Cell Association and Interference Coordination in Heterogeneous LTE-A Cellular Networks

IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 28, NO. 9, DECEMBER 2010 1479

Cell Association and Interference Coordination inHeterogeneous LTE-A Cellular Networks

Ritesh Madan, Jaber Borran, Ashwin Sampath, Naga Bhushan, Aamod Khandekar, and Tingfang Ji

Abstract—Embedding pico/femto base-stations and relay nodesin a macro-cellular network is a promising method for achievingsubstantial gains in coverage and capacity compared to macro-only networks. These new types of base-stations can operateon the same wireless channel as the macro-cellular network,providing higher spatial reuse via cell splitting. However, thesebase-stations are deployed in an unplanned manner, can havevery different transmit powers, and may not have traffic ag-gregation among many users. This could potentially result inmuch higher interference magnitude and variability. Hence,such deployments require the use of innovative cell associationand inter-cell interference coordination techniques in order torealize the promised capacity and coverage gains. In this paper,we describe new paradigms for design and operation of suchheterogeneous cellular networks. Specifically, we focus on cellsplitting, range expansion, semi-static resource negotiation onthird-party backhaul connections, and fast dynamic interferencemanagement for QoS via over-the-air signaling. Notably, ourmethodologies and algorithms are simple, lightweight, and incurextremely low overhead. Numerical studies show that theyprovide large gains over currently used methods for cellularnetworks.

Index Terms—Inter-cell interference management, femtocells

I. INTRODUCTION

LONG Term Evolution-Advanced (LTE-A) wireless net-works are being designed to improve spectral efficiency

per unit area by shrinking cell size via deployment of a diverseset of base-stations [1]. Fig. 1 (from [1]) shows a cellularsystem of macro base-stations deployed in a planned regularmanner with transmit power of up to 40 W, and overlaidwith pico, femto, and relay base-stations which transmit atsubstantially lower power (100 mW to 2 W) and are typi-cally deployed in an unplanned manner. These overlaid base-stations improve coverage and provide capacity gain via higherspatial reuse.

The heterogeneous deployment paradigm differs frommacro-only deployment in the following ways:Interference: Since, heterogeneous cellular networks are

unplanned, femtocells can be closed (i.e., only users in itssubscriber group are allowed to connect to it), and base-stations can have very different transmission powers, het-erogeneous cellular networks can have much more severeinterference characteristics than macro-only cellular networks;power control may not suffice in such scenarios. For example,in a macro-only cellular network, a mobile always connectsto the strongest base-station, and hence, an interferer’s signalis always received at a lower power than the desired signal.

Manuscript received 15 September 2009; revised 28 July 2010.The authors are with Qualcomm (e-mail: {rmadan, mborran, asampath,

nbhush, aamodk, tji}@qualcomm.com).Digital Object Identifier 10.1109/JSAC.2010.101209.

Fig. 1. Heterogeneous network consisting of a mix of macro, pico, femto, andrelay base-stations [1].

In a heterogeneous network, a mobile may connect to a closerpico base-station (to enable cell splitting) even though thereceived power from a macro base-station could be higher.This can lead to a net gain in throughput if resource allocationis done carefully to ensure that the loss in rate to due higherinterference doesn’t dominate the gain in rate due to higherspatial reuse.Traffic Load: Femtocells and picocells typically serve far

fewer users than macrocells. Hence, the traffic in femtocellsand picocells is aggregated less, and so the load can vary ata much faster timescale. This also leads to more interferencevariation. For example, if a femtocell serves only one user,then the queue of packets at the base-station awaiting trans-mission can transition between empty and non-empty on theorder of a few ms. Hence, to use resources more efficiently,resource coordination across cells has to occur much moredynamically than the macro-only case.

A large amount of prior work has focused on resourceallocation for macro-cellular networks. In this case, the as-sociation, i.e., the base-station which serves a mobile isassumed to be given; since all the macro base-stations typicallytransmit at the same power and are usually equally loaded,the mobile is typically best served by the base-station whosesignal it receives with the highest power. Moreover, given thehigh traffic aggregation within a cell and mild interferenceconditions, reuse one scheme is used to serve most of theusers within the cell [2]. For users closer to the cell-edge,we can use fractional frequency reuse (FFR) whereby theneighboring base-stations of each cell lower their transmitpowers on a relatively small fraction of the bandwidth –this bandwidth can then be used to serve cell-edge users [3],[4]. Mechanisms to enable relatively slow time scale inter-cell interference coordination (ICIC) have been incorporatedinto the current LTE standard [5]. On a different note, forpower and bandwidth allocation within a single cell, therehas been much theoretical analysis, especially, for the casewhere a single user is scheduled in each subframe1 (see, for

1In LTE, time is slotted – resource allocation is performed every subframewhich is one ms.

0733-8716/10/$25.00 c© 2010 IEEE

1480 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 28, NO. 9, DECEMBER 2010

example, [6], [7]), while more practical techniques based onthese insights have been studied in, for example [8], [9], [10].We refer the reader to [10] for a comprehensive overview ofpast results on resource allocation to users within a cell.

Resource allocation for femtocells has received attentionrecently. Uplink interference scenarios for joint macro andfemto UMTS deployments along with power control, inter-frequency switch, attenuation, and handover for controllinginterference rise-over-thermal have been studied in [11]. Powercontrol algorithms for joint femto and macro deploymentswere also studied in [12]. Tradeoffs (for both the operatorand users) between open and closed femtocells for OFDMAand CDMA cellular deployments were studied in [13]. Amore theoretical analysis to obtain a set of achievable ratesin linearly deployed closed and open access femtocells forsingle cell and multi-cell processing is done in [14]. We referthe reader to [15] for a survey of work in the area.

