This is a repository copy of Robust User Scheduling with COST 2100 Channel Model for Massive MIMO Networks.

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1 This is a reository coy of Robust User Scheduling with COST 00 Channel Model for Massive MIMO Networks. White Rose Research Online URL for this aer: htt://erints.whiterose.ac.uk/5447/ Version: Published Version Article: Bashar, Manijeh, Burr, Alister Graham orcid.org/ and Cumanan, Kanaathiillai orcid.org/ (08) Robust User Scheduling with COST 00 Channel Model for Massive MIMO Networks. Iet microwaves antennas & roagation. ISSN htts://doi.org/0.049/iet-ma Reuse This article is distributed under the terms of the Creative Commons Attribution (CC BY) licence. This licence allows you to distribute, remix, tweak, and build uon the work, even commercially, as long as you credit the authors for the original work. More information and the full terms of the licence here: htts://creativecommons.org/licenses/ Takedown If you consider content in White Rose Research Online to be in breach of UK law, lease notify us by ing erints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. erints@whiterose.ac.uk htts://erints.whiterose.ac.uk/

2 IET Microwaves, Antennas & Proagation Research Article Robust user scheduling with COST 00 channel model for massive MIMO networks ISSN Received on 7th Aril 07 Revised 4th November 07 Acceted on st November 07 doi: 0.049/iet-ma Manijeh Bashar, Alister Burr, Katsuyuki Haneda, Kanaathiillai Cumanan Deartment of Electronic Engineering, University of York, Heslington, York, UK Deartment of Electronics and Nanoengineering, Aalto University School of Electrical Engineering, Esoo, Finland Abstract: The roblem of user scheduling with reduced overhead of channel estimation in the ulink of massive multile-inut multile-outut (MIMO) systems has been investigated. The authors consider the COST 00 channel model. In this aer, they first roose a new user selection algorithm based on knowledge of the geometry of the service area and location of clusters, without having full channel state information at the BS. They then show that the correlation in geometry-based stochastic channel models (GSCMs) arises from the common clusters in the area. In addition, exloiting the closed-form Cramer Rao lower bounds, the analysis for the robustness of the roosed scheme to cluster osition errors is resented. It is shown by analysing the caacity uer bound that the caacity strongly deends on the osition of clusters in the GSCMs and users in the system. Simulation results show that though the BS receiver does not require the channel information of all users, by the roosed geometry-based user scheduling algorithm the sum rate of the system is only slightly less than the well known greedy weight clique scheme. Introduction Massive multile-inut multile-outut (MIMO) is a romising technique to achieve high data rate [ 3]. However, higherformance multiuser MIMO (MU-MIMO) ulink techniques rely on the availability of full channel state information (CSI) of all user terminals at the base station (BS) receiver, which resents a major challenge to their ractical imlementation. This aer considers an ulink MU system, where the BS is equied with M antennas and serves K s decentralised single antenna users (M K s ). In the ulink mode, the BS estimates the ulink channel and uses linear receivers to searate the transmitted data. The BS receiver uses the estimated channel to imlement the zero-forcing (ZF) receiver, which is suitable for massive MIMO systems [4]. To investigate the erformance of MIMO systems, an accurate small-scale fading channel model is necessary. Most standardised MIMO channel models such as IEEE 80., the Third Generation Partnershi Project satial model and the COST 73 model rely on clustering [5]. Geometry-based stochastic channel models (GSCMs) are mathematically tractable models to investigate the erformance of MIMO systems [6]. The concet of clusters has been introduced in GSCMs to model scatterers in the cell environments [6]. In [7], Samimi and Raaort use clusters to characterise an accurate statistical satial channel model in millimetre-wave (mmwave) bands by grouing multiath