A decentralized beam selection for mmWave beamspace multi-user MIMO system

Int. J. Electron. Commun. (AEÜ) 111 (2019) 152884

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Regular paper

A decentralized beam selection for mmWave beamspace multi-user MIMO system Rahul Pal ⇑, K.P. Sarawadekar, K.V. Srinivas Indian Institute of Technology (Banaras Hindu University), Varanasi, India

a r t i c l e

i n f o

Article history: Received 26 April 2019 Accepted 25 August 2019

Keywords: mmWaves MU-MIMO Discrete lens array Beamspace Precoding Auction algorithm Distributed auction algorithm

a b s t r a c t A millimeter beamspace multi-user multi-input-multi-output system is a key enabling technology of 5G to fulfil the demand for high data rate. But, it suffers from high RF complexity. However, RF Complexity can be reduced by the beam selection algorithm. Hence, few beam selection algorithms were proposed with a centralized approach. In this paper, a decentralized beam selection algorithm for millimeter wave beamspace multi-user MIMO is discussed. Unlike the centralized beam selection algorithm, the decentralized beam selection algorithm doesn’t require a central unit or access point to select beams. The users themselves play an active role to select beams by sharing the local information with the neighbour users. This is also the requirement of a dynamic network. The performance thoroughly confides on the network cooperation to select beams in an efficient manner. The proposed decentralized beam selection algorithm enables the access point to be free from handling of a large channel matrix. Therefore, this low complexity beam selection algorithm is a better alternative. The performance and complexity of the proposed beam selection algorithm are examined in the following section. Ó 2019 Elsevier GmbH. All rights reserved.

1. Introduction The demand of a larger bandwidth for the next-generation networks, 5G can be fulfilled by deploying millimeter wave frequencies (mmWave) (30–300 GHz), which can dispense signal bandwidth up to 2 GHz [1]. The integration of mmWave frequencies and multi-input-multi-output (MIMO) technology has been discussed in [2,3]. Particularly, hybrid architecture [4–7] is employed at the access point (AP) because of its tremendous advantage. Hybrid architecture is a concatenation of digital and analog architecture. In the analog architecture, RF beamforming is employed whereas digital precoder is employed in the digital architecture. As a result, an AP accompanied with a larger antenna array followed by a hybrid architecture steers the narrow beams towards users and each steered beam requires a radio frequency (RF) chain, which is connected with N antenna elements. This system has a large antenna array and hence require N number of RF chains to generate N number of beams. This increases the RF complexity. The radiated mmWaves from a larger antenna array propagate in the wireless medium. Evidently, the effective aperture of any antenna is proportional to square of wavelength (k) of the radiated ⇑ Corresponding author. E-mail address: [email protected] (R. Pal). https://doi.org/10.1016/j.aeue.2019.152884 1434-8411/Ó 2019 Elsevier GmbH. All rights reserved.

waves. In turn, the mmWave propagation is highly narrow or sparse, and the line-of-sight (LoS) path predominates over nonline-of-sight (NLoS) paths [8,9]. Therefore, discrete lens array (DLA) is deployed at the access point (AP) [9] and the conventional or spatial channel is transformed into the beamspace channel, and the sparsity is exploited. The system with a DLA is capable of steering orthogonal beams in the fixed angular directions, which covers the entire angular space as shown in Fig. 1. RF complexity is still the main hurdle of this high dimensional beamspace system because each beam requires a dedicated RF chain. But, the power consumption per RF chain is 250 mW for mmWave frequencies [9], and it leads to high power consumption. To circumvent this hurdle, beam selection algorithm was deployed at AP, which enforces the system to select only equitable beam while other beams remain inactive. It implies that we can reduce the required number of RF chains. Hence, beam selection algorithms with different performance and complexity are proposed in [10–14]. The algorithm in [10] selects beams of the highest channel magnitude. In turn, the same beam can be selected by multiple users. It degrades the system performance. Further, the algorithm [10] is improved by the beam selection algorithms [11–13]. Interference-aware beam selection algorithm in [11] selects beams considering multi-user interference at users’ side. The algorithms in [12] select beams by maximizing signal-to-interference-noise-

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Fig. 1. Block diagram.

