Using Multiple Co-Channel Femtocells as Relays toIncrease the Performance of the Outdoor User

Samuel Baraldi Mafra, Hirley Alves, Richard Demo Souza, Evelio M. G. Fernandez, and Joao Luiz Rebelatto

Abstract—The deployment of femtocells comes as a solutionto increase indoor coverage although it may also increase theinterference level in the network. In this paper we evaluate theuse of multiple co-channel femtocells as relays to the outdooruser in a cognitive radio context, where the outdoor user canbe seen as a primary user and the indoor users are seen assecondary users. We show that multiple co-channel femtocells,besides allowing several secondary users to access the spectrum,may considerably increase the performance of the primary userif the femtocells act as relays to the primary signal. Moreover,results show that with the increase of the number of cooperativeco-channel femtocells the capacity constraints on the backhaulcan be relaxed.

Keywords—Cognitive Radio, Cooperative Communications,Femtocells, Heterogeneous Networks, Outage Analysis

I. INTRODUCTION

FEMTOCELLS are covered by low cost and low powerbase stations (BS), providing coverage in indoor en-

vironments where the macrocell signal is limited or notdetectable. Femtocells often provide access to the cellularnetwork through a digital subscriber line or optical fiberconnection. With the inclusion of femto base stations, indoorusers perceive an improved signal quality due to the proximitybetween transmitter and receiver, resulting in a highly efficientcommunication and large transmission rates [1]. Moreover,femtocells can operate either under the so-called open accessmode, where all users (indoor and outdoor) may access thefemtocell, or under the closed access mode, in which onlypreviously allowed users can connect to the femtocell.

The co-existence of macrocell and femtocells gives riseto a two-tier architecture. In this scenario we have [2]: i)cross-tier interference, in which the femtocell interferes onthe macrocell and vice-versa; and ii) co-tier interference,which is the interference between neighbor femtocells. Forinstance, the interference can be addressed by means of powercontrol techniques [3], [4], OFDMA [5], [6], cognitive radiosolutions [7]–[12], etc. For instance, in [11], the authorspropose a scheme of spectrum reuse based on cognitive radio,where the channel reuse is determined according to eachfemtocell’s channel environment, leading to a great SINR

Manuscript received February 11, 2013. This work was supported byCAPES (Brazil), CNPq (Brazil), and Infotech Graduate School, Universityof Oulu (Finland).

Samuel Baraldi Mafra, Richard Demo Souza, and Joao Luiz Rebelatto arewith Federal University of Technology-Parana (UTFPR), Curitiba-PR, Brazil(e-mails: mafrasamuel@gmail.com,{ richard, jlrebelatto}@utfpr.edu.br)

Hirley Alves is with Centre for Wireless Communications (CWC), Oulu,Finland.(e-mail: halves@ee.oulu.fi).

Evelio M. G. Fernandez is with Federal University of Parana (UFPR)Curitiba-PR, Brazil (e-mail: evelio@eletrica.ufpr.br).

improvement. A cognitive WiMAX architecture is proposedin [12], where the base station and users intelligently adjustparameters such as power, channel, etc. The results show asubstantial performance improvement in comparison to theprotocol without the cognitive radio technique. Another al-ternative to deal with the interference is through the use ofcooperative communications [13], where one or more nodeshelp the communication between source and destination byacting as relays. The way the relay behaves is determinedby the cooperative protocols [13]. One of the most wellknown cooperative protocols is the decode-and-forward (DF),in which the relay tries to decode the source message and thenre-encodes and forwards it to the destination.

Two methods of cooperation between secondary users (fem-tocell) and primary users (macrocell) in a cognitive hetero-geneous network are investigated in [14]: i) the cooperativerelay model, where the secondary user relays the message ofthe primary user, but is not able to transmit its own messageconcurrently with the primary user; and ii) the interferencemodel, where the secondary user is allowed to transmit itsown message concurrently with the primary user, as long asthe interference imposed to the primary user remains below arequired threshold.

In [15], the use of femtocell as a relay for both indoorand outdoor users is proposed. The system performance isevaluated in terms of outage probability. The use of thefemtocell home BS (or HBS) as a relay increases the networkperformance. In closed access it is possible to obtain thesame outage probability than in a system without femtocells,thus completely eliminating the cross-tier interference. In openaccess, the authors demonstrate that performance is even betterthan in a system without femtocells, as both users benefit ofthe relaying provided by the HBS.

