Partially Overlapping Tones for Uncoordinated Networks

IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 62, NO. 9, SEPTEMBER 2014 3363

Partially Overlapping Tones forUncoordinated Networks

Alphan Sahin, Erdem Bala, Ismail Güvenç, Senior Member, IEEE, Rui Yang, and Hüseyin Arslan

Abstract—In an uncoordinated network, the link-level perfor-mance of a wireless receiver might degrade significantly due tothe interference from other transmitters that share the samespectrum. As a solution, in this study, the concept of partiallyoverlapping tones (POT) is introduced. In POT, interference energyobserved at a victim receiver is mitigated by partially overlappingthe individual subcarriers via an intentional carrier frequencyoffset between the links. It is argued that the self-interferencearising due to the use of POT can be more easily addressedthan the dominant other-user interference, potentially yieldinghigher spectral efficiencies with POT. Using a spatial Poisson pointprocess based framework, a tractable bit error rate analysis isprovided to demonstrate potential benefits emerging from POT insystem-level scenarios.

Index Terms—Non-orthogonal schemes, partially overlappingtones, Poisson point process, uncoordinated networks, waveform.

I. INTRODUCTION

R ECENTLY, traditional broadband wireless networks arefalling short of satisfying the emerging data traffic de-

mands, arising due to the desire for always-on, ubiquitous, andhigh-throughput connectivity. Satisfaction of these demandsconstitutes the main driving force for heterogeneous networks(HetNets) in which multiple tiers with varying coverage rangesco-exist within the same network. In HetNets, interferenceamong the tiers or the devices might dominate the noise,which leads to interference-limited networks. The interferenceissues become prominent especially when dense and unplanneddeployments as in device-to-device (D2D) communications andfemtocell networks are taken into account. In addition, whenthe coordination mechanisms to cope with the interference isnot available (e.g., as in Wi-Fi and self-organizing networks),

Manuscript received December 12, 2013; revised June 1, 2014; acceptedAugust 7, 2014. Date of publication August 20, 2014; date of current versionSeptember 19, 2014. This study has been supported by InterDigital Commu-nications, Inc. The associate editor coordinating the review of this paper andapproving it for publication was M. C. Gursoy.

A. Sahin is with the Department of Electrical Engineering, University ofSouth Florida, Tampa, FL 33620-5399 USA (e-mail: [email protected]).

E. Bala and R. Yang are with InterDigital Communications, Inc.,Melville, NY 11747 USA (e-mail: [email protected]; [email protected]).

I. Güvenç is with the Department of Electrical and Computer Engineering,Florida International University, Miami, FL 33174 USA (e-mail: [email protected]).

H. Arslan is with the Department of Electrical Engineering, University ofSouth Florida, Tampa, FL 33620-5399 USA, and also with the College ofEngineering, Istanbul Medipol University, Beykoz 34810, Istanbul (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TCOMM.2014.2349908

the certain presumptions about the network characteristics maynot be valid in practice. Such presumptions may include timingsynchronization among the links, and a-priori knowledge of thechannel information and other key parameters at the receiver.In such uncoordinated network scenarios where the interfer-ence coordination mechanisms are not feasible or effective,alternative approaches for reducing other user interference arerequired.

In this paper, we investigate mitigation of the other userinterference through exploiting the time-frequency character-istics of a carrier waveform in multicarrier communications.A waveform, which is one of the core elements of a commu-nication system, describes the formation of data transmissionresources in signal space [1], [2]. When the performance of awireless network is limited by noise, the main considerationfor the waveform design aims to enhance the individual linkproperties, e.g., through reducing the interference created bythe time and frequency dispersion of the propagation channel[3]. However, interference due to the other users is occasionallya major factor limiting the performance of a wireless network,and therefore, the impact of the other-user interference mightbe more significant compared to the interference due to thechannel dispersion.

In the literature, traditionally, the other user interference at adesired receiver is treated without considering the impact of theutilized waveform. Most of the solutions devised to address theinterference problem rely either on media access control (MAC)based coordination or interference cancellation techniques. Forexample, interference coordination mechanisms with properscheduling and resource allocation can be used to minimize theeffects of inter-cell interference [4]. In the physical layer, meth-ods such as interference cancellation [5], multiuser detection[6], and interference alignment [7] can be utilized to handle theother-user interference by exploiting the differences betweenthe desired and the interfering signal strengths, multiple accesscodes, and multipath channel characteristics.

In this study, a new strategy is proposed to reduce the otheruser interference in uncoordinated networks, which exploits thetime-frequency characteristics of the carrier waveforms. Themain contributions of this paper are as follows:

• We introduce the concept of partially overlapping tones(POT), which allows the subcarriers allocated to inter-fering links to overlap partially with the subcarriers of adesired user. The overlap is achieved by introducing an in-tentional carrier frequency offset (CFO) between the linksand its amount is controlled by appropriately designing thetime-frequency utilization of the waveforms.

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3364 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 62, NO. 9, SEPTEMBER 2014

• It is shown that with orthogonal waveforms, there isa tradeoff between other-user interference and spectralefficiency. In other words, mitigation of the other-userinterference can be achieved at the expense of a loss inspectral efficiency.

• It is further shown that with non-orthogonal waveforms,there is a tradeoff between other-user interference andself-interference. Mitigation of the other-user interferencecan be achieved at the expense of higher self-interference,while the density of the symbols on time-frequency planeremains unchanged.

• Using spatial Poisson point process (PPP) models, atractable bit error rate (BER) analysis is provided foran unplanned network deployment. The analysis helpsto understand the system-level performance for variousnetwork densities and waveform designs.

The rest of this paper is organized as follows. Relatedwork is discussed in Section II, and the system model includ-ing the physical layer parameters is described in Section III.Section IV introduces the concept of POT for orthogonal andnon-orthogonal waveform structures. Subsequently, the BERanalysis considering a Poisson field of interferers is provided inSection V, and the numerical results evaluating the performanceof the proposed approach are provided in Section VI. Finally,Section VII provides some concluding remarks.

II. RELATED WORK

The utilization of overlapping channels to improve through-put in a multiple-access wireless network has been investigatedin several papers in the literature [8]–[13]. In these works, it isargued that the channel separation between the two pairs of Wi-Finodes can be interpreted as the physical separation betweenthe nodes. Therefore, if partially overlapping channels are usedcarefully, it can provide greater spatial re-use. However, thesepapers consider the total spectrum utilization of the transmis-sion, and do not investigate the impact of partial overlapping onindividual subcarriers. The partially overlapping spectrum con-cept also appears within the context of self-organizing networks[14], [15]. In [14], the interference issues between femtocellsare addressed using the orthogonal and partially overlappingresource blocks. An efficient overlapping pattern is introducedbased on the self-organization characteristics of femtocells.In [15], a similar strategy is also applied to self-organizingnetworks in Long Term Evolution (LTE) systems. Game the-oretic approaches to investigate the overlapping resource allo-cation is also studied in the literature. In [16], multi-channelspectrum sharing is modeled as a spectrum market, wherethe primary users offer their subchannels to secondary users,with the constraint that the interference from the secondaryusers should be lower than a threshold. For converging intoan equilibrium in this spectrum market, a distributed algorithmis developed, which needs time to converge into equilibrium.However, to the best of our knowledge, detailed time-frequencyinterference analysis due to partially overlapping waveforms inthe frequency domain is not available in the literature.

