User Subgrouping in Multicast Massive MIMO over Spatially Correlated Rayleigh Fading Channels
Alejandro de la Fuente, Giovanni Interdonato, Giuseppe Araniti
aa r X i v : . [ ee ss . SP ] F e b User Subgrouping in Multicast Massive MIMO overSpatially Correlated Rayleigh Fading Channels
Alejandro de la Fuente ∗† , Giovanni Interdonato ‡ , Giuseppe Araniti †∗ Department of Signal Theory and Communications, University Rey Juan Carlos † DIIES Department, University Mediterranea of Reggio Calabria ‡ Department of Electrical and Information Engineering, University of Cassino and Southern LazioEmail: [email protected]
Abstract —Massive multiple-input-multiple-output (MaMIMO)multicasting has received significant attention over the lastyears. MaMIMO is a key enabler of 5G systems to achieve theextremely demanding data rates of upcoming services. Multicastin the physical layer is an efficient way of serving multipleusers, simultaneously demanding the same service and sharingradio resources. This work proposes a subgrouping strategy ofmulticast users based on their spatial channel characteristics toimprove the channel estimation and precoding processes. Weemploy max-min fairness (MMF) power allocation strategy tomaximize the minimum spectral efficiency (SE) of the multicastservice. Additionally, we explore the combination of spatialmultiplexing with orthogonal (time/frequency) multiple access.By varying the number of antennas at the base station (BS)and users’ spatial distribution, we also provide the optimalsubgroup configuration that maximizes the spectral efficiencyper subgroup. Finally, we show that serving the multicastusers into two orthogonal time/frequency intervals offers betterperformance than only relying on spatial multiplexing.
Index Terms —Massive MIMO, multicasting, spatial correla-tion, 5G, digital precoding.
I. I
NTRODUCTION
Upcoming mobile services demand stringentperformance requirements, both in terms of data rates,latency, and the number of connected devices [1].Massive multiple-input-multiple-output (MaMIMO) playsa key role in fifth-generation (5G) systems to fulfill theserequirements [2], [3]. This technology makes use of manyantennas at the base station (BS) to jointly and coherentlyserve multiple users in the same time/frequency resourcesby yielding array gain, spatial multiplexing gain, and spatialdiversity [4], [5]. Importantly, MaMIMO can offer, in most ofthe propagation environments, two fundamental features thatare known as favorable propagation and channel hardening :as the number of BS antennas increases, users’ channelsbecome nearly pairwise orthogonal and deterministic,respectively [6]. All this leads to a significant increase inspectral and energy efficiency.Long Term Evolution Advanced (LTE-A)systems fully support broadcast/multicasttransmissions through the use of theevolved Multimedia Broadcast and Multicast Service (eMBMS)[7], [8]. The eMBMS is implemented as an LTE-A subsystemto share the physical resources between unicast and multicast transmissions. The standard allows the system an efficientresource utilization when multiple users simultaneouslydemand the same content.We recently witnessed an increasing interest in multicastMaMIMO transmissions in millimeter-wave (mmWave) andsub-6 GHz bands. The authors in [9] propose a multicastMaMIMO strategy using a unique pilot sequence for all themulticast users receiving the same service. This pilot sequenceis used in a power control scheme to equalize the throughputamong all the users. Sadeghi et al. have extended this proposalto multi-group multicast joint with unicast services in multicelldeployments. They have also developed low complexity solu-tions for multicast and unicast precoders [10]–[12]. In [13],the authors present a framework to achieve optimal multicastbeamforming. The low-dimensional structure in the optimalsolution benefits the numerical computation in large antennasystems. In [14], the authors show how to shape the beams todeliver multicast information to the users in mmWave. Theydemonstrate that restricting the wireless links to be unicastonly may be strongly suboptimal. Furthermore, the authorsin [15] develop a mathematical framework to estimate theparameters of the mmWave BSs for handling a mixture ofmulticast and unicast sessions. This framework allows thenetwork designers to achieve a lower bound on the requireddensity of the BSs.To the best of our knowledge, existing works on MaMIMOmulticasting employ uncorrelated fading channel models.However, practical scenarios must take into account spatialcorrelations which affect the favorable propagation , mainly ina poor-scattering propagation environment. This effect reducesmutual-orthogonality among different users.