comonents (MPCs) into clusters. mmwave communication suffers from very large ath losses, and hence requires large antenna arrays in comensation. [6]. This aer investigates the throughut in the ulink for the massive MIMO with carrier frequency in the order of GHz, but the rinciles can also aly to other frequency bands including mmwave. Most existing massive MIMO techniques rely on the availability of the full CSI of all users at the BS, which resents a major challenge in imlementing massive MIMO. As a result, massive MIMO techniques with reduced CSI requirement are of great interest. An imortant issue in massive MIMO systems is investigating user scheduling, in which MU diversity gain with imerfect CSI is considered [8]. Recently, a range of user scheduling schemes have been roosed for large MIMO systems. Most of these such as that described in [9] require accurate knowledge of the channel from all otential users to the BS which in the frequency-division dulex (FDD) massive MIMO case is comletely infeasible to obtain. In [0], Xu et al. roosed a greedy user selection scheme by exloiting the instantaneous CSI of all users. However, in this aer we focus on a simlified and robust user scheduling algorithm, by considering massive MIMO simlifications and the effect of the cell geometry.. Contributions of this work This work investigates a new user selection algorithm for highfrequency stochastic geometry-based channels with large numbers of antennas at the BS receiver. We investigate user scheduling by considering the massive MIMO assumtion. The roosed geometry-based user scheduling (GUS) is similar to the greedy weight clique (GWC) algorithm, but with a different cost function. In the GUS algorithm, the BS selects users based only on the geometry of the area, whereas in the GWC the BS uses the channel of the users for user scheduling. Given a ma of the area of the micro-cell, we erform efficient user scheduling based only on the osition of users and clusters in the cell. In GSCMs, MPCs from common clusters cause high correlation which reduces the rank of the channel. In this aer, we investigate the effect of common clusters on the system erformance. Moreover, we assume that the sace-alternating generalised exectation (SAGE) algorithm [, ] is used (offline) to estimate the direction of arrival (DoA) and the delay of the ath. The erformance analysis shows the significant effect of the distinct clusters on the system throughut. We rove that to maximise the caacity of system, it is required to select users with visibility of the maximum number of distinct clusters in the area. Next, we show that the osition of clusters in the area can be given by geometrical calculation. Our results and contributions are summarised as follows: Close analytical aroximations for massive MIMO systems are found. Using the ma of the area and ositions of users, a new user scheduling scheme is roosed under the assumtion of no CSI at the BS, other than the location of clusters. Since the ositions of clusters in the area are fixed, we assume that cluster localisation can be done offline. Simulation results show that the roosed scheme significantly reduces the overhead channel estimation in massive MIMO

3 where w k and h k are, resectively, the kth rows of the matrix W = [w T, w T,, w Ks ] T and the kth column of H = [h, h,, h Ks ].. Geometry-based stochastic channel model In GSCMs, the double directional channel imulse resonse is a suerosition of MPCs. The channel is given by [3] h(t, τ, ϕ, θ) = j = a i, jδ(ϕ ϕ i, j)δ(θ θ i, j)δ(τ τ i, j), i = (5) N C Fig. General descrition of the cluster model. The satial sreads for the cth cluster are given systems comared with conventional user scheduling algorithms, esecially for indoor and outdoor of micro-cells. To investigate the robustness of the roosed algorithm to cluster localisation, the erformance degradation is shown for different values of the error in cluster localisation and simulation results show the robustness of the roosed user scheduling algorithm to oor cluster localisation.. Outline The rest of this aer is organised as follows. Section describes the system model. The roosed user scheduling scheme is