QoE-Aware Beamforming Design for Massive MIMO Heterogeneous Networks

1 QoE-A wa re Beamforming Design for Massi v e MIMO Heterogeneous Networks Hadis Abarghouyi ∗ , S. Mohammad Razavizadeh ∗ , and Emil Bj ¨ ornson † ∗ School of Electrical Engineering, Iran Uni versity of Science and T echnology (IUST), T e hr a n, Iran E-mail: hadis.abarg houyi@gmail.com, smrazavi@ iust.ac.ir † Department of Electrical Engineering (ISY), Link ¨ oping Uni versity , Link ¨ oping, Sweden E-mail: emil.bjornson@liu.s e Abstract One of the main go als of the future wireless networks is improving the users’ quality of experience (QoE). In this pap er , we consider the prob lem of QoE-based resource allocation in the downlink of a massi ve multiple-inpu t multiple-o utput (MIMO) hetero geneou s network (HetNet). The ne twork consists of a macro cell with a number of small cells embed ded in it. The small cells’ base statio n s (BSs) are equippe d with a few antennas, while the macro BS is eq u ipped with a massi ve n umber of antenn as. W e consider the two ser v ices V ideo and W eb Browsing and design the b eamform in g vector s at the BSs. Th e objec ti ve is to maxim ize the aggregated M ean Opinion Score (MOS) of the users und er constraints on th e BSs’ po we rs an d the req uired quality of serv ice (QoS) o f the users. W e a lso consider extra con straints on the QoE of u sers to more stro ngly en force the QoE in the b eamform ing de sign. T o reduce the c o mplexity of the optimization pro blem, we suggest subop timal and computationally efficient solutions. Our re sults illustrate that in creasing the nu mber o f antenn as at th e BSs an d also increasing the nu mber of small cells’ antennas in the network lea d s to a hig her user satisfaction. Index T erms Quality of Experien ce (QoE) , W eb b rowsing, Massi ve MIMO, HetNets, power allocation , mea n opinion score (M OS) , Quality of Ser vice (QoS), video serv ice, 5G. 2 I . I N T R O D U C T I O N In future wi reless networks (or 5G networks) the u s ers will request more d ata traffi c and div erse services than today . T wo important technologies th at ha ve been p ro p o sed for future wireless networks are small cells and massive m ultiple-input mu l tiple-output (MaMIMO). Small cells can be used in com bination with macro cells to form multi-ti er or heterogeneous networks (HetNets) that can provide hig her capacity and quali ty than con ventional homo geneous networks [1]. On the o t her hand, M aMIMO is a technolog y in which base stations (BSs) in a cellular network are equipped with a large number of antennas (up to a fe w hundred) that can sim ultaneously serve a large number of users. M aMIMO can also be deployed i n the HetNets for achieving hi gher performance, which is t h e case t hat we cons ider in this paper . Service and network providers ha ve studied various QoS metrics to optimi ze and enhance their network’ s performance. QoS metrics such as packet loss rate, transfer delay , throughpu t and covera ge are m ainly based on technical performance rather than users’ experience. Recent studies show that although the con ventional t echni cal criteria b ased on the Qo S are impo rtant, they are not suffi cient for m easuring the users’ experience. In fact, the us ers’ perception is af fected b y bot h technical and non t echnical (human-based) parameters [2]. Hence, for assurin g better user experience, service providers ha ve been switching their focus to percei ved end to end qualit y , referred as Quality of Experience (QoE). ITU-T describes QoE as “The overall acceptability of an app l ication or service, as percei ved subjectiv ely by the end-user” [3]. In general, QoE can be ev aluated by subj ective as well as ob j ectiv e methods . The s u bjectiv e methods are based on e valuations given by hu m an feelings about a service. One o f the common subjective assessment methods is based on Mean Opinion Score (MOS) [4]. This p arameter is a real num b er ranging from 1 to 5 which are related to bad, poor , fair , good and excellent, respectiv ely . Despite t heir advantages, the sub j ectiv e assessment s of QoE are usually tim e- consuming, diffic ult, costl y and not real-time [5]. Therefore researchers hav e recently provided some objective QoE assess ments models which are extracted from the QoS parameters. The objective assessment of QoE encompasses communicati on process measurements and could help service p roviders to indi rectly estimate the users’ sati sfaction from t echnical parameters. The equations that relate the QoE to the QoS parameters are obtained by experimental measurements and math ematical analyses [6]-[8]. For example, in [6] the authors use the results of exper imental measurements to establish some m odels such as linear , exponential and l o garithmic functions. 