Cache-Aided Non-Orthogonal Multiple Access

Transcription

1 ache-aided Non-Othogonal Multile Access Lin Xiang, Deick Wing Kwan Ng, Xiaohu Ge, Zhiguo Ding, Vincent W.S. Wong, and Robet Schobe Abstact In this ae, we oose a novel joint caching and non-othogonal multile access NOMA scheme to facilitate advanced downlink tansmission fo next geneation cellula netwoks. In addition to eaing the conventional advantages of caching and NOMA tansmission, the oosed cache-aided NOMA scheme also exloits data fo intefeence cancellation which is not ossible with seaate caching and NOMA tansmission designs. Futhemoe, as caching can hel to educe the esidual intefeence owe, seveal decoding odes ae feasible at the eceives, and these decoding odes can be flexibly selected fo efomance otimization. We chaacteize the achievable ate egion of cache-aided NOMA and investigate its benefits fo minimizing the time equied to comlete video file delivey. Ou simulation esults eveal that, comaed to seveal baseline schemes, the oosed cache-aided NOMA scheme significantly exands the achievable ate egion fo downlink tansmission, which tanslates into substantially educed file delivey times. I. INTRODUTION Wieless caching is a content-centic netwoking solution to meet the lage downlink caacity demands intoduced by video steaming in fifth geneation 5G cellula netwoks [1] [6]. Recently, caching at steaming use equiments UEs, e.g. smathones and tablets, has been advocated [7], [8] to enhance the steaming quality of exeience QoE while educing i.e., offloading ove-the-ai taffic. This oses significant challenges fo the design of cache lacement and delivey as the aggegate cache caacity is distibuted acoss non-cooeating devices with small individual cache memoy sizes. Besides, the actual equests of the UEs ae difficult to edict duing cache lacement due to the uses mobility and the andom natue of the uses equests. In the liteatue, coded caching has been oosed as an effective solution fo caching at UEs [7], [8]. By exloiting the data as side infomation, a coded multicast fomat is ceated fo simultaneous eo-fee video delivey to multile uses, which leads to a multilicative efomance gain that scales with the aggegate cache memoy size of the UEs. Howeve, coded caching has an exonential-time comutational comlexity. Moeove, the caching concets oosed in [7], [8] ae mainly alicable to noiseless and eo-fee communication links, e.g. in wieline netwoks. Fo wieless netwoks imaied by fading and noise, howeve, the efomance of coded multicast is limited by the weakest use with the ooest channel condition within the multicast gou. On the othe hand, non-othogonal multile access NOMA is an efficient aoach fo wieless multiuse tansmission that alleviates the advese effects of fading [9], [10]. Diffeent fom multicast and coded multicast, NOMA ais multile simultaneous downlink tansmissions on the same time-fequency esouce via owe domain o code domain multilexing [11]. Stong uses with favoable channel conditions can cancel the intefeence caused by weak uses with oo channel conditions that ae aied on the same timefequency esouce, and hence, achieve a high data ate at low tansmit owes. Theefoe, high tansmit owes can be allocated to weak uses to achieve communication fainess [12]. NOMA has also been extended to multicaie and multiantenna systems; see [13], [14] and efeences theein. So fa, wieless caching and NOMA wee eithe investigated seaately o combined in a staightfowad manne [15]. Fo the latte case, NOMA was shown to imove the efomance of both caching and delivey in [15]. In this ae, howeve, the joint design of caching and NOMA is advocated to maximize the efomance gains intoduced by caching at UEs. We show that the joint design of caching and NOMA can significantly outefom the staightfowad combination of caching and NOMA. To this end, we conside a simle distibuted caching scheme fo video file delivey. By slitting the video files into seveal subfiles, sueosition tansmission