ratio (SINR), maximizing the capacity but holding high complexity. The QR-based [13] and maximum weight matching (MWM)-based [14] beam selection algorithm are presented with the new precoder which outperforms [10–12]. QR-based beam selection algorithm selects the beam while pre-canceling the multi-user interference whereas MWM-based beam selection doesn’t take account of interference. Thus, the QR-based beam selection algorithm [13] is superior to MWM-based beam selection algorithm [14]. The aforementioned algorithms have been deployed in a centralized way. Unlike centralized algorithms, decentralized algorithm [15] distributes the computation to the multiple processors and these processors are the users themselves. Therefore, the users themselves play an active role to perform the beam selection and all of them form a dynamic network topology. Consequently, beam selection is performed by sharing information between neighbouring users in the network. The information exchange between users takes some time and causes some delay which depends on the distance between connected users in the network [15]. Thus, the performance of the decentralized algorithm also depends on the network cooperation among the users. In this paper, we are proposing two beam selection algorithms which approach to a concept of real bidding to maximize the following objective:

each user having a single receive antenna, is considered here. The antenna elements in the ULA are spaced d ¼ 2k units from each other, where k is the carrier wavelength. We consider N  K and such a massive MIMO system can be described, in the spatial domain, as


þ w;
H Px

¼H y

Thus, we are investigating both the centralized and decentralized algorithm to examine performance and complexity Notation: Matrices and vectors are denoted by boldface upperth

case and lowercase letters, respectively. aij and xi denote ðijÞ th

ment of matrix A and i

ele-

element of vector x, respectively. Aj

i


1; . . . ; h
K 2 CNK is the channel matrix and h
2 CN1
¼ h where H k  th    H
is the channel vector of k user and hk ¼ h1k ; h2k ; . . . ; hNk 2 CN1 th

is the channel vector to the k user which is containing the channel
2 CNK is the precoding matrix gain from N elements of the ULA. P to cancel the multi-user interference and x 2 CK1 is the transmit symbol vector, and the average power constraint is satisfied by h i
2 6 q. y
is the received information vector. w
is the additive E kPxk  
 CN 0; r2 IK . The white Gaussian noise (AWGN) vector with w channel model for mmWave communications for user k [16] is given as


¼ h k

rffiffiffiffiffiffiffiffiffiffiffi L N X ð‘Þ  ð‘Þ  b a hk ; L þ 1 ‘¼0 k ð0Þ

1. A centralized beam selection algorithm: the central unit assigns beam to users through well-developed auction algorithm. 2. A decentralized beam selection algorithm: beams are assigned to users without a central unit through a distributed auction algorithm with an assumption that one of the nearest users to AP in the network will feedback index number of the beams to AP as shown in Fig. 1.

ð1Þ

h

where bk

ð2Þ

ð‘Þ

and bk ; ‘ ¼ 1; . . . ; L, denote the complex-valued path

gain of the LoS and ‘th NLoS for user k, respectively. The array steering vector corresponding to the LoS for user k is given by,

 i   1 h ð0 Þ ð0Þ a hk ¼ pffiffiffiffi exp |2phk i ; i2I N N

ð3Þ

where I N ¼ fi  ðN  1Þ=2; i ¼ 0; 1; . . . ; N  1g is a set of index set ð0Þ

ð0Þ

hk ¼ 0:5 sin /k is the spatial frequency evaluated by the angle of   th ð0Þ arrival (AOA) /k 2  p2 ; p2 of the LoS at k user. The array steering   ð‘Þ vector corresponding to the ‘th NLoS component, a hk , is obtained  p p ð‘Þ ð‘Þ ð‘Þ by using hk ¼ 0:5 sin /k , where /k 2  2 ; 2 is the AOA of the ‘th th

NLoS component at k

user.

th

denotes matrix A with its j row removed and kAkF denotes Frobenius norm of A. IN is N  N identity matrix. Superscripts 1; T; H;  indicate inverse, transpose, conjugate transpose, and conjugation, respectively.

