Energy Management of Dense Wireless Heterogeneous Networks Over Slow Timescales

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1 Energy Management of Dense Wireless Heterogeneous Networks Over Slow Timescales Binnan Zhuang, Dongning Guo, and Michael L. Honig Department of Electrical Engineering and Computer Science Northwestern University 2145 Sheridan Road, Evanston, IL USA Abstract Future cellular networks are expected to be heterogeneous with dense deployments of base transceiver stations and access points (wireless nodes). Energy consumption and interference management are two major issues in such networks. The goal of this work is to develop a framework for deciding if particular nodes should be powered off to reduce interference and save energy. This is envisioned to occur over slow timescales, i.e., on the order of minutes. The active nodes should provide a target quality of service (QoS) to all mobile users. A network utility maximization problem is formulated, which takes as input the network topology and aggregate demand information, and optimizes over the set of active nodes and the assignment of demands to the nodes. Centralized and distributed algorithms are presented that search for a local optimum, and numerical results are presented to illustrate the performance. 1. INTRODUCTION Commercial wireless networks are evolving towards dense deployments of cells of different sizes, referred to as dense, heterogeneous networks (HetNets) [1]. The motivation to shrink cells is driven by the scarcity of spectrum resources and the increasing demand for broadband data services. Different types of short-range low power small cells (micro/pico/femto along with distributed antennas) will be deployed for rate enhancement along with macro cells for wide area coverage and for serving highly mobile users. How to configure a HetNet to serve such a mix of demands is therefore an important problem. As the number of wireless nodes increases, so does the energy cost of the network. Energy efficiency in This work was supported by a gift from Futurewei Technologies. HetNets has been studied in [2 5]. The common approach to saving energy is to turn off redundant nodes during lightly loaded periods. In these papers, the goal is to minimize the cost of energy under quality of service (QoS) constraints without considering interference. However, when interference is also taken into account, it may be possible to improve QoS (or reduce the required power and bandwidth resources) while simultaneously saving energy. We consider a HetNet with macro cells for serving highly mobile users and micro cells for providing high data rates to relatively stationary users. The user demands are viewed as extrinsic variables. The network topology is adapted by turning the base transceiver stations (BTSs) for the micro cells on and off. The macro- BTSs are assumed to be always on to guarantee coverage. We assume that turning a BTS off puts it in the deep sleep mode considered in [6]. That greatly reduces the associated power consumption for that BTS, but it may take ten seconds or more to reactivate the BTS [7]. Hence topology adaptation occurs on a much slower timescale than channel-aware scheduling, which occurs over periods of a few milliseconds [8]. Topology adaptation must therefore rely on aggregated information about the demands collected over a period T, possibly lasting a few minutes. To determine which BTSs to turn on or off, we formulate an optimization problem in which the objective consists of the utility derived from the service minus the weighted energy cost. The utility depends on the signal and interference powers averaged over the demands. The problem is then to maximize the objective subject to the constraint that all demands are served and that the utilization (load) for each cell is no greater than an upper bound. In addition to determining the set of active nodes, the allocation of demands across nodes is also optimized. This problem is a mixed integer program, which is NP hard. We present centralized