Other-user interference is not typically easy to handle inpractice due to its asynchronous nature and the difficulty to

know its statistical characteristics, which depend on the deploy-ment model and waveform structure utilized in the network.Orthogonal frequency division multiplexing (OFDM) is a well-investigated multicarrier scheme in asynchronous interferencescenarios, e.g., for femtocell-macrocell coexistence [17]–[19].By providing some intentional timing offset between the tiers,the different types of interference, i.e., inter-carrier interference(ICI) and inter-symbol interference (ISI), can be convertedinto each other in [19]. This is achieved by keeping the totalother-user interference as constant. A theoretical BER analysisinvestigating the ISI versus ICI trade-offs in OFDM down-link is provided in [20]. In [21], coexistence scenarios arediscussed within the context of cognitive radio. Moreover, toevaluate various waveforms including OFDM, a frameworkbased on spectrally-encoded access schemes is introduced. Thetheoretical BER performance under additive white Gaussiannoise (AWGN) scenarios is provided for multi-carrier code di-vision multiple access (MC-CDMA) and other multiple accesstechniques, considering the underlay/overlay/hybrid operationsof the cognitive networks. In [22], BER degradation due tothe adjacent channel interference is investigated by empha-sizing superiority of filter bank multicarrier (FBMC) basedcellular systems over an OFDM based approach. Althoughthe aforementioned investigations provide useful intuitions onthe performance degradation, the analyses are performed foridealistic assumptions, such as grid-based cell deployment anduniform user density. In [23], it is emphasized that even if thegeographical user density is uniform, the distance of the userslinked to the corresponding serving points might not be uniformdue to the irregular base station deployment and shadowingcharacteristics. In [24], [25], homogeneous PPPs are consideredto model the deployment of the base stations. This approach,which is pessimistic compared to highly idealized grid-basedmodels and real deployment scenarios, yields a tractable toolthrough stochastic geometry based techniques. In [26] and[27], analytical models for uplink and K-tier heterogeneousnetworks are provided using PPPs. Impact of interference co-ordination on the spectral efficiency in HetNets has also beenstudied in [28]–[30] using stochastic geometry techniques.

There are limited studies that investigate the effects of wave-form parameters on the statistics of aggregate interference in aPoisson field of interferers. For example, coexistence betweenultra wide band (UWB) and narrow band systems is investi-gated using PPPs and impact of pulse shape is emphasizedfor aggregate network emission [24]. In [31], BER analysesare provided for quadrature amplitude modulation (QAM) andphase shift keying (PSK) modulations using PPPs, withoutspecifically considering the impact of waveforms.

III. SYSTEM MODEL

Before describing the proposed POT architecture, first, asystem model for the considered multi-user wireless scenariowill be introduced in this section. Consider an uncoordinatednetwork where transmission points (TPs) and their correspond-ing reception points (RPs) are distributed in an area as arealization of homogeneous 2-D PPP of Φ with the intensityλ as in Fig. 1. Interfering TPs and interfered RPs are called

SAHIN et al.: PARTIALLY OVERLAPPING TONES FOR UNCOORDINATED NETWORKS 3365

Fig. 1. Illustration of interference in an uncoordinated network. Without lossof generality, the victim reception point (RP) is located at the origin of thepolar coordinates and interfering transmission points (TPs), i.e., aggressors, aredistributed in an area as a realization of a 2-D PPP.

aggressors and victims, respectively. Without loss of generality,the victim of interest is located at the origin of the polarcoordinates (0,0). The distance between the ith aggressor andthe victim is given as ri, and the minimum distance betweenthe aggressors and the victim is set to rmin. While the distancebetween RP and its associated TP for ith aggressor link isdenoted by di, the same distance is expressed by dε for thedesired link for the victim. Also, it is assumed that aggressorsare farther away than dε, i.e., ri > rmin ≥ dε, which is widelyconsidered for the interference analyses based on PPPs [32]. Inthe following subsections, a signal model for transmission andreception based on multicarrier schemes and a channel modelthat includes large and small scale effects are given for furtherdiscussions on POT.

A. Signal Model for Transmission

The transmitted signal from the desired TP and the transmit-ted signals from the ith aggressor can be expressed as

sε(t) =∞∑

n=−∞

N−1∑l=0

Xεnlg

εnl(t), (1)

si(t) =∞∑

n=−∞

N−1∑l=0

Xinlg

inl(t), (2)

respectively, where Xεnl and Xi

nl are the information symbolswhich are independent and identically distributed (i.i.d.) withzero mean on the lth subcarrier and nth symbol, N is thenumber of subcarriers, and gεnl(t) and ginl(t) are the synthesisfunctions which map information symbols into time-frequencyplane based on a rectangular lattice as

gεnl(t) = gε(t− nτ0)ej2πlν0t, (3)

ginl(t) = gi(t− nτ0)ej2πlν0t. (4)

The family of functions in (3) and (4) are often referred as aGabor frame or a Weyl-Heisenberg frame, where gε(t) and gi(t)are the prototype filters employed at the transmitters, ν0 is thesubcarrier spacing, and τ0 is the symbol spacing [33], [34]. Forthe sake of notation simplicity, ν0 and τ0 are given in units ofF and T , respectively (e.g., ν0 = 1.2× F and τ0 = 1.3× T ),

where F = 1/T a design parameter. Without loss of generality,the energy of gε(t) and the energy of gi(t) are normalized as

‖gε(t)‖2L2(R) =∥∥gi(t)∥∥2L2(R)

=

∞∫−∞

|gε(t)|2 dt = 1, (5)

where L2(R) denotes the square-integrable function space overR and ‖ · ‖ is the L2-norm of a function.

B. Large Scale Effects

Considering various path loss models depending on theenvironment, the path loss is characterized by Lm(d) = a+b log10(d) where the path loss parameters a and b are scalarsand the argument is the distance in meters. The received in-terference power from the ith aggressor and the desired signalpower at victim location per subcarrier are denoted by Pi andPε, respectively. Impact of shadowing is not considered in thisstudy. The main reason for this issue is to give insights on thePOT rather than introducing extra complexity for the systemmodel. However, using the methodologies proposed for themoment generation function of the summations of lognormaldistributed lognormal variables [35] and [36], it is possible toinclude the impact of shadowing in the theoretical analysis.

For the link transmission, open loop fractional power controlis applied and some amount of the path loss, i.e., β(a+b log10(·)), is compensated, where β ∈ [0, 1] is the path losscompensation parameter. Note that the TP might transmit withthe maximum transmit power in some cases. However, sincelink distances considered are small, the possibility of transmis-sion at maximum power is excluded.

C. Small Scale Effects

Time-varying multipath channel is taken into account be-tween all RPs and TPs. Channel impulse response is charac-terized by h(τ, t) =

∑L−1�=0 ��(t)δ(τ − τ�) where L denotes the

total number of multipaths, � is the path index, and τ� is thedelay of the �th path. It is assumed that the path gains, ��(t),are independent and identically distributed variables and thesignals experience Rayleigh fading, which is a common modelfor interference analysis. Also, the expected channel power isconsidered as

∑L−1�=0 E[|��(t)|2] = 1. For the sake of notation,

the channel between ith interfering TP and the victim RP isexpressed as hi(τ, t), while the channel between desired TPsand the victim RP is denoted by hε(τ, t).

D. Synchronization

As discussed in [37] and [38], synchronization with thereceived signal in the presence of interference might be chal-lenging, especially at low signal-to-interference-plus-noise ra-tios (SINRs). However, the impairments like timing offset andCFO are often related to the preamble structure rather than thedata portion of the frame. Therefore, perfect synchronizationis assumed in this paper at the TP/RP pair of interest. Be-sides, timing misalignment between the aggressor’s signals andsynchronization point of the victim is taken into account. The


timing misalignment of ith aggressor signal with respect to thesynchronization point of the victim RP is denoted by Δti and itsdistribution fΔti(Δti) is assumed as uniform between 0 and τ0.Besides, intentional CFO between ith aggressor and the victimRP is given by Δfi to generate POT which is discussed inSection IV. The impact of CFO due to the oscillator mismatchesbetween the aggressor’s signals and desired signal is ignored.This is because of the fact that the impact of CFO due to theoscillator mismatches is relatively smaller than Δfi for POT.For example, when carrier spacing is set to 15 kHz and CFOis 500 Hz, normalized CFO becomes 0.033 (500 Hz/15 kHz).However, the amount of normalized Δfi for POT, throughoutthe study, is at least 0.5, which is significantly larger than theCFO due to the hardware impairments.

