Fuzzy handoff algorithms for wireless communication

Fuzzy Sets and Systems 110 (2000) 379–388www.elsevier.com/locate/fss

Fuzzy hando� algorithms for wireless communicationGeorge Edwardsa;∗, Abraham Kandel b, Ravi Sankar c

a Electrical Engineering Department, University of Denver, 2390 South York Street,Denver, CO 80208, USA

bComputer Science and Engineering Department, University of South Florida, 4202 East Fowler Avenue,ENB 118 Tampa, FL 33620, USA

cDepartment of Electrical Engineering, University of South Florida, 4202 East Fowler Avenue,ENB 118 Tampa, FL 33620, USA

Received July 1996; received in revised form March 1998

Abstract

In order to manage the high call density expected of future cellular systems, microcells must be used. A migration tomicrocells will increase the number of hando�s, and require faster hando� algorithms – in terms of decision making. In thecase of line-of-sight transmission, it is important that the hando� algorithm detects the cell boundary early enough, otherwisethis will lead to channel dragging into the new cell subsequently increasing the chance of co-channel interference. In thecase of non-line-of-sight transmission, a mobile station on turning a street corner will experience a phenomenon known asthe Manhattan corner e�ect that causes the received signal level to drop by 20–30 dB in 20–30m. This corner e�ect problemcan lead to a loss of communication if not identi�ed early enough. This paper presents two new hando� techniques usingfuzzy logic as possible solutions to microcellular hando�. The �rst algorithm uses an adaptive fuzzy predictor, while thesecond uses a fuzzy averaging technique. The results of the simulation show that fuzzy is a viable option for microcellularhando�. c© 2000 Elsevier Science B.V. All rights reserved.

1. Introduction

The current trend of exponential growth in the useof personal communication services is causing the in-dustry to examine ways to use the available bandwidthmore e�ciently. Natural solutions to bandwidth e�-ciency include using more e�cient modulation tech-niques as well as better coding algorithms. But thesechanges will not be su�cient and there will be aneed to reduce the cell dimension in third generation

∗ Corresponding author. Tel.: +1303 871 4252; fax: +1303 8714450.E-mail address: [email protected] (G. Edwards)

systems. This will be necessary particularly in urbanareas where future systems must be capable of han-dling tra�c that far exceeds today’s peak load. Thedimension of the reduced microcell is expected to beon the order of a few hundred meters, a large stepdown from today’s macrocells that are on the order ofseveral kilometers.A key function in cellular communications is hand-

o�. Hando� is the process whereby a mobile station(MS) switches channels or both channel and base sta-tion (BS) in order to continue communication becauseof degradation in the received signal [5, 9]. In the for-mer the MS switches to another channel in the sameBS, while, in the latter the MS switches to a new

0165-0114/00/$ - see front matter c© 2000 Elsevier Science B.V. All rights reserved.PII: S 0165 -0114(98)00094 -3

380 G. Edwards et al. / Fuzzy Sets and Systems 110 (2000) 379–388

Fig. 1. The e�ect of hysteresis.

BS because it has crossed a cell boundary. Hando�control in cellular communication may be centralizedor distributed. In a centralized hando� system the Mo-bile Switching Center (MSC) – which is connected tothe BSs and supervises the network – is responsiblefor making the hando� decision, while in a distributedsystem, the MS is responsible.Existing hando� algorithms measure signal

parameters such as the received signal strengthindication (RSSI), bit-error ratio (BER), andcarrier-to-interference ratio (C=I) [5, 6, 9, 11]. Theseparameters can be used in isolation or in combina-tion to determine when a hando� is needed. Mosthando� algorithms add a hysteresis margin to theparameter of interest in order to provide hando� sta-bility and prevent hando� wa�ing between BSs. Thee�ect of hysteresis on the received signal strengthmeasured at a MS is illustrated in Fig. 1. The contin-uous lines show the pathloss slopes for BS1 and BS2.These slopes show that in the absence of hysteresisthe hando� would take place at point A. The addi-tion of a hysteresis margin H shifts the signal crosspoint from A to B, thus ensuring that when a hand-o� decision is made the signal from the new, targetBS is de�nitely stronger than that from the currentBS. This, however, comes at the price of a delayedhando�.