2 and distributed algorithms for finding a local optimum, and illustrate the performance by presenting simulation results for a particular network with randomly placed nodes. The contribution of this work is the introduction of the slow timescale framework to study the tradeoff between mobile utility and energy cost taking interference into account. We also propose algorithms that attempt to optimize this tradeoff, and show that they can provide a substantial improvement relative to assigning each demand to the BTS with strongest received signal. Other related work in [9, 10] provides a stochastic geometry framework for analyzing coverage, SINR distribution, and ergodic capacity in a HetNet. The demand model assumes a stationary set of users with full buffers, and does not account for different loads across the different cells. Different cell loads are considered in [11]; however, in order to apply the stochastic geometry framework, the load for each BTS is assume to be a random variable independent of the real demands of the users, whereas in our model, the load per BTS is determined by the demand assignment. Consequently, the on/off status of a BTS is related to the demand distribution as well as the on/off status of other BTSs, which makes the model intractable under the stochastic geometry framework. The system model is introduced in the next section. The definition of network utility and the problem formulation are presented in Section 3. Centralized and distributed algorithms for finding a local optimum are proposed in Section 4. Simulation results are presented in Section 5, and conclusions are given in Section SYSTEM MODEL We consider a heterogeneous network deployed in a two-dimensional region with m micro-btss and M macro-btss. The total number of BTSs in the HetNet is N = m+m. The geographic region served is partitioned into a uniform hexagonal array, where the hexagons designate the geographic resolution of the model, as opposed to individual cells. That is, each cell (macro or micro) generally contains multiple hexagons. (The particular hexagons covered by a cell is determined by the demand assignment algorithm.) There are a total of hexagons in the network. Each BTS i, i = 1,,N, is assumed to be at the vertex of a hexagon, and user demand occur at a lattice point at the center of each hexagon. A regional snapshot of the network is shown in Fig. 1. The location of mobiles in hexagon k is given by the coordinates of the center point (x k,y k ). The location of BTS i is given by the coordinates of its corresponding vertex, denoted by ( x i,ȳ i ). This discrete model can be made arbitrarily close to the actual de- Figure 1. Network Deployment ployment and demand distribution by shrinking the size of the hexagons. The pathloss from BTS i to mobiles in hexagon k is L ik = (( x i x k ) 2 + (ȳ i y k ) 2 ) α 2, (1) where α is the pathloss exponent. Each micro or macro- BTS transmits with constant power P i. The receive power at the mobiles in hexagon k from BTS i is P ik = P i L ik G ik, (2) where G ik models slow fading, which commonly follows a log-normal distribution. Given the preceding HetNet structure, we propose to adjust the network topology by turning micro-btss on or off every time period T. Decisions are based on the set of aggregate demands {d k } over the hexagons within T, which may last many seconds or minutes. So far, we have been vague about the notion of demand. In this paper, we use demand to model extrinsic source of demand for cellular service, which must all be satisfied. More generally, the demand can be treated as a function of some extrinsic demand and the QoS, which is elastic and dependent on the QoS. For concreteness, the demand in a hexagon is simply understood here as the number of bits sent to users in the hexagon during one period T. The network performance metric is taken to be the sum over user utilities minus a cost term related to energy consumption. There can be many definitions of

3 user utility over the slow timescale considered. Here we assume that the long-term utility of the mobiles in hexagon k served by BS i is proportional to the bandwidth, and depends on the average received power and the average interference, i.e., U ik = Bu(P ik,i ik + n k ), where n k is the noise level in hexagon k, B is the bandwidth shared by all micro and macro-btss, and I ik is the received interference to be expressed shortly. The utility function u(, ) could be the averaged data rate over time, or equivalently, the expectation of log(1 + SINR) over the distribution of SINR assuming it is an ergodic process (i.e., the demand statistics must be stationary within each interval T ). In the absence of an explicitly defined SINR distribution we adopt the surrogate metric ( R ik = Blog 1 + P ) ik. (3) I ik + n k We emphasize that the framework developed in this paper is general enough to incorporate other types of utility functions (e.g., which may emphasize latency). The load at each BTS i is determined by its utilization ratio for serving the demand in hexagon k, given by γ ik = f ikd k R ik, (4) where f ik is the percentage of user demand in hexagon k served by BTS i. The utilization ratio of BTS i is then k=1 γ ik, which represents the fraction of the time BTS i transmits to serve its assigned demands. Hence any mobile not served by BTS i receives interference