3 In [7], the aut h ors present a M OS model to map the page response time to QoE metrics using a Lorentzian funct i on. In [8], the authors propose models to describe the user perception of web browsing and video servi ce in terms of some Qo S parameters. In wireless networks and especially in MaMIMO HetNets, the con ventional criteria to allocate resources to users or improving the network p erformance are based on the QoS parameters [9]-[10]. Howe ver , recently researchers hav e begun t o examine QoE con cept for optimi zing th e network parameters. For example, in [11] the aut h ors show that the Qo E-based resource allocation is more effic ient than t he QoS-based methods in responding t o users’ demand [12]-[16]. In [12], cooperativ e networks have been studied and t he QoE m etric is used in opt i mizing the relay deployment in the network. In [13], the authors p ropose a Qo E based power allocation method for video streaming over wireless networks. In [14], the authors opti mize th e agg regated MOS of the users in a heterogeneous network consi sted of one femtocell and on e macro-cell. [15 ] proposes a beamforming method t o maxim ize the aggregated MOS in cognitive radio networks. In [16], t he authors in vestigate the QoE i mprovement in a MIMO cognitive network. Howe ver , to the best of ou r knowledge, the QoE criterion has not been taken int o account t o im prove the performance of the M aMIMO HetNets. In thi s paper , we propose a QoE-based joint beamformin g and po w er allocation schem e for th e downlink of a MaMIM O HetNet. The network is providing a web browsing or video st reaming service to its users. These two services are expected to be am ong the b asic services of the futu re 5G networks. Therefore it is important to provide an appropriate lev el of user satisfaction for these services [6]-[7], [17]. The heterogeneous network that we consider in cl u des one macro cell wit h mu l tiple small cells embedded in its cove rage area. The macro base stati on (MBS) is equipped with an array with a large num ber of ant enn as. There are also mu ltiple antennas at the small cell base s t ations (SBSs). T his network serves a num ber of single antenna users. W e try to maximize the QoE of all users b y optimizing the beamforming vectors and provide an efficient algorithm to solve the optimization problem. The o b jectiv e of the optimization problem is to maximize the aggregated MOS of all users i n the network, while s ati sfying constraint s on t h e users’ QoS and t he power of the MBS and the SBSs. In addition, we include other cons traints on the minimu m QoE of t he users t o guarantee a m i nimum user satis faction. Our simulation results s how that install ing small cells in the network (i.e., using HetNet) leads to a higher users’ satisfaction. On the ot h er hand, increasing the number of antennas at the M BS has similar effec ts on the Qo E. These result s can be interesting for the network operators who 4       Fig. 1: Illus tration of a MaMIMO HetN et consisted o f one m acro cell and N s small cells [10]. seek solutio n s to fulfill their user satis faction. In summ ary , t he main contributions of this paper are as follow: • QoE-based Beamformin g design for heterogeneous M aMIMO networks. • Improving QoE for two different s ervices of web browsing and v i deo application. • Considering subjective QoE parameter (MOS) as the objective and constraint of the opti- mization prob l em. • Proposing new s uboptimal b ut ef ficient method to solve two h ard and non-con vex optim i za- tion probl em s. • Presenting th e effect of adding s m all cells to the network or using a large num ber of antennas at the M BSs on the users’ satisfaction in fut u re 5G networks. The rest of th is paper is organized as foll ows: In Section II, we describe the system model. Then we formulate the optimization problems in Section III , to maximize the aggre g ated MOS of the network for the two adopt ed services. In Section IV, we solve the non-con vex op timization problems by con verting them t o equiva lent con vex problems and u sing i terativ e alg orithms. Finally , in Section V, we illus t rate t h e results by numerical examples. Notations : ( . ) H and k . k denote t h e conjugate transpose and Euclid ean norm, respectiv ely . C N ( 0 , R ) d eno tes a circularly-symm etric complex Gaussian random vector with zero mean and cov ariance matri x R . I I . S Y S T E M M O D E L In this paper , we consider the downlink of a t wo-tier MaMIMO HetNet consisting of N s small cells which are deployed in the coverage area of a macro cell as in Fig.1. Th e MBS and SBSs us e non-coherent join t transmiss i on coordinated multip o int beamforming to provide a web 5 browsing or video service for K s ingle antenna users. In thi s technique, the MBS and SBSs cooperate in transferring data t o the users, but ev ery BS sends a separate stream of data. The MBS i s equipped with M antennas and i n this paper we are p ri m arily i n terested in the M aMIMO regime where M ≫ K [10]. The number of antennas at the j th SBS is denoted by N j . As we m entioned earlier , M OS is a qualitative measure for assessing