2. Statement of the problem and proposed solutions

In cellular communications the transmitted sig-nal received at the MS (or BS) may be modeled as

follows:

sa(t)=m(t)r(t); (1)

m(t) is assumed to be lognormally distributed [6, 11],and r(t) is a fast fading component that is assumedto be removed by �ltering at the receiver. Since m(t)is lognormally distributed, it is preferable to examinethe sampled signal in dB (or dBm) which can be rep-resented as:

s(n)= 20 log(m(nT )): (2)

The distribution of s(n) is Gaussian with an averagevalue � and standard deviation �. The standard devi-ation varies in the range between 5 and 20 dB, whilethe average � is dependent on the distance d, in me-ters, between the base and mobile stations as follows:

�(d)= k1− k2 log(d); (3)

where k1 depends on the transmitted power and k2varies in the range 20–60. Thus, the received line-of-sight (LOS) signal consists of a deterministic and aswell a random component.Eq. (3) indicates the relationship between distance

and strength for the deterministic signal component;it states that the received LOS signal at the MS isstrong, when the MS is close to the BS and weakwhenit is far away. Although the spatial signal will obeyEq. (3), it will contain some measure of uncertaintybecause of the random component included. The prob-lem is further exacerbated under the non-line-of-sight(NLOS) condition because of the imposition of thecorner e�ect phenomenon.The primary function of a hando� algorithm is to

make an estimate of the deterministic signal com-ponent – which is used for making the hando�decision. Indeed, a major criterion for the hando�algorithm is that it must be capable of making adecision in a region of uncertainty. Conventionalhando� algorithms use averaging techniques to nul-lify the e�ect of the random component. Many ofthese algorithms add a hysteresis margin to the aver-age in order to provide stability. It is felt that thesealgorithms (and there is a delay in moving averages)will be too slow for microcellular condition and, inparticular, the microcellular corner e�ect and so newand better algorithms must be developed. This paperproposes a couple of fuzzy-based hando� algorithms

G. Edwards et al. / Fuzzy Sets and Systems 110 (2000) 379–388 381

because of fuzzy logic’s inherent strength in solvingproblems exhibiting uncertainty [3, 4, 13], and thefact that many of the terms used above for describingthe signal, e.g., strong, close, weak, far are fuzzy innature.The high call volume anticipated over future cellu-

lar network will over-load the MSC if a centralizedcontrol is used, thus the work proposed in this paperis in support of a distributed system. This judgmentis based on practical argument and has nothing to dowith the application of fuzzy. The fuzzy algorithmswill monitor the trend in the received signals (RSSI)from the current and target BSs, and use fuzzy logictechniques to determine when a hando� is needed. Thefuzzy algorithms are labeled as I and II.

2.1. Fuzzy algorithm I

In algorithm I, the hando� mechanism is accom-plished in two stages. It uses an adaptive fuzzy predic-tor in its front-end (or �rst-stage) to predict the nextincoming signal samples from the BSs under consid-eration. The fuzzy predictor uses the past signal his-tory to predict a future value. The structure for theadaptive fuzzy predictor is shown in Fig. 2, and likeits classical counterpart, it attempts to minimize insome sense the error signal that is the di�erence be-tween the true and estimated signals. Thus, assumingthe time series for the RSSI signal to be {x(n)}, wheren∈{1; 2; 3; : : :}, then for a one-stage look ahead pre-dictor, the problem can be stated as follows: givenx(n−N+1); x(n−N+2); : : : ; x(n), determine x(n+1).In this example, the past N samples are used to com-pute the next (future) sample. Since a fuzzy controllerworks with fuzzy sets and rules, the �rst step towardsa solution is to establish fuzzy sets over the universeof discourse for each of the N inputs and the output.This step is followed by the development of appropri-ate fuzzy rules to span the input=output fuzzy space.This can be expedited by forming n, N -input=outputpairs as follow:

[x(n− N ); : : : ; x(n− 1): x(n)];[x(n− N − 1); : : : ; x(n− 2): x(n− 1)];...

