Maximizing network capacity in an heterogeneousmacro-micro cellular scenarioFrancesco Ivan Di Piazza, Stefano Mangione, and Ilenia Tinnirello

Universita di Palermo, Italy

Abstract—The problem of resource allocation in cellular net-works has been traditionally faced at two different levels: at thenetwork level, in terms of frequency planning and reuse patterndesign, and at the cell level, in terms of cell capacity optimizationsbased on channel-dependent scheduling, link adaptation, powercontrol, and so on. While this second aspect has been deeplyinvestigated in literature, the first aspect has been mainly facedwith static or semi-dynamic reuse utilization solutions.In this paper we deal with the problem of multi-cellular

resource allocation in heterogeneous OFDMA environments withreuse factor equal to 1, where base stations with differentpower constraints coexist. In particular, we analyze the effectsof different allocation schemes, independently performed in eachcell, on the aggregated network-level performance. By means ofsimulation results, we enlighten the network scenarios in whichnetwork planning and mobile station feedbacks are (or not are)advantageous.

I. INTRODUCTIONFuture generation wireless networks have to cope with the

scarcity of the spectral resource in areas with heavy userdemand. Therefore, they have to simultaneously pursue themaximization of spectral reuse and per-link capacity. Thesetwo needs have been traditionally faced by decoupling themulti-cell resource allocation problem from the single cellcapacity optimization. In other words, in current approaches,resource allocation is performed in two different levels, interms of a priori frequency planning at the network leveland run-time scheduling, power control and link adaptation atthe cell level. Indeed, each resource allocation level stronglyaffects the performance of the other one. For example, theinterference suffered in each cell depends on the reuse pattern[1], while advanced scheduling techniques (based on channelor user location information) can allow shorter reuse distances.Recent literature is considering joint optimization solutions

for the multi-cell [2], [3], [4] and single-cell [5], [6] resourceallocation problem. While the degrees of freedom of suchan optimization offers a significant space for improving theoverall network performance, the actual feasibility of thesesolutions is limited because of the computational complexityof the optimization and the significant overhead due to therequired signaling. In order to reduce the signaling, someallocation solutions introduce artificial ”structures” devised tomake interference more predictable. For example groupingcontiguous multi-carriers, shaping power according to a pre-defined profile, [7], [8] switching periodically transmissionbeams, and so on, can help in reducing the optimization spaceand the required interference information. As far as concernsthe complexity, several heuristic solutions have been proposed

for adapting general optimization principles to simple anddistributed implementations. However, most of these schemeswork in homogeneous scenarios (i.e. considering that all cellsare experiencing similar interfering conditions) and in verylow or very high Signal to Noise Ratio (SNR) regimes [9].In this paper we deal with the problem of multi-cell and

single-cell resource allocation in OFDMA systems with reusefactor equal to 1, when the interference conditions experiencedin the network are heterogeneous. Given the complexity ofthe joint allocation, scheduling and power control problem,we simplify the network load scenario by considering a singleuser per cell. Although this assumption hides the multi-userdiversity gain, it allows to compare different (greedy andnon-greedy) channel reuse policies without considering anyuser scheduling scheme (whose effect could complicate theinterpretation of the results). We assume that greedy reusepolicies are devised to utilize all the carriers available in thecell, while non-greedy policies utilize a pre-defined ratio of thecarriers. We compared the performance of different allocationschemes in macro-cellular and micro-cellular propagation en-vironments, where we introduced heterogeneous peak powersfor different BSs (emulating a mixed macro-micro cellularnetwork). In most of the considered scenarios, we noticedthat water filling allocations, performed independently by eachcell, provide better performance than the other tested allocationschemes.The rest of the paper is organized as follows. In section II we

describe the OFDMA network model considered in this paper.In section III we introduce the signal and interference modelsand summarize common allocation approaches that we used inour simulative study. In section IV we present our simulationresults. Finally, conclusions are drawn in section V.