resented in Section 3. Section 4 resents erformance analysis of the roosed user scheduling with no estimated CSI. The robustness of the roosed user scheduling algorithm to cluster localisation errors is investigated in Section 5. Numerical results are resented in Section 6. Finally, Section 7 concludes this aer..3 Notation Note that in this aer, uercase and lowercase boldface letters are used for matrices and vectors, resectively. The notation E{ } denotes exectation. Moreover, stands for absolute value. Conjugate transose of vector x is x H. Finally x T and X denote the transose of vector x and the seudo-inverse of matrix X, resectively. System model We consider ulink transmission in a single cell massive MIMO system with M antennas at the BS and K > M single antenna users. The M received signal at the BS when K s (K s M) users have been selected from the ool of K users, is given by r = k Hx + n, () where x reresents the symbol vector of K s users, k is the average ower of the kth user and H denotes the aggregate M K s channel of all selected users. The BS is assumed to have CSI only of the selected users. We are interested in a linear ZF receiver which can be rovided by evaluating the seudo-inverse of H, the aggregate channel of all selected users according to where denotes the number of MPCs, t is time, τ denotes the delay, δ denotes the Dirac delta function and ϕ and θ reresent the DoA and direction of dearture (DoD), resectively. Similar to [3], we grou the MPCs with similar delay and directions into clusters. Three kinds of clusters are defined; local clusters, single clusters and twin clusters. Local clusters are located around users and the BS while single clusters are reresented by one cluster and twin clusters are characterised by two clusters related, resectively, to the user and BS side as shown in Fig.. A local cluster is a single cluster that surrounds a user; single clusters can also occur in a different osition. Twin clusters consist of a linked air of clusters, one of which defines the angles of dearture of multiaths from the transmitter, whereas the other defines the angles of arrival at the receiver [3]. There are a large number of clusters in the area; however, just some of them can contribute to the channel. The circular visibility region (VR) determines whether the cluster is active or not for a given user. The MPC's gain scales by a transition function that is given by A VR (r MS ) = π arctan L c + d MS, VR R C λl c, (6) where r MS is the centre of the VR, R C denotes the VR radius, L C reresents the size of the transition region and d MS, VR refers to the distance between the mobile stations (MSs) and the VR centre. For a constant exected number of clusters N C, the area density of VRs is given by ρ C = N C π R C L C. (7) All clusters are ellisoids in the environment and can be characterised by the cluster satial delay sread, elevation sread and azimuth sread. Once the ositions of the BS and users are fixed, we need to determine the ositions of the clusters in the area by geometrical calculations. For the local clusters, we consider a circle around the users and the BS, so that the size of the local cluster can be characterised by the cluster delay sread (a C ), elevation sread (h C ) and the osition of MPCs [3]. For local clusters, the cluster delay, azimuth and elevation sreads can be given by a C = Δτc 0, (8a) W = H = H H H H H. () Then after using the detector, the received signal at the BS is b C = a C, h C = d C, BS tan θ BS, (8b) (8c) y = k WHx + Wn. (3) Let us consider equal-ower allocation between users, i.e. = (P t /k), in which P t denotes the total ower. The achievable sum rate of the system is obtained as K s R = log + k = w k h k K + i =, i k w k h i, (4) where c 0 denotes the seed of light, d C, BS is the distance between the cluster and the BS, Δτ refers to the delay sread and θ BS is the elevation sread seen by the BS. The delay sread, angular sreads and shadow fading are correlated random variables and for all kinds of clusters are given by [4] Δτ c = μ τ / d 0 σ τ (Z c /0), (9a) 000