of the equested un subfiles is enabled duing delivey. If the content is hit, i.e., equested by the caching UE, the oosed cache-aided NOMA scheme enables taditional offloading of the video taffic. Othewise, the missed data, which is not equested by the caching UE, is still exloitable as side infomation to facilitate atial intefeence cancellation fo NOMA. The esulting cacheenabled intefeence cancellation I can neithe be exloited by seaate caching and NOMA designs no by the scheme in [15]. With I, data is useful duing file delivey even if the uses equests cannot be accuately edicted a ioi. Moeove, joint I and successive intefeence cancellation SI imoves the intefeence mitigation caability at the UEs and inceases the numbe of ossible decoding odes comaed to conventional NOMA. Futhemoe, the efomance of both stong and weak uses can benefit fom I. Howeve, adative adjustment of the decoding ode accoding to the cache and channel statuses is citical fo eaing the benefits of cache-aided NOMA. Hence, we investigate the joint decoding ode selection and owe and ate allocation otimization oblem fo minimization of the file delivey time fo fast video delivey. The main contibutions of this ae ae as follows: We oose a novel cache-aided NOMA delivey scheme fo sectally efficient downlink tansmission. Theeby, data is exloited fo cancellation of NOMA intefeence. We chaacteize the achievable ate egion of the oosed scheme. We jointly otimize the NOMA decoding ode and the ate and owe allocations fo minimization of the delivey time. As the fomulated otimization oblem is nonconvex, we oose an iteative method to solve it otimally via solving a sequence of convex oblems. We show by simulation that the oosed scheme leads to a consideably lage achievable ate egion and a significantly educed delivey time comaed to seveal baseline schemes, including the staightfowad combination of caching and NOMA. Notations: and R + denote the sets of comlex and nonnegative eal numbes, esectively. E is the exectation oeato. N µ, σ 2 eesents the comlex Gaussian disti-

2 bution with mean µ and vaiance σ 2. 1 [ ] denotes an indicato function which is 1 when the event is tue and 0 othewise. Fo decoding the eceived signals, the notation i n x f means that x f is the nth decoded signal at UE i. Similaly, i n x f, x f means that signals x f and x f ae jointly decoded in the nth decoding ste. Finally, Γ log Γ denotes the caacity function of an additive white Gaussian noise AWGN channel, whee Γ is the signal-to-intefeence-lusnoise atio SINR. II. SYSTEM MODEL We conside cellula video steaming fom a base station BS to two UEs indexed by i and j, esectively. The BS and the UEs have a single antenna, esectively. UEs i and j equest files W A and W B of sizes V A and V B bits, esectively, whee W A W B. The esective equests ae denoted as i, A and j, B. Each UE is equied with a cache of size k bits. Theeby, UE k {i, j} can lace otions of file f {A, B} into its cache io to the time of equest, e.g. duing the ealy monings when cellula taffic is low. As the cache lacement is comleted befoe the uses equests ae known, the uses may cache files which they late do not equest. We assume that UE k, k {i, j}, has c kf [0, 1] otion of file W f, f {A, B}. A. ache Status and File Slitting Let us define the minimum and maximum otions of content fo file W f by c f min c kf and c f max c kf, k {i,j} k {i,j} which coesond to the cache status at use k f ag min k {i,j} c kf and k f ag max k {i,j} c kf, 2 f {A, B}, esectively. Based on and 2, fou cache configuations ae ossible at the time of equest: ase I: i = k B and j = k A, i.e., i = k A and j = k B ; ase II: i = k B and j = k A, i.e., i = k A and j = k B ; ase III: i = k B and j = k A, i.e., i = k A and j = k B ; ase IV: i = k B and j = k A, i.e., i = k A and j = k B. In aticula, ase I eflects the scenaio whee the nonequesting use has a lage otion of file W f than the equesting use, which constitutes an unfavoable cache lacement