Machine Learning Inspired Energy-Efficient Hybrid Precoding for MmWave Massive MIMO Systems

Transcription

1 Machie Learig Ispired Eergy-Efficiet Hybrid Precodig for MmWave Massive MIMO ystems Xiyu Gao, Liglog Dai, Yig u, huagfeg Ha, ad Chih-Li I Tsighua atioal Laboratory for Iformatio ciece ad Techology (TList), Departmet of Electroic Egieerig, Tsighua Uiversity, Beijig, Chia Gree Commuicatio Research Ceter, Chia Mobile Research Istitute, Beijig 00053, Chia Abstract Hybrid precodig is a promisig techique for mmwave massive MIMO systems, as it ca cosiderably reduce the umber of required radio-frequecy () chais without obvious performace loss. However, most of the existig hybrid precodig schemes require a complicated phase shifter etwor, which still ivolves high eergy cosumptio. I this paper, we propose a eergy-efficiet hybrid precodig architecture, where the aalog part is realized by a small umber of switches ad iverters istead of a large umber of high-resolutio phase shifters. Our aalysis proves that the performace gap betwee the proposed hybrid precodig architecture ad the traditioal oe is small ad eeps costat whe the umber of ateas goes to ifiity. The, ispired by the cross-etropy (CE) optimizatio developed i machie learig, we propose a adaptive CE (ACE)-based hybrid precodig scheme for this ew architecture. It aims to adaptively update the probability distributios of the elemets i hybrid precoder by miimizig the CE, which ca geerate a solutio close to the optimal oe with a sufficietly high probability. imulatio results verify that our scheme ca achieve the ear-optimal sum-rate performace ad much higher eergy efficiecy tha traditioal schemes. I. ITRODUCTIO Millimeter-wave (mmwave) massive multiple-iput multiple-output (MIMO) has bee cosidered as a promisig techology for future 5G wireless commuicatios [], sice it ca provide wider badwidth [] ad achieve higher spectral efficiecy [3]. However, i MIMO systems, each atea usually requires a dedicated radio-frequecy () chai (icludig high-resolutio digital-to-aalog coverter, mixer, etc.) to realize the fully digital sigal processig (e.g., precodig) [4]. For mmwave massive MIMO, this will result i uaffordable hardware complexity ad eergy cosumptio, as the umber of ateas becomes huge ad the eergy cosumptio of chai is high [5]. To reduce the umber of required chais, hybrid precodig has bee recetly proposed [6]. Its ey idea is to decompose the fully digital precoder ito a large-size aalog beamformer (realized by the aalog circuit) ad a small-size digital precoder (requirig a small umber of chais). Thas to the low-ra characteristics of mmwave chaels [], a small-size digital precoder ca achieve the spatial multiplexig gais, maig hybrid precodig ejoy the ear-optimal performace [5]. evertheless, most of the existig hybrid precodig schemes require a complicated phase shifter etwor, where each chai is coected to all ateas with high-resolutio phase shifters [6], [7]. Although this architecture ca provide high desig freedom to achieve the ear-optimal performace, it requires hudreds or eve thousads of high-resolutio phase shifters with high hardware cost ad eergy cosumptio [5]. To solve this problem, two categories of schemes have bee proposed very recetly. The first category is to directly employ fiite-resolutio phase shifters istead of high-resolutio phase shifters [8], [9]. It ca reduce the eergy cosumptio of phase shifter etwor without obvious performace loss, but it still requires a large umber of phase shifters with cosiderable eergy cosumptio. The secod category is to utilize the switch etwor to replace the phase shifter etwor [0] []. It ca sigificatly reduce the hardware cost ad eergy cosumptio, but it suffers from a obvious performace loss. I this paper, we propose a switch ad iverter (I)- based hybrid precodig architecture with cosiderably reduced hardware cost ad eergy cosumptio. Istead of usig phase shifters, the aalog part of the proposed architecture is realized by a small umber of eergy-efficiet switches ad iverters. The, we provide the performace aalysis to quatify the performace gap betwee the proposed hybrid precodig architecture ad the traditioal oes. After that, ispired by the crossetropy (CE) optimizatio