4 β c = τ β 0 σ β (Y c /0), (9b) A C = max ex k τ (τ C τ 0 ), ex k τ (τ B τ 0 ), (8) S m = 0 σ s (X c /0), (9c) where Δτ c refers to the delay sread, β c denotes angular sread and S m is the shadow fading of cluster c. Moreover, X c, Y c and Z c denote correlated random variables with zero mean and unit variance. Correlated random rocess can be comuted by Cholesky factorisation [4]. Cholesky factorisation can be used to generate a random vector with a desired covariance matrix [5]. The MPCs ositions can be drawn from the truncated Gaussian distribution given by [3] f (r) = ex r μ r, o r r T πσ r, o σ r, o 0 otherwise, (0) where r T denotes the truncation value. For single clusters, the cluster delay, azimuth and elevation sreads can be given by a C = Δτc 0 /, b C = d C, BS tan ϕ BS, h C = d C, BS tan θ BS. (a) (b) (c) To get the fixed ositions of the single clusters, the radial distance of the cluster from the BS drawn from the exonential distribution [3] f (r) = 0 r < r min ex r r min otherwise. σ r σ r () To determine the fixed osition of the cluster, the angle of the cluster can be drawn from the Gaussian distribution with a standard deviation σ ϕ, C. For the twin clusters, for both the BS and user side clusters we have a C = Δτc 0, (3a) b C = d C, BS tan ϕ BS. For the BS side cluster, the elevation sread can be given by while for the MS side cluster, we have (3b) h C = d C, BS tan θ BS, (4) h C = d C, MS tan θ MS. (5) Fig. gives an examle of the geometry of the Cth cluster. For twin clusters, the distance between the cluster and the BS and the distance from the VR centre and the MS is given by [3] d C, BS tan Φ C, BS = d C, MS tan Φ C, MS. (6) The delay of a cluster is reresented by [3] τ C = (d C, BS + d C, MS + d C )/c 0 + τ C, link, (7) where the geometrical distance between twin clusters is reresented by d C, d C, MS denotes the geometrical distance between the user and the centre of the VR, d C, BS refers to the distance between the BS and the cluster and finally τ C, link is the cluster link delay between the twin clusters. Hence, the cluster ower attenuation is given by [3] where k τ denotes the decay arameter and τ B is the cut-off delay. We assume Rayleigh fading for the MPCs within each cluster. Hence, the comlex amlitude of the ith MPC in the jth cluster in (5) is given by a i, j = L A VR A C A MPC e jπ f cτ i, j, (9) where L is the channel ath loss, A MPC is the ower of each MPC which is characterised by the Rayleigh fading distribution and τ i, j is the delay of the ith MPC in cluster j given by [3] τ i, j = d MPC i, j, BS + d MPCi, j, MS c 0 + τ i, C, link. (0) By assuming a fixed orthogonal frequency-division multilexing subcarrier, we can dro the variable τ i, j from (39). For the nonline-of-sight (NLoS) case of the micro-cell scenario, the ath loss exression can be given by [6] L = 6log 0 d + 0log 0 4π λ, () where d and λ denote the distance (in metres) and the wavelength (in metres), resectively. 3 Geometry-based US In this section, we consider user scheduling with ZF based on the osition of clusters and users in the area. To avoid a huge channel estimation load in the ulink of a massive MIMO system with many users and antennas, we roose to estimate only the channels of the selected users. The reduction in the amount of channel estimation required between each transmit and receive antenna is the imortant result of the roosed scheme. The gain achieved by selecting users with the strongest channel is referred to as MU diversity and requires CSI of all users [7]. However, we roose a new user selection scheme which relies on maximising the number of distinct clusters seen by the scheduled users. In the next sections, we rove that the roosed scheme results in less interuser interference and increases the users signal-to-interferencelus-noise ratio and the system's sum rate. In the following section, we resent a scheme to select users which maximises the long-term sum rate and as it is based on the osition of the users and does not need the estimated channel of all users in the ulink, and hence can be a ractical user selection scheme for large MIMO systems. For this case, the erformance analyses are found in the next section. 