For heterogeneous macro-pico deployments, we study(i) novel association schemes to take into account the differenttransmit powers of pico and macro base-stations, and (ii) jointassociation and resource allocation algorithms which are fairacross cells and maximize system efficiency; we focus onmaximizing sum utility of average rates. Specifically, wedesign heuristics which are distributed and computationallysimple. We make use of only the measurements available inLTE or which can be easily enabled in LTE-Advanced [16].The heuristics are shown to offer tremendous performanceimprovement over algorithms designed for macro-only deploy-ments.

For femtocell networks, we design a simple lightweightmechanism and algorithm for interference management anddistributed scheduling across cells for a mix of delay QoSand best effort traffic. Only one round of information exchange(via two transmissions) is considered in each subframe to keepthe latency for coordination and control overhead low. Thealgorithm is a heuristic to maximize a weighted sum rate ateach time [17], [18]. We make no assumption on the regularityof the traffic, and hence the weights can change arbitrarilyfrom one subframe to another. The two main challenges insuch a design are (i) for a given receiver, each interferer has noknowledge of the traffic at the other interferers due to the dis-tributed nature, and (ii) the initial point becomes very criticalsince multiple iterations are not considered. Prior works suchas [19], [20], [21] consider only combinatorial interferencemodels and can require multiple iterations of coordinationevery subframe leading to a higher control overhead and alarger delay in coordination. Also, they focus on stabilizingpolicies or maximization of sum utility of rates. The workin [22] considers a multiple iteration algorithm for a relatedoptimization problem for a class of objective functions whichdoes not include the one in this paper. Modifications to theabove algorithms to work for the system model, objectives,and constraints in this paper are not straightforward.

The rest of the paper is organized as follows. Section IIdiscusses new criteria (as compared to macro-only deploy-ments) for association of a mobile to a serving base-station toobtain good spatial reuse in heterogeneous cellular networks.Section III describes the system model in the context of whichwe design intercell resource allocation and interference mitiga-

Fig. 2. Range Expansion example. The coverage areas are determined on basisof received signal power when both macro and pico base-stations transmit atmaximum power. If a mobile within the coverage area of the macro associateswith a pico base-station based on lower path loss (to enable cell splitting andspatial reuse) it receives interference from the macro base-station at a higherpower than the signal from the pico base-station.

tion algorithms. Section IV describes distributed joint resourcepartitioning and association algorithms for determining whichbase-station each mobile should associate with, what powereach base-station should transmit over each sub-band, and howmany resources should be assigned to a mobile to maximizethe sum utility of average rates. In Section V, we study moredynamic inter-cell interference management algorithms whereone round of information exchange between neighboring cellsis used to determine the transmission scheme in each subframeof 1 ms. Finally, Section VI contains conclusions.

II. CELL ASSOCIATION: CELL SPLITTING & RANGE

EXPANSION

We denote the set of base-stations by B and the setof mobiles by M. The maximum transmit power of eachmobile is identical, and we denote it by P mob. The maximumtransmit power, P max

i , of each base-station i in a heterogeneousnetwork varies depending on whether the base-station is afemto, pico, or macro base-station. The average channel gainbetween mobile i and base-station j is denoted by Gavg

ij – thisencompasses the antenna gain path loss, and shadowing.

If base-station j transmits at maximum power, the averagepower at which mobile i receives the downlink signals frombase-station j is G

avgij P max

j . Hence, if the handoff boundariesbetween cells is based on the received power at the mobiles onthe downlink, each type of base-station will have a differentcoverage area for the downlink. On the uplink, since all themobiles have the same maximum transmit power, the uplinkcoverage area is only a function of the relative channel gainsbetween a mobile and different base-stations. Thus, the uplinkand downlink handoff boundaries based on received power canbe different unlike in the macro-cellular case – this makesthe association or server selection problem more complex.Specifically, if a mobile is associated with the base station withthe strongest downlink signal, it can cause strong interferenceon the uplink to a base station that is closer to the terminal(in terms of path loss or channel gain) but has lower transmit

MADAN et al.: CELL ASSOCIATION AND INTERFERENCE COORDINATION IN HETEROGENEOUS LTE-A CELLULAR NETWORKS 1481

Fig. 3. Range Expansion. Left: Rate CDFs with and without range expansion. Right: User Association Statistics with and without range expansion.

power. On the other hand, if it is associated with the basestation with the strongest uplink received signal, it may receivestrong interference from a base station that is farther away (interms of path loss or channel gain) but has a much largertransmit power. Noise injection can reduce the mismatch butonly at the expense of reducing system efficiency by artificiallyrequiring higher transmit powers from the terminals on theuplink and creating unnecessary interference in the network.

In the presence of sufficient number of lower power base-stations such as pico base-stations, the larger coverage ofmacro base-stations can limit the amount of cell-splitting (i.e.,spatial reuse) by letting more mobiles associate with it. Thismay lead to the case where the macro base-stations becomeresource constrained while the pico base-stations serve veryfew mobiles. Using a simple example topology, we demon-strate the benefits of range expansion where a mobile mayassociate with a pico base-station even though the receivedpower from the closest macro base-station on the downlink ishigher. However, this can lead to more interference from themacro base-station at the mobile which is associated with thepico base-station. This is illustrated in Fig. 2. This necessitatesresource partitioning where the macro base-station lowerspower on a fraction of the spectral or temporal resourceswhich can then be used by such mobiles. Fig. 3 shows therate CDFs and user association statistics for a small networkof two macro base stations (with 43dBm transmit power and17dB antenna gain) and 10 pico base stations (with 30 dBmtransmit power and 5dB antenna gain), with and withoutrange expansion. The range expansion here is achieved byassociating a mobile with the base-station to which it hasminimum path loss and a fixed partitioning of a total of fourresources, equally between the macro and pico base stations.The plot on the right shows that more mobiles associate withthe pico base-station when association is based on minimumpath loss compared to when association is based on receivedsignal power. The plot on the left shows the CDF of mobilethroughput for three different schemes. We observe that forrange expansion with reuse one, a large fraction of mobilesactually see a deterioration in rate due to the large interference

caused by the macro base-station when the mobile associateswith a pico base-station as discussed above. Thus, for gains ofcell splitting to be realized when base-stations have differenttransmit powers, we need partitioning of resources betweenthe different cells – simple fixed partitioning itself leads tosubstantial throughput gains.