In this paper we consider a similar scenario as in [15],but assuming the existence of multiple co-channel underlaidHBSs. We show that having multiple co-channel HBSs, be-sides allowing more secondary indoor users to access thespectrum, can increase the performance of the primary outdooruser when the multiple co-channel HBSs act as relays tothe outdoor user signal. Moreover, we show that by havingmultiple underlaid HBSs, besides increasing the performanceof the outdoor user, we can reduce the backhaul capacityrequirement.

The remainder of this paper is organized as follows. Sec-tion II introduces the system model, while Section III describesthe outage probability analysis of the indoor and the outdoorusers. Section IV presents some numerical results and, finally,Section V concludes the paper.

166978-1-4799-0404-4/13/$31.00 ©2013 IEEE TSP 2013

II. SYSTEM MODEL

We consider the uplink of a two tier heterogeneous networkcomposed of a base station (BS), 𝑁 femtocells, and a macrooutdoor user, as depicted in Fig. 1. As we focus on a singlechannel, we assume one indoor user per femtocell. The macrooutdoor user can be seen as the primary user while the indooruser can be seen as the secondary user in a cognitive radiocontext. The 𝑁 indoor users and the outdoor user transmit atthe same time and frequency. It is also assumed that eachHBS has 𝐿 antennas, while the macro BS and all usersare considered to be single antenna devices1. Each HBStries to decode the messages of the outdoor user and of itscorresponding indoor user. Therefore, the femtocells operatein the open access mode with respect to the outdoor user,while the messages of other femtocell indoor users are treatedas noise. Each HBS is connected to the macro BS by meansof a wired, assumed error free, backhaul link.

If the HBS of the 𝑘-th femtocell, 𝑘 ∈ {1, 2, ⋅ ⋅ ⋅ , 𝑁},decodes the messages of the outdoor and its indoor user, thenthat femtocell allocates 𝛿𝑘 ⋅𝐶𝑘 bits per channel use (bpcu) of itsbackhaul capacity to the 𝑘-th indoor user and (1−𝛿𝑘)⋅𝐶𝑘 bpcuto the outdoor user, where 𝐶𝑘 is the total backhaul capacity ofthe 𝑘-th femtocell and 0 ≤ 𝛿𝑘 ≤ 1. We impose an additionalconstraint in the choice of 𝛿𝑘 so that 𝛿𝑘 ⋅ 𝐶𝑘 is always atleast as large as the indoor user required capacity. If the 𝑘-thHBS correctly decoded only one of the two messages, then itdedicates the total backhaul capacity 𝐶𝑘 for either the outdooror the corresponding indoor user. The macro BS only tries todecode the outdoor user, as decoding the indoor users at themacro BS does not bring considerable additional gains, unlessthe femtocell is very close to the macro BS. Moreover, if themacro BS tries to decode all indoor users then the complexitygrows very large with the increase of 𝑁 .

The channel fading between the indoor user of the 𝑘-thfemtocell and the macro BS is denoted as 𝑔𝑘, while 𝑔𝑜 is thechannel fading between the outdoor user and the macro BS.Moreover, ℎ𝑖

𝑗,𝑘 corresponds to the channel between the indooruser of the 𝑗-th femtocell and the 𝑖-th antenna of the HBS inthe 𝑘-th femtocell, 𝑘 ∈ {1, 2, ⋅ ⋅ ⋅ , 𝑁} and 𝑖 ∈ {1, 2, ⋅ ⋅ ⋅ , 𝐿},while ℎ𝑖

𝑜,𝑘 is the channel between the outdoor user and the𝑖-th antenna of the HBS in the 𝑘-th femtocell. All channelsare assumed to be independent of each other and follow aRayleigh quasi-static fading model. Indoor and outdoor userstransmit with rates 𝑅𝑘 and 𝑅𝑜 bpcu, respectively.

The received signal at the macro BS is given by

𝑦𝑏 =

√𝑃𝑜

𝜅𝑜,𝑏𝑔𝑜𝑥𝑜 +

𝑁∑𝑘=1

√𝑃𝑘

𝜅𝑘,𝑏𝑔𝑘𝑥𝑘 + 𝑤𝑏, (1)

where 𝑃𝑜 and 𝑃𝑘 are the transmit powers of the outdoor userand the indoor user in the 𝑘-th femtocell, respectively, 𝜅𝑜,𝑏 ≥ 1is the path loss between the outdoor user and the macro BS,𝜅𝑘,𝑏 is the path loss between the 𝑘-th indoor user and themacro BS, 𝑥𝑜 and 𝑥𝑘 are the unity energy Gaussian complex

1Including additional antennas to the macro BS would not qualitativelychange our conclusions, and therefore we decided to consider a single antennamacro BS for the sake of simplicity. However, this extension can be consideredin a future work.

IndoorUser

HBS

Outdoor User

TransmissionLink

Interference Link

Base Station

IndoorUser

HBS

Fig. 1. System model with 𝑁 = 2 femtocells and one macrocell user

messages from the outdoor user and the 𝑘-th indoor user,and 𝑤𝑏 is additive white Gaussian noise with variance 𝑁0/2per dimension, while without loss of generality we assumehereinafter that 𝑁0 = 1. The messages transmitted by theindoor users are seen as noise at the macro BS, as it tries todecode only the outdoor user message 𝑥𝑜.

The signal received at the 𝑖-th antenna of the 𝑘-th HBS is

𝑦𝑖𝑘 =

√𝑃𝑘

𝜅𝑘,𝑘ℎ𝑖𝑘,𝑘𝑥𝑘+

√𝑃𝑜

𝜅𝑜,𝑘ℎ𝑖𝑜,𝑘𝑥𝑜+

𝑁∑𝑗=1𝑗 ∕=𝑘

√𝑃𝑗

𝜅𝑗,𝑘ℎ𝑖𝑗,𝑘𝑥𝑗+𝑤𝑖

𝑘, (2)

where 𝑃𝑗 is the transmit power of the indoor user in the 𝑗-thfemtocell, 𝜅𝑗,𝑘 is the path loss between the indoor user in the𝑗-th femtocell and the HBS in the 𝑘-th femtocell, the other 𝜅’sfollow a similar definition, respecting the notation used so far,while 𝑤𝑖

𝑘 is additive Gaussian noise just as 𝑤𝑏. The first termin (2) corresponds to the message transmitted by the indooruser of the 𝑘-th femtocell while the second term correspondsto the message of the outdoor user. The HBS tries to decodethese two messages, while the messages of the other 𝑁 − 1indoor users (third term) are seen as noise.

In this work, as in [16], [17], we consider a path loss modelwhich describes a real femtocell scenario, so that the path lossbetween an indoor or outdoor user and a HBS and betweenan indoor user and the macro BS is defined as

𝜅(𝑑𝐵) = 39.676 + 20 log10 𝑑+ 𝑞𝑊 +𝑊 ′, (3)

where the first term corresponds to the free-space loss, 𝑑 isthe distance between transmitter and receiver in meters, 𝑊 isthe wall partition loss (assumed to be 5dB), 𝑞 is the number of

167

walls between transmitter and receiver, and 𝑊 ′ is the outdoor-indoor penetration loss (assumed to be 10dB) and which isused only when applies. Moreover, the outdoor-to-macro BSpath loss model is defined as 𝜅(𝑑𝐵) = 15.3 + 37.6 log10 𝑑.

The average signal-to-noise ratio (SNR) of the outdoor andindoor users to the macro BS are respectively given by 𝛾𝑜,𝑏 =𝑃𝑜

𝜅𝑜,𝑏and 𝛾𝑘,𝑏 = 𝑃𝑘

𝜅𝑘,𝑏, while the SNR of the link between

the outdoor and indoor user of the 𝑗-th femtocell to the 𝑖-th antenna of the HBS in the 𝑘-th femtocell are respectivelygiven by 𝛾𝑖

𝑗,𝑘 = 𝛾𝑗,𝑘 = 𝑃𝑘

𝜅𝑗,𝑘and 𝛾𝑖

𝑜,𝑘 = 𝛾𝑜,𝑘 = 𝑃𝑜

𝜅𝑜,𝑘.

III. OUTAGE PROBABILITY ANALYSIS

First we consider the outage probability seen at the 𝑘-thfemtocell. Thus, let 𝒫𝑘,𝑏𝑜𝑡ℎ be the probability that the HBS ofthe 𝑘-th femtocell correctly decoded its corresponding indooruser and the outdoor user. Then, supposing a multiple accesschannel (MAC) model and using some of the results in [18],we can write

𝒫𝑘,𝑏𝑜𝑡ℎ = 1− 𝒫𝑘,𝑜𝑢𝑡 − 𝒫𝑘,𝑜𝑢𝑡, (4)

where 𝒫𝑘,𝑜𝑢𝑡 is the probability that the HBS correctly decodedonly the outdoor user, while 𝒫𝑘,𝑜𝑢𝑡 is the probability that theHBS did not decode the outdoor user. Moreover, 𝒫𝑘,𝑜𝑢𝑡 canbe defined as 𝒫𝑘,𝑜𝑢𝑡 = Pr{𝒜∩ℬ}, where events 𝒜 and ℬ are

𝒜 := log2

(1 +

∑𝐿𝑖=1 ∣ℎ𝑖

𝑜,𝑘∣2𝛾𝑜,𝑘1 +

∑𝐿𝑖=1 ∣ℎ𝑖

𝑘,𝑘∣2𝛾𝑘,𝑘 + 𝜃

)≥ 𝑅𝑜, (5)

ℬ := log2

(1 +

∑𝐿𝑖=1 ∣ℎ𝑖

𝑘,𝑘∣2𝛾𝑘,𝑘1 + 𝜃

)< 𝑅𝑘, (6)

where we assume that the HBS applies maximum ratio com-bining (MRC) among the receive antennas, where 𝜃 is givenby:

𝜃 =

𝑁∑𝑗=1,𝑗 ∕=𝑘

𝐿∑𝑖=1

∣ℎ𝑖𝑗,𝑘∣2𝛾𝑗,𝑘. (7)

Note that (5) and (6) are found considering the capacityregion of the two-user MAC where the outdoor user is decodedfirst (seeing the 𝑘-th indoor user as noise), while in theattempt to decode the 𝑘-th indoor user the interference fromthe outdoor user is removed as the latter could be decoded.Moreover, 𝜃 represents the interference from the other 𝑁 − 1indoor users (which are not decoded at the HBS).

The probability 𝒫𝑘,𝑜𝑢𝑡 can be defined as 𝒫𝑘,𝑜𝑢𝑡 = 𝒫𝑘,𝑛𝑜𝑛𝑒+𝑃𝑘,𝑖𝑛, where 𝒫𝑘,𝑛𝑜𝑛𝑒 and 𝒫𝑘,𝑖𝑛 are the probabilities that theHBS could not decode both users and the probability thatthe HBS could decode only the corresponding indoor user,respectively. Moreover the probability 𝒫𝑘,𝑖𝑛 is given by

𝒫𝑘,𝑖𝑛 = Pr{𝒞 ∩ 𝒟}, (8)

where, still considering a two user MAC, events C and D are

𝒞 := log2

(1 +

∑𝐿𝑖=1 ∣ℎ𝑖

𝑘,𝑘∣2𝛾𝑘,𝑘1 +

∑𝐿𝑖=1 ∣ℎ𝑖

𝑜,𝑘∣2𝛾𝑜,𝑘 + 𝜃

)≥ 𝑅𝑘, (9)

𝒟 := log2

(1 +

∑𝐿𝑖=1 ∣ℎ𝑖

𝑜,𝑘∣2𝛾𝑜,𝑘1 + 𝜃

)< 𝑅𝑜. (10)

The probability 𝒫𝑘,𝑛𝑜𝑛𝑒 is given by

𝒫𝑘,𝑛𝑜𝑛𝑒 = Pr{ℰ ∩ ℱ ∩ 𝒢}, (11)

where events ℰ , ℱ and 𝒢 are

ℰ := log2

(1 +

∑𝐿𝑖=1 ∣ℎ𝑖

𝑘,𝑘∣2𝛾𝑘,𝑘1 +

∑𝐿𝑖=1 ∣ℎ𝑖

𝑜,𝑘∣2𝛾𝑜,𝑘 + 𝜃

)< 𝑅𝑘, (12)

ℱ := log2

(1 +

∑𝐿𝑖=1 ∣ℎ𝑖

𝑜,𝑘∣2𝛾𝑜,𝑘1 +

∑𝐿𝑖=1 ∣ℎ𝑖

𝑘,𝑘∣2𝛾𝑘,𝑘 + 𝜃

)< 𝑅𝑜, (13)

𝒢 := log2

(1 +

∑𝐿𝑖=1 ∣ℎ𝑖

𝑜,𝑘∣2𝛾𝑜,𝑘 + ∣ℎ𝑖𝑘,𝑘∣2𝛾𝑘,𝑘

1 + 𝜃

)< 𝑅𝑜+𝑅𝑘.

(14)Next, we write the outage probability of the outdoor user

at the macro BS, 𝒪𝑏𝑠∣e, conditioned on the correspondingvector of decoding events e = [𝑒1, ..., 𝑒𝑁 ] at the 𝑁 femtocells.A given decoding event at the 𝑘-th femtocell is defined as𝑒𝑘 ∈ Φ = {𝑜𝑢𝑡, 𝑖𝑛, 𝑏𝑜𝑡ℎ, 𝑛𝑜𝑛𝑒}, 𝑘 ∈ {1, 2, ..., 𝑁}, where𝑜𝑢𝑡 means that only the outdoor user could be decoded atthe 𝑘-th femtocell, 𝑖𝑛 represents the situation in which onlythe corresponding indoor user is decoded, 𝑏𝑜𝑡ℎ indicates thatboth users could be decoded, and 𝑛𝑜𝑛𝑒 means that neither theoutdoor nor the indoor user could be decoded. For instance,suppose that 𝑁 = 2 and that the vector of decoding events ise = [𝑜𝑢𝑡, 𝑏𝑜𝑡ℎ]. Then, e indicates that in the first femtocellonly the outdoor user could be decoded while in the secondfemtocell both the corresponding indoor user and the outdooruser could be decoded.

Thus, the outage probability of the outdoor user at themacro BS given a specific vector of decoding events at the𝑁 femtocells is given by

𝒪𝑏𝑠∣e = log2

(1 +

∣ℎ𝑜,𝑏∣2𝛾𝑜,𝑏1 +

∑𝑁𝑘=1 𝛽𝑘 ⋅ ∣ℎ𝑘,𝑏∣2𝛾𝑘,𝑏

)

<

(𝑅𝑜 −

𝑁∑𝑘=1

(𝑎𝑘 ⋅ (1− 𝛿𝑘)𝐶𝑘)−𝑁∑

𝑘=1

𝑏𝑘 ⋅ 𝐶𝑘

), (15)

where the binary variable 𝑎𝑘 is equal to one if the 𝑘-thfemtocell could decode both users, so that a capacity of(1 − 𝛿𝑘)𝐶𝑘 over the backhaul is used to convey informationon the outdoor user message to the macro BS. The binaryvariable 𝑏𝑘 is equal to one if the 𝑘-th femtocell could decodeonly the outdoor user, while the binary variable 𝛽𝑘 is equal toone if the 𝑘-th femtocell could not decode the indoor user2.The possible values of 𝑎𝑘, 𝑏𝑘 and 𝛽𝑘 are given in Table I.

In order to write the overall outdoor user outage probabilityat the macro BS for a given number 𝑁 of co-channel fem-tocells, we need to consider all possibilities to the vector ofdecoding events e weighted by their corresponding probabili-ties. Thus, for the general case with 𝑁 femtocells, the overalloutdoor user outage probability 𝒪𝑏𝑠 can be written as:

𝒪𝑏𝑠 =∑∀𝑖∈Φ

...∑∀𝑗∈Φ

𝒫1,𝑖...𝒫𝑁,𝑗 ⋅ 𝒪𝑏𝑠∣e=[𝑖,...,𝑗]. (16)

2We assume that the backhaul capacity is always at least equal to therequired capacity of the indoor user. Therefore, if the indoor user is decodedat the HBS, then its interference can be removed at the macro BS.

168

TABLE IVALUES OF 𝑎𝑘 , 𝑏𝑘 AND 𝛽𝑘 FOR THE POSSIBLE DECODING EVENTS AT THE

FEMTOCELLS.

𝑒𝑘 𝑎𝑘 𝑏𝑘 𝛽𝑘

𝑜𝑢𝑡 0 1 1𝑏𝑜𝑡ℎ 1 0 0𝑛𝑜𝑛𝑒 0 0 1𝑖𝑛 0 0 0

Since the cardinality (number of elements) of the set Φ is∣Φ∣ = 4, it turns out that the number of elements in (16) isgiven by ∣Φ∣𝑁 . For instance, in the case of a single co-channelfemtocell (𝑁=1), (16) reduces to:

𝒪𝑏𝑠 =∑

∀𝑖∈{𝑜𝑢𝑡,𝑖𝑛,𝑏𝑜𝑡ℎ,𝑛𝑜𝑛𝑒}𝒫1,𝑖 ⋅ 𝒪𝑏𝑠∣e=[𝑖]

=𝒫1,𝑏𝑜𝑡ℎ ⋅ 𝒪𝑏𝑠∣𝑏𝑜𝑡ℎ + 𝒫1,𝑜𝑢𝑡 ⋅ 𝒪𝑏𝑠∣𝑜𝑢𝑡+ (17)

𝒫1,𝑛𝑜𝑛𝑒 ⋅ 𝒪𝑏𝑠∣𝑛𝑜𝑛𝑒 + 𝒫1,𝑖𝑛 ⋅ 𝒪𝑏𝑠∣𝑖𝑛.

Additionaly, the indoor user outage probability 𝒪𝑘,𝑖𝑛 at the𝑘-th femtocell is given by

𝒪𝑘,𝑖𝑛 = 𝒫𝑘,𝑜𝑢𝑡 + 𝒫𝑘,𝑛𝑜𝑛𝑒. (18)

As a reference, we also consider the case where thefemtocells are absent. In this case the outdoor user outageprobability at the macro BS is given by

𝒪𝑁𝐹 = Pr(log2(1 + ∣ℎ𝑜𝑏∣2𝛾𝑜,𝑏) < 𝑅𝑜)

= 1− exp

(−2𝑅𝑜 − 1

𝛾𝑜,𝑏

). (19)

IV. NUMERICAL RESULTS

In this section we discuss some numerical results regardingthe performance of the outdoor user at the macro BS. Weassume 𝑁 ∈ {1, 2, 3}, 𝐿 ∈ {1, 2}, 𝑞 = 4 (number of wallsbetween two femtocells), 𝑞 = 2 for (in)outdoor users to HBSand indoor user to BS links, and 𝑅𝑜 = 𝑅𝑖 = 1 bpcu.

Fig. 2 shows the outdoor user outage probability as a func-tion of 𝛾𝑜𝑏. We assume 𝑃𝑘(𝑑𝐵) = 𝑃𝑜(𝑑𝐵)−20, 𝑑𝑜𝑏 = 200 m,𝑑𝑜𝑘 = 25 m, 𝑑𝑘𝑘 = 5 m, 𝑑𝑘𝑏 = 200 m, 𝑑𝑗𝑘 = 50 m, backhaulcapacity 𝐶 = 2 bpcu, 𝛿𝑘 = 1/2 and 𝐿 = 1 (single antenna).As expected, we conclude that the outdoor user experienceslarger diversity gains as 𝑁 grows, once the HBSs act as relaysto the outdoor user. For instance, for 𝒪𝑏𝑠 = 10−3 and 𝑁 = 1 again of around 22dB can be observed with respect to the casewithout femtocells, and more 8dB can be added if 𝑁 = 2. If𝑁 = 3 we have only an additional 3dB SNR gain, showingthat we have diminishing returns with the increase of 𝑁 .

Fig. 3 depicts the outdoor user outage probability asa function of 𝛾𝑜𝑏 and different backhaul capacities 𝐶 ∈{1.33, 1.4, 1.5, 2} bpcu. Notice that with two co-channel fem-tocells (𝑁 = 2) with reduced backhaul capacity (𝐶 =1.5 bpcu) the outage probability is very close to that with asingle femtocell with larger backhaul capacity (𝐶 = 2 bpcu).In the case of three femtocells (𝑁 = 3) the same performancecan be obtained with an even more reduced backhaul capacity(𝐶 = 1.33 bpcu). By increasing the number of co-channelfemtocells we can decrease the backhaul capacity requirement,

−20 −10 0 10 20 30 4010

−3

10−2

10−1

100

γob

(dB)

Obs

No femtocellN=1 C=2 bpcuN=2 C=2 bpcuN=3 C=2 bpcu

Fig. 2. Outdoor user outage probability as a function of 𝛾𝑜𝑏 for differentnumber of single antenna co-channel femtocells.

what may also decrease the overall implementation and oper-ational costs of the femtocells. Moreover, from the figure wecan also conclude that exists a strict trade-off between 𝑁 and𝐶 once we observe a larger diversity gain when 𝐶 growsfrom 1.4 to 1.5 bpcu for 𝑁 = 2. Such gains are in the orderof several dBs (> 10dB) and are even larger if the indoorusers can afford a higher backhaul capacity. Therefore, wecan see that the achievable diversity gain is directly related tothe backhaul capacity.

The deployment of multiple co-channel femtocells canincrease the performance of the outdoor user and reduce thebackhaul capacity. The increase in performance comes fromthe increased spatial diversity that can be exploited by theoutdoor user, once the HBSs act as relays, while the reducedbackhaul capacity comes from the fact that this additionalspatial diversity is distributed. It is illustrative to compare thecase of multiple single antenna co-channel femtocells withthe case of a single femtocell with multiple antennas. Thisis done in Fig. 4, considering 𝑁 ∈ {1, 2}, 𝐿 ∈ {1, 2} and𝐶 ∈ {1.8, 1.9, 2} bpcu. As expected, a single femtocell with

−20 −10 0 10 20 30 4010

−3

10−2

10−1

100

γob

(dB)

Obs

N=2 C=1.4 bpcuN=1 C=2 bpcuN=2 C=1.5 bpcuN=3 C=1.333 bpcuN=2 C=2 bpcu

Fig. 3. Outdoor user outage probability as a function of 𝛾𝑜𝑏, 𝑁 , and 𝐶.

169

−20 −10 0 10 20 30 4010

−3

10−2

10−1

100

γob

(dB)

Obs

No femtocellN=1, L=2, C=1.8 bpcuN=1, L=2, C=1.9 bpcuN=1, L=1, C=2 bpcuN=2, L=1, C=2 bpcuN=1, L=2, C=2 bpcu

Fig. 4. Outdoor user outage probability as a function of 𝛾𝑜𝑏, 𝐿, and 𝐶.

𝐿 antennas can offer the same diversity order to the outdooruser as 𝑁 = 𝐿 HBSs with a single antenna each. Moreover,the outage probability is even smaller with a single femtocellwith 𝐿 antennas due to the array gain (similar to what happenswhen comparing MRC and selection combining). However,note that by having multiple antennas in a single femtocell weare not able to reduce the backhaul capacity requirement with-out compromising performance. This result shows the benefitof having multiple co-channel femtocells, in which case weare able to reduce the backhaul capacity requirement withoutconsiderably compromising the performance of the outdooruser. Moreover, by having multiple co-channel femtocells weincrease the area spectral efficiency.

Finally, Fig. 5 shows the indoor user outage probability asa function of 𝛾𝑘,𝑘, 𝑁 , and 𝐿. The performance of the indooruser improves considerably with additional receive antennasat the HBS. However, note that the channel conditions at thefemtocell are in general much better than in the macrocell, sothat the indoor user often operates at a high SNR 𝛾𝑘,𝑘. Finally,note that both this improved indoor user performance seen inFig. 5 and the savings in backhaul capacity seen in Fig. 3, can

0 10 20 30 40 50 6010

−3

10−2

10−1

100

γk,k

(dB)

Ok,

in

N=2 L=1N=1 L=2

Fig. 5. Indoor user outage probability as a function of 𝛾𝑘,𝑘 , 𝑁 and 𝐿.

be concurrently achieved if we consider the use of multipleco-channel HBSs with multiple antennas.

V. CONCLUSION

We investigated the use of multiple co-channel HBSs asrelays to the outdoor user. The performance of the outdooruser considerably increases with the increase in the numberof cooperative HBSs. Additionally, capacity constraints on thebackhaul can be relaxed with the increase of the number ofcooperative HBSs given a target outage probability. As a futurework we intend to consider multiple antennas at the macro BS,as well as to investigate the case of multiple co-channel HBSswith the inclusion of dedicated relays at the femtocells, in away to improve the performance of both outdoor and indoorusers.

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