3. Proosed GUS In this section, an algorithm is roosed for increasing the system throughut based on the geometry of the system and without estimating the channels of all users in the area. Once the set of active users has been determined, the receiver BS estimates the channels of the selected users and the users transmit data. Next, the erformance of the roosed user selection algorithm to maximise the sum rate is evaluated. In large MIMO systems with large numbers of users estimating the channels of all users, it is ractically difficult. So the roosed user scheduling algorithm can be an efficient way to reduce the overhead of channel estimation. First, we generate the matrix V, as the following equation: where V = v v v v v NC v NC K K K v v v NC, () 3

5 channel and the caacity of the system, esecially at finite signalto-noise ratio (SNR). These common clusters also affect the multilexing gain of the system. Fig. illustrates the concet of common and distinct clusters. When the number of objects is less than the number of BS antennas and all objects are shared between the users, achieving maximum multilexing gain is imossible [8, 9]. For ease of mathematical tractability, we analyse the caacity of a correlated three-user ulink using an uer bound. In the case of a large number of antennas at the BS, the caacity uer bound can be achieved in the case of distinct clusters. Note that in the case of a large number of transmit antennas, the elements of HH H converge to the correlation matrix so that R HH H. Hence, we have Fig. Examle of users common cluster which causes correlation v i j = j j L, i A VR, i j A C, i, (3) where L j j denotes the channel ath loss for user j, A VR, i is the MPC ower attenuation which is a function of the distance between the user i and the centre of the VR related to the jth cluster and is given j by (6) and A C, i denotes the cluster ower attenuation given by (8) for the user j and the ith cluster. So, the matrix V is a function of the distance from the BS to users, the distance of the BS from clusters and from users to the centre of the VR. Algorithm : GUS algorithm. Initialise W 0 = [,, K], S 0 =, i =.. Reeat until S 0 = K s. 3. i = i π(i) = arg max k Wi f ( v k ) = arg max k Wi v k, S 0 S 0 {π(i)}, v^(i) = v (π(i)). 5. W i = k W i, k π(i), v k v^ (i) / v k v^ (i) < ϵ h. 6. If W = 0, end. Note that increasing ϵ h allows the users to have a larger number of shared clusters. If the value of ϵ h is too high, Algorithm selects users with a large normalised correlation which can reduce the sum rate due to the interference in the number of selected users. For a low ϵ h, the number of users in set V 0 in ste 5 decreases and Algorithm selects a small number of users. Suose W 0 contains user indices considered in the roosed algorithm. Finally, S 0 contains K s = S 0 indices of the selected users. 4 Performance analysis If erfect CSI is available at the BS, and assuming Gaussian inut, the ergodic caacity is given by C = E log det I + P t K s HH H, (4) where the term P t /K s is due to the equal-ower allocation, I is an identity matrix and the channel matrix is given at the bottom of this age, where C(K) denotes the clusters seen by the kth user and α = π(d/λ), where d denotes the sacing between two antenna elements. In GSCMs, common clusters can reduce the rank of the C = E log log det I + P t K HH H det I + P t K R, (5) (see (6)) where R is the channel correlation matrix and is given by where R = E H H H = r r 3 r r 3 r 3, (7) r 3 r = E h H h = ζ e jβ, (8a) r 3 = E h H h 3 = ζ 3 e jβ 3, (8b) r 3 = E h H h 3 = ζ 3 e jβ 3. (8c) The term r can be given by (see (9)) where a i, j, the amlitude of the i MPCs in cluster j, is given by (39), and the terms r 3 and r 3 can be derived in the same way. By substituting the terms r, r 3 and r 3 into (5), the caacity maximisation roblem in a three-user scenario can be formulated as C = max log ( + ) 3 ζ + ζ 3 + ζ 3 ζ, ζ 3, ζ 3 β, β 3, β ζ ζ 3 ζ 3 sin(β β 3 + β 3 ) ζ ζ 3 ζ 3, (30) where = (P t /K). To maximise (30), the gradient search method results in ζ = ζ 3 = ζ 3 = 0, for different values of β, β 3 and β 3, which is the case when common clusters do not occur between the users in the cell. In the case of distinct clusters between user m and user n, we have rclζ mn = E j C(n) i = a i, j a g, l l C(m) g = = 0. (3) Equation (3) yields ζ mn = 0, which maximises the caacity given by (30). For the case of massive MIMO systems with a large number of users in the cell, having distinct clusters for all users is ractically difficult. In a real scenario, it is not ossible to force the term ζ mn H = N j C() i = a i, j l C() i = N j C() i = a i, j e jα sin ϕ i, j l C() i = N a i, l m C(K) i = a i, l e jα sin ϕ N i, l m C(K) i = N j C() i = a i, j e jα(m )sin ϕ i, j l C() i = a i, l e jα(m )sin ϕ i, l m C(K) i = a i, m a i, m e jα sin ϕ i, m a i, m e jα(m )sin ϕ i, m, (6) 4

