Context-Aware Handover in HetNets - DEI UniPd
The final version of this manuscript appeared in the Proceedings of the European Conference on Networks and Communications 2014, June 23/26, 2014, Bologna, Italy. DOI: not yet available
Context-Aware Handover in HetNets Francesco Guidolin Irene Pappalardo Andrea Zanella Michele Zorzi Dept. of Information Engineering, University of Padova, via Gradenigo 6/B, 35131 Padova, Italy {fguidolin, pappalar, zanella, zorzi}@dei.unipd.it
Abstract—In this paper, we focus on the average performance experienced by a mobile user while crossing a pico/femtocell as a function of context parameters, such as user speed, pico/femto cell radius, transmit power of main and subsidiary base stations. The analysis is based on a mathematical model that provides an approximate expression of the average Shannon capacity experienced by a mobile user when crossing the femtocell. The optimal handover policy obtained from such a model is then validated through simulations against other policies, showing that a context-aware handover policy may achieve better performance than handover policies based on a more limited set of context parameters. Index Terms—Small cells, HetNets, Handover, Context awareness, LTE, mobile user.
I. I NTRODUCTION
T
HE demand for high speed connectivity will dramatically increase in the next years [1]. One of the most promising approaches to tackle this problem is the deployment of Heterogeneous Networks (HetNets) that include Base Stations (BSs) with widely varying transmit powers (and, hence, coverage areas), carrier frequencies, backhaul connection types, and communication protocols. A typical HetNet, in fact, considers the deployment of pico and/or femto BSs within a macro cell, served by a “main” BS, in order to provide better coverage and higher connection speed to users at the border of the macro cell, or in spots where the density of users is particularly high. The higher density of BSs with different coverage areas and backhaul connectivity, however, raises new technical challenges, in particular for the management of user mobility [2]. A main problem concerns the Handover (HO) process that, in the HetNet scenario, is performed not only to maintain network connectivity, but also to gain higher performance. According to the specifications of 3rd Generation Partnership Project (3GPP) [3], the User Equipment (UE) is required to periodically measure the Reference Symbols Received Power (RSRP) from the surrounding cells. When the difference between the RSRP received from a surrounding BS and the serving BS remains above a given HO threshold for a period of time equal to the Time-To-Trigger (TTT) parameter, the UE disconnects from the serving BS and connects to the BS with the strongest received signal, thus completing the HO procedure. Typically, HO threshold and TTT parameters are fixed and equal for all users. However, a static setting of these parameters is not suitable for HetNets because of the large This work was supported by the project “A Novel Approach to Wireless Networking based on Cognitive Science and Distributed Intelligence,” funded by Fondazione CaRiPaRo under the framework Progetto di Eccellenza 2012.
variety in size and density of cells [4]. For example, a long TTT may result in poor performance since the mobile UE may experience an extremely low Signal to Interference plus Noise Ratio (SINR) during the TTT interval, an event that is referred to as Handover Failure. On the other hand, a small TTT may trigger HO to a pico BS even when the UE crosses the picocell at the edges, so that a second HO to the main BS is performed immediately after, thus resulting in the so-called Handover Ping-Pong. The optimization of the TTT value is then important to improve the connection reliability, increase the performance of the users, reduce the signaling among BSs and the UEs, and improve the energy efficiency of the system. Therefore, a more sophisticated scheme to make handover decisions in HetNets is required. Several solutions have been proposed in the literature to improve mobility management in HetNets. In [5] the authors evaluated the performance of the picocell range expansion technique where the UEs virtually bias the received power levels toward the picocell in order to increase the number of pico UEs. In [6] the authors improved the mobility performance in a Long Term Evolution (LTE) HetNet by heuristically adapting the TTT parameters to the speed of the users. Similarly, in [7] the TTT values are adapted according to the mobility of the users based on the statistics of the HO performance. In [8] the HO parameters are adjusted according to the type of handover, e.g., macro-to-pico or pico-to-pico handover. The handover ping-pong problem is considered in [9] where the number of unnecessary HOs is reduced by exploiting the concepts of dwell probability and handover priority. The control of the Cell Individual Offset (CIO) parameter is proposed by [10] to reduce the number of HO failures. Although these solutions improve the efficiency of HO in HetNets, the literature still lacks a systematic analysis of the impact of all the HO parameter settings in different contexts. In this work, we provide a first contribution in this direction. by deriving an approximate expression of the average Shannon capacity experienced by a mobile UE while crossing the femtocell, as a function of the TTT value, the UE’s speed, and the power profiles for both pico and macro BSs. A similar work has been conducted by [12], where however the trajectory of the UE across the HetNet is supposed to be known, and the analysis was focused on the handover failure parameter only. We instead relax this assumption and propose a more general model that can be used to derive context-aware HO strategies in HetNet scenarios, based on easily accessible parameters, such as UE’s speed and channel conditions. The rest of the paper is organized as follows. Section II introduces the channel model, the HO process, and the UE
M-BS
0
d
dM F
R F-BS
where points d0 and d are shown in Figure 1. Using (1) into (2), we get ( η −η ∆ΓM F −(R−δ))ηM M d0M d0F F 10 10 = (dM F(R−δ) ηF (3) ∆ΓM F (dM F +(R+δ))ηM ηM −ηF 10 d0M d0F 10 = (R+δ)ηF
H
b
ω φ δ
d
c
Fig. 1: Reference scenario: macrocell BS – M-BS (), femtocell BS – F-BS (N), and HO line H approximated as a circumference of radius R with center c. Linear trajectory followed by a UE when entering the femtocell at point b with incidence angle ω.