III. DOWNLINK INTERFERENCE MANAGEMENT

TECHNIQUES

A. System Model

We focus on the downlink. At subframe t, the channel gainfrom base-station j to mobile i on the downlink is Gij(t);G(t) denotes the corresponding channel gain matrix. Thesevalues account for fast fading and shadowing in additionto path loss and antenna gains. The total data bandwidthavailable for transmission is divided into M sub-bands ofequal bandwidth B. A sub-band is the resource granularityat which transmissions are coordinated across multiple cells.Each base-station i can transmit at maximum power P max

i

over each sub-band2. The achievable spectral efficiency ona single sub-band when the base-station has knowledge of thesignal to interference and noise ratio (SINR) is a functions : R+ �→ R+ of the SINR. Such a function is typicallyobtained via a link level simulation of the modulation andcoding scheme for a specific transmission scheme on, forexample, the data channel in LTE. For given SINR, we cantake the achievable rate to be, for example, the rate at whichthe BER is below 10−5.

Each mobile i measures the following signal-to-noise ratio(SNR) related quantities and feeds them back to its servingbase-station: (i) the channel gain from its serving base-stationS(i), GiS(i)(t), (ii) the channel gains from a subset ofthe interfering base-stations, denoted by Ni; specifically, itcan measure {Gij(t) : j ∈ Ni}, and (iii) total noise powerspectral density (PSD) and ambient interference (other thanthat from the neighboring base-stations above), N0. In LTE,

2We impose a per sub-band constraint on the maximum power – thisassumption is not limiting in high interference environments.


these measurements are made and fed back to the base-stationperiodically. In low mobility environments, such as indoorswithin a femto cell, the channel gains change slowly, andso, we assume that the base-station knows the instantaneousvalues of these gains. In all environments, the base-station S(i)is assumed to have the knowledge of G

avgiS(i), {Gavg

ij : j ∈ Ni}.

B. Time-scales

In this paper, we study two broad classes of interferencemanagement techniques; we classify them according to thetime-scale of coordination:1) Semi-static Interference Management: Here, neighbor-

ing interfering cells coordinate resources over 100s of ms.The resources allocated to the different cells for transmissionshould be such that the system efficiency is maximized whilemaintaining fairness for data flows across cells.2) Fast Dynamic Interference Management: Here, resource

negotiation is done at a much faster time-scale; specifically, weconsider schemes where resource coordination is done everyms. In the case of femtocells, this can lead to better utilization(at the cost of more overhead) of the spectrum and meet QoSdelay targets for a larger number of flows as compared tosemi-static schemes. This is because of the lack of trafficaggregation across the few mobiles served by each cell. Ina femtocell network, there may be subframes where there areno packets waiting for transmission in a cell – in this case,the resources allocated to this cell can be used by neighboringcells.

IV. JOINT ASSOCIATION AND SEMI-STATIC RESOURCE

ALLOCATION

A. Optimization Problem

Since semi-static coordination occurs over 100s of ms, theobjective is to partition resources so as to maximize the sum ofutilities of average rates for mobiles across cells. Specifically,if the average rate of a mobile i is xi, the utility for theuser is Ui(xi), where U is a concave, increasing function.Moreover, since the optimizations are done over 100s of ms,they are based on the average channel gains Gavg

ij ; we dropthe superscript ”avg” in this section to simplify notation.

Let S(j) be the base-station which serves mobile j. LetpS(j)m denote the transmission power at base-station S(j)over sub-band m; in general we will use pim to denote thetransmission power of base-station i over sub-band m. Then,the spectral efficiency for serving mobile j on sub-band m isgiven by

ρ(p, j, S(j), m) = s

(pS(j)mGjS(j)∑

k �=S(j) Gjkpkm + N0B

),

If fraction βj,S(j),m of sub-band m at base-station S(j) isallocated to mobile j, the resulting sum utility across thenetwork is∑

j∈MUj

(M∑

m=1

βj,S(j),mρ(p, j, S(j), m)

).

Our goals are: (i) for given association mapping {S(j) :j ∈ M}, optimize over the variables βj,S(j),m’s, pjm’s, and(ii) optimize over the association mapping {S(j) : j ∈ M}.

1) Two User Example: Figure 4 shows the level sets oftwo different utility functions superimposed on the rate regionof two links (where each link consists of a base-station andassociated mobile) which interfere with each other. The rateregion shown includes rate combinations achievable by powercontrol and by time-sharing across different power controlmodes. Association is assumed to be fixed. In the first case(left graph), the optimal rate combination is achieved by asingle choice of transmit powers used always. For the secondcase (right graph), the optimal operating point is one obtainedby time-sharing between a scheme where only user 1 transmitsand a power controlled scheme where both the users transmitsimultaneously. Thus, the optimal transmission scheme (foreach link or cell) is both a function of topology as well as theutility function. This cannot be captured by a combinatorialinterference model where it is assumed that either the two linkscan transmit simultaneously always (and see no interferencefrom each other) or only one link can transmit at a given time;combinatorial interference models capture well carrier sensemultiple access (CSMA) type of medium access control, infor example, IEEE 802.11, [23].