2. System model A downlink communication system having an AP equipped with a uniform linear array (ULA) with N antenna elements and K users,

3. Beamspace representation A conventional spatial channel model is presented in the previous section. For the propagation of mmWave frequencies, the LoS component predominates over NLoS components and the channel is sparse in the angular domain, i.e., beamspace domain. The channel can be transformed from the conventional spatial domain to beamspace by deploying a DLA at the AP. DLA plays the role of a spatial discrete Fourier transform (DFT). Let U 2 CNN be a DFT

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matrix, consisting of column vectors corresponding to N fixed spatial frequencies. Each column vector corresponding predefined direction is given by hi ¼ Ni ; i 2 I N and it is orthogonal to the remaining columns. Hence, all N column vectors are covering the entire angular space. The matrix U is given by



i U ¼ a hi ¼ N i2I N

ð4Þ

The downlink system, in beamspace domain, is given by,

y ¼ HH Px þ w;

ð5Þ


¼ ½h1 ; . . . ; hK  2 C where H ¼ U H is the beamspace channel     H matrix and hk ¼ h1k ; h2k ; . . . ; hNk 2 CN1 is the beamspace channel H

NK

th

vector to the k user which is containing the gain from N beams, respectively. P is the beamspace digital precoder to cancel the multi-user interference. w is the additive white Gaussian noise   (AWGN) vector with w  CN 0; r2 IK . Each row vector in the beamspace channel, i.e., H corresponds to a single beam. Each beam requires an RF chain. Selecting only equitable beams, out of N, reduces the required number of RF chains as discussed in [10]. The main task is to select the equitable beams without incurring considerable performance loss. We formulate the problem of selecting K beams out of N. A downlink system, after beam selection, in beamspace domain is given by

~ H Px ~ þ w; ~¼H ~ y

ð6Þ

~ 2 CKK is the beamspace channel matrix. P ~ 2 CKK is the where H corresponding precoder to cancel the multi-user interference. P Hence, we achieve the sum rate Rsum ¼ k Rk , where Rk ¼ log2 ð1 þ SINRk Þ is the rate achieved by user k and SINRk is the signal-to-noise plus interference ratio at user k [13]. 4. Beam selection DLA provides N beams out of which single beam is assigned to each user. So, we need only K RF chains. The beams should be selected to maximize the sum rate in the mmWave beamspace MU-MIMO system. Thus, the selection of K beams out of N is the problem which we are addressing here. In this paper, beam selection is modelled as a resource allocation problem. As in [17], auction algorithm can be used to allocate resources such as bandwidth [18], power to the users [19–21]. Similarly, in the MU-MIMO system, beams can be considered as resources and those can be allocated (or assigned) to the users in an optimal manner through a central auctioneer using the auction algorithm. Further, the auction algorithm has a distributed variant, that doesn’t require a central unit to do the allocation [15]. In this paper, we make use of both the centralized and distributed framework of the auction algorithm. So far, in the open literature, all the existing beam selection algorithms use centralized solutions, namely maximum magnitude [10], interference-aware [11], maximum SINR [12] and QR-decomposition based beam selection [13], MWM-based beam selection [14]. 4.1. Beam selection through auction algorithm In auction algorithm, a central unit, or, an auctioneer, conducts an auction of items among the bidders, and bidders raise the price of items which they desire the most. After getting bids from all the bidders, the auctioneer sells each item to the highest bidder of that item. Let K ¼ f1; . . . ; K g and N ¼ f1; . . . ; N g be the set of users and beams, respectively. Let wkn be the benefit gained by user k from beam n and pn be the price that a user has to pay for beam n. Thus, the net benefit to user k from beam n is equal to ðwkn  pn Þ. Each

user wishes access to a beam that offers a maximal net benefit to him/her. Equivalently, user k wants to get access to beam nk , where

nk ¼ arg maxfwkn  pn g

ð7Þ

n2N

where nk ¼ arg maxn2N fwkn  pn g is the beam that results in highest net benefit for user k. If this condition satisfies for all users then algorithm gets terminated otherwise unassigned users (The users who desire the same beam, but which is already assigned to another user) increase the price of beam or bidding amount for which they are benefited the most in such a way

n o 0 bk ¼ wknk  pnk ; bk ¼ max fwkn  pn g;