QoE, w h ich can be expressed in terms of some objectiv e parameters [4]. For the adopted applications i n this paper , an experimental relation between the QoE and QoS parameters can be expressed as follows. For web browsing, this relatio n can be expressed as [8], MOS we b = − K 1 ln ( d ( R )) + K 2 . (1) In (1), the constants K 1 and K 2 are selected in such a way that the value of MOS we b falls in the range of 1 to 5 . In additi on, d ( R ) [s] represents the page response time or the delay between a request for a web page and reception of th e entire content of that web page. d ( R ) depends on parameters such as the web page size, roun d trip tim e (R TT) (the tim e int erv al that an IP packet tra vels from the server to the UE and returns [7]), and the t y pe of u t ilized protocols (such as TCP and HTTP) which can be writt en as [8] d ( R ) = 3R TT + FS B · R + L  MSS B · R + R TT  − 2MSS  2 L − 1  B · R , (2) where B [Hz], R [bit/s/Hz], FS [bit] and MSS [bit] are the bandwidth, spectral effi ciency , web page size and maximu m segment size (the IP datagram s i ze excluding the TCP/IP h eader [7]), respectiv ely . L = min[ L 1 , L 2 ] is a parameter that specifies the num ber o f slow start cycles with idle periods (the cycles i n packet exchange between UE and server during web page download [7]), where L 1 and L 2 are defined as [8] L 1 = log 2  1 2 + B · R · R TT 2MSS  , L 2 = log 2  1 2 + FS 4MSS  . (3) For video service (H.264/MPEG-4 V ideo Coding), the MO S is ob tained as [18] MOS video = g log (PSNR) + e, (4) where g and e are two constant s that are selected in such a way that the value of MOS video falls in the range of 1 to 5. PSNR sh ows peak SNR and is defined as PSNR = u + v r B · R r  1 − r B · R  . (5) 6 u , v and r parameters als o characterize a sp ecific video stream. All subchann els between the us ers and the M BS or SBSs are modeled as flat fading channels. The channel between th e k th user and the MBS and between th e k th user and the j th SBS is denoted by h k , 0 ∈ C M × 1 and h k ,j ∈ C N j × 1 , respectively . W e assum e that perfect channel state information is a vailable at the BSs. The transmitted signal vectors from the MBS and the j th SBS are represented by x 0 ∈ C M × 1 and x j ∈ C N j × 1 , respectiv ely . The receiv ed signal at the k th us er is modeled as y k = h H k , 0 x 0 + N s X j = 1 h H k ,j x j + n k , (6) where n k ∼ C N (0 , σ 2 k ( mW )) is the Additive White Gaussi an Noise (A WGN) at t he receiv er . The transm i tted signals x 0 and x j are obt ained by applying appropriate beamformi ng vectors at the BSs as x j = K X l =1 w l,j d l,j , j = 0 . 1 , ..., N s , (7) where w l, 0 ∈ C M × 1 and w l,j ∈ C N j × 1 ( j = 1 , ..., N s ) denote t h e beamforming vectors at t h e MBS and the j th SBS corresponding t o the l th user , respecti vely , d l,j is the information sym bol transmitted to th e l th user by the j th BS ( j = 0 is related to the MBS). It is ass u med that the information sym bols are ind epend ent and ha ve unit power (1 m w). In the following sections, w e show h ow to efficiently design the beamforming vectors and the transm itted power of the base stations. I I I . P RO B L E M F O R M U L A T I O N In this section , to find the opti mum beamforming based on QoE maxim i zation, we con s ider two p roblems corresponding to two different ado p ted services. The target of the t wo probl em s is t o maximize the aggregated MOS of t he users su b j ect to s o me const raints on QoS and Qo E of users. Since the value of R TT in 5G networks is very sm all and we also consider only a few subcarriers, we can ignore it in calcul ati ng the MOS parameter in (1) [8]. Hence, for web services the MOS of k th user can be represented by MOS w eb k ( w ) = K 1 ln  B · R k ( w ) FS k  + K 2 , (8) where w = { w k ,j | k = 1 , ..., K , j = 0 , 1 , ..., N s } is the set of beamformi ng vectors. For video service, we hav e 7 MOS video k ( w ) = g lo g (PSNR( w )) + e, (9) where PSNR( w ) = u + v r B · R k ( w ) r  1 − r B · R k ( w )  . (10) W e also assu me constraint s on the users’ QoS which are defined in terms of the mi nimum required data rate of R k ,min B · R k ( w ) ≥ R k ,min , ∀ k (11) where R k ( w ) = log 2  1 + P N s j = 0 | h H k ,j w k ,j | 2 P N s j = 0 P K l =1 ,l 6 = k | h H k ,j w l,j | 2 + σ 2 k  , (12) is the achiev able sum spectral efficienc y of the k th user , when the us er is decodi ng data streams from th e BSs i n a sequent ial manner using successive int erference cancelatio n [10]. In this paper , we consider t h e per -antenna power constraints at all BSs which is more practical than total power constraints when each antenna has i ts own radio frequency chain [19]. The per - antenna power constraints for the MBS and the j th SBS can also be expressed, respectiv ely , as K X k =1 w H k , 0 D q , 0 w k , 0 ≤ P 0 ,q q = 1 , ..., M , (13) K X k =1 w H k ,j D q ,j w k ,j ≤ P j,q , j = 1 , ..., N s q = 1 , ..., N j , (14) where D q , 0 ∈ C