6 r = E h H h = E j C() i = a i, j a g, l l C() g = + j C() i = a i, j e jα sin ϕ i, j l = C() g = a g, l e jα sin ϕ g, l (9) + + j C() i = a i, j e jα(m )sin ϕ i, j l C() g = a g, l e jα(m )sin ϕ g, l, zero. The roosed user scheduling algorithm selects users which do not have common clusters and consequently forces the variable ζ mn to be small. A threshold is set for the ower of a cluster to be considered active. In the COST channel model, each user interacts with several clusters in the area and the cluster ower deends on the distance between the user and the centre of VR and also the distance between the cluster and the BS. We define a threshold which can determine the minimum ower that a cluster may have relative to the total owers. As in [0], we set the cluster ower threshold to 0.0 total ower for a cluster to be active. A cluster is shared between two users if contributes to both users, which means the cluster owers seen by the users are more than the threshold. Hence, the otimum value of ζ mn can be achieved only when there is no common cluster in the cell. 5 Robustness of the roosed user scheduling algorithm 5. Cluster localisation The BS can estimate the DoA [], and hence the direction of the scattering objects should be available at the BS. There is a well known algorithm to estimate the delay, DoA and the DoD of the channel aths; SAGE-based algorithm [, ]. As a result, the BS can identify the direction of the clusters which can be seen by the users in the cell area, and hence build u a ma of the location of the scattering objects. The convenient tool that has overcome the challenge of making the osition of the scatterers available is the use of environment mas [3], which also shows how measured angles of arrival can be identified with hysical objects in the environment, and hence can be located on the ma. Successive interference cancellation has also been introduced in [] for scattering object identification: it uses the channel imulse resonse eaks in the delay domain to ma scatterers to twodimensional coordinates. 5. Robustness To study the robustness of the roosed algorithm to cluster localisation error, we use the well known SAGE algorithm [, ], oerating offline, as mentioned above. In cluster localisation, we consider a receiver BS with an antenna array consisting of M sensors located at a reference oint [, ]. Moreover, we consider lanar wavefronts. The closed-form Cramer Rao lower bound (CRLB) for the delay, azimuth (ν) and elevation (θ) of the ath are given by [] CRLB(τ) = γ O 8π BW CRLB(θ) = M Δ cos(ν) γ O CRLB(ν) = γ O M Δ, where BW is the bandwidth and and Δ = 4π (3a) (3b) (3c) d 7 λ 3 M x 3 8M x M x 4, (33) γ O = M I N f (ν) γ I, (34) where I is the number of eriods of the received signal, N denotes the length of the used seudo-noise sounding sequence available at the receiver and γ I is the SNR at the inut of each antenna [, ]. Moreover, the antenna electric field attern can be given by [] f (ν) = ν 6.79ν + 5.7ν 3.7ν 3. (35) The distance between the BS and cluster (d BS, C ) is given by geometrical calculation cτ d BS, C = h BS h MS + d BS, C sin(ν) + d BS, MS d BS, C cos(ν)cos(θ), (36) where c denotes the velocity of light, d BS, MS is the distance between the user and the BS in the x y-lane and h BS and h MS are the BS and user heights. The distance between the user and cluster is easily given by d MS, C + d BS, C = cτ. (37) After the offline localisation, the BS can build u the matrix V ~ at the beginning of each time slot, as the following equation: where V ~ = v ~ i j = v ~ v ~ v ~ v ~ v ~ N C v ~ N C v ~ K v ~ K L j A ~ j VR, i v ~ K N C, (38) A ~ j C, i, (39) where A ~ j VR, i and A ~ j C, i can be calculated by the distances obtained in (37). Finally, for the matrix V, the following equation holds: V = V ~ + E, (40) where E is due to the estimation error in cluster localisation. Then, we use V ~ instead of V in the roosed algorithm. The numerical results verify the robustness of the roosed algorithm to this error. 