Suresh Venkatachalaiah, Richard J. Harris and John E. Murphy. School of Electrical and Computer Engineering. Royal Melbourne Institute of Technology.
Improving Handoff in Wireless Networks using Grey and Particle Swarm Optimisation Suresh Venkatachalaiah, Richard J. Harris and John E. Murphy School of Electrical and Computer Engineering Royal Melbourne Institute of Technology GPO Box 2476V, Vic. 3001, Australia {suresh,richard,murphy}@catt.rmit.edu.au ABSTRACT The major goal of wireless communications is to allow a user to access the capabilities of global networks at anytime without the problems of location and mobility.Accuracy in mobility prediction holds the key to such a capability while handing off a call. Handoff is the call handling mechanism invoked when a mobile node moves from one cell to another. The problems associated with handoff can be classifed as handoff latency and unnecessary handoff. There have been many proposals put forward for measurement of received signal strength based on hysteresis. In order to solve handoff problems, a promising technique is to perform mobility prediction. An approach, which is the focus of this paper, involves the use of a Grey model to make handoff decisions. In this paper, we describe the use of the Grey model in combination with fuzzy logic and PSO algorithms. Since prediction error is inevitable, the output from the Grey model can be compensated for by the use of a fuzzy controller and then fine-tuned using Particle Swarm Optimisation (PSO) algorithms. In the past, many papers have discussed reducing the errors by learning constants, which is a very tedious or a lengthy process. The proposed technique minimises the number of handoffs and it is shown to have a very short calculation time and better prediction accuracy compared with hysteresis based decisions. Keywords: - Handoff, Handover, Grey Model, Particle Swarm Optimisation, Moving Average filter. 1. INTRODUCTION The cellular concept was a major break-through in solving the problem of spectral congestion and user capacity many years ago. In a wireless network, packet loss can occur because of handover failure or fading signal strength. To avoid such packet losses, we
should provide handoff capabilities that give better performance with respect to link maintenance and interference. When a mobile node moves into a different cell while on a call, the radio link or the channel is automatically changed to a new link belonging to the new base-station [4][5]. Processing of the handoff algorithm is important to any cellular radio system. As more capacity is needed, a smaller cell size is considered which usually results in more frequent handoffs. There are many handoff algorithms that have been proposed [8][2][13] which generally take account of the bit-error rate and relative signal strength. It is important to decide, for the signal strength based and hysteresis algorithms, that they are not using any momentary fading while the mobile is moving away from the serving base station. Many algorithms that are hysteresis based reduce unnecessary handoff but increase the decision delay time. However, a mobility prediction technique is a promising approach that helps to improve this handoff capability [13][7][10]. In this paper, the technique proposed is a combination of Grey prediction, fuzzy logic [9][11] and Particle Swarm Optimisation[12]. The parameters considered in this paper utilise the RSSI values from the base station. The Grey system was developed in 1982 and was used for systems, which have very little data from which to analyse or predict future data[1]. A Grey system involves known and partially known information. It considers a fully known system as “white”, a system with no information as “black” and a system with partial information as “Grey”. This theory has been widely applied, as it needs only a limited amount of data for the construction of the model. As little as four measurements of the signal strength are required to enable a prediction to be made. As the process needs only minimal data, we have faster computational time and good prediction accuracy. However the technique proposed will compensate for any errors using fuzzy parameters and fine-tune it with a PSO algorithm [12]. Section 2 will discuss the