from BTS i with probability k=1 γ ik. The long-term average interference at mobiles in hexagon k served by BTS i is then I ik = N j=1 j i χ j (I 0 + m=1 γ jm )P jk, (5) where I 0 represents a nominal interference level associated with each active BTS and χ j is the binary variable indicating the on/off status of BTS j. For purposes of our model, the key difference between micro and macro-btss is that the macro-btss are always active (χ n = 1), but micro-btss can be turned off for energy savings and interference reduction. In addition to topology adaptation (determining micro on/off status χ i ), we also wish to determine the best user demand distribution among BTSs. This implies optimizing over the variables { f ik }. The long-term average rates, BTS utilization ratios, and long-term average interference are coupled together. In fact, they are uniquely determined by the network topology and aggregate demand information. For given d k, eqs. (3) to (5) are essentially functions of f ik and χ i. It is difficult to solve the multivariate nonlinear system formed by eqs. (3) to (5) for given f ik and χ i. Instead of a closed-form representation, numerical iterations are used to calculate the actual rate, interference, and utilization ratios. 3. The Optimization Problem The goal is to maximize the network utility as a function of sum user utility and energy consumption. The single mobile utility per unit bandwidth in hexagon k served by BTS i is defined as a function of the power of the useful signal and the interference. For concreteness, we let it take the form U ik = log(p ik ) alog(i ik ). (6) If the parameter a = 1, U ik is simply the logarithm of the signal to interference ratio (SIR). Since the performance of a dense cellular network is typically interference limited, SIR is a good approximation of received SINR. The choice of (6) instead of (3) allows a heavier penalty on low-sinr mobiles, which helps to provide a minimum QoS for most mobiles. The total utility (7) of the network is the sum user (mobile) utility minus the total energy cost: U = N i=1( k=1 f ik d k U ik βw i χ i ), (7) where w i is the maintenance power of BTS i. The parameter β has the operational meaning as the ratio of one unit of total utility per unit time per bandwidth to the cost of one unit energy expenditure per unit time. The optimization problem is formulated as: maximize {χ i },{ f ik } subject to U N f ik = 1, i=1 k=1 γ ik q i χ i, R ik = Blog γ ik = f ikd k R ik, I ik = N j=1 j i k i ( 1 + P ) ik, k,i I ik + n k k,i χ j (I 0 + m=1 γ jm )P jk, k,i. (8) The first constraint states that every demand has to be served either by a micro-bts or a macro-bts. The

4 second constraint means the utilization ratio of BTS i should not exceed q i if BTS i is on and is zero if the BTS is off. The value of q i reflects an operating point that would be chosen by the service provider, and may correspond to a particular average latency. Of course, different utility functions can be used in (6) and (7). The user s utility could be any function of the received SINR, and the total utility could be any function of user utility and BTS power consumption. For example, a step function could be used in (6) for a guaranteed rate service and additional terms can be added in (7) for other types of costs. 4. ADAPTIVE ALGORITHMS The optimization problem (8) is a mixed integer programming (MIP) problem, which is in general NPhard. In this section both centralized and distributed algorithms are proposed to solve (8) Centralized Algorithm For the centralized solution, we propose a gradient search algorithm, which determines the assignment of demands to BTSs in an inner loop, given a fixed on/off pattern {χ i }. The on/off pattern is adjusted in an outer loop by sequentially flipping the on/off state of each micro-bts, and determining if the objective increases. First, we calculate the marginal increase in the objective with respect to an increase in f ik given the current rate, interference and utilization ratios: U = d k U ik a f ik N j=1 m=1 j i f jm d m P im d k I jm R ik, (9) where the second term is due to the interference from BTS i to mobiles served by other BTSs. Since the demand in hexagon k have to be served, we can only move fraction of the demand served by a particular BTS to another BTS. Therefore, every iteration we attempt to move a fraction of the demand in each hexagon k to a BTS with a larger marginal utility. Taking hexagon k for example, we start the handoff attempt from the micro i with the smallest marginal objective U f. We move δ ik ik = min(, f i,k ) of the demand from micro i to the micro j with the largest marginal objective, where is a step-size. If the utilization