M × M and D q ,j ∈ C N j × N j are positive semidefinite zero weightin g m atrices with only one ′ 1 ′ at t h e q th diagonal element . P 0 ,q and P j,q ( P 0 ,q ≫ P j,q , j = 1 , . . . , N s ) represent the maximum transm i tted powers from the q th antenna of the MBS and the j th SBS, respectiv ely . Our objectiv e is to m aximize the aggregated MOS of all u sers. Howe ver maximizin g a aggregated MOS does not g uarantee t hat every user will be satisfied. Hence Qo E const raints are added to t he problems to mo re st rongly enforce the QoE i n the beamform ing design and ensure fairness between the users. This is done by defining a minimu m s at i sfaction th reshold for each user as below MOS w eb k ( w ) ≥ MOS w eb k ,min , (15) 8 and MOS video k ( w ) ≥ MOS video k ,min . (16) From n ow on, the MOS of k th user for both services are represented by MOS k ( w ) . U s ing (8)-(16), the opt imization problem to determine the beamforming vectors is written as maximize w k,j ∀ k ,j K X k =1 MOS k ( w ) (17) s.t. K X k =1 w H k , 0 D q , 0 w k , 0 ≤ P 0 ,q , q = 1 , ..., M (17.a) K X k =1 w H k ,j D q ,j w k ,j ≤ P j,q , j = 1 , ..., N s (17.b) q = 1 , ..., N j B · R k ( w ) ≥ R k ,min (17.c) M O S k ( w ) ≥ M O S min,k , (17.d) The problem is n on-con vex and hence, it cannot be solved effic iently . In next section, we wi ll present a method for con verting it to a con vex o p timization problem. I V . O P T I M A L B E A M F O R M I N G A N D P OW E R A L L O C A T I O N In this section , we present methods for solving the optimization problem in (17) and therefore designing the beamforming vectors and the t rans m itted power of the M BS and SBSs. A. W eb Br owsing Service By con s idering R k ,min = B · log 2 (1 + SINR k ,min ) and simple mani p ulation of the QoS constraints, the optimi zati o n problem in (17) is conv erted t o maximize w k,j ∀ k ,j K X k =1 K 1 ln  B · R k ( w ) FS k  + K 2 (18) s.t. (17 .a ) − (17 .b ) P N s j = 0 | h H k ,j w k ,j | 2 P N s j = 0 P K l =1 ,l 6 = k | h H k ,j w l,j | 2 + σ 2 k ≥ SINR k ,min P N s j = 0 | h H k ,j w k ,j | 2 P N s j = 0 P K l =1 ,l 6 = k | h H k ,j w l,j | 2 + σ 2 k ≥ A k , 9 where A k = 2 FS k B · exp  MOS min,k − K 2 K 1  − 1 . Since the ob j ectiv e function in (18) i s not concav e and the two last constraints also are not con vex, the prob l em is a non-con vex problem. The constraints can be con verted to con vex constraint s by defining some p ositive sem idefinite matrices as W k ,j = w k ,j w H k ,j , (19) where rank( W k ,j ) ≤ 1 1 . These constraint s lead to un ique w k ,j in above equation (Lemma 3 i n [20]). Hence, we have maximize W k,j ∀ k ,j K X k =1 K 1 ln  B · R k ( W ) FS k  + K 2 (20) s.t. K X k =1 tr ( D q , 0 W k , 0 ) ≤ P 0 ,q q = 1 , ..., M (20.a) K X k =1 tr ( D q ,j W k ,j ) ≤ P j,q j = 1 , ..., N s q = 1 , ..., N j (20.b)  N s X j = 0 h H k ,j  1 + 1 SINR k ,min  W k ,j h k ,j − N s X j = 0 K X l =1 h H k ,j W l,j h k ,j  ≥ σ 2 k (20.c)  N s X j = 0 h H k ,j  1 + 1 A k  W k ,j h k ,j − N s X j = 0 K X l =1 h H k ,j W l,j h k ,j  ≥ σ 2 k (20.d) rank( W k ,j ) ≤ 1 , (20.e) where R k ( W ) = log 2 1 + P N s j = 0 h H k ,j W k ,j h k ,j P N s j = 0 P K l =1 ,l 6 = k h H k ,j W l,j h k ,j + σ 2 k ! , (21) and W = { W k ,j | k = 1 , ..., K , j = 0 , 1 , ..., S } is the set of beamforming matrices. The rank constraints and the objective function are not con vex and concave, respective ly . Th erefore, w e 1 Note that rank( W k,j ) = 0 i mplies W k,j = 0 . 10 consider an equi valent con vex optimization problem b y calculating the superlev el sets of the objective function as maximize W k,j ,z k ∀ k ,j K X k =1 K 1 ln( z k ) + K 2 s.t. B · R k ( W ) FS k ≥ z k , z k > 0 (20 .a ) − (20 .e ) . (22) The new objective function is con cave, but the new con s traints are st i ll non-con vex. W e con vert them to con vex fun cti ons by i n troducing addit i onal optimization variables. Defining the lower bo und for the sp ectral ef ficiency of each user R k ( W ) as log 2 ( t k ) , (22) can be rewritten as maximize W k,j ,z k ,t k ∀ k ,j K X k =1 K 1 ln( z k ) + K 2 (23) s.t. log 2 ( t k ) ≥ z k · FS k B (23.a) P N s j = 0 h H k ,j W k ,j h k ,j P N s j = 0 P K l =1 ,l 6 = k h H k ,j W l,j h k ,j + σ 2 k ≥ t k − 1 (23.b) t k > 0 , z k > 0 (23.c) (20 .a ) − (20 .e ) . (23.d) Considering that P N s j = 0 P K l =1 ,l 6 = k h H k ,j W l,j h k ,j + σ 2 k ≤ s k , (23) can be con verted to the following maximize W k,j ,z k ,t k ,s k ∀ k ,j K X k =1 K 1 ln( z k ) + K 2 (24) s.t. log 2 ( t k ) ≥ z k · FS k B (24.a) N s X j = 0 h H k ,j W k ,j h k ,j ≥ ( t k − 1) s k (24.b) N s X j = 0 K X l =1 ,l 6 = k h H k ,j W l,j h k ,j + σ 2 k ≤ s k (24.c) (23 .c ) − (23 .d ) . (24.d) This problem is still n o n-con vex, because of the quasiconcav e form of the t k s k function. There- fore, we replace it by a looser upper bou nd which i s a con vex function. For any λ k > 0 the bound is defined as [21] 11 λ k 2 t 2 k + 1 2 λ k s 2 k ≥ t k s k , (25) where the equality i s