E. Signal Model for Reception

Considering all interfering TPs, and assuming a wide-sensestationary uncorrelated scattering (WSSUS) channel model[39], the received signal at the victim receiver is given by

r(t) =√Pε

∫τ

∫ν

Hε(τ, ν)sε(t− τ)ej2πνtdνdτ

︸︷︷︸Desired signal

+∑i∈Φ

√Pi

∫τ

∫ν

Hi(τ, ν)si(t+Δti − τ)ej2πνtdνdτ

︸︷︷︸Interfering signals

+ ω(t)︸︷︷︸Noise

,

(6)

where Hε(τ, ν) and Hi(τ, ν) are the Fourier transformations ofhε(τ, t) and hi(τ, t), respectively, and w(t) is the AWGN withzero mean and variance σ2

noise. to get the information symbolon the kth subcarrier and mth symbol, the received signal in (6)is correlated by the analysis function which is given by

γεmk(t) = γε(t−mτ0)e

j2πkν0t. (7)

Then, the output of the correlator is sampled using a certainsampling frequency, to obtain the received symbol as

Xεmk = 〈r(t), γε

mk(t)〉Δ=

∫t

r(t)γε∗mk(t)dt

=√PεX

εmkA

εmkmk︸︷︷︸

desired part

+√

Pε

K−1∑n=−K+1

n �=m

N−1∑l=0l �=0

XεnlA

εnlmk

︸︷︷︸self−interference part

+∑i∈Φ

√Pi

K−1∑n=−K+1

N−1∑l=0

XinlA

inlmk︸︷︷︸

other−user interference

+ Wk︸︷︷︸noise

. (8)

In (8),

Aεnlmk =

∫τ

∫ν

Hε(τ, ν)

∫t

gεnl(t− τ)γε∗mk(t)e

j2πνtdtdνdτ,

(9)

Ainlmk =

∫τ

∫ν

Hi(τ, ν)

∫t

ginl(t−Δti − τ)ej2πΔfi(t−Δti−τ)

× γε∗mk(t)e

j2πνtdtdνdτ, (10)

and they show the correlation between the symbols (n, l) and(m, k), which also captures the dispersion due the channelpropagation effects. As it is seen in (8), while other-user in-terference is caused by aggressor links, self-interference canoccur due to the time-varying multipath channel, hardwareimpairments, or use of a pulse shape which is not a Nyquistfilter. Considering (8), instantaneous SINR can be expressed as

SINR

=

Gε︷︸︸︷|Aε

mkmk|2K−1∑

n=−K+1n �=m

N−1∑l=0l �=k

|Aεnlmk|2

︸︷︷︸Iself

+∑i∈Φ

Pi

Pε

K−1∑n=−K+1

N−1∑l=0

∣∣Ainlmk

∣∣2︸︷︷︸

Gi︸︷︷︸Ii︸︷︷︸

Iother︸︷︷︸Itotal

+σ2noise

Pε

,

(11)

where K is the filter length in terms of symbol spacing, Itotalis the total interference, Iself and Iother are the self-interferenceand other-user interference, respectively, Ii is the interferencedue to ith aggressor, Gε and Gi are the interference gainsincluding fading and filter characteristics, and

Pi

Pε= d

b−βb10

ε dβb10i r

−b10i . (12)

Note that K is related to the representation of the filter in timedomain. As long as K is selected properly, the filter truncationhas a minor impact on self-interference compared to the inter-ference due to the time-varying multi-path channel or hardwareimpairments at the RP and/or the TP. While Gε is a randomvariable with unit mean exponential distribution because of theRayleigh fading [20], [22], Gi can be characterized for a givenΔti and Δfi by an exponential distribution where its expectedvalue is given by

σ2i (Δti,Δfi)=

K−1∑n=−K+1

N−1∑l=0

∣∣⟨ginl(t−Δti)ej2πΔfit, γε(t)

⟩∣∣2 .(13)

Conventionally, σ2i (Δti,Δfi) is considered as 1 for link-level

analyses [25], similar to the expected value of Gε. However,expressing it as in (13) gives flexibility to include the impact oftransmit and receive filters and calculate interference when anadditional processing is performed to reduce other-user inter-ference. Finally, Iself is also a random variable with exponential


Fig. 2. Illustrations for full overlapping and partial overlapping. While full-overlapping tones cause significant other-user interference, the main portionof the interference is mitigated by the receive filter with the concept of POT.(a) Fully overlapping tones. (b) Partially overlapping tones.

distribution where, considering the Rayleigh fading assumption[22], its expected value is given by

σ2self =

K−1∑n=−K+1

n �=m

N−1∑l=0l �=k

|〈gεnl(t), γε(t)〉|2 . (14)

Essentially, calculations of both σ2self and σ2

i (Δti,Δfi) arebased on the projection operation onto receive filters, whichcan be derived via corresponding ambiguity functions [2]. Itis worth mentioning that Iself and Gε are correlated randomvariables since the transmitted symbols pass through similarmultipath channels, which needs to be taken into account whenIself exists.

IV. PARTIALLY OVERLAPPING TONES

The main goal of the POT approach is to mitigate other-user interference given in (13) by using the waveform struc-ture. It relies on intentional CFO between aggressor’s Gaborsystem and victim’s Gabor system. For example, while oneof the links operates at carrier frequency fc, the other linkoperates at fc + ν0/2. By allowing this operation, instead offull-overlapping between the subcarriers of the links, POT isobtained. This approach also fits the asynchronous nature ofother-user interference as it does not introduce any timingconstraint between interfering signals. One can interpret theintentional CFO as an alignment strategy in frequency domain.

In Fig. 2, a motivating example based on filtered multi-tone (FMT) is illustrated for POT. In FMT, each subcarrieris generated via a band-limited filter [40]. As opposed to theconventional understanding of OFDM, the subcarriers are notoverlapped in frequency domain. By providing additional guardbands, orthogonality between subcarriers is maintained. Notethat these guard bands are also useful to provide immunityagainst self-interference due to the time-frequency impair-ments. As shown in Fig. 2, these guard bands are exploitedfurther and used to mitigate the other-user interference. Byapplying an intentional CFO between two different links, other-

user interference mitigation is provided in an uncoordinatednetwork.

POT is fundamentally related to the utilization of the time-frequency plane by the waveform structure. Transmit filter,receiver filter, and density of symbols in time-frequency planedetermine the available resource opportunities jointly for theother-user interference mitigation by using POT, as exemplifiedin Fig. 2. Besides, further utilization of the waveform structurevia non-orthogonal schemes along with POT lead to a trade-off for uncoordinated networks: other-user interference versusself-interference. This trade-off is desirable in an uncoordi-nated network as long as self-interference is handled via self-interference cancellation methods, e.g., equalization. In thefollowing subsections, orthogonality of schemes is stressed inconjunction with POT. POT with orthogonal schemes and non-orthogonal schemes are investigated theoretically along withnumerical results and their potential drawbacks.

A. Partially Overlapping Tones With Orthogonal Schemes

For orthogonal schemes, transmitter and receiver utilize thesame prototype filter, i.e., gε(t) = γε(t). In addition, innerproducts of the different basis functions derived from the proto-type filter is zero, i.e., 〈gεnl(t), γε

mk(t)〉 = 0 for n = m and l =k. Many fundamental schemes, e.g., OFDM, FMT, and FBMC,rely on orthogonality. In digital communication, orthogonalityin a multicarrier scheme is generally perceived as a necessarycondition. It simplifies the receiver algorithms significantly andprovides optimum signal-to-noise ratio (SNR) performance inAWGN channels. Besides these features, orthogonal schemeshave another fundamental property due to orthogonal basisfunctions at the receiver: the energy of a signal before theprojection onto receive filters is equal to the energy after theprojection onto receiver filters. This is typically expressedthrough the Plancherel formula1 given by

‖s(t)‖2 =∑m,k

|〈s(t), γεmk(t)〉|2 , (15)

where s(t) is an arbitrary signal and {γεmk(t)} is the set of

orthonormal basis functions at the receiver. Assume that s(t) isthe interfering signal. When an orthogonal transformation, e.g.,discrete Fourier transformation (DFT), is applied to s(t) at thereceiver, the total amount of the interference does not changeafter the transformation. This issue leads to an undesirableresult: the only way to mitigate the other-user interference is todiscard some of the subcarriers or to construct an incompleteGabor system, i.e., τ0ν0 > 1 [2], [3], which causes schemeswith lower spectrally efficiency. In other words, POT withorthogonal schemes would be beneficial only when some ofthe subcarriers are not utilized or τ0ν0 > 1. Indeed, the norm-preserving feature of orthogonal transformations at the re-ceivers explain why orthogonal schemes do not directly provideimmunity against the other-user interference.