ratio constraint is satisfied, k=1 γ jk + δ ikd k R jk < q j, (10) then the handoff will be executed. If the utilization ratio constraint is violated, then we try to offload to the micro with second largest marginal objective. Once a successful handoff is made, we terminate the attempts for hexagon k. If no handoff is made after trying all possible receiving BTSs, we start offloading from the BTS l, which has the second smallest marginal objective. After each iteration, i.e., all hexagons have adjusted their demand distributions, we update the rate, interference and utilization ratios based on the new values { f ik }. The iterations continue until the distribution variables { f ik } converge, or a maximum number of iterations is reached. The convergence speed is related to the step size. The on/off status is also adapted by a gradient search scheme. For each iteration we sequentially flip the on/off state of each micro-bts. When the state is flipped, the set of demand assignments { f ik } is updated using the gradient-ascent inner loop. If the total utility (7) is improved, the new state is retained, otherwise the BTS reverts to its previous state. One pass through all micro-btss is counted as a single iteration. We terminate the iterations when the on/off pattern converges. The pseudo code for the centralized algorithm is shown as Algorithm Distributed Algorithm We also propose a distributed algorithm, which requires only local information exchange. The motivation for this distributed algorithm is that the candidate BTSs offering high SIR will be closely located to a demand, and the received interference by mobiles served by one BTS mostly comes from adjacent BTSs. Thus, we consider information exchange among a BTS and its L nearest neighbor BTSs. In the proposed distributed algorithm each BTS adjusts its on/off state and demand assignments asynchronously. To avoid two neighbors adjusting their state at the same time, we divide T into t smaller time slots. We assign an index from one to t to each BTS, where two neighbors cannot be assigned the same index. 1 When micro-bts i s turn arises, it first updates its on/off state, and then updates its demand assignments. When macro-bts j s turn arises, it only needs to adjust its demand assignments. When updating its on/off state, micro-bts i evaluates the regional objective given that it is in either state. If it is currently active, then it first computes the curent regional sum utility: U i,on = j {A i,i} k {k f jk >0} f jk d k U jk βw j χ j, (11) 1 This is a graph coloring problem. To reduce the complexity of the index assignment, we can increase the number of slots t.

5 Algorithm 1 Centralized Algorithm 1: Initialize with an arbitrary on/off pattern {χ i } and demand distributions { f ik }. 2: while {χ i } have not converged do 3: for i = 1,...,m do 4: Set χ i = χ i 5: Adapt the demand distributions 6: while the set of demand assignments { f ik } have not converged do 7: Compute the partial derivatives (9) 8: for k = 1,..., do 9: Order the micros in an ascending sequence of marginal utility with indices {a i } i = 1,,m. 10: for j = N,...,2 do 11: for i = 1,..., j 1 do 12: Attempt to offload δ ai k = min(, f ai k) of d k from micro a i to micro a j. 13: if (10) is satisfied and χ a j = 1 then 14: f ai k = f ai k δ ai k, f a j k = f a j k + δ ai k, γ ai k = γ ai k δ a i kd k h R ai kt, γ a j k = γ a j k + δ a i kd k h R a j kt 15: Finish offloading for hexagon k and go to hexagon k : end if 17: end for 18: end for 19: if The total utility is improved then 20: eep the current status χ i. 21: else 22: χ i = χ i. 23: end if 24: end for 25: end while 26: end for 27: end while where A i is the index set of micro i s L nearest neighbors. Under the hypothesis of shutting off, micro i will offload all its demands to the L closest neighbors offering the highest user utility. (demands from different hexagons served by micro-bts i may be offloaded to different BTSs.) Assuming the offloading happens and micro-bts i is turned off, the SIR of mobiles served by these L micro-btss will change due to the change in utilization ratio and elimination of background interference I 0 from micro BS i. Therefore, we recalculate the regional sum utility: U i,off = j {A i } k {k f jk >0} f jk d k U jk βw j χ j. (12) If U i,on < U i,off, then we shut down micro i and offload its demand. Otherwise, micro i continues to serve its current demand. If micro i is off, then we first calculate U i,off based on current receive power and interference. Then we check all hexagons that are currently served by micro i s L nearest neighbors. For any of those hexagons k, if micro i offers the highest mobile utility U ik, then the corresponding fraction of demands j Ai f jk are sent to micro i. Assuming all these handoffs happen and micro i is on, U i,on is calculated with the updated mobile utilities. If U i,on > U i,off, then micro i is turned on. Otherwise, micro i stays off. The demand distribution updates are the same as in the centralized algorithm, except that BTS i can only handoff its demands to its L nearest neighbors. 