mobility model. Section III derives the analytical performance metric adopted for the optimization of the TTT values. Section IV depicts the results for different scenarios and presents a comparison among the performance obtained with the proposed TTT and with a fixed TTT value. Conclusions are drawn in Section V. II. S YSTEM M ODEL We consider the same scenario adopted in [17] and here reported for the reader’s convenience. The scenario consists of a macro BS (M-BS) and a femto BS (F-BS), placed at distance dM F . At any given point a, a mobile UE measures the RSRPs ΓM (a) and ΓF (a) from M-BS and F-BS, respectively. We initially assume a simple path-loss channel model that does not include multipath and shadowing effects. In Section IV, we will discuss how the TTT selection strategy changes when considering fading effects. A model that natively accounts for Rayleigh fading can be found in [17]. The (average) power received in position a from h-BS can then be expressed in dB scale as [14] Γh (a) = Γtx h − 10ηh log(dh (a)/d0h )
(1)
where Γtx h is the transmit power of h-BS, ηh the path loss exponent, d0h the reference distance for the far field model to apply, and dh (a) the distance of point a to h-BS, with h ∈ {M,F}. In the following we will assume ηF ≤ ηM , as usual in the literature [15]. The HO process starts when the SINR1 experienced by the UE drops below a certain threshold that, for the sake of simplicity, we assume equal to 0 dB.2 Therefore, the HO starts whenever the mobile UE crosses the closed line H formed by the points a such that ΓM (a) = ΓF (a). For mathematical tractability, however, it is convenient to adopt the model proposed in [11] that approximates H as a circumference of radius R centered in a point c at distance δ from the F-BS in the opposite direction with respect to M-BS, as shown in Figure 1. Parameters R and δ can be found by setting ΓM (a) = ΓF (a) , for a ∈ {d0 , d} ,
(2)
1 Note that we neglect the noise term in the SINR because the considered scenario is interference-limited. 2 Our model can be generalized to nonzero hysteresis margins, but at the cost of a more involved notation and analysis.
tx where ∆ΓM F = Γtx M − ΓF . The solutions R and δ of (3) can be easily obtained with numerical methods. We identify the femtocell as the area inside the circle H, while the macrocell includes the femtocell and the surrounding area. When the UE connected to M-BS enters the femtocell, a TTT timer is initialized to the value T . If the UE exits the femtocell before the timer expires, the HO process is interrupted and the UE stays connected to M-BS. Conversely, if the timer expires while the UE is still in the circle, the HO is actually performed and the UE disconnects from the M-BS and connects to the F-BS in a time TH . Similarly, when a UE connected to F-BS exits the femtocell, another HO process is started to connect back to the M-BS. We assume that T is the same in both cases, though the analysis can be easily generalized to different T for macro-to-femto and femto-tomacro handovers. We assume that the UE crosses the femtocell at constant speed v, following a straight trajectory. With reference to the polar coordinate system depicted in Figure 1, a trajectory is uniquely identified by the angular coordinate φ of point b where the UE crosses the femtocell border H entering the circle, and by the incidence angle ω formed by the trajectory with respect to the radius passing through b. As done in [11], we assume that the UE can enter the femtocell from any point and with any angle, so that the parameters φ and ω are modeled as independent random variables with uniform distribution in the intervals [0, 2π] and [−π/2, π/2], respectively. Finally, for any given point a, we define the connection state S of the UE to be M , F or H depending on whether the UE is connected to the M-BS, the F-BS or is temporarily disconnected because Handing over from one to the other.
III. AVERAGE CAPACITY As done in [17], for any given straight path ` that crosses the femtocell, we define the mean trajectory performance as Z X 1 CS (a)χa (S)da (4) C` = |`| ` S∈{M,F,H} R where |`| is the trajectory’s length, ` is a line integral, χa (S) is 1 if the UE’s state at point a is S and zero otherwise, while CS (a) is the performance experienced by the UE at point a when it is in state S. In this paper, we focus on the average Shannon capacity experienced by the UE while crossing the femtocell, so that we define ΓM (a) ΓF (a) CM (a) = log 1 + ; CF (a) = log 1 + ; ΓF (a) ΓM (a) CH (a) = 0 ; (5) where ΓM (a) and ΓF (a) are given in (1). Note that we assign zero capacity during the actual switching from one BS to the other one (state H) in order to account for the various costs
TABLE I: Integration intervals for the internal (1st and 2nd rows) and
external (3rd and 4th rows) trajectory components. See (13), (16), and (17) for the definition of the different functions. S
Coefficient ψ(a, S) = n In,S (a) and conditions on yT and yH [αn (a, S), βn (a, S)] [0, ωT (a)] n=1 [ωT (a), ωmax (a)] M n = 0 if yT ∈ [0, xtan (a)] [ωT (a), ωmax (a)] n = 2 if yT > xtan (a) [0, ωH (a)) n=1 n = 0 if yT + yH ∈ [0, xtan (a)] [ωH (a), ωmax (a)] F [ωH (a), ωmax (a)] n = 2 if yT + yH > xtan (a) n=0 [ωmin (a), ω ˜ H (a)] M n=1 [max{˜ ωH (a), ωmin (a)}, π/2] n=0 [min{˜ ωT (a), ω ∗ }, π/2] F n=1 [ωmin (a), min{˜ ωT (a), ω ∗ }]
of the handover process (energy, time, signaling, etc). Without such a penalty, indeed, the optimal strategy would obviously consist in performing HO with zero TTT any time the SINR condition is met. We observe that C` strongly depends on the TTT value: short TTT values increase the chance of HO, thus improving the SINR in the femtocell at the cost of the zero capacity penalty during the period TH ; on the other hand, large TTT values may let the UE cross the femtocell without switching to F-BS, thus suffering a lower SINR inside the femtocell, but avoiding the loss due to TH . Since the UE can follow any trajectory, we average the capacity along all the straight lines of length L that enter the femtocell with random incidence angle, thus obtaining3 Z π/2 Z L X 2 C¯ = CS (a(x, ω))χa(x,ω) (S)dx dω , Lπ 0 0 S∈{M,F,H} (6) with a(x, ω) being the point at distance x from b along the trajectory with incidence angle ω. It is convenient to express (6) as C¯ = C¯int + C¯ext
(7)
where 2 C¯int = Lπ S∈{M,F,H}
π/2
Z
Z
X
2R cos ω
CS (a(x, ω))χa(x,ω) (S)dx dω (8) 0
0
is the contribution to the average capacity due to the part of the trajectory inside the femtocell, while 2 C¯ext = Lπ S∈{M,F,H}
Z π/2Z
X
L
CS (a(x, ω))χa(x,ω) (S)dx dω (9) 0
2R cos ω
is the contribution of the part external to the femtocell. In the following we work out each part separately.