construction of the Grey prediction model. Section 3 discusses the simplified fuzzy reasoning; Section 4 discusses the comparisons between a moving average filter [6]; Section 5 discusses on Particle Swarm Optimisation; Section 6 discusses a simulation model; Section 7 discusses on Simulation Parameters; Section 8 discusses on results and the final section presents out the conclusions. 2. GREY MODEL In this theory [1][10], the model uses a sequence of raw data values that are generated by the system. The approach is to convert the raw data into a series of meaningful data values, which is done by the accumulating generating operation (AGO) that is a key feature of Grey system theory. The accumulated generating operation is carried out in the following way to create a new series. Let the sum of the first and second element in the raw data be the second element of the new series. Let the first, second and third element be the third element of the new series and so on. The derived new series is called the Onetime accumulated generating series of the original series. Its mathematical relations are presented in Eqs. (1) − (4). Let the original series be X (0) = {X (0) (0), X (0) (1), · · · · · · , X (0) (n)}
(1)
which represent the measurements of the received signal strengths of the given system, Then the onetime accumulated generating series is X (1) = {X (0) (0), X (1) (1), · · · · · · , X (1) (n)}
(2)
Where, X
(1)
(k) =
k X
X (0) (i) k = 1, 2 · · · n
(3)
i=0
The superscript of (1) in Eq. (3) in X (1) (k) represents the onetime AGO which is denoted as 1-AGO. If the superscript is (r) then it represents r times AGO and is often denoted as r-AGO. The elements of the r-AGO series are: X (r) (k) =
k X
X (r−1) (i) k = 1, 2 · · · n
(4)
the Grey input. This is a first order differential equation model with one variable, which will be denoted by GM (1, 1). From Eqs.(3) and (5) and the ordinary least squares method, we have h iT a ˆT ≡ a b (6) h a
iT b = (B T B)−1 B T Yn
where B is known as the accumulated data matrix and Yn is a constant vector. B=
£ ¤ − 21 X (1) (1), X (1) (2) , .. . £ ¤ − 12 X (2) (1), X (3) (2) ,
1 .. . 1
£ ¤ − 12 X (1) (r − 1), X (1) (r) ,
1 T
Yn = [X (0) (2), X (0) (3) · · · X (0) (r), ]
(8)
Thus, the initial condition of X (1) (1) = X (0) (1) can be derived. The solution of the equation is given by ³ ´ ˆ (1) (i) = X (0) (1)− b e−a(i−1) + b X a a 3. SIMPLIFIED FUZZY REASONING
(9)
The error from the Grey model is treated as the input to the fuzzy modelling which is compensated for by fuzzy inference rules and Particle Swarm Optimisation. The input is expressed by x1 , x2 , · · · xm and the output is expressed by y, the inference rule of simplified fuzzy reasoning which can be expressed by the following : Rule i: IF x1 is Ai1 and x(m) is Aim THEN y is wi (where i = 1, 2, · · · n) Where, i is a rule number, Ai1 , · · · Aim are the membership functions of the antecedent part, and wi is the real number of the consequent part. The membership function, Ai1 of the antecedent part is expressed by an isosceles triangle. The parameters that determine the triangle are the values of aij and bij shown in Fig. 1. The output of the fuzzy reasoning can be given as
i=0
The purpose of AGO is to reduce the randomness of the series and increase the smoothness of the series. The whitened differential equation model can be expressed as dX (1) (t) + aX (1) (t) = b (5) dt Where a and b are constants to be determined. a is known as the developing coefficient and b is known as
(7)
Aij (xj ) = 1 −
2· | xj − aij | bij
(10)
where (j = 1, 2, · · · m) and i is a rule number. µi = Ai1 (x1 ).Ai2 (x2 ). · · · Aij (xm ).
(11)
Pn i=1 µi .wi y= P n i=1 µi
(12)
of the equation, we can see that the older values xi are weighted by increasing powers of α. The graphs show the weighted moving average and the exponential weighted moving average plotted in Fig. 4. 5. PARTICLE SWARM OPTIMISATION
Figure 1: Membership function µi is the membership function value of the antecedent part. The inference rules are tuned so as to minimise the objective function E that can be expressed by the following E=
1 2 (y − yr ) 2
(13)
where yr is the desirable output data. The objective function E is interpreted as the inference error between the desirable output yr and the output of the fuzzy reasoning scheme y [9].
