Rate-splitting multiple access for downlink communication systems: bridging, generalizing, and outperforming SDMA and NOMA

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1 Mo et l. EURASIP Journl on Wireless Communitions n Networing 208) 208:33 RESEARCH Open Aess Rte-splitting multiple ess for ownlin ommunition systems: riging, generlizing, n outperforming SDMA n NOMA Yijie Mo *, Bruno Clerx 2 n Vitor O.K. Li Astrt Spe-ivision multiple ess SDMA) utilizes liner preoing to seprte users in the sptil omin n relies on fully treting ny resiul multi-user interferene s noise. Non-orthogonl multiple ess NOMA) uses linerly preoe superposition oing with suessive interferene nelltion SIC) to superpose users in the power omin n relies on user grouping n orering to enfore some users to fully eoe n nel interferene rete y other users. In this pper, we rgue tht to effiiently ope with the high throughput, heterogeneity of qulity of servie QoS), n mssive onnetivity requirements of future multi-ntenn wireless networs, multiple ess esign nees to eprt from those two extreme interferene mngement strtegies, nmely fully tret interferene s noise s in SDMA) n fully eoe interferene s in NOMA). Consiering multiple-input single-output rost hnnel, we evelop novel multiple ess frmewor, lle rte-splitting multiple ess RSMA). RSMA is more generl n more powerful multiple ess for ownlin multi-ntenn systems tht ontins SDMA n NOMA s speil ses. RSMA relies on linerly preoe rte-splitting with SIC to eoe prt of the interferene n tret the remining prt of the interferene s noise. This pility of RSMA to prtilly eoe interferene n prtilly tret interferene s noise enles to softly rige the two extremes of fully eoing interferene n treting interferene s noise n provies room for rte n QoS enhnements n omplexity reution. The three multiple ess shemes re ompre, n extensive numeril results show tht RSMA provies smooth trnsition etween SDMA n NOMA n outperforms them oth in wie rnge of networ los unerloe n overloe regimes) n user eployments with iversity of hnnel iretions, hnnel strengths, n qulities of hnnel stte informtion t the trnsmitter). Moreover, RSMA provies rte n QoS enhnements over NOMA t lower omputtionl omplexity for the trnsmit sheuler n the reeivers numer of SIC lyers). Keywors: RSMA, NOMA, SDMA, MISO BC, Liner preoing, Rte region, Weighte sum rte, Rte splitting Introution With the rmti upsurge in the numer of evies expete in 5G n eyon, wireless networs will e operte in vriety of regimes rnging from unerloe to overloe where the numer of sheule evies is smller n lrger thn the numer of trnsmit ntenns *Corresponene: moyijie@hu.h Deprtment of Eletril n Eletroni Engineering, The University of Hong Kong, Po Fu Lm Ro, Hong Kong, Chin Full list of uthor informtion is ville t the en of the rtile t eh ess point, respetively). Moreover, ue to the heterogeneity of evies high-en suh s smrtphones n low-en suh s Internet of Things n Mhine-Type Communitions evies), eployments, n pplitions in 5G n eyon, the trnsmitter will nee to serve simultneously users with ifferent pilities, eployments, n qulities of hnnel stte informtion t the trnsmitter CSIT). This mssive onnetivity prolem together with the emns for high throughput n heterogeneity of qulity of servie QoS) hs reently spurre TheAuthors). 208Open Aess This rtile is istriute uner the terms of the Cretive Commons Attriution 4.0 Interntionl Liense whih permits unrestrite use, istriution, n reproution in ny meium, provie you give pproprite reit to the originl uthors) n the soure, provie lin to the Cretive Commons liense, n inite if hnges were me.

2 Mo et l. EURASIP Journl on Wireless Communitions n Networing 208) 208:33 Pge 2 of 54 interests in re-thining multiple ess for the ownlin of ommunition systems. In this pper, we propose new multiple ess lle rte-splitting multiple ess RSMA). In orer to fully ssess the novelty of the propose multiple ess prigm n the esign philosophy, we first review the stte of the rt of two mjor multiple esses, nmely non-orthogonl multiple ess NOMA) [], lso lle Multi-User Superposition Trnsmission MUST) in 3GPP LTE Rel-3 [2] n spe-ivision multiple ess SDMA). We ientify their enefits n limittions n me ritil oservtions, efore motivting the introution of the novel n more powerful RSMA.. SDMA n NOMA: the extremes Contrry to orthogonl multiple ess OMA) tht sheules users or groups of users in orthogonl imensions, e.g., time TDMA) n frequeny FDMA), NOMA superposes users in the sme time-frequeny resoure vi the power omin or the oe omin, leing to the power-omin NOMA e.g., []) n oe-omin NOMA e.g., sprse oe multiple ess SCMA) [3]). Power-omin NOMA relies on superposition oing SC) t the trnsmitter n suessive interferene nelltion SIC) t the reeivers enote in short s SC SIC) [, 4 6]. Suh strtegy is motivte y the well-nown result tht SC SIC hieves the pity region of the single-input single-output SISO) Gussin) rost hnnel BC) [7, 8]. It is lso well nown tht the pity region of the SISO BC is lrger thn the rte region hieve y OMA e.g., TDMA) when users experiene isprity of hnnel strengths [8]. On the other hn, when users exhiit the sme hnnel strengths, OMA se on TDMA is suffiient to hieve the pity region [8]. The enefit of single-ntenn NOMA using SC SIC is therefore to e le, espite the presene of single trnsmit ntenn in SISO BC, to ope with n overloe regime in spetrlly effiient mnner where multiple users experiene potentilly very ifferent hnnel strengths/pth losses e.g., ell-enter users n ell-ege users) on the sme time/frequeny resoure. The limittion of single-ntenn NOMA lies in its omplexity s the numer of users grows. Inee, for K-userSISOBC,thestrongestuserneestoeoe using SIC the K messges of ll o-sheule users n therefore peel off K lyers efore essing its intene strem. Though SIC of smll numer of lyers shoul e fesile in prtie 2, the omplexity n lielihoo of error propgtion eomes quily signifint for lrge numer of users. This lls for wys to erese the numer of SIC lyers t eh user. One oul ivie users into smll groups of users with isprte hnnels n pply SC SIC in eh group n sheule groups on orthogonl resoures using OMA), ut tht my le to some performne loss n lteny inrese. In nowys wireless networs, ess points re often equippe with more thn one ntenn. This sptil imension opens the oor to nother well-nown type of multiple ess, nmely SDMA. SDMA superposes users in the sme time-frequeny resoure n seprtes user vi proper use of the sptil imensions. Contrry to the SISO BC, the multi-ntenn BC is nonegre, i.e., users nnot e orere se on their hnnel strengths in generl settings. This is the reson why SC SIC is not pity-hieving, n the omplex irty pper oing DPC) is the only strtegy tht hieves the pity region of the multiple-input singleoutput MISO) Gussin) BC with perfet CSIT [9]. DPC, rther thn performing interferene nelltion t the reeivers s in SC SIC, n e viewe s form of enhne interferene nelltion t the trnsmitter n relies on perfet CSIT to o so. Due to the high omputtionl uren of DPC, liner preoing is often onsiere the most ttrtive lterntive to simplify the trnsmitter esign [0]. Interestingly, in MISO BC, multi-user liner preoing MU LP), e.g., either in lose form or optimize using optimiztion methos, though suoptiml, is often very useful when users experiene reltively similr hnnel strengths or long-term signl-to-noise rtio SNR) n hve semi-orthogonl to orthogonl hnnels []. SDMA is therefore ommonly implemente using MU LP. The liner preoers rete ifferent ems with eh em eing llote frtion of the totl trnsmit power. Hene, similrly to NOMA, SDMA n lso e viewe s superposition of users in the power omin, though users re seprte t the trnsmitter sie y sptil emformers rther thn y the use of SIC t the reeivers. SDMA se on MU LP is well-estlishe multiple ess tht is nowys the si priniple ehin numerous tehniques in 4G n 5G suh s multiuser multiple-input multiple-output MU MIMO), oorinte multipoint CoMP) oorinte emforming, networ MIMO, millimeter-wve MIMO, n mssive MIMO. The enefit of SDMA using MU LP is therefore to rep ll sptil multiplexing enefits of MISO BC with perfet CSIT with low preoer n reeiver omplexity. The limittions of SDMA re threefol. First, it is suite to the unerloe regime n performne of MU LP in the overloe regime quily rops s it requires more trnsmit ntenns thn users to e le to effiiently mnge the multi-user interferene. When the MISO BC eomes overloe, the urrent n populr pproh for the trnsmitter is to sheule group of users over orthogonl imensions e.g., time/frequeny) n perform liner preoing in eh

3 Mo et l. EURASIP Journl on Wireless Communitions n Networing 208) 208:33 Pge 3 of 54 group, whih my inrese lteny n erese QoS epening on the pplition. Seon, its performne is sensitive to the user hnnel orthogonlity n strengths n requires the sheuler to pir semi-orthogonl users with similr hnnel strengths together. The omplexity of the sheuler n quily inrese when n exhustive serh is performe, though low-omplexity suoptiml) sheuling n user-piring lgorithms exist [0]. Thir, it is optiml from egrees of freeom 3 DoF), lso nown s sptil multiplexing gin, perspetive in the perfet CSIT setting ut not in the presene of imperfet CSIT [2]. The prolem of SDMA esign in the presene of imperfet CSIT hs een to strive to pply frmewor motivte y perfet CSIT to senrios with imperfet CSIT, not to esign frmewor motivte y imperfet CSIT from the eginning [2]. This les to the wellnown severe performne loss of MU LP in the presene of imperfet CSIT [3]. In view of SC SIC enefits in SISO BC, ttempts hve een me to stuy multi-ntenn NOMA. Two lines of reserh hve emerge tht oth rely on linerly preoe SC SIC. The first strtegy, whih we simply enote s SC SIC, is iret pplition of SC SIC to the MISO BC y egring the multi-ntenn rost hnnel. It onsists in orering users se on their effetive slr hnnel fter preoing) strengths n enfore reeivers to eoe messges n nel interferene) in suessive mnner. This is vote n exemplifie for instne in [4 7]. This NOMA strtegy onverts the multi-ntenn non-egre hnnel into n effetive single-ntenn egre hnnel, s t lest one reeiver ens up eoing ll messges. While suh strtegy n ope with the eployment of users experiening ligne hnnels n ifferent pth loss onitions, it omes t the expense of srifiing n nnihilting ll sptil multiplexing gins in generl settings. By foring one reeiver to eoe ll strems, the sum DoF is reue to unity 4. This is the sme DoF s tht hieve y TDMA/singleuser emforming or OMA). This is signifintly smller thn the sum DoF hieve y DPC n MU LP in MISO BC with perfet CSIT, whih is the minimum of the numer of trnsmit ntenns n the numer of users 5. Moreover, this loss in multiplexing gin omes with signifint inrese in reeiver omplexity ue to the multi-lyer SIC ompre to the tret interferene s noise strtegy of MU LP. As remey to reover the DoF loss, we oul envision ynmi swithing etween NOMA n SDMA, reminisent of the ynmi swithing etween SU MIMO n MU MIMO in 4G [8]. One woul ynmilly hoose the est option etween NOMA n SDMA s funtion of the hnnel sttes. A prtiulr instne of this pproh is ten in [9]where ynmi swithing etween SC SIC n zero-foring emforming ZFBF) ws investigte. The seon strtegy, whih we enote s SC SIC per group, onsists in grouping K users into G groups. Users within eh group re serve using SC SIC, n users ross groups re serve using SDMA so s to mitigte the inter-group interferene. Exmples of suh strtegy n e foun in [, 20 24]. This strtegy n therefore e seen s omintion of SDMA n NOMA where the multi-ntenn system is effetively eompose into G hopefully non-interfering single-ntenn NOMA hnnels. For this SC SIC per group pproh to perform t its est, users within eh group nee to hve their hnnels ligne n users ross groups nee to e orthogonl. Similrly to SDMA, multi-ntenn NOMA esigns lso rely on urte CSIT. In the prtil senrio of imperfet CSIT, NOMA esign relies on the sme ove two strtegiesutoptimizesthepreoersostoopewith CSIT imperfetion n resulting extr multi-user interferene. As n exmple, the MISO BC hnnel is gin egre in [7] n preoer optimiztion with imperfet CSIT is stuie. The enefit of multi-ntenn NOMA, similrly to the single-ntenn NOMA, is the potentil to ope with n overloe regime where multiple users experiene ifferent hnnel strengths/pth losses n/or re losely ligne with eh other. The limittions of multi-ntenn NOMA re fourfol. First, the use of SC SIC in NOMA is funmentlly motivte y egre BC in whih users n e orere se on their hnnel strengths. This is the ey property of the SISO BC tht enles SC SIC to hieve its pity region. Unfortuntely, motivte y the promising gins of SC SIC in SISO BC, the multi-ntenn NOMA literture strives to pply SC SIC to non-egre MISO BC. This fores to egre non-egre BC n therefore les to n ineffiient use of the sptil imensions in generl settings, leing to DoF loss. Seon, NOMA is not suite for generl user eployments sine egring MISO BC is effiient when users re suffiiently ligne with eh other n exhiit isprity of hnnel strengths, not in generl settings. Thir, multi-ntenn NOMA omes with n inrese in omplexity t oth the trnsmitter n the reeivers. Inee, multi-lyer SIC is neee t the reeivers, similrly to the single-ntenn NOMA. However, in ition, sine there exists no nturl orer for the users hnnels in multi-ntenn NOMA euse we el with vetors rther thn slrs), the preoers, the groups, n the eoing orers hve to e jointly optimize y the sheuler t the trnsmitter. Ting s n exmple, the pplition of NOMA se on SC SIC to three-user MISO BC, we nee to optimize three preoers, one for