two points, or not cross it at all (the tangent case is neglected having zero probability). In case of crossing, we denote by p (10) d± = R cos ω ± a2 − R2 sin2 ω the length of the trajectory when it√intersects the circle. Then, by changing variable x with a = x2 + R2 − 2xR cos ω, (8) can be written as 2 C¯int = Lπ S∈{M,F,H}
Z π/2Z
X
CS (a) √ 0
Let us now focus on (8). Under the simplified circular model for the femtocell, the SINR depends only on the distance a of point a(x, ω) from the femtocell center. Given any circle of radius a ≤ R centered in c, the trajectory can either cross it in 3 For
the symmetry of the problem, the entrance point b is irrelevant.
ψ(a,S) 1−(R/a)2 sin2 ω
da dω ;
R sin ω
(11) where CS (a) denotes the capacity at distance a from the femtocell center when the UE’s state is S, while ψ(a, S) counts the number of intersection points at which UE’s state is S, i.e., ψ(a, S) = χd− (S) + χd+ (S) where χd± (S) is one if, after traveling a distance d± along the trajectory, the UE’s state is S, and zero otherwise. Changing the order of integration in (11) we get
Z
2 C¯int = Lπ S∈{M,F,H} X
R
Z
0
a sin−1 ( R )
√
CS (a)
ψ(a,S) 1−(R/a)2 sin2 ω
dωda . (12)
0
Now, denoting by yT = v T and yH = v TH the distance covered by the UE during the TTT time T and the handover time TH , respectively, it is easy to realize that, for points within the femtocell, χd (M ) = 1 if d < yT , χd (F ) = 1 if d > yT + yH , and χd (H) = 1 otherwise. Therefore, for any given a, the inner integration interval in (12) can be split into subintervals In (a, S) = [αn (a, S), βn (a, S)], as specified in Table I for S ∈ {M, F }, where the function ψ(a, S) is constant and equal to n ∈ {0, 1, 2}. The interval extremes are given by 2 2 2 1 −1 −1 R + yT − a ωmax (a) = sin (a/R) ; ωT (a) = cos ; 2RyT 0 2 1 R + (yT + yH )2 − a2 ωH (a) = cos−1 ; (13) 2R(yT + yH ) 0 p xtan (a) = R2 − a2 ; 1
with bxe0 = min(1, max(0, x)). In practice, ωmax (a) is the incidence angle of the trajectory that is tangent to a circle of radius a centered on c and xtan (a) is the length at which this trajectory touches that circle, while ωT (a) and ωH (a) are the incidence angles for which the trajectory intersects the circle at distance yT and yT + yH from the ingress point, respectively. By using these intervals, after some algebraic steps that we omit due to space constraints, we can express the average capacity (12) as
Z
A. Internal component
R
2 C¯int = Lπ S∈{M,F,H} X
R
R CS (a) G β1 (a, S), β2 (a, S), da a
0
(14) where G (φ1 , φ2 , k) = F (φ2 , k)−F (φ1 , k) with F (φ, k) being the incomplete elliptic integral of the first kind, which can be computed with standard methods.
2.3
Following the same rationale used for the inner component, we can express (9) as
2.2
√
Z
2 Lπ S∈{M,F,H}
C¯ext =
X
Z
R2 +L2
π/2
√
CS (a) R
ψ(a,S) 1−(R/a)2 sin2 ω
ωmin (a)
dωda (15)
where ψ(a, S) = χd+ (S) and −1
ωmin (a) = cos
L2 + R2 − a2 2RL
Z
2 Lπ S∈{M,F,H}
C¯ext =
2.1 2 1.9 1.8 1.7 1.6 1 Km/h 20 Km/h 50 Km/h 100 Km/h Tmin
1.5 1.4
1 .