fo both uses but cannot be avoided in actice as use equests cannot be edicted accuately. In the following, due to the limited sace, we only conside ase I. Howeve, the deivations fo ase I can be extended to ases II IV in a elatively staightfowad manne. Let Z k Z k,a, Z k,b, k {i, j}, denote the cache status of UE k, whee Z k,f, f {A, B}, is the content of file W f. We assume that the video data of file W f is sequentially oganized. Moeove, based on diffeent use equests and cache configuations, W f is slit into thee subfiles W f0, W f1, W f2 fo adative file delivey. As illustated in Fig. 1, W f0 and W f2 of size c f V f and 1 c f V f bits ae the video chunks which ae and un at both UEs, esectively, wheeas subfile W f1 of size c f c kf V f bits is only at UE k f. Hence, we have Z kf,f = W f0 and Z kf,f = W f0, W f1, f {A, B}. As the data Z kf,f is the efix of Z kf,f, the consideed caching scheme is efeed to as efix caching in [16]. W A W B un un UEi un un UEj W A0 W A1 W A2 W B0 W B1 W B2 Fig. 1. Illustation of file slitting fo cache-aided NOMA, assuming the cache configuation in ase I. B. NOMA Tansmission Fo video delivey, we assume a fequency flat quasi-static fading channel, whee the channel coheence time exceeds the time needed fo comletion of file delivey. The eceived signal at UE k is given by y k = h k x + z k, 3 whee h k denotes the channel gain between the BS and UE k, and is constant duing the tansmission of file W f. x is the tansmit signal and z k N 0, σk 2 is the AWGN at UE k. The BS is assumed to know the cache statuses Z i and Z j duing video delivey. Hence, the BS only tansmits the un subfiles equested by the UEs. Theeby, fo file W f, subfiles W f1, W f2, f {A, B}, ae encoded emloying fou indeendent codebooks at the BS and the coesonding codewods ae sueosed befoe being boadcasted ove the channel accoding to the NOMA incile. The esulting BS tansmit signal is given by x = i,1 x A1 + i,2 x A2 + x B1 + x B2, 4 whee x fs, f {A, B}, s {1, 2}, is the codewod coesonding to subfile W fs, and E [ x fs 2 ] = 1. Futhemoe, k,s 0, k {i, j}, s {1, 2}, denotes the tansmit owe of x fs. As the channel is static, we conside time-invaiant owe allocation, i.e., the owes, k,s, ae fixed duing file delivey. The total tansmit owe at the BS is constained to P, i.e., 1: k,s P. 5 k {i,j} s {1,2} We define i,1, i,2,, and P { R } as the owe allocation vecto and the coesonding feasible set, esectively.. Joint I and SI Decoding The oosed cache-aided NOMA scheme enables I at the eceive, which is not ossible fo conventional NOMA. The joint I and SI eceive efoms I eocessing of the eceived signal befoe SI decoding as illustated in Fig. 2. In aticula, the intefeence caused by tansmit signal x A1 x B1, which is equested by UE i UE j, can be canceled at UE j UE i by exloiting the data Z j,a Z i,b. Hence, the esidual eceived signal afte I

3 Received signal + - x Encode cache miss ached data channel h k cache hit I eocessing Decodes 1 + x Encodes channelh k Decodes D x channelh k + SI decoding... Encodes D Video layback Fig. 2. Joint I and SI decoding at eceive k {i, j} fo cacheaided NOMA. s 1,..., s D, D 4, eesent the esidual signals x fs, f {A, B}, s {1, 2}, which ae not canceled by I but decoded successively by emloying SI. eocessing is given by y I i = h i i,1 x A1 + i,2 x A2 + x B2 + z i, 6 y I j = h j i,2 x A2 + x B1 + x B2 + z j. 7 Remak 1. Fo the oosed cache-aided NOMA scheme, c kf otion of file W f is not tansmitted at all, while c f c kf otion of file W f can be emoved fom the eceived signal of the non-equesting UE k via I, whee k, f {i, A, j, B} and k k. As such, the oosed scheme can exloit c f otion of W f fo efomance imovement, even fo the unfavoable cache configuation of ase I, wheeas a staightfowad combination of caching and NOMA can only exloit the otion c kf of the equested file [15]. As I educes the multiuse intefeence owe, multile decoding odes become ossible fo SI ocessing of yk I. Fo examle, thee ae 4! = 