Published in: ICWMC 2015, The Eleventh International Conference on Wireless and Mobile Communications

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1 Aalborg Universitet Throughput Analysis of Full Duplex Counication with Asyetric Traffic in Sall Cell Systes Mahood, Nurul Huda; Berardinelli, Gilberto; Mogensen, Preben Elgaard; Frederiksen, Frank Published in: ICWMC 215, The Eleventh International Conference on Wireless and Mobile Counications Publication date: 215 Docuent Version Accepted author anuscript, peer reviewed version Link to publication fro Aalborg University Citation for published version APA): Mahood, N. H., Berardinelli, G., Mogensen, P. E., & Frederiksen, F. 215). Throughput Analysis of Full Duplex Counication with Asyetric Traffic in Sall Cell Systes. In ICWMC 215, The Eleventh International Conference on Wireless and Mobile Counications pp. 57-6). IARIA. International Conference on Wireless and Mobile Counications General rights Copyright and oral rights for the publications ade accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requireents associated with these rights.? Users ay download and print one copy of any publication fro the public portal for the purpose of private study or research.? You ay not further distribute the aterial or use it for any profit-aking activity or coercial gain? You ay freely distribute the URL identifying the publication in the public portal? Take down policy If you believe that this docuent breaches copyright please contact us at vbn@aub.aau.dk providing details, and we will reove access to the work iediately and investigate your clai. Downloaded fro vbn.aau.dk on: deceber 21, 218

2 Throughput Analysis of Full Duplex Counication with Asyetric Traffic in Sall Cell Systes Nurul H. Mahood 1, Gilberto Berardinelli 1 and Preben Mogensen 1,2 1 Wireless Counication Networks Section, Dept. of Electronics Systes Aalborg University, Aalborg, Denark eail: {nh, gb, p}@es.aau.dk Frank Frederiksen 2 2 Nokia Networks Aalborg, Denark eail: frank.frederiksen@nokia.co Abstract Full duplex counication proises a 1% throughput gain by enabling siultaneous transission and reception. However, such siultaneous counication leads to a corresponding increase in the network interference. In addition, full duplex counication can only be exploited when traffic is available in both uplink and downlink directions; while, cellular network traffic tend to be downlink heavy in practice. The potential throughput gains of full duplex counication over conventional half duplex transission in a sall cell network with asyetric traffic conditions are investigated in this contribution using network analysis tools fro stochastic geoetry. The analytical findings are further confired through coputer-based Monte-Carlo siulations. Asyetric downlink/uplink traffic pattern and the increased network interference steing fro full duplex transissions are found to liit its potential perforance to well below the proised 1% throughput gain. Index Ters Full duplex counication; sall cells; stochastic geoetry; 5G. I. INTRODUCTION Full duplex counication, i.e. siultaneous transission and reception over the sae frequency band, proises a 1% throughput gain over conventional half duplex HD) transissions. Historically, full duplex FD) counication had been considered ipractical due to the overwheling loopback interference fro the transission-end. Recent advances in selfinterference cancellation SIC) in both analog and digital doain allow suppressing this loopback interference to within tolerable liits, thereby aking FD counication appealing with viable costs [1]. In that respect, FD has the potential of becoing a significant breakthrough in the design of a novel 5th Generation 5G) radio access technology. Alongside the self interference, the proise of doubling the network throughput TP) through FD counication with respect to HD transission ay be jeopardized by a nuber of other factors. Siultaneous transissions fro both ends of a counication link inevitably results in extra interference to the network copared to conventional HD transission [2]. Furtherore, FD transissions can only be exploited with traffic available at both downlink DL) and uplink