POT offers intentional CFO between the different links basedon the fact that timing synchronization between TPs in an

1It corresponds to Parseval’s theorem for Fourier series.


Fig. 3. Other-user interference mitigation without introducing self-interference, but loss in spectral efficiency. (a) Impact of timing misalignmentwhen root raised cosine filter is employed along with FMT. (b) Trade-offbetween spectral efficiency and other-user interference.

uncoordinated network is a challenging issue. However, theintentional CFO approach also introduces some constraints onthe waveform structure. For example, orthogonal multicarrierschemes which provide non-overlapping subcarriers in fre-quency domain, e.g., FMT, comply with the intentional CFOapproach introduced by POT. On the other hand, POT might notbe as beneficial for approaches where the orthogonality is main-tained strictly on certain localizations in the time-frequencyplane, as in the case of OFDM. Considering this issue, analysesthroughout the present study are performed based on FMT.

In Fig. 3, considering timing misalignment between an ag-gressor and the victim, Δti is swept for one symbol periodwhen Δfi = ν0/2. FMT is generated based on root-raised-cosine (RRC) filter. Note that RRC filter is a band-limitedfilter and the excess bandwidth of the RRC filter is controlledvia a roll-off factor of α, where 0 ≤ α ≤ 1. In Fig. 3(a),σ2i (Δti,Δfi) is calculated numerically, based on (13). In case

of full overlapping, σ2i (Δti,Δfi) is mitigated maximally when

Δti = 0.5× T , τ0 = T , and ν0 = (1 + α)× F . This is be-cause of the reduction of the ICI components maximally due tothe additional guard bands, when timing misalignment occurs.In case of partial overlapping, impact of Δti is removed totally,and σ2

i (Δti,Δfi) is significantly reduced since the receivefilters reject the main portion of the interference, dependingon the utilized α. Assuming the aggressor interference has auniform timing misalignment characteristics, trade-off betweenspectral efficiency and other-user interference is given for twodifferent FMT cases in Fig. 3(b). When ν0 is set to (1 + α)×F , σ2

i (Δti,Δfi) decreases for both full overlapping and partialoverlapping due to the less ICI components with the timingmisalignment, as given in Fig. 3(a). When α is fixed to 0.2,other-user interference is mitigated more via partial overlap-ping, since this approach provides more gap in frequency forother-user interference mitigation.

Major concern of using POT with orthogonal schemes mightbe having less spectrally efficient transmission for the sakeof other-user interference mitigation. However, as indicatedbefore, it allows the devices interrupted by the interference toachieve a better BER performance with a simple approach.

B. Partially Overlapping Tones WithNon-Orthogonal Schemes

Similar to the orthogonal schemes, transmitter and receiverutilize the same prototype filters for non-orthogonal structures,i.e., gε(t) = γε(t). However, the inner products of the trans-lated and modulated prototype filters with different indexes arenot zero, i.e., 〈gεnl(t), γε

mk(t)〉 = 0 for n = m and l = k. Forinstance, one can construct a non-orthogonal frequency divi-sion multiplexing (NOFDM) scheme by using the rectangularlattice of OFDM with non-Nyquist transmit filters and receivefilters, e.g., Gaussian functions. For non-orthogonal schemes,the receiver filters construct a non-orthogonal transformation.Therefore, the condition given in (15) is relaxed as

A ‖s(t)‖2 ≤∑m,k

|〈s(t), γεmk(t)〉|2 ≤ B ‖s(t)‖2 , (16)

where {γεmk(t)} is the set of non-orthogonal basis functions at

the receiver, A and B are the lower bound and upper bound,respectively, and 0 < A ≤ B < ∞. Based on (16), when anon-orthogonal transformation is applied at the receiver, theenergy of s(t) does not have to be preserved after the trans-formation. In other words, the non-orthogonal transformationsat the receivers are able to alter the amount of the observedinterference energy. Hence, when POT is taken into accountwith non-orthogonal schemes, it is possible to mitigate other-user interference even when τ0ν0 = 1.

To understand the utilization of POT with non-orthogonalschemes, consider a rectangular lattice in time and frequencywhere τ0ν0 = 1 and the prototype filters at the transmitterand the receiver are based on Gaussian functions, as illus-trated in Fig. 4. Note that Gaussian function is the optimally-concentrated pulse in time-frequency domain and it isexpressed as

p(t) = (2ρ)1/4e−πρt2 , (17)


Fig. 4. Illustration for the trade-off between self-interference and other-userinterference with the concept of POT. The desired signal and interferingsignal are represented as solid and dashed lines, respectively. (a) Less self-interference, but more other-user-interference. (b) More self-interference, butless other-user-interference.

where ρ is the control parameters for the dispersion of the pulsein time and frequency and ρ > 0. When ρ = 1, the filter hasisotropic dispersion in time and frequency as given in Fig. 4(a).For smaller ρ, the dispersion in time domain increases andcauses more overlapping between the symbols in time, yieldingmore self-interference, i.e., ISI, as shown in Fig. 4(b). Whenthis scheme is considered with the concept of POT (Δfi =ν0/2), it yields a trade-off between the other-user interferenceand self-interference. As illustrated in Fig. 4(b), while smallerρ gives more gap to accommodate the other-user interference,it causes more self-interference problem.

When there is no control on the interfering signals (e.g.,absence of timing synchronization, no prior information aboutthe interfering signal parameters, etc.), orthogonal schemesdo not provide immunity against other-user interference un-less they sacrifice their throughput (e.g., splitting the wholebandwidth into two parts for a simple two-user scenario). Atthis point, non-orthogonal schemes with POT introduce an

important advantage due to the following practical consider-ation: Self-interference problem (such as the ISI problem) iseasier to address than other-user interference problem in anuncoordinated network. There are effective solutions availablein the literature to cope with the ISI problem since the receiverknows the details about its own signal. Essentially, the POTwith non-orthogonal schemes converts one problem (other-userinterference) to another problem (self-interference), which iseasier to address with known solutions, e.g., equalization.

Considering the density of the symbols on time-frequencyplane of the victim RP, it is important to emphasize thedifferences between faster-than-Nyquist (FTN) signaling [41]and POT with non-orthogonal schemes. In FTN signaling, thedensity of the symbols in time-frequency plane is intentionallyincreased to a value which is higher than the Nyquist rate,i.e., τ0ν0 < 1. However, each individual link operates at theNyquist rate, i.e., τ0ν0 = 1, for POT. The time-frequency planeof the victim RP is packed due to the aggressors’ signals, whichis common in co-channel interference problems. In addition,POT does not suggest a structured symbol packing into thetime-frequency plane, as in FTN signaling. It allows timingmisalignment among the individual links.

Similar to the investigations on timing misalignment givenin Section IV-A, Δfi is set to ν0/2 and Δti is swept for onesymbol period. The impact of timing misalignment is givenin Fig. 5(a). In case of full overlapping, when Δti = 0, thereceive filter has full correlation with the concentric symbolof the aggressor and partial correlations with the neighboringsymbols. Hence, the total energy after the correlation becomesmore than 1. In case of partial overlapping, receive filters onlycapture energy from only the neighboring symbols of aggres-sors, which yields that σ2

self < 1 as in Fig. 5(a). In Fig. 5(b),the trade-off between self-interference and average other-userinterference is given, assuming uniform timing misalignment.As in Fig. 5(b), Gaussian filter provides a flexible trade-offbetween self-interference and other-user interference.