ð8Þ

n2N ;n–nk

0

Note that bk is the highest net benefit and bk is the second highest net benefit for user k and the bidding increment for his/her desired beam is given by dk

dk ¼ bk  bk þ ; 0

ð9Þ

where  is a participating price which enforces the algorithm to achieve an equilibrium condition. Now, let n be the beam for which the bidding amount has been incremented by the unassigned users who belong to set U ðnÞ, where U ðnÞ # U, where U is a set of unassigned users, and U ðnÞ – £. The price of beam n is increased by the highest bidding amount maxk2U ðnÞ dk and beam n is assigned to the highest bidder kðnÞ where kðnÞ ¼ arg maxk2U ðnÞ dk . Thus, the highest bidder who was unassigned user in U ðnÞ is now assigned to nth beam and the previously assigned user to nth beam becomes unassigned. This process is repeated until all the users are assigned. The detailed discussion is given by Algorithm 1. Algorithm 1. Beam selection through auction algorithm 1: Requirement: the price list pn and the benefits wkn , k 2 K; n 2 N 2: Initialize: pn ¼ 0; 8n 2 N ; U ¼ £ 3: for k ¼ 1 ! K do 4: nk ¼ arg maxn2N fwkn  pn g 5: if Beam nk is unassigned then 6: Assign beam nk to user k 7: else 8: U ¼ U [ fkg (Add k to the set of unassigned users) 9: end if 10: end for 11: while U – £ do 12: 13: 14: 15: 16:

0

Initialize: N ¼ £ for k 2 U do

n o nk ¼ arg maxn2N wknk  pnk 0

0

N ¼ N [ nk n o bk ¼ wknk  pnk 0

17: bk ¼ maxn2N ;n–nk fwkn  pn g 18: Compute bidding increment for desired beam: 0 dk ¼ bk  bk þ  19: end for 0

20: for n 2 N do 21: Assign beam n to user kðnÞ, where kðnÞ ¼ arg maxk2U ðnÞ dk 22: If beam n was previously assigned to another user, make him/her an unassigned user and add to set U. 23: Increase the price of beam n by maxk2U ðnÞ dk . 24: end for 25: end while

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4.2. Beam selection through distributed auction algorithm

selection. Zero-forcing (ZF) is one of the precoding schemes but ~ is a ill-conditioned matrix ZF degrades the performance when H

For the centralized beam selection algorithms, AP requires channel information. But, AP gets heavily loaded due to large dimension of channel handling matrix and it becomes a bottleneck to process over a large matrix dimension to select equitable beams. Therefore, we are proposing a decentralized beam selection which has been proven a better alternative in Section 6. Thus, a decentralized beam selection through a distributed auction algorithm is discussed in the followings. As in [15], the distributed auction algorithm distributes the computation among all the users. Unlike the auction algorithm, the price list of beams is not shared through a common memory because only local communication is possible among the neighbouring users. But, for the correct assignment of beams, the updated price list should be known to each user. Therefore, each user updates their price list using the neighbour user’s protocol agreement. However, the performance of the distributed auction algorithm may vary with network topology, and the information exchange can occur between two nearest users in the formed network-topology. In the beginning, each user bids for the desired beam and store the price list. But, each user is unaware of other highest bidders. So, they set theirselves as the highest bidders. Let K ¼ f1; . . . ; K g and N ¼ f1; . . . ; N g be the set of users and beams, respectively. As shown in [15], let ak ðt Þ be the assignment status of user k at time t, such that ak ðt Þ ¼ n if user k is assigned to beam n, where k 2 K; n 2 N . Furthermore, the price list of user k corresponding to each beam is represented as pkn ðtÞ P 0, n 2 N at time t and the highest bidders with the largest index is given as g kak ðtÞ ¼ k at time t, ak ðtÞ ¼ arg maxn2N fwnk  pnk g. All users are allowed to update their price list as well as the corresponding highest bidders according to protocol agreement among the neighbour users (2 Dk ðt Þ, is a set of the neighbour users to user k) with the aid of local information as per communication cycle. Each user inquires the highest bidders and bidding amount via the information exchange with the neighbour users. If the bidding amount is found to be higher which is made by another user then user updates the highest bidding amount and corresponding the highest bidders. Next, each user increases the bidding amount for the beam that gives him/ 0 her maximal net benefit by an amount dk ¼ bk  bk þ , where

and is not applicable to rank deficient matrix. A precoder that elime inates multi-user interference, based on QR decomposition of H,

n

bk ¼ wknk 0

bk ¼

o  pknk ðtÞ ;

max

n–ak ðtþ1Þ;n2N

fwkn  pkn ðtÞg;