UL) directions; whereas in practice, networks have a traffic profile skewed in favor of the DL direction. The TP perforance of wireless networks with FD capable radios have been investigated in [3] [5] aong others. The authors in [3] show that FD capabilities can significantly increase the aggregate throughput of current cellular systes with FD enabled access points AP) and HD user equipents UE) under syetric traffic conditions and relatively isolated cells. On a different note, reference [5] considers a large wireless network and analytically investigates the TP gain of FD counication using stochastic geoetry tools. Building on our earlier syste level siulations based exercise investigating the perforance of local area network with FDcapable radios [4], the TP perforance of FD counication in a sall cell syste is analytically derived in this contribution. We consider a fixed nuber of sall cells, where the APs and UEs in each cell transit randoly with independent transission probabilities. Statistics of the rando interference power at a generic receiver are thereby obtained analytically, and applied to evaluate the corresponding ergodic TP for the equivalent FD/HD syste. Analytical findings are further validated through siulations. Siilar to [5], stochastic geoetry based tools are used in this study to odel the wireless network. However, reference [5] odels the wireless network as a Poisson point process PPP), which better reflects an ad-hoc network with a large nuber of nodes [6]. Here, the network is odelled as a binoial point process BPP), which closely reflects a local area network with an arbitrary nuber of sall cells [6]. Furtherore, we derive the TP gain of FD while in [5] only upper and lower bounds are found. Finally, we address asyetric UL/DL traffic profiles which are typically disregarded in analytical studies. Organization: Section II introduces the syste odel, followed by statistical representation of the su interference power in Section III. Nuerical results and concluding rearks are then presented in Sections IV and V respectively. II. SYSTEM MODEL We consider a local area syste with a nuber of sall cells distributed in a circular area R of radius R in the twodiensional plane R 2. Each sall cell consists of an AP and a single active UE. Our analysis focuses on the perforance of a generic reference cell with the desired receiver located at the origin. K interfering cells are assued to be uniforly distributed around the reference cell, as shown in Figure 1. The locations of the interfering nodes i.e. APs and UEs) can be odelled as realizations of rando spatial point processes. Such an assuption allows us to analyze the proble in hand using tools fro stochastic geoetry [6]. Each interfering cell can be odelled as two independent and identically distributed iid) points in R representing the AP and UE respectively. The resulting wireless network with a fixed nuber of nodes can

3 be odelled as the BPP, which closely represents a sall cell syste [6]. A slotted ALOHA access protocol is considered, where at any given tie, the AP and UE in cell k transits data with independent access probabilities AP,k and UE,k respectively. The desired transitter receiver separation distance is fixed at d eters. Assuing R d, the UL and the DL transissions in the reference cell can be considered to experience siilar interference conditions. Figure 1. Syste Model depicting the Reference cell at the center of R with a rando nuber of interfering cells in FD or HD transission ode. Signal Model: The interference power at the desired receiver fro a rando interferer k located r k eters away is given by ζ k = ηgβr k ), where η = η pν is a constant path loss factor accounting for the transit power p, the interference isolation aong neighbouring cells ν coonly known as wall loss) and η : the path loss at reference distance. A. Su Interference Power fro Multiple Interferers Let Ω {F DAP ), F DUE), HD} denote the index of set of interferers with the respective transission ode. Note that, the APs and UEs can both transit siultaneously with FD transission, whereas either the AP or the UE of a particular cell transits in the conventional HD case. The su interference power for the various transission odes is odelled in this subsection. 