Contributions:
We consider spatially correlated fadingchannels to study the delivery of multicast service. Wepropose a user subgrouping method based on the levelof the user mutual-orthogonality. Our strategy reduces thepilot contamination making precoding more effective. Wealso consider optimal max-min fairness (MMF) power controland optimize the number of subgroups that maximizes thespectral efficiency (SE). Finally, we analyze the benefits ofsplitting the multicast users into two different time/frequencyschedules.I. S
YSTEM M ODEL
Let us consider a multicast transmission in a single-cellMaMIMO system with fully digital precoding. We assume thesystem has a BS equipped with a uniform linear array (ULA)with M antennas serving K single-antenna users. We denotethe set of multicast users as K , i.e., K = { , . . . , K } . Let h gk ∈ C M × be the channel between the BS and user k included in subgroup g (we detail the subgrouping model insubsection II-A). The block-fading model is herein assumed.Although uncorrelated Rayleigh fading channels are widelyemployed to study MaMIMO multicasting performance [10],it is more likely to have spatially correlated fading in practicalscenarios. Hence, h gk ∼ CN ( , R gk ) , (1)where R gk ∈ C M × M is the positive semi-definite spatialcorrelation matrix at user k in subgroup g , incorporating path-loss, shadowing, and spatial correlation fading. We denote thecorresponding large-scale fading coefficient as β gk = 1 M tr ( R gk ) , (2)while the small-scale fading follows a Rayleigh distribution.We parameterize the correlation matrices R gk using theazimuth angles from the BS to the users. The BS receives fromuser k a signal that consists of the superposition of N multi-path components. Each multipath component reaches the BS asa planar wave from a particular angle ϕ k ( n ) ∈ [Φ k , Φ k + φ k ] for n = 1 , . . . , N , where Φ k is the 2D nominal angle betweenuser k and the BS and φ k is a random deviation from thenominal angle whose standard deviation in radians is calledangular standard deviation (ASD). Hence, h gk = N X n =1 ρ k ( n ) a k ( ϕ k ( n )) , (3)where ρ k ( n ) ∈ C represents the gain and phase of the n thphysical path for user k and a k ( ϕ k ( n )) ∈ C M is the steeringvector of the ULA given by a k ( ϕ k ) = h e j πδ cos ϕ k . . . e j πδ ( M −
1) cos ϕ k i ⊺ , (4)where δ is the distance between adjacent antennas, normalizedby the wavelength. Both the nominal angle Φ k and the ASDcharacterize the spatially correlated Rayleigh fading channels.The BS estimates the spatial correlation matrix of each user onthe large-scale fading time-scale (i.e., over several coherenceblocks). Therefore, we can reasonably assume R gk , ∀ k ∈ K ,to be known at the BS. A. Multicast MaMIMO subgrouping
Multicast subgrouping consists in splitting the K users,demanding the same multicast service, into G disjoint sub-groups based on their channel similarities. The objective ofsubgrouping the users is to increase the aggregated SE (ASE).A specific and unique transmission setting characterizes eachmulticast subgroup. Let K g and K g denote the set and the Fig. 1: Massive MIMO multicasting scenario with user subgrouping based onthe spatial characteristics. number of multicast users in subgroup g , respectively (i.e., |K g | = K g ). Moreover, let G be the set of subgroups. Hence,we have K = P Gg =1 K g .Fig. 1 illustrates an example of user subgrouping-basedmulticast transmission in a single-cell MaMIMO system. Theusers are grouped based on the level of orthogonality of theirspatial correlation matrices, namely users with similar spatialcharacteristics belong to the same subgroup. B. Channel estimation