24 ossible decoding odes based on 6 and 7, comaed to 2! = 2 fo conventional NOMA. This leads to a substantially inceased flexibility in decoding the video data based on yk I. Otimizing the SI decoding ode and the esective tansmission ates and owe allocations based on the cache status and channel conditions enhances the efomance of video delivey. On the othe hand, decoding ode otimization is a combinatoial oblem, which may incease comlexity. Howeve, by caeful insection of the SI decoding conditions, we show in Section III that the otimal decoding ode is contained in a small subset of all ossible decoding odes, and hence the associated comlexity is limited. III. AHIEVABLE RATE REGION AND DELIVERY TIME MINIMIZATION In this section, we evaluate the achievable ate egion of the oosed cache-aided NOMA scheme. Based on the deived esults, we then minimize the delivey time duing file tansfe by otimizing the decoding ode and the owe and ate allocation. Let i,1, i,2,, j,2 be the ate allocation vecto, whee k,s 0 is the ate fo deliveing x fs to UE k, k, f {i, A, j, B}, s {1, 2}. We define α k k {i, j}, as the effective noise vaiance at UE k. Without loss of geneality, we assume <, i.e., UE i has a lage channel gain than UE j. σ2 k, h k 2 A. Deivation of Achievable Rate Region Accoding to 6 and 7, two subfiles, x f1 and x f2, ae deliveed to each use and x B1 x A1 is canceled at UE i j by I. Moeove, x A2 and x B2, which ae intefeence signals at one use, ae commonly eceived at both uses, wheeas x A1 and x B1 ae eceived only at the equesting uses. The intefeence signals can be decoded and canceled only if the SI decoding condition is fulfilled, i.e., the eceived SINR fo x A2 and x B2 at the non-equesting uses, UE j and UE i, has to exceed that at the equesting uses, UE i and UE j, esectively. In contast, signals x A1 and x B1 can be decoded without such constaint. Deending on which signal is decoded fist, thee cases can be distinguished: fo the fist two cases, signals x A1 and x B1 ae decoded fist at the equesting uses, esectively, wheeas, fo the thid case, the intefeence signals x A2 and x B2 ae decoded fist. Fo these cases, as 6 and 7 constitute a non-degaded boadcast channel, the coesonding achievable ate egions have to be evaluated fo secific owe egions individually. 1 UE i x A1 : If UE i decodes x A1 fist, signals y i = h i i,2 x A2 + x B2 + z i and y j = h j i,2 x A2 + j,2 x B2 + x B1 +z j have to be decoded subsequently. The achievable ate egion is ovided in Poosition 1. Poosition 1. When UE i x A1, the ate egion R 1 P 1 R 2 P 2 is achievable, whee i,1 i,1 = R 1 P 1 i,2 i,2 = j,s P 1 j,s j,s = + j,2,2 = i,1 i,1 = R 2 P 2 i,2 i,2 = P 2 = j,2 j,2 = i,1 i,2+ i,2+, s = 1, 2 + i,2+ i,1 i,2++α i i,2+ + with P 1 = P and P 2 { P > }. Fo R 1 P 1, the decoding odes fo UEs i and j ae given as i x A1 2 x B2 3 x A2 and j x B1, x B2, esectively. Fo R 2 P 2, the decoding odes ae i 2 x A1 x A2 and j 2 3 x A2 x B2 x B1, esectively. Poof: Please efe to Aendix A. Remak 2. In Poosition 1, the intefeence fo decoding x A2 is educed afte x A1 has been decoded and canceled fom. Hence, decoding x A1 fist is desiable when e.g. W A1 has a smalle size and/o equies a lowe delivey ate than W A2. The decoding odes fo R 1 P 1 favo the delivey of x A2 to UE i as it exeiences no intefeence afte SI, and thus can attain a high data ate i,2 even fo small tansmit owes i,2. In contast, the decoding odes fo R 2 P 2 favo the delivey of x B1 to UE j. This imlies that R 2 P 2 exands R 1 P 1 along. yi I 2 UE j x B1 excluding UE i x A1 : 1 Decoding and canceling x B1 fist imoves the SINR of x B2 at UE j, which is desiable when subfile W B1 has a smalle size than W B2. The esulting signals afte x B1 has been canceled ae y i = h i i,1 x A1 + i,2 x A2 + x B2 + z i and y j = h j i,2 x A2 + x B2 + z j. The coesonding achievable ate egion is given in Poosition 2. 1 The achievable ate egion fo UE j x B1 and UE i x A1 is aleady included in R 1 P 1, and hence, excluded heein.