1) Distribution of the Nuber of Interfering Cells: Due to the assued slotted ALOHA rando access ode, the nuber of active interfering cells is a rando variable r.v.). Assuing each cell transits independently with probability Ω ; let Λ Ω Ω ) represent the nuber of active interferers for the transission ode Ω with λ {, 1,..., K} being its realization. By virtue of the assued BPP network odel, the probability ass function PMF) of Λ Ω Ω ) is given as [8] ) K f ΛΩ Ω)λ; Ω ) = λ Ω 1 Ω ) K λ. 1) λ 2) Su Interference Power with HD Transission: In the conventional HD case, a particular cell can only transit in either the UL or the DL direction. Considering independent UL and DL traffic, the transission probability of a particular cell is given by HD = AP + UE AP UE. Note, henceforth we assue AP,k = AP and UE,k = UE k. The su interference power with HD transission is then readily given by ζ HD = k Λ HD HD ) ζ k, where ζ k is the interference fro a single rando interferer. 3) Su Interference Power with FD Transission: With FD transissions, the AP and the UE can both transit siultaneously as long as there are available packets to transit. Therefore, the APs and the UEs can be treated as two different sets of interferers with the respective transission probabilities AP and UE. Correspondingly, the total interference with FD transission is the su of the interference contributions fro the set of APs and the UEs, i.e. ζ F D = ζ F DAP ) + ζ F DUE), where ζ F DAP ) = k Λ F DAP ) AP ) ζ k and ζ F DUE) = k Λ F DUE) UE ) ζ k. B. Ergodic Throughput Calculation In this contribution, we consider the Shannon rate Rγ) = log γ) as a easure of the instantaneous throughput, where γ is the instantaneous signal to interference plus noise ratio SINR). Let φ denote the desired signal power at the considered receiver. The instantaneous SINR for the transission ode Ω {F D, HD} can be expressed as γ Ω = φ ζ Ω+N, where N is the additive white Gaussian noise power. The ergodic TP can be obtained by averaging the instantaneous TP over the distribution of the SINR i.e. R Ω = E γω [log γ Ω )], where E X [ ] is the expectation operator over the distribution of the r.v. X. This expectation requires a two-fold integration over the distributions of φ and ζ Ω, and is not easy to evaluate directly. A sipler expression for the ergodic TP involving a single integration can instead be obtained using the oent generating functions MGF) of the φ and ζ Ω as follows [9] R Ω = 1 ln2) M ζω s / N ) 1 M φ s / N )) s exp s) ds, 2) where M ζω s) and M φ s) are the MGFs of ζ Ω and φ respectively, which are derived in Section III below. Eq. 2) can be easily evaluated using atheatical software or suitable nuerical integration techniques. Throughput Gain of Full duplex over Half duplex The TP gain of FD over HD transission is given as ξ = T P F D T P HD T P HD, 3) where T P HD = HD R HD and T P F D = AP + UE )R F D are the average TP at the reference cell with HD and FD transission ode, respectively. III. STATISTICAL REPRESENTATION OF THE SIGNAL POWERS Following [1], we define the MGF of a r.v. x to be a function of the coplex variable s with a negative arguent as follows: M x s) = E [exp sx)]. The MGFs M ζω s) and M φ s) of the r.vs ζ Ω and φ are derived in this section. A. MGF of the Desired Signal Power φ Assuing the transit power at the desired transitter, and the desired channel fading power gain are given by p and g respectively, the power of the received signal of interest is φ = η p g βd). Considering g, which is the only r.v. in φ, to be Gaa distributed with paraeter ), the MGF of φ readily evaluates to M φ s) = 1 + sηpβd) [1].

4 B. MGF of the Single Cell Interference Power ζ k The MGF of the interference power fro a rando [ interferer ] k located r k eters away is given by M ζk s) = E exp sζ k ) = [ ] exp sηgβ r k )). E g,βrk ) Corollary III.1. The distribution of the distance dependent path loss βr k ) is given by f βrk )t) = 2 αr 2 t 2 α 1 t 1 1) α, 1+R) α t 1. 4) Proof. Under unifor distribution of a user, the distribution of the rando distance r k between a generic receiver located at the origin and a rando transitter k in R is given by f rk r) = 2r R for r R [8]. The distribution of βr 2 k ) in Eq. 4) follows directly fro f rk r) through a change of variable involving t βr k ) = 1 + r k ) α. Using conditional expectations, the MGF of ζ k can be expanded as M ζk s) = E t [ ] [E ] g exp sηgt) t. Considering g to be Gaa distributed with paraeter, the inner expectation over the r.v. g conditioned on t evaluates to 1 + sηt ) [1]. Elaborating the outer expectation over the r.v. t, M ζk s) can be expanded as M ζk s) = 1 + sηt ) fβrk )t) dt. Using Eq. 4), the above integral can then be expressed as M ζk s) = 2 αr R) α t 2 α 1 t 1 α 1 ) 1 + sηt dt. 5) Considering a change of variable involving u = sηt followed by soe algebraic anipulations, Eq. 5) can be reduced to the following closed for expression [7] M ζk s) = 2 αr 2 [ sη ) 2 α sη B sη ) 1 α sη B sη1 + R) α, ; 2 ) α, 1 sη1 + R) α, ; 1 α, 1 )], 6) where B z 1, z 2 ; a, b) is the difference of two incoplete beta functions known as the generalized incoplete beta function: B z 1, z 2 ; a, b) B z 2 ; a, b) B z 1 ; a, b) ; with the incoplete beta function defined as B z; a, b) = z ua 1 1 u) b 1 [11, Eq ]. C. MGF of the Su Interference Power ζ Ω With ultiple interfering cells, the total interference power ζ Ω is the su of the interference powers fro the individual interfering cells; i.e. ζ Ω = k Λ ζ ΩΩ k, where ζ ) k is the interference fro a single rando interferer. Theore III.2. The MGF of the su interference power ζ Ω fro K cells transitting randoly with independent transission probability Ω is [ M ζω s; Ω ) = 1 Ω 1 Mζk s) ]) K, 7) where M ζk s) is given by Eq. 6). Proof. Using conditional expectations, the MGF of ζ Ω can be written as M ζω s; Ω ) = E [M ΛΩΩ ) ζ Ω s) λ], where M ζω s) λ is the MGF of the su interference power fro λ iid interferers. Utilizing the fact that M X+Y ) s) = M X s)m Y s) for independent r.vs X and Y, we obtain M ζω s) λ = M ζk s)) λ. Using Eq. [ 1) and the law of total probability, M ζω s; Ω ) = E ΛΩΩ ) Mζ λ s) ] can thereby be expanded as M ζω s; Ω ) = K λ= ) K Ω M ζk λ s)) λ ) K λ, 1 Ω which reduces to Eq. 7) by virtue of the Binoial Theore. D. MGF of the Su Interference Power with FD and HD transissions Having derived the expression of the MGF for the su interference power, we now specifically address the MGF of the su interference power with FD and HD transission as a function of the respective channel access probabilities discussed in Section II-A. In the conventional HD case, a particular cell transits with channel access probability HD. The ensuing su interference power MGF M ζhd s; HD ) is then readily given by Th. III.2. With FD counication, the APs and the UEs are treated as two independent sets of interferers having transission probabilities AP and UE respectively. The resulting su interference power is ζ F D = ζ F D,AP + ζ F D,UE. Applying Th. III.2, the corresponding MGF is thereby obtained as M ζf D s) = M ζf D,AP s; AP )M ζf D,UE s; UE ). The ergodic TP with FD or HD transission can now be readily coputed by inserting the respective su interference power MGF into Eq. 2). IV. NUMERICAL RESULTS Matlab R based Monte Carlo siulation results validating the derived analytical findings are presented in this Section. At least 1, independent snapshots of each scenario are siulated to ensure statistical reliability. The following general siulation paraeters are assued to reflect a typical dense sall cell syste: path loss exponent α = 3, cell radius R = 1, transit power p = 13 db, reference path loss η = 38 db, gaa paraeter = 2 and desired AP-UE distance d = 1. A. Ipact of Traffic Asyetry in Isolated Cell The ipact of traffic asyetry on the TP gain with FD transission is investigated first. To this end, a single cell scenario i.e. ζ F D = ζ HD = ) is considered. The ensuing TP gain for this special case is ξ = AP UE AP + UE AP UE, as presented in Figure 2. The analytical TP gains are found to atch closely with the siulation results, thereby validating the derived findings. Interestingly, the proised 1% TP gain is only achieved with a full buffer traffic at both transission directions i.e. AP = UE = 1). In general, the TP gain is low when either of the two transission probabilities AP and UE are low.

5 TP gain %) = 1 =.5 = UE Analytical TP gain UE Figure 2. TP gain of FD over HD transission with asyetric traffic. B. Ipact of Traffic Asyetry in FD Syste The FD TP gain is next investigated in a syste level setting with ultiple interferers and with variable transission probabilities AP and UE. Figure 3 presents the TP gain of FD over HD vs UE with K = 1 potential interferers for different values of AP. The analytical TP gains are found to closely atch the siulation results, as in Figure 2. The axiu TP gain with FD is ore than halved in a syste level scenario with wall loss of up to 5 db due to the resulting increase in inter-cell interference ICI) with FD transission. The TP gain is expectedly found to iprove with increasing isolation aong the cells i.e. the wall loss). This reinforces the fact that the increased network interference due to FD transissions has an adverse ipact on the proised TP gains. TP gain %) = 1 = UE Analytical TP gain ν = 2 db ν = 5 db Wall Loss, ν =.5 db UL Figure 3. Throughput gain of FD over HD counication in a syste level setting with 1 potential interferers with various transission probabilities AP and different wall loss values ν. An interesting paradox is observed for the AP = UE scenario. The ICI is reduced at low transission probabilities i.e. low AP ). However, opportunities to exploit FD counication, which is enabled by overlapping channel access at both ends is also reduced; thereby resulting in the observed low TP gain. Although detailed results had to be oitted due to space constraint, our study further reveals that the TP gain of FD also reduces with increasing the network size K and decreasing the paraeters R and α. V. CONCLUSION The potential TP gain of FD counication over conventional HD transissions in a dense sall cell scenario, as targeted by the upcoing 5G radio access technology, is analytically derived and cross validated through extensive Monte Carlo siulations in this contribution. An ideal SIC transceiver odel is assued in order to isolate the ipact of the interference coupling and the traffic asyetry. TP gains obtained nuerically are found to closely atch the siulation results. The derived analytical results provide with a rather siple odel to evaluate the potential perforance of FD counication in a syste level setting without invoking lengthy syste level siulations. The results reveal that the ean TP gain of FD over HD is only 1% for an isolated cell. In a syste level setting, the TP gains depend on two critical factors; naely the interference coupling aong the cells, and the availability of traffic at both ends in order to exploit the FD potential. The interference coupling aong the cells is in turn a function of the wall loss, the path loss exponent, fading paraeters and the user density. Contrary to the proised 1% gain, odest gains of around 4% was observed considering realistic paraeter values. As part of the future work, we plan to extend our study of FD by considering ore practical constraints on the transceiver operations; and investigate algoriths that can better exploit the potential of FD counication. REFERENCES [1] S. Hong et al., Applications of self-interference cancellation in 5G and beyond, IEEE Counications Magazine, pp , Feb [2] A. Sabharwal et al., In-band full-duplex wireless: Challenges and opportunities, IEEE Journal on Selected Areas in Counications, vol. 32, no. 9, pp , Sep [3] S. Goyal et al., Full duplex operation for sall cells, subitted to IEEE Transactions on Vehicular Technology, Apr [Online]. Available: [4] N. H. Mahood, G. Berardinelli, F. Tavares, and P. Mogensen, On the potential of full duplex counication in 5G sall cell networks, in Proc. IEEE 81st Vehicular Technology Conference: VTC-Spring, Glasgow, Scotland, May 215, to appear. [5] Z. Tong and M. Haenggi, Throughput analysis for wireless networks with full-duplex radios, in Proc. Wireless Counications and Networking Conference WCNC), New Orleans, USA, Mar [6] J. G. Andrews et al., A prier on spatial odeling and analysis in wireless networks, IEEE Counications Magazine, vol. 58, no. 11, pp. 2 9, Nov. 21. [7] N. H. Mahood, F. Yilaz, M.-S. Alouini, and G. E. Øien, Heterogeneous next-generation wireless network interference odel-and its applications, Transactions on Eerging Telecounications Technologies, vol. 25, no. 5, pp , May 214. [8] J. Illian, A. Penttinen, H. Stoyan, and D. Stoyan, Statistical Analysis and Modelling of Spatial Point Patterns, 1st ed. West Sussex, England: John Wiley & Sons, Jan. 28. [9] K. A. Hadi, A useful lea for capacity analysis of fading interference channels, IEEE Transaction on Counications, vol. 58, no. 2, pp , Feb. 21. [1] M. K. Sion and M.-S. Alouini, Digital Counication over Fading Channels, 2nd ed. New Jersey, USA: John Wiley & Sons, Dec. 25. [11] M. Abraowitz and I. Stegun, Eds., Handbook of Matheatical Functions with Forulas, Graphs, and Matheatical Tables, 2nd ed. New York, USA: Dover Publications, 1972.