We assume that the users in the same subgroup are assignedthe same pilot sequence, while mutually orthogonal pilotsare assigned over different subgroups. As co-pilot users havelinearly dependent channel estimates, the BS cannot separatethe users of the same subgroup in the spatial domain. Conse-quently, the BS can effectively construct as many precodingvectors as the number of orthogonal pilots (which must be atleast equal to G ), and the same precoding vector is employedto all the users of the same subgroup.Let Ψ = [ ψ , . . . , ψ G ] ∈ C τ p × G be the pilot matrix where ψ g is the pilot sequence of length τ p symbols assigned toall the users in subgroup g . Without loss of generality, weset τ p = G to obtain G mutually orthogonal uplink pilots, Ψ H Ψ = τ p I G ( G is known at the channel estimation stage).The uplink (UL) pilot signal received at the BS is Y = X g ∈G X k ∈K g √ q gk h gk ψ ⊺ g + N , (5)where q gk is proportional to the UL pilot powerper user k ∈ K g , and N ∈ C M × τ p is theadditive white Gaussian noise (AWGN) with i.i.d. elementsdistributed as CN (0 , σ ) . To estimate the channel of user k in subgroup g , the BS first correlates the received signal with ψ ∗ g , obtaining y UL gk = √ q gk τ p h gk + X k ′ ∈K g \{ k } √ q gk ′ τ p h gk ′ + n k , (6)where n k ∼ CN ( , σ I M ) is AWGN. Then, theminimum mean square error (MMSE) channel estimate is16, Sec. 3.2] ˆ h gk = √ q gk R gk X k ′ ∈K g (cid:0) τ p q gk ′ R gk ′ + σ I M (cid:1) − y UL gk . (7)Let h g denote the composite channel of subgroup g given by h g = τ p K g X k =1 (cid:0) √ q gk h gk (cid:1) . (8)The MMSE estimate of the composite channel is ˆ h g = τ p X k ∈K g q gk R gk X k ∈K g (cid:0) τ p q gk R gk + σ I M (cid:1) − y UL gk . (9)We stack the G composite channel vectors in a matrix ˆ C = [ˆ h , . . . , ˆ h G ] ∈ C M × G and use ˆ C to formulate thezero-forcing (ZF) precoding vector intended for subgroup g as w g = v g k v g k , (10)where w g ∈ C M × , E (cid:2) k w g k (cid:3) = 1 , and v g is the g -thcolumn vector of the matrix V = ˆ C ( ˆ C H ˆ C ) − . C. Downlink data transmission and spectral efficiency
We assume that the BS transmits data to the multicastusers by using ZF precoding. Specifically, the same precodingvector, modulation and coding scheme (MCS) are employedfor all the users in the same subgroup. Let us denote thedata symbols for every user k ∈ K g as x g (unit vari-ance random variables and uncorrelated), with p g being thetransmit power allocated to the multicast subgroup g . Weassume that the users have access only to the statisticalchannel state information (CSI), i.e., E [ h H gk w g ] . Hence, thedownlink (DL) data signal received at user k ∈ K g can bewritten as y gk = √ p g E (cid:2) h H gk w g (cid:3) x g + √ p g (cid:0) h H gk w g − E (cid:2) h H gk w g (cid:3)(cid:1) x g + X g ′ ∈G\{ g } √ p g ′ h H gk w g ′ x g ′ + n k , (11)where the first term denotes the desired signal, the secondterm is interference due to the user’s lack of CSI, the thirdterm denotes the inter-subgroup interference and finally n k ∼CN (0 , σ k ) is the AWGN. By invoking the capacity-boundingtechnique in [17, Sec. 2.3.4], which treats the second, third andfourth term of (11) as effective uncorrelated noise, a downlinkachievable spectral efficiency is given bySE gk = (cid:18) − τ p τ c (cid:19) log (1 + γ gk ) , (12) where τ c is the coherence block length and γ gk is the effectivesignal-to-interference-plus-noise ratio (SINR) given by γ gk = p g (cid:12)(cid:12)(cid:12) E (cid:2) h H gk w g (cid:3)(cid:12)(cid:12)(cid:12) G X g ′ =1 p g ′ E (cid:20)(cid:12)(cid:12)(cid:12) h H gk w g ′ (cid:12)(cid:12)(cid:12) (cid:21) − p g (cid:12)(cid:12)(cid:12) E (cid:2) h H gk w g (cid:3)(cid:12)(cid:12)(cid:12) + σ k , (13)where the expectations are w.r.t. the channel realizations.Recall that each subgroup receives the same service but witha different MCS, which must support the user’s SE with theworst channel condition in the subgroup. Thus, all the users k ∈ K g experience the SE given bySE g = min k ∈K g SE gk . (14)III. M A MIMO
MULTICASTING
The literature of MaMIMO multicasting [9]–[13] essentiallypresents two fundamental delivery strategies. The first optionconsists of serving each user individually by a unicast trans-mission as in conventional MaMIMO. This approach limitsthe number of unicast users to the number of orthogonalpilots (assuming no pilot reuse) and requires the numberof BS antennas to be larger than the number of users (forthe ZF precoding to be performed). Alternatively, multicasttransmission may take place over one joint transmission to thewhole multicast group. In this case, only one pilot sequence,MCS are used for all the users.
A. User subgrouping based on spatial characteristics
We propose an alternative strategy to deliver a mul-ticast service in a MaMIMO system, which consistsof forming disjoint subgroups of multicast users, eachserved with a specific MCS. The soundness of this ap-proach was shown in single-input-single-output (SISO) andmultiple-input-multiple-output (MIMO) systems, using bothwideband and subband channel information [18], [19].The proposed subgrouping criterion relies on the spa-tial characteristics of the users: users with similar spatialcharacteristics, and thereby which cause much interferenceto each other, are grouped all together. To this end, weconsider the normalized channels h gk / p E {k h gk k } and h g ′ k ′ / p E {k h g ′ k ′ k } of any pair of multicast users k ∈ K g , k ′ ∈ K g ′ . The level of orthogonality of the channel direc-tions, quantified by the variance of the inner product of thenormalized channels V " h H gk h g ′ k ′ p E [ k h gk k ] E [ k h g ′ k ′ k ] = tr ( R gk R g ′ k ′ ) M β gk β g ′ k ′ , (15)gives a measure of how much interference the users cause toeach other: the larger the value, the smaller the orthogonalitylevel of the channel directions and the higher the mutualinterference between the two users. V in (15) denotes the variance operator. A necessary but not sufficientcondition for favorable propagation is that (15) → , as M → ∞ [16]. efore pilot assignment and channel estimation, assumingperfect knowledge of the large-scale fading parameters, theBS forms the user subgroups such that the users in the samesubgroup present similar channel characteristics, hence lowlevels of orthogonality, i.e., those users for which (15) returnsa large value.The K-means algorithm and its multiple variants providea simple method to efficiently cluster the multicast usersinto disjoint subgroups [20]. This algorithm aims at findinga partition of the K users into G subgroups, minimizingthe mean square error (MSE) according to the selected metric[21]. B. Max-min fairness power control
Optimal max-min fairness power control is of practicalinterest and it has been extensively investigated for MaMIMOsystems [16], [17]. The MMF optimization problem subject toaverage power constraints at the BS is formulated as P : maximize p g min g ∈G ,k ∈K g SE gk s.t. X g ∈G p g ≤ P DL . (16)Expression (12) can be rewritten asSE gk = (cid:18) − τ p τ c (cid:19) log p g a gk X g ′ ∈G p g ′ b gkg ′ + σ k , (17)where a gk = (cid:12)(cid:12)(cid:12) E (cid:2) h H gk w g (cid:3)(cid:12)(cid:12)(cid:12) , b gkg ′ = E (cid:20)(cid:12)(cid:12)(cid:12) h H gk w g ′ (cid:12)(cid:12)(cid:12) (cid:21) for g ′ = g and b gkg = E (cid:20)(cid:12)(cid:12)(cid:12) h H gk w g (cid:12)(cid:12)(cid:12) (cid:21) − (cid:12)(cid:12)(cid:12) E (cid:2) h H gk w g (cid:3)(cid:12)(cid:12)(cid:12) .Maximizing the minimum SE is equivalent to maximizingthe minimum SINR. Therefore, we can rewrite P in epigraphform as P : maximize p g Γ s.t. p g a gk X g ′ ∈G p g ′ b gkg ′ + σ k ≥ Γ ∀ k ∈ K g , g ∈ G X g ∈G p g ≤ P DL , (18)where Γ is an auxiliary variable that must satisfy the constraint γ gk ≥ Γ , ∀ g ∈ G , and k ∈ K g . P is still non-convexsince the SINR constraint is neither convex nor concave withrespect to p g . To overcome such non-convexity, we use asuccessive convex approximation (SCA). Note that for a fixedvalue of Γ ≥ , the SINR constraint in P can also be writtenin a linear form as p g a gk ≥ Γ X g ′ ∈G j p g ′ b gkg ′ + σ k . Algorithm 1
SCA algorithm for optimal max-min fairnesspower control with multicast user subgroups
Constant : P DL , ε Input : { a gk } , { b gkg ′ } Initialization : Γ min ← max ← min g,k (cid:18) P DL a gk σ k (cid:19) p ∗ g ← , ∀ g ∈ G do Γ = Γ max +Γ min Solve (18) if feasible then Γ min ← Γ p ∗ g ← p g , ∀ g ∈ K else Γ max ← Γ end ifwhile Γ max − Γ min > ε Output : Γ min , p ∗ g If Γ is fixed, P is a linear feasibility program, and theoptimal solution can be efficiently computed by using interior-point methods, for example, with the toolbox CVX [22].Letting Γ vary over an SINR search range { Γ min , Γ max } ,the optimal solution can be efficiently computed by using thebisection method [23], in each step solving the correspondinglinear feasibility problem for a fixed value of Γ .Algorithm 1 describes the SCA algorithm providing thepower allocation that maximizes the minimum SINR amongthe multicast users. It works for a pre-determined subgroupingconfiguration (i.e., the formation of the K g sets of users). C. Time/frequency schedule in MaMIMO multicasting
