- Email: [email protected]
Fuzzy handoff algorithms for wireless communication
Fuzzy Sets and Systems 110 (2000) 379–388
www.elsevier.com/locate/fss
Fuzzy hando algorithms for wireless communication George Edwards a; ∗ , Abraham Kandel b , Ravi Sankar c a Electrical
Engineering Department, University of Denver, 2390 South York Street, Denver, CO 80208, USA b Computer Science and Engineering Department, University of South Florida, 4202 East Fowler Avenue, ENB 118 Tampa, FL 33620, USA c Department 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 to microcells will increase the number of hando s, and require faster hando algorithms – in terms of decision making. In the case of line-of-sight transmission, it is important that the hando algorithm detects the cell boundary early enough, otherwise this will lead to channel dragging into the new cell subsequently increasing the chance of co-channel interference. In the case of non-line-of-sight transmission, a mobile station on turning a street corner will experience a phenomenon known as the Manhattan corner e ect that causes the received signal level to drop by 20 –30 dB in 20 –30 m. This corner e ect problem can lead to a loss of communication if not identi ed early enough. This paper presents two new hando techniques using fuzzy logic as possible solutions to microcellular hando . The rst algorithm uses an adaptive fuzzy predictor, while the second uses a fuzzy averaging technique. The results of the simulation show that fuzzy is a viable option for microcellular c 2000 Elsevier Science B.V. All rights reserved. hando .
1. Introduction The current trend of exponential growth in the use of personal communication services is causing the industry to examine ways to use the available bandwidth more eciently. Natural solutions to bandwidth eciency include using more ecient modulation techniques as well as better coding algorithms. But these changes will not be sucient and there will be a need to reduce the cell dimension in third generation ∗ Corresponding author. Tel.: +1303 871 4252; fax: +1303 871 4450. E-mail address: [email protected] (G. Edwards)
systems. This will be necessary particularly in urban areas where future systems must be capable of handling trac that far exceeds today’s peak load. The dimension of the reduced microcell is expected to be on the order of a few hundred meters, a large step down from today’s macrocells that are on the order of several kilometers. A key function in cellular communications is hando . Hando is the process whereby a mobile station (MS) switches channels or both channel and base station (BS) in order to continue communication because of degradation in the received signal [5, 9]. In the former the MS switches to another channel in the same BS, while, in the latter the MS switches to a new
c 2000 Elsevier Science B.V. All rights reserved. 0165-0114/00/$ - see front matter PII: S 0 1 6 5 - 0 1 1 4 ( 9 8 ) 0 0 0 9 4 - 3
380
G. Edwards et al. / Fuzzy Sets and Systems 110 (2000) 379–388
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 assumed to be removed by ltering at the receiver. Since m(t) is lognormally distributed, it is preferable to examine the sampled signal in dB (or dBm) which can be represented as: s(n) = 20 log(m(nT )): Fig. 1. The e ect of hysteresis.
BS because it has crossed a cell boundary. Hando control in cellular communication may be centralized or distributed. In a centralized hando system the Mobile Switching Center (MSC) – which is connected to the BSs and supervises the network – is responsible for making the hando decision, while in a distributed system, the MS is responsible. Existing hando algorithms measure signal parameters such as the received signal strength indication (RSSI), bit-error ratio (BER), and carrier-to-interference ratio (C=I) [5, 6, 9, 11]. These parameters can be used in isolation or in combination to determine when a hando is needed. Most hando algorithms add a hysteresis margin to the parameter of interest in order to provide hando stability and prevent hando waing between BSs. The e ect of hysteresis on the received signal strength measured at a MS is illustrated in Fig. 1. The continuous lines show the pathloss slopes for BS1 and BS2 . These slopes show that in the absence of hysteresis the hando would take place at point A. The addition of a hysteresis margin H shifts the signal cross point from A to B, thus ensuring that when a hando decision is made the signal from the new, target BS is de nitely stronger than that from the current BS. This, however, comes at the price of a delayed hando . 2. Statement of the problem and proposed solutions In cellular communications the transmitted signal received at the MS (or BS) may be modeled as
(2)
The distribution of s(n) is Gaussian with an average value and standard deviation . The standard deviation varies in the range between 5 and 20 dB, while the average is dependent on the distance d, in meters, between the base and mobile stations as follows: (d) = k1 − k2 log(d);
(3)
where k1 depends on the transmitted power and k2 varies in the range 20 – 60. Thus, the received line-ofsight (LOS) signal consists of a deterministic and as well 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 is strong, when the MS is close to the BS and weak when it is far away. Although the spatial signal will obey Eq. (3), it will contain some measure of uncertainty because of the random component included. The problem is further exacerbated under the non-line-of-sight (NLOS) condition because of the imposition of the corner e ect phenomenon. The primary function of a hando algorithm is to make an estimate of the deterministic signal component – which is used for making the hando decision. Indeed, a major criterion for the hando algorithm is that it must be capable of making a decision in a region of uncertainty. Conventional hando algorithms use averaging techniques to nullify the e ect of the random component. Many of these algorithms add a hysteresis margin to the average in order to provide stability. It is felt that these algorithms (and there is a delay in moving averages) will be too slow for microcellular condition and, in particular, the microcellular corner e ect and so new and better algorithms must be developed. This paper proposes a couple of fuzzy-based hando algorithms
G. Edwards et al. / Fuzzy Sets and Systems 110 (2000) 379–388
because of fuzzy logic’s inherent strength in solving problems exhibiting uncertainty [3, 4, 13], and the fact that many of the terms used above for describing the signal, e.g., strong, close, weak, far are fuzzy in nature. The high call volume anticipated over future cellular network will over-load the MSC if a centralized control is used, thus the work proposed in this paper is in support of a distributed system. This judgment is based on practical argument and has nothing to do with the application of fuzzy. The fuzzy algorithms will monitor the trend in the received signals (RSSI) from the current and target BSs, and use fuzzy logic techniques to determine when a hando is needed. The fuzzy algorithms are labeled as I and II. 2.1. Fuzzy algorithm I In algorithm I, the hando mechanism is accomplished in two stages. It uses an adaptive fuzzy predictor in its front-end (or rst-stage) to predict the next incoming signal samples from the BSs under consideration. The fuzzy predictor uses the past signal history to predict a future value. The structure for the adaptive fuzzy predictor is shown in Fig. 2, and like its classical counterpart, it attempts to minimize in some sense the error signal that is the di erence between the true and estimated signals. Thus, assuming the time series for the RSSI signal to be {x(n)}, where n ∈ {1; 2; 3; : : :}, then for a one-stage look ahead predictor, the problem can be stated as follows: given x(n−N +1); x(n−N +2); : : : ; x(n), determine x(n+1). In this example, the past N samples are used to compute the next (future) sample. Since a fuzzy controller works with fuzzy sets and rules, the rst step towards a solution is to establish fuzzy sets over the universe of discourse for each of the N inputs and the output. This step is followed by the development of appropriate fuzzy rules to span the input=output fuzzy space. This can be expedited by forming n, N -input=output pairs 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)]:
381
Fig. 2. Adaptive fuzzy predictor.