B. Interference Neighborhood

The above optimization problems require high complexitycentralized computation. However, we note that channel gainsare usually correlated with geographic distance between nodes,and nodes that are farther away from each other are notlikely to cause significant interference to each other. Hence,a given base-station is assumed to make decisions only onthe basis of a subset of (aggressor) base-stations which eithercause a lot of interference to a mobile it serves or whoseserved (victim) mobiles receive a lot of interference fromthis base-station. This set can be defined in various ways.For example, we define a quantity γi,j for mobile i andbase-station j as γij = GijP

maxj /N0B, where P max

j is themaximum transmit power over a single sub-band. For a givenassociation mapping S, the interference neighborhood of abase-station i based on threshold γ is given by I(i, S) ={i′ ∈ B : ∃j s.t. i = S(j) and γji′ > γ}. Interferenceneighborhoods can be represented by a conflict or jamminggraph G(S) = (B, E(S)), with node set B, and an edge setE(S) where two base-stations i and i′ are connected by anedge if i ∈ I(i′, S) or i′ ∈ I(i, S).

C. Adaptive Association and Resource Partitioning

We denote the set of transmission powers for base-stationi in each sub-band by Pi. We first focus on optimal resourcepartitioning for given association.1) Fixed Transmission Powers: If the transmission power

pim of each base-station i over sub-band m is fixed, then theoptimal resource allocation in each cell i can be computed byoptimizing over βj,S(j),m’s to maximize

∑j:S(j)=i

Uj

(M∑

m=1

βj,S(j),mρ(p, j, S(j), m)

)

where S(j)’s, and hence ρ(p, j, S(j), r)’s are given. It iseasy to show that the resulting optimization problem is a


0 1 2 3 4 50

0.5

1

1.5

2

2.5

R1

R2

optimal rate pair

0 1 2 3 4 50

0.5

1

1.5

2

2.5

R1

R2 optimal rate pair

Fig. 4. Optimal operating point for different utility functions. Left: U1(x1) = log x1, U2(x2) = 5 log x2. Right: U1(x1) = 3 log x1, U2(x2) = log x2.

convex optimization problem, and can be solved efficientlyby exploiting structure using methods in, for example, [24].2) Transmission Power Adaptation: The adaptation of

transmission powers on the sub-bands is done across base-stations in an iterative manner using coordination messages.We now describe the main steps qualitatively. During eachiteration, a base-station (a) evaluates the total utility in itscell by solving the above optimization problem for differentcombinations of its transmission power and its neighbors’transmission powers on a sub-band, (b) communicates thisinformation to its neighboring base-stations, (c) uses thereceived messages to compute the total utility in its neigh-borhood for different combinations of transmission powers,and selects the transmission power level on the basis of thiscomputation.

We use a similar iterative process to determine associationupdates. Specifically, during each iteration, a base-stationevaluates the total utility in a neighborhood when a mobileit serves is associated with itself or another neighboring base-station; the evaluation of total utility is done for a combinationof transmission powers for base-stations in a neighborhoodover a sub-band. Thus, in a given iteration, a mobile maybecome associated with a different base-station and its originalserving base-station may reduce transmission power on a sub-band so that the new serving base-station can use it.

D. Numerical Results

Computing an optimal resource partitioning and associationscheme is prohibitive for reasonably sized networks; theresulting optimization problem is combinatorial. Specifically,for N base-station, M mobiles, R sub-bands, P power levels,the complexity is O(NMPRN ). We first consider a smallernetwork of one macro base-station (maximum transmit powerof 43 dBm), two pico base-stations (maximum transmit powerof 30 dBm), and five mobiles to compare the performanceof our heuristic in the previous subsection for resource par-titioning and association to an optimal centralized resourcepartitioning and association scheme. Specifically, the base-stations are placed on a line with 100 m separation suchthat the pico base-stations are on either side of the macrobase-station, and mobiles are dropped uniformly at randomin the area; we simulate multiple random drops of mobiles.We consider M = 3 sub-bands, and on-off power controlfor pico and three power levels for macro base-station. The

association scheme for a sample drop and the rate cdf formultiple drops computed by our heuristic are shown in Fig. 5.The plot illustrates that association is based on both receivedpower and path loss – for example, two mobiles are associatedwith the macro base-station even though they are closer to apico base-station. The rate CDF shows that at least for thissmall topology, our heuristic results in a near optimal resourcepartitioning and association scheme. The average rate for ourheuristic is about 4% less than that of the optimal scheme.

Figure 6 shows the rate CDFs for different association andresource partitioning schemes for two different utility func-tions, namely U(x) = log x (proportional fair) and U(x) =−1/x3 (more fair than proportional fair) for a network of twomacro base stations, 10 pico base stations, and 20 mobiles.The number of sub-bands, M = 4. The resource partitioningschemes considered here are “reuse one”, “fixed resourcepartitioning” of (2, 2) between macro and pico base stations,and “adaptive resource partitioning”. The association schemesinclude “no range expansion” (association based on maximumdownlink received power), “range expansion” (associationbased on minimum path loss), and “adaptive association” asdescribed above. The resulting average utility is mapped backto a single user’s rate, and shown for each scheme. As seen inthese figures, substantial gains can be achieved through rangeexpansion along with adaptive resource coordination amongdifferent base stations in the network. Furthermore, jointadaptive association and resource partitioning can provideadditional gains and increased robustness.

V. DYNAMIC INTERFERENCE MANAGEMENT

In this section, we focus on dynamic interference manage-ment algorithms, where coordination across cells is done everysubframe (Δt = 1 ms in LTE); we prioritize packets basedon marginal utilities of average rates for best effort usersand head-of-line delay for delay QoS users in each subframe.Specifically, we focus on networks of only femtocells withclosed subscriber group (CSG) – each mobile can associateonly with its owner’s femtocell. We assume one mobile perfemtocell. Since, the association is given, we index the links(femto base-station and served mobile pairs) as 1, . . . , N . Bymobile i we refer to the mobile for link i, and by base-stationi we refer to the femto base-station for link i.