II. NETWORK MODELWe consider Base Stations (BSs) located in a regular grid

(according to an hexagonal cell geometry), while mobilestations are distributed in the whole topology in a random way.Each BS serves a unique Mobile Station (MS), associated tothe BS from which it senses the best channel. Therefore, beingN the number of BSs, the network includes N cells and Nusers. Thanks to the toroidal implementation of the grid, theBSs in the rightmost side of the network are adjacent to theones in the leftmost side and, similarly, the BSs placed at thetop are adjacent to the ones placed at the bottom positions.The network heterogeneity is introduced by simply settingheterogeneous values of the maximum power available at each

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Fig. 1. Network and interference model. Base stations are deployed on atoroidal surface and use the same band in the whole network.

cell, which in turns correspond to an heterogeneous coveragearea among the cells. Figure 1 shows an example of networktopology with 12 cells, in which the network heterogeneityis represented by heterogeneous BS symbols. In the example,three BSs can use a maximum transmission power higher thanthe other 9 BSs.We also assume that the same band is available at each

BS and can be allocated according to an OFDMA accessscheme. Let KFFT be the total number of carriers and letK be the number of carriers actually used for transportingdata. In each symbol interval, each carrier can be in prin-ciple modulated with an adaptive scheme according to thechannel quality perceived by the receiver. In order to limitthe signaling overhead required for informing the transmitterabout the receiver channel quality and for communicating theallocation map to the MSs, we adopt the common solutionto group multiple subcarriers into a single allocation unit,called Physical Base Unit (PBU). As specified for examplein the IEEE 802.16e standard [10], PUSC (Partial Usage ofSub Channels) and AMC (Adaptive Modulation and Coding)are permutation schemes that define non-adjacent and adjacentsubcarrier groupings for a subchannel, respectively. In ourwork we consider the AMC approach, according to whichKPBU adjacent carriers are grouped together. The total numberof allocation units results U = �K/KPBU�.The channel gain between each MS and the serving BS

(or the interfering BSs) is evaluated according to the channelmodel described in the 3GPP/3GPP2 SCM specifications [11].

III. RESOURCE ALLOCATION IN OFDMA SYSTEMS

A. Signal Model

Let i be the cell index (also corresponding to a BS and a MSindex) in the range [1, N ] and let k be the carrier index in therange [1, K]. We denote the downlink channel gain betweenthe i-th BS and the j-th MS as γi,j and the fading coefficientfor the k-th carrier as a complex number hk

i,j . The receivedsignal yi,k at the user i in the k-th carrier is generally givenby:

yi,k = γi,ihki,ix

ki +

N∑

j �=i

γj,ihkj,ix

kj + nk

i , (1)

where xki is the signal transmitted by BS i on carrier k, and

nki is an additive thermal noise on the same carrier.Let pk

i = E{|xki |

2} the power allocated in cell i on thek-th carrier and let pi = (p1

i , p2i , · · · p

Ki ) the power allocation

vector in cell i. Since each cell i has a maximum transmitpower constraint Pi, in each symbol time

∑k pk

i ≤ Pi. TheSignal to Noise and Interference Ratio (SINR) in each carrieris given by:

SINRki =

γ2i,i|h

ki,i|

2pki

σ2 +∑N

j �=i γ2j,i|h

kj,i|

2pkj

(2)

Assuming that adaptive coding and modulation allows to reachthe channel capacity of each subcarrier, by using a singletransmission format for a whole PBU, a conservative estimateof the capacity (in bits/channel usage) available in a genericl-th PBU (l ∈ [1, U ]) is given by:

Cli = KPBU min

k∈PBUl

log(1 + SINRki ) (3)

where PBUl represents the set of carriers included in the l-thPBU (i.e. the set {KPBU ·(l−1), KPBU ·(l−1)+1, . . . , KPBU ·l−1}). Obviously, the capacity depends not only on the powerallocated within cell, but also on the power allocated in all theother cells.

B. Resource Allocation SchemesSince we are considering a single user in each cell, for

each BS, the problem of resource allocation, which usuallyinvolves both power allocation and user scheduling, is limitedto the power allocation only, i.e. to the selection of the pi

vector in each cell i. Different allocation policies, with differ-ent complexity-performance tradeoff and signaling overheads,have been proposed so far in literature. For example, a simplesolution minimizing both complexity and feedback signals isan homogeneous repartition of the transmit power on all thetransport carriers:

pki = Pi/K, ∀k ∈ [1, K] (4)

We call this allocation policy as uniform power allocation.Another approach largely studied in literature is based on

the maximization of the aggregated capacity of the cell. Thevector pi has K components that vary in the space Π = R

K+ ,

being R+ the set of non-negative real numbers. Therefore, thepower vector can be determined as:

pi = arg maxpi∈Π

U∑

l=1

Cli(p1, p2, · · ·pN ) (5)

under the constraint∑K

k=1 pki ≤ Pi, and can be easily found

with the water filling algorithm [12], [13]. Since this optimiza-tion requires the knowledge of the SINR values experiencedin each carrier, it also requires a feedback from the receiverto the BS, which can be sampled in time and quantized inorder to limit the signaling overhead. Moreover, we used asingle quantized sample per-PBU (rather than a single sampleper-carrier), in order to further reduce the signaling overhead.