By using an appropriate training algorithm such as orthogonal least-squares learning, table-lookup scheme, nearest-neighborhood cluster, recursive mean square, or least-mean-square techniques, etc., the fuzzy rules can be established [12]. The fuzzy rules will be in terms of If–Then propositions as follows: R(1) : IF x1 is O11 and : : : and xN is ON1 ; THEN xN +1 is P 1 ; (2) R : IF x1 is O12 and : : : and xN is ON2 ; THEN xN +1 is P 2 ; .. .
R(k) : IF x1 is O1k and : : : and xN is ONk ; THEN xN +1 is P k ; where Oil and P l 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 output linguistic variables for the fuzzy system. In this research, the ANDing (intersection) of the membership functions 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 and target base stations RSSIs are computed for the present and future time instants. The two di erence signals for times t and t + 1 are fed to the back-end (or second fuzzy stage) of algorithm I. The output of the second fuzzy stage is a crisp value that indicates the degree to which a hando from the current to the target BS is desirable. Thus, a threshold value can be set and whenever this value is exceeded a hando command is issued.
382
G. Edwards et al. / Fuzzy Sets and Systems 110 (2000) 379–388
sense logic can be easily expedited using fuzzy techniques. The actual averaging function is continuous, which is good since it ensures graceful performance characteristics. 3. Benchmark algorithms Fig. 3. Fuzzy block diagram.
The block diagram for each fuzzy stage appears as in Fig. 3. The input and output of the fuzzy system are x ∈ RN and y ∈ R, respectively. Information to the fuzzy system rst enters the Fuzzi er, where it is fuzzi ed. The fuzzi ed data is passed to the inference engine. The inference engine matches the fuzzi ed data against a set of fuzzy rules using fuzzy techniques to produce output fuzzy sets. The output fuzzy sets are then passed to the defuzzi er which computes a crisp output value by the centroid algorithm [12]. 2.2. Fuzzy algorithm II In fuzzy algorithm II, a fuzzy averaging technique is used to determine hando . This fuzzy algorithm performs a short-time average (to borrow a term from conventional signal processing algorithm) on the difference signal l between the current and target BSs. A hando is issued whenever the average of the di erence signal l exceeds the bounds of what is considered acceptable too often. Unlike algorithm I, which uses the future signal value (based on the past) to make a hando decision, algorithm II keeps a running fuzzy average of the past. In this way, it keeps track of the signal trend based on the past and uses this information to make a hando decision. This approach is similar to the ranging algorithms in [2, 8]. In algorithm II, l is considered to take on the heuristic values of being acceptable, unacceptable or any combination of gray area in between. This algorithm thus makes a hando to the target BS whenever the average of the di erence signal violates the belief of what is considered acceptable more often than not. In a practical sense it means, if the di erence signal keeps turning up in favor of the target BS being the better base for communication, then the natural thing to do is to switch to it. This kind of common
Hando is based on the BS’s RSSI, measured in dBm. The fuzzy hando algorithms were tested and compared to conventional hando algorithms, which act as benchmarks. Two benchmark algorithms based on signal averaging (Algorithm a) and signal averaging with hysteresis (Algorithm b) were used for performance comparison. The algorithms are described below: Algorithm a: signal averaging This algorithm computes average RSSI values for the current and target BSs, i and j, respectively. The hando decision is made as follows: if yi (n)¿yj (n); choose BSi otherwise choose BSj ;
(5)
where, 1 y(n) = N
n X
s(k);
k = n−N +1
N is the size of the averaging window and s(k) is the RSSI 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 hysteresis In this algorithm, along with the averaging technique mentioned above, a hysteresis margin H is added to the current BS’s signal. Given the scenario where the current and target BSs are i and j, respectively 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 chosen from the set {2, 5}.