There are two potential drawbacks of considering POTwith non-orthogonal schemes compared to POT with or-thogonal schemes: 1) necessity for a self-interference can-cellation method, e.g., equalization, since the filters do notsatisfy Nyquist criterion, and 2) colored noise due to thenon-orthogonal receiver filters. For the first issue, the intro-duced complexity due to self-interference cancellation methodmight be preferable in comparison with the complexities ofthe methods for handling asynchronous other-user interference.For the second point, note that non-orthogonal transforma-tions always introduce correlation between symbols [3]. If asequence-based equalizer, e.g., maximum likelihood sequenceestimator (MLSE), is employed, a whitening filter should alsobe utilized to improve the performance of the receiver [42].Assuming the small link distances for the TP/RP pairs, noisemay be considered as a secondary problem when interferenceis a dominant issue.

V. AVERAGE BER ANALYSIS

In this section, average BER analysis is provided for POTwith orthogonal schemes that do not introduce self-interference


Fig. 5. Other-user interference mitigation without loss in spectral efficiencyand power, but at the expense of self-interference. (a) Impact of timingmisalignment when Gaussian filter is employed. (b) Trade-off between self-interference and other-user interference.

as discussed in Section IV-A. To obtain a tractable theoreticalBER analysis, a useful method for BER calculations intro-duced in [43] is combined with spatial PPP approaches [24],[25], [31]. First, BER is expressed using the SINR given in(11). Then, its expected value is obtained considering other-user interference. Its computation complexity is significantlyreduced by using the spatial PPP model and the ambiguityfunction. For non-orthogonal schemes, the investigation onBER performance is performed through the numerical analysesin Section VI, since achievable BER performance dependshighly on the employed self-interference cancellation methodat the receiver.

A closed-form expression for BER of a square M -QAM inAWGN channel is readily available in the literature and it isgiven by

BER(SNR) =

√M−2∑q

cqerfc

((2q + 1)

√SNR2

), (18)

where M is the constellation size, cq are the constants de-

pending on the modulation order and∑√

M−2q=0 cq = 1/2 [44].

For instance, cq = {1/2} and q = {0} for 4-QAM and cq ={3/8, 2/8,−1/8} and q = {0, 1, 2} for 16-QAM, respectively.

By substituting (11) into (18), BER is obtained for givenItotal, Gε, and dε as

BER(Eb/N0|Gε, Itotal, dε)

=

√M−2∑q=0

cqerfc

(2q − 1√

2

√Gε

Itotal +M−1

3 log2 M1

Eb/N0

). (19)

Since the target is to calculate average BER under interference,the terms, Itotal, and Gε, have to be averaged out. In order toobtain average BER, we refer to following lemma introducedin [43].

Lemma-I: Let x and y be unit-mean exponential and arbi-trary non-negative random variables, respectively. Then

Ex,y

[erfc

(√x

ay + b

)]= 1− 1√

π

∞∫0

e−z(1+b)

√z

Ly(az)dz,

where Ly(z) = Ey[e−yz] is the moment generation function

(MGF) with negative argument (or Laplace transformation) ofrandom variable y.

If Lemma-I is applied to (19) (see e.g., [20], [22], [43], [45]),the average BER is obtained as

BER(Eb/N0|, dε)

=

√M−2∑q=0

cq

⎛⎝1− 1√

π

∞∫0

e−z(1+ 2

(2q−1)2M−1

3 log2 M1

EbN0

)√z

×LItotal

(2z

(2q − 1)2

)dz

⎞⎠ ,

(20)

=1

2− 1√

π

√M−2∑q=0

cq

∞∫0

e−z(1+ 2

(2q+1)2M−1

3 log2 M1

EbN0

)√z

× LItotal

(2z

(2q + 1)2

)dz. (21)

Therefore, the complexity introduced by (19) reduces to calcu-late Laplace transformation of Itotal. In the following subsec-tions, Laplace transformation of Itotal is calculated in cases ofsingle aggressor and multiple aggressors.

A) Single Aggressor: If only ith aggressor is considered, theLaplace transformation of the total interference is obtained as

LItotal(z) =EItotal

[e−zItotal

](a)= EIi

[e−zIi

](b)=

τ0∫0

fΔti(Δti)

1 + zdb−βb10

ε dβb10i r

−b10i σ2

i (Δti,Δfi)dΔti, (22)


where (a) follows from the assumptions of zero self-interference via orthogonal schemes, (b) is because of theexponential distribution of Iother and the randomness of timingmisalignment. Considering the uniform timing misalignmentassumption and being a constant function of σ2

i (Δti,Δfi)respect to Δti, as in Fig. 3(a), (22) is simplified as

LItotal(z) =1

1 + zdb−βb10

ε dβb10i r

−b10i σ2

i (Δfi). (23)

A. Multiple Aggressors

When multiple aggressors exist in the network, the choice ofΔfi within the link affects the performance of POT. In order toavoid the coordination, it is assumed that Δfi is selected ran-domly from the set Ω given by [ψ0, ψ1, . . . , ψr, . . .]. The selec-tion is performed based on a probability mass function (PMF)where pr corresponds to the probability of rth intentional CFO.Based on this assumption, the Laplace transformation of thetotal interference is obtained as

LItotal(z) =EItotal [e−zItotal ]

(a)= EΦ,Ii

[e−z∑

i∈ΦIi]= EΦ

[∏i∈Φ

EIi [e−zIi ]

](24)

(b)= exp

⎡⎣−2πλ

∞∫rmin

(1− EIi [e

−zIi ])νdν

⎤⎦ , (25)

where (a) is because of zero self-interference via orthogo-nal schemes, and (b) is caused by the probability generatingfunctional of PPP, which states Ey[

∏i∈Φ f(x)] = exp

∫R2(1−

f(x))dx for an arbitrary function f(x) and the assumption ofi.i.d. interference from each aggressor Ii and independent Φfrom other random variables in the interference function Iother[25]. Considering the randomness of aggressors’ distances di,EIi [e

−zIi ] is obtained as

EIi [e−zIi ] =Edi,Gi

[e−z

PiPε

Gi

]

=∑r

pr

∞∫0

fu(u)

1 + zdb−βb10

ε uβb10 ν

−b10 σ2

i (ψr)du (26)

which is based on the Laplace transformation of an exponen-tially disturbed random variable, uniform timing misalignmentassumption, and being a constant function of σ2

i (Δti,Δfi)respect to Δti. In (26), the probability density function (PDF)of di is given by fu(u) = 2πλue−λπu2

[26]. Then, LItotal(z) isobtained as

LItotal(z) = exp

⎡⎣− 2πλ

×∞∫

rmin

⎛⎝1−

∑r

pr

∞∫0

2πλue−λπu2

1+zdb−βb10

ε uβb10 ν

−b10 σ2

i (ψr)du

⎞⎠ νdν

⎤⎦

(27)

by substituting (26) into (25). Note that (27) does not alwaysyield a closed-form solution since

∫∞0 (xe−ax2

/(1 + bxc))dxproduces an expression in terms of standard mathematicalfunctions depending on a, b, and c. Nonetheless, (27) does notrequire Monte Carlo simulations.

VI. NUMERICAL RESULTS

Numerical results are given in order to validate analyticalfindings with simulations and to investigate the performanceof uncoordinated networks along with POT. In the simulations,POT with orthogonal schemes and POT with non-orthogonalschemes are exhibited by utilizing FMT with RRC filter andzero forcing equalization and by using NOFDM with Gaussianfilter and symbol-spaced MLSE equalization, respectively. Foreach tone, the channel response is considered to have 7 tapsand the trace-back depth is set to 20. Unless otherwise stated,the numerical results are obtained for Rayleigh channels.