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The allocation problem has been also formulated by con-sidering different optimization strategies, including fairnessfigures, energy consumption, heterogeneous user requirements,and so on. However, in most cases these studies considereach cell independently, reflecting actual network scenarioswhere each BS decides its allocation policy in a totallyindependent and distributed manner. Indeed, the extension ofthe allocation problem to the multi-cell scenario, althoughformally immediate, presents several challenges and leads to asignificant increment of the dimensionality of the optimizationspace. For example, the capacity-maximizing approach citedabove can be extended to the whole network, by consider-ing an allocation problem involving a vector p of vectorsp1, p2, · · ·pN , varying in ΠN :

p = arg maxp∈ΠN

N∑

i=1

U∑

l=1

Cli(p) (6)

This optimization problem is non-convex [14] and standardoptimization techniques do not apply directly. Moreover, evenneglecting the computational issues, the solution requires acentralized allocator knowing instantaneous inter-cell channelgains (and thus creating acute signaling overheads).The central problem considered in this paper is understand-

ing if the single-cell capacity maximizing policy gives goodperformance also from a network perspective, in terms ofaggregated network capacity. Specifically, we compared thewater-filling performance (independently performed in eachcell) under different channel reuse ratios, i.e. when a pre-defined fraction of transport carriers is left empty. Indeed, wenoticed that the traditional frequency planning principle is inagreement with the result in [15], where it is shown that fora network with two cells only the capacity-maximizing powerallocation is binary (i.e. in each network resource, BSs haveto use a transmit power equal to the maximum possible or tozero).

IV. SIMULATION RESULTS

A. Simulation Model

We implemented an interacting MATLAB/C++ custom-made simulator. Specifically, the network topology and thechannel evolutions have been implemented in C++, while theallocation policies and the capacity computation have beenimplemented in MATLAB. The simulator has a clock-drivenarchitecture, whose time unit is given by the symbol time. TheC++ routine is executed at the beginning of the simulationand provides the BSs grid, the MS positions, and the N2 ·Kchannel gain coefficients at each simulation symbols t ∈ [0, T ].We chose to use an independent C++ simulator for simulatingthe channel because this task is the most critical one froma computation point of view. Since the channel coefficientsdepend on the physical and propagation environment andevolve independently from the allocation policies, the channelsimulation can be carried out independently from the alloca-tions, without affecting the overall simulation accuracy.

For each simulation time t, the allocation module is runsequentially at each BS, in order to determine the powerallocations in each PBU. Such a sequential allocation isonly a simulation feature and does not affect the systemperformance. In fact, whenever the allocation module requiresa channel state feedback, we assume that the feedback issignaled in the previous frame. Therefore, the interference isevaluated by considering all the allocations performed at timet− 1. interference evaluation. We implemented the followingresource allocation schemes:

• Uniform: According to this scheme, no signaling isrequired and the BS just transmits in each carrier withthe constant power given by (4).

• Water Filling: In this case, the power allocation vectoris determined by the water filling algorithm. The SINRvalues experienced at time t−1 are used as the estimatesof the expected SINR values at time t. Therefore, wesuppose that the SINR values are signaled at each symboltime by means of an error-free dedicated control channel.

• Fractional Water Filling: This scheme is similar to theprevious one, but it is applied to a pre-defined sub-set ofthe available carriers. Specifically, at each time t, the BSselects a number r ·K of transport carriers over which itapplies the water filling algorithm. The ratio r is a schemetunable parameter, while the carrier selection is based onthe best SINR values experienced at time t− 1.