G. Edwards et al. / Fuzzy Sets and Systems 110 (2000) 379–388
4. Fuzzy sets and rules The algorithms were tested using two di erent signal models in order to test for robustness. This allows us to examine the strengths and weaknesses of each algorithm under various environmental conditions. The signal models were taken from popular ones in the literature. The models are labeled A and B and are attributed to [1, 6], respectively. The signals generated using the two models are shown in Figs. 4 and 5, respectively. Fuzzy sets and rules were established based on these signals. 4.1. Description of fuzzy algorithm I In algorithm I, the input variable to the fuzzy predictor is the measured RSSI, while the output from it is the predicted value for the next incoming signal. The input (output) universe of discourse on which the fuzzy sets were de ned for the linguistic variable, RSSI is given below. The fuzzy sets take on the linguistic values weak, medium, and strong (referring to the strength of the signal) and are represented below by membership functions A1 , A2 and A3 , respectively, over the interval [−90,−20] dBm. if x6− 80; 1 A1 (x) = (−45 − x)=35 if − 80 ¡ x ¡− 45; 0 if x ¿− 45; 0 if x6− 80; (x + 80)=35 if − 80 ¡ x ¡− 45; A2 (x) = (−30 − x)=15 if − 45 ¡ x ¡− 30; 0 if x ¿− 30; if x 6− 45; 0 if − 45 ¡ x ¡− 30; A3 (x) = (x + 45)=15 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 erence signals l between the current and the target BSs – computed at time t (current time) and t + 1 (predicted one time slice ahead) – form the input. The signals can be written more compactly as lt and lt+1 , respectively. The universes lt and lt+1 are similar
383
and the fuzzy sets de ned on them are shown in Fig. 6. The inputs on lt and lt+1 are linked by fuzzy implications to the output hando factor. The fuzzy sets for the hando factor are shown in Fig. 7. The fuzzy rules that link the input sets to the output sets are as follows: lF lt is neg and l t+1 is neg THEN hando factor is high. lF lt is neg and l t+1 is az THEN hando factor is med. lFlt is neg and l t+1 is pos THEN hando factor is low. lF lt is az and l t+1 is neg THEN hando factor is high. lF lt is az and l t+1 is az THEN hando factor is med. lF lt is az and l t+1 is pos THEN hando factor is low. lF lt is pos and l t+1 is neg THEN hando factor is high. lF lt is pos and l t+1 is az THEN hando factor is med. lF lt is pos and l t+1 is pos THEN hando factor is low. The crisp hando factor computed after defuzzi cation is used to determine when a hando is required as follows: if hando factor ¿ 0:87; then hando otherwise do nothing: (7) lt should be noted in Fig. 6, that the universe of discourse is truncated, i.e., it ranges between [−7,7] dB. This was done consciously to avoid the time penalty involved since the algorithm would need to perform two sets of fuzzi cation and defuzzi cation routines, thus in cases where a hando is improbable the second stage of the algorithm is bypassed. 4.2. Description of fuzzy algorithm II ln the case of fuzzy algorithm II, the hando is again based on the di erence signal. ln this algorithm the di erence signal is considered to be acceptable (A) or unacceptable (U ) or shades of area in between. These fuzzy sets are shown in Fig. 8. The fuzzy algorithm tracks the di erence signal in an averaging manner. Once the average exceeds a level of what is considered
384
G. Edwards et al. / Fuzzy Sets and Systems 110 (2000) 379–388
Fig. 4. Model A signal.
Fig. 5. Model B signal.
G. Edwards et al. / Fuzzy Sets and Systems 110 (2000) 379–388
385
Table 1 MSE (root-MSE) for fuzzy and Wiener lter
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 computed as follows:
Algorithm
Model A
Model B
Fuzzy Wiener lter
1.04 (1.02) 6.22 (2.49)
25.92 (5.09) 50.28 (7.09)
For the performance comparisons of the adaptive fuzzy predictor with the classical adaptive predictor, the future signal value is predicted based on one past sample. The justi cation for a rst-order predictor can be found in [6, 7]. The predictive capability of the fuzzy predictor was compared to that of the adaptive Wiener lter by performing prediction tests on signals A and B. The MSE (and root-MSE) for the fuzzy predictor and adaptive Wiener lter is shown in Table 1. The mean-square error is de ned as follows: |S|
1 X (xi − xˆ i )2 ; MSE = |S|
(9)
i=1
5. Performance results
where xi and xˆ i are the actual and estimated RSSl values, respectively, at time i, and |S| is the sample size. The results in Table 1 show that the fuzzy predictor produced a smaller MSE based on our experimental data. This provided the justi cation for the use of a fuzzy predictor in the rst stage of fuzzy algorithm I. Fig. 9 shows that the actual and the fuzzy predicted signals for the model A signal pro le. The fuzzy predicted signal is seen to track the actual signal very closely.
5.1. Justi cation for fuzzy predictor
5.2. Hando results
A classical linear adaptive predictor can be represented by a similar block diagram to that shown for the adaptive fuzzy predictor in Fig. 2. The basic goal of any predictor is to minimize the mean-square error (MSE) of its output, en . lf one considers the block diagram in Fig. 2 for a moment to represent an adaptive Wiener lter, then its predictive algorithm may be summarized PNas follows [10]: 1. xˆ n = − i=1 ai (n)xn−i , 2. en = xn − xˆ n , 3. ai (n +1)= ai (n)−2en xn−i for 16i6K, where is the adaptation coecient.
Tables 2 and 3 show the performance of each algorithm relative to signal models A and B, respectively. For this study, the performance criteria were based mainly on the stability of the hando algorithm. An initiated hando should be stable and not produce a situation whereby the call is passed back and forth between two base stations. ln addition, we investigated the timeliness of the hando response (delay) based on the signal pro le. The tables show which BS is connected to the MS as it travels from BS1 to BS2 . The values (in brackets) represent displacement intervals in meter followed by the communicating BS number.
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 erence signal in the fuzzy sets, unacceptable and acceptable, respectively. This algorithm determines that a hando is necessary whenever the average exceeds a threshold of 3.0.
386
G. Edwards et al. / Fuzzy Sets and Systems 110 (2000) 379–388
Fig. 8. Fuzzy sets for Acceptable and Unacceptable.
Fig. 9. Actual and predicted signal.