ð10Þ

has been proposed in [13]. We implement the same precoder for cancelling the multi-user interference. After implementing this th

precoder, the received symbol for k

~ k ; k ¼ 1; . . . ; K; ~k ¼ ~rkk ~xk þ w y

5. Precoding and complexity In this section, we discuss precoding and complexity of beam selection algorithm, respectively. We also compare the complexity of the proposed beam selection algorithms with the existing beam selection algorithms. Beam selection algorithm select beams for the users, whereas precoding is employed to eliminate the multi-user interference, ~ after beam evaluated through the reduced channel matrix, i.e., H

ð12Þ

th where ~r kk is the effective channel gain of k user and is the k   ~ R. ~ H ~ ¼Q ~ w ~ k is the AWGN with  CN 0; r2 . diagonal element of R; th

Algorithm 2. Beam algorithm for user k

selection

through

distributed

auction

1: Requirement: the price list pkn and the benefits wkn , k 2 K; n 2 N 2: Initialize: the price of each beam is 0 except the most desired beam, pkak ðtÞ ðt Þ þ dk ; ak ðt Þ 2 N and the highest bidders g kak ðtÞ ðtÞ ¼ k 3: User k updates the price list by information exchange from the neighbor users:

n o pkn ðt þ 1Þ ¼ max pknðtÞ ; plnðtÞ l2Dk ðt Þ

4: User k updates the highest bidders by information exchange from the neighbor users:

g nk ðt þ 1Þ ¼

max g mn ðtÞ fpnkðtÞ ;plnðtÞ g k ðtÞ

m2arg maxl2D

5: if pkak ðtÞ 6 pkak ðtþ1Þ and g kak ðtÞ – k do 6:

User k updates the status of the assignment:

ak ðt þ 1Þ ¼ arg max fwkn  pkn ðt þ 1Þg 1Pn6N

7:

User k updates the highest bidder:

bkak ðtþ1Þ ðt þ 1Þ ¼ k 8:

User k computes the bidding amount for beam ak ðt þ 1Þ:

dk ¼ bk  bk þ  0

ð11Þ

and nk ¼ ak ðt þ 1Þ ¼ arg maxn2N fwkn  pkn g is the beam that results in the highest net benefit for user k. Note that bk is the highest net 0 benefit and bk is the second highest net benefits, dk is the bidding increment for the desired beam, and  is a participating price which enforces the algorithm to achieve an equilibrium condition. Thus, this algorithm needs to be run separately by all users and the several communication cycles (D) are required to achieve the correct assignment. Note that, when the price list doesn’t get change, the algorithm terminates. The detailed discussion is given by Algorithm 2.

user can be expressed as,

9:

User k increases the price of the beam ak ðt þ 1Þ:

pkak ðtþ1Þ ¼ pkak ðtþ1Þ þ dk 10: else 11: The assignment status for user k remains the same:

a k ð t þ 1Þ ¼ a k ð t Þ 12. end if

Now, we are going to discuss the complexity of beam selection through the auction and distributed auction   and algorithm and that holds complexity order of O N 3   2 maxn;k fwnk gminn;k fwnk g e , respectively. But, the complexity of O DN d  the QR-based [13] and MWM-based [14] beam selection algorithm     PNK1 is ðN  iÞO 2ðN  iÞK 2 and O NK 2 , respectively. The i¼0 complexity of beam selection through the auction and distributed

R. Pal et al. / Int. J. Electron. Commun. (AEÜ) 111 (2019) 152884

auction algorithm is much lower than QR-based beam selection [13], and approximates to MWM-based beam selection algorithm [14]. Further, the complexity of beam selection through a distributed auction algorithm is constant despite changing K.