4 Poosition 2. When UE j x B1 but UE i x A1 is excluded, the achievable ate egion is given by R 3 P 3 R 4 P 4, whee i,s i,s, s = 1, 2 R 3 P 3 i,1+ i,1 + i,2 P 3 i,2++α j j,2 j,2 i,2+ i,1 i,1 R 4 P 4 i,2 i,1+ P 4 i,2++ j,2 j,2 with P 3 { P i,1 < } and P 4 = P\P 3. The decoding odes achieving R 3 P 3 ae UE i 2 x B2 x A1, x A2 and UE j 2 x B1 x B2. Moeove, the decoding odes fo R 4 P 4 ae UE i j 2 3 x B1 x A2 x B2. Poof: Please efe to Aendix B. 2 x A2 x A1 and UE 3 UE j x A2, x B2 and UE i x A2, x B2 : Recall that decoding the intefeence signals fist is only ossible if the SI condition is fulfilled. In this case, the achievable ate egion is given in Poosition 3. Poosition 3. When UE j x A2, x B2 and UE i x A2, x B2, the achievable ate egion is given by R 5 P 5 R 6 P 6 R 7 P 7, whee i,s i,s, s {1, 2} R 5 P 5 i,1+ i,1 + i,2 P 5 i,2+ j,2 j,2 + i,2+ i,1 i,1 + R 6 P 6 i,2 i,1+ j,2+ P 6 j,2 j,2 i,2+ + i,1 i,1 R 7 P 7 i,2 i,1+ j,2+ j,s P 7 j,s, s = 1, j,2 j,2 with P 5 { P i,1 < + }, P 6 = P 7 = P\P 5, and 1 [ i,2 > i,1 + ]. The decoding odes achieving R 5 P 5 ae UE i 2 x B2 x A1, x A2 and UE j 2 x B2 x B1. Moeove, R 6 P 6 is achieved by the decoding odes UE i 2 x A2 { xa1, if = 1, x B2 3 x A1, othewise, and UE j 2 x B2 x B1. Finally, R 7 P 7 is achieved by the decoding odes UE i 2 2 x A2 x A1 and UE j x A2 x B1, x B2. Poof: Please efe to Aendix. Remak 3. Diffeent fom conventional NOMA, file slitting in the oosed cache-aided NOMA scheme enables joint decoding ootunities. Fo examle, joint decoding of x B1 and x B2 at UE j is ossible in R 1 P 1, as the two signals ae eceived by UE j ove the same AWGN channel with noise vaiance i,2 +. Theefoe, UE j can choose the decoding ode fo these files without estiction. Similaly, joint decoding of x A1 and x A2 is ossible at UE i in R 3 P 3 and R 5 P 5, esectively. We note that emloying file slitting in conventional NOMA would not incease the achievable ates at UEs. Howeve, if a otion of file is at one of the UEs, the achievable ates of the UEs can be inceased by emloying file slitting in the oosed cacheaided NOMA as this enables I. Finally, combining the esults in Poositions 1 3, the oveall achievable ate egion is R 7 n=1 R np n. Note that R n P n can be witten in geneal fom as R n P n = { 2: } ks k,s, k {i, j}, s {1, 2} 3: k1 + k2 k,1,2, k {i, j} P n 8 whee k,s and k,1,2 ae the esective caacity bounds fo decoding signal x fs, s {1, 2}, and signals {x f1, x f2 } at use k {i, j}. B. Rate and Powe Allocation fo Fast Delivey Let T be the time equied to comlete the delivey of the equested files. We have T = max k {i,j}, s {1,2} β k,s k,s, 9 fo R, whee β k,1 c f c kf V f and β k,2 1 c f V f fo k, f {i, A, j, B} denote the effective volume of data to be deliveed to use k. To avoid tivial esults, we assume thoughout this section that β k,1 + β k,2 > 0, k {i, j}, i.e., each use equests some video data that is not 2. onsequently, the delivey time otimization oblem is fomulated as P1: min T 10 R, P, T 0 s.t. 4: ks T β k,s, k {i, j}, s {1, 2}, whee 4 ensues comletion of file delivey at time T. Poblem P1 is geneally nonconvex as the caacity functions in 2 and 3 in 8 ae not jointly convex with esect to and, and 4 is bilinea. Howeve, the otimal solution of Poblem P1 can be obtained by solving a sequence of convex oblems as will be shown in the following. In aticula, assume that the otimal solution lies in R n. Fo each feasible owe allocation, the ate egion R n, cf. 8, educes to a olyhedon. onsequently, the otimal ate allocation, denoted as i,1, i,2,, j,2, can be obtained as the ate tule on the dominate face 3 of R n [17]. Fo examle, fo n = 1, we have i,1 = i,1 and i,2 = i,2 as the ates of UE i ae only constained by 2. In contast, as the ates of UE j ae constained by both 2 and 3, we have = j,2 + i,2 +αj 2 Othewise, k,1 = k,2 = 0 and k,1 = k,2 = 0. 3 Fo a olyhedon, any oint that lies outside the dominant face is dominated elementwise by some oint on the dominant face [17].