Table 2 Hando performance under condition of model A Algorithm
[lnterval in m] attached BS
Fuzzy algorithm I Fuzzy algorithm II Algorithm a (N = 5) Algorithm b (N = 5; H = 2) Algorithm b (N = 5; H = 5) Algorithm a (N = 10) Algorithm b (N = 10; H = 2) Algorithm b (N = 10; H = 5)
[0, 175] 1, [175.5, 305.5] 2, [306, 343.5] 1, [344, 500] [0, 172] 1, [172.5, 273] 2, [273.5, 337] 1, [337.5, 500] [0, 168] 1, [168.5, 251] 2, [251.5, 333.5] 1, [334, 500] [0, 171.5] 1, [172, 293.5] 2, [294, 337] 1, [337.5, 500] [0, 177.5] 1, [176, 306.5] 2, [307, 344.5] 1, [345, 500] [0, 169.5] 1, [170, 252] 2, [252.5, 334.5] 1, [335, 500] [0, 172.5] 1, [173, 295] 2, [295.5, 338] 1, [338.5, 500] [0, 177] 1, [177.5, 307.5] 2, [308, 345.5] 1, [346, 500]
2 2 2 2 2 2 2 2
G. Edwards et al. / Fuzzy Sets and Systems 110 (2000) 379–388
387
Table 3 Hando performance under condition of model B Algorithm
[lnterval in m] attached BS
Fuzzy algorithm I Fuzzy algorithm II Algorithm a (N = 5)
[0, 357] 1, [359, 700] 2 [0, 361] 1, [363, 700] 2 [0, 317] 1, [319, 325] 2, [327, 353] 1, [355, 383] 2, [385, 391] 1, [393, 700] 2 [0, 319] 1, [321, 327] 2, [329, 361] 1, [363, 700] 2 [0, 377] 1, [379, 700] 2 [0, 359] 1, [361, 700] 2 [0, 365] 1, [367, 700] 2 [0, 407] 1, [409, 700] 2
Algorithm Algorithm Algorithm Algorithm Algorithm
b b a b b
(N = 5; H = 2) (N = 5; H = 5) (N = 10) (N = 10; H = 2) (N = 10; H = 5)
6. Discussion and conclusion The performances of two new hando algorithms using fuzzy logic were investigated in a microcellular setting. Two popular signal models were used in the simulation in order to examine the robustness of the fuzzy algorithms under di erent signal conditions. Table 1 shows the fuzzy predictor performed better than the classical predictor and so a decision was made in 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 signal strength for BS2 is superior to that of BS1 , while the reverse occurs over the interval [250, 330] m. Table 2 shows that both fuzzy algorithms respond appropriately and that the hando s were made in the proper regions. Hando s for the classical methods (benchmark algorithms) were also proper. ln the case of model B, the signal values change abruptly and there is also no localized region within the proper coverage of BS1 where the signal from BS2 appears stronger or vice versa. Thus, one would expect that a hando should occur somewhere in the middle between the two cells. Table 3 shows that the fuzzy algorithms again behave appropriately, with hando s occurring in the region of the cell boundary. Both algorithms – algorithm a with N = 5 samples and algorithm b with N = 5 samples and H = 2 dB – performed poorly, and produced signal waing, i.e., the MS was unnecessarily handed o back and forth between the two BSs. This is a setback for the classical approach since its best hope for coping with the fast response 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 experiments show the algorithm could become unstable under some signaling conditions. The algorithm b with N = 10 samples and H = 2 dB produced a marginal to late hando , while the same algorithm with N = 10 samples H = 5 dB de nitely produced a late hando . The fuzzy algorithms were seen to be very robust and provide appropriate hando response under the di erent signaling environment. Future work will examine the proposed hando algorithms under the Manhattan corner e ect condition. Here, the algorithm a with N = 10 samples which had performed well in the LOS experiments is not expected to do well because of the inherent delay using so many samples. ln closing, the second fuzzy algorithm is recommended because of its computational simplicity.
References [1] N. Amitay, Modeling and computer simulation of wave propagation in lineal line-of-sight microcells, lEEE Trans. Vehicular Technol. 41 (4) (1992) 337–342. [2] J. Brown, G. Klir, Range tests made fuzzy, lEEE lnternat. Conf. on Fuzzy Systems, San Francisco, CA, February 1993, pp. 1214 –1219. [3] D. Brubaker, Fuzzy-logic system solves control problem, EDN Magazine, June 1992, pp. 121–127. [4] E. Cox, Adaptive fuzzy systems, lEEE Spectrum 30 (2) (1993) 27–31. [5] O. Grimlund, B. Gudmundson, Hando strategies in microcellular systems, Proc. lEEE Vehicular Technology Conf., May 1991, pp. 505–510.
388
G. Edwards et al. / Fuzzy Sets and Systems 110 (2000) 379–388
[6] M. Gudmundson, Analysis of handover algorithms, Proc. lEEE Vehicular Technology Conference, May 1991, pp. 537–542. [7] V. Kapoor, G. Edwards, R. Sankar, Hando criteria for personal communication networks, Proc. ICC, New Orleans, May 1994, Vol. 3, pp. 1297–1301. [8] G. Klir, B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice-Hall, Englewood Cli s, NJ, 1995. [9] W. Lee, Mobile Cellular Telecommunications Systems, McGraw-Hill, New York, 1989.