The rational of considering both water filling and fractionalwater filling is that utilizing or non utilizing all the resourcesavailable in each cell can lead to different interference levelsamong the cells. Since water filling intrinsically discardsthe carriers experiencing the worst channel and interferingconditions, we consider the fractional water filling as a kind ofdynamic and distributed scheme for resource repartition amongthe cells.After that all the cells run the allocation scheme (whose

convergence time is assumed to be negligible), the new SINRvalues are computed and the actual capacity available at timet is evaluated by using these SINR values. Unless otherwisespecified, table I summarizes the numerical settings adoptedin simulation, where Tsym is the symbol duration, B is theavailable band, and dsite is the distance between two BSs.As far as concerns the modeling of the signaling overhead,required by the water filling schemes, we assume that eachMS feeds back to its serving BS the m-bit quantized ChannelState Information (CSI):

CSIki =SINRk

i

pki

=γ2

i,i|hki,i|

2

σ2 +∑N

j �=i γ2j,i|h

kj,i|

2pkj

. (7)

The CSI values corresponding to carriers belonging to thesame PBU are summed, thus obtaining an average informa-tion per-PBU. These informations, m-bit quantized, are feedbacked by each MS to its serving BS. Since the FractionalWater Filling works only on a sub-set of PBUs, a possiblesignaling compression scheme is using a U -element bitmap,identifying the used PBUs Uused, and signaling only the Uused

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Parameter ValueCarrier Frequency 2100 MHz

KFFT 128K 84N 12

KPBU 7Tsym 16 μs

B 6.6 MHzdsite 250 m

TABLE IMAIN SYSTEM PARAMETERS.

quantized ratios (7). With this assumption, it results a per-MSoverhead Oi rate estimate of:

Oi =U + mUused

q · Tsym

, (8)

where q is the number of OFDMA symbols between twoconsecutive signaling updates.

B. Performance Evaluation with heterogeneous powerWe run a first set of simulations using heterogeneous

Pi values among the cells. Specifically, we considered twodifferent power classes, called high-power and low-power BSs,employing respectively a peak power equal to 1 W and 0.1W. The lower power level of 0.1 W has been chosen inorder to guarantee an outage probability lower than 1%. Weconsidered 20 different seeds for generating the mobile stationpositions, the channel transfer functions and path losses, andthe assignment of high-power BSs, and then averaged theaggregated capacity resulting in each scenario.Figures 2 and 3 show the aggregated network capacity

as the number of high-power BSs varies, in two differentpropagation environments. The figures plot the network grosscapacity, without considering the resource consumption dueto the signaling overhead. Different allocation policies arecompared. From the figures, we see that the simple uniformallocation scheme, requiring no feedback from the MSs,provides results comparable with the water filling schemein case of micro-propagation model, while it under-performswater filling (with r ≥ 0.5) in case of macro-propagationmodel. This phenomenon is due to the fact that in the micro-cellular propagation model it is included a LOS component,with probability max(1 − d/300, 0), being d the distance inmeters between the BS and the MS. Since we are simulatingan inter-site distance equal to 250m, it is very likely that theMSs have a LOS channel in the micro environment1. TheLOS component lead to high channel gains (which are alsocomparable from a PBU to another) and to a limited inter-cell interference. Therefore, selective power allocations andfrequency planning are useless or even harmful. These higherchannel gains are also responsible of the different aggregatedcapacity values plotted in figures 3 and 2, where the networkcapacity in the micro-cellular environment is about three timesthe one experienced in the macro-cellular one.

1Note that, in order to exploit such high spectral efficiencies, MIMOtransmission schemes would need to be implemented, but this extension hasnot been considered in this paper and is left as a further work.

0

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1 2 3 4 5 6 7 8 9 10 11 12

Agg

rega

ted

capa

city

[Mbp

s]

Number of BSs @ 1 Watt

r=1r=0.7r=0.5r=0.1

uniform

Fig. 2. Aggregated network capacity as a function of the number of high-power BSs, in a micro-cellular propagation environment.

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r=1r=0.7r=0.5r=0.1

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Fig. 3. Aggregated network capacity as a function of the number of high-power BSs, in a macro-cellular propagation environment.