satisfied by λ k = s k t k . By usin g (18)–(25), the optim i zation probl em in (24) can be written as equatio n (26). maximize W k,j ,z k ,t k ,s k ∀ k ,j K X k =1 K 1 ln( z k ) + K 2 (26) s.t. log 2 ( t k ) ≥ z k · FS k B (26.a) N s X j = 0 h H k ,j W k ,j h k ,j ≥ λ k 2 t 2 k + 1 2 λ k s 2 k − s k (26.b) (24 .c ) − (24 .d ) . (26.c) By relaxi ng the constraint rank( W k ,j ) ≤ 1 , the optimization problem is translated to (27), wh ose solutions are the same as t h e original p roblem. It is proved in Lemma 3 [20] that the solutio n of thi s problem wi ll surly s atisfy the rank conditio n. maximize W k,j ,z k ,t k ,s k ∀ k ,j K X k =1 K 1 ln( z k ) + K 2 (27) s.t. (26 .a ) − (26 .b ) (24 .c ) (23 .c ) (20 .a ) − (20 .d ) . All the constraint i n (27) are con vex, and hence, this p rob lem can be solved efficiently by st andard techniques. Because of λ k in (25), there m ay be a difference betw een the optimal solut i ons o f (17) and (27). In T able I, we propose an iterative algorithm to reduce this. It shoul d be noted that ou r proposed algorithm is a Sequential Parametric Con vex Approxim ation as described in [22]. In addition , based on Proposi tion 3.2 in [22], a KKT point to the prob lem is achiev ed. 12 T ABLE I Algorithm 1: The proposed algorithm for solving equation (17) 1. Initialize λ k > 0 , ∀ k such that the optimization v ari ables belong t o the feasible set of (27). 2. Solve (27) to obtain the optimal solutions of t k and s k ∀ k (called t ∗ k and s ∗ k ). 3.Update λ k by using the λ ∗ k = s ∗ k t ∗ k , ∀ k . 4.If | λ ∗ k − λ k | ≤ ǫ , where ǫ is a predefined threshold, stop the algorithm. E lse replace the λ k by λ ∗ k and return to step 2. B. V ideo Service For vi deo service, we u s e (9) to write th e optim ization p roblem in (17) as follows: maximize w k,j ∀ k ,j K X k =1 MOS k ( w ) (28) s.t. K X k =1 w H k , 0 D q , 0 w k , 0 ≤ P 0 ,q , q = 1 , ..., M (28.a) K X k =1 w H k ,j D q ,j w k ,j ≤ P j,q , j = 1 , ..., N s (28.b) q = 1 , ..., N j P N s j = 0 | h H k ,j w k ,j | 2 P N s j = 0 P K l =1 ,l 6 = k | h H k ,j w l,j | 2 + σ 2 k ≥ SINR k ,min (28.c) P N s j = 0 | h H k ,j w k ,j | 2 P N s j = 0 P K l =1 ,l 6 = k | h H k ,j w l,j | 2 + σ 2 k ≥ A k (28.d) where A k = 2     √ B · r v X k + s B · r X 2 k v 2 +4 r · B 2 B     2 − 1 is obtained as: g log u + v r B · R k ( W ) r  1 − r B · R k ( W )  ! + e ≥ MOS k ,min (29) By sim plifying this equation, 13 B · R k ( W ) − p B · R k ( W ) · r v X k − r ≥ 0 (30) where X k = 10  MOS k,min − e g  − u. The A k is obtained by solvi n g this equat i on and usin g (21). Then from (19), t h e problem in (28) is con verted to maximize W k,j ∀ k ,j K X k =1 MOS k ( W ) (31) s.t. (20 .a ) − (20 .e ) where W = { W k ,j | k = 1 , ..., K , j = 0 , 1 , ..., S } is t he set of beamformi n g matrices and MOS k ( W ) = g log u + v r B · R k ( W ) r (1 − r B · R k ( W ) ) ! + e ! (32) where R k ( W ) is defined in (21). The rank constraints and t he obj ectiv e function are not con vex and concav e, respectively . Therefore, we consider an equivalent con vex optim ization problem by calcul at i ng the superlevel sets of the o b jectiv e function. Assume u + v r B · R k ( W ) r  1 − r B · R k ( W )  ≥ z k (33) and also p B · R k ( W ) ≥ t 1 k (34) R k ( W ) ≥ log 2 ( t 2 k ) (34.a) t 2 k > 0 . (34.b) Then B · log 2 ( t 2 k ) ≥ t 2 1 k and (33) is conv erted to a conv ex equation as t 1 k − r t 1 k ≥ z k − u v √ r. By using (34.a) and (21), P N s j = 0 h H k ,j W k ,j h k ,j P N s j = 0 P K l =1 ,l 6 = k h H k ,j W l,j h k ,j + σ 2 k ≥ t 2 k − 1 . (35) By considerin g P N s j = 0 P K l =1 ,l 6 = k h H k ,j W l,j h k ,j + σ 2 k ≤ s k , (35) is con verted to N s X j = 0 h H k ,j W k ,j h k ,j ≥ s k ( t 2 k − 1) . (36) 14 Using (25), (36) is con verted to t he con vex constraints N s X j = 0 h H k ,j W k ,j h k ,j ≥ λ k 2 t 2 2 k + 1 2 λ k s 2 k − s k . (37) Therefore, by using (33 )-(37), (31) is con verted to maximize W k,j ,z k ,t 1 k ,t 2 k ,s k ∀ k ,j K X k =1 ( g log ( z k ) + e ) (38) s.t. t 1 k − r t 1 k ≥ z k − u v √ r (38.a) B · lo g 2 ( t 2 k ) ≥ t 2 1 k (38.b) N s X j = 0 h H k ,j W k ,j h k ,j ≥ { λ k 2 t 2 2 k + 1 2 λ k s 2 k − s k } (38.c) N s X j = 0 K X l =1 ,l 6 = k h H k ,j W l,j h k ,j + σ 2 k ≤ s k (38.d) t 1 k > 0 , t 2 k > 0 , z k > 0 (38.e) (20 .a ) − (20 .e ) . (38.f) By removing the constraint (20.e), the probl em (38) i s con verted to a relaxed prob lem as maximize W k,j ,z k ,t 1 k ,t 2 k ,s k ∀ k ,j K X k =1 ( g log( z k ) + e ) (39) s.t. (38 .a ) − (38 .e ) (20 .a ) − (20 .d ) . All the constraint functions of (38) are con vex and hence the problem can be solved efficiently by standard techni ques. In tabl e I. t he proposed alg orithm for solving this prob l em is shown which replaces t k , t ∗ k and (27) with t 2 k , t ∗ 2 k and (39). The simulatio n results of proposed algorithm s for web browsing and vi d eo will be given in the next section. V . N U M E R I C A L R E S U L T S This section numerically eva luates t he proposed schemes in the