[10] S.J. Orfandis, Optimum Signal Processing: An lntroduction, 2nd ed., McGraw-Hill, New York, 1988. [11] R. Vijayan, J. Holtzman, Analysis of hando algorithms using non-stationary signal strength measurements, Proc. lEEE Globecom, December 1992, pp. 1405–1409. [12] L. Wang, Adaptive Fuzzy Systems and Control, PrenticeHall, Englewood Cli s, NJ, 1994. [13] L. Zadeh, Fuzzy logic, lEEE J. Comput. 21 (1988) 83–93.
www.elsevier.com/locate/fss
Fuzzy hando algorithms for wireless communication George Edwards a; ∗ , Abraham Kandel b , Ravi Sankar c a Electrical
Engineering Department, University of Denver, 2390 South York Street, Denver, CO 80208, USA b Computer Science and Engineering Department, University of South Florida, 4202 East Fowler Avenue, ENB 118 Tampa, FL 33620, USA c Department 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 to microcells will increase the number of hando s, and require faster hando algorithms – in terms of decision making. In the case of line-of-sight transmission, it is important that the hando algorithm detects the cell boundary early enough, otherwise this will lead to channel dragging into the new cell subsequently increasing the chance of co-channel interference. In the case of non-line-of-sight transmission, a mobile station on turning a street corner will experience a phenomenon known as the Manhattan corner e ect that causes the received signal level to drop by 20 –30 dB in 20 –30 m. This corner e ect problem can lead to a loss of communication if not identi ed early enough. This paper presents two new hando techniques using fuzzy logic as possible solutions to microcellular hando . The rst algorithm uses an adaptive fuzzy predictor, while the second uses a fuzzy averaging technique. The results of the simulation show that fuzzy is a viable option for microcellular c 2000 Elsevier Science B.V. All rights reserved. hando .
1. Introduction The current trend of exponential growth in the use of personal communication services is causing the industry to examine ways to use the available bandwidth more eciently. Natural solutions to bandwidth eciency include using more ecient modulation techniques as well as better coding algorithms. But these changes will not be sucient and there will be a need to reduce the cell dimension in third generation ∗ Corresponding author. Tel.: +1303 871 4252; fax: +1303 871 4450. E-mail address: [email protected] (G. Edwards)
systems. This will be necessary particularly in urban areas where future systems must be capable of handling trac that far exceeds today’s peak load. The dimension of the reduced microcell is expected to be on the order of a few hundred meters, a large step down from today’s macrocells that are on the order of several kilometers. A key function in cellular communications is hando . Hando is the process whereby a mobile station (MS) switches channels or both channel and base station (BS) in order to continue communication because of degradation in the received signal [5, 9]. In the former the MS switches to another channel in the same BS, while, in the latter the MS switches to a new
c 2000 Elsevier Science B.V. All rights reserved. 0165-0114/00/$ - see front matter PII: S 0 1 6 5 - 0 1 1 4 ( 9 8 ) 0 0 0 9 4 - 3
380
G. Edwards et al. / Fuzzy Sets and Systems 110 (2000) 379–388
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 assumed to be removed by ltering at the receiver. Since m(t) is lognormally distributed, it is preferable to examine the sampled signal in dB (or dBm) which can be represented as: s(n) = 20 log(m(nT )): Fig. 1. The e ect of hysteresis.
BS because it has crossed a cell boundary. Hando control in cellular communication may be centralized or distributed. In a centralized hando system the Mobile Switching Center (MSC) – which is connected to the BSs and supervises the network – is responsible for making the hando decision, while in a distributed system, the MS is responsible. Existing hando algorithms measure signal parameters such as the received signal strength indication (RSSI), bit-error ratio (BER), and carrier-to-interference ratio (C=I) [5, 6, 9, 11]. These parameters can be used in isolation or in combination to determine when a hando is needed. Most hando algorithms add a hysteresis margin to the parameter of interest in order to provide hando stability and prevent hando waing between BSs. The e ect of hysteresis on the received signal strength measured at a MS is illustrated in Fig. 1. The continuous lines show the pathloss slopes for BS1 and BS2 . These slopes show that in the absence of hysteresis the hando would take place at point A. The addition of a hysteresis margin H shifts the signal cross point from A to B, thus ensuring that when a hando decision is made the signal from the new, target BS is de nitely stronger than that from the current BS. This, however, comes at the price of a delayed hando . 2. Statement of the problem and proposed solutions In cellular communications the transmitted signal received at the MS (or BS) may be modeled as
(2)
The distribution of s(n) is Gaussian with an average value and standard deviation . The standard deviation varies in the range between 5 and 20 dB, while the average is dependent on the distance d, in meters, between the base and mobile stations as follows: (d) = k1 − k2 log(d);
(3)
where k1 depends on the transmitted power and k2 varies in the range 20 – 60. Thus, the received line-ofsight (LOS) signal consists of a deterministic and as well 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 is strong, when the MS is close to the BS and weak when it is far away. Although the spatial signal will obey Eq. (3), it will contain some measure of uncertainty because of the random component included. The problem is further exacerbated under the non-line-of-sight (NLOS) condition because of the imposition of the corner e ect phenomenon. The primary function of a hando algorithm is to make an estimate of the deterministic signal component – which is used for making the hando decision. Indeed, a major criterion for the hando algorithm is that it must be capable of making a decision in a region of uncertainty. Conventional hando algorithms use averaging techniques to nullify the e ect of the random component. Many of these algorithms add a hysteresis margin to the average in order to provide stability. It is felt that these algorithms (and there is a delay in moving averages) will be too slow for microcellular condition and, in particular, the microcellular corner e ect and so new and better algorithms must be developed. This paper proposes a couple of fuzzy-based hando algorithms
G. Edwards et al. / Fuzzy Sets and Systems 110 (2000) 379–388
because of fuzzy logic’s inherent strength in solving problems exhibiting uncertainty [3, 4, 13], and the fact that many of the terms used above for describing the signal, e.g., strong, close, weak, far are fuzzy in nature. The high call volume anticipated over future cellular network will over-load the MSC if a centralized control is used, thus the work proposed in this paper is in support of a distributed system. This judgment is based on practical argument and has nothing to do with the application of fuzzy. The fuzzy algorithms will monitor the trend in the received signals (RSSI) from the current and target BSs, and use fuzzy logic techniques to determine when a hando is needed. The fuzzy algorithms are labeled as I and II. 2.1. Fuzzy algorithm I In algorithm I, the hando mechanism is accomplished in two stages. It uses an adaptive fuzzy predictor in its front-end (or rst-stage) to predict the next incoming signal samples from the BSs under consideration. The fuzzy predictor uses the past signal history to predict a future value. The structure for the adaptive fuzzy predictor is shown in Fig. 2, and like its classical counterpart, it attempts to minimize in some sense the error signal that is the di erence between the true and estimated signals. Thus, assuming the time series for the RSSI signal to be {x(n)}, where n ∈ {1; 2; 3; : : :}, then for a one-stage look ahead predictor, the problem can be stated as follows: given x(n−N +1); x(n−N +2); : : : ; x(n), determine x(n+1). In this example, the past N samples are used to compute the next (future) sample. Since a fuzzy controller works with fuzzy sets and rules, the rst step towards a solution is to establish fuzzy sets over the universe of discourse for each of the N inputs and the output. This step is followed by the development of appropriate fuzzy rules to span the input=output fuzzy space. This can be expedited by forming n, N -input=output pairs 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)]:
381
Fig. 2. Adaptive fuzzy predictor.