5. NUMERICAL RESULTS We now illustrate the performance of the centralized and distributed algorithms through numerical simulations. The test network is deployed in a m 2 area. The inter-site distance (ISD) of the hexagons is 25m. A macro-bts is located at the center of this network, and 99 micro-btss are dropped uniformly over the vertices of the hexagons. The demand in each hexagon is drawn from a Poisson distribution with mean λ (independent across hexagons). The so-called Maximum Reference Signal Receive Power (maxrsrp) scheme is used as benchmark. The maxrsrp association assigns demand in hexagon k to the BTS i, which offers the strongest receive power P 2 ik. We assume micro-btss assigned no demand by the maxrsrp association are automatically turned off. Parameters used in the simulation are micro-bts P i = 1 w for i = 1,,99, macro-bts P 100 = 10 w, q i = 0.8 for all i, here. 2 The cell range expansion technique introduced in [12] is ignored

6 UE traffic 60 on micro BTS off micro BTS micro BTS on/off status meter Figure 2. Total utility versus demand intensity λ. α = 3, h = 1 Mb, B = 10 Mhz, T = 300 s, I 0 = 0.1, and n k = 10 6 w for all k. For the distributed algorithm we choose the five nearest neighbors for regional on/off and demand adaptation. Fig. 2 shows total utility versus demand intensity λ for the three algorithms. These results show that the centralized and distributed algorithms significantly improve the total utility over the maxrsrp algorithm when unit energy cost is relatively high. The gain shrinks as the unit energy cost decreases. For βw i = 1, the energy cost is already negligible. The total utility improvement comes from shutting down a micro-bts serving few demands to reduce interference at mobiles served by other BTSs. To study the on/off pattern, we run the centralized algorithm on a smaller m 2 network with ISD=10m, m=50, M = 0, and λ = 10. The on/off result is shown in Fig. 3. The size of the circle indicates the relative amount of demand in the corresponding hexagon. According to Fig. 3, BTSs close to hexagons with larger demands remain active; BTSs close to hexagons with smaller or no demands are turned off. Since λ = 10 corresponds to a light load, only a small portion of the micro-btss remain active, each serving a relatively large area. The centralized algorithm converges in three iterations. The distributed algorithm usually takes about five or six iterations to converge regardless of the size of the network. However, each iteration in the centralized algorithm must test the on/off and demand distribution status of all the m micro-btss sequentially. In contrast, the distributed algorithm only takes t rounds to test the on/off and demand distribution status, although meter Figure 3. On/off status of micro cells using the centralized algorithm. in each round BTSs that are far apart can be updated in parallel. The single-bts on/off and demand distribution adaptation has computational complexity O(N 2 ) for the centralized algorithm and O(L 2 ) for the distributed algorithm, where is the average number of hexagons served by a BTS and its L nearest neighbors. Therefore the running times of the centralized and distributed algorithm are O(N 3 ) and O(tL 2 ), respectively. Note that is often much smaller than due to the limited number of hexagons that can be served by the L + 1 neighboring BTSs. The distributed algorithm runs much faster than the centralized algorithm as the network grows larger, i.e., as and N increase. However, the shorter running time of the distributed algorithm is at the expense of frequent information exchange among neighboring BTSs. 6. CONCLUSIONS We have proposed a framework for jointly adapting demand associations with the set of active nodes in dense HetNets over a slow timescale. This framework requires knowledge of only aggregate demand information with long-term average performance metrics. The network utility objective can include a long-term average mobile rate along with energy consumption, taking interference into account. For the specific choice of network utility objective considered, both centralized and distributed optimization algorithms were proposed. Based on simulation results, we find that interference from closely deployed

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