[x(1); : : : ; x(N ): x(N + 1)]:

Fig. 2. Adaptive fuzzy predictor.

By using an appropriate training algorithm such as or-thogonal least-squares learning, table-lookup scheme,nearest-neighborhood cluster, recursive mean square,or least-mean-square techniques, etc., the fuzzy rulescan be established [12]. The fuzzy rules will be interms of If–Then propositions as follows:

R(1): IF x1 is O11 and : : : and xN is O1N ;

THEN xN+1 is P1;R(2): IF x1 is O21 and : : : and xN is O

2N ;

THEN xN+1 is P2;...R(k): IF x1 is Ok1 and : : : and xN is O

kN ;

THEN xN+1 is Pk;

where Oli and Pl are fuzzy sets in Ui ⊂ R, where R is

the set of real numbers. The symbols �x=(x1; : : : ; xN )T

∈U1×· · ·×UN and xN+1 ∈Ui are the input and outputlinguistic variables for the fuzzy system. In this re-search, the ANDing (intersection) of the membershipfunctions A∩B is de�ned for all x∈X by the equation

(A∩B)(x)=min[A(x); B(x)]: (4)

The di�erence signals, �l, between the current andtarget base stations RSSIs are computed for the presentand future time instants. The two di�erence signals fortimes t and t+1 are fed to the back-end (or secondfuzzy stage) of algorithm I. The output of the secondfuzzy stage is a crisp value that indicates the degreeto which a hando� from the current to the target BSis desirable. Thus, a threshold value can be set andwhenever this value is exceeded a hando� commandis issued.


Fig. 3. Fuzzy block diagram.

The block diagram for each fuzzy stage appearsas in Fig. 3. The input and output of the fuzzy sys-tem are �x∈RN and y∈R, respectively. Information tothe fuzzy system �rst enters the Fuzzi�er, where it isfuzzi�ed. The fuzzi�ed data is passed to the inferenceengine. The inference engine matches the fuzzi�eddata against a set of fuzzy rules using fuzzy techniquesto produce output fuzzy sets. The output fuzzy sets arethen passed to the defuzzi�er which computes a crispoutput value by the centroid algorithm [12].

2.2. Fuzzy algorithm II

In fuzzy algorithm II, a fuzzy averaging techniqueis used to determine hando�. This fuzzy algorithmperforms a short-time average (to borrow a term fromconventional signal processing algorithm) on the dif-ference signal �l between the current and target BSs.A hando� is issued whenever the average of the di�er-ence signal �l exceeds the bounds of what is consid-ered acceptable too often. Unlike algorithm I, whichuses the future signal value (based on the past) tomake a hando� decision, algorithm II keeps a runningfuzzy average of the past. In this way, it keeps trackof the signal trend based on the past and uses this in-formation to make a hando� decision.This approach is similar to the ranging algorithms

in [2, 8]. In algorithm II, �l is considered to take onthe heuristic values of being acceptable, unacceptableor any combination of gray area in between. This algo-rithm thus makes a hando� to the target BS wheneverthe average of the di�erence signal violates the be-lief of what is considered acceptable more often thannot. In a practical sense it means, if the di�erence sig-nal keeps turning up in favor of the target BS beingthe better base for communication, then the naturalthing to do is to switch to it. This kind of common

sense logic can be easily expedited using fuzzy tech-niques. The actual averaging function is continuous,which is good since it ensures graceful performancecharacteristics.

3. Benchmark algorithms

Hando� is based on the BS’s RSSI, measured indBm. The fuzzy hando� algorithms were tested andcompared to conventional hando� algorithms, whichact as benchmarks. Two benchmark algorithms basedon signal averaging (Algorithm a) and signal averag-ing with hysteresis (Algorithm b) were used for per-formance comparison. The algorithms are describedbelow:

Algorithm a: signal averagingThis algorithm computes average RSSI values for

the current and target BSs, i and j, respectively. Thehando� decision is made as follows:

ifyi(n)¿yj(n); choose BSi

otherwise choose BSj; (5)

where,

y(n)=1N

n∑k = n−N+1

s(k);

N is the size of the averaging window and s(k) is theRSSI sample at time k.The averaging window used in this work has sample

sizes chosen from the set {5, 10}.