By using an appropriate training algorithm such as orthogonal least-squares learning, table-lookup scheme, nearest-neighborhood cluster, recursive mean square, or least-mean-square techniques, etc., the fuzzy rules can be established [12]. The fuzzy rules will be in terms of If–Then propositions as follows: R(1) : IF x1 is O11 and : : : and xN is ON1 ; THEN xN +1 is P 1 ; (2) R : IF x1 is O12 and : : : and xN is ON2 ; THEN xN +1 is P 2 ; .. .
R(k) : IF x1 is O1k and : : : and xN is ONk ; THEN xN +1 is P k ; where Oil and P l 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 output linguistic variables for the fuzzy system. In this research, the ANDing (intersection) of the membership functions 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 and target base stations RSSIs are computed for the present and future time instants. The two di erence signals for times t and t + 1 are fed to the back-end (or second fuzzy stage) of algorithm I. The output of the second fuzzy stage is a crisp value that indicates the degree to which a hando from the current to the target BS is desirable. Thus, a threshold value can be set and whenever this value is exceeded a hando command is issued.
382
G. Edwards et al. / Fuzzy Sets and Systems 110 (2000) 379–388
sense logic can be easily expedited using fuzzy techniques. The actual averaging function is continuous, which is good since it ensures graceful performance characteristics. 3. Benchmark algorithms Fig. 3. Fuzzy block diagram.
The block diagram for each fuzzy stage appears as in Fig. 3. The input and output of the fuzzy system are x ∈ RN and y ∈ R, respectively. Information to the fuzzy system rst enters the Fuzzi er, where it is fuzzi ed. The fuzzi ed data is passed to the inference engine. The inference engine matches the fuzzi ed data against a set of fuzzy rules using fuzzy techniques to produce output fuzzy sets. The output fuzzy sets are then passed to the defuzzi er which computes a crisp output value by the centroid algorithm [12]. 2.2. Fuzzy algorithm II In fuzzy algorithm II, a fuzzy averaging technique is used to determine hando . This fuzzy algorithm performs a short-time average (to borrow a term from conventional signal processing algorithm) on the difference signal l between the current and target BSs. A hando is issued whenever the average of the di erence signal l exceeds the bounds of what is considered acceptable too often. Unlike algorithm I, which uses the future signal value (based on the past) to make a hando decision, algorithm II keeps a running fuzzy average of the past. In this way, it keeps track of the signal trend based on the past and uses this information to make a hando decision. This approach is similar to the ranging algorithms in [2, 8]. In algorithm II, l is considered to take on the heuristic values of being acceptable, unacceptable or any combination of gray area in between. This algorithm thus makes a hando to the target BS whenever the average of the di erence signal violates the belief of what is considered acceptable more often than not. In a practical sense it means, if the di erence signal keeps turning up in favor of the target BS being the better base for communication, then the natural thing to do is to switch to it. This kind of common
Hando is based on the BS’s RSSI, measured in dBm. The fuzzy hando algorithms were tested and compared to conventional hando algorithms, which act as benchmarks. Two benchmark algorithms based on signal averaging (Algorithm a) and signal averaging with hysteresis (Algorithm b) were used for performance comparison. The algorithms are described below: Algorithm a: signal averaging This algorithm computes average RSSI values for the current and target BSs, i and j, respectively. The hando decision is made as follows: if yi (n)¿yj (n); choose BSi otherwise choose BSj ;
(5)
where, 1 y(n) = N
n X
s(k);
k = n−N +1
N is the size of the averaging window and s(k) is the RSSI 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 hysteresis In this algorithm, along with the averaging technique mentioned above, a hysteresis margin H is added to the current BS’s signal. Given the scenario where the current and target BSs are i and j, respectively 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 chosen from the set {2, 5}.