MaMIMO multicasting exploits spatial multiplexingthrough DL precoding to handle the intra-cell interferenceamong different subgroups [24]. Alternatively, multicastsubgroups can be served over orthogonal time/frequencyresources (time/frequency scheduling) [18], [19].According to [25], the optimal number oftime/frequency multicast subgroups that maximizesthe ASE is either one or two in multicastorthogonal frequency division multiplexing (OFDM)systems. Hence, we compare two setups underlying theproposed user subgrouping strategy: i) all the multicastusers served in the same time/frequency resource (spatialmultiplexing), and ii) users served over two orthogonaltime-frequency intervals (time-frequency multiplexing). Inthe latter, a set of subgroups is served in a fraction of thetime-frequency resources denoted by < θ < , whereasthe rest of the subgroups is served in a fraction − θ ofthe resources. This user scheduling takes place by using theK-means algorithm based on the large-scale fading coefficient β gk .The ASE for the time/frequency schedule is given bySE = (cid:18) − τ p τ c (cid:19) X g ∈G ˆ θ g K g log (1 + ˆ γ gk ) , (19)where ˆ θ g is equal to either θ or − θ depending on whichinterval the subgroup g is scheduled, and ˆ γ gk = p g (cid:12)(cid:12)(cid:12) E (cid:2) h H gk w g (cid:3)(cid:12)(cid:12)(cid:12) G X g ′ ∈S g p g ′ E (cid:20)(cid:12)(cid:12)(cid:12) h H gk w g ′ (cid:12)(cid:12)(cid:12) (cid:21) − p g (cid:12)(cid:12)(cid:12) E (cid:2) h H gk w g (cid:3)(cid:12)(cid:12)(cid:12) + σ k , (20)and S g denotes the set of the indices of the subgroupsscheduled in the same time-frequency interval as subroup g ,i.e., the subgroups interfering with subgroup g .IV. N UMERICAL RESULTS
In this section, we use numerical simulations to assess theperformance of our multicast MaMIMO subgrouping strategy.We have employed different configurations of multicast users,along with a cell of m. We have placed the users inclusters with a radius of m to assess users’ effect with similarchannel characteristics. We have employed spatially correlatedfading channels based on each user’s nominal angle to theBS and an ASD of ◦ . The path-loss (in dB) is given by . log ( f ) + 37 . log ( d ) , where f is the operatingfrequency in GHz, and d is the 2D distance between the BSand the user in meters [11]. We have modeled a correlatedshadowing with a variance of dB, which presents a lowinter-cluster correlation and an extremely high intra-clusterone. We have employed a ULA with M transmit antennas atthe BS. The total amount of power available for DL transmis-sion is W, the UL pilot power is W, and the length of thepilot sequence is G (i.e., the number of multicast subgroups).We consider a noise power spectral density of − dBm/Hz,a receiver noise figure of dB, and an operating bandwidth of MHz at a carrier frequency of GHz (e.g., applicable insub-6 GHz-non-line of sight (NLOS) scenarios). We assumeda channel coherence of time/frequency samples. We haverun Monte Carlo simulations for different configurations ofmulticast users, over random spatial distributions with channel realizations.First, we analyze the subgrouping based on spatial multi-plexing without the time/frequency schedule. Fig. 2 presentsthe ASE of the multicast MaMIMO service, using the sub-grouping strategy for different distributions of users in clustersuniformly and randomly placed along with the cell. Wecompare the utilization of various criteria to select the numberof spatial multicast subgroups (only 1 subgroup, the number ofgeographical clusters of users, unicast transmissions to everyuser, and the optimal number of multicast subgroups basedon matrix R gk ). We can observe how the ASE decreaseswith the dispersion of the users, i.e., users placed in clusters of users present higher ASE than clusters of users and even more than uncorrelated users. Whenthe number of users is low compared to the number of x x x x x x x x x x x x x x x x x x Number of clusters x user/cluster A gg r ega t ed SE ( b / s / H z ) G = 1G = number of geographical clustersG = min (K,M)G = optimal number of spatial subgroups
M = 64 antennas M = 128 antennas
Fig. 2: Aggregated SE using spatial subgrouping in only 1 time/freq block.Comparison of using 1 multicast transmission, number of geographical clus-ters, unicast, or optimum number of multicast subgroups. Different randomdistributions of users and clusters with 64 and 128 transmit antennas. transmit antennas, i.e., users with transmit antennas, and users with transmit antennas, the ASE achievedusing unicast transmissions is close to the optimal resultsachieved with our spatial subgrouping proposal. However,when the number of users increases and these users are placedin clusters, the utilization of multicast spatial subgroupingoffers notably better performance than unicast transmissions.In any case, the higher the number of users, the lower theASE. Consequently, individual