4 Mo et l. EURASIP Journl on Wireless Communitions n Networing 208) 208:33 Pge 4 of 54 eh user, long with the six possile eoing orers. Inresing the numer of users les to n exponentil inrese in the numer of possile eoing orers. SC SIC per group ivies users into multiple groups ut tht pproh les to joint esign of user orering n user grouping. To erese the omplexity in user orering n user grouping, multi-ntenn NOMA SC SIC n SC SIC per group) fores users elonging to the sme group to shre the sme preoer emforming vetor) []. Unfortuntely, suh restrition n only further hurt the overll performne sine it shrins the overll optimiztion spe. Fourth, multi-ntenn NOMA is sujet to the sme rw s SDMA in the presene of imperfet CSIT, nmely its esign is not motivte y ny funmentl limitsofmisobcwithimperfetcsit. The ey is to reognize tht the limittions n rws of SDMA n NOMA originte from the ft tht those two multiple esses funmentlly rely on two extreme interferene mngement strtegies, nmely fully tret interferene s noise n fully eoe interferene. Inee, while NOMA relies on some users to fully eoe n nel interferene rete y other users, SDMA relies on fully treting ny resiul multi-user interferene s noise. In the presene of imperfet CSIT, CSIT inury results in n itionl multi-user interferene tht is trete s noise y oth NOMA SC SIC per group) n SDMA..2 RSMA: riging the extremes In ontrst, with RSMA, we te ifferent route n eprt from the SDMA n NOMA literture n those two extremes of fully eoe interferene n tret interferene s noise. We introue more generl n powerful multiple ess frmewor se on linerly preoe rte splitting RS) t the trnsmitter n SIC t the reeivers. This enles to eoe prt of the interferene n tret the remining prt of the interferene s noise [2]. This pility of RSMA to prtilly eoe interferene n prtilly tret interferene s noise enles to softly rige the two extreme strtegies of fully treting interferene s noise n fully eoing interferene. This ontrsts shrply with SDMA n NOMA tht exlusively rely on the two extremes or omintion thereof. In orer to prtilly eoe interferene n prtilly tret interferene s noise, RS splits messges into ommon 6 n privte messges n relies on superimpose trnsmission of ommon messges eoe y multiple users n privte messges eoe y their orresponing users n trete s noise y o-sheule users). Users rely on SIC to first eoe the ommon messges efore essing the privte messges. By justing the messge split n the power llotion to the ommon n privte messges, RS hs the ility to softly rige the two extreme of fully tret interferene s noise n fully eoe interferene. The ie of RS tes to Crleil s wor n the Hn n Koyshi HK) sheme for the two-user singlentenn interferene hnnel IC) [25]. However, the use of RS s the uiling lo of RSMA is motivte y reent wors tht hve shown the enefit of RS in multintenn BC n the reent progress on hrterizing the funmentl limits of multi-ntenn BC n IC) with imperfet CSIT. Hene, importntly, in ontrst with the onventionl RS HK sheme) use for the two-user SISO IC, we here use RS in ifferent setup, nmely ) in BC n 2) with multiple ntenns. The use n enefits of RS in multi-ntenn BC only ppere in the lst few yers 7. The pity region of the K-user MISO BC with imperfet CSIT remins n open prolem. As n lterntive, reent progress hs een me to hrterize the DoF region of the unerloe n overloe MISO BC with imperfet CSIT. In [26], novel informtion theoreti upperoun on the sum DoF of the K-user unerloe MISO BC with imperfet CSIT ws erive. Interestingly, this sum DoF oinies with the sum DoF hieve y linerly preoe RS strtegy t the trnsmitter with SIC t the reeivers [27, 28]. RS with SIC) is therefore optimum to hieve the sum DoF of the K-user unerloe MISO BC with imperfet CSIT, in ontrst with MU LP tht is lerly suoptimum n so is SC SIC sine it hieves sum DoF of unity 8 )[28]. It turns out tht RS with flexile power llotion is not only optimum for the sum DoF ut for the entire DoF region of n unerloe MISO BC with imperfet CSIT [29]. The DoF enefit of RS in imperfet CSIT settings were lso shown in more omplite unerloe networs with multiple trnsmitters in [30] n multi-ntenn reeivers [3]. Consiering user firness, the optimum symmetri DoF or mx-min DoF), i.e., the DoF tht n e hieve y ll users simultneously, of the unerloe MISO BC with imperfet CSIT with MU LP n RS ws stuie in [32]. RS symmetri DoF ws shown to outperform tht of MU LP. Finlly, moving to the overloe MISO BC with heterogeneous CSIT qulities, multi-lyer power prtitioning strtegy tht superimposes egre symols on top of linerly preoe rte-splitte symols ws shown in [33] to hieve the optiml DoF region. TheenefitsofRShvelsoppereinmulti-ntenn settings with perfet CSIT. In n overloe multigroup multist setting with perfet CSIT, onsiering gin firness, the symmetri DoF hieve y RS, MU LP, n egre NOMA trnsmissions where reeivers eoe messges n nel interferene in suessive mnner s in SC SIC) ws stuie in [34]. It ws shown tht RS here gin outperforms oth MU LP n SC SIC. The DoF metri is insightful to ientify the multiplexing gins of the MISO BC t high SNR ut fils to pture

5 Mo et l. EURASIP Journl on Wireless Communitions n Networing 208) 208:33 Pge 5 of 54 the iversity of hnnel strengths mong users. This limittion is ountere y the generlize DoF GDoF) frmewor, whih inherits the trtility of the DoF frmewor while pturing the iversity in hnnel strengths [35]. In [36, 37], the GDoF of n unerloe MISO BC with imperfet CSIT is stuie, n here gin, RS is use s prt of the hievility sheme. The DoF GDoF) superiority of RS over MU LP n SC SIC in ll those multi-ntenn settings with perfet n imperfet CSIT) omes from the ility of RS to etter hnle the multi-user interferene y evolving in regime in etween the extremes of fully treting it s noise n fully eoing it. Importntly,therteenhnementsofRSoverMU LP, s preite y the DoF nlysis, re reflete in the finite SNR regime s shown in numer of reent wors. In [38], finite SNR rte nlysis of RS in MISO BC in the presene of quntize fee ws nlyze n it ws shown tht RS enefits from CSI fee overhe reution ompre to MU LP. Using optimiztion methos, the preoer esign of RS t finite SNR ws investigte in [28] for the sum rte n rte region mximiztion with imperfet CSIT, in [32] for mx-min fir trnsmission with imperfet CSIT, n in [34] for multi-group multi-st with perfet CSIT. Moreover, the enefit of RS over MU LP in the finite SNR regime ws shown in mssive MIMO [39], millimeterwve systems [40] n multi-ntenn eployments sujet to hrwre impirments [4]. Finlly, the performne enefits of the power-prtitioning strtegy relying on RS in the overloe MISO BC with heterogeneous CSIT ws onfirme using simultions t finite SNR in the presene of iversity of hnnel strengths [33]. In prtiulr, in ontrst to the RS use in [2, 28, 29, 32 34, 38, 40, 4] tht relies on single ommon messge, [39] s well s [30]) showe the enefits in the finite SNR regime of multi-lyer hierrhil) RS relying on multiple ommon messges eoe y vrious groups of users. In this pper, in view of the limittions of SDMA n NOMA n the ove literture on RS in multi-ntenn BC, we esign novel multiple ess, lle rte-splitting multiple ess RSMA) for ownlin ommunition system 9. RSMA is muh more ttrtive solution performne n omplexity-wise) tht retins the enefits of SDMA n NOMA ut tles ll the forementione limittions of SDMA n NOMA. Consiering MISO BC, we me the following ontriutions. First, we show tht RSMA is more generl lss/frmewor of multi-user trnsmission tht enompsses SDMA n NOMA s speil ses. RSMA is shown to reue to SDMA if hnnels re of similr strengths n suffiiently orthogonl with eh other n to NOMA if hnnels exhiit suffiiently iverse strengths n re suffiiently ligne with eh other. This is the first pper to expliitly reognize tht SDMA n NOMA re oth susets of more generl trnsmission frmewor se on RS 0. Seon, we provie generl frmewor of multilyer RS esign tht enompsses existing RS shemes s speil ses. In prtiulr, the single-lyer RS of [28, 29, 32 34, 38, 40, 4] n the multi-lyer hierrhil n topologil) RS of [30, 39] re speil instnes of the generlize RS strtegy evelope here. Moreover, the use of RS ws primrily motivte y multi-ntenn eployments sujet to multi-user interferene ue to imperfet CSIT in those wors. The enefit of RS in the presene of perfet CSIT n/or iversity of hnnel strengths in multi-ntenn setup, s onsiere in this pper, is less investigte. RS ws shown in [34] to oost the performne of overloe multi-group multi-st. However, no ttempt hs een me so fr to ientify the enefit of RS in multi-ntenn BC with perfet CSIT n/or iversity of hnnel strengths. Thir, we show tht the rte performne rte region, weighte sum-rte with n without QoS onstrints) of RSMA is lwys equl to or lrger thn tht of SDMA n NOMA. Consiering MISO BC with perfet CSIT n no QoS onstrints, RSMA performne omes loser to the optiml DPC region thn SDMA n NOMA. In senrios with QoS onstrints or imperfet CSIT, RSMA lwys outperforms SDMA n NOMA. Sine it is motivte y funmentl DoF nlysis, RSMA is lso optiml from DoF perspetive in oth perfet n imperfet CSIT n therefore optimlly exploit the sptil imensions n the vilility of CSIT, in ontrst with SDMA n NOMA tht re suoptiml. Fourth, we show tht RSMA is muh more roust thn SDMA n NOMA to user eployments, CSIT inury, n networ lo. It n operte in wie rnge of prtil eployments involving senrios where the user hnnels re neither orthogonl nor ligne n exhiit similr strengths or iversity of strengths, where the CSI is perfetly or imperfetly nown to the trnsmitter, n where the networ lo n vry etween the unerloe n the overloe regimes. In prtiulr, in the overloe regime, the RSMA frmewor is shown to e prtiulrly suite to ope with vriety of evie pilities, e.g., high-en evies long with hep Internetof-Things IoT)/Mhine-Type Communitions MTC) evies. Inee, the RS frmewor n e use to p the IoT/MTC trffi in the ommon messge, while still elivering high-qulity servie to high-en evies. Fifth, we show tht the performne gin n ome with lower omputtionl omplexity thn NOMA for oth the trnsmit sheuler n the reeivers. In ontrst to NOMA tht requires omplite user grouping n orering n potentil ynmi swithing etween SDMA, SC SIC n SC SIC per group) t the trnsmit

6 Mo et l. EURASIP Journl on Wireless Communitions n Networing 208) 208:33 Pge 6 of 54 sheuler n multiple lyers of SIC t the reeivers, simple one-lyer RS tht oes not require ny user orering, grouping, or ynmi swithing t the trnsmit sheuler n single lyer of SIC t the reeivers still signifintly outperforms NOMA. In ontrst to SDMA, RSMA is less sensitive to user piring n therefore oes not require omplex user sheuling n piring.however, RSMA omes with slightly higher enoing omplexity thn SDMA n NOMA ue to the enoing of the ommon strems on top of the privte strems. Sixth, though SC SIC is optiml to hieve the pity region of SISO BC, we show tht single-lyer RS is lowomplexity lterntive tht only requires single lyer of SIC t eh reeiver n hieves lose to SC SIC with multi-lyer SIC) performne in SISO BC eployment. As tewy messge, we note tht the ility of wireless networ rhiteture to prtilly eoe interferene n prtilly tret interferene s noise n le to enhne throughput n QoS, inrese roustness, n lowere omplexity ompre to lterntives tht re fore to operte in the extreme regimes of fully treting interferene s noise n fully eoing interferene. It is lso worth ming the nlogy with other types of hnnels where the ility to rige the extremes of treting interferene s noise n fully eoing interferene hs ppere. Consiering two-user SISO IC, interferene is fully eoe in the strong interferene regime n is trete s noise in the we interferene regime. Between those two extremes, interferene is neither strong enough to e fully eoe nor we enough to e trete s noise. The est nown strtegy for the two-user SISO IC is otine using RS so-lle HK sheme). RS in this ontext is well nown to e superior to strtegies relying on fully treting interferene s noise, fully eoing interferene, or orthogonliztion TDMA, FDMA) [25, 35]. Limiting ourselves to those extremes strtegies is suoptiml [25, 35]. The rest of the pper is orgnize s follows. The system moel is esrie in Setion 2. The existing multiple esses re speifie in Setion 3. In Setion 4, the propose RSMA n its low-omplexity strutures re esrie n ompre with existing multiple esses. The orresponing weighte sum rte WSR) prolems re formulte, n the weighte MMSE WMMSE) pproh to solve the prolem is isusse. Numeril results re illustrte insetion 5, followe y onlusions n future wors in Setion 6. Nottions: The olfe upperse n lowerse letters re use to represent mtries n vetors. The supersripts ) T n ) H enote trnspose n onjugtetrnspose opertors, respetively. tr ) n ig ) re the tre n igonl entries, respetively. is the solute vlue, n is the Eulien norm. E{ } refers to the sttistil expettion. C enotes the omplex spe. I n 0 stn for n ientity mtrix n n ll-zero vetor, respetively, with pproprite imensions. CNδ, σ 2 ) represents omplex Gussin istriution with men δ n vrine σ 2. A is the rinlity of the set A. 2 Systemmoel Consier system where se sttion BS) equippe with N t ntenns serves K single-ntenn users. The users reinexeythesetk = {,..., K}. Letx C N t enotes the signl vetor trnsmitte in given hnnel use. It is sujet to the power onstrint E{ x 2 } P t. The signl reeive t user- is y = h H x + n, K ) where h C Nt is ) the hnnel etween the BS n user-. n CN 0, σn, 2 is the itive white Gussin noise AWGN) t the reeiver. Without loss of generlity, we ssume the noise vrines re equl to one for ll users. The trnsmit SNR is equl to the totl power onsumption P t. We ssume CSI of users is perfetly nown t the BS in the following moel. The imperfet CSIT senrio will e isusse in the propose lgorithm n the numeril results. Chnnel stte informtion t the reeivers CSIR) isssumetoeperfet. In this wor, we re intereste in emforming esigns for signl x t the BS. Speifilly, the ojetive of emforming esigns is to mximize the WSR of users sujet to power onstrint of the BS n QoS onstrints of eh user. We firstly stte n ompre two seline multintenn multiple esses, nmely SDMA n NOMA. Then, RSMA is expline. The WSR prolem of eh strtegy will e formulte, n the lgorithm opte to solve the orresponing prolem will e stte in the following setions. 3 SDMA n NOMA In this setion, we esrie two seline multiple esses. The messges W,..., W K intene for users to K, respetively, re enoe into K inepenent t strems s =[ s,..., s K ] T inepenently. Symols re mppe to the trnsmit ntenns through preoing mtrix enote y P =[ p,..., p K ], where p C Nt is the preoer for user-. The superpose signl is x = Ps = K p s. Assuming tht E{ss H } = I, the trnsmit power is onstrine y trpp H ) P t. 3. SDMA SDMA se on MU LP is well-estlishe multiple ess. Eh user only eoes its esire messge y treting interferene s noise. The signl-to-interfereneplus-noise rtio SINR) t user- is given y γ = h H p 2 j =,j K hh p j )

7 Mo et l. EURASIP Journl on Wireless Communitions n Networing 208) 208:33 Pge 7 of 54 For given weight vetor u = [u,..., u K ],thewsr hieve y MU LP is R MU LP u) = mx u R P s.t. K tr PP H) P t R R th, K where R = log 2 + γ ) isthehievlerteofuser-. u is non-negtive onstnt whih llows resoure llotion to prioritize ifferent users. R th ounts for ny potentil iniviul rte onstrint for user-. Itensures the QoS of eh user. The WMMSE lgorithm propose in [42] is opte to solve prolem 3). The min ie of the WMMSE lgorithm is to reformulte the WSR prolem into its equivlent WMMSE prolem n solve it using the lternting optimiztion AO) pproh. The rte region of the MU LP strtegy is pproximte y R MU LP u) for ifferent rte weight vetors u. The resulting rte region R MU LP is the onvex hull enlosing the resulting points. In generl, solution to prolem 3) woul provie the optiml MU LP emforming strtegy for ny hnnel eployment in etween ligne n orthogonl hnnels n with similr or iverse hnnel strengths). 3.2 NOMA NOMA relies on superposition oing t the trnsmitter n suessive interferene nelltion t the reeiver. As isusse in the introution, the two min strtegies in multi-ntenn NOMA re the SC SIC n SC SIC per group. SC SIC n e trete s speil se of SC SIC per group where there is only one group of users SC SIC In SC SIC, the preoers n eoing orers hve to e optimize jointly. The eoing orer is vitl to the rte otine t eh user. To mximize the WSR, ll possile eoing orers of users re require to e onsiere. Denote π s one of the eoing orers, the messge of user-π) is eoe efore the messge of user-πj), j. The messges of user-π), i re eoe t user-πi) using SIC. The SINR experiene t user-πi) to eoe the messge of user-π), i is given y γ πi) π) = 3) h H πi) p π) 2 j>,j K hh πi) p πj) ) For given weight vetor u = [u,..., u K ] n fixe eoing orer π, the WSR hieve y SC SIC is R SC SIC u, π) = mx u π) R π) P s.t. K tr PP H) P t R R th, K 5) where R π) = min i,i K {log 2 + γ πi) π) )}. In [4], the prolem 5) with equl weights is solve y the pproximtion tehnique minoriztion-mximiztion lgorithm MMA). To eep single n unifie pproh to solve the WSR prolem of ifferent emforming strtegies, we still use the WMMSE lgorithm to solve it. By pproximting the rte region with set of rte weights,therteregionr SC SIC π) with ertin eoing orer π is ttine. To hieve the rte region of SC SIC, ll eoing orers shoul e onsiere. The lrgest hievle rte region of SC SIC is efine s the onvex hull of the union over ll eoing orers s R SC SIC = onv π R SC SIC π)) SC SIC per group Assuming the K users re ivie into G groups, enote s G ={,..., G}. In eh group, there is suset of users K g, g G. The user groups stisfy the following onitions: K g K g =,ifg = g,n g G G g =K.Denote π g s one of the eoing orers of the users in K g,the messge of user-π g ) is eoe efore the messge of user-π g j), j. The messges of user-π g ), i re eoe t user-π g i) using SIC. The SINR experiene t user-π g i) to eoe the messge of user-π g ), i is given y γ πg i) π g ) = h H π g i) p π g ) 2 j>,j K g h H π g i) p π g j) 2 + I πg i) +, 6) j K g hh π g i) p j 2 is the inter- where I πg i) = g G,g =g group interferene suffere t user-π g i). For given weight vetor u =[ u,..., u K ], fixe grouping metho G nfixeeoingorerπ ={π,..., π G },thewsr hieve y SC SIC per group is R group SC SIC u, G, π) = mx P s.t. tr PP H) P t u πg )R πg ) g G K g R R th, K where R πg ) = min i,i Kg {log 2 + γ πg i) π g ))}. Similrly to the SC SIC strtegy, the prolem n e solve y using the WMMSE lgorithm. To mximize the WSR, ll possile grouping methos n eoing orers shoul e onsiere. Remr : As esrie in the introution, it is ommon in the multi-ntenn NOMA literture SC SIC n SC SIC per group) to fore users elonging to the sme group to shre the sme preoer, so s to erese the omplexity in user orering n user grouping. Note tht, in the system moel esrie for oth SC SIC n SC SIC per group, we onsier the most generl frmewor where eh 7)

8 Mo et l. EURASIP Journl on Wireless Communitions n Networing 208) 208:33 Pge 8 of 54 messge is preoe y its own preoer. Hene, we here o not onstrin symols to e superimpose on the sme preoer s this woul further reue the performne of NOMA strtegies n therefore leing to even lower performne. Hene, the performne otine with NOMA in this wor n e seen s the est possile performne hieve y NOMA. 4 Methos propose rte-splitting multiple ess In this setion, we firstly introue the ie of RS y introuing two-user exmple K = 2) n threeuser exmple K = 3). Then, we propose the generlize frmewor of RS n speify two low-omplexity RS strtegies. We further ompre RSMA with SDMA n NOMA from the funmentl struture n omplexity spets. Finlly, we isuss the generl optimiztion frmewor to solve the WSR prolem. 4. Two-user exmple We first onsier two-user exmple. There re two messges W n W 2 inteneforuser-nuser-2, respetively. The messge of eh user is split into two prts, { W 2, W } { for user- n W 2 2, W 2 2 } for user-2. The messges W 2, W 2 2 re enoe together into ommon strem s 2 using oeoo shre y oth users. Hene, s 2 is ommon strem require to e eoe y oth users. The messges W n W 2 2 re enoe into the privte strem s for user- n s 2 for user-2, respetively. The overll t strems to e trnsmitte se on RS is s =[ s 2, s, s 2 ] T. The t strems re linerly preoe vi preoer P =[ p 2, p, p 2 ],wherep 2 C N t is the preoer for the ommon strem s 2. The resulting trnsmit signl is x = Ps = p 2 s 2 + p s + p 2 s 2. We ssume tht tr ss H) = I, n the totl trnsmit power is onstrine y tr PP H) P t. At user sies, oth user- n user-2 firstly eoe the t strem s 2 y treting the interferene from s n s 2 s noise. Therefore, eh user eoes prt of the messge of the other interfering user enoe in s 2. The interferene is prtilly eoe t eh user. The SINR of the ommon strem t user- is h γ 2 H = p 2 2 h H p 2 + h H p ) One s 2 is suessfully eoe, its ontriution to the originl reeive signl y issutrte.aftertht,user- eoes its privte strem s y treting the privte strem of user-j j = ) s noise. The two-user trnsmission moel using RS is shown in Fig.. The SINR of eoing the privte strem s t user- is h H γ = p 2. 9) h H p j 2 + The orresponing hievle rtes of user- for the strems s 2 n s re R 2 ) = log 2 + γ 2 n R = log 2 + γ ).Toensurethts 2 is suessfully eoe y oth users, the hievle ommon rte shll not exee R 2 = min { R 2, } R2 2. All ounry points for thetwo-userrsrteregionneotineyssuming tht R 2 is shre etween users suh tht C 2 is the th user s portion of the ommon rte with C 2 + C2 2 = R 2. Following the two-user RS struture esrie ove, the totl hievle rte of user- is R,tot = C 2 + R.For given pir of weights u = [u, u 2 ], the WSR hieve y the two-user RS pproh is R RS2 u) = mx u R,tot + u 2 R 2,tot 0) P, s.t. C 2 + C2 2 R 2 0) tr PP H) P t 0) R,tot R th, {, 2} 0) 0 0e) where = [ C 2, ] C2 2 is the ommon rte vetor require to e optimize in orer to mximize the WSR. For Fig. Two-user trnsmission moel using RS

9 Mo et l. EURASIP Journl on Wireless Communitions n Networing 208) 208:33 Pge 9 of 54 fixe pir of weights, prolem 0) nesolveusing the WMMSE pproh in [28], exept we hve perfet CSIT here. By lulting R RS2 u) for set of ifferent rte weights u, we otin the rte region. In ontrst to MU LP n SC SIC, the RS sheme esrie ove offers more flexile formultion. In prtiulr, inste of hr swithing etween MU LP n SC SIC, it llows oth to operte simultneously if neessry, n hene smoothly riges the two. In the extreme of treting multi-user interferene s noise, RS oils own to MU LP 2 y simply lloting no power to the ommon strem s 2. In the other extreme of fully eoing interferene, RS oils own to SC SIC y foring one user, sy user-, to fully eoe the messge of the other user, sy user-2. This is hieve y lloting no power to s 2, enoing W into s n enoing W 2 into s 2,suhtht x = p 2 s 2 + p s. User- n user-2 eoe s 2 y treting s s noise n user- eoes s fter neling s 2.A physil-lyer multisting strtegy is otine y enoing oth W n W 2 into s 2 n lloting no power to s n s 2. Remr 2 : It shoul e note tht while the RS trnsmit signl moel resemles rosting system with unist privte) strems n multi-st strem, the role of the ommon messge is funmentlly ifferent. The ommon messge in unist-multi-st system rries puli informtion intene s whole to ll users in the system, while the ommon messge s 2 in RS enpsultes prts of privte messges, n is not entirely require y ll users, lthough eoe y the two users for interferene mitigtion purposes [2]. Remr 3 : A generl frmewor is opte where potentilly eh user n split its messge into ommon n privte prts. Note however tht epening on the ojetive funtion, it is sometimes not neee for ll users to split their messges. For instne, for sum-rte mximiztion sujet to no iniviul rte onstrint, it is suffiient to hve only one user to split its messge [28]. However, when it omes to stisfying some firness WSR, QoS onstrint, mx-min firness), splitting the messge of multiple users ppers neessry [28, 32, 34]. 4.2 Three-user exmple We further onsier three-user exmple. Different from the { two-user se, the messge of user- is split into W 23, W 2, W 3, W }. Similrly, the messge of user- 2 n user-3 is split into { W2 23, W2 2, W 2 23, W 2 2 } { n W 23 3, W3 3, W 3 23, W 3 3 }, respetively. The supersript represents speifi group of users whose messges with the sme supersript re going to e enoe together. For exmple, W 23, W2 23,nW3 23 re enoe into the ommon strem s 23 intene for ll the three users. W 2 n W 3 re orresponingly enoe with the split messges of user-2 W2 2 n user-3 W3 3 into t strems s 2 n s 3. s 2 is the prtil ommon strem intene for user- n user-2. Hene, user- n user-2 will eoe s 2 while user-3 will eoe its intene strems y treting s 2 s noise. Similrly, we otin s 23 prtilly enoe for user- 2nuser-3.W, W 2 2,nW 3 3 re enoe into privte strems s, s 2,ns 3,respetively. The vetor of t strems to e trnsmitte is s = [s 23, s 2, s 3, s 23, s, s 2, s 3 ] T. After liner preoing using preoer P = [p 23, p 2, p 3, p 23, p, p 2, p 3 ], the signls re superpose n rost. The eoing proeure when K = 3 is more omplex ompring with tht in the two-user exmple. The min ifferene lies in eoing prtil ommon strems for two-users. Define the strems to e eoe y l users s l-orer strems. The 2-orer strems to e eoe t user- re s 2 ns 3. The 2-orer strems to e eoe t user-2 n user-3 re s 2 ns 23 n s 3 ns 23,respetively.As the -orer n 2-orer strems to e eoe t ifferent users re not the sme, we te user- s n exmple. The eoing proeure is the sme for other users. User- eoes four strems s 23, s 2, s 3,ns se on SIC while treting other strems s noise. The eoing proeure strts from the 3-orer strem ommon strem) n progresses ownwrs to the -orer strem privte strem). Speifilly, user- first eoes s 23 n sutrts its ontriution from the reeive signl. The SINR of the strem s 23 t user- is γ 23 = i {2,3,23} h H p 23 2 h H p i = h H p 2 +. ) After tht, user- eoes two strems s 2, s 3 n trets interferene of s 23 s noise. Both eoing orers of eoing s 2 followe y s 3 n s 3 followe y s 2 shoul e onsiere in orer to mximize the WSR. Denote π l s one of the eoing orer to eoe l-orer strems. There is only one -orer strem n one 3-orer strem to e eoe t eh user. Therefore, only one eoing orer exists for oth π n π 3.Inontrst, eh user is require to eoe two 2-orer strems. Denote s π2, i) s the ith t strem to e eoe t user- se on the eoing orer π 2. One instne of π 2 is , where s 2 is eoe efore s 3 n s 3 is eoe efore s 23 t ll users. Sine only t strems s 2 n s 3 re eoe t user-, the eoing orer t user- se on π 2 is π 2, = 2 3. Hene, s π2, ) = s 2 n s π2, 2) = s 3. The t strem s π2, ) is eoe efore s π2, 2). The SINRs of eoing strems s π2, ) n s π2, 2) t user- re

10 Mo et l. EURASIP Journl on Wireless Communitions n Networing 208) 208:33 Pge 0 of 54 γ π 2,) = γ π 2,2) = h H p π 2, ) 2 h H p π 2, 2) 2 + h H p = h H p ) h H p π2, 2) 2 h H p = h H p ) User- finlly eoes s y treting other t strems s noise. The three-user RS trnsmission moel with the eoing orer π 2 = is shown in Fig. 2. TheSINRofeoings t user- is h H γ = p 2 h H p =2 h H p ) The orresponing rte of eh t strem is lulte in the sme wy s in the two-user exmple. To ensure tht s 23 is suessfully eoe y ll users, the hievle ommon rte shll not exee R 23 = min { R 23, R 23 2, R 23 } 3.Toensurethts2 is suessfully eoe y user- n user-2, the hievle ommon rte shll not exee R 2 = min { R 2, } R2 2. Similrly, we hve R 3 = min { R 3 } n R23 = min { R 23 2, } R23 3. All ounry points for the three-user RS rte region n e otine y ssuming tht R 23, R 2, R 3,nR 23 re shre y the orresponing group of users. Denote the portion of the ommon rte llote to user- for the messge s 23 s C 23,wehveC 23 +, R3 3 C C3 23 = R 23. Similrly, we hve C 2 + C2 2 = R 2, C 3 + C3 3 = R 3,nC C3 23 = R 23. Following the three-user RS struture esrie ove, the totl hievle rte of eh user is R,tot = C 23 + C 2 + C3 + R, R 2,tot = C C2 2 + C R 2,nR 3,tot = C C3 3 + C R 3. For given weight vetor u = [u, u 2, u 3 ] n fixeeoingorerπ = [π, π 2, π 3 ], the WSR hieve y the three-user RS pproh is R RS3 u, π) = mx P, 3 u R,tot = 5) s.t. C 23 + C C3 23 R 23 5) C 2 2 R 2 5) C 3 3 R 3 5) C R 23 5e) tr PP H) P t 5f) R,tot R th, {, 2, 3} 5g) 0 5h) where = [ C 23, C2 23, C3 23, C 2, C2 2, C3, C3 3, C23 2, ] C23 3 istheommonrtevetorrequiretoeoptimizein orer to mximize the WSR. By lulting R RS3 u, π) for set of ifferent rte weights u, we otin the rte region R RS3 π) of ertin eoing orer π. The rte region of the three-user RS is hieve s the onvex hull of the union over ll eoing orers s R RS = onv π R RSπ) ). Similr to the two-user se, SC SIC n MU LP re gin esily ientifie s speil su-strtegies of RS y swithing off some of the strems. Prolem 5) is non-onvex n non-trivil. We propose n optimiztion lgorithm in Setion 4.7 to solve it se on the WMMSE pproh. Fig. 2 Three-user trnsmission moel using RS

11 Mo et l. EURASIP Journl on Wireless Communitions n Networing 208) 208:33 Pge of Generlize rte-splitting We further propose generlize RS frmewor for K users. The users re inexe y the set K ={,..., K}. For ny suset A of the users, A K, the BS trnsmits tstrems A to e eoe y the users in the suset A while trete s noise y other users. s A los messges of ll the users in the suset A. The messge intene for user- K)issplits{W A A K, A }.Themessges {W A A} of users with the sme supersript A re enoe together into the strem s A. The strem orer efine in Setion 4.2 is pplie to the generlize RS. The strem orer of t strem s A is A. For given l K, therere K) l istint l-orer strems. For exmple, we hve only one K-orer strem tritionl ommon strem) while we hve K -orer strems privte stems). Define s l C K l ) s the l-orer t strem vetor forme y ll l-orer strems in {s A A K, A =l}. Note tht when l = K, there is single K-orer strem. s K reues to s K. For exmple, when K = 3, the 3-orer strem vetor is s 3 = s 23.The -orer n the 2-orer strem vetors re s = [s, s 2, s 3 ] T n s 2 = [s 2, s 3, s 23 ] T,respetively.Thetstremsre { linerly preoe vi the preoing mtrix P l forme y pa A K, A =l }. The preoe strems re superpose n the resulting trnsmit signl is x = K P l s l = l= K l= A K, A =l p A s A. 6) At user sies, eh user is require to eoe the intene strems se on SIC. The eoing proeure strts from the K-orer strem n then goes own to the -orer strem. A given user is involve in multiple l-orer strems with n exeption of the K-orer n -orer strems. Denote π l s one of the eoing orers to eoe the l-orer t strems s l for ll users. The l-orer strem vetor to e eoe t user- se on ertin eoing orer π l is s πl, = [ H,whereSl, s πl, ),, s πl, S l, )] ={s A A K, A = l, A } is the set of l-orer strems to e eoe t user-. We ssume s πl, i) is eoe efore s πl, j) if i < j. The SINR of user- to eoe the l-orer strem s πl, i) with ertin eoing orer π l is γ π l,i) = hh p π l, i) 2 I πl, i) +, 7) where l I πl, i) = h H p π l, j) 2 + j>i l = + h H p A 2 A K, / A S l, j= h H p π l, j) 2 is the interferene t user- to eoe s πl, i). j>i hh p π l, j) 2 is the interferene from the remining non-eoe l-orer strems in s πl,. l l = S l, j= h H p π l, j) 2 is the interferene from lower orer strems s πl,, l < l to e eoe t user-. A K, / A hh p A 2 is the interferene from the strems tht re not intene for user-. The orresponing hievle rte of user- for the t strem s πl, i) is R π l,i) = log 2 + γ π ) l,i). To ensure tht the strems shre y more thn two users re suessfully eoe y ll users, the hievle rte of eh user in the suset A A K,2 A K) to eoe the A -orer strem s A shll not exee { R A = min R A A }. 8) For given l K, thel-orer strems to e eoe t ifferent users re ifferent. s A is eoe t user- A) se on the eoing orer π A,. R A eomes therteofreeivingstrems A t ll users in the user group A with ertin eoing orer π A. All ounry points for the K-userRSrteregionneotiney ssuming tht R A is shre y ll users in the user group A. Denote the portion of the ommon rte llote to user- A) s C A,wehve A CA = R A. Following the RS struture esrie ove, the totl hievle rte of user- is R,tot = C A + R, 9) A K, A where R istherteofthe-orerstrems.itisintene for user- only. No ommon rte shring is require for R. For given weight vetor u = [u,, u K ] n ertin eoing orer π = {π,..., π K },thewsr hieve y RS is R RS u, π) = mx P, s.t. A C A u R,tot K tr PP H) P t R A, A K R,tot R th, K 0 20) P = [P,..., P K ] is the preoing mtrix of ll orer strems. is the ommon rte vetor forme y { C A A K, A }. For fixe weight vetor, prolem 20) n e solve using the WMMSE pproh isusse in Setion 4.7 y estlishing rte-wmmse reltionships for ll t strems. By lulting R RS u, π) for set of ifferent rte weights u, we otin the rte region R RS π) of ertin eoing orer π. To hieve the rte region, ll eoing orers shoul e onsiere. The pity

12 Mo et l. EURASIP Journl on Wireless Communitions n Networing 208) 208:33 Pge 2 of 54 region of RS is efine s the onvex hull of the union over ll eoing orers s ) R RS = onv R RS π). 2) π 4.4 Struture n low-omplexity rte-splitting The generlize RS esrie in Setion 4.3 is le to provie more room for rte n QoS enhnements t the expense of more lyers of SIC t reeivers. Hene, though the generlize RS frmewor is very generl n n e use to ientify the est possile performne, its implementtion n e omplex ue to the lrge numer of SIC lyers n ommon messges involve. To overome the prolem, we introue two low-omplexity RS strtegies for K users, -lyer RS n 2-lyer hierrhil RS HRS). Those two RS strtegies require the implementtion of one n two lyers of SIC t eh reeiver, respetively lyer RS Inste of trnsmitting ll orer strems, -lyer RS trnsmits the K-orer ommon strem n -orer privte strems. Only one SIC is require t eh reeiver. The { messge of eh user is split into two prts W K, W }, K. The messges W K,..., WK K re jointly enoe into the K-orer strem s K intene to e eoe y ll users. W is enoe into s to e eoe y user- only. The overll t strems to e trnsmitte se on -lyer RS is s = [s K, s,..., s K ] T. The t strems re linerly preoe vi preoer P = [p K, p,..., p K ]. The resulting trnsmit signl is x = Ps = p K s K + K p s.figure3 shows -lyer RS moel. Reers re referre to Fig. in [2] for etile illustrtion of the -lyer RS rhiteture. At user sies, ll users firstly eoe the t strem s K y treting the interferene from s,..., s K s noise. The SINR of the K-orer strem t user- is h H γ K = p 2 K j K h H p j ) One s K is suessfully eoe, its ontriution to the originl reeive signl y issutrte.aftertht,user- eoes its privte strem s y treting the -orer privte strems of other users s noise. The SINR of eoing the privte strem s t user- is h H γ = p 2 j K,j = h H p j ) The orresponing hievle rtes of user- ) for the strems s K n s re R K = log 2 + γ K n R = log 2 + γ ).Toensurethts K is suessfully eoe y ll users, the hievle ommon rte shll not exee R K = min { R K,..., } RK K. RK is shre mong users suh tht C K is the th user s portion of the ommon rte with K CK = R K. Following the two-user RS struture esrie ove, the totl hievle rte of user- Fig. 3 One-lyer RS moel of K users. The ommon strem s K is shre y ll the users

13 Mo et l. EURASIP Journl on Wireless Communitions n Networing 208) 208:33 Pge 3 of 54 is R,tot = C K + R. For given weight vetor u = [u,..., u K ], the WSR hieve y the K-user -lyer RS pproh is R lyerrs u) = mx u R,tot 24) P, K s.t. C K R K 24) K tr PP H) P t R,tot R th, K 0 24) 24) 24e) where = [ C K,..., ] CK K. For given weight vetor, prolem 24) n e solve using the WMMSE pproh in [28]. In ontrst to NOMA, this -lyer RS oes not require ny user orering or grouping t the trnsmitter sie sine ll users eoe the ommon messge using single lyer of SIC) efore essing their respetive privte messges. We lso note tht the -lyer RS is su-sheme of the generlize RS n is super-sheme of MU LP sine y not lloting ny power to the ommon messge, the -lyer RS oils own to MU LP). However, for K > 2, SC SIC n SC SIC per group re not su-shemes of -lyer RS even though they were sushemes of the generlize RS). This explins why, in [2], the uthors lrey ontrste -lyer RS n NOMA n expresse tht the two strtegies nnot e trete s extensions or susets of eh other. This -lyer RS ppere in mny senrios sujet to imperfet CSIT in [28, 29, 32 34, 38, 40, 4] lyer HRS The K users re ivie into G groups G = {,..., G} with K g, g G users in eh group. The user groups stisfy the sme onitions s in Setion Besies the K-orer strem n -orer strems, 2-lyer HRS lso llows the trnsmission of K g -orer strem intene for users in K g. The overll t strems to e trnsmitte se on 2-lyer RS is s = [ s K, s K,..., s KG, s,..., s K ] T. The t strems re linerly preoe vi preoer P = [ p K, p K,..., p KG, p,..., p K ]. The resulting trnsmit signl is x = Ps = p K s K + g G p K g s Kg + K p s. Figure 4 shows n exmple of 2-lyer HRS. The users re ivie into two groups, K ={, 2}, K 2 ={3, 4}. s 234 is 4-orer strem intene for ll the users while s 2 n s 34 re 2-orer strems for users in eh group only. Eh user is require to eoe three strems s K, s Kg, n s. We ssume K g.thetstrems K is eoe first y treting the interferene from ll other strems s noise.thesinrofthek-orer strem t user- is h H γ K = p 2 K g G h H p K 2 g + j K h H p j ) One s K is suessfully eoe, its ontriution to the originl reeive signl y is sutrte. After tht, user- eoes its group ommon strem s Kg y treting other group ommon strems n -orer privte strems s noise. The SINR of eoing the K g -orer strem s Kg t user- is h γ K H g = p K 2 g g G,g =g h H p K g 2 + j K h H p. j ) After removing its ontriution to the reeive signl, user- eoes its privte strem s.thesinrof eoing the privte strem s t user- is γ = g G,g =g h H p 2 h H p K g 2 + j K,j = h H p. j ) The orresponing hievle rtes of user- for the ) strems s K, s Kg, n s re R K = log 2 + γ K, ) R K g = log 2 + γ K g n R = log 2 + γ ).The hievle ommon rte of s K n s Kg shll not exee R K = min { R K,..., } RK K n RKg = min {R K g K g }, respetively. R K is shre mong users suh tht C K is the th user s portion of the ommon rte with K CK = R K. R Kg is shre mong users in the group K g suh tht C K g is the th user s portion of the ommon rte with K g C K g = R Kg. Following the two-user RS struture esrie ove, the totl hievle rte of user- is R,tot = C K + CK g + R,where K g. For given weight vetor u =[ u,..., u K ], the WSR hieve y the K-user 2-lyer HRS pproh is R 2 lyerhrs u) = mx u R,tot 28) P, K s.t. K C K R K 28) C Kg R Kg, g G K g 28) tr PP H) P t 28) R,tot R th, K 28e) 0 28f) where is the ommon rte vetor forme y { C K, C K g K, K g, g G }. For given weight

14 Mo et l. EURASIP Journl on Wireless Communitions n Networing 208) 208:33 Pge 4 of 54 Fig. 4 Two-lyer HRS exmple, K = 4, G = 2, K ={, 2}, K 2 ={3, 4} vetor, prolem 28) n e solve y simply moifying the WMMSE pproh isusse in Setion 4.7. Compring with SC SIC per group where K g lyers of SIC re require t user sies, 2-lyer HRS only requires two lyers of SIC t eh user. Moreover, the user orering issue in SC SIC per group oes not exist in 2-lyer HRS. The strems of higher strem orer will lwys e eoe efore the strems of lower strem orer. Onelyer RS is the simplest rhiteture sine only one SIC is neee t eh user n it is su-sheme of the 2-lyer HRS. We lso note tht we n otin -lyer RS per group from the 2-lyer HRS y not lloting ny power to s K. Note tht SC SIC n SC SIC per group re not neessrily su-shemes of the 2-lyer HRS. The 2-lyer HRS strtegy ws first introue in [39] in the mssive MIMO ontext. 4.5 Enompssing existing NOMA n SDMA A omprison of NOMA, SDMA n RSMA re shown in Tle. Compring with NOMA n SDMA, the most importnt hrteristi of RSMA is tht it prtilly eoes interferene n prtilly trets interferene s noise through the split into ommon n privtes messges. This pility enles RSMA to mintin goo performne for ll user eployment senrios n ll networ los, s it will pper lerer in the numeril results of Setion 5. Let us further isuss how the propose frmewor of generlize RS in Setion 4.3 ontrsts n enompsses NOMA, SDMA, n RS strtegies. We first ompre the four-user MIMO NOMA sheme illustrte in Fig. 5 of [] with the four-user 2-lyer HRS strtegy illustrte in Fig. 4. InFig. 5of[], user- n user-2 re superpose in the sme em. User-3 n user-4 shre nother em. The users re eoe se on SC SIC within eh em. As for the four-user 2-lyer HRS strtegy in Fig. 4, the enoe strems re preoe n trnsmitte jointly to users. If we set the ommon messge s 2 to e enoe y the messge of user-2 only n eoe y oth user- n user-2, the ommon messge s 34 to e enoe y the messge of user-4 n eoe y user-3 n user- 4, we lso set the preoers p 2 n p to e equl, the preoers p 34 n p 3 to e equl, n the preoers of other strems to e 0, then the propose RS sheme reues to the sheme illustrte in Fig. 5 of []. Similrly, the K-user RS moel n e reue to the K-user MIMO NOMA sheme. Therefore, the MIMO NOMA sheme propose in [] is prtiulr se of our RS frmewor. In view of the ove isussions, it shoul now e ler tht SDMA n the multi-ntenn NOMA strtegies isusse in the introution relying on SC SIC n SC SIC per group) re ll speil instnes of the generlize RS frmewor.