developed i machie learig [3], we propose a adaptive CE (ACE)-based hybrid precodig scheme for this ew architecture. pecifically, accordig to the probability distributios of the elemets i hybrid precoder, this scheme first radomly geerates several cadidate hybrid precoders. The, it adaptively weights these cadidate hybrid precoders accordig to their achievable sum-rates, ad refies the probability distributios of elemets i hybrid precoder by miimizig the CE. Repeatig such procedure, we ca fially geerate a hybrid precoder close to the optimal oe with a sufficietly high probability. imulatio results verify that our scheme ca achieve the ear-optimal sum-rate performace ad much higher eergy efficiecy tha traditioal schemes. otatio: Lower- ad upper-case boldface letters deote vectors ad matrices, respectively; ( ) T, ( ) H, ( ), tr ( ), ad F deote the traspose, cojugate traspose, iversio, trace, ad Frobeius orm of a matrix, respectively; deotes the absolute operator; E( ) deotes the expectatio; deotes the roecer product; I is the idetity matrix. II. YTEM MODEL I this paper, we cosider a typical mmwave massive MI- MO system, where the base statio (B) employs ateas /7/$ IEEE

2 ad chais to simultaeously serve K sigle-atea users (the extesio to users with multiple-ateas is also possible as will be explaied later). To fully achieve the multiplexig gais, we assume = K [9]. For hybrid precodig systems as show i Fig., the K received sigal vector y for all K users ca be preseted by y = HF F BB s +, () Digital precoder chai chai Fiite-resolutio phase shifters where H =[h, h,, h K ] H is the chael matrix with h presetig the chael vector betwee the B ad the th user, s is the K trasmitted sigal vector for all K users satisfyig E ( ss H) = I K, F of size is the aalog beamformer realized by aalog circuit (differet architectures icur differet hardware costraits as will be discussed later), F BB is the basebad digital precoder of size K satisfyig the total trasmit power costrait as F F BB F = ρ, where ρ is total trasmit power. Fially, C ( ) 0,σ I K of size K is the additive white Gaussia oise (AWG) vector, where σ presets the oise power. For the chael vector h of the th user, we adopt the geometric chael model to capture the characteristics of mmwave massive MIMO chaels as [5] h = L L l= ( ) α (l) a ϕ (l),θ(l), () where L deotes the umber of paths for user, α (l) ad ϕ (l) (θ (l) ) for l L are the complex gai ad azimuth (elevatio) agle of departure (AoD) of the path l for user, a (ϕ, θ) presets the array steerig vector. For the typical uiform plaar array (UPA) with elemets i horizo ad elemets i vertical ( = ), we have [6] a (ϕ, θ) =a az (ϕ) a el (θ), (3) [ where a az (ϕ) = ] e jπi(d T /λ)siϕ for i I( ), [ a el (θ) = ] e jπj(d T /λ)siθ for j I( ), I () ={0,,, }, λ is the sigal wavelegth, ad d (d ) is the horizotal (vertical) atea spacig. At mmwave frequecies, we usually have d = d = λ/ [4]. III. EERGY EFFICIET HYBRID PRECODIG I this sectio, we first describe the proposed I-based hybrid precodig architecture. The, we propose a ACEbased hybrid precodig scheme for this ew architecture. Fially, the complexity aalysis is provided. A. The proposed I-based hybrid precodig architecture Fig. (a) ad (b) show the traditioal precodig architectures, i.e., the oe with fiite-resolutio phase shifters (Pbased architecture) [9] ad the oe with switches (W-based architecture) [], respectively. As show i Fig. (a), the traditioal P-based architecture requires a complicated phase shifter etwor, ad the correspodig eergy cosumptio ca be preseted as P P architecture = ρ + P + P P + P BB, (4) Digital precoder Digital precoder (a) (b) (c) Aalog beamformer witches Aalog beamformer Iverters ad switches Aalog beamformer Fig.. Hybrid precodig: (a) traditioal P-based architecture; (b) traditioal W-based architecture; (c) proposed I-based architecture. where P, P P, ad P BB are the eergy cosumptio of chai, fiite-resolutio phase shifter, ad basebad, respectively. ote that although the P-based architecture ejoys high desig freedom to achieve the earoptimal performace [9], it requires a large umber (e.g., =64 6 = 04 [9]) of phase shifters. Moreover, the eergy cosumptio of fiite phase shifter is also cosiderable (e.g., P P = 40mW for 4-bit phase shifter []), These mae the traditioal P-based architecture still suffer from high eergy cosumptio [4]. By cotrast, as show i Fig. (b), W-based architecture ca efficietly relieve such problem by employig a small umber ( istead of ) of eergy-efficiet switches. The eergy cosumptio of W-based architecture ca be preseted as P W architecture = ρ + P + P W + P BB, (5) where P W is the eergy cosumptio of switch, which is much lower tha P P (e.g., P W =5mW[]). evertheless,