−150 −100 −50 0 50 100 150

−50

0

50

100

(m)

(m)

Macro BS (46dBm)Pico BS (30dBm)MobileAssociationR

min Link

1 10 1005 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

User Throughput (Mbps)

CD

F

heuristicoptimal

Fig. 5. Adaptive resource partitioning and association for small topology. Left: Example association from a single drop. The Rmin link corresponds to themobile which obtains minimum rate. Right: Rate CDF for optimal scheme and heuristic.

Fig. 6. CDF of user rates for different resource partitioning and association schemes. Left: Log Utility. Right: Utility function U(x) = −1/x3.

A. Rate Adaptation

We assume that the base-stations indicate their transmitpower in advance (as a result of exchanging messages forcoordination) by transmitting reference signals with the trans-mit power. The mobiles can thus measure the expected SINRand feed it back to the base-station just like the currentchannel quality indicator (CQI) reports (based off constantpower pilots) in LTE. The base-station can thus use an optimalmodulation and coding scheme, and the rate achieved by user ion sub-band m at subframe t is simply a function of the SINR(for transmission power pim(t) ∈ P for link i over sub-bandm)

rim(G(t), p(t)) = Bs

(Gii(t)pim(t)∑

j �=i Gij(t)pjm(t) + N0B

).

The rate achieved by user i at subframe t over all M sub-bandsis ri(G(t), p(t)) =

∑Mm=1 rim(G(t), p(t)).

B. Traffic Types & Centralized Scheduling

We consider two different types of traffic flows/applicationsin this paper: best effort and delay QoS.

(1) Best Effort Elastic Flows: A flow, i, which is best-effort elastic is associated with an average rate xi(t) ∈ R+

at subframe t which is updated every subframe as follows:

xi(t + 1) = (1 − αi)xi(t) + αiri(G(t), p(t)), ∀t ≥ 0,

where 0 < αi < 1 is a flow specific constant. This constantis used to determine relative emphasis on the rates at whichthe flow was served in the past and the current achieved rate.The user experience at subframe t is then a strictly concaveincreasing function Ui : R+ �→ R of the average rate xi(t).(2) Delay QoS Flows: For such flows the end-user experi-

ence is a function of the packet delays. We denote the queue-length of flow i at time t by qi(t), and the correspondinghead-of-line delay by di(t). Motivated by the results in [17],[25], we prioritize the flows by a monotonic increasing func-tion of head-of-line delay and the queue-length, denoted by


0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

K1

K2

link 1 at max power

link 2 silent

links 1,2 atmax power

link 2 at max. power

link 1 silent

Fig. 7. Two user example. Optimal operating point as a function of relativepriorities when a transmitter can either be silent or transmit at full power.

f : R+ × R+ �→ R. Thus, the priority of a QoS flow i attime t is f(qi(t), di(t)). Commonly used functional forms forf include log(qi(t)), log(di(t)), exp(qi(t)), exp(di(t)), qi(t),di(t). Different metrics provide different tradeoff betweenmaximizing instantaneous served rate and balancing queues;see for example, [10], and the references therein.

For a mix of best effort (set B) and QoS flows (set Q),we use a prioritization constant, λ, to determine the relativeprioritization between a best effort and a QoS flow. Then, thepriority of flow i at time t is given by

Ki(t) =

⎧⎨⎩

f(qi(t), di(t)) if i ∈ Q,

λU ′i(xi)/αi if i ∈ B.

We consider the following centralized high complexity sched-uler as a baseline. At each time t, for m = 1, . . . , M ,(1) set pim(t)’s to maximize

N∑i=1

Ki(t)rim(G(t), p(t)), (1)

(2) update Ki(t) assuming rim(G(t), p(t))Δt bits have beenscheduled from buffer of user i.The resulting scheduler (i) roughly speaking, maximizes thesum of utilities of average rates for small αis when all flowsare best effort (follows from [18]), and (ii) stabilizes thequeues for a feasible rate arrival vector when all flows areQoS [17], [21].Example

We now consider the rate region for two links whosetransmitters interfere with the receiver of the other link. Forexample, consider the (normalized) channel gain matrix to

be given by G =[

31.0 1.60.2 1.0

]. This could occur in a

scenario where the transmitter of the second link is closerto the receiver of the first link than the receiver of the secondlink. The optimal operating point (shown in Fig. 7) in asubframe and sub-band is a function of the ratio of relativepriorities K1 and K2. For illustration, we consider an on-offscheme – the three operating points are (i) both transmitterstransmit at full power, (ii) only link one’s transmitter transmitsat full power, and (iii) only link two’s transmitter transmitsat full power. Extension to multiple level power control is

straightforward. We see that when either link has much higherpriority than the other link, it is optimal for the other link to besilent. However, for a sizeable range of relative priorities, theoptimal transmission scheme is one where both transmitterstransmit. Thus, the optimal operating point depends on boththe interference scenario and the relative priorities of the users.Moreover, whether or not two transmitters should transmitsimultaneously depends on the relative priorities in a subframeand the channel gain matrix. This cannot be captured bya combinatorial interference model (static resource sharingmodel) where either the two links are considered to conflictwith each other or the two links are considered to be conflict-free.

C. Over-the-air (OTA) Coordination

In order to coordinate transmission on the downlink acrossmultiple base-stations via a single iteration of informationexchange, the base-station in each cell i needs to be awareof the following information for neighboring cells Ni: (i) theresources over which base-stations in neighboring cells intendto transmit, (ii) the priority of traffic in neighboring cells(iii) the reduction in rate that a base-station’s transmissioncauses at a victim mobile in another cell with which it inter-feres – for this, the link quality of the mobile being interferedwith (composed of serving gain Gii(t) and a quantity callednominal interference Inom

i (t) at mobile i, described later inthis section) and the (cross) link gain to the victim mobilebeing interfered with is required.

