Robust multiple beamforming massive mimo system based on cylindrical antenna arrays

This paper proposes a multiple beamforming system with robust optimum criteria to exploit the channel and minimize the inter-user interference among the cells. This system uses combined cylindrical array antenna multiple beamforming architecture with spatial multiplexing.

Nghiên cứu khoa học công nghệ ROBUST MULTIPLE BEAMFORMING MASSIVE MIMO SYSTEM BASED ON CYLINDRICAL ANTENNA ARRAYS Le Trung Tan1, Nguyen Huu Trung1*, Thai Trung Kien2 Abstract: The demand for high bit-rate service transmission is increasing for the next generation of wireless systems such as the 5th generation mobile communication system (5G) and digital video broadcasting-next generation handheld (DVB-NGH) Massive Multiple-input multiple-output (MIMO) transmission is one of the most promising techniques to fulfill this demand for high transmission rates It provides high diversity order, increased data-rate and high spectral efficiency This paper proposes a multiple beamforming system with robust optimum criteria to exploit the channel and minimize the inter-user interference among the cells This system uses combined cylindrical array antenna multiple beamforming architecture with spatial multiplexing The characteristics of the proposed system model is demonstrated using computer simulations under different criteria Key words: Massive MIMO; Multiple-beamforming; Array antenna; Spatial multiplexing I INTRODUCTION The bandwidth-intensive immersive media services such as video services contribute a significant percent of data traffic in wireless networks Full high definition (Full HD) video is also being increasingly shared through social media such as YouTube, and 4K ultra HD (UHD) broadcasting is a short future [1-3] Massive Multiple-input multiple-output (MIMO) wireless systems employ a large number of transmit and receive antennas (usually greater than 100 elements), often called massive MIMO, have been of great interest in recent years because of their potential to dramatically improve spectral efficiency of future wireless systems and increase the transmission data rate through spatial multiplexing to deliver multiple streams of data within the same resource block (time and frequency) [4] Massive MIMO systems exploit multipath propagation to improve system reliability in terms of bit error rate (BER) performance, without the expense of additional bandwidth [5] Moreover, massive MIMO, by beamforming method, can increase the power efficiency by scaling down the transmit power of each terminal inversely proportional to the number of elements of antenna array at base stations [6] It can steer multiple beams to a number of user ends to enhance SNR ration Orthogonal frequency division multiplexing (OFDM) is becoming the chosen modulation technique for wireless communications [7] OFDM can provide large data rates with sufficient robustness to radio channel impairments OFDM can provide large data rates with sufficient robustness to radio channel impairments These advantages make Massive MIMO a promising solution to achieve a higher data rate for future wireless systems especially when combined with the benefits of orthogonal frequency-division multiplexing (OFDM) [8] Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san CNTT, 11 - 2018 83 Công nghệ thông tin Multiple beamforming is a technique that uses antenna arrays to produce a number of simultaneously available adjustable radiation patterns, which can point to the desired coverage areas and minimize the impact of unwanted noise and interference, thereby improving the quality of desired signal Basically, beamforming if an optimal spatial filter [9] Antenna arrays using a beamforming technique can eliminate interferers having a direction of arrival different from that of a desired signal Multi-polarized arrays can also eliminate undesired signals having different polarization from the desired signal, even if the signals have the same direction of arrival To increase the bandwidth, the mmWave frequencies in 5G systems require appropriate beamforming method [10-12] The Base station (BTS) of wireless systems such as 4G, LTE, DVB-T contains RF transceivers that are connected to the antennae The base stations have three or six-sector deployments An array of RF transceivers and antenna elements allows electronic baseband control of phase and amplitude to shape and steer the radiated beam [13] For sectored configuration, BTS usually uses standard dual polarized antenna for MIMO The basic antenna consists of an array of dual polarization columns For example, 4x4 MIMO antenna for each sector has columns and RF connectors to form separate beams The