In Fig. 6, the impact of POT is presented in a Rayleighchannel for the aforementioned trade-offs when a dominantaggressor interrupts the transmission with the equal receivedsignal power (i.e., signal-to-interference ratio (SIR) is set to0 dB). In Fig. 6(a), α is set to 0.2 and the subcarrier spacingis swept from 1.2× F to 2× F , referring to the POT withorthogonal schemes. Also, simulation results are verified withthe theoretical results based on (21) and (23). As it can beseen in Fig. 6(a), efficacy of POT in the BER performanceincreases with the subcarrier spacing, which also causes lessspectrally efficient schemes. In Fig. 6(b), the same analysisis performed for NOFDM to address the POT with non-orthogonal schemes. When other-user interference does notexist, orthogonal schemes reach the Rayleigh bound and intro-duce superior BER performance compared to non-orthogonalschemes. This is mainly because of the fact that MLSE losesits optimality under the colored noise scenario caused bythe non-orthogonal transformation at the receiver. However,when the other-user interference exists, orthogonal schemescapture the total amount of the other-user interference and BERperformance deteriorates significantly. In contrast to orthog-onal waveforms, non-orthogonal schemes become prominentwith the concept of POT under the other-user interference.By providing sufficient non-orthogonality, e.g., ρ = 0.1, BERperformance remains the same as the case without other-userinterference for NOFDM for low to medium SNR, as it can beseen in Fig. 6(b). Essentially, the results show that BER perfor-mance is enhanced without sacrificing the spectral efficiency atthe expense of complexity at the receiver.

In Fig. 7, the impact of POT on BER performance is shownwhen there are multiple aggressors. In the simulation, the pathloss is modeled with the parameters given in [46] as

L(d) = 11.8 + 45 log10(fc) + 40 log10(d/1000), (28)

where fc is the carrier frequency in MHz (3500 MHz) andd is the distance in meters. Using given parameters, the pathloss formula is calculated as L(·) = 51.3 + 40 log(·) where theargument is in terms of meters. Accordingly, a and b are setto 51.3 and 40, respectively. The intensity of TPs and rmin


Fig. 6. BER performance with partial overlapping when there is a singleaggressor. (a) RRC/FMT/4QAM (Analytical results are based on (21) and (23)).(b) Gaussian/NOFDM/4QAM.

are set to 1/(π502) and 25 m, respectively. In order to seethe best possible BER performance, all aggressors’ signals arepartially overlapped with the desired signal. Then, BER curvesare obtained for different victim link distance dε. As expected,BER is directly related to the user distance. Especially, thedegradation becomes severe for the users located at far dis-tances. In Fig. 7(a), it is shown that orthogonal schemes allowbetter BER performance with the concept of POT by losingtheir spectral efficiencies. Also, simulation results match withthe theoretical results based on (21) and (27). In Fig. 7(b), theimpact of non-orthogonal schemes on BER performance areshown for the same scenario and better BER performance is ob-tained for high Eb/N0 without any spectral efficiency loss, butcomplexity at the receiver. In Figs. 6(b) and 7(b), it is importantto emphasize that one may obtain the optimum ρ, consideringthe amount of the attainable self-interference and the amountof mitigated other-user interference. Although the selection ofρ = 0.1 significantly improves the BER performance when theamount of the other-user interference is equal to signal power,

Fig. 7. BER performance with partial overlapping when there are multipleaggressors modeled with PPP. (a) RRC/FMT/4QAM (Analytical results arebased on (21) and (27)). (b) Gaussian/NOFDM/4QAM.

as in Fig. 6(b), the same scheme might not yield optimum BERperformance when other-user interference becomes weaker dueto the path loss. Essentially, this issue indicates that there is apoint where non-orthogonality starts to be harmful. Therefore,the best selection of ρ depends on the equalizer performanceand the amount of the other-user interference.

In order to provide further insights into the link-level per-formance, the link capacity is investigated when POT withNOFDM (Gaussian filter, ρ = 0.1) is taken into account inthe network. The path loss is characterized as in (28) and theintensity of TPs is set to 1/(π502). It is assumed that each RPis associated with the closest TP and dε and di are larger than10 m. As a case study, four equally-spaced CFO levels,i.e., Δfi ∈ {0× ν0, 0.25× ν0, 0.5× ν0, 0.75× ν0}, are con-sidered. For the selection of Δfi, a game-theoretic approachis followed. For each iteration, each link chooses Δfi thatminimizes the perceived other-user interference. The iterationsare performed until the equilibrium is achieved. After the


equilibrium is obtained, the capacity of the victim link (i.e.,located at the center coordinates) is calculated as

C =1

S

S∑z=1

log2

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎝1 +

σ2z

σ2noise

Pε︸︷︷︸1/SNR

+∑

i∈ΦPi

Pεσ2i (Δfi)

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎠

, (29)

where S is the number of symbols in time domain and σz arethe singular values of the matrix which maps the modulationsymbols into the signal for one subcarrier. It is important toemphasize that singular value decomposition (SVD) convertsthe correlated channels into a set of parallel channels and σz

corresponds to the gain of the zth parallel channel, which allowsthe summation in (29). In (29), the interference between eachsubcarrier is neglected considering the narrow dispersion of theGaussian filter in frequency when ρ = 0.1. Besides, the impactof multipath channel is excluded and the distribution of theother-user interference is assumed to be Gaussian. Neverthe-less, (29) is still beneficial to make the comparison on the linkcapacity.

The main difference between orthogonal schemes and non-orthogonal schemes is observed on the values of σ2

z . Whenthe energy of the prototype filter is normalized to 1 as in(5), the summation of σ2

z is always equal to S for (29). ForOFDM, the singular values are equally balanced, indicatingidentical parallel channels. However, they lose their uniformityfor NOFDM. Hence, NOFDM is a suboptimum scheme interms of capacity. However, when the other-user interferenceis taken into consideration, POT with NOFDM mitigates theother-user interference at the expense of non-uniform σ2

z .Therefore, POT with NOFDM affects the both the numeratorand the denominator of SINR in (29). Considering this issue,the link capacity results are shown in Fig. 8(a) and (b). InFig. 8(a), the link capacity is given when dε is kept constant,i.e., dε ∈ {20 m, 35 m, 50 m}. While OFDM performs betterthan NOFDM when dε = 20 m, OFDM loses its efficacy forthe larger link distances, since it is more vulnerable to the other-user interference. In Fig. 8(b), average link capacity is obtainedwithout keeping dε constant. While OFDM provides betterperformance for low SNR, POT with NOFDM outperformsOFDM for high SNR.

VII. CONCLUDING REMARKS

In this study, the concept of POT is introduced by allowingintentional CFO between the interfering links to mitigate theother-user interference, and its performance is investigatedconsidering orthogonal and non-orthogonal waveforms. It isshown that when the other-user interference is inevitable andthere is no coordination on the interfering channels, spectralefficiency has to be sacrificed for orthogonal schemes in orderto achieve other-user interference mitigation. On the otherhand, transmission over orthogonal schemes enjoys the absenceof self-interference, which allows less complex receiver ar-chitectures compared to non-orthogonal schemes. Particularly,

Fig. 8. Link capacity for conventional OFDM (rectangular filter) and POTwith NOFDM (Gaussian filter, ρ = 0.1). (a) Average link capacity for givenSNR and victim link distance (dε). (b) Average link capacity for given SNR.

orthogonal schemes which have non-overlapping subcarriersin frequency, e.g., FMT, can be effectively used with theintentional CFO approach introduced by POT. As opposedto orthogonal waveforms, non-orthogonal schemes, used inconjunction with POT, introduce an important advantage atthe receiver: self-interference problem is easier to address thanother-user interference problem in an uncoordinated network.By utilizing non-orthogonal waveforms, POT is able to changethe type of interference from other-user interference to self-interference. This conversion is beneficial when the receiver hasproper self-interference cancellation mechanisms. Especially,it is promising when two pairs sharing the same spectrum areclose to each other.