We now describe the main heuristic for distributed interfer-ence management and scheduling across multiple femtocells.assuming zero delay for coordination.

Coordination is achieved between two neighboring cellsthrough the following two transmissions, illustrated in Fig. 8followed by the steps in Sec. V-A for SINR estimation at themobile and rate adaptation.(1) CoordReq: In the first step, the serving base-stationcommunicates the following to a served mobile: (a) thepriority of the traffic pending transmission to the mobile,Ki(t), and (b) the set of sub-bands over which it wantsto schedule transmissions to the mobile, Mi(t). The base-station computes these on basis of the packets buffered fortransmission to the mobile.(2) CoordMsg: The mobile then broadcasts a message toits neighboring interfering base-stations, Ni, to relay theabove information in addition to channel information so thatthe interfering base-stations can determine the amount ofinterference they create at the victim mobile. The broadcastmessage contains (a) Ki(t), (b) Mi(t), and (c) nominal SINRbased on setting interference equal to a nominal interference,Inomi (t). The nominal interference computation is described

later in this section. In addition, a base-station j that receivesthe CoordMsg can infer information about the cross-linkgain to victim mobile i based on the received power ofthe CoordMsg. Specifically, the transmission power of theCoordMsg (transmitted by mobile i) is scaled such that theinterfering base-station j can infer (Gij(t)/Gii(t)P max

i ).

We note that the above information exchange occurs oncein a subframe and only between neighboring cells. Only one


Fig. 8. Interference Coordination Across Cells. Left: The CoordReq message is transmitted by the base-station to its mobile. It contains the priority of thetraffic, Ki(t), and the set of sub-bands, Mi(t) over which it intends to serve the mobile. Right: The CoordMsg is broadcast by the mobile to nearbybase-stations which interfere with it. It contains the information in the CoordReq, and also conveys additional information about the serving channel and theinterference channels.

priority metric for all sub-bands is exchanged. Thus, theinformation exchanged is much less than that needed for thecentralized scheduling to maximize objective in (1). We nowdescribe the simple computations involved.

D. Resource Selection

The number of sub-bands contained in the CoordReq mes-sage transmitted by a base-station to its mobile is based onthe amount of data pending transmission to the mobile:

|Mi(t)| = min[M,

⌈qi(t)/Δt

Bs (Gii(t)P max/(Inomi (t) + N0B))

⌉]

i.e., it is assumed that the user will see an SINR based on thenominal interference and we attempt to serve all the packetsin the queue in a sub-frame. Since, the distributed heuristicinvolves only one round of information exchange, choosingthe sub-bands intelligently can lead to better performance than,for example, selecting in an i.i.d. manner across links, asillustrated by following example.Example: Consider two links which cannot transmit simul-

taneously on the same sub-band, and bandwidth is dividedinto two sub-bands. Furthermore assume that the transmitterof only one link transmits on one sub-band, it gets a rate of oneunit per slot. In a given subframe, without loss of generality,assume that link one has higher priority. Moreover, if bothlinks attempt to transmit on a sub-band, the higher prioritylink gets to use the sub-band (through perfect contentionresolution). Now consider two schemes: (i) Independent sub-band selection: Here, if a transmitter has non-zero but less thanor equal to one unit of data, it selects a sub-band to transmitover independently of the other transmitter. If it has morethan one unit of data, it transmits over both sub-bands. (ii)Coordinated sub-band selection: Similar to the above scheme,but transmitter one uses sub-band one (and transmitter twouses sub-band two) if it has less than or equal to one unit ofdata. When one of the transmitters has more than one unit ofdata, both the schemes give the same rate. However, when bothtransmitters have less than one unit of data, (higher priority)link one gets the same rate under both schemes, while linktwo on an average gets half the rate for the uncoordinatedscheme as compared to the rate for the coordinated scheme.

In general, we construct a conflict graph [26], where theset of links which have a conflict (due to high interference)with link i is denoted by Ci.3 The links are then colored viadistributed randomized coloring [27], where two links i andj are allocated a different color if i ∈ Cj or j ∈ Ci. Thisresults in each link having a color or a preferred sub-band,mpref

i . Then, the base-station for each link i can select |Mi(t)|sub-bands in the following order: (i) preferred sub-band mpref

i ,(ii) sub-bands which are not preferred sub-bands for links inCi, (iii) other sub-bands.

E. Transmission Power Computation

Each base-station computes the transmission power to amobile in its cell as a function of the CoordMsgs received fromvictim mobiles; this power is indicated on the downlink pilotsto the victim mobiles. The goal is to maximize the sum ofrates weighted by priority as in (1). Each base-station tradeoffsthe value (rate times priority) its own mobile can obtain byserving it at high power versus the value an out of cell mobilewill obtain if the base-station lowers its transmit power. Atbase-station i, for each sub-suband m, we first compute thevictim mobile, vim(t) to which base-station i’s transmissioncauses the maximum estimated reduction in rate times priorityKj(t):

vim(t) = argmaxj∈Ni:m∈Mj(t)

Kj(t)

(s

(Gjj(t)P max

Inomj (t) + N0B

)

− s

(Gjj(t)P max

Inomj (t) + N0B + Gij(t)P max

)).