G. Edwards et al. / Fuzzy Sets and Systems 110 (2000) 379–388
4. Fuzzy sets and rules The algorithms were tested using two di erent signal models in order to test for robustness. This allows us to examine the strengths and weaknesses of each algorithm under various environmental conditions. The signal models were taken from popular ones in the literature. The models are labeled A and B and are attributed to [1, 6], respectively. The signals generated using the two models are shown in Figs. 4 and 5, respectively. Fuzzy sets and rules were established based on these signals. 4.1. Description of fuzzy algorithm I In algorithm I, the input variable to the fuzzy predictor is the measured RSSI, while the output from it is the predicted value for the next incoming signal. The input (output) universe of discourse on which the fuzzy sets were de ned for the linguistic variable, RSSI is given below. The fuzzy sets take on the linguistic values weak, medium, and strong (referring to the strength of the signal) and are represented below by membership functions A1 , A2 and A3 , respectively, over the interval [−90,−20] dBm. if x6− 80; 1 A1 (x) = (−45 − x)=35 if − 80 ¡ x ¡− 45; 0 if x ¿− 45; 0 if x6− 80; (x + 80)=35 if − 80 ¡ x ¡− 45; A2 (x) = (−30 − x)=15 if − 45 ¡ x ¡− 30; 0 if x ¿− 30; if x 6− 45; 0 if − 45 ¡ x ¡− 30; A3 (x) = (x + 45)=15 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 erence signals l between the current and the target BSs – computed at time t (current time) and t + 1 (predicted one time slice ahead) – form the input. The signals can be written more compactly as lt and lt+1 , respectively. The universes lt and lt+1 are similar
383
and the fuzzy sets de ned on them are shown in Fig. 6. The inputs on lt and lt+1 are linked by fuzzy implications to the output hando factor. The fuzzy sets for the hando factor are shown in Fig. 7. The fuzzy rules that link the input sets to the output sets are as follows: lF lt is neg and l t+1 is neg THEN hando factor is high. lF lt is neg and l t+1 is az THEN hando factor is med. lFlt is neg and l t+1 is pos THEN hando factor is low. lF lt is az and l t+1 is neg THEN hando factor is high. lF lt is az and l t+1 is az THEN hando factor is med. lF lt is az and l t+1 is pos THEN hando factor is low. lF lt is pos and l t+1 is neg THEN hando factor is high. lF lt is pos and l t+1 is az THEN hando factor is med. lF lt is pos and l t+1 is pos THEN hando factor is low. The crisp hando factor computed after defuzzi cation is used to determine when a hando is required as follows: if hando factor ¿ 0:87; then hando otherwise do nothing: (7) lt should be noted in Fig. 6, that the universe of discourse is truncated, i.e., it ranges between [−7,7] dB. This was done consciously to avoid the time penalty involved since the algorithm would need to perform two sets of fuzzi cation and defuzzi cation routines, thus in cases where a hando is improbable the second stage of the algorithm is bypassed. 4.2. Description of fuzzy algorithm II ln the case of fuzzy algorithm II, the hando is again based on the di erence signal. ln this algorithm the di erence signal is considered to be acceptable (A) or unacceptable (U ) or shades of area in between. These fuzzy sets are shown in Fig. 8. The fuzzy algorithm tracks the di erence signal in an averaging manner. Once the average exceeds a level of what is considered
384
G. Edwards et al. / Fuzzy Sets and Systems 110 (2000) 379–388
Fig. 4. Model A signal.
Fig. 5. Model B signal.
G. Edwards et al. / Fuzzy Sets and Systems 110 (2000) 379–388
385
Table 1 MSE (root-MSE) for fuzzy and Wiener lter
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 computed as follows:
Algorithm
Model A
Model B
Fuzzy Wiener lter
1.04 (1.02) 6.22 (2.49)
25.92 (5.09) 50.28 (7.09)
For the performance comparisons of the adaptive fuzzy predictor with the classical adaptive predictor, the future signal value is predicted based on one past sample. The justi cation for a rst-order predictor can be found in [6, 7]. The predictive capability of the fuzzy predictor was compared to that of the adaptive Wiener lter by performing prediction tests on signals A and B. The MSE (and root-MSE) for the fuzzy predictor and adaptive Wiener lter is shown in Table 1. The mean-square error is de ned as follows: |S|
1 X (xi − xˆ i )2 ; MSE = |S|
(9)
i=1
5. Performance results
where xi and xˆ i are the actual and estimated RSSl values, respectively, at time i, and |S| is the sample size. The results in Table 1 show that the fuzzy predictor produced a smaller MSE based on our experimental data. This provided the justi cation for the use of a fuzzy predictor in the rst stage of fuzzy algorithm I. Fig. 9 shows that the actual and the fuzzy predicted signals for the model A signal pro le. The fuzzy predicted signal is seen to track the actual signal very closely.
5.1. Justi cation for fuzzy predictor
5.2. Hando results
A classical linear adaptive predictor can be represented by a similar block diagram to that shown for the adaptive fuzzy predictor in Fig. 2. The basic goal of any predictor is to minimize the mean-square error (MSE) of its output, en . lf one considers the block diagram in Fig. 2 for a moment to represent an adaptive Wiener lter, then its predictive algorithm may be summarized PNas follows [10]: 1. xˆ n = − i=1 ai (n)xn−i , 2. en = xn − xˆ n , 3. ai (n +1)= ai (n)−2en xn−i for 16i6K, where is the adaptation coecient.
Tables 2 and 3 show the performance of each algorithm relative to signal models A and B, respectively. For this study, the performance criteria were based mainly on the stability of the hando algorithm. An initiated hando should be stable and not produce a situation whereby the call is passed back and forth between two base stations. ln addition, we investigated the timeliness of the hando response (delay) based on the signal pro le. The tables show which BS is connected to the MS as it travels from BS1 to BS2 . The values (in brackets) represent displacement intervals in meter followed by the communicating BS number.
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 erence signal in the fuzzy sets, unacceptable and acceptable, respectively. This algorithm determines that a hando is necessary whenever the average exceeds a threshold of 3.0.
386
G. Edwards et al. / Fuzzy Sets and Systems 110 (2000) 379–388
Fig. 8. Fuzzy sets for Acceptable and Unacceptable.
Fig. 9. Actual and predicted signal.