Throughout the study, POT is presented for limited numberof intentional CFO levels, e.g., fc and fc + ν0/2. Althoughthe POT with two intentional CFO levels heuristically matchesto scenarios with two TP/RP pairs, it might be a suboptimumsolution for scenarios with more than two TP/RP pairs. How-ever, it is possible to utilize multiple CFO levels to extend


POT to multiple-user scenarios. In addition, although POTis motivated for uncoordinated networks in this study, it ispossible to consider the concept of POT with the abilities ofcoordinated networks. For example, if the coordinator has priorknowledge on the communicating devices, e.g., SINR levels,location information, or beamforming abilities, one may obtainthe optimum intentional CFO levels to maximize the systemperformance. It is important to emphasize that the availability ofsuch features, e.g., a-priori knowledge on channel information,gives significant flexibility to coordinate the interference. Insuch cases, further studies are required to investigate how toutilize the availability of advanced coordination mechanismswith the POT framework, which is left as a future work.

REFERENCES

[1] C. Shannon, “Communication in the presence of noise,” Proc. IEEE,vol. 86, no. 2, pp. 447–457, Sep. 1998.

[2] A. Sahin, I. Güvenç, and H. Arslan, “A survey on multicarrier communica-tions: Prototype filters, lattice structures, implementation aspects,” IEEECommun. Surveys Tuts., vol. 16, no. 3, pp. 1312–1338, 3rd Qtr., 2014.

[3] W. Kozek and A. Molisch, “Nonorthogonal pulseshapes for multicarriercommunications in doubly dispersive channels,” IEEE J. Sel. Areas Com-mun., vol. 16, no. 8, pp. 1579–1589, Oct. 1998.

[4] D. Lopez-Perez et al., “Enhanced intercell interference coordination chal-lenges in heterogeneous networks,” IEEE Wireless Commun., vol. 18,no. 3, pp. 22–30, Oct. 2011.

[5] J. Andrews, “Interference cancellation for cellular systems: A contem-porary overview,” IEEE Wireless Commun., vol. 12, no. 2, pp. 19–29,Apr. 2005.

[6] S. Verdu, Multiuser Detection. Cambridge, U.K.: Cambridge Univ.Press, 1998.

[7] V. Cadambe and S. Jafar, “Interference alignment and degrees of freedomof the k-user interference channel,” IEEE Trans. Inf. Theory, vol. 54,no. 8, pp. 3425–3441, Aug. 2008.

[8] A. Mishra, V. Shrivastava, S. Banerjee, and W. Arbaugh, “Partially over-lapped channels not considered harmful,” SIGMETRICS Perform. Eval.Rev., vol. 34, no. 1, pp. 63–74, Jun. 2006.

[9] Y. Ding, Y. Huang, G. Zeng, and L. Xiao, “Channel assignment withpartially overlapping channels in wireless mesh networks,” in Proc. 4thAnnu. Int. WICON, Brussels, Belgium, 2008, pp. 38:1–38:9.

[10] Y. Cui, W. Li, and X. Cheng, “Partially overlapping channel assignmentbased on node orthogonality for 802.11 wireless networks,” in Proc. IEEEINFOCOM, 2011, pp. 361–365.

[11] O. Ileri, I. Hokelek, H. Arslan, and E. Ustunel, “Improving data capacityin cellular networks through utilizing partially overlapping channels,”in Proc. IEEE SIU Conf. Signal Process. Commun. Appl., Apr. 2011,pp. 1121–1124.

[12] P. Duarte, Z. Fadlullah, A. Vasilakos, and N. Kato, “On the partiallyoverlapped channel assignment on wireless mesh network backbone: Agame theoretic approach,” IEEE J. Sel. Areas Commun., vol. 30, no. 1,pp. 119–127, Jan. 2012.

[13] M. Fu, H. Crussiere, and M. Helard, “Spectral efficiency optimization inoverlapping channels using TR-MISO systems,” in Proc. IEEE WCNC,Apr. 2013, pp. 3770–3775.

[14] D. Lopez-Perez, X. Chu, A. Vasilakos, and H. Claussen, “Power mini-mization based resource allocation for interference mitigation in OFDMAfemtocell networks,” IEEE J. Sel. Areas Commun., vol. 32, no. 2, pp. 333–344, Feb. 2014.

[15] D. Lopez-Perez, X. Chu, A. Vasilakos, and H. Claussen, “On distributedand coordinated resource allocation for interference mitigation in self-organizing LTE networks,” IEEE/ACM Trans. Netw., vol. 21, no. 4,pp. 1145–1158, Aug. 2013.

[16] S.-S. Byun, I. Balashingham, A. Vasilakos, and H.-N. Lee, “Computationof an equilibrium in spectrum markets for cognitive radio networks,”IEEE Trans. Comput., vol. 63, no. 2, pp. 304–316, Feb. 2014.

[17] V. Chandrasekhar, J. Andrews, and A. Gatherer, “Femtocell networks: Asurvey,” IEEE Commun. Mag., vol. 46, no. 9, pp. 59–67, Sep. 2008.

[18] M. Sahin, I. Güvenç, and H. Arslan, “Opportunity detection forOFDMA-based cognitive radio systems with timing misalignment,”IEEE Trans. Wireless Commun., vol. 8, no. 10, pp. 5300–5313,Oct. 2009.

[19] A. Sahin, I. Güvenç, and H. Arslan, “Analysis of uplink inter-carrier-interference observed at femtocell networks,” in Proc. IEEE ICC, 2011,pp. 1–6.

[20] K. Hamdi and Y. Shobowale, “Interference analysis in downlink OFDMconsidering imperfect intercell synchronization,” IEEE Trans. Veh. Tech-nol., vol. 58, no. 7, pp. 3283–3291, Sep. 2009.

[21] V. Chakravarthy et al., “Novel overlay/underlay cognitive radio wave-forms using SD-SMSE framework to enhance spectrum efficiency—PartI: Theoretical framework and analysis in AWGN channel,” IEEE Trans.Commun., vol. 57, no. 12, pp. 3794–3804, Dec. 2009.

[22] Y. Medjahdi, M. Terre, D. L. Ruyet, D. Roviras, and A. Dziri, “Perfor-mance analysis in the downlink of asynchronous OFDM/FBMC basedmulti-cellular networks,” IEEE Trans. Wireless Commun., vol. 10, no. 8,pp. 2630–2639, Aug. 2011.

[23] A. Sahin, E. Guvenkaya, and H. Arslan, “User distance distribution foroverlapping and coexisting cell scenarios,” IEEE Wireless Commun. Lett.,vol. 1, no. 5, pp. 432–435, Oct. 2012.

[24] M. Win, P. Pinto, and L. Shepp, “A mathematical theory of networkinterference and its applications,” Proc. IEEE, vol. 97, no. 2, pp. 205–230, Feb. 2009.

[25] J. Andrews, F. Baccelli, and R. Ganti, “A tractable approach to coverageand rate in cellular networks,” IEEE Trans. Commun., vol. 59, no. 11,pp. 3122–3134, Nov. 2011.

[26] T. D. Novlan, H. S. Dhillon, and J. G. Andrews, “Analytical modeling ofuplink cellular networks,” CoRR, vol. abs/1203.1304, 2012.

[27] H. Dhillon, R. Ganti, F. Baccelli, and J. Andrews, “Modeling and analysisof K-tier downlink heterogeneous cellular networks,” IEEE J. Sel. AreasCommun., vol. 30, no. 3, pp. 550–560, Apr. 2012.

[28] A. Merwaday, S. Mukherjee, and I. Güvenç, “On the capacity analysis ofHetNets with range expansion and eICIC,” in Proc. IEEE GLOBECOM,Atlanta, GA, USA, Dec. 2013, pp. 1–6.

[29] A. Merwaday, S. Mukherjee, and I. Güvenç, “HetNet capacity withreduced power subframes,” in Proc. IEEE WCNC, Istanbul, Turkey,Apr. 2014, pp. 1–6.

[30] A. Merwaday, S. Mukherjee, and I. Güvenç, “Capacity analysis of LTE-advanced HetNets with reduced power subframes and range expansion,”CoRR, vol. abs/1403.7802, 2014.

[31] P. Pinto and M. Win, “Communication in a Poisson field ofinterferers—Part I: Interference distribution and error probability,” IEEETrans. Wireless Commun., vol. 9, no. 7, pp. 2176–2186, Jul. 2010.

[32] X. Lin, J. G. Andrews, and A. Ghosh, “A comprehensive frame-work for device-to-device communications in cellular networks,” CoRR,vol. abs/1305.4219, 2013.

[33] D. Gabor, “Theory of communication. Part 1: The analysis of informa-tion,” J. Inst. Elect. Eng.—III, Radio Commun. Eng., vol. 93, no. 26,pp. 429–441, Nov. 1946.

[34] P. Sondergaard, Finite Discrete Gabor Analysis 2007.[35] C. Tellambura and D. Senaratne, “Accurate computation of the MGF of

the lognormal distribution and its application to sum of lognormals,” IEEETrans. Commun., vol. 58, no. 5, pp. 1568–1577, May 2010.

[36] N. Mehta, J. Wu, A. Molisch, and J. Zhang, “Approximating a sum ofrandom variables with a lognormal,” IEEE Trans. Wireless Commun.,vol. 6, no. 7, pp. 2690–2699, Jul. 2007.

[37] M. Marey and H. Steendam, “Analysis of the narrowband interferenceeffect on OFDM timing synchronization,” IEEE Trans. Signal Process.,vol. 55, no. 9, pp. 4558–4566, Sep. 2007.

[38] M. Morelli and M. Moretti, “Robust frequency synchronization forOFDM-based cognitive radio systems,” IEEE Trans. Wireless Commun.,vol. 7, no. 12, pp. 5346–5355, Dec. 2008.

[39] P. Bello, “Characterization of randomly time-variant linear channels,”IEEE Trans. Commun. Syst., vol. CS-11, no. 4, pp. 360–393, Dec. 1963.

[40] G. Cherubini, E. Eleftheriou, and S. Olcer, “Filtered multitone modulationfor very high-speed digital subscriber lines,” IEEE J. Sel. Areas Commun.,vol. 20, no. 5, pp. 1016–1028, Jun. 2002.

[41] J. Anderson, F. Rusek, and V. Owall, “Faster-than-Nyquist signaling,”Proc. IEEE, vol. 101, no. 8, pp. 1817–1830, Aug. 2013.

[42] J. Proakis and M. Salehi, Digital Communications. New York, NY,USA: McGraw-Hill, 2007, ser. McGraw-Hill Higher Education.

[43] K. Hamdi, “A useful technique for interference analysis in Nakagamifading,” IEEE Trans. Commun., vol. 55, no. 6, pp. 1120–1124, Jun. 2007.

[44] K. Cho and D. Yoon, “On the general BER expression of one- and two-dimensional amplitude modulations,” IEEE Trans. Commun., vol. 50,no. 7, pp. 1074–1080, Jul. 2002.

[45] K. Hamdi, “Precise interference analysis of OFDMA time-asynchronouswireless ad-hoc networks,” IEEE Trans. Wireless Commun., vol. 9, no. 1,pp. 134–144, Jan. 2010.

[46] “Guidelines for evaluation of radio interface technologies for IMA-advanced,” Geneva, Switzerland, Rep. ITU-R M.2135, 2009.


Alphan Sahin received the B.S. degrees in elec-trical engineering and telecommunication engineer-ing from Istanbul Technical University, Turkey, in2005 and 2006, respectively. He received the M.S.degree in electrical engineering from Istanbul Tech-nical University in June 2008 and the Ph.D. degreein electrical engineering from University of SouthFlorida, Tampa, FL, in 2013. From 2006 to 2009, hewas with the Scientific and Technological ResearchCouncil of Turkey where he was involved with theseveral projects related to the information security

as a Researcher. Since spring 2014, he has been affiliated with Texas A&MUniversity at College Station, TX, as a postdoctoral Research Associate. His re-search interests are related to the signal processing techniques emphasizing onthe physical layer of wireless communication systems. His current research in-terests include waveform design, time-frequency analysis, interference-immunesystems, signal recovery, and statistical inference methods.

Erdem Bala received the B.Sc. and M.Sc. degreesfrom Bogazici University, Istanbul, Turkey, and thePh.D. degree from the University of Delaware, DE,all in electrical engineering. He has been withInterDigital, NY as a Research Engineer since 2007.His previous work experience includes positions asR&D Engineer at Nortel Networks and Intern atMitsubishi Research Labs. At InterDigital, he hasworked on the standardization of 3GPP LTE andLTE-Advanced, advanced relaying schemes, coexis-tence in unlicensed spectrum, and waveform design.

Currently, he is involved in the design of 5G air interface for future wirelesscommunication systems.

Ismail Güvenç (SM’10 ) received the Ph.D. degreein electrical engineering from University of SouthFlorida in 2006, with an outstanding dissertationaward. He was with Mitsubishi Electric ResearchLabs during 2005, and with DOCOMO InnovationsInc. between 2006 and 2012, working as a ResearchEngineer. Since August 2012, he has been an Assis-tant Professor with Florida International University.

His recent research interests include heteroge-neous wireless networks and future radio accessbeyond 4G wireless systems. He has published more

than 80 conference and journal papers, and several standardization contribu-tions. He co-authored/co-edited three books for Cambridge University Press,is an editor for IEEE COMMUNICATIONS LETTERS and IEEE WIRELESS

COMMUNICATIONS LETTERS, and was a Guest Editor for four special issuejournals/magazines on heterogeneous networks. Dr. Guvenc is an inventor/coinventor in 23 U.S. patents, and has another four pending U.S. patentapplications. He is also a recipient of the 2014 Ralph E. Powe Junior FacultyEnhancement Award.

Rui Yang received the M.S. and Ph.D. degreesin electrical engineering from the University ofMaryland, College Park, in 1987 and 1992, respec-tively. He has 15 years of experience in the researchand development of wireless communication sys-tems. Since he joined InterDigital Communicationsin 2000, he has led several product developmentand research projects. He is currently a PrincipleEngineer at InterDigital Labs, leading a project onbaseband and RF waveforms for future wirelesscommunication systems. His interests include digital

signal processing, air interface design. He has received more than 15 patentawards in those areas.

Hüseyin Arslan received the B.S. degree fromMiddle East Technical University (METU), Ankara,Turkey, in 1992 and the M.S. and Ph.D. degreesin 1994 and 1998, respectively, from SouthernMethodist University (SMU), Dallas, TX, USA.From January 1998 to August 2002, he was with theresearch group of Ericsson Inc., NC, USA, wherehe was involved with several project related to 2Gand 3G wireless communication systems. BetweenAugust 2002 and December 2013, he was with theElectrical Engineering Dept. of University of South

Florida, Tampa, FL, USA. Since December 2013, he has been with the IstanbulMedipol University. In addition, he has worked as a part time Consultant forvarious companies and institutions including Anritsu Company, Savronik Inc.,and The Scientific and Technological Research Council of Turkey.

Dr. Arslan’s research interests are related to advanced signal processingtechniques at the physical and medium access layers, with cross-layer designfor networking adaptivity and Quality of Service (QoS) control. He is interestedin many forms of wireless technologies including cellular radio, wirelessPAN/LAN/MANs, fixed wireless access, aeronautical networks, underwaternetworks, in-vivo networks, and wireless sensors networks. The current re-search interests are on physical layer security, signal intelligence, cognitiveradio, small cells, powerline communications, smart grid, UWB, multi-carrierwireless technologies, dynamic spectrum access, co-existence issues on het-erogeneous networks, aeronautical (High Altitude Platform) communications,in-vivo channel modeling and system design, and underwater acoustic com-munications. He has served as technical program committee chair, technicalprogram committee member, session and symposium organizer, and workshopchair in several IEEE conferences. He is currently a member of the editorialboard for IEEE TRANSACTIONS ON COMMUNICATIONS, Physical Communi-cation Journal by Elsevier, and IEEE Communications Surveys and Tutorials.He has also served eight years as a member of the editorial board for WirelessCommunication and Mobile Computing Journal by Wiley.

Documents

Partially Overlapping Tones for Uncoordinated Networks