(16)
0
Determining the values of ψ(a, S) for points outside the femtocell is slightly more involved than in the previous case. 1 We start observing that, if ω > ω ∗ = cos−1 byT /(2R)e0 then S = M for any d, since the mobile leaves the femtocell before the time to handover T has elapsed. If ω ≤ ω ∗ , the state at distance d+ is M only if the distance crossed outside the femtocell is larger than yT + yH .4 Instead, we have χd+ (F ) = 1 if ω < ω ∗ and the distance traveled outside the femtocell is less than yT . In the other cases, we obviously have χd+ (H) = 1. As before, by splitting the integration interval into two subintervals In (a, S) in which ψ(a, S) is constant and equal to 0 or 1, from (15) we get X
Avarege capacity [bit/s/Hz]
B. External component
√ R2 +L2
R CS (a) G α1 (a, S), β1 (a, S), da a
R
where the interval extremes in Table I are given by 2 1 a − R2 − yT 2 ω ˜ T (a) = cos−1 2RyT 0 2 1 2 a − R − (y + yH )2 T −1 . ω ˜ H (a) = cos 2R(yT + yH ) 0
(17)
IV. P ERFORMANCE E VALUATION Based on the model derived in Section III, we analyze the impact of the choice of T on the selected performance index, namely, the average Shannon capacity, and we derive an optimal strategy, depending on the scenario parameters. Successively, we test our policy against different strategies by simulating the handover process in a more realistic scenario that also includes Rayleigh fading. The numerical results have been obtained by setting TH = 200 ms, and the transmit power of M-BS and F-BS to 46 dBm and 23 dBm, respectively [18]. Figure 2 shows the analytical capacity given by (7) as a function of T , for several values of the UE speed. We can see that, increasing the TTT, the average capacity first decreases and, then, increases again, till it reaches an asymptotic value that corresponds to the average capacity in case HO is never triggered. We remark that these results have been obtained 4 Note that the HO can also start inside the femtocell and be completed after the UE has exited the femtocell. This case, which can be easily accounted for in the model, is quite cumbersome to be described and, hence, is not discussed further.
1.3 0
0.5
1 T [s]
1.5
2
Fig. 2: Average capacity values vs TTT values, for various values of the mobile users speed.
by considering the analytical model only and, hence, neglect the effect of fading, which will be discussed later. In this condition, the observed behavior reflects the balance between two opposite factors. On the one hand, a very short TTT favors the trajectories that have a significant internal component, i.e., that cut the cell close to its center and that experience a higher capacity if the UE switches to the F-BS as soon as possible. On the other hand, more peripheral trajectories suffer the loss due to the handover operations that is not compensated by the capacity gain obtained by connecting to the F-BS. When TTT increases, the capacity loss incurred by the inner trajectories dominates the gain of the peripheral trajectories, so that the net effect is a decrease of the average capacity. Above a certain TTT, this behavior changes and, for sufficiently large values of TTT, the capacity saturates since HO is never triggered. We note that, for very low values of the UE speed, immediate handover is recommended because most trajectories will stay in the femtocell a time long enough to recover from the capacity loss incurred during the HO time TH . The situation is the opposite for high speeds, from which it is better to set a very large TTT value to avoid HO. This argument, however, neglects the effect of Rayleigh fading that, with very short TTT values, will likely result in severe ping-pong effect. Assuming signals are affected by independent Rayleigh fading processes, the ping-pong effect can be mitigated by setting T larger than a specific value, here denoted as Tmin , which can be computed for each value of the UE speed using the results presented in [16]. We choose Tmin to have a probability lower than 0.01 that the HO is improperly triggered by fading processes. An alternative approach that considers the effect of the Rayleigh fading in the HO decision can be found in [17]. According to our mathematical analysis, then, the optimal handover strategy consists in either performing HO as soon as possible, i.e., setting T = Tmin , or not performing HO at all, i.e., using T = ∞. This choice is bound to the context through the speed threshold vth , below which HO is triggered with T = Tmin , and above which HO is not triggered at all. Fig. 3 shows the speed thresholds vth for different combinations of ηF and ηM values. The speed threshold ranges from 1 to 180 Km/h, while the value 200 Km/h indicates that,
1.9
CAW TMIN FIX
vth [Km/h]
200 180 160 140 120 100 80 60 40 20 0
0.3 0.4 0.5 0.6 0.7 0.8 ηF/ηM 0.9
1 3
3.5
4
4.5
5
5.5
6
6.5
Average Capacity bit/s/Hz
1.8 200 180 160 140 120 100 80 60 40 20 0
1.7
1.6
1.5
1.4
ηM 1.3 0
20
40
60
80 100 Speed [Km/h]
120
140
160
180
Fig. 3: vth for different pathloss ratios.
Fig. 4: Average capacity obtained with different approaches.
in the considered scenario, the best strategy is to avoid HO. We note that the vth trend depends on the specific pathloss exponents and not only on their ratio. Moreover, since the cell coverage is determined by the η values, we can notice that vth is directly proportional to the cell size. Then, to optimize the handover procedure it is important to know the mobility characteristics of the users and the channel parameters. Finally, we compare via Monte-Carlo simulations the performance obtained with three different policies, i.e., [CAW]: the context-aware policy that performs handover only when v < vth ; [FIX]: a policy with TTT fixed to T = 100 ms for every speed; [TMIN]: a minimum TTT policy, where T = Tmin for each speed value. The M-BS and F-BS are placed at a distance dM F = 500 m. The signals received from M-BS and F-BS are generated according to two independent path-loss plus Rayleigh fading channel models, with path-loss exponents ηM = 4 and ηF = 2, respectively, and coherence time depending on the UE speed. For every Monte-Carlo run, we compute the average capacity experienced by a user that crosses the femtocell coverage area with a linear trajectory of length L equal to twice the macrocell radius. Fig. 4 shows the average capacity obtained using the three different policies. Note that, at low speeds, the FIX strategy suffers from the ping-pong effect that determines a strong performance degradation. Conversely, TMIN and CAW perform much better by allowing HO after the minimum TTT required to limit the ping-pong effect. For larger speed values, CAW gains over TMIN because it skips HO, avoiding the loss due to the two TH in a short time interval. In this case, also the FIX policy with T = 100 ms achieves the best performance, since the TTT is long enough to avoid handover for the considered scenarios, though performance may drop for other scenarios. The capacity fluctuations are due to the fast fading effect.
R EFERENCES
V. C ONCLUSIONS AND F UTURE W ORK In this paper we have analyzed the UE capacity during the HO process, showing that the impact of the context parameters on the optimal HO policy is quite significant. This result highlights the importance of binding the HO procedure to the context and, hence, to develop context-aware handover procedures. As future work, we plan to couple the model with a machine-learning estimator of context parameters required by the model.
