Signal-based evaluation of handoff algorithms

790 IEEE COMMUNICATIONS LETTERS, VOL. 9, NO. 9, SEPTEMBER 2005 Signal-Based Evaluation of Handoff Algorithms Malka N. Halgamuge, Student Member, IEEE, Hai Le Vu, Member, IEEE, Kotagiri Ramamohanarao, and Moshe Zukerman, Senior Member, IEEE Abstract— We propose a new framework, based on signal quality, for performance evaluation and comparison between existing handoff algorithms. It includes new call quality measures and an off-line cluster-based computationally-simple heuristic algorithm to find a near optimal handoff sequence used as a benchmark. We then compare existing handoff algorithms and identify the trade-off between signal quality and number of handoffs. Index Terms— Cellular networks, wireless, handoff, handover, performance evaluation, signal quality. I. I NTRODUCTION I NCREASED demand for mobile services has led to a reduction in cell radius and more handoffs. It is therefore of importance to provide telecommunication providers with the right criterion for evaluating handoff algorithms and choosing the one that enables them to meet customers quality of service (QoS) requirements at competitive cost. In this paper, we promote the user signal level as a key criterion for evaluation of handoff algorithms in addition to other handoff evaluation approaches such as delay [1] and call dropping probability [2]. We also introduce an offline heuristic algorithm which obtains a near optimal “best” handoff sequence (BHS) that can be used as a benchmark. We consider the following handoff strategies. • The Threshold method [4] initiates a handoff when (Ss < THO ) ∩ (Sn > Ss ), where Ss is a signal strength of a serving base station, Sn is the highest signal strength among neighboring base stations, THO is a predefined threshold. • The Hysteresis method [3] initiates a handoff when Sn > Ss + H, where H is a given hysteresis threshold. • The Threshold with Hysteresis method [3] is a combination of above two methods. It initiates a handoff when (Ss < THO )∩(Sn ≥ Ss +H). This method is often used in practice with +3 dB hysteresis margin. • Fuzzy Handoff Algorithm (FHA) [5] uses prototypes assigned to each cell to determine the serving base station. II. P ROPOSED M EASURES FOR H ANDOFF E VALUATION Consider a cellular mobile network with M base stations designated B1 , B2 , ...., BM . Define B = {B1 , B2 , ...., BM }. Manuscript received February 3, 2005. The associate editor coordinating the review of this letter and approving it for publication was Prof. CarlaFabiana Chiasserini. This work was supported by the Australian Research Council (ARC). The authors are with the ARC Special Research Center for Ultra-Broadband Information Networks, an affiliated program of National ICT Australia, Department of Electrical and Electronic Engineering, The University of Melbourne, Melbourne, VIC 3010, Australia ([email protected]). Digital Object Identifier 10.1109/LCOMM.2005.09011. Let a sample path l be an arbitrary path in which a mobile user is traveling. Consider a set of paths denoted Θ for the purpose of evaluating handoff algorithms. Sample points are points on the sample path for which the signal strength received from base stations are measured. Let Sij be the signal strength at sample point i received from base station Bj . Define a handoff sequence x or x(l) of sample path l, as a sequence of base stations assigned to the sample points in l, assigning bi ∈ B to the ith sample point, i.e., x =< b1 , b2 , ..., bN > where N is the number of sample points. (Note that bi and bj , ∀i, j may designate the same base station.) For every sample path, define the set of all possible handoff sequences as X = {xi |0 < i ≤ M N }. The number of handoffs γ(x) in a handoff sequence x equals to the number of changes in the base station sequence. For example, the handoff sequence x = {B1 , B1 , B2 , B3 , B3 , B3 } has γ(x) = 2. For a given handoff sequence x ∈ X, define, Si (x) = Sij such that Bj = bi , bi ∈ x. Let Smin be the minimum signal strength below which the signal quality is unacceptable to the user. Let Smax > Smin be the signal strength beyond which the marginal benefit is considered negligible. For a given sample path and its associated handoff sequence, we define the following signal quality measures. 1) Average Received