Table 2 Hando performance under condition of model A Algorithm
[lnterval in m] attached BS
Fuzzy algorithm I Fuzzy algorithm II Algorithm a (N = 5) Algorithm b (N = 5; H = 2) Algorithm b (N = 5; H = 5) Algorithm a (N = 10) Algorithm b (N = 10; H = 2) Algorithm b (N = 10; H = 5)
[0, 175] 1, [175.5, 305.5] 2, [306, 343.5] 1, [344, 500] [0, 172] 1, [172.5, 273] 2, [273.5, 337] 1, [337.5, 500] [0, 168] 1, [168.5, 251] 2, [251.5, 333.5] 1, [334, 500] [0, 171.5] 1, [172, 293.5] 2, [294, 337] 1, [337.5, 500] [0, 177.5] 1, [176, 306.5] 2, [307, 344.5] 1, [345, 500] [0, 169.5] 1, [170, 252] 2, [252.5, 334.5] 1, [335, 500] [0, 172.5] 1, [173, 295] 2, [295.5, 338] 1, [338.5, 500] [0, 177] 1, [177.5, 307.5] 2, [308, 345.5] 1, [346, 500]
2 2 2 2 2 2 2 2
G. Edwards et al. / Fuzzy Sets and Systems 110 (2000) 379–388
387
Table 3 Hando performance under condition of model B Algorithm
[lnterval in m] attached BS
Fuzzy algorithm I Fuzzy algorithm II Algorithm a (N = 5)
[0, 357] 1, [359, 700] 2 [0, 361] 1, [363, 700] 2 [0, 317] 1, [319, 325] 2, [327, 353] 1, [355, 383] 2, [385, 391] 1, [393, 700] 2 [0, 319] 1, [321, 327] 2, [329, 361] 1, [363, 700] 2 [0, 377] 1, [379, 700] 2 [0, 359] 1, [361, 700] 2 [0, 365] 1, [367, 700] 2 [0, 407] 1, [409, 700] 2
Algorithm Algorithm Algorithm Algorithm Algorithm
b b a b b
(N = 5; H = 2) (N = 5; H = 5) (N = 10) (N = 10; H = 2) (N = 10; H = 5)
6. Discussion and conclusion The performances of two new hando algorithms using fuzzy logic were investigated in a microcellular setting. Two popular signal models were used in the simulation in order to examine the robustness of the fuzzy algorithms under di erent signal conditions. Table 1 shows the fuzzy predictor performed better than the classical predictor and so a decision was made in 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 signal strength for BS2 is superior to that of BS1 , while the reverse occurs over the interval [250, 330] m. Table 2 shows that both fuzzy algorithms respond appropriately and that the hando s were made in the proper regions. Hando s for the classical methods (benchmark algorithms) were also proper. ln the case of model B, the signal values change abruptly and there is also no localized region within the proper coverage of BS1 where the signal from BS2 appears stronger or vice versa. Thus, one would expect that a hando should occur somewhere in the middle between the two cells. Table 3 shows that the fuzzy algorithms again behave appropriately, with hando s occurring in the region of the cell boundary. Both algorithms – algorithm a with N = 5 samples and algorithm b with N = 5 samples and H = 2 dB – performed poorly, and produced signal waing, i.e., the MS was unnecessarily handed o back and forth between the two BSs. This is a setback for the classical approach since its best hope for coping with the fast response 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 experiments show the algorithm could become unstable under some signaling conditions. The algorithm b with N = 10 samples and H = 2 dB produced a marginal to late hando , while the same algorithm with N = 10 samples H = 5 dB de nitely produced a late hando . The fuzzy algorithms were seen to be very robust and provide appropriate hando response under the di erent signaling environment. Future work will examine the proposed hando algorithms under the Manhattan corner e ect condition. Here, the algorithm a with N = 10 samples which had performed well in the LOS experiments is not expected to do well because of the inherent delay using so many samples. ln closing, the second fuzzy algorithm is recommended because of its computational simplicity.
References [1] N. Amitay, Modeling and computer simulation of wave propagation in lineal line-of-sight microcells, lEEE Trans. Vehicular Technol. 41 (4) (1992) 337–342. [2] J. Brown, G. Klir, Range tests made fuzzy, lEEE lnternat. Conf. on Fuzzy Systems, San Francisco, CA, February 1993, pp. 1214 –1219. [3] D. Brubaker, Fuzzy-logic system solves control problem, EDN Magazine, June 1992, pp. 121–127. [4] E. Cox, Adaptive fuzzy systems, lEEE Spectrum 30 (2) (1993) 27–31. [5] O. Grimlund, B. Gudmundson, Hando strategies in microcellular systems, Proc. lEEE Vehicular Technology Conf., May 1991, pp. 505–510.
388
G. Edwards et al. / Fuzzy Sets and Systems 110 (2000) 379–388
[6] M. Gudmundson, Analysis of handover algorithms, Proc. lEEE Vehicular Technology Conference, May 1991, pp. 537–542. [7] V. Kapoor, G. Edwards, R. Sankar, Hando criteria for personal communication networks, Proc. ICC, New Orleans, May 1994, Vol. 3, pp. 1297–1301. [8] G. Klir, B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice-Hall, Englewood Cli s, NJ, 1995. [9] W. Lee, Mobile Cellular Telecommunications Systems, McGraw-Hill, New York, 1989.
[10] S.J. Orfandis, Optimum Signal Processing: An lntroduction, 2nd ed., McGraw-Hill, New York, 1988. [11] R. Vijayan, J. Holtzman, Analysis of hando algorithms using non-stationary signal strength measurements, Proc. lEEE Globecom, December 1992, pp. 1405–1409. [12] L. Wang, Adaptive Fuzzy Systems and Control, PrenticeHall, Englewood Cli s, NJ, 1994. [13] L. Zadeh, Fuzzy logic, lEEE J. Comput. 21 (1988) 83–93.