(2)

The first spectral efficiency quantity is the spectral efficiencyachieved at nominal SINR at mobile j; the nominal SINRis contained in the CoordMsg transmitted by mobile j. Thesecond spectral efficiency quantity can be written as follows:

3The construction of the conflict graph and the allocation of preferred sub-bands is done in a semi-static manner, for example, based on the channelstates with fast fading averaged out. A specific conflict criterion based oncross-link gains is: Ci =

˘∀j �= i such that Gij/Gii ≥ θ¯

, where θ is aconstant threshold, and Gij is the average of Gij(t) computed over theorder of time when shadowing states change.


s

⎛⎝ 1

Inomj (t)+N0B

Gjj(t)P max + Gij(t)P max

Gjj(t)P max

⎞⎠ . (3)

Now, as per Sec. V-C, nominal SINR (Inomj (t) +

N0B)/(Gjj(t)P max) is signalled in the CoordMsg broadcastby mobile j, while Gij(t)P max/(Gjj(t)P max) can be deter-mined at base-station i based on the received signal powerof the CoordMsg transmitted by mobile j. Finally, the datatransmission power for base-station i over sub-band m isdetermined as follows:

pim(t) =argmaxπ∈P

(Ki(t)s

(Gii(t)π

Inomi (t) + N0B

)

+Kvim(t)(t) s

(Gvim(t)vim(t)(t)P max

Inomvim(t)(t) + Gvim(t)i(t)π + N0B

)).

(4)

The second term on the right hand side can be computed usingthe approach for computation of (3).

Thus, note that over each sub-band, the base-station com-putes the transmission power based on maximizing the totalestimated value to its served mobile and to a single victimmobile. If the transmission powers of all the other base-stations were fixed, the second term (for victim mobile) shouldbe summed over all victim mobiles to which the base-stationcauses interference. Since this is not the case and only oneround of information exchange occurs, considering only onevictim mobile in the trade-off above is more robust; oursimulations showed that summing over all victim mobilesleads to an over-estimation of the value gained by othermobiles by lowering the transmit power leading to too muchpower back-off in the network.

F. Nominal Interference Computation

In the computations in Sec. V-D and V-E, the vector Inom(t)is used to compute a reference rate to decide how manysub-bands a mobile should contend for (as a function ofits buffer length, see Sec. V-D) and to decide what rate amobile can achieve in presence of interference from nearbybase-stations (see equations (2), (4)). This initial referencerate computation is critical because our heuristic is one-shot.From equation (4), we see that the value of Inom

i (t) influencesthe amount that other transmitters lower their transmit powerto allow transmissions on link i to take place at a higherSINR. Only interfering base-stations which cause significantinterference at receiver of link i as compared to Inom

i (t) willreduce their transmit power.

Inomi (t) is computed at the receiver of link i based on

channel measurements. For each link i, let us order thecross-link gains Gij(t), j ∈ Ni, in decreasing order; thecorresponding permutation of (j = 1, . . . , N − 1) is denotedby (σ(1), . . . , σ(N − 1)). Now, for argument’s sake, if the khighest interferers are silenced and link i gets 1/(k + 1) ofthe spectral resources, the rate achieved by link i is

MB

k + 1s

(Gii(t)P max∑N−1

j=k+1 Giσ(j)(t)P max + N0B

). (5)

0 1 2 3 4 50

2

4

6

8

10

12

14

16

18

20

num interferers silenced

min

. SIN

R im

prov

emen

t

−10 dB0 dB10 dB

Fig. 9. Minimum SINR improvement to break even when orthogonalized with1 to 5 interferers for different user SINRs in reuse one: -10 dB, 0 dB, 10 dB.

We denote by kopt(i, t) the value of k ≤ |Ni| which maximizesthe above rate during subframe t. Then, we set Inom

i (t) =∑N−1j=kopt(i,t)+1 Giσ(j)(t)P max. Thus, the nominal interference

is computed as the residual interference when an optimalnumber of interferers transmit at zero power, where it isassumed that when k interferers back off, a link will beallocated 1/(k+1) spectral resources. Thus, we capture both,the improvement in the SINR and the loss of degrees offreedom in the spectral domain when more interferers backoff. Of course, this is a heuristic and based on symmetryarguments.

Fig. 9 shows the minimum improvement in SINR as afunction of k for the quantity in equation (5) to be greaterthan the rate in reuse one; this is plotted for three differentSINRs in reuse one: -10dB, 0dB, 10dB. We observe that onlywhen a high improvement in SINR is obtained by removingan interferer, the increase in rate due to a higher SINRcompensates for the loss in spectral resources. For example,even for a user with reuse one SINR of -10 dB, more than 6 dBof SINR improvement is required when three interferers aresilenced; for a user with reuse one SINR of 10 dB, the SINRhas to improve by more than 10 dB to compensate for the lossin bandwidth when just one interferer is made orthogonal.

G. Numerical Comparison with Optimal Scheme

The deployment and channel model used for simulation isthat in [28]. Shannon capacity formula is used as the spectralefficiency function, s, which maps SINR to rate. Femtocellsare deployed in a 3×3 apartment cluster, where each apartmentis of the same size, 10 m by 10 m. In each apartment,a base-station and a mobile are dropped independently anduniformly at random. The maximum transmit power at eachbase-station is 100 mW, the total bandwidth is 5 MHz, andthe noise power spectral density is −174 dBm/Hz. We modelpath loss (in dB) as 127 + 30 log10(d) for distance d in km,lognormal shadowing with a standard deviation 10 dB, andRayleigh fast fading with a Doppler of 5 Hz. The shadowingbetween a given mobile and different base-stations have acorrelation coefficient of 0.5. Four users are delay sensitiveand five users are best-effort (modeled by full-buffer). For thedelay sensitive users, each burst of packets is 50KB (this is


0.01 0.1 1 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

rate (Mbps)

cdf

heuristicoptreuse one

(a) Average rates of best effort users

0 25 50 75 100 125 150 175 2000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

90 percentile delay (ms)

cdf


(b) 90th percentile delays for delay QoS users

0 20 40 60 80 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Median delay (ms)

cdf


(c) Median delays for delay QoS users

Fig. 10. 50% delay QoS flows with 50KB packets and average inter-arrivaltime of 100 ms.

equivalent to an average rate of 4 Mbps), and the packet inter-arrival times are exponentially distributed with a mean of 100ms. The utility function for best-effort users is log while thepriority metric for QoS users is head-of-line delay; the relativenormalization of priorities for the two kinds of traffic is suchthat a full buffer user with average spectral efficiency of onehas the same priority as a QoS flow with head-of-line delayof one subframe. Only on-off power control is considered butsimilar results hold for general power control. CoordMsgsare transmitted by the base-station to its mobile when thebuffer is non-empty with probability 0.5 – this randomizationhelps reduce the probability of deadlocks where a base-station

lowers its transmit power for a neighboring cell whose base-station in turn lowers its power for yet another cell.