N Signal Strength (ARSS(x)) is defined by N1 i=1 Si (x). 2) Number of Acceptable Sample Points (N ASP (x)) represents the number of sample points of the handoff sequence with signal strength above Smin . Let Ωx = {i|Si (x) ≥ Smin }, then N ASP (x) = |Ωx |, where |Υ| denotes the number of elements (cardinality) in the set Υ. 3) The concept of Call Quality Signal Level (CQSL(x)) proposed in this paper combines the above two measures and is defined by
Ai (x) − CN (x), (1) CQSL(x) = i∈Ωx |Ωx | where Ai (x) = Si (x) if Si (x) < Smax , otherwise Ai (x) = Smax , and N (x) = (N − |Ωx |) is the number of samples with signal strength lower than Smin , and C is the cost (or the penalty) for an unacceptable
sample point. We assign i∈Ωx Ai (x)/|Ωx | to zero when |Ωx | = 0. Let p be the maximum allowed proportion of sample points with signal quality below Smin , i.e., N (x)/N ≤ p. The p value may be agreed between the service provider and the user. Assuming |Ωx = 0|, the minimum value
that CQSL(x) can take is when (i) N (x)/N = p and (ii) i∈Ωx Ai (x)/|Ωx | = Smin in (1). We choose C such that the above minimum value c 2005 IEEE 1089-7798/05$20.00
HALGAMUGE et al.: SIGNAL-BASED EVALUATION OF HANDOFF ALGORITHMS is greater than or equal to zero. The parameter C in (1) can be bounded as follows:
Ai (x)/|Ωx | Smin = . (2) C ≤ i∈Ωx N (x) pN Here we choose the cost to be linear. However, we could also set it up dynamically to reflect the fact that consecutive unacceptable sample points are worse than a single unacceptable sample point. Using (1) and (2), we obtain
Ai (x) Smin (N − |Ωx |) CQSL(x) ≥ i∈Ωx − . (3) |Ωx | pN The measures ARSS(x), N ASP (x), and CQSL(x) are defined for any x ∈ X on an arbitrary sample path l ∈ Θ. For a given handoff algorithm there is at least one optimal handoff sequence for a given l according to the algorithms criteria. Assuming that all sample paths are independent, and equally important, different handoff algorithms will be evaluated by averaging the values of these measures over all the sample paths. For example we use the average: CQSL =
l [CQSL(x(l))]/η, where η = |Θ|. In (3) the parameter p is related to call dropping probability. In practice, a call is dropped if either the high co-channel interference, or the signal level below a certain threshold Sdrop < Smin (call dropping condition) is maintained for d consecutive samples in the handoff sequence. (We use this simple criteria to model duration of bad connections.) Let Pdrop be the probability that a call is dropped. For a sample path l, let δl be the probability of receiving a signal strength below Sdrop . Let µl be the probability of receiving co-channel interference above a specified value. Therefore, the call dropping probability in the sample path l with Nl > d consecutive sample points is given by the following recursive formulae: Pld (1 Pdropl (Nl ) = Pdropl (Nl − 1) + − Pl )(1 − Pdropl (Nl − d − 1)), (4) where the probability of having a single sample point satisfying the call dropping condition is Pl = 1 − (1 − δl )(1 − µl ), Pdropl (Nl < d) = 0 and Pdropl (Nl = d) = Pld . If the cochannel interference is neglected then Pl = δl . The average call dropping probability over η sample paths is: Pdrop (Nl , d) = η 1 Pdropl (Nl ). η (5) l=1 Given a number of sample points Nl , the value of d can be determined such that Pdrop (Nl , d) in (5) is below a certain threshold according to a QoS requirement. The value of p in (3) is chosen to be ≥ d/Nl . Knowing p, for a given handoff sequence of a sample path with Nl = N sample points, we can calculate the minimum value of CQSL(x) using (3). Furthermore we introduce the signal quality per handoff: λ = CQSL/γ,
(6) where γ = l [γ(x(l))]/η. We will use (6) to compare different handoff methods in section IV. 791 III. T HE B EST H ANDOFF S EQUENCE (BHS) Our aim here is to obtain the BHS defined by the following multiple objective unconstrained optimization problem: max (1 − a)ψ(x) − aγ(x), (7) x∈X
