post-DoctoralFellow in the Division of Applied Sciences, Har-vard University, Cambridge, MA. In August 1996,he joined the faculty of the School of Electrical

Engineering, Cornell University, Ithaca, NY, as an Assistant Professor. Hehas also held academic positions at CUNY and Rice University, Houston, TX.His research interests are in the areas of wireless communications, detectionand estimation theory, and information theory. His current topics of researchinclude capacity analysis for cellular CDMA systems, sequential acquisitiontechniques for CDMA systems, handoff and power control algorithms forwireless networks, and decentralized dynamic decision making.

Dr. Veeravalli is a corecipient of the 1996 IEEE Browder J. ThompsonBest Paper Award.

Owen E. Kelly (S’91–M’96) received the B.A.Sc.degree in systems design engineering in 1989 fromthe University of Waterloo, Ont., Canada, and theM.S. and Ph.D. degrees in electrical engineering in1994 and 1996 from Rice University, Houston, TX.

He is currently a Post-Doctoral Fellow at theWireless Information Network Laboratory, RutgersUniversity, Piscataway, NJ, working on mobile lo-cation estimation and simulation of large wirelessnetworks. His research interests are in the areas ofstatistical modeling and decision problems and the

application of related techniques in the field of wireless communications.

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A locally optimal handoff algorithm for cellular communications