Vik+1
4. MOVING AVERAGE FILTER Filtering is a procedure used to reduce the noise of a measured signal [6]. There are many different ways to reduce noise, one of them being “Averaging”. Depending on requirements, we use different types of averaging filters, with one of them being a moving average filter which considers all the data points to be equally important. The average at the k th instant is based on the most recent set of n values which is given by ´ 1³ x¯k = x ¯k−1 + xk − x(n−k) (14) n Hence, from the above equation we note that we need to store the values of x(k−n) which require up to n storage locations. On the other hand, the exponential moving average filter places greater importance on more recent data by discounting the older data in an exponential manner. The form of the exponential moving average filter is as follows: x¯k = α¯ xk−1 + (1 − α)xk
Particle swarm optimisation (PSO)[12] is a population based stochastic optimisation technique developed by Dr.Eberhart and Kennedy in 1995 and was inspired by the social behaviour of flocks of birds or schools of fish. PSO learned from a scenario is used to solve optimisation problems. In PSO each single solution is a “bird” in search space and is called a “particle”. PSO is initialised with a group of random particles (solutions) and searches for an optimum by updating generations. In every iteration, each particle is updated by the following two “best” values. The first one is the best solution (fitness) it has achieved so far. The best value is stored. This value is called the pbest. Another “best” value that is tracked by the optimiser is the best value is a global best and called gbest. The particle will have velocities, which direct the flying of the particle. In each generation the velocity and the position of the particle will be updated. The equations for the velocity and the positions are given by equations (16) and (17) respectively.
(15)
The value of the filter constant α monitors the degree of the filtering action. We can also notice that the calculation of x¯k does not require the storage values of x. It can be shown that as we keep increasing the RHS
=
wvik + c1 rand1 × (pbesti − ski ) + c2 rand2 × (gbest − ski ) (16) xki + 1 = xki + vik + 1
(17)
where, vik vik+1 w cj rand1,2 ski pbesti gbest xk+1
velocity of the particle i at iteration k velocity of the particle i at iteration k + 1 inertia weight acceleration coefficients random numbers between 0 and 1 current position of i at iteration k pbest of the particle i gbest of the group position of the particle at iteration k + 1 6. SIMULATION MODEL
In this model, we have selected two base stations A and B, which are separated by D meters. The mobile device moves from one cell to another with a constant velocity and the received signal strength is sampled at a constant distance ds in meters. The model we are considering includes slow fading. The received signal strengths at and bt (in dB) when the mobile is at a given distance are given by at = K1 − K2 log kds + ut
(18)
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The preliminary results of the Grey prediction in Fig. 2 show a plot of the actual values of received signal strength and corresponding predicted values. The Grey model tracks the curve with some error. The Grey model does not predict large variations in the input data. To compare the performance of the Grey prediction model, we have compared it with a moving averages filter and the exponential moving average filter in figure Fig. 4. The moving average filter largely depends on the weights as it averages the value. Large variations in the prediction values are shown in the graph Fig. 3 by plotting the absolute error. However, work has been done to improve the model performance by fuzzy rules and PSO algorithms. The Fuzzy parameters tuned using the self-tuning algorithm [9] works with a learning constant set to the parameters initially, which reduces the error with every iteration. The selftuning algorithm takes a very long time to converge to the minimum value set. On the other hand, PSO works
5
Exponential Moving Average
0
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8. RESULTS
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(19)
2 Straight Path 10 m 2000 m 30 db 0 dB Lognormal fading 8dB
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Number of Base Stations Trajectory Sampling distance Distance between base stations Path loss (K ) Transmitter power Fading Process Standard Deviation (uk )
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Figure 3: The predicted errors from the GM (1, 1) based model 0
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Figure 4: The weighted moving averages with different weights and the exponential weighed moving averages on a searching technique, that initialises a group of particles and takes their best value. Convergence with respect to the self-tuning algorithm is shown in Fig. 5, which clearly shows that PSO fairs much better than the self-tuning algorithm. In the Fig. 6 we have shown the tracking capability of the algorithm where prediction accuracy is greater. 9. CONCLUSIONS In this paper, we have presented a technique for prediction of received signal strength values, which aids in providing efficient handoffs in wireless networks. We have evaluated the Grey model and further work has been done to perform error compensation. To improve prediction accuracy, we take the output and calculate the error between the predicted output and actual output. This would be treated using the fuzzy rules by actually compensating the error and fine-tuning it with a PSO algorithm. Grey prediction uses very little data ( as little as four measurements ) to predict the next sig-
nal strength. Even though the prediction accuracy of the Grey model is accurate it still deviates from accurately predicting values, which have a large variation but our simulation model shows the improvement by using fuzzy inference rules and PSO algorithm. The simulation results show that the model can improve prediction performance. The model uses the PSO algorithm, which is far better than any other search technique that we have tried as it converges faster than other techniques. In future wireless networks, prediction techniques will be increasingly important because handoff will become more frequent in small cells and resources will be limited for various applications.