5 Algoithm 1 Bisection seach fo ρ n. 1: initialization: Given LB, UB, and toleance ϵ; 2: eeat 3: ρ n LB + UB/2; 4: Solve the feasibility oblem of 11 fo ρ n; 5: if 11 is infeasible then 6: UB ρ n; 7: else 8: LB ρ n; 9: end if 10: until UB LB < ϵ. and j,2 = j,2 i,2 +αj and = i,2 +αj fo decoding ode j 2 x B1 x B2 and j,2 = j,2 fo i,2 + +αj decoding ode j 2 x B2 x B1, and the otimal owe allocation = i,1, i,2,, j,2. In the same manne, the otimal ate allocation fo all n {1,..., 7} can be obtained. Substituting the otimal ate allocations and letting ρ n = 1/T, P1 can be equivalently efomulated as T = min n {1,...,7} ρ n with ρ n max ρ n 11 P n, ρ n 0 s.t. 5: k,s ρ n β k,s, k {i, j}, s {1, 2}. The otimal value ρ n can be found iteatively by emloying Algoithm 1. In aticula, in each iteation, the feasibility of oblem 11 is checked fo a given ρ n, cf. line 4. Fo given ρ n, we have ρ n ρ n if 11 is feasible, i.e., ρ n is a lowe bound on ρ n, and ρ n ρ n othewise, i.e., ρ n is an ue bound on ρ n. Hence, a bisection seach can be alied to iteatively udate the value of ρ n until the ga between the lowe and the ue bounds vanishes, wheeby ρ n is obtained. Moeove, efficient convex otimization algoithms can be emloyed [18] in line 4 of Algoithm 1. This is because although 5 is a linea factional constaint of the fom log at c fo a, b R 4 b T +1 + and c R +, it can be tansfomed into an equivalent convex constaint of the fom a 2 c 1 b T 2 c 1 such that an equivalent convex fomulation of oblem 11 is obtained. IV. PERFORMANE EVALUATION In this section, the efomance of the oosed cacheaided NOMA is evaluated by simulation. onside a cell of adius R = 2 km, whee the BS is deloyed at the cente of the cell and the stong and the weak uses, UE i and UE j, ae unifomly distibuted on discs of adii R i = 0.2 km and R j = 0.6 km, esectively. Fo modeling the wieless channel, the 3GPP ath loss model Uban Maco NLOS scenaio in [19] is adoted. The small-scale fading coefficients ae indeendent and identically distibuted i.i.d. Rayleigh andom vaiables. The video files have size V A = V B =500 MBytes. Moeove, the system has a bandwidth of 5 MHz. The noise owe sectal density is dbm/hz. Finally, we set the maximal tansmit owe as P = 35 dbm and the cache status as c ia = 0.2, c ib = 0.8, c ja = 0.8, and c jb = 0.2. A. Baseline Schemes 1 Baseline 1 ache-aided othogonal multile access OMA: As baseline, we conside time-division multile access TDMA fo tansmitting the un otions of the equested files. In aticula, τ and 1 τ factions of time ae allocated fo tansmission to UE i and UE j, esectively, whee τ [0, 1]. onsequently, the caacity egion fo all ossible time allocations is given by R OMA = { } τ [0,1] i, j i τ P, j 1 τ P. Note that, with Baseline 1, caching only facilitates conventional offloading of the hit data. 2 Baseline 2 onventional NOMA with and without caching: If caching is ossible, Baseline 2 is a staightfowad combination of caching and NOMA, wheeby the equested data hit by the cache is offloaded and only the emaining data is tansmitted by alying NOMA. If caching is not ossible, Baseline 2 educes to the conventional NOMA scheme. In both cases, the BS tansmits signals x = i x A + j x B fo deliveing files W A and W B, whee { the owe allocations i and j satisfy P NOMA i, j R 2 + i + j P }. The eceived signals at UEs i and j ae given by, y i = h i i x A + j x B + zi, 12 y j = h j i x A + j x B + zj. Fo Baseline { 2, the same caacity egion R NOMA P NOMA = P NOMA i, j i i, j j } i+ is achieved by SI with and without caching [17], whee x B is decoded and canceled befoe decoding x A at UE i. Fo Baselines 1 and 2, the ate and time/owe allocation is otimized fo minimization of the delivey time in a simila manne as fo the oosed cache-aided NOMA scheme. B. Simulation Results In Fig. 3, we comae the achievable ate egions of the oosed cache-aided NOMA scheme and the baseline schemes fo = 10 3 and = Fo the oosed scheme, the ate achievable by UE k is given by k,1 + k,2, k {i, j}. Note that the achievable ate egions of all consideed schemes ae indeendent of the values of c kf, k, f {i, A, j, B}. In aticula, Baseline 2 with and without caching achieves the same ate egion. Fom Fig. 3, we obseve that all consideed schemes achieve the same cone oints 0, 10.0 and 13.2, 0, since the maximal ate fo each UE is fundamentally limited by its channel status. Baseline 1 achieves the smallest ate egion as it emloys OMA to avoid intefeence. As NOMA intoduces additional degees of feedom fo the uses, Baseline 2 has a lage achievable ate egion than Baseline 1. The exansion of the ate egion is moe significant fo the weak use than fo the stong use since the stong use consumes a small tansmit owe, and hence, causes little intefeence to the weak use. The oosed cache-aided NOMA scheme achieves the lagest ate egion among all consideed schemes as