pre vious sections. W e con sider the downlink of a HetNet consis ting of one macro cell with radius 500 [m] and four small cells 15 each wit h radius 40 [m] that are deployed at the same area (see Fig. 1). The four SBSs are equally sp aced on a circle of radius 250 [m], centered at the MBS. W e assum e that there are 6 u sers in the M acro cell and one user in each small cell (total us ers K = 10 ). Th e users are uniformly distributed in the coverage area (between the radius es of 35 [m] and 500 [m] for M acro cell users and between th e radiuses of 3 [m] and 40 [m] for small cell users). W e assume that all the SBSs have equal n u mber of antennas, i.e. N j = N , for j = 1 , ..., N s where N = 1 , 2 , 3 . The maximum power at all ant enn as at the SBSs or MBS are − 10 . 9 [dBm] and 18 [dBm], respectively . Assume that the bandwidth of all s ubcarriers is 15 [kHz] [10]. Th e p at h and penetration loss at a distance d [km] from the MBS and SBSs are 148 . 1 + 37 . 6 log 10 ( d ) [dB] and 1 27 + 30 log 10 ( d ) [dB], respectively . W e consider st and ard d e viation of 7 [dB] for log- normal shadow fading [10]. W e model the s m all scale fading channel s by independent Rayleigh var iables as h k ,j ∼ C N (0 , R k ,j ) , R k ,j ∝ I . In the following, we present the results for the two services of web browsing and vid eo separately . A. W eb Br owsing For web browsing service, we assume that t h e user n umber 1 to 10 are respectively receiving web page sizes of 1 8 , 3 0 , 5 0 , 1 00 , 200 , 320 , 40 0 , 500 , 650 and 1000 [kB]. As sume the minimum and m aximum spectral effi ciency for each user are 2 [bit/s/ Hz] and 7 [bit/s/Hz], respectiv ely . K 1 and K 2 in (1) are obtained by assigning the minim u m MOS to R min and t h e maximum to R max that results in K 1 = 3 . 194 and K 2 = 1 5 . 1978 (here we use the average F S = 3 20 [kB] [8]). In addition, the MSS and RTT are 14 60 [byte] and 30 [ms], respectively [8]. Fig. 2 shows the av erage MOS of t he us ers versus the number o f the M BS ant ennas i n a HetNet and compares i t with a homog eneou s network. The HetNet consists of one MBS and four smal l cells wit h different number of antennas. It should be noted that the results for homogeneous network are obtained by settin g N s = 0 . Here, to obtain the aver age MOS, the agg regated MOS of all users is divided by K (total number of users). In this figure, we see that the ave rage MOS of the HetNet is always better t h an the homogeneous network. For example, in the case of M=20 , it is shown that adding small cells t o the network leads to abou t 14 %-21 % improvement in the a verage MOS. In addition, increasing the numb er of M BS antennas from 20 t o 8 0, improves the avera ge MOS of the hom ogeneous network and HetNet( N = 1 ) for about 23% and 9%, respectiv ely . In other words, these results show that employing s m all cells or MaMIMO MBS 16 20 30 40 50 60 70 80 3.8 4 4.2 4.4 4.6 4.8 5 The number of MBS antennas (M) Average MOS hetnet (N=3) hetnet (N=2) hetnet (N=1) homogeneous network Fig. 2: A verage MOS of t h e users vs. th e number of the MBS ant ennas M i n a HetNet with N s = 4 SBS i n comparison wi th a homogeneous network for web browsing service. in th e n et work leads to more user satisfaction. Also the need for adding small cells is much smaller when the BS has more antennas. This figure also shows by i ncreasing the number of th e SBSs’ ant ennas, the av erage MOS of the network w i ll be improved. An interestin g result t hat can be o b served from this figure is that a good a verage MOS can be o btained either by a homogeneous MaMIMO MBS or a HetNet MaM IM O with less number of antennas at the MBS. For example, the a verage MOS of 4.5 is reached eit h er by M = 40 in homogeneous network or M = 20 in a HetNet with four two-antenna SBSs. Fig. 3a and 3b s hows t he performance of the p roposed algorithm w h en MOS w eb min,k = 1 and MOS w eb min,k = 2 , respectiv ely . It should be noted that MOS w eb min,k = 1 implies that there is no QoE const rain t in the optimization prob lems. In addi tion, the figures depict the MOS of each user in the MaM IMO HetNet w h ere th e MBS is equipped with 20 antennas, and the SBSs are equipped with 1, 2, and 3 antennas. Am ong the 10 users that are i n the network, the first six users are always within t he Macro cell covera ge area and each of the l ast four users is wit hin one small cell. Comparing Fig. 3a with Fig. 3b clarifies t h at the network wit h MOS w eb min,k = 2 is more robust t o the sizes of web pages. In other words, by con sidering QoE const raints i n Fig. 3b, t he MOS of the users are im proved in comparison with the Fig. 3a (i.e. the case that there is no t any QoE cons t raints). For example the user 10 with F S = 1000 [kB] gets MOS of 1 and 2 in Fig. 3 a and Fig. 3b, respectively . 17 1 2 3 4 5 6 7 8 9 10 1 1.5 2 2.5 3 3.5 4 4.5 5 User index MOS of each user hetnet (N=3) hetnet (N=2) hetnet (N=1) homogeneous network (a) MOS web min,k = 1 , ∀ k . 