where ψ(x) = i∈Ωx Ai (x)/|Ωx | − Smin (N − |Ωx |)/pN , and a ∈ [0, 1], the weight factor indicates the relative importance of the two objectives ψ(x) and γ(x). Since all the paths are independent, maximisation of CQSL(x(l)) for any path l also maximizes CQSL. Note that in [1] only two base stations are considered and therefore an exhaustive search for the optimal handoff sequence is used. In our case exhaustive search is impractical because of a large number of possible sample paths (M N ) involved. Therefore, we propose a heuristic method based on the so-called cluster approach. Let Gij , referred to as a cluster, be a set of signal strengths ≥ Smin from base station j associated with a group of consecutive sample points {i, i + 1, ..., i + Lij − 1}, where
i+L −1 1 ≤ Lij = |Gij | ≤ N − i + 1. Let Wij = r=i ij Srj /Lij . In order to solve (7) our heuristic algorithm maximises ψ(x) by finding maximum average signal level Wij and at the same time minimises the number of handoffs γ(x) by choosing longest clusters (max Lij ). Let Hij be the parameter associated with a cluster Gij which is defined as the weighted value Hij = αLij + (1 − α)Wij , (8) where α ∈ [0, 1]. According to (8) when α = 0, Hij = Wij , and hence maximises signal quality, and when α = 1, Hij = Lij , and hence maximises the cluster length. Let Φ be a signal strength matrix of N × M , received from M base stations with N sample points for a particular sample path. Here, we aim to find the BHS as a set of Gij starting from the first row (i = 1) until the last row (i = N ) in Φ, which maximizes the optimization function (7). Our heuristic algorithm is described as follows. Step 0: Set i = 1. Step 1: At the ith sample point in Φ the algorithm finds all clusters which start from this ith sample point, it then selects the cluster Gij ∗ with maximum value of Hij , i.e., Gij ∗ = arg max Gij Hij . If there is only a single cluster starts from the ith sample point, then automatically it will be selected. If there is no cluster starting from i then go to Step 2. The algorithm assigns the base station j ∗ associated with the selected cluster as the serving base station for the {i, i + 1, .., i + Lij ∗ − 1} sample points. If i + Lij ∗ < N then return to Step 1 with i = i + Lij ∗ until i = N . Step 2: Starting from row i the algorithm skips all the rows in Φ until it finds a new row u with a cluster Guv containing at least one sample point with signal strength > Smin (i.e. Luv ≥ 1). Return to Step 1 with this uth sample point to find the Guv∗ cluster with maximum value of Huv . In addition, for the above skipped sample points between {i, .., u − 1}, the algorithm assigns the previous serving base station j ∗ (no handoff) or the new serving base station v ∗ (handoff) such that the average signal strength over all the skipped sample points is maximized. If no such uth sample point is found, then we assign the previous serving base station j ∗ as the new serving 792 IEEE COMMUNICATIONS LETTERS, VOL. 9, NO. 9, SEPTEMBER 2005 TABLE I ” KNEE ” PARAMETER VALUES FOR ALL HANDOFF ALGORITHMS 20 15 10 5 CQSL (dB) Tk (dB) CQSL (dB) λ,γ  N ASP /γ BHS 15 17.05 16.88 , 1.01 93.90 Thres+Hys 15 15.73 13.44 , 1.17 78.11 Hysteresis 6 15.56 14.27 , 1.09 83.73 Threshold 14 14.09 10.59 , 1.33 68.25 FHA 25 9.18 4.70 , 1.95 42.15 Method 0 −5 −10 Best Handoff Sequence (BHS) Threshold Hysteresis Threshold + Hysteresis FHA −15 −20 0 1 2 3 4 5 6 γ Fig. 1. Comparison of the various handoff algorithms base station. If u + Luv∗ < N then return to Step 1 with i = u + Luv∗ until i = N . IV. S IMULATION R ESULTS Here we compare the different handoff methods introduced in Section I using the quality measures of (3) and (6). We consider M = 3 adjacent cells with 100 m radius. The base stations are located in a plane with the following coordinates: (100, 150), (250, 75) and (250, 250) [meters]. We randomly generate η = 1000 sample paths, each with N = 100 where each pair of consecutive points are one meter apart. A log-normal propagation model [6] was assumed to generate signal strengths in each sample point along all the sample paths, i.e., Sij = K1 − K2 log(r) + F , where K1 = 85; K2 = 35 are