joint I and SI allows moe intefeence to be canceled comaed to Baseline 2 which can only efom SI. This tanslates into a lage sum ate gain fo the oosed scheme. With the oosed scheme, significant efomance gains ae ossible fo both the weak and the stong use due to I. In Fig. 4, we show the otimal aveage delivey times of the oosed cache-aided NOMA scheme and Baselines 1 and 2 as functions of the distance of the weak UE to the BS R j. The efomance is aveaged ove diffeent ealizations of the use locations and the channel fading. Fo a given R j, as exected fom the achievable ate egion esults in Fig. 3, Baseline 1 equies the longest time to comlete video file delivey. The oosed cache-aided NOMA scheme outefoms both Baseline 2 without caching and Baseline 2 with caching. This is due to the exloitation of I, which

6 Achievable ate fo UE j [bs/hz] Fig. 3. Achievable ate egion of the oosed scheme and Baselines 1 and 2 fo = 10 3 and = V. ONLUSION In this ae, a joint caching and NOMA tansmission design was esented fo sectally efficient downlink communication. The oosed scheme exloits unequested data fo cancellation of NOMA intefeence, which is not ossible with seaate caching and NOMA tansmission. The achievable ate egion of the oosed cache-aided NOMA scheme was chaacteized, and the otimal decoding ode and the otimal owe and ate allocations fo minimization of the delivey time wee investigated. Simulation esults showed that the oosed scheme can significantly exand the achievable downlink ate egion fo both the stong and the weak uses. Moeove, the delivey time of both uses can be effectively educed to achieve fast video delivey. Fo ease of illustation, the oosed cache-aided NOMA was only evaluated fo the imotant case of two aied NOMA uses. The extension of cache-aided NOMA to multile uses will be consideed in futue wok. Otimal aveage delivey time [min] Fig. 4. Otimal aveage delivey time vesus the distance between the weak use and the BS. is ossible only with the oosed joint caching and NOMA tansmission design. Howeve, diffeent fom the achievable ate egion, the delivey times of Baseline 1, Baseline 2 with caching, and the oosed scheme citically deend on the amount of data. As R j inceases, UE j, the weak use, suffes fom an inceased ath loss, which in tun educes the channel gain of UE j. Moeove, since the delivey time of the weak use dominates the oveall delivey time, we obseve fom Fig. 4 that the otimal delivey time inceases with R j fo all consideed schemes. Howeve, Baseline 1 is the least efficient among the consideed schemes, and its delivey time inceases by about 80% as R j inceases fom 0.2 km to 2 km. By exloiting NOMA and the esulting inceased degees of feedom, Baseline 2 effectively educes the efomance degadation caused by the weak use. Fo examle, even without caching, the delivey time of Baseline 2 is 40% 50% lowe than that of Baseline 1 when UE j is located at R j = 0.2 km R j = 2 km. Moeove, when a cache is available, Baseline 2 can also exloit caching fo offloading of the delivey data, which futhe educes the delivey time comaed to Baseline 1 by an additional 12% 10% fo R j = 0.2 km R j = 2 km. The oosed scheme enjoys the best efomance and its delivey time is about 80% lowe than that of Baseline 1 fo the consideed values of R j. APPENDIX A PROOF OF PROPOSITION 1 As i x A1, i,1 i,1 is achievable fo decoding x A1 at UE i. To deive the achievable ate egion, we need to check the decodability of the intefeing signals x B2 and x A2 at UE i and j, esectively. Let us conside the following two owe egions. Fo P 1 \P 2, we have +, i.e., UE j cannot decode x A2 befoe decoding x B1 as the SI decoding condition is not met. Also, fo any, R 2 +, x A2 cannot be decoded befoe decoding x B2 at UE j as i,2 < < On the othe hand, fo any, R 2 +, x B2 can be always decoded and canceled at UE i befoe x A2 is decoded as < ; and hence, i,2 i,2 is achievable. In contast, UE j cannot decode x A2 in any case. onsequently, the feasible decoding odes ae UE i 2 3 x B2 x A2 and UE j x B1, x B2, wheeby ate egion R 1 P 1 \P 2 is achieved. 2 Fo P 2, we have > + >, i.e., x A2 can be decoded at UE j befoe x B1 is decoded if and only if UE i 2 x A2. Assume x A2 is decoded last at UE i such that UE j cannot decode x A2 in any case. Then, ate egion R 1 P 2 is achievable. On the othe hand, suose x A2 is decoded fist at UE i. Then, UE j can achieve a highe ate fo by decoding x A2 befoe decoding x B1, which is only ossible afte x B2 has been decoded accoding to 13. Thus, the ate egion R 2 P 2 is achievable. Theefoe, the ate egion R 1 P 1 R 2 P 2 is achievable, and any ate vecto outside the egion R 1 P 1 R 2 P 2 cannot be achieved by SI decoding. This comletes the oof. APPENDIX B PROOF OF PROPOSITION 2 By decoding x B1 fist, i,2++ is achievable fo UE j. To obtain the achievable ate egion, two owe egions have to be consideed.

7 Fo P 3, we have i,2 >, 14 i, α j j,2 >, 15 i,1 + i,2 + i,2 + which imly that x A2 cannot be decoded at UE j in geneal, cf. 14, but x B2 can always be decoded at UE i, cf. 15. onsequently, UE j can decode x B2 only by teating x A2 as noise wheeas UE i will fist decode x B2 and cancel its contibution to the eceived signal befoe decoding x A1 and x A2. Theefoe, the achievable ate egion is given by R 3 P 3. 2 Fo P 4, we have i,2, 16 i, α j j,2, 17 i,1 + i,2 + i,2 + α j j,2 j,2. 18 i,1 + That is, at UE i, x B2 cannot be decoded fist, cf. 17. Hence, we only need to conside UE i x A2. In this case, UE j is able to cancel the intefeence fom x A2 befoe decoding x B2 due to 16. Howeve, at UE i, x B2 cannot be canceled befoe decoding x A1 due to 18, i.e., UE i 2 x B2 is infeasible. Theefoe, the achievable ate egion is given by R 4 P 4, whee UE i cannot decode x B2 while UE j can decode and cancel x A1 befoe decoding x B2. Theefoe, the ate egion in Poosition 2 is achievable, which comletes the oof. APPENDIX PROOF OF PROPOSITION 3 Fist, assume UE j x B2 and UE i x A2, x B2. If P 5, we have >, 19 i,1 + i,2 + i,2 + + α j > >. 20 i,1 + + By 19, UE i can decode and cancel x B2 as <. Thus, UE i x B2, which leads to the esidual eceived signals y i = h i i,1 x A1 + i,2 x A2 + zi and y j = h j x B1 + i,2 x A2 + zj. By 20, UE j cannot decode x A2 based on y j. Theefoe, the decoding odes UE i 2 x B2 x A1, x A2 and UE j 2 x B2 x B1 ae feasible and achieve ate egion R 5 P 5. Howeve, if P 6, UE i cannot decode x B2 fist due to 19. Then, fo the assumtion of UE i x A2, x B2, we only need to conside the case UE i x A2. We have >, 21 + i,1 + i.e., UE j can cancel x A2 befoe decoding x B1. On the othe hand, UE i cannot cancel x B2 befoe decoding x A1 unless = 0, wheeby we have j,2 j,2 i,2+ + i,1+. Hence, ate egion R 6 P 6 is achievable. Next, assume UE j x A2 and UE i x A2, which equies i,2 ++ > i,2 i,1+, o equivalently, P 7. In this case, as j,2 j,2 > + > j,2 i,1+, UE i cannot decode x B2. Hence, the decoding odes UE i 2 x A2 x A1 and UE j 2 x A2 x B1, x B2 ae feasible and achieve ate egion R 7 P 7. Finally, fo UE j x A2 and UE i x B2, feasible owe and ate allocations do not exist. In aticula, fo such a ate egion to exist, the following inequalities would have to hold, i,2 >, i,1 + α i j,2 >, 23 i,1 + i,2 + + which ensue feasibility of UE j x A2 and UE i x B2, esectively. Eqs. 22 and 23 ae equivalent to i,1 > + and i,1 <, esectively, which lead to i,2 + < 0. That is, 22 and 23 cannot be met fo feasible owes. Theefoe, the ate egion in Poosition 3 is achievable, which comletes the oof. REFERENES [1] X. Wang, M. hen, T. Taleb, A. Ksentini, and V. Leung, ache in the ai: Exloiting content caching and delivey techniques fo 5G systems, IEEE ommun. Mag., vol. 52, no. 2, , Feb [2] V. W. S. Wong, R. Schobe, D. W. K. 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