Fig. 10 shows the results for an optimal centralized scheme(Sec. V-B), for our heuristic, and for reuse one schemewhere a transmitter transmits on randomly selected sub-bandsdepending on the amount of traffic in the buffer. We makethe following observations from the results: (1) For the reuseone scheme, about 70% of the delay sensitive flows have 90thpercentile packet delay of more than 200 ms while about 30%full buffer users have rate less than 10 kbps. This is due tolarge amount of interference in a femto environment. (2) Boththe centralized scheme and the distributed heuristic lead tosubstantially improved performance for both full buffer anddelay sensitive users. Of course, the distributed heuristic doesnot perform as well as the optimal algorithm. But with justone round of very few bits of information exchange, it leadsto 90th percentile delays of less than 25 ms for almost all QoSusers, and rates above 5 Mbps for 90% of full buffer users.

VI. CONCLUSIONS

In this paper, we first studied association and resourcepartitioning schemes for heterogeneous networks. The nu-merical results demonstrate that simple lightweight heuristicscan lead to significant performance gains over techniquescurrently used in macro-only cellular networks. Moreover,such techniques are essential to realize the potential capacityand coverage gains from deploying unplanned heterogeneousnetworks. The heuristics are general and extend to any notionof fairness based on a concave increasing utility functionof average rate. For femtocell networks, we designed simplefast distributed mechanisms and algorithms for dynamic inter-ference management every subframe. Such schemes providetremendous gains over reuse one and are near optimal whenthe number of interfering links is small.

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Ritesh Madan received a Ph.D. in 2006 and a M.S.in 2003 from Stanford University, and a B.Tech fromthe Indian Institute of Technology (IIT) Bombayin 2001, all in Electrical Engineering. At Stanford,he was a recipient of the Sequoia Capital StanfordGraduate Fellowship. He is currently at CorporateR&D in Qualcomm, NJ. His research interests in-clude methods for resource allocation in wirelessnetworks, stochastic control, and optimization.

Jaber Borran received the B.S. degree in Electricaland Electronics Engineering and the M.S. degreein Electrical and Communications Engineering fromSharif University of Technology, Tehran, Iran, in1993 and 1996, respectively, and the Ph.D. de-gree in Electrical Engineering from Rice University,Houston, Texas, in 2003. He received the silvermedal in the International Mathematics Olympiad,1989, Germany, and was a recipient of the NokiaMobile Phones R&D Intern Scholarship in 2002.He is currently a Staff Engineer at Qualcomm Inc.,

San Diego, CA. His research interests include wireless communications andinformation theory.

Ashwin Sampath is a Principal Engineer/Managerat Corporate R&D, Qualcomm, in Bridgewater, NJ.Prior to joining Qualcomm in 2005, he held po-sitions in Texas Instruments (2003-2005) and BellLabs, Lucent Technologies (1997-2003). In additionto several publications, he holds 23 patents in thefield of 3G and 4G wireless communications withadditional ones pending. He obtained his PhD inElectrical Engineering at WINLAB, Rutgers Uni-versity, in 1997.

Naga Bhushan obtained his B. Tech. degree inElectronics from I.I.T. Chennai, India in 1989, andM.S an Ph.D degrees in Electrical Engineering fromCornell University in 1992 and 1994 respectively.He has been working as a Systems Engineer atQualcomm since 1994, where he is now a VicePresident of Technology in the Corporate R&Dgroup. His areas of interest include channel coding,link adaptation techniques, modem design and op-timization. Naga Bhushan has been involved in thedesign, development and performance optimization

of advanced wireless communication systems such as cdma2000 EV-DO,Ultra Mobile Broadband (UMB) and 3GPP LTE-Advanced.

Aamod Khandekar received his B.Tech. Degree inElectrical Engineering from IIT Bombay in 1998and his Ph.D. in Electrical Engineering from theCalifornia Institute of Technology in 2002. He hasbeen working at Qualcomm since 2002, where hiswork has involved the design and standardization ofwireless communication systems.

Tingfang Ji received his B.S. degree in electronicengineering from Tsinghua University China in1995, his M.S and Ph.D degree both in electricalengineering from the University of Toledo Ohio andthe University of Michigan, Ann Arbor in 1997 and2001, respectively. From 2001 to 2003 he was amember of the technical staff at the Bell Labora-tory Advanced Technology department involved incellular technologies and Ultra Wide Band research.Since 2003, he has been with the Corporate R&Ddivision of Qualcomm Inc, where he is currently a

senior staff engineer and manager. From 2003 to 2007, he was one of the keytechnical contributors to the development of wideband OFDMA technologiesthat evolved into IEEE 802.20 and 3GPP2 UMB standards. Since 2007, he hasbeen actively contributing to the development and standardization of 3GPPLTE Advanced technolgies. His research interests include the PHY/MAC/RFaspects of heterogeneous networks, carrier aggregation, network MIMO, andrelay networks.

Cell Association and Interference Coordination in Heterogeneous LTE-A Cellular Networks

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