Algorithm b: signal averaging with hysteresisIn this algorithm, along with the averaging tech-

nique mentioned above, a hysteresis margin H isadded to the current BS’s signal. Given the scenariowhere the current and target BSs are i and j, respec-tively the hando� algorithm now becomes:

if yi(n) +H¿yj(n); choose BSi

otherwise choose BSj; (6)

where the hysteresis values for H (in dB) is chosenfrom the set {2, 5}.


4. Fuzzy sets and rules

The algorithms were tested using two di�erent sig-nal models in order to test for robustness. This allowsus to examine the strengths and weaknesses of eachalgorithm under various environmental conditions.The signal models were taken from popular ones inthe literature. The models are labeled A and B andare attributed to [1, 6], respectively. The signals gen-erated using the two models are shown in Figs. 4 and5, respectively. Fuzzy sets and rules were establishedbased on these signals.

4.1. Description of fuzzy algorithm I

In algorithm I, the input variable to the fuzzy pre-dictor is the measured RSSI, while the output fromit is the predicted value for the next incoming sig-nal. The input (output) universe of discourse on whichthe fuzzy sets were de�ned for the linguistic variable,RSSI is given below. The fuzzy sets take on the lin-guistic values weak, medium, and strong (referring tothe strength of the signal) and are represented belowby membership functions A1, A2 and A3, respectively,over the interval [−90,−20] dBm.

A1(x)=

1 if x6− 80;(−45− x)=35 if − 80¡x¡− 45;0 if x¿− 45;

A2(x)=

0 if x6− 80;(x + 80)=35 if − 80¡x¡− 45;(−30− x)=15 if − 45¡x¡− 30;0 if x¿− 30;

A3(x)=

0 if x6− 45;(x + 45)=15 if − 45¡x¡− 30;1 if x¿− 30:

The fuzzy rules for stage 1 are:IF RSSIin is strong, THEN RSSIout is strong.IF RSSIin is medium, THEN RSSIout is medium.IF RSSIin is weak, THEN RSSIout is weak.In the second stage of fuzzy algorithm I the di�er-

ence signals �l between the current and the target BSs– computed at time t (current time) and t+1 (pre-dicted one time slice ahead) – form the input. The sig-nals can be written more compactly as �lt and �lt+1,respectively. The universes �lt and �lt+1 are similar

and the fuzzy sets de�ned on them are shown in Fig. 6.The inputs on �lt and �lt+1 are linked by fuzzy im-plications to the output hando� factor. The fuzzy setsfor the hando� factor are shown in Fig. 7. The fuzzyrules that link the input sets to the output sets are asfollows:lF �lt is neg and �lt+1 is negTHEN hando� factor is high.lF �lt is neg and �lt+1 is azTHEN hando� factor is med.lF�lt is neg and �lt+1 is posTHEN hando� factor is low.lF �lt is az and �lt+1 is negTHEN hando� factor is high.lF �lt is az and �lt+1 is azTHEN hando� factor is med.lF �lt is az and �lt+1 is posTHEN hando� factor is low.lF �lt is pos and �lt+1 is negTHEN hando� factor is high.lF �lt is pos and �lt+1 is azTHEN hando� factor is med.lF �lt is pos and �lt+1 is posTHEN hando� factor is low.The crisp hando� factor computed after defuzzi�-

cation is used to determine when a hando� is requiredas follows:

if hando� factor¿ 0:87; then hando�

otherwise do nothing: (7)

lt should be noted in Fig. 6, that the universe of dis-course is truncated, i.e., it ranges between [−7,7] dB.This was done consciously to avoid the time penaltyinvolved since the algorithm would need to performtwo sets of fuzzi�cation and defuzzi�cation routines,thus in cases where a hando� is improbable the sec-ond stage of the algorithm is bypassed.