3 sice oly ateas are active simultaeously, W-based architecture caot fully achieve the array gais of mmwave massive MIMO, leadig to a obvious performace loss [5]. To overcome the problems faced by traditioal architectures, we propose the I-based architecture as show i Fig. (c), which ca be cosidered as a better trade-off betwee the ear-optimal P-based architecture ad the eergy-efficiet W-based architecture. pecifically, i the proposed I-based architecture, each chai is oly coected to a sub atea array with M = / (assumed to be a iteger) ateas istead of all ateas [6]. Moreover, each chai is coected to the sub atea array via oly oe iverter ad M switches istead of phase shifters. The eergy cosumptio of I-based architecture ca be preseted by P I architecture =ρ+ P + P I +P W +P BB, (6) where P I is the eergy cosumptio of iverter. It worth poitig out that the iverters ca be realized by the digital chip with the eergy cosumptio similar to switches (i.e., P I P W ) [5]. As a result, by comparig (4)-(6), we ca coclude that the eergy cosumptio of the proposed Ibased architecture is much lower tha that of P-based oe. Furthermore, as all ateas are used, I-based architecture ca also achieve the potetial array gais of mmwave massive MIMO, which will be further proved as follows. To do this, we eed to first explai the hardware costraits iduced by the proposed I-based architecture, which are differet from those of the traditioal oes. The first costrait is that the aalog beamformer F should be a bloc diagoal matrix istead of a full matrix as f f 0 F =....., (7) f where f is the M aalog beamformer o the th sub atea array. The secod costrait is that sice oly iverters ad switches are used, all the ozero elemets of F should belog to {, +}. (8) Based o these costraits, we have the followig Lemma. Lemma. Assume that the chael h of user oly has sigle path, i.e., L =[]. Whe ad /M =, the ratio ζ betwee the array gais achieved by I-based architecture ad that achieved by P-based architecture with sufficietly high-resolutio phase shifters ca be preseted by 4 lim ζ =, M = π. (9) Proof: For the traditioal P-based architecture with sufficietly high-resolutio phase shifters, the phases of the elemets i the aalog beamformer ca be arbitrarily adjusted to capture the power of h. Therefore, the array gais achieved by P-based architecture is α (). By cotrast, the array gais achieved by I-based architecture ca be preseted by h H f = α () a H (ϕ ) f (0) = α () M e j φ m m= = α () M cos ( ) M φm + si ( ) φm, m= m= where f is the th colum of F icludig the zeros ad φ m deotes the phase quatizatio error. ice the ozero elemets i f belog to {, +}, φm ca be assumed to follow the uiform distributio U ( π/,π/) for m M [0]. The, we have M lim ζ = cos ( ) M φm + si ( ) φm M /M= m= m= = ( [ ( )]) ( [ ( )]) E cos φm + E si φm 4 = π, () which verifies the coclusio i Lemma. Lemma idicates that although the proposed I-based architecture suffers from some loss of array gais compared to the ear-optimal P-based architecture, the performace loss eeps costat ad limited, which does ot grow as the umber of B ateas goes to ifiity. Recallig the low eergy cosumptio of I-based architecture, we ca coclude that our scheme is a better trade-off betwee the traditioal architectures, which will be also verified by simulatio. ext, we will desig a ear-optimal hybrid precodig scheme for Ibased architecture with quite differet hardware costraits. B. ACE-based hybrid precodig scheme We aim to desig the aalog beamformer F ad the digital precoder F BB to maximize the achievable sum-rate R, which ca be preseted as ( F opt, BB) Fopt =argmax R, F,F BB s.t. F F, () F F BB F = ρ, where F deotes the set with all possible aalog beamformers satisfyig the two costraits (7) ad (8) described above, ad the achievable sum-rate R ca be preseted by K R = log ( + γ ), (3) = where γ presets the sigal-to-iterferece-plus-oise ratio (IR) of the th user as h H γ = F f BB, (4) K h H F f BB + σ