SE is significantly reduced. Alarge number of MaMIMO spatially multiplexed transmissionsand the utilization of a common precoding vector for manymulticast users lead to a low channel gain when a high numberof multicast users are served using MaMIMO transmissions inthe same time/frequency interval.To overcome this limitation, we test the proposal of combin-ing spatial and time/frequency subgrouping. Fig. 3 shows theASE for the initial configurations employing only optimal spa-tial subgrouping and the combination of spatial subgroupingwith scheduling using two intervals (using one or two intervalsprovides higher ASE depending on the users’ distribution).Observing the scenario with a more considerable distancebetween the number of users and transmit antennas, i.e., users and transmit antennas, the option of using only spa-tial multiplexing is almost always the optimal configuration.Nevertheless, when this relation is diminishing, the designsplitting the users suffering from highly different large-scalefading coefficient ( β gk ) into two time/frequency schedulingresources is hugely beneficial. Note that uncorrelated userscannot be served by transmit antenna using MaMIMO spa-tial multiplexing. However, splitting these users into twoscheduling blocks allows the system to deliver the multicastservice with an extraordinary improvement in the ASE.Finally, we employ the configuration with clusters of users/cluster to evaluate the impact of the number of BSantennas on the subgrouping strategy’s performance. Fig. 4illustrates the ASE for a variable number of BS antennas. Weassess the performance of these options: i ) a unique multicastgroup ( G = 1 ) without the time/frequency schedule, ii ) the op- x x x x x x x x x x x x x x x x x x Number of clusters x user/cluster A gg r ega t ed SE ( b / s / H z ) No schedulingScheduling - 2 coh. blocksBest configuration
M = 64 antennas M = 128 antennas
Fig. 3: Aggregated SE using spatial subgrouping in only 1 time/freq block, 2time/freq blocks, or the best configuration. Different random distributions ofusers and clusters with 64 and 128 transmit antennas.
64 128 256
Number of BS transmit antennas (M) A gg r ega t ed SE ( b / s / H z ) G = 1 (no scheduling)G = optimal number of spatial subgroups (no scheduling)G = optimal number of spatial subgroups (sched - 2 coh. blocks)G = optimal number of spatial subgroups (best config)
Fig. 4: ASE versus the number of BS transmit antennas. Comparison amongunicast transmissions and subgrouping with only spatial multiplexing, andwith time/frequency scheduling. Config: clusters x users/cluster. timal number of spatial subgroups without the time/frequencyschedule, iii ) the optimal number of spatial subgroups withthe time/frequency schedule, and iv ) the best configuration between ii ) and iii ).When the number of users is comparable with the numberof transmit antennas (i.e., antennas), using two schedulingintervals provides the highest ASE in almost every users’distribution. Hence, the average performance of schedulingand best config options are practically equal. As we increasethe number of transmit antennas and keep the users’ de-ployment, spatial multiplexing without scheduling becomesthe best configuration in some users’ distributions. Thus, themaximum ASE for some users’ allocations is obtained usingspatial multiplexing without scheduling and with schedulingfor others. Consequently, the larger the transmit antennas, thehigher the improvements of using the best config option.V. C ONCLUSION
This work studies the multicast transmission in a MaMIMOsystem, considering spatially correlated fading channels. Sub-grouping the multicast users, based on their large-scale spatialcorrelation matrices, allows the system to improve the channelestimation using common pilots and precoding processes. Wehave used a DL power allocation scheme based on MMF. We conclude that the optimal subgroup configuration highlydepends on random users’ distribution and the spatial chan-nel correlation. Correlation matrices information allows thesystem to create multicast subgroups in scenarios where theusers are randomly placed in clusters. Nevertheless, the ASEdramatically drops when the number of users increases, mostlywhere they are not set in clusters. Our proposal of splitting themulticast users into two time/frequency schedule blocks basedon their large-scale fading coefficient presents a significantimprovement in the ASE. Hence, a resource allocation strategythat first decides using one or two time/frequency scheduleblocks and then creates spatial subgroups provides an attractiveimprovement in the ASE results.VI. A
CKNOWLEDGEMENT
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