1 2 3 4 5 6 7 8 9 10 1 1.5 2 2.5 3 3.5 4 4.5 5 User index Average MOS of each user hetnet (N=3) hetnet (N=2) hetnet (N=1) homogeneous network (b) MOS web min,k = 2 , ∀ k . Fig. 3: MOS of the users in a network with M = 20 an tennas, K = 10 users and different nu m ber of antenn as at the SBSs for W eb browsing ser v ice. The last fo u r users are deployed in th e small cells. B. V ideo services In this part, we present t he numerical results for video service. The network parameters are similar to th e pre vio us case. The parameters in (9) and (10) are designed by usi ng [18] for PSNR between 30-42 d B. These p arameters are u = 28 . 046 , v = 0 . 038 and r = 5 . 024 . Th e parameters g and e in (9) are also set to 2 7 . 37 and − 39 . 43 , respectively . Fig. 4 shows th e a verage M OS by considering MOS video min,k = 1 (i . e. without considering any QoE constraints i n (31)). This figure compares the average M OS of a h o mogeneous network consisting o f one MBS w i th a HetNet consisti ng of one m acro cell and fou r small cells with diffe rent number of antennas. This figure indicates that for a giv en number of MBS antennas M , the av erage MOS of a HetNet is alw ays better than i n a homog eneou s network. For example, for t he case when M = 20 , it is sho wn that adding small cells to the network leads to about 13%-20% improvement in av erage MOS. In add ition, in creasing the number of MBS antennas from 20 to 80, imp rove s the a verage MOS of t he homogeneous network and HetNet (about 33% and 19%, respectiv ely). In other words, these results sh ow that employing small cell s or MaMIMO MBS in th e network leads to higher user satisfaction. Also the need for addin g sm all cells is much sm aller when the BS has more antennas. This figure also s h ows by increasing the number of the ant enn as at the SBSs, the average MOS of the network will be improved. An interesting result that can be ob s erved from this figure is that a good ave rage MOS can be obtained either by a homogeneous MaMIMO MBS o r a HetNet MaMIM O with less number of 18 antennas at th e MBS. For example, the av erage MOS of 2.7 1 is reached either by M = 5 0 in homogeneous network o r M = 40 in a HetNet with four two-antenna SBSs. Figs. 5a and 5b sho ws th e performance of the proposed algorithm when MOS w eb min,k = 1 , ∀ k and MOS w eb min,k = 2 . 5 , ∀ k , respecti vely . In additio n , the figures depict the MOS of each user in t he MaMIMO HetNet where the MBS is equi pped wit h 20 ant ennas, and the SBSs are equipped with 1, 2, and 3 antennas. There are 10 users i n the n etwork which are numbered from 1 to 10 (on the horizontal axis ). In additi on, t he first six users are always placed in the Macro cell cov erage area and each of the last four users is withi n o n e small cell. These figures show th e advantage of HetNets in improving MOS of each user w h ich are con cl u d ed from so l ving the propo sed scheme. In other terms, it can b e seen in Fig. 5b the MOS of the users are improved b y considering QoE constraints in comparison with Fig. 5a (when we do n o t consider QoE constraints). For example the user 10 gets the M OS of 2.07 and 2.51 i n Fig. 5a and 5b, respectively (about 21% improvement in QoE). Therefore the user 10 is more satisfied th an before. V I . C O N C L U S I O N This paper proposed a joint beamformi ng and power allocation scheme for MaMIMO HetNets. W e provided algorithms to op t imize the beamfoming vectors at the MBS and SBSs based on maximizing the aggregated MOS of the network. W e consider two different services of web browsing and video in the network. The resulting o ptimization problems of two provided algorithms were not conv ex, hence we transform ed t hem to con vex optimization problem to design the beamforming vectors. Our simulation results show that increasing the number of antennas at th e MBS or SBSs leads to a better QoE of users. In additio n , we showed that the QoE can be im proved by adding small cells to the homogeneous network in both web browsing and vid eo services. R E F E R E N C E S [1] I. Hwang, B. S ong, and S. S. Soliman, “ A holistic vie w on hy per-dens e heterogeneo us and small cell netwo rks, ” IEEE Communications Magazine , vol. 51, no. 6, pp. 20-27, June 2013. [2] M. Agiwal, A. Roy , and N. Saxena, “Next generation 5G wireless network s:A comprehensi ve surve y , ” IEEE Communications Surve ys and T utorials , v ol. PP , no. 99, pp. 1-40 , F eb . 201 6. [3] Q. W u, Z. Du, P . Y ang, Y . D. Y ao, and J. W ang, “Traf fic-A ware online network selection in heterogeneo us wireless networks, ” IEE E T ransactions on V ehicular T echnolog y , vol. 65, no. 1, pp. 381 -397, Jan. 2015. 19 20 30 40 50 60 70 80 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 The number of MBS antennas (M) Average MOS hetnet (N=3) hetnet (N=2) hetnet (N=1) homogeneous network Fig. 4: A verage MOS of t h e users vs. th e number of the MBS ant ennas M i n a HetNet with N s = 4 SBS i n comparision with a homogeneous network for video service. 1 2 3 4 5 6 7 8 9 10 1.8 2 2.2 2.4 2.6 2.8 3 User index MOS of each user hetnet (N=3) hetnet (N=2) hetnet (N=1) homogeneous network (a) MOS video min,k = 1 . 1 2 3 4 5 6 7 8 9 10 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 User index MOS of each user hetnet (N=3) hetnet (N=2) hetnet (N=1) homogeneous network (b) MOS video min,k = 2 . 5 . Fig. 5: MOS of the users in a network with M = 20 an tennas, K = 10 users and different nu m ber of antenn as at the SBSs for video serv ic e . T he last four u sers are dep loyed in the small cells. [4] D. W u, Q. W u, Y . Xu, and Y . C. Liang, “QoE and Energy aware resource allocation in small cell networks with power selection, load management and channel allocation, ” IEEE T ransac tions on V ehicular T echnolo gy , vol. 66, no. 8, pp. 7461-747 3, Jan. 2017. [5] P . T . Quang, K. Piamrat, K. D. Si ngh, and C. V iho, “V ideo streaming over Ad-hoc networks: a QoE-based Optimal Routing Solution, ” IEE E T ransactions on V ehicular T echn ology , vol. 62, no. 2, pp. 1533-1 546, Apr . 2016. [6] J. S haikh, M. Fi edler , and D. Collange, “Quality of Experience from user and network perspectiv es, ” Annals of T elecommunications , vol. 65, no . 1, pp. 47-5 7, Feb . 2010. [7] P . Ameigeiras, J. J. Ramos-Munoz, J. Nav arr o-Ort iz, P . Mogensen, and M. L opez-Soler , “QoE oriented cross-layer design of a resource all ocation algorithm in beyond 3G systems, ” Computer C ommunications , vol. 33, no. 5, pp . 571-582, Mar . 2010. [8] M. Rugelj, U. S edlar , M. V olk, J. Sterle, M. Hajdinjak, and A. Ko s, “Nov el cross-layer QoE-aware radio resource allocation algorithms in multiuser OFDMA systems, ” IEEE T ransactions on Communications , vol. 62, no. 9, pp . 3196 -3208, Sep. 20 2014. [9] A. Kazerouni, F . J. Lopez-Martinez, and A. Goldsmith, “Increasing capacity i n Massive MIMO cellular networks via small cells, ” in Pr oc. Gl obal Communications Confer ence W orkshops. , 2014 , pp. 258-363 . [10] E. Bj ¨ ornson, M. K ountouris, and M. Debbah, “Massiv e MIMO and small Cells: improving energ y efficienc y by optimal soft-cell coordination, ” in Pr oc. International Confer ence on T elecommunications ( ICT) , 2013, pp. 1-5. [11] Z. Du, Q. W ,u, P . Y ang, Y . Xu, J. W ang, and Y . D. Y ao, “Exploiting user demand di versity in heterogeneo us wireless networks, ” IEE E T ransactions on W i r eless Commun ications , vo l. 14, no. 8, pp. 4142-41 55, Aug. 201 5. [12] S. Lin, W . Sheen, and C. Huang, “Downlink performance and optimization of r el ay-assisted cellular networks, ” in P r oc. W ir eless Communications and Networking Confer ence (WCNC) , 2009, pp. 5-8. [13] S. T hako lsri, W . Keller , and E. Steinbach, “ Application-driv en cross layer optimization for wireless networks using MOS-based utilit y f unctions, ” in P r oc. Communica tions and Networking in China (ChinaCOM.) , 2009, pp. 1-5. [14] Y . Deyu, S. Mei, T . Y inglei, W . Xiaojun, and L. Guofeng, “QoE-oriented resource allocation for ,multiuser- multiservice femtocell networks, ” China Commun ications , vol. 12 , no. 10, pp. 27-41, Oct. 201 5. [15] K. W u, L. Guo, T . Song, and J. L i n, “Bi o-Inspired multi-user beamforming for QoE provisioning in cognitiv e radio networks, ” in P r oc. Network Infrastructure and Digital Content (IC-NIDC) Internation al conference, 2012, pp. 173-177. [16] R. Imran, M. Odeh, N. Zorba, and C. V erikoukis, “Quality of Experience for spatial cognitiv e systems within multiple antenna scenarios, ” T ransactions on W ir eless Communications , vol. 12, no. 8, pp. 4153-416 1, Aug. 2013. [17] D. W u, Q. W u, Y . Xu, J. Jing, and Z. Qin, “QoE-Based Distributed Multichannel Allocation in 5G Heterogeneous Cellular Networks: A Matching-Coalitional Game Solution, ” IEE E Access , vol. 5, pp. 61-71, Sep. 2016. [18] L. U. Choi, M. T . Ivrlac, E. Steinbach, and J. A. Nossek, “Sequence-le vel models for distortion-rate behavio ur of compressed video, ” in Pr oc. IEEE International Confer ence on Ima ge Pr ocessing , 200 5, pp . II - 486-9. [19] S. Zhang, R. Zhang, and T . J. Lim, “Massi ve MIMO with per-an tenna power constraint, ” in Pr oc. Global Confer ence on Signal and Information P r ocessing (GlobalS IP) , 201 4, pp. 642-646. [20] E. Bj ¨ ornso n, N. Jalden, M. Bengtsson, and B. Ot tersten, Optimalit y “Optimality properties, distributed strategies, and measurement-based ev aluation of coordinated multicell OF DMA transmission, ” IE EE T ransac tions of Signal Proce ssing , vol. 59, no. 12, pp. 6086-6101, Jan. 2011. [21] T . Lv , H. Gao, R. Cao, and J. Zhou, “Coordinated secure beamforming in K-user interference channel with multiple eav esdroppers, ” IEEE Communication s Letters , vol. 5, no . 2, pp. 212215, Jan. 2016. [22] A. Beck, A. Ben-T al, and L. T etruashvili, “ A sequential parametric con ve x approximation method wit h applications to noncon vex truss topology design problems, ” Jo urnal of Global Optim ization , vol. 47, no. 1, pp. 29-5 1, May , 2010.