4 where f BB is the th colum of F BB. It is worth poitig out that the costraits (7) ad (8) o the aalog beamformer F are o-covex. This maes () very difficult to be solved. Fortuately, as all the ozero elemets of F belog to the set {, +}, the umber of possible F is fiite. Therefore, () ca be regarded as a o-coheret combiig problem [3]. To solve it, we ca first select a cadidate F, ad compute the optimal F BB accordig to the effective chael matrix HF without o-covex costraits. After all possible F s have bee searched, we ca obtai the optimal aalog beamformer F opt ad digital precoder F opt BB. However, such exhaustive search scheme requires to search possible F s ad F BB s, which ivolves uaffordable complexity as is usually large i mmwave massive MIMO systems (e.g., =64, ). To solve this problem, we propose a ACE algorithm, which ca be cosidered as a improved versio of the CE algorithm developed from machie learig [3]. At first, we would lie to briefly itroduce the covetioal CE algorithm, which is a probabilistic model-based algorithm to solve the combiig problem by a iterative procedure. I each iteratio, the CE algorithm first geerates cadidates (e.g., possible hybrid precoders i our problem) accordig to a probability distributio. The, it computes the objective value (e.g., achievable sum-rate i our problem) of each cadidate, ad selects elite best cadidates as elite [3]. Fially, based o the selected elites, the probability distributio is updated by miimizig the CE. Repeatig such procedure, the probability distributio will be refied to geerate a solutio close to the optimal oe with a sufficietly high probability. However, although the CE algorithm has bee widely used i machie learig [3], it still has some disadvatages. Oe is that the cotributios of all elites are treated as the same. Ituitively, the elite with better objective value should be more importat whe we update the probability distributio. Therefore, if we ca adaptively weight the elites accordig to their objective values, better performace ca be expected. Followig this idea, we propose a ACE algorithm to solve (). The pseudo-code of the proposed ACE-based hybrid precodig scheme is summarized i Algorithm, which ca be explaied as follows. At the begiig, we formulate the ozero elemets i F as vector [ ) f = ( f T ), T ) ] ( f, ( f T T, ad set the probability parameter u =[u,u,,u ] T as a vector, where 0 u presets the probability that f =/, f is the th elemet of f. The, by iitializig u (0) = ( is the all-oe vector), we assume that all the ozero elemets of F belog to {, +} with equal probability, sice o priori iformatio is available. Durig the ith iteratio, i step, we first geerate cadidate aalog beamformers {F s } s= based o the probability distributio Ξ ( F; u (i)) (i.e., geerate {f s } s= accordig to u(i), ad reshape them as matrices belog to F). The, i step, we ote that the covergece of the proposed ACE-based hybrid precodig scheme ca be proved by extedig the Theorem i [7]. Iput: Chael matrix H; umber of iteratios I; umber of cadidates ; umber of elites elite. Iitializatio: i =0; u (0) =. for 0 i I. Radomly geerate cadidate aalog beamformers {F s } s= based o Ξ ( F; u (i)) ;. Compute correspodig digital precoders {F s BB } s= based o the effective chael H s eq = HF s ; 3. Calculate the achievable sum-rate {R (F s )} s= (3); 4. ort {R( (F s ) )} s=( i a ) desced order ( as ) R F [] R F [] R F [] ; 5. elect elites as F [], F[],, F[elite] ; 6. Calculate weight w s for each elite F [s], { s } elite; 7. Update u (i+) accordig to {w s } elite s= ad F [s] elite ; s= 8. i = i +; ed for Output: Aalog beamformer F [] ; Digital precoder F[] BB. Algorithm : The proposed ACE-based hybrid precodig calculate the correspodig digital precoder F s BB accordig to the effective chael H s eq = HF s for s. ote that there are lots of advaced digital precoder schemes [3]. I this paper, we adopt the classical ZF digital precoder with the earoptimal performace ad low complexity as the example [3], ad F s BB ca be computed as G s = ( H s ) ( H eq H s ) ) eq( H s H, eq F s BB = β s G s, (5) where β s = ρ/ F s Gs F is power ormalized factor. After that, i step 3, the achievable sum-rate {R (F s )} s= are calculated by substitutig F s ad Fs BB (also a fuctio of F s ) ito (3). We sort {R (Fs )} s= i a desced order i step 4. The, the elites ca be obtaied i step 5. I the covetioal CE algorithm, the ext step is to usig elites to update u (i+) by miimizig CE, which is equivalet to [3] u (i) elite ( l Ξ F [s] ; u(i)), (6) u (i+) =argmax s= ( ) where Ξ F [s] ; u(i) deotes the probability to geerate F [s]. As metioed above, i (6), the cotributios of all elites are treated as the same, leadig to performace degradatio. To solve this problem, we propose to weight each elite adaptively based o its achievable sum-rate. pecifically, we first defie a auxiliary parameter T presetig the average achievable sum-rate of all elites as T = elite elite s= R ( The, the weight ( w s of ) the elite F [s] step 6 as w s = R F [s] modified as F [s] /T. Based o {w s } elite s= s= ). (7) ca be calculated i, (6) ca be u (i+) elite ( =argmax w s l Ξ F [s] u (i) ; u(i)). (8)

5 ( ) ote that Ξ F [s] ; u(i) =Ξ ( f [s] ; u (i)), ad the th elemet f [s] of f [s] is a Beroulli radom variable, where f [s] with probability u (i) ad f [s] u (i). Therefore, we have ( ( ) Ξ F [s] ; u(i)) = u (i) = =/ = / with probability (+ f [s] ) ( u (i) ) ( f [s] ). (9) After substitutig (9) ito (8), the first derivative of the target i (8) with respect to u (i) ca be derived as elite w s + f [s] f [s] ( ). (0) u (i) u (i) s= ettig (0) to zero, u (i+) ca be updated i step 7 as ( elite f ) s= w [s] s + u (i+) = elite s= w s. () uch procedure above will be repeated (i = i + i step 8) util the maximum umber of iteratios I is reached, ad the aalog beamformer ad digital precoder will be selected as F [] ad F[] BB, respectively. Fially, it is worth poitig out that the proposed ACE-based hybrid precodig scheme ca be also exteded to the sceario where users employ multiple ateas. I this case, the aalog beamformers at the B ad users should be joitly searched by the ACE algorithm. C. Computatioal complexity aalysis I this subsectio, the computatioal complexity of the proposed ACE-based hybrid precodig scheme is discussed. From Algorithm, we ca observe that the complexity of the ACE-based hybrid precodig scheme maily comes from steps, 3, 6, ad 7. I step, we eed to compute effective chael matrices { Heq} s ad digital precoders s= {F s BB } s= accordig to (5). Therefore, the complexity of this part is O ( K ). I step 3, the achievable sum-rate of each cadidate is computed. ice we employ the digital ZF precoder, the IR γ s of the th user for the sth cadidate is simplified to γ s =(βs /σ). As a result, this part oly ivolves the complexity O (). I step 6, we calculate elite weights based o (7), which is quite simple with the complexity O ( elite ). Fially, i step 7, the probability parameter u (i+) is updated accordig to () with the complexity O ( elite ). I summary, after I iteratios, the total computatioal complexity of the proposed ACE hybrid precodig scheme is O ( IK ). ice K is usually small, I ad also do ot have to be very large as will be verified i the ext sectio, we ca coclude that the complexity of the proposed ACE-based hybrid precodig scheme is acceptable, which is comparable with the simple least squares (L) algorithm. IV. IMULATIO REULT I this sectio, we provide the simulatio results i terms of achievable sum-rate ad eergy-efficiecy to evaluate the performace of the proposed ACE-based hybrid precodig Fig.. Achievable sum-rate compariso. I Fig. 3. Achievable sum-rate agaist ad I. scheme. The simulatio parameters are described as follows: We assume that the B employs a UPA with atea s- pacig d = d = λ/. For the th user, we geerate the chael h based o (), where we assume: ) L =3;) α (l) C(0, ) for l L ;3)ϕ (l) ad θ (l) follow the uiform distributio U ( π, π) for l L []. Fially, the sigal-to-oise ratio (R) is defied as ρ/σ. Fig. shows the achievable sum-rate compariso i a typical mmwave massive MIMO system with =64, = K =4. I Fig., the proposed CE-based (i.e., usig the covetioal CE algorithm to solve ()) ad ACEbased hybrid precodig schemes are desiged for I-based architecture, where we set = 00, elite =40, ad I =0 for Algorithm, the covetioal two-stage hybrid precodig scheme is desiged for P-based architecture with 4-bit phase shifters [9], ad the covetioal atea selectio (A)-based hybrid precodig scheme is desiged for W-based architecture [] with switches. Firstly, we ca observe from Fig. that the proposed ACE algorithm outperforms the traditioal CE algorithm, where the R gap is about db. ote that the ACE algorithm oly ivolves oe additioal step (i.e., step 6iAlgorithm ) with egligible complexity. Therefore, the proposed ACE algorithm is more efficiet. Moreover, Fig. also shows that the proposed ACE-based hybrid precodig ca

6 K Fig. 4. Eergy efficiecy compariso. achieve the sum-rate much higher tha the covetioal Abased hybrid precodig, as it ca achieve the potetial array gais i mmwave massive MIMO systems. Fially, we ca observe that the performace gap betwee ACE-based hybrid precodig ad two-stage hybrid precodig is limited ad eeps costat, which further verifies the coclusio i Lemma. Fig. 3 shows the achievable sum-rate of the proposed ACEbased hybrid precodig agaist the umber of cadidates ad the umber of iteratios I, whe elite / =0., =64, = K =4, ad R = 0 db. From Fig. 3, we ca observe that whe is small, icreasig will lead to a obvious improvemet i the sum-rate performace. However, whe is sufficietly large, such tred is o loger obvious. This idicates that the umber of cadidates does ot have to be very large, e.g., = 00 is eough. Furthermore, Fig. 3 also idicates that the proposed ACE-based hybrid precodig ca coverge with a small umber of iteratios, e.g., I =0. These observatios verify the ratioality of the parameters for Algorithm we used i Fig.. Fig. 4 shows the eergy efficiecy compariso whe =64 is fixed ad = K varies from to 6. The parameters for Algorithm are the same as Fig.. Accordig to [5], [6], the eergy efficiecy ca be defied as the ratio betwee the achievable sum-rate ad the eergy cosumptio, which should be (4), (5), ad (6) for twostage hybrid precodig, A-based hybrid precodig, ad ACEbased hybrid precodig, respectively. I this paper, we adopt the practical values ρ = 30mW [6], P = 300mW [6], P BB = 00mW [5], P P = 40mW (4-bit phase shifter) [5], ad P W = P I =5mW [5]. From Fig. 4, we ca observe that the proposed ACE-based hybrid precodig with I-based architecture ca achieve much higher eergy efficiecy tha the others, especially whe K is ot very large (e.g., K ). Furthermore, it is iterestig to observe that whe K 8, the eergy efficiecy of the two-stage hybrid precodig with Pbased architecture is eve lower tha that of the fully digital ZF precodig. This is due to the fact that as K grows, the umber of phase shifters i P-based architecture icreases rapidly. As a result, the eergy cosumptio of the phase shifter etwor will be huge, eve higher tha that of chais. V. COCLUIO I this paper, we propose a eergy-efficiet I-based hybrid precodig architecture, where the aalog part is realized by a small umber of switches ad iverters. The performace aalysis proves that the performace gap betwee the proposed I-based architecture ad the traditioal ear-optimal oe eeps costat ad limited. The, by employig the idea of CE optimizatio i machie learig, we further propose a ACEbased hybrid precodig scheme with low complexity for Ibased architecture. imulatio results verify that our scheme ca achieve the satisfyig sum-rate performace ad much higher eergy efficiecy tha traditioal schemes. REFERECE [] A. L. widlehurst, E. Ayaoglu, P. Heydari, ad F. Capolio, Millimeter-wave massive MIMO: The ext wireless revolutio? IEEE Commu. Mag., vol. 5, o. 9, pp. 56 6, ep. 04. [] T.. Rappaport,. u, R. Mayzus, H. Zhao, Y. Azar, K. Wag, G.. Wog, J. K. chulz, M. amimi, ad F. Gutierrez, Millimeter wave mobile commuicatios for 5G cellular: It will wor! IEEE Access, vol., pp , May 03. [3] T. L. Marzetta, ocooperative cellular wireless with ulimited umbers of base statio ateas, IEEE Tras. Wireless Commu., vol. 9, o., pp , ov. 00. [4] H. Xie, F. Gao,. Zhag, ad. Ji, A uified trasmissio strategy for TDD/FDD massive MIMO systems with spatial basis expasio model, to appear i IEEE Tras. Veh. 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