6. Simulation results and discussion In this section, we discuss performance metric, specifically, the spectral efficiency of the proposed beam selection algorithm, beam selection through the auction and distributed auction algorithm, evaluated through simulations. We also compare the performance of the proposed beam selection algorithm with the existing beam selection algorithms. The downlink communication system having an access point equipped with N = 256 elements ULA and K users, where each user has a single receive antenna. Spatial channel between the AP and user k; k 2 f1; . . . ; K g, is considered to be having one LoS ð0Þ

component with complex-valued path gain bk  CN ð0; 1Þ and two NLoS components with complex-valued path gain     ð1Þ ð2Þ bk  CN 0; 102 ; bk  CN 0; 101 . The complex-valued path gains b‘k ; ‘ ¼ 0; 1; 2 are considered to be uncorrelated to each other. The spatial frequencies, h‘k ; k ¼ 0; 1; 2, of user k, are uniformly dis  tributed in the interval  12 ; 12 and independent of each other. We are considering line topology for the network formation. Further, for the proposed algorithm, the wkn is the benefit gain by user k from beam n, which is captured by beamspace channel vector of   H   user k as j hk j2 RN1 ¼ j h1k j; j h2k j; . . . ; j hNk j , and j hk j is comprising of non-complexed N elements.

5

Figs. 2 and 3 is a plot of the spectral efficiency for K ¼ 16 and K ¼ 20 users, respectively of beam selection through the auction and distributed auction algorithm against SNR in dB. We compared the performance with the maximum magnitude [10], interference aware[11], QR-based [13], MWM-based [14] beam selection algorithms. In the maximum magnitude beam selection, a single beam can be selected by the multiple users. Thus, it degrades the system performance. On the other hand, inference aware beam selection selects the beams who provide maximum rate while nullifying the interference. But, the interference is eliminated through a ZF precoding. As we discussed in Section 5, ZF degrades the performance when the beamspace channel is a ill-conditioned matrix and is not applicable to rank deficient matrix. Finally, the proposed algorithms–beam selection through the auction and the distributed algorithms–outperforms existing maximum magnitude [10], interference aware [11] beam selection algorithm. Further, the performance of the proposed algorithms is inferior to the QR-based beam selection [13] because of not taking account of interference as QR-based beam selection does. However, its performance is very close to MWM-based beam selection algorithm [14]. Note that, the performance of beam selection through auction and the distributed algorithm is almost the same, as shown in Fig. 2 and 3. On the other hand, we discussed complexity of plotted beam selection algorithms of Figs. 2 and 3 in Section 5. It is found that the complexity of beam selection through a distributed auction algorithm is much lesser than QR-based beam selection [13], and it is constant despite changing K. Thus, beam selection through a distributed auction algorithm holds comparably very low complexity with achieving considerable excellent performance.

Fig. 2. The sum rate performance against SNR (dB) for K = 16 users.

Fig. 3. The sum rate performance against SNR (dB) for K = 20 users.

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7. Conclusion We are considering downlink mmWave communication system having an access point equipped with a N elements ULA, and K users, and each user is having a single receive antenna. Transforming the mmWave channel from spatial domain to the beamspace domain and selecting beams in a decentralized way would alleviate the number of required RF chains, particularly, reduce the complexity burden of the AP by distributing the computation to each user. We have proposed low complexity beam selection through the auction and distributed auction algorithms. Beam selection through a distributed auction algorithm or decentralized beam selection enables AP to be free from handling of a large channel matrix dimension. Therefore, we developed a decentralized beam selection which is proven a better alternative. Yet, we focus on beam selection through a distributed auction algorithm for multi-cell communication with different typologies to understand the future aspect of the mmWave communication system. Declaration of Competing Interest There are no conflict of interest in this work. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.aeue.2019.152884. References [1] Rappaport TS, Sun S, Mayzus R, Zhao H, Azar Y, Wang K, et al. Millimeter wave mobile communications for 5G cellular: it will work! IEEE Access 2013;1:335–49. https://doi.org/10.1109/ACCESS.2013.2260813. [2] Sun S, Rappaport TS, Heath RW, Nix A, Rangan S. Mimo for millimeter-wave wireless communications: beamforming, spatial multiplexing, or both? IEEE Commun Magaz 2014;52(12):110–21. https://doi.org/10.1109/ MCOM.2014.6979962. [3] Heath RW, lez Prelcic NG, Rangan S, Roh W, Sayeed AM. An overview of signal processing techniques for millimeter wave mimo systems. IEEE J Select Top Signal Process 2016;10(3):436–53. [4] Castanheira D, Lopes P, Silva A, Gameiro A. Hybrid beamforming designs for massive mimo millimeter-wave heterogeneous systems. IEEE Access 2017;5:21806–17. https://doi.org/10.1109/ACCESS.2017.2762361.

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