Interference Management in Full-Duplex Wireless Cellular Networks via Fractional Programming

Transcription

1 Interference Management n Full-Duplex Wreless Cellular Networs va Fractonal Programmng Invted Paper) Kamng Shen and We Yu Electrcal and Computer Engneerng Department Unversty of Toronto, ON M5S 3G4, Canada Emal: {shen,weyu}@ece.utoronto.ca Abstract Mutual nterference s a ey obstacle n the realstc adopton of full-duplex FD) technque n future wreless cellular networs. Interference s a much more pressng problem for FD system than for the conventonal half-duplex HD) system, because FD allows the same tme-frequency resource to be used for both upln and downln, thus possbly creatng myrad nterference between multple transmssons throughout the networ. Wthout proper nterference control, FD may not even outperform HD n a multcell setup. The man objectve of ths paper s to show that coordnated schedulng and power control enables wreless cellular networs to reap sgnfcant system-level performance mprovement due to FD. Toward ths end, ths paper utlzes fractonal programmng to derve a sequence of convex reformulatons that allow dstrbuted and effcent teratve optmzaton. Numercal results suggest that the proposed system-level nterference management can provde 3-4% rate gan for an optmzed FD multcell networ as compared to optmzed HD. I. INTRODUCTION Full-duplex FD) transmsson, whose hstory can be traced bac to the early radar system n 194s [1], revves n these years as a potental technque to rase spectral effcency for the future wreless cellular networs. Ths s due manly to the recent progress n analog and dgtal echo cancellaton whch now allows self-nterference suppresson of up to 11dB [2]. A lne of recent wors [1] [6] have verfed the success of FD technque n nearly doublng spectral effcency for an solated end-to-end wreless ln. Real-world wreless systems, however, never consst of just a sngle ln. When multple transmsson lns are densely present n the same geographcal area, as can often occur n urban cellular networs, the aggressve explotaton of tmefrequency resources n FD would also brng n myrad nterln nterference, whch can easly negate the benefts of usng FD. Ths wor ams to show that a careful control of nterference pattern by coordnatng the ln schedules and transmt powers s capable of reganng n part the loss due to nterference. Toward ths goal, the paper formulates a networ utlty maxmzaton problem nvolvng mxed nteger optmzaton for user schedulng) and nonconvex optmzaton for power control), and proceeds to show that ths problem can be transformed to a fractonal program to facltate ts dstrbuted and effcent soluton. Pror wors on nterference mtgaton for FD are mostly based on heurstcs. For nstance, [7] proposes an opportunstc way of selectng between FD and half-duplex HD) modes; [8] employs a heurstc penalty term to render the resource allocaton nterference-aware; [9] proposes to schedule the users geographcally far apart so as to avod strong nterference. Other exstng wors, e.g., [1] and [11], focus on the snglecell scenaro, and fnd the optmal schedule and power settngs under some partcular condtons. Our paper dstngushes from the pror wors wth two aspects. Frst, we tae a system level perspectve by consderng the maxmzaton of the overall networ utlty of the average user rates n the long run, rather than a oneshot objectve such as sum of nstantaneous rates. Second, we treat the problem from a rgorous optmzaton perspectve; the proposed algorthm s more relable and sgnfcantly outperforms the benchmars. II. SYSTEM MODEL Consder a wreless multcell networ n whch the BSs and the user termnals are deployed wth one transmt antenna and one receve antenna each. Let B be the set of BSs n the networ; let K be the set of users that are assocated wth BS. The users are scheduled wthn each cell on a slot-to-slot bass n the tme doman. At tme slot t, n cell, denote the ndex of the user scheduled n upln as u [t] and denote the ndex of the user scheduled n downln as d [t]; denote the upln transmt power spectral densty PSD) of the scheduled user u as u [t] and denote the downln transmt PSD of the BS as p [t]. For convenence, the total frequency bandwdth s normalzed to 1, and the channels are assumed to be flatfadng across the band. The BS-to-BS, the user-to-bs, the BSto-user, and the user-to-user channel strengths are denoted as G bb,,, and G uu, respectvely where q 1 and q 2 are respectvely the recever and transmtter ndces. Denote the addtve whte Gaussan bacground nose PSD level asσ 2. We assume that only the BSs are capable of transmttng and recevng sgnals n the same tme-frequency resource bloc n FD mode, but not the user termnals; ths s a common assumpton n the lterature [8], [9], [11]. The long-term system-level objectve s to maxmze a proportonal farness utlty functon of the networ. Let Rul and R be the long-term average rates of user respectvely

2 n the upln and the downln. The log-utlty objectve s utlty = α ul log R )+α ul log R ) 1) B K B K where the factors α ul and α account for the prortes of upln and downln data streams. To mae the optmzaton over the user schedules and the PSDs tractable, we optmze the ncremental change n logutlty n each tme slot t, whch s approxmated as a weghted sum of nstantaneous rates: f o [t] = B where the weghts are determned by w ul [t+1] = αul R ul [t]ru ul [t]+ wd [t]rd [t], 2) B [t] and w α [t+1] = R 3) [t],.e., n proporton to the nverse of the upln and the downln average rates evaluated for user up untl tme t. In the remander of ths paper, we drop the tme ndex t for brevty. The nstantaneous upln and downln ratesru ul andrd n an FD multcell networ are computed as follows. For upln, ntroduce a factor ϕ 1 as the fracton of resdual echo after self-nterference cancellaton e.g., ϕ = n the perfect cancellaton case). The upln rate s expressed as u = log 1+ R ul j, + j,u u G bb,j p j +ϕp. +σ2 4) In the denomnator of the SINR term n the above expresson,.e., j Gbu, + j Gbb,j p j +ϕp +σ2, the frst term accounts for the upln sgnal nterference comng from the other scheduled upln users, the second term accounts for the downln sgnal nterference comng from all the BSs n the nearby cells, and the thrd term accounts for self nterference. In the downln, the nstantaneous data rate s computed as R d = log 1+ d, p j Guu d, + j Gub d,j p j +σ2 5) In the denomnator of the SINR term n the above expresson,.e., j Guu + j Gub j +σ2, the frst term accounts d, d,j p for the nterference due to the upln users, whle the second term accounts for the nterference due to the nearby BSs. Wth the system model as characterzed above, we can formulate a coordnated schedulng and power optmzaton problem for maxmzng the FD networ utlty as follows: maxmze f o u,d,,p ) 6a) subject to u,d K 6b) u Pmax ul 6c) p Pmax 6d) where Pmax ul and Pmax are the maxmum transmt PSD constrants n the upln and the downln, respectvely. ). The above optmzaton nvolves nteger varables u, d ) as well as contnuous varables p j,pul u ); the problem s stll nonconvex even when the nteger varables are fxed. Therefore, drectly solvng such a problem s qute dffcult. III. APPROACH The man dea of our approach s to apply the fractonal programmng technque [12] to decouple the denomnator and numerator of the SINR term. The resultng reformulaton s lnear over the nteger varables and also concave over the contnuous varables; an effcent optmzaton then follows. A. Fractonal Programmng Transform Our fractonal programmng approach reles on the followng two theorems, whch are proposed n a prevous wor [12]. Theorem 1 Weghted Sum Log-Ratos). Gven a nonempty constrant set X, as well as weghtw, numerator functon A x) and denomnator functon B x) > for = 1,...,K, the weghted sum log-ratos problem s equvalent to maxmze x X,γ maxmze x X K K w log 1+ A ) x) B x) 7) w log1+γ ) γ + 1+γ ) )A x) A x)+b x) where γ s an auxlary varable ntroduced for each rato. Theorem 2 Weghted Sum Ratos). Gven the same X, w, A x), and B x) as assumed n Theorem 1, the weghted sum ratos problem s equvalent to maxmze x X,y maxmze x X K K w A x) B x) ) w 2y A x) y 2 B x) where y s an auxlary varable ntroduced for each rato. 8) 9) 1) Gong bac to our problem 6), applyng Theorem 1 allows us to recast the orgnal objectve functonf o tof r as dsplayed n 11) at the bottom of the next page, where γ ul and γ correspond to the upln and downln SINRs n cell, respectvely. Observe that f r s a concave functon of γ when the other varables are held fxed. Thus, by settng γ f r =, we obtan the optmal γ explctly as γ ul ) = γ ) =,u u j Gbu, + j Gbb,j p j +ϕp d, p j Guu d, + j Gub d,j p j +σ2. +σ2 12a) 12b)

3 We remar that the solutons of γ can be nterpreted as the upln/downln SINRs n the networ. Further, we decouple the numerator and denomnator for the weghted sum ratos of f r by usng Theorem 2; the resultng new objectve functon f q s shown n 13) at the bottom of the page. Then, solvng the orgnal problem 6) amounts to maxmzng f q over the prmal varables u,d,p) as well as the auxlary varables γ, y). Wth γ optmally updated by 12) n an teratve fashon, t remans to optmze the rest varables n f q. B. Jont User Schedulng and Power Control When all the other varables are fxed, f q turns out to be a concave functon of y, so the soluton for y can be found n closed form by solvng y f q =, that s y ul ) = y ) = j Gbu, w ul1+γul )Gbu,u u + j Gbb wd 1+γ )Gub d, p,j p j +ϕp +σ2 j Guu d, + j Gub d,j p j +σ2. 14a) 14b) To optmze downln power, we set p f q = for each BS to obtan the optmal downln transmt PSD p ) = mn 2 P max ul, y wd 1+γ )Gub d, yj )2 d + j, yj ul)2 G bb j, +yul )2 ϕ. j j 15) The optmal downln schedule decson d can be obtaned by recognzng that the f q expresson s of the form f q = ξd + const 16) B where const refers to a constant term when all the varables excludng d are held fxed, and the parameter ξ can be predetermned for every user assocated wth BS as follows: ξ = w log1+γ ) wγ +2y w 1+γ )Gub, p y )2 j G uu, + j,j p j. 17) Note that ξ can be ntutvely nterpreted as a utlty mnus a cost, wth ts frst three terms beng the utlty and the last term beng the nterference cost. The downln schedulng decson now amounts to choosng the optmal downln user that maxmzes the utlty-mnus-cost value n each cell,.e., { argmax ξ d =, fmax { ξ } > K K 18), otherwse where refers to the decson of not schedulng any user. A smlar set of optmzatons can be done n the upln. Assumng that user s scheduled for upln transmsson by ts assocated BS, the optmal upln transmt PSD of user s found by solvng f q / u = wth u set to,.e., y ul ) = mn P max ul, w ul 2 1+γul )Gbu, j y j )2 G uu d + j, j yul j )2 j,. 19) For the upln schedule decson, we recognze that the f q expresson s of the form f q = ξu ul + const 2) B where const s a constant term when all the varables excludng u are held fxed, and the parameter ξ ul s evaluated for every user assocated wth BS as below: ξ ul = w ul log1+γ ul ) wγ ul ul +2y ul w ul1+γul )Gbu, pul j y ul j )2 j, pul j y j )2 G uu d j, pul. 21) f r u,d,,p,γ ul,γ ) = B log1+γ ul ) γ ul + B B + B wd log1+γ ) wd γ + B B 1+γ ul)gbu,u u j Gbu, + j Gbb,j p j +ϕp +σ2 wd 1+γ )Gub d, p j Guu d, + j Gub d,j p j +σ2 11) f q u,d,,p,γ ul,γ,y ul,y ) = log1+γ ul ) γ ul +2y ul 1+γ ul)gbu,u u y ul B +wd log1+γ ) w d γ +2y wd 1+γ )Gub d, p y ) 2 )2 j j, + G bb,jp j +ϕp j G uu d, + j d,j p +σ 2 j +σ2 13)

4 Smlar to the downln case, ths upln schedulng parameter also has a utlty-mnus-cost nterpretaton. The optmal upln schedule decson can be determned n a dstrbuted fashon across all the cells as follows: { argmax u = ξ ul {, f max ξ ul } > K K, otherwse. 22) Combnng the above optmzaton steps gves rse to the followng coordnated algorthm: Algorthm 1 User schedulng and power control for FD Intalzaton: Intalze all the varables to feasble values. repeat 1) Update γ ul and γ by 12); 2) Update y ul and y by 14); 3) Update p by 15) and then d by 18); 4) Update by 19) and then u by 22); untl Convergence Algorthm 1 s guaranteed to converge, wth the sum weghted rate objectve f o nondecreasng after each teraton. In partcular, for fxed u and d, the fnal and p after convergence are locally optmal n terms of f o. Unle the heurstcs n [7] [9], our proposed algorthm does not requre parameter tunng and therefore s easer to mplement. IV. SIMULATION RESULTS We now llustrate the effectveness of the proposed algorthm. Consder a cellular topology of 7 wrapped-around hexagonal cells, wth one pco-bs located at the centre of each cell. The BS-to-BS dstance s.4m. The same 4MHz-wde frequency band s fully used n every cell. There are a total of 15 users unformly dstrbuted wthn the networ. Every user s assocated wth the BS wth the strongest channel. Followng [1], we set the maxmum transmt PSD to be -55dBm/Hz for both the pco-bss and the users correspondng to a maxmum transmt power of 21dBm), and set the bacground nose PSD to be -176dBm/Hz. The channel path-loss model s log 1 d) +τ n db), where d n m) refers to the dstance between the two termnals of the channel, and τ s a Gaussan random varable wth 8dB standard devaton accountng for shadowng. Equal prortes are assgned to the upln and the downln utltes wth α ul = α = 1. The followng methods serve as benchmars: FD baselne: Users are scheduled by a round-robn polcy n both upln and downln; all the termnals transmt at maxmum PSD. HD baselne: FDD mode s adopted wth equal amount of bandwdth for upln and downln; users are scheduled by a round-robn polcy n both upln and downln; all the termnals transmt at maxmum PSD. Fg. 1 and 2 shows the cumulatve dstrbuton of the upln and downln user rates acheved wth coordnated user schedulng and power optmzaton for both HD and FD and wth ether perfect echo cancellaton or 11dB cancellaton, as Cumulatve dstrbuton HD baselne HD coordnated FD baselne 11dB echo cancellaton) FD coordnated 11dB echo cancellaton) FD baselne perfect cancellaton) FD coordnated perfect cancellaton) Data rate Mbps) Fg. 1: Cumulatve dstrbuton of upln user rates: FD vs HD Cumulatve dstrbuton HD baselne HD coordnated FD baselne 11dB echo cancellaton) FD coordnated 11dB echo cancellaton) FD baselne perfect cancellaton) FD coordnated perfect cancellaton) Data rate Mbps) Fg. 2: Cumulatve dstrbuton of downln user rates: FD vs HD compared to the baselnes. Observe that the performance of the FD baselne s n fact worse than HD baselne, llustratng the fact that due to the excessve nterference FD may even be harmful as compared to HD wth no nterference management. The proposed coordnated algorthm sgnfcantly mproves the user throughput for both HD and FD baslnes, but the mprovement s much more sgnfcant for FD. The fgure also shows the case wth perfect self-nterference cancellaton. Some further gan s observed but the performance mprovement of FD as compared to HD does not approach a factor of 2 even wth perfect cancellaton. Fg. 3 compares the networ log-utlty of FD and HD schemes wth or wthout coordnated optmzaton as functons of self-nterference reducton capablty of FD. It s shown that the proposed FD coordnated scheme can provde utlty benefts even wth modest echo cancellaton capablty of 1dB, whle the FD baselne performs no better than the HD even at perfect cancellaton, because of the nter-ln nterference nduced by FD. These results ndcate that nterference control

5 3 255 Sum log utlty HD baselne HD coordnated FD baselne FD coordnated Sum data rate over upln and downln Mbps) dB echo cancellaton Perfect cancellaton nfnty Self nterference canellaton level db) Fg. 3: Networ utlty of FD vs HD at varyng cancellaton levels Iteraton number Fg. 5: Convergence of overall networ throughput by Algorthm 1 Proporton of lns selectng FD %) nfnty Self nterference cancellaton level db) Fg. 4: Proporton of lns selectng FD n Algorthm 1 wth the proposed FP technque can effectvely allevate the negatve effects from mperfect self-nterference cancellaton and from nter-ln nterference due to FD. The optmzaton approach proposed n ths paper s mplctly capable of swtchng between FD and HD, snce the power optmzaton are ncluded n the overall framewor. Fg. 4 shows the percentage of lns that use FD n the optmzed soluton as functon of the self-nterference cancellaton capablty. At 11dB echo cancellaton, almost 96% of the lns use FD, whle wth lower echo cancellaton capablty, the Algorthm 1 s able to adaptvely choose between FD and HD modes. Fnally, Fg. 5 shows that the proposed optmzaton algorthm has a fast convergence, reachng over 9% of the sum rate mprovement after only 5 teratons. V. CONCLUSION Ths paper proposes an nterference-aware user schedulng and power control algorthm for the FD wreless multcell networs. Fractonal programmng technques are ntroduced to reformulate the orgnal problem n a form where the nteger and contnuous varables can be effcently optmzed n an teratve fashon. The results of ths paper show that nterference management s crucal n an FD cellular networ; wth proper nterference management, FD can mprove user throughput of a multcell networ by about 3-4% as compared to HD. REFERENCES [1] A. Sabharwal, P. Schnter, D. Guo, D. W. Blss, S. Rangarajan, and R. Wchman, In-band full-duplex wreless: Challenges and opportuntes, IEEE J. Sel. Areas Commun., vol. 32, no. 9, pp , Sept [2] J. I. Cho, M. Jan, K. Srnvasan, P. Levs, and S. Katt, Achevng sngle channel, full duplex wreless communcaton, n Proc. ACM MobCom, 21, pp [3] E. Aryafar, M. Khojastepour, K. Sundaresan, S. Rangarajan, and M. Chang, MIDU: Enablng MIMO full duplex, n Proc. ACM MobCom, 212, pp [4] E. Everett, A. Saha, and A. Sabharwal, Passve self-nterference suppresson for full-duplex nfrastructure nodes, IEEE Trans. Wreless Commun., vol. 13, no. 2, pp , Feb [5] A. C. Cr, R. Wang, and Y. Hua, Weghted-sum-rate maxmzaton for b-drectonal full-duplex MIMO systems, n Aslomar Conf. Sgnals, Syst., Comput., Oct. 213, pp [6] Z. Zhang, X. Cha, K. Long, A. V. Vaslaos, and L. Hanzo, Full duplex technques for 5G networs: Self-nterference cancellaton, protocol desgn, and relay selecton, IEEE Commun. Mag., vol. 53, no. 5, pp , May 215. [7] T. Rhonen, S. Werner, and R. Wchman, Hybrd full-duplex/halfduplex relayng wth transmt power adaptaton, IEEE Trans. Wreless Commun., vol. 1, no. 9, pp , Sept [8] B. D, S. Bayat, L. Song, and Y. L, Rado resource allocaton for full-duplex OFDMA networs usng matchng theory, n IEEE Conf. Comput. Commun. INFOCOM) Worshops, Oct. 214, pp [9] M. Duarte, A. Fe, and S. Valentn, A matchng game for decoupled upln-downln user assocaton n full-duplex small cell networs, n IEEE Int. Conf. Commun. ICC), May 216. [1] H. Ju and R. Zhang, Optmal resource allocaton n full-duplex wreless-powered communcaton networ, IEEE Trans. Commun., vol. 62, no. 1, pp , Oct [11] G. C. Alexandropoulos, M. Kountours, and I. Atzen, User schedulng and optmal power allocaton for full-duplex cellular networs, n IEEE Worshop Sgnal Process. Advances Wreless Commun. SPAWC), July 216. [12] K. Shen and W. Yu, Fractonal programmng for communcaton systems, Part II: Schedulng, Preprnt, 217.