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Context-Aware Handover in HetNets Francesco Guidolin Irene Pappalardo Andrea Zanella Michele Zorzi Dept. of Information Engineering, University of Padova, via Gradenigo 6/B, 35131 Padova, Italy {fguidolin, pappalar, zanella, zorzi}@dei.unipd.it
Abstract—In this paper, we focus on the average performance experienced by a mobile user while crossing a pico/femtocell as a function of context parameters, such as user speed, pico/femto cell radius, transmit power of main and subsidiary base stations. The analysis is based on a mathematical model that provides an approximate expression of the average Shannon capacity experienced by a mobile user when crossing the femtocell. The optimal handover policy obtained from such a model is then validated through simulations against other policies, showing that a context-aware handover policy may achieve better performance than handover policies based on a more limited set of context parameters. Index Terms—Small cells, HetNets, Handover, Context awareness, LTE, mobile user.
I. I NTRODUCTION
T
HE demand for high speed connectivity will dramatically increase in the next years [1]. One of the most promising approaches to tackle this problem is the deployment of Heterogeneous Networks (HetNets) that include Base Stations (BSs) with widely varying transmit powers (and, hence, coverage areas), carrier frequencies, backhaul connection types, and communication protocols. A typical HetNet, in fact, considers the deployment of pico and/or femto BSs within a macro cell, served by a “main” BS, in order to provide better coverage and higher connection speed to users at the border of the macro cell, or in spots where the density of users is particularly high. The higher density of BSs with different coverage areas and backhaul connectivity, however, raises new technical challenges, in particular for the management of user mobility [2]. A main problem concerns the Handover (HO) process that, in the HetNet scenario, is performed not only to maintain network connectivity, but also to gain higher performance. According to the specifications of 3rd Generation Partnership Project (3GPP) [3], the User Equipment (UE) is required to periodically measure the Reference Symbols Received Power (RSRP) from the surrounding cells. When the difference between the RSRP received from a surrounding BS and the serving BS remains above a given HO threshold for a period of time equal to the Time-To-Trigger (TTT) parameter, the UE disconnects from the serving BS and connects to the BS with the strongest received signal, thus completing the HO procedure. Typically, HO threshold and TTT parameters are fixed and equal for all users. However, a static setting of these parameters is not suitable for HetNets because of the large This work was supported by the project “A Novel Approach to Wireless Networking based on Cognitive Science and Distributed Intelligence,” funded by Fondazione CaRiPaRo under the framework Progetto di Eccellenza 2012.
variety in size and density of cells [4]. For example, a long TTT may result in poor performance since the mobile UE may experience an extremely low Signal to Interference plus Noise Ratio (SINR) during the TTT interval, an event that is referred to as Handover Failure. On the other hand, a small TTT may trigger HO to a pico BS even when the UE crosses the picocell at the edges, so that a second HO to the main BS is performed immediately after, thus resulting in the so-called Handover Ping-Pong. The optimization of the TTT value is then important to improve the connection reliability, increase the performance of the users, reduce the signaling among BSs and the UEs, and improve the energy efficiency of the system. Therefore, a more sophisticated scheme to make handover decisions in HetNets is required. Several solutions have been proposed in the literature to improve mobility management in HetNets. In [5] the authors evaluated the performance of the picocell range expansion technique where the UEs virtually bias the received power levels toward the picocell in order to increase the number of pico UEs. In [6] the authors improved the mobility performance in a Long Term Evolution (LTE) HetNet by heuristically adapting the TTT parameters to the speed of the users. Similarly, in [7] the TTT values are adapted according to the mobility of the users based on the statistics of the HO performance. In [8] the HO parameters are adjusted according to the type of handover, e.g., macro-to-pico or pico-to-pico handover. The handover ping-pong problem is considered in [9] where the number of unnecessary HOs is reduced by exploiting the concepts of dwell probability and handover priority. The control of the Cell Individual Offset (CIO) parameter is proposed by [10] to reduce the number of HO failures. Although these solutions improve the efficiency of HO in HetNets, the literature still lacks a systematic analysis of the impact of all the HO parameter settings in different contexts. In this work, we provide a first contribution in this direction. by deriving an approximate expression of the average Shannon capacity experienced by a mobile UE while crossing the femtocell, as a function of the TTT value, the UE’s speed, and the power profiles for both pico and macro BSs. A similar work has been conducted by [12], where however the trajectory of the UE across the HetNet is supposed to be known, and the analysis was focused on the handover failure parameter only. We instead relax this assumption and propose a more general model that can be used to derive context-aware HO strategies in HetNet scenarios, based on easily accessible parameters, such as UE’s speed and channel conditions. The rest of the paper is organized as follows. Section II introduces the channel model, the HO process, and the UE
M-BS
0
d
dM F
R F-BS
where points d0 and d are shown in Figure 1. Using (1) into (2), we get ( η −η ∆ΓM F −(R−δ))ηM M d0M d0F F 10 10 = (dM F(R−δ) ηF (3) ∆ΓM F (dM F +(R+δ))ηM ηM −ηF 10 d0M d0F 10 = (R+δ)ηF
H
b
ω φ δ
d
c
Fig. 1: Reference scenario: macrocell BS – M-BS (), femtocell BS – F-BS (N), and HO line H approximated as a circumference of radius R with center c. Linear trajectory followed by a UE when entering the femtocell at point b with incidence angle ω.
mobility model. Section III derives the analytical performance metric adopted for the optimization of the TTT values. Section IV depicts the results for different scenarios and presents a comparison among the performance obtained with the proposed TTT and with a fixed TTT value. Conclusions are drawn in Section V. II. S YSTEM M ODEL We consider the same scenario adopted in [17] and here reported for the reader’s convenience. The scenario consists of a macro BS (M-BS) and a femto BS (F-BS), placed at distance dM F . At any given point a, a mobile UE measures the RSRPs ΓM (a) and ΓF (a) from M-BS and F-BS, respectively. We initially assume a simple path-loss channel model that does not include multipath and shadowing effects. In Section IV, we will discuss how the TTT selection strategy changes when considering fading effects. A model that natively accounts for Rayleigh fading can be found in [17]. The (average) power received in position a from h-BS can then be expressed in dB scale as [14] Γh (a) = Γtx h − 10ηh log(dh (a)/d0h )
(1)
where Γtx h is the transmit power of h-BS, ηh the path loss exponent, d0h the reference distance for the far field model to apply, and dh (a) the distance of point a to h-BS, with h ∈ {M,F}. In the following we will assume ηF ≤ ηM , as usual in the literature [15]. The HO process starts when the SINR1 experienced by the UE drops below a certain threshold that, for the sake of simplicity, we assume equal to 0 dB.2 Therefore, the HO starts whenever the mobile UE crosses the closed line H formed by the points a such that ΓM (a) = ΓF (a). For mathematical tractability, however, it is convenient to adopt the model proposed in [11] that approximates H as a circumference of radius R centered in a point c at distance δ from the F-BS in the opposite direction with respect to M-BS, as shown in Figure 1. Parameters R and δ can be found by setting ΓM (a) = ΓF (a) , for a ∈ {d0 , d} ,
(2)
1 Note that we neglect the noise term in the SINR because the considered scenario is interference-limited. 2 Our model can be generalized to nonzero hysteresis margins, but at the cost of a more involved notation and analysis.
tx where ∆ΓM F = Γtx M − ΓF . The solutions R and δ of (3) can be easily obtained with numerical methods. We identify the femtocell as the area inside the circle H, while the macrocell includes the femtocell and the surrounding area. When the UE connected to M-BS enters the femtocell, a TTT timer is initialized to the value T . If the UE exits the femtocell before the timer expires, the HO process is interrupted and the UE stays connected to M-BS. Conversely, if the timer expires while the UE is still in the circle, the HO is actually performed and the UE disconnects from the M-BS and connects to the F-BS in a time TH . Similarly, when a UE connected to F-BS exits the femtocell, another HO process is started to connect back to the M-BS. We assume that T is the same in both cases, though the analysis can be easily generalized to different T for macro-to-femto and femto-tomacro handovers. We assume that the UE crosses the femtocell at constant speed v, following a straight trajectory. With reference to the polar coordinate system depicted in Figure 1, a trajectory is uniquely identified by the angular coordinate φ of point b where the UE crosses the femtocell border H entering the circle, and by the incidence angle ω formed by the trajectory with respect to the radius passing through b. As done in [11], we assume that the UE can enter the femtocell from any point and with any angle, so that the parameters φ and ω are modeled as independent random variables with uniform distribution in the intervals [0, 2π] and [−π/2, π/2], respectively. Finally, for any given point a, we define the connection state S of the UE to be M , F or H depending on whether the UE is connected to the M-BS, the F-BS or is temporarily disconnected because Handing over from one to the other.
III. AVERAGE CAPACITY As done in [17], for any given straight path ` that crosses the femtocell, we define the mean trajectory performance as Z X 1 CS (a)χa (S)da (4) C` = |`| ` S∈{M,F,H} R where |`| is the trajectory’s length, ` is a line integral, χa (S) is 1 if the UE’s state at point a is S and zero otherwise, while CS (a) is the performance experienced by the UE at point a when it is in state S. In this paper, we focus on the average Shannon capacity experienced by the UE while crossing the femtocell, so that we define ΓM (a) ΓF (a) CM (a) = log 1 + ; CF (a) = log 1 + ; ΓF (a) ΓM (a) CH (a) = 0 ; (5) where ΓM (a) and ΓF (a) are given in (1). Note that we assign zero capacity during the actual switching from one BS to the other one (state H) in order to account for the various costs
TABLE I: Integration intervals for the internal (1st and 2nd rows) and
external (3rd and 4th rows) trajectory components. See (13), (16), and (17) for the definition of the different functions. S
Coefficient ψ(a, S) = n In,S (a) and conditions on yT and yH [αn (a, S), βn (a, S)] [0, ωT (a)] n=1 [ωT (a), ωmax (a)] M n = 0 if yT ∈ [0, xtan (a)] [ωT (a), ωmax (a)] n = 2 if yT > xtan (a) [0, ωH (a)) n=1 n = 0 if yT + yH ∈ [0, xtan (a)] [ωH (a), ωmax (a)] F [ωH (a), ωmax (a)] n = 2 if yT + yH > xtan (a) n=0 [ωmin (a), ω ˜ H (a)] M n=1 [max{˜ ωH (a), ωmin (a)}, π/2] n=0 [min{˜ ωT (a), ω ∗ }, π/2] F n=1 [ωmin (a), min{˜ ωT (a), ω ∗ }]
of the handover process (energy, time, signaling, etc). Without such a penalty, indeed, the optimal strategy would obviously consist in performing HO with zero TTT any time the SINR condition is met. We observe that C` strongly depends on the TTT value: short TTT values increase the chance of HO, thus improving the SINR in the femtocell at the cost of the zero capacity penalty during the period TH ; on the other hand, large TTT values may let the UE cross the femtocell without switching to F-BS, thus suffering a lower SINR inside the femtocell, but avoiding the loss due to TH . Since the UE can follow any trajectory, we average the capacity along all the straight lines of length L that enter the femtocell with random incidence angle, thus obtaining3 Z π/2 Z L X 2 C¯ = CS (a(x, ω))χa(x,ω) (S)dx dω , Lπ 0 0 S∈{M,F,H} (6) with a(x, ω) being the point at distance x from b along the trajectory with incidence angle ω. It is convenient to express (6) as C¯ = C¯int + C¯ext
(7)
where 2 C¯int = Lπ S∈{M,F,H}
π/2
Z
Z
X
2R cos ω
CS (a(x, ω))χa(x,ω) (S)dx dω (8) 0
0
is the contribution to the average capacity due to the part of the trajectory inside the femtocell, while 2 C¯ext = Lπ S∈{M,F,H}
Z π/2Z
X
L
CS (a(x, ω))χa(x,ω) (S)dx dω (9) 0
2R cos ω
is the contribution of the part external to the femtocell. In the following we work out each part separately.