4.2. Description of fuzzy algorithm II

ln the case of fuzzy algorithm II, the hando� is againbased on the di�erence signal. ln this algorithm thedi�erence signal is considered to be acceptable (A) orunacceptable (U ) or shades of area in between. Thesefuzzy sets are shown in Fig. 8. The fuzzy algorithmtracks the di�erence signal in an averaging manner.Once the average exceeds a level of what is considered


Fig. 4. Model A signal.

Fig. 5. Model B signal.


Fig. 6. Fuzzy sets for the di�erence signal.

Fig. 7. Hando� factor fuzzy sets.

acceptable, i.e., it is over an unacceptable threshold,then a hando� will be issued. The average is computedas follows:

b(�ln)=max[0; b(�ln−1) + U (�ln)−A(�ln)]; (8)where �ln is the di�erence signal at time n, U (•)and A(•) the membership values for the di�erencesignal in the fuzzy sets, unacceptable and acceptable,respectively. This algorithm determines that a hando�is necessary whenever the average exceeds a thresholdof 3.0.

5. Performance results

5.1. Justi�cation for fuzzy predictor

A classical linear adaptive predictor can be repre-sented by a similar block diagram to that shown forthe adaptive fuzzy predictor in Fig. 2. The basic goalof any predictor is to minimize the mean-square er-ror (MSE) of its output, en. lf one considers the blockdiagram in Fig. 2 for a moment to represent an adap-tive Wiener �lter, then its predictive algorithm maybe summarized as follows [10]:1. x̂n=− ∑N

i=1 ai(n)xn−i,2. en= xn− x̂n,3. ai(n+1)=ai(n)−2�enxn−i for 16i6K ,

where � is the adaptation coe�cient.

Table 1MSE (root-MSE) for fuzzy and Wiener �lter

Algorithm Model A Model B

Fuzzy 1.04 (1.02) 25.92 (5.09)Wiener �lter 6.22 (2.49) 50.28 (7.09)

For the performance comparisons of the adaptivefuzzy predictor with the classical adaptive predictor,the future signal value is predicted based on one pastsample. The justi�cation for a �rst-order predictor canbe found in [6, 7]. The predictive capability of thefuzzy predictor was compared to that of the adaptiveWiener �lter by performing prediction tests on signalsA and B. The MSE (and root-MSE) for the fuzzy pre-dictor and adaptive Wiener �lter is shown in Table 1.The mean-square error is de�ned as follows:

MSE=1|S|

|S|∑i=1

(xi− x̂i)2; (9)

where xi and x̂i are the actual and estimated RSSlvalues, respectively, at time i, and |S| is the samplesize.The results in Table 1 show that the fuzzy predictor

produced a smaller MSE based on our experimentaldata. This provided the justi�cation for the use of afuzzy predictor in the �rst stage of fuzzy algorithm I.Fig. 9 shows that the actual and the fuzzy predictedsignals for the model A signal pro�le. The fuzzy pre-dicted signal is seen to track the actual signal veryclosely.

5.2. Hando� results

Tables 2 and 3 show the performance of each algo-rithm relative to signal models A and B, respectively.For this study, the performance criteria were basedmainly on the stability of the hando� algorithm. Aninitiated hando� should be stable and not produce asituation whereby the call is passed back and forth be-tween two base stations. ln addition, we investigatedthe timeliness of the hando� response (delay) basedon the signal pro�le. The tables show which BS is con-nected to the MS as it travels from BS1 to BS2. Thevalues (in brackets) represent displacement intervalsin meter followed by the communicating BS number.


Fig. 8. Fuzzy sets for Acceptable and Unacceptable.

Fig. 9. Actual and predicted signal.