6 Numerical results and discussion In this section, simulation results have been rovided to validate the erformance of the roosed schemes with different arameters. 6. Simulation arameters for COST 00 channel model We evaluate the throughut of the system, averaging over 50 iterations. A square cell with a side length of R has been considered so that we call R the cell size and also assume users are uniformly distributed in the cell. As in [4], we assume that there is no user closer than R th = 0. R to the BS. We simulate a microcell environment for the NLoS case and set the oerating frequency 5

7 Fig. 3 Average sum rate versus the cell size for different values of M = 00, M = 00, Ks = 50 and 40. We set the total number of users in the cell K = 400 Fig. 5 Channel estimation load versus value of error of antennas at the receiver BS for different values of total number of users in the cell Fig. 6 Average sum rate versus the estimation error for different values of total number of selected users in the cell and the cell size Fig. 4 Average sum rate versus total number of users for different values of M = 00, M = 00, Ks = 50, 40, R = 600 m and 000 m f C = GHz. The external arameters and stochastic arameters are extracted from chater 6 of [4] and chater 3 of [3]. The BS and user heights are assumed to be hbs = 5 and hms =.5, resectively. In (7), NC = 3, RC = 50 and LC = 0. Moreover, we consider NP = 6 aths er cluster. 6. Simulation results For this network setu, the average sum rate is evaluated for the three scenarios. In the GUS scheme, it has been roosed that the receiver BS selects users which maximise the number of distinct clusters in the cell. We evaluate the average throughut of the GWC scheme [3, 4] and random selection of users. For the case of GWC, similar to [4], we set the otimal channel direction constraint to achieve the best erformance for GWC, so the comlexity of GWC is much higher than GUS. Fig. 3 deicts the average sum rate with total number of receive antennas at the BS M = 00 and 00, and two values of the number of selected users Ks = 40 and 50 while adoting the roosed scheme with ZF receiver. As exected, since GWC exloits erfect CSI, it has the best throughut. As seen in Fig. 3, the erformance of the roosed algorithm is slightly lower than the case, in which the BS exloits full CSI and erforms GWC. Interestingly, for bigger cells, the sueriority of the roosed 6 scheme is more obvious in terms of achieving erformance close to that of the GWC scheme. In Fig. 4, we have lotted the average sum rate for the case of GWC and GUS versus total number of users in the cell (K) with different numbers of receive antennas at the BS M and of selected users Ks. In terms of average sum rate, Fig. 4 shows that the roosed scheme results in only a small sum rate reduction even with a smaller total number of users. The amount of channel estimation load required in both GWC and the roosed GUS is resented in Fig. 5. As this figure shows the channel estimation load of the roosed GUS is far less than that of the GWC scheme. To investigate the robustness of the roosed scheme to different values of the error, we set e = Ω CRLB(ρ), (4) where e denotes the absolute value of the estimation error, Ω is an integer number and CRLB(ρ) is given by (3a) (3c), where the arameter ρ can be the delay, azimuth and elevation. Fig. 6 shows the average sum rate with total number of receive antennas at the BS M = 400, and two values of the number of selected users Ks = 0 and 40 versus the value of the estimation error. We set the SNR at the inut of each antenna γi = 0 db and BW = 0 MHz. Moreover, in (3a) (3c), Mx = 5, N = 7, which are extracted from []. This figure shows the robustness of the roosed algorithm to oor cluster localisation.

8 7 Conclusions We have investigated the user scheduling roblem in massive MIMO systems and roosed a new GUS scheme which maximises the ulink throughut of the users, considering the FDD mode. By alying knowledge of the location of clusters and users and the geometry of the system, we suose that the BS does not need to estimate the channels of all users and selects users based only on the location of users and clusters in the area. Next, exloiting CRLB, we have develoed a robustness analysis for the roosed scheme. The results show that while sum rate slightly decreases along with the reduced overhead of channel estimation, the roosed algorithm can be an efficient scheme to reduce the comlexity of user scheduling in massive MIMO systems. In addition, the simulation results demonstrate good robustness against the estimation error. 8 References [] Zaone, A., Sanguinetti, L., Bacci, G., et al.: Energy-efficient ower control: a look at 5G wireless technologies, IEEE Trans. Signal Process., 06, 64, (7), [] Björnson, E., Jorswieck, E.A., Debbah, M., et al.: Multiobjective signal rocessing otimization: the way to balance conflicting metrics in 5G systems, IEEE Signal Process. Mag., 04, 3, (6),. 4 3 [3] Marzetta, T.L.: Noncooerative cellular wireless with unlimited numbers of base station antennas, IEEE Trans. Commun., 00, 9, (), [4] Ngo, H.Q., Larsson, E.G., Marzetta, T.L.: Energy and sectral efficiency of very large multiuser MIMO systems, IEEE Trans. Commun., 03, 6, (4), [5] Hofstetter, H., Molisch, A.F., Czink, N.: A twin-cluster MIMO channel model. Proc. First Euroean Conf. Antennas and Proagation, Nice, France, November 006 [6] Molisch, A.F., Tufvesson, F.: Proagation channel models for nextgeneration wireless communications systems, IEEE Trans. Commun., 04, 97, (0), [7] Samimi, M.K., Raaort, T.S.: Statistical channel model with multi frequency and arbitrary antenna beamwidth for millimetre-wave outdoor communications. Proc. IEEE Globecom, San Diego, CA, USA, December 05 [8] Liu, H., Gao, H., Yang, S., et al.: Low-comlexity downlink user selection for massive MIMO systems, IEEE Syst. J., 07,, (), [9] Lee, G., Sung, Y.: A new aroach to user scheduling in massive multi-user MIMO broadcast channels, IEEE Trans. Commun., 08, 66, (4), [0] Xu, Y., Yue, G., Mao, S.: User grouing for massive MIMO in FDD systems: new design methods and analysis, IEEE Access, 04,, [] Tschudin, M., Heddergott, R., Truffer, P.: Validation of a high resolution measurement technique for estimating the arameters of iminging waves in indoor environments. Proc. IEEE Personal, Indoor and Mobile Radio Communications (PIMRC), Boston, MA, USA, Setember 998 [] Fleury, B.H., Tschudin, M., Heddergott, R., et al.: Channel arameter estimation in mobile radio environments using the SAGE algorithm, IEEE J. Sel. Areas Commun., 999, 7, (3), [3] Verdone, R., Zanella, A.: Pervasive mobile and ambient wireless communications: COST action 00 (Sringer-Verlag, London, 0) [4] Correia, L.M.: Mobile broadband multimedia networks (Academic Press, San Diego, 006) [5] Golub, G.H., Van Loan, C.F.: Matrix comutations (Johns Hokins, Baltimore, 996) [6] Feuerstein, M.J., Blackard, K.L., Raaort, T.S., et al.: Path loss, delay sread, and outage models as a function of antenna height for microcellular system design, IEEE Trans. Veh. Technol., 994, 43, (3), [7] Yoo, T., Goldsmith, A.: On the otimality of multiantenna broadcast scheduling using zero-forcing beamforming, IEEE J. Sel. Areas Commun., 006, 4, (3), [8] Burr, A.G.: Multilexing gain of multiuser MIMO on finite scattering channels. Proc. Wireless Communication Systems (ISWCS), York, UK, Setember 00 [9] Burr, A.G.: Caacity bounds and estimates for the finite scatterers MIMO wireless channel, IEEE J. Sel. Areas Commun., 003,, (5), [0] Zhu, M., Eriksson, G., Tufvesson, F.: The COST 00 channel model: arameterization and validation based on outdoor MIMO measurements at 300 MHz, IEEE Trans. Wirel. Commun., 03,, (), [] Godara, L.C.: Handbook of antennas in wireless communications (CRC Press, Boca Raton, 00) [] Santos, T., Karedal, J., Almers, P., et al.: Scatter detection by successive cancellation for UWB method and exerimental verification. Proc. IEEE Vehicular Technology Conf., Singaore, May 008 [3] Yoo, T., Goldsmith, A.: Sum-rate otimal multi-antenna downlink beamforming strategy based on clique search. Proc. IEEE Globecom, vol. 3, St. Louis, MO, USA, December 005 [4] Lu, P., Yang, H.C.: Sum-rate analysis of multiuser MIMO system with zeroforcing transmit beamforming, IEEE Trans. Commun., 009, 57, (9),