two points, or not cross it at all (the tangent case is neglected having zero probability). In case of crossing, we denote by p (10) d± = R cos ω ± a2 − R2 sin2 ω the length of the trajectory when it√intersects the circle. Then, by changing variable x with a = x2 + R2 − 2xR cos ω, (8) can be written as 2 C¯int = Lπ S∈{M,F,H}
Z π/2Z
X
CS (a) √ 0
Let us now focus on (8). Under the simplified circular model for the femtocell, the SINR depends only on the distance a of point a(x, ω) from the femtocell center. Given any circle of radius a ≤ R centered in c, the trajectory can either cross it in 3 For
the symmetry of the problem, the entrance point b is irrelevant.
ψ(a,S) 1−(R/a)2 sin2 ω
da dω ;
R sin ω
(11) where CS (a) denotes the capacity at distance a from the femtocell center when the UE’s state is S, while ψ(a, S) counts the number of intersection points at which UE’s state is S, i.e., ψ(a, S) = χd− (S) + χd+ (S) where χd± (S) is one if, after traveling a distance d± along the trajectory, the UE’s state is S, and zero otherwise. Changing the order of integration in (11) we get
Z
2 C¯int = Lπ S∈{M,F,H} X
R
Z
0
a sin−1 ( R )
√
CS (a)
ψ(a,S) 1−(R/a)2 sin2 ω
dωda . (12)
0
Now, denoting by yT = v T and yH = v TH the distance covered by the UE during the TTT time T and the handover time TH , respectively, it is easy to realize that, for points within the femtocell, χd (M ) = 1 if d < yT , χd (F ) = 1 if d > yT + yH , and χd (H) = 1 otherwise. Therefore, for any given a, the inner integration interval in (12) can be split into subintervals In (a, S) = [αn (a, S), βn (a, S)], as specified in Table I for S ∈ {M, F }, where the function ψ(a, S) is constant and equal to n ∈ {0, 1, 2}. The interval extremes are given by 2 2 2 1 −1 −1 R + yT − a ωmax (a) = sin (a/R) ; ωT (a) = cos ; 2RyT 0 2 1 R + (yT + yH )2 − a2 ωH (a) = cos−1 ; (13) 2R(yT + yH ) 0 p xtan (a) = R2 − a2 ; 1
with bxe0 = min(1, max(0, x)). In practice, ωmax (a) is the incidence angle of the trajectory that is tangent to a circle of radius a centered on c and xtan (a) is the length at which this trajectory touches that circle, while ωT (a) and ωH (a) are the incidence angles for which the trajectory intersects the circle at distance yT and yT + yH from the ingress point, respectively. By using these intervals, after some algebraic steps that we omit due to space constraints, we can express the average capacity (12) as
Z
A. Internal component
R
2 C¯int = Lπ S∈{M,F,H} X
R
R CS (a) G β1 (a, S), β2 (a, S), da a
0
(14) where G (φ1 , φ2 , k) = F (φ2 , k)−F (φ1 , k) with F (φ, k) being the incomplete elliptic integral of the first kind, which can be computed with standard methods.
2.3
Following the same rationale used for the inner component, we can express (9) as
2.2
√
Z
2 Lπ S∈{M,F,H}
C¯ext =
X
Z
R2 +L2
π/2
√
CS (a) R
ψ(a,S) 1−(R/a)2 sin2 ω
ωmin (a)
dωda (15)
where ψ(a, S) = χd+ (S) and −1
ωmin (a) = cos
L2 + R2 − a2 2RL
Z
2 Lπ S∈{M,F,H}
C¯ext =
2.1 2 1.9 1.8 1.7 1.6 1 Km/h 20 Km/h 50 Km/h 100 Km/h Tmin
1.5 1.4
1 .
(16)
0
Determining the values of ψ(a, S) for points outside the femtocell is slightly more involved than in the previous case. 1 We start observing that, if ω > ω ∗ = cos−1 byT /(2R)e0 then S = M for any d, since the mobile leaves the femtocell before the time to handover T has elapsed. If ω ≤ ω ∗ , the state at distance d+ is M only if the distance crossed outside the femtocell is larger than yT + yH .4 Instead, we have χd+ (F ) = 1 if ω < ω ∗ and the distance traveled outside the femtocell is less than yT . In the other cases, we obviously have χd+ (H) = 1. As before, by splitting the integration interval into two subintervals In (a, S) in which ψ(a, S) is constant and equal to 0 or 1, from (15) we get X
Avarege capacity [bit/s/Hz]
B. External component
√ R2 +L2
R CS (a) G α1 (a, S), β1 (a, S), da a
R
where the interval extremes in Table I are given by 2 1 a − R2 − yT 2 ω ˜ T (a) = cos−1 2RyT 0 2 1 2 a − R − (y + yH )2 T −1 . ω ˜ H (a) = cos 2R(yT + yH ) 0
(17)
IV. P ERFORMANCE E VALUATION Based on the model derived in Section III, we analyze the impact of the choice of T on the selected performance index, namely, the average Shannon capacity, and we derive an optimal strategy, depending on the scenario parameters. Successively, we test our policy against different strategies by simulating the handover process in a more realistic scenario that also includes Rayleigh fading. The numerical results have been obtained by setting TH = 200 ms, and the transmit power of M-BS and F-BS to 46 dBm and 23 dBm, respectively [18]. Figure 2 shows the analytical capacity given by (7) as a function of T , for several values of the UE speed. We can see that, increasing the TTT, the average capacity first decreases and, then, increases again, till it reaches an asymptotic value that corresponds to the average capacity in case HO is never triggered. We remark that these results have been obtained 4 Note that the HO can also start inside the femtocell and be completed after the UE has exited the femtocell. This case, which can be easily accounted for in the model, is quite cumbersome to be described and, hence, is not discussed further.