Table 2Hando� performance under condition of model A

Algorithm [lnterval in m] attached BS

Fuzzy algorithm I [0, 175] 1, [175.5, 305.5] 2, [306, 343.5] 1, [344, 500] 2Fuzzy algorithm II [0, 172] 1, [172.5, 273] 2, [273.5, 337] 1, [337.5, 500] 2Algorithm a (N =5) [0, 168] 1, [168.5, 251] 2, [251.5, 333.5] 1, [334, 500] 2Algorithm b (N =5; H =2) [0, 171.5] 1, [172, 293.5] 2, [294, 337] 1, [337.5, 500] 2Algorithm b (N =5; H =5) [0, 177.5] 1, [176, 306.5] 2, [307, 344.5] 1, [345, 500] 2Algorithm a (N =10) [0, 169.5] 1, [170, 252] 2, [252.5, 334.5] 1, [335, 500] 2Algorithm b (N =10; H =2) [0, 172.5] 1, [173, 295] 2, [295.5, 338] 1, [338.5, 500] 2Algorithm b (N =10; H =5) [0, 177] 1, [177.5, 307.5] 2, [308, 345.5] 1, [346, 500] 2


Table 3Hando� performance under condition of model B

Algorithm [lnterval in m] attached BS

Fuzzy algorithm I [0, 357] 1, [359, 700] 2Fuzzy algorithm II [0, 361] 1, [363, 700] 2Algorithm a (N =5) [0, 317] 1, [319, 325] 2, [327, 353] 1, [355, 383] 2,

[385, 391] 1, [393, 700] 2Algorithm b (N =5; H =2) [0, 319] 1, [321, 327] 2, [329, 361] 1, [363, 700] 2Algorithm b (N =5; H =5) [0, 377] 1, [379, 700] 2Algorithm a (N =10) [0, 359] 1, [361, 700] 2Algorithm b (N =10; H =2) [0, 365] 1, [367, 700] 2Algorithm b (N =10; H =5) [0, 407] 1, [409, 700] 2

6. Discussion and conclusion

The performances of two new hando� algorithmsusing fuzzy logic were investigated in a microcellu-lar setting. Two popular signal models were used inthe simulation in order to examine the robustness ofthe fuzzy algorithms under di�erent signal conditions.Table 1 shows the fuzzy predictor performed betterthan the classical predictor and so a decision was madein favor of going with a fuzzy predictor.Looking at the signal pro�le for the model A, one

can see in the interval [170, 250]m that the signalstrength for BS2 is superior to that of BS1, while thereverse occurs over the interval [250, 330]m. Table 2shows that both fuzzy algorithms respond appropri-ately and that the hando�s were made in the proper re-gions. Hando�s for the classical methods (benchmarkalgorithms) were also proper.ln the case of model B, the signal values change

abruptly and there is also no localized region withinthe proper coverage of BS1 where the signal from BS2appears stronger or vice versa. Thus, one would expectthat a hando� should occur somewhere in the middlebetween the two cells. Table 3 shows that the fuzzyalgorithms again behave appropriately, with hando�soccurring in the region of the cell boundary. Bothalgorithms – algorithm a with N =5 samples andalgorithm b with N =5 samples and H =2dB – per-formed poorly, and produced signal wa�ing, i.e., theMS was unnecessarily handed o� back and forth be-tween the two BSs. This is a setback for the classicalapproach since its best hope for coping with the fastresponse time required for the Manhattan corner con-

dition would be to use a small window=hysteresis size.But, by using a small window=hysteresis our experi-ments show the algorithm could become unstable un-der some signaling conditions. The algorithm b withN =10 samples and H =2dB produced a marginal tolate hando�, while the same algorithm with N =10samples H =5dB de�nitely produced a late hando�.The fuzzy algorithms were seen to be very robust

and provide appropriate hando� response under thedi�erent signaling environment. Future work will ex-amine the proposed hando� algorithms under theMan-hattan corner e�ect condition. Here, the algorithm awith N =10 samples which had performed well in theLOS experiments is not expected to do well because ofthe inherent delay using so many samples. ln closing,the second fuzzy algorithm is recommended becauseof its computational simplicity.

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Fuzzy handoff algorithms for wireless communication