MSE vs iteration 0.6
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10. ACKNOWLEDGEMENTS Figure 5: The outputs of the PSO and the self-tuning algorithm
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The authors wish to thank Australian Telecommunications Co-operative Research Centre for their financial support. We would also like to thank the people of the CATT Centre and S.M. Guru, Mechatronics Research Group, University of Melbourne for their sugestions. 11. REFERENCES
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[1] J. L. Deng, “Introduction to Grey system theory”, J. Grey Syst., Vol. 1, No. 1, 1989, pp. 1-24.
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[2] Chiu,M.H. and Bassiouni,M.A. “Predictive schemes for handoff prioritisation in cellular networks based on mobile positioning”, IEEE Journal on Selected Areas in Communications, Vol. 18, Issue 3, March 2000, pp. 510-522.
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[4] T.S.Rappaport, “Wireless Communications Principles and practice, 3rd Ed ”, Prentice Hall publication, New Jersey, 1996.
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[5] N. D. Tripathi, J. H. Reed and H. F. VanLandinoham “Handoff in cellular systems”, IEEE Personal Communications, Vol. 5, No. 6, 1996, pp. 26-37.
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[3] Yo-Ping Huang and Sheng-Fang Wang “Identifying the fuzzy grey prediction model by genetic algorithms”, Proceedings of IEEE International Conference on Evolutionary Computation, 1996., 20-22 May 1996, pp. 720-725.
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[6] Janacek, G. and Swift, L., “Time series Forecasting, Simulation, Applications”, Ellis Horwood, Great Britain, 1993.
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Figure 7: A closer look at the prediction accuracy of the model using the PSO algorithm
[7] Sheu, S.T. and Wu, C.C., “Using Grey prediction theory to reduce handoff overhead in cellular communication systems”, “The 11th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, 2000. PIMRC 2000. ”, Vol. 2, No. 6, 2000, pp. 782786.
[8] Shi, Y. and Mizumoto, M., “Soft handoffs in CDMA mobile systems”, “IEEE Personal Communications”, Vol. 4, Issue 6, 1997, pp. 6-17. [9] N. D. Tripathi, J. H. Reed and H. F. VanLandinoham “A learning algorithm for tuning fuzzy inference rules”, Fuzzy Systems Conference Proceedings, 1999. FUZZ-IEEE ’99. 1999 IEEE International, Vol. 1, 1999, pp. 378-382. [10] Jiann-Rong Wu and Ming Ouhyoung, “A 3D tracking experiment on latency and its compensation methods in virtual environments”, Proceedings of the 8th annual ACM symposium on User interface and software technology, Pittsburgh, Pennsylvania, United States, December 15-18, 1995, pp. 41-49, ACM Press.
[11] Nomura, H. and Hayashi, I. and Wakami, N., “A learning method of fuzzy inference rules by descent method”, IEEE International Conference on Fuzzy Systems, 1992., San Diego, CA, USA, 8-12 March 1992, pp. 203-210. [12] James Kennedy,J. and Eberhart R.C., “Swarm Intelligence”,Morgan Kaufmann Publishers, San Francisco, CA,2001. [13] Su, W. and Lee, S. J. and Gerla, M., “Mobility prediction in wireless networks”, MILCOM 2000, 21st Century Military Communications Conference Proceedings, 2000, pp. 491-495.