constants, r is the distance to the base station, and F is Gaussian distributed (N (0, σ 2 )) representing the shadowing effect. We set σ = 3 dB as in [1], shadowing correlation distance equals 20 m, Smin = 15 dB as in [5] and Smax = 1.5Smin . All the sample paths are straight lines that start from points in the square area {(100, 100), (200, 100), (200, 200), (100, 200)}. Their directions are randomly chosen between [0, 2π] uniformly. Note that Pdrop is computed by (5) as a decreasing function of d, where d ≥ 3 gives the call dropping ≤ 1%. The p value in (3) is selected such that p ≥ d/N = 0.03. Here we use p = 0.1. The values of CQSL and γ in Fig. 1 are obtained by varying the THO threshold in the Threshold method and Threshold + Hysteresis method (with +3 dB hysteresis margin), and the H hysteresis threshold in the Hysteresis method, respectively, from 1 to 30 dB. A similar range was used when varying the so-called similarity threshold in the FHA method. As a benchmark value, we show in Fig. 1 the CQSL and γ of the BHS for different values of α ∈ [0, 1] in (8). Observe that these values are almost unchanged (insensititive) for different α values which indicates that we can use either Lij or Wij for the cluster selection. The complexity of the proposed heuristic algorithm is O(M N ) in comparison to the complexity O(M N ) using exhaustive search. Using the same network but with N = 20 sample points, the difference between a solution resulted from an exhaustive search and ours was never more than 0.24%. Fig. 1 shows that the Hysteresis method and Threshold + Hysteresis method (with +3 dB hysteresis margin) provide the best values that are closest to BHS. When high numbers of handoffs can be tolerated Threshold method will be as efficient as the above two. Our simulations indicate FHA is less desirable in comparison to other methods. Based on Fig. 1, optimum parameter settings for each handoff method can be obtained from the “knee” point of the corresponding curves (similar to [1]). For example the “knee” point for the Threshold handoff method is a point with CQSL = 14.09 dB and γ = 1.33 values according to Fig. 1. This is when the threshold THO is set to 14 dB which produces highest CQSL with lowest average number of handoffs. In Table I we compare all handoff methods at their “knee” CQSL in (3), λ in points using the following quantities:
(6) and N ASP /γ, where N ASP = l [N ASP (x(l))]/η. The optimal threshold for each method at the “knee” point is presented in column identified with Tk in dB. The benchmark BHS has the highest λ and N ASP /γ values. We repeated our experiment for various N values (N = 50, 100, 200) and found the results to be consistent. V. C ONCLUSION A signal level based criterion is developed for the evaluation of handoff algorithms. We have proposed new call quality measures and developed an off-line cluster-based computationally-simple heuristic algorithm to find a near optimal handoff sequence that can be used as a benchmark. Our results show that there is substantial room for improvement in existing handoff algorithms with respect to the signal level measures as well as number of required handoffs. R EFERENCES [1] K. D. Wong and D. C. Cox, “A pattern recognition system for handoff algorithms,” IEEE J. Select. Areas Commun., vol. 18, pp.1301–1312, July 2000. [2] P. L. Hiew and M. Zukerman, “Efficiency comparison of several channel allocation schemes for digital mobile communication networks,” IEEE Trans. Vehic. Technol., vol. 49, pp. 724–733, May 2000. [3] S. Moghaddam, V. Tabataba, and A. Falahati, “New handoff initiation algorithm (optimum combination of hysteresis and threshold based methods),” in Proc. IEEE Vehic. Technol. Conf., Sept. 2000, pp. 1567– 1574. [4] ETSI, GSM Technical Specification, GSM 08.08, version 5.12.0 ed., France, June 2000. [5] H. Maturino-Lozoya, D. Munoz-Rodriguez, F. Jaimes-Romero, and H. Tawfik, “Handoff algorithms based on fuzzy classifiers,” IEEE Trans. Vehic. Technol., vol. 49, pp. 2286–2294, Nov. 2000. [6] M. Gudmundson, “Correlation model for shadow fading in mobile radio systems,” Electronics Lett., vol. 27, pp. 2145–2146, Nov. 1991.