Whenever the LOS component is not present and thechannel gains vary significantly from a PBU to another, powerallocations based on water filling provide better performancethan uniform power allocations. For example, in figure 3 thewater filling scheme outperforms the uniform power schemeof more than 20 Mbps. Most interesting, the fractional waterfilling with r = 0.5 and r = 0.7 provides an aggregatedcapacity higher than the water filling one. When the numberof high-power BSs is equal to 12, such a difference is about20 Mbps. Such a difference can be even higher if we considerthat the fractional water filling requires a signaling overheadlower that water filling. The higher capacity perceived undera fractional water filling scheme can be interpreted as theevidence that a resource repartition among the cells (i.e. acontrol on the inter-cell interference) is advantageous for thispropagation scenario.

C. Impact of PBU and signaling overhead

In order to enlighten the effects of the network hetero-geneity and the capacity quantization due to the per-PBUallocations, we run some simulation with KPBU set to 1.Figure 4 compares the cumulative distribution functions (CDF)

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103 104 1050

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Capacity (Kbps)

CD

F

High−power BS 100%High−power BS 66%High−power BS 33%

Water−FillingUniform

Fig. 4. Cumulative Distribution Function of the per-cell capacity underdifferent allocation schemes, in the macro propagation environment.

of the per-cell capacity perceived under different allocationschemes in the macro-cellular environment. For improvingthe readability of the figure, being the water filling withr = 1 the best scheme, the case referring to the fractionalwater filling with r < 1 is not plotted. From the figurewe can see that the network heterogeneity does not affectsignificantly the CDF for the uniform allocation case, whileit increases the probability that the cell capacity is low incase of water filling. Moreover, the average values of thesedistributions are higher than 1/12 of the value obtained in theprevious simulations, because we fully exploit the capacityof each carrier (i.e. KPBU mink∈PBUl

log(1 + SINRki ) ≤∑

k∈PBUllog(1 + SINRk

i )).Figure 5 shows again the aggregated network capacity for

different KPBU values corresponding to a variable number ofPBUs U = �K/KPBU�. For improving the figure readability,we only plotted the water filling allocation approach (r = 1)and the fractional water filling with r = 0.5. The increase ofcapacity with decreasing PBU size can be readily explained byrecalling that the capacity estimate (3) is (very) conservative.Except the case U = 84, which corresponds to PBUs withone carrier only, from the figure it is evident that a dynamicnetwork repartition among the cells is always advantageous,especially when the number of BSs employing a transmissionpower equal to 1 W is high.Note that also this figure refers to a gross network capacity.

A simple estimation of the net network capacity is given intable II, where we computed the resource consumption dueto the signaling overhead for m = 4 and q = 12. Althoughq = 12 could seem a too frequent (12 ·16μs) feedback updatein our mobility scenario, we evaluated the signaling overheadfor a more general mobility scenario. The table proves thatthe fractional water filling can be even more beneficial thanexpected, thanks to the chosen signaling format.

V. CONCLUSIONS

In this paper we performed a simulative study devisedto compare different power allocation schemes for OFDMA

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U=84; r=1U=84; r=0.5U=21; r=1U=21; r=0.5U=7; r=1U=7; r=0.5U=2; r=1U=2; r=0.5

Fig. 5. Aggregated network capacity as a function of the number of high-power BSs and PBU size, in a macro-cellular propagation environment.

BSs@1W r No Signaling With Signaling7 21 84 7 21 84

0 1 72.3 108.2 144.9 70.1 101.6 118.70 0.5 75.4 106.8 129.1 74.1 102.9 113.46 1 90.2 127.5 163.5 88.0 120.9 137.36 0.5 98.2 131.6 154.9 96.9 127.7 139.212 1 106.1 143.7 181.5 103.9 137.1 155.312 0.5 121.4 160.8 185.9 120.1 156.9 170.2

TABLE IIAVERAGE NETWORK CAPACITY VALUES WITH AND WITHOUT SIGNALING[MBPS], FOR ZERO, HALF AND ALL HIGH-POWER BSS, M=4, Q=12.

systems with a reuse factor equal to 1, in an heterogeneousmacro-micro cellular environment. In order to focus on thepower allocation only, we considered a single user per-celland neglected the impact of user scheduling on the networkperformance. We considered greedy allocation schemes, i.e.schemes utilizing all the carriers available in each cell, andnon-greedy schemes, i.e. schemes leaving some resourcesempty, in order to reduce interference with other cells. Fromour results, we found that in most cases greedy policiesperform better than non-greedy ones.

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