1.3 0
0.5
1 T [s]
1.5
2
Fig. 2: Average capacity values vs TTT values, for various values of the mobile users speed.
by considering the analytical model only and, hence, neglect the effect of fading, which will be discussed later. In this condition, the observed behavior reflects the balance between two opposite factors. On the one hand, a very short TTT favors the trajectories that have a significant internal component, i.e., that cut the cell close to its center and that experience a higher capacity if the UE switches to the F-BS as soon as possible. On the other hand, more peripheral trajectories suffer the loss due to the handover operations that is not compensated by the capacity gain obtained by connecting to the F-BS. When TTT increases, the capacity loss incurred by the inner trajectories dominates the gain of the peripheral trajectories, so that the net effect is a decrease of the average capacity. Above a certain TTT, this behavior changes and, for sufficiently large values of TTT, the capacity saturates since HO is never triggered. We note that, for very low values of the UE speed, immediate handover is recommended because most trajectories will stay in the femtocell a time long enough to recover from the capacity loss incurred during the HO time TH . The situation is the opposite for high speeds, from which it is better to set a very large TTT value to avoid HO. This argument, however, neglects the effect of Rayleigh fading that, with very short TTT values, will likely result in severe ping-pong effect. Assuming signals are affected by independent Rayleigh fading processes, the ping-pong effect can be mitigated by setting T larger than a specific value, here denoted as Tmin , which can be computed for each value of the UE speed using the results presented in [16]. We choose Tmin to have a probability lower than 0.01 that the HO is improperly triggered by fading processes. An alternative approach that considers the effect of the Rayleigh fading in the HO decision can be found in [17]. According to our mathematical analysis, then, the optimal handover strategy consists in either performing HO as soon as possible, i.e., setting T = Tmin , or not performing HO at all, i.e., using T = ∞. This choice is bound to the context through the speed threshold vth , below which HO is triggered with T = Tmin , and above which HO is not triggered at all. Fig. 3 shows the speed thresholds vth for different combinations of ηF and ηM values. The speed threshold ranges from 1 to 180 Km/h, while the value 200 Km/h indicates that,
1.9
CAW TMIN FIX
vth [Km/h]
200 180 160 140 120 100 80 60 40 20 0
0.3 0.4 0.5 0.6 0.7 0.8 ηF/ηM 0.9
1 3
3.5
4
4.5
5
5.5
6
6.5
Average Capacity bit/s/Hz
1.8 200 180 160 140 120 100 80 60 40 20 0
1.7
1.6
1.5
1.4
ηM 1.3 0
20
40
60
80 100 Speed [Km/h]
120
140
160
180
Fig. 3: vth for different pathloss ratios.
Fig. 4: Average capacity obtained with different approaches.
in the considered scenario, the best strategy is to avoid HO. We note that the vth trend depends on the specific pathloss exponents and not only on their ratio. Moreover, since the cell coverage is determined by the η values, we can notice that vth is directly proportional to the cell size. Then, to optimize the handover procedure it is important to know the mobility characteristics of the users and the channel parameters. Finally, we compare via Monte-Carlo simulations the performance obtained with three different policies, i.e., [CAW]: the context-aware policy that performs handover only when v < vth ; [FIX]: a policy with TTT fixed to T = 100 ms for every speed; [TMIN]: a minimum TTT policy, where T = Tmin for each speed value. The M-BS and F-BS are placed at a distance dM F = 500 m. The signals received from M-BS and F-BS are generated according to two independent path-loss plus Rayleigh fading channel models, with path-loss exponents ηM = 4 and ηF = 2, respectively, and coherence time depending on the UE speed. For every Monte-Carlo run, we compute the average capacity experienced by a user that crosses the femtocell coverage area with a linear trajectory of length L equal to twice the macrocell radius. Fig. 4 shows the average capacity obtained using the three different policies. Note that, at low speeds, the FIX strategy suffers from the ping-pong effect that determines a strong performance degradation. Conversely, TMIN and CAW perform much better by allowing HO after the minimum TTT required to limit the ping-pong effect. For larger speed values, CAW gains over TMIN because it skips HO, avoiding the loss due to the two TH in a short time interval. In this case, also the FIX policy with T = 100 ms achieves the best performance, since the TTT is long enough to avoid handover for the considered scenarios, though performance may drop for other scenarios. The capacity fluctuations are due to the fast fading effect.
R EFERENCES
V. C ONCLUSIONS AND F UTURE W ORK In this paper we have analyzed the UE capacity during the HO process, showing that the impact of the context parameters on the optimal HO policy is quite significant. This result highlights the importance of binding the HO procedure to the context and, hence, to develop context-aware handover procedures. As future work, we plan to couple the model with a machine-learning estimator of context parameters required by the model.
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