disadvantage of this system is the fixed structure for each sector The number of antenna elements for each beam is fixed [14] In this paper, in order to create a large angular coverage with good radiation pattern characteristics, the ability to change the number of antenna elements for each sector adapt to the number of users in that direction, we propose a multiple beamforming system with robust optimum criteria to exploit the channel and minimize the inter-user interference among the cells This system uses combined cylindrical array antenna multiple beamforming architecture with spatial multiplexing The resulted narrow beam width enhances the SNR ration, therefore the capacity is increased The rest of the paper is organized as follows In the next section, the proposed system model is introduced Section III presents simulation results Concluding remarks and directions for further researches are mentioned in the last section II SYSTEM MODEL 2.1 Signal model Beamformers use an array of antenna elements that are individually phased in such a way as to form beams (or nulls) in a desired direction Typical beamforming antennas have highly correlated, closely spaced elements and columns Figure describes a wireless connection between a centralized sectorized base stations and 84 L T Tan, N H Trung, T T Kien, “Robust multiple … cylindrical antenna arrays.” Nghiên cứu khoa học công nghệ numerous fixed or nomadic users The base station is capable of generating a number of beams Let us consider a multiple beamforming system with cylindrical equispaced array antenna The inter-element distance is d The system has M elements per ring and the number of ring for multiple beamforming is N The number of element is = × The system model is illustrated on Fig Denote s(t) is transmitted signal of an arbitrary beam, the pointing angle associated with s(t) is , vector of array transmitting from Nt elements at time instant t is expressed as : ( )= ( , ) ( ) (1) Where ( , ) is steering vector ( )/ ( , ) = ( )/ … ( ) ( )/ (2) With is the carrier frequency and c is the speed of light Steering vector depends on the direction of departure and the frequency For simplicity, we denote ( , ) is a The single beamforming model is expressed as ( ) = ( ) The multiple beamforming model is expressed as: ( )= ( ) (3) Where = [ ( , ), ( , ), … ( , )] according to P beams There are two general beamforming systems, including narrow band beamforming and broad band beamforming In narrow band beamforming model, the output signal of beamformer at time instant t is ( ) obtained by linear combination of signals of elements as: ∗ ( )=∑ ( ) (4) For broadband model, the output signal is expressed as [15]: ( )=∑ ∗ , ∑ ( − ) (5) With − is number of delay stages at each channel of ith element of the array The trasmitted signal is expressed as: ( )= ( ) (6) Where is the signal vector Vector = ∗ , ∗ ,…, ∗ =[ of length represents the weights as: ]∗ The response of single beamformer is expressed as: ( , )= (7) (8) The beampattern is defined as squared magnitude of ( , ) Note that each of weight in vector w impacts to the response of beamformer in terms of time and space Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san CNTT, 11 - 2018 85 Công nghệ thông tin Output power or variance of estimated signal is determined as: {| | } = { } (9) Where { } denotes mean If the signal is wide sense stationary, the covariance matrix = { } is statistical independent over time Although signal statistic is not often stationary, but we design and evaluate the performance of optimized beamforming based on the hypothesis that the signal is wide sense stationary The covariance matrix of the narrow band signal s(t) at frequency ( , = = Where ) ( , )= is: (10) is the average transmit signal power 2.2 Channel model Figure Cylindrical array antenna based multiple beamforming scenario For each beam, the massive MIMO channel model is as follows: ⋮ = ℎ ⎡ , ⎢ℎ , ⎢ ⋮ ⎢ ⎣ℎ , ℎ , ℎ , … ⋮ ℎ , ⋯ ⋱ … ℎ ℎ ℎ , , , ⎤ ⎥ ⎥ ⎥ ⎦ ⋮ + ⋮ (11) In the matrix format: = + (12) Where = , ,…, is a set of signals received from NR receive antennas of mobile station Because MIMO spatial multiplexing system takes advantage of transmit diversity in space over time caused by fading and multipath 86 L T Tan, N H Trung, T T Kien, “Robust multiple … cylindrical antenna arrays.” Nghiên cứu khoa học công nghệ combined with signal orthogonalization The signal detection in the receiver is sequence detection Therefore, for sequence detection procedure, we set up signals and channels as follows: Suppose that data is divided into blocks including K symbols In each block, to avoid inter block interference, we insert P vector zero containing N elements and N is the number of useful data samples with K = N + P The channel is Finite Impulse Response fading channel (FIR) having L multipath on each link from one transmit antenna to one receive antenna Choose P to satisfy ≥ − Signal received at the jth receive antenna in discrete time domain is of the form: [ ]=∑ ∑ ℎ, [ ] [ − ]+ (13) th Where, [ ] is the signal sample received at the j antenna at the discrete time [ ], [ ], … , [ ] k vector [ ] = is output vector at the time k with = 0,1, … , − being elements of received vector = ( [0], [1], … , [ − ; ℎ , is the lth element of the channel response , where l = 0, 1,… L – 1; transmitted signal vector at time k [ ] = [ ], [ ], … , [ ] ; The noise that [ ], [ ], … , affects the received signal samples is [ ] = [ ] ; The transmitted signal vector = ( [0], [1], … , [ − 1]) ; The AWGN noise vector = ( [0], [1], … , [ − 1]) The channel matrix H can be parameterized as [16] = ∑ ∑ Λ ( , )Λ ( , ) ( , ) ( , ) (14) Where = 1⁄ is is a normalization factor, is the complex gain of the each path , are the azimuth and elevation angle of arrival or departure of the l-th path at the p-th cluster, respectively Λ ( , ) and Λ ( , ) represent the antenna element gain for the transmitter and receiver, respectively ( , ) and ( , ) represent the steering vector of the receiver and transmitter antenna array, respectively We assume that the antenna elements are isotropic elements and there is no inter-element coupling/interference between elements The gain functions are equal unit, e.g Λ , =Λ , = However, the isotropic elements could be replaced by other antenna types such as patch antennas, etc., taking into account the corresponding gain functions 2.3 Optimum beamforming for proposed multiple beamforming system The proposed multiple beamforming system functional block diagram is presented in Figure The beamformer function splits the RF signal into P beams to feed each active element of the phased array It performs high-resolution phase Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san CNTT, 11 - 2018 87 Công ngh nghệệ thông tin and amplitude weighting, which is needed to synthesize beamforming patterns and adaptively null potential interferers The signal processing blocks for OFDM modulation include ITTF, P/S (parallel to serial), CP (c (cyclic yclic prefix insert) and DAC to form output signal The mixer converts the baseband signal up to carrier frequency Figure Proposed multiple beamforming system functional block diagram diagram The final block is the front front-end, end, which contains a high high-power power and highhighefficiency transmit PA, a transmit/receive switch, and low low-noise noise amplifier (LNA) Beamforming is an important technique in array processing in order to optimize desired signal while minimizing interferences Statistically optimal beamforming techniqu techniques es include maximization of SNR, Minimum Mean Squared Error, MMSE, Linearly Constrained Minimum Variance, LCMV, minimum variance distortionless response, MVDR are widely applied [17] Design of the beamformer under statistically optimal method requires statistical properties of the source and the statistical characteristics of the channel The optimum criteria are described as follow 2.3.1 Maximization of SNR The weight vector is solution of maximization of SNR problem: = argmax argmax (15) } and } are General solution requires both both = { = { covariance matrices of signal and noise Depending on applications, the calculation of and are different For example, can be estimated during absence of signal, is estimated from signal and known DOA by equation (10) We have, 88 L T Tan, N H Trung, T T Kien, “Robust multiple … cylindrical antenna arrays arrays.”” Nghiên cứu khoa học công nghệ multiplying the weight vector by a scale is not changing SNR Because steering vector ( , ) is fixed for a fixed signal, choose a weight vector to satisfy ( , ) = with c is a constant The problem of SNR maximization becomes minimizing interference: } = argmin ( = argmax{ ), s.t = (16) Using the method of Lagrange multipliers, solution of the equation [18]: (17) 2.3.2 Minimum Mean Squared Error, MMSE Minimum Mean Squared Error method minimizes the error signal between transmitted signal and a reference signal d(t) In this model, desired user assumes to transmit this reference signal, i.e ( ) = α ( ) where α is amplitude of reference signal d(t) and d(t) is known at the receiver The output signal of the beamformer is to track reference signal [19] MMSE method seeks the weight to minimize average error signal power: = argmin {| ( )| } (18) The average error signal power: {| ( )| } {| ( ) − ( )| } = {| = − ∗ − + ∗2 = − − ∗ } Where = { Derivative (15) by and set to zero: | ( )| = − + ∗ =0 (19) (20) We have the solution: = (21) This solution is known as optimal Wiener filter This method requires reference signal to train the beamformer 2.3.3 Linearly Constrained Minimum Variance LCMV LCMV method belongs to minimization of output power of the beamformer methods This method keeps the response according to direction of arrival of the desired signal fixed in order to preserve desired signal while minimizing the impact of undesired components including noise and interference that come from other directions other than desired direction We have the output response of signal source with direction of arrival and frequency is determined by ( , ) Linear constraint for the weighs ( , ) = , where c is a constant to ensure that all signals with satisfies Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san CNTT, 11 - 2018 89 Công nghệ thông tin frequency come from direction of arrival are passed with response c Minimization of output due to interference is equipvalent to minimizing the output power (minimum ouput power): }, s.t ( , )= = arg {| | } = arg min{ (22) Using the method of Lagrange multipliers, find min[ ( ; λ)] Where: ( ; λ) = {| | } + λ( − )= = + λ( − ) (23) +λ (24) = (25) Solution of the equation: = −λ In practice, uncorrelated noise component ensures is invertible If c = the beamformer is called minimum variance distortionless response, MVDR, beamformer Solution of MVDR beamformer is equipvalent to maximization of ( , ) ( , )+ SNR solution by replacing by and applying invert ] = [ ] matrix lemma [ + − + , we have: R ⇒R =R = [R + − ] =R =R − (26) − = = R R (27) III NUMERICAL RESULTS In this section, we provide simulation results to compare the proposed multiple beamforming system with cylindrical array antenna and present the total achievable capacity of the system for the proposed system The performance of the system is performed by means of the Monte-Carlo simulation The Monte-Carlo simulation algorithm includes serial steps: Set up system configuration; create user data; MIMO precoding; create OFDM symbols; insert CP; create beamforming; receive signals; equalize MIMO; equalize MUD; demodulate OFDM, compare with source data, calculate BER The last estimate is calculated as the average of all Q measured values after each simulation Bit error rate BER is used to define the performance of the system The system performance in simulation is Normalized Root Mean Square Error, NRMSE, the final value is the average value of all Q values after each simulation: = mean 90 ∑ ( ) ( ) ( ) ( ( )) (28) L T Tan, N H Trung, T T Kien, “Robust multiple … cylindrical antenna arrays.” Nghiên cứu khoa học công nghệ In the simulation, the configuration of array is cylindrical array with number of Massive MIMO antennas is 200 to veify the performance after SNR, the distance between two consecutive antenna elements is λ⁄2 Simulated signal has frequency fc = 20 GHz, N = 10000 snapshots Table Simulation parameters Parameters Unit Simulation schemes Carrier frequency fc GHz 10-22 at SNR [-50dB÷50dB] symbol 1024 AWGN n(t) V SNR dB [-50dB÷50dB] INR dB SIR dB OFDM symbol [ ] = [ ] − Number of interference [ ] Array geometry Cylindical array Number of samples N Sample 10000 Number of antennas M 100÷300 Sample resolution and beamforming weight bit 32 (complex double) Monte-Carlo Q 200 ⁄2 d Normalized root mean square error (NRMSE) Normalized root mean square error (NRMSE) ⁄(2 ) Radius of Cylincrical array The simulation results are presented in Figure (a-d) according to SNR ranges providing NRMSE of proposed system for MVDR, LCMV and FrostBeamformer algorithms The FrostBeamformer shows the best performance among beamforming algorithms (a) Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san CNTT, 11 - 2018 (b) 91 Normalized root mean square error (NRMSE) Normalized root mean square error (NRMSE) Công nghệ thông tin (c) (d) Normalized Array Gain [dB] Normalized Array Gain [dB] Figure NRMSE according to SNR (a,b), number of antennas (c,d) of the proposed massive MIMO system (a) (b) 90 0.9 120 60 0.8 0.8 0.6 150 0.7 30 0.4 0.6 0.2 0.5 180 0.4 0.3 210 330 0.2 240 300 270 0.1 0 20 40 60 80 100 120 140 160 180 Angle [degree] (c) (d) Figure Plot of array factor with 200-element Cylindrical Array; dual beam (a,b) and single beam (c) of the proposed massive MIMO system Figure represents array factor in cases of single beamforming and multiple beamforming schemes, the number of elements is 200, SNR = 0dB, one interferer with INR = 0dB, carrier frequency is 20GHz Figure (a), (b) presents MVDR 92 L T Tan, N H Trung, T T Kien, “Robust multiple … cylindrical antenna arrays.” Nghiên cứu khoa học công nghệ algorithm with dual beam and single beