Enhanced performance of heterogeneous networks through fullduplex relaying
 Hirley Alves^{1, 2}Email author,
 Mehdi Bennis^{1},
 Richard Demo Souza^{2} and
 Matti Latvaaho^{1}
DOI: 10.1186/168714992012365
© Alves et al.; licensee Springer. 2012
Received: 21 November 2011
Accepted: 23 November 2012
Published: 22 December 2012
Abstract
In this article, we focus on the uplink of a heterogeneous network composed of a macrocell and an underlaid femtocell. We address the problem of the interference caused by the macro user (MU) on the femtocell [femto base station (FBS) and users]. The femtocell is composed of an user, a femto relay, which can be seen as another FBS or a dedicated relay, and an FBS. We assume a fullduplex relay (FDR) node which is able to transmit and receive simultaneously while suffering from residual selfinterference. We focus on the performance of the femtocell according to different positions of the MU user. We derive closedform expressions for the outage probability and spectral efficiency (throughput) taking into account the selfinterference of the FDR node. Moreover, we assume that the nodes are able to apply successive interference cancellation on the MU signal. Our results show that FDR can considerably enhance the performance of the femtocell, even in the presence of strong selfinterference at the FDR, allowing the femtocell to operate in a high rate regime.
1 Introduction
In recent years, the demand for higher data rates increased considerably and new technologies have been able to respond to the demand by efficiently reusing the spectrum. Moreover, it is known that in a wireless network an effective way to increase capacity is by making transmitter and receiver closer [1]. Femtocells appear as a less expensive alternative to meet that demand by increasing indoor coverage and spectral efficiency. Nevertheless, due to reduced spectrum availability the femtocell will have to support spectrum sharing techniques. The coexistence in the same spectrum of macro and femtocells increases the spectral efficiency but poses several challenges, such as additional interference between macro and femtocells [1] which becomes a major concern when these networks do not cooperate [2]. Therefore, for optimum performance the femtocells have to control the interference induced on the macro user (MU), as well as to manage the interference caused by the MU[3, 4].
The interference conditions in a femtocell network are directly related to the access policy used at the femto base station (FBS), which can be categorized as closed or open [5, 6]. In the case when the femtocell employs a closed policy, the femtocell subscribers are only served by the FBS. On the other hand, in an open access policy the femtocell may accept connections of nonsubscriber users. A closed access policy may reduce the femtocell performance due to interference from MUs, while an open access policy increases the number of handovers for MUs and requires more resources of the femtocell. For instance, in [7] the transmission capacity of open and closed access policies is evaluated in the uplink (UL) of a heterogeneous network. Moreover, it is shown that in the UL open access is preferable since a reduction in interference is obtained. Conversely, as shown in [6], in the downlink (DL) the closed access policy is preferred by the femto users (FUs) which contrasts with the preference of the MUs. Chu et al. [8, 9] investigate the DL of a heterogeneous network where macro and femtocells share the spectrum. The femtocell operates in a subset of the resource allocated to the macrocell which reduces the interference caused by the femtocell. Chu et al. [8] developed a resource allocation scheme, while in [9] an outage probability analysis is derived. In [10], resource allocation is investigated based on the opportunistic reuse of the macrocell spectrum. The results show that by increasing performance of the FUs, the MU suffers extra interference which limits its performance.
Moreover, in this article we assume that the macrocell network is operating in frequency division duplex (FDD) mode while the small cells are (re)using the macrocell UL resources and operate in FD mode, which means that unused resources by the macrocell can locally be reused within small cells where some nodes can transmit and receive simultaneously in an FD fashion. The use of FD nodes can potentially increase the capacity of small cells, while adhering to the crosstier interference constraint imposed by the macrocell. Note that the proposed scheme solves the multiplexing loss of HD schemes, the DL/UL switching point optimization required in the classical time division duplex (TDD) [11] underlay at UL FDD. Thus, the macrocell operation is oblivious to the presence of underlaid small cells, which are opportunistic in nature.
Differently form other works in TDD underlay femtocells [12–14], we analytically investigate the performance of a single femtocell, considering that the femtocell nodes are able to employ selective cooperative protocols. Moreover, we assume a single femtocell composed by an FU (source  S), an FDR, which can be another FBS or a dedicated node, and the intended destination (D) or access point. The relay helps the communication between the FU and the FBS by forwarding the source message. The practical relay is assumed to operate in the FD mode, which means that it is able to transmit and receive simultaneously, and hence is subject to selfinterference from the transmitted to the received signal. Next we address the related work in cooperative and fullduplex schemes.
1.1 Related work on FDR
Cooperative communication is an alternative to achieve spatial diversity even with single antenna devices [15]. In a cooperative scheme a relay helps the source to communicate with the destination, and its behavior is dictated by the cooperative protocols such as amplifyandforward and the decodeandforward (DF), or their variants selective and incremental [15, 16].
In the SelectiveDF (SDF), the relay forwards the source message only if that is error free. Nevertheless, with half duplex (HD) radios the cooperation suffers a multiplexing loss, once the relay listen in a first slot (time/frequency) and then retransmits the message in a second slot. Several solutions have been proposed trying to overcome the problem of the HD constraint as in [17, 18] and references therein. On the other hand, incremental cooperative protocols, such as incrementalDF (IDF), can overcome the spectral inefficiency of HD cooperation through the exploitation of a return channel between nodes [15, 16, 19]. In the IDF protocol, the relay only cooperates with the source if a retransmission is requested by the destination, so that it is not necessary to previously allocate a slot for the relay operation.
Another way to overcome the spectral inefficiency of the HD cooperative schemes is through cooperative FD relaying, which does not suffer from multiplexing loss and can achieve a higher capacity than HD cooperative protocols [16]. Probably the most known FD schemes are multihop (FDMH) and block Markov encoding (FDBM). The FDMH scheme is the simplest relaying technique, while FDBM is the best known performance achieving FD method. However, FDBM is quite complex to be implemented in practice. Moreover, perfect isolation (ideal) between transmitted and received signals is often not possible. In practice, isolating the transmitted and received signals is not straightforward, once the transmitted power is normally much larger than the received power [16]. Therefore, practical FD schemes have been proposed in which it is considered that there is a power leakage between transmitted and received signals, also known as loop interference or selfinterference [20–22]. For instance, Riihonen et al. [20] show that practical FDMH is feasible even if the relay faces strong selfinterference. Moreover, it is also shown that FDMH relaying enhances capacity when compared to the HD scheme. In addition, similar conclusions were obtained in [21–24]. In [25], a practical FD system is proposed and the authors show that the selfinterference can be attenuated by more than 39 dBs through transmit and receive antenna separation.
1.2 Proposed scheme
As aforementioned, differently form other works in TDD underlay femtocells [12–14], we analytically investigate the performance of a single femtocell, considering that the femtocell nodes are able to employ selective cooperative protocols. Moreover, the relay is a practical FD relay, and to the best of the authors’ knowledge the usage of FD nodes within the femtocell cannot be found in the literature. We analyze the femtocell performance in terms of outage probability and spectral efficiency. We also assume that the relay and the FBS are able to apply successive interference cancellation (SIC) techniques [26]. We analyze the performance considering mainly two scenarios regarding the position of the MU: (i) the MU is far from the femtocell, and therefore does not interfere on the femtocell communication; and (ii) the MU is close to the femtocell, and the interference has to be taken into account. The main contributions of this article are twofold: (i) derivation of some closed form outage probability expressions considering SIC in the FD scenario; (ii) performance analysis of FD relaying in a heterogeneous network. Furthermore, our results show that FD relaying can considerably enhance performance within the femtocell, allowing the femto nodes to operate in a higher rate regime when compared to the MU.
The rest of this article is organized as follows. Section 2 presents the system model. Section 3 introduces the outage and spectral efficiency analysis. In Section 4, some numerical results are presented. Finally, Section 5 concludes the article.
2 System model

The MU is far from the femtocell, and therefore the femtocell can operate normally on the same resource, considering that the MU does not interfere with the femtocell, and its signal is seen as noise.

The MU is near the femtocell and therefore interferes on the femtocell communication.
We consider that both R and D are able to employ SIC on the MU interference signal. Therefore, R and D see a multiple access channel and the rate regions and individual outage probabilities can be defined as in [26, 27], respectively. As shown in [28], SIC can successfully be applied in cellular networks, while an example of application on a femtocell scenario can be found in [29, 30], where HD nodes are able to cancel the interference through SIC.
where the first term corresponds to the freespace path loss, d_{ ij } is the distance between transmitter i and receiver j, W is the wall partition loss, which we assume to be 5 dB, q is the number of walls between the transmitter and receiver (assumed q=1 except for the S D link, where we assume q=2) and X_{ σ }is a zero mean Gaussian distributed random variable (in dB) with standard deviation σ=6 dB [14].
where W^{ ′ }is the outdoor penetration loss that is assumed equal to 10 dB, and X_{ σ }is a zero mean Gaussian distributed random variable with standard deviation σ=8 dB [14].
2.1 FDMH relaying
where h_{ ij }represents the fading channel coefficients between the nodes i∈{S R MU} and j∈{R D}, while h_{ LI }is the complex fading coefficient of the loop interference [22] and κ_{ ij }is the inverse of the path loss between nodes i and j. The transmit power of each node is P_{ i }where i∈{S R MU}. Notice that when the MU is far from the femtocell we can assume that κ_{ MUR }and κ_{ MUD }→0, and therefore the MU does not interfere on the femtocell. Moreover, the additive complex Gaussian noises are represented by the terms n_{ R } and n_{ D }. In addition, the source message is represented by x_{ S }, while the message transmitted by the relay x_{ R }is a function of the received signal from the source. Moreover, E[∣x_{ S }∣^{2}= E[∣x_{ R }∣^{2}= 1, where E[·] is the mathematical expectation. Notice that the transmitted relay signal is a delayed version of the source signal, and we assume that the delay is long enough to guarantee that the transmitted and received signals at the relay are uncorrelated. Notice that once we assume that the S–D link has worse largescale fading condition than the S–R and R–D links, it is reasonable to assume that D will see the S–D signal as noise instead of interference [20, 23, 34].
while the instantaneous and average SNR of the selfinterference link can be written, respectively, as ${\gamma}_{\mathrm{LI}}=\frac{{P}_{R}\phantom{\rule{0.3em}{0ex}}\Phi \phantom{\rule{0.3em}{0ex}}\mid {h}_{\mathrm{LI}}{\mid}^{2}}{{N}_{0}}$ and ${\stackrel{\u2015}{\gamma}}_{\mathrm{LI}}=\frac{{P}_{R}\phantom{\rule{0.3em}{0ex}}\Phi \phantom{\rule{0.3em}{0ex}}E[\mid {h}_{\mathrm{LI}}{\mid}^{2}]}{{N}_{0}}$. We assume that the selfinterference channel suffers a constant attenuation which is represented by Φ. Moreover, as shown in [25], in a practical scenario it is possible to attenuate the selfinterference by as much as 40 dB according to the set of techniques employed, as for instance spatial antenna separation.
Notice that the relay suffers interference from the MU and from itself, while D is interfered only by the MU.
2.2 HDMH relaying
where the notation follows the one used above. Moreover, the SNR and SINR are defined just as above, with the only difference that in HDMH there is no selfinterference at the relay.
For DT the SINR is simply ${\gamma}_{D}^{\mathit{\text{dir}}}=\frac{{\gamma}_{\mathrm{SD}}}{{\gamma}_{\mathrm{MUD}}+1}$.
3 Outage and spectral efficiency analysis
In this section, we characterize the outage and spectral efficiency of FDMH and HDMH relaying schemes described in Section 2.
3.1 DT
 1.
(a) Both messages are decoded;
 2.
(b) Only S is decoded and therefore MU is in outage;
 3.
(c) Only MU is decoded and therefore S is in outage;
 4.
(d) Unable to decode, both S and MU are in outage.
Notice that the underbraces in (15) correspond to the integration regions of Figure 2b.
If the MU is far away from the femtocell we can assume that there is no interference at D, and therefore SIC is not necessary. Consequently, we can rewrite the outage probability of the DT simply as ${\mathcal{O}}_{\mathrm{dir}}=1exp\left(\frac{{2}^{\mathcal{R}}1}{{\stackrel{\u2015}{\gamma}}_{\mathrm{SD}}}\right)$.
3.2 HD relaying
Next, we derive the outage probability of the HDMH relaying scheme. Following the same rationale used to derive the rate regions and the individual outage probability of the S–D link, we can obtain, through appropriate substitutions, the individual outage probabilities of the S–R and R–D links, ${\mathcal{O}}_{\mathrm{SR}}$ and ${\mathcal{O}}_{\mathrm{RD}}$, respectively. Thus, at the S–R link we take (15) and substitute ${\stackrel{\u2015}{\gamma}}_{\mathrm{MUD}}$, ${\stackrel{\u2015}{\gamma}}_{\mathrm{SD}}$ by ${\stackrel{\u2015}{\gamma}}_{\mathrm{MUR}}$, ${\stackrel{\u2015}{\gamma}}_{\mathrm{SR}}$, respectively. At the R–D link we substitute only ${\stackrel{\u2015}{\gamma}}_{\mathrm{SD}}$ by ${\stackrel{\u2015}{\gamma}}_{\mathrm{RD}}$.
Notice that the communication is successful only if both links are not in outage. Moreover, similar to the direct scheme when the MU is far away from the femto cell we can, respectively, rewrite the outage probabilities of the S–R and R–D links as ${\mathcal{O}}_{\mathrm{SR}}=1exp\left(\frac{{2}^{\mathcal{R}}1}{{\stackrel{\u2015}{\gamma}}_{\mathrm{SR}}}\right)$ and ${\mathcal{O}}_{\mathrm{RD}}=1exp\left(\frac{{2}^{\mathcal{R}}1}{{\stackrel{\u2015}{\gamma}}_{\mathrm{RD}}}\right)$.
The factor $\frac{1}{2}$ present in the spectral efficiency of the HDMH scheme is a consequence of the HD constraint of the cooperative HD schemes with selective protocols.
3.3 FDR
The outage probability of the S–R link when the MU is near to the femtocell could not be derived in closedform. Moreover, as D is an HD device, and therefore the individual outage probability of the R–D link of FDMH can be derived in the same manner as in HDMH.
Notice that the great advantage of FD relaying is that it is possible to achieve the same maximum spectral efficiency as DT, which is twice the maximum spectral efficiency achieved by HD. However, as the FD relay suffers from selfinterference, it is not clear if the net results are positive or not. In the next section, we numerically investigate this issue.
4 Numerical results
In this section, we present some numerical results considering the position of the MU. Moreover, we analyze the performance of the femtocell for different values of selfinterference attenuation and information rates. We perform a semianalytic analysis of the heterogeneous network studied since we do not derive a closedform expression for the S–R link of the FDMH scheme when the MU is near the femtocell, instead we employ Monte Carlo simulations in which we consider at least 10^{6} channel realizations for each SNR value. Furthermore, we recall that we derived closedform expressions for all other links. We assume that the FBS has a radius of r_{ f }=20 m, while the MBS has a radius of r_{ m }=400 m. The FU (or S) and the FD relay are positioned over a straight line towards D, so that d_{ SR }=d_{ RD }=20 m, while d_{ SD }=40 m. We assume that the S–D link faces two walls, therefore in this case q=2. We also consider that the carrier frequency is 2.3 GHz, and without loss of generality we assume that N_{0}=1. The other path loss parameters are described in Section 2. Moreover, we assume that the femtocell nodes have the same power P. Thus, considering a fair comparison in terms of total power, since the cooperative schemes employ a total power equal to P_{ T }=2P, we assume that in the DT scheme the source uses P_{ S }=2P, and also that the MU always transmits with P_{ MU }=2P.
5 Conclusions
In this article, we evaluate the performance of a heterogeneous network composed of a cooperative femtocell underlaid in a macrocell network. We consider a practical FD relay within the femtocell, which means that transmission and reception occur simultaneously and that selfinterference is taken into account. We derive some closedform expressions for the outage probability involving SIC, and we perform a semianalytical performance analysis in terms of outage probability and spectral efficiency. We recall that by the usage of FD relaying we are able to solve problems related to the HD constraint, e.g., the problem of the hidden node, and the problem of multiplexing loss. Furthermore, our results show that FD relaying also allows the nodes within the femtocell to operate with much higher spectral efficiency than in the case of HD relaying, or with a considerable SNR advantage over the direct noncooperative transmission.
6 Endnote
^{a}Throughout this article the logarithm function is taken to base 2 unless stated otherwise.
Declarations
Acknowledgements
This study was conducted in the framework of the ICT project ICT4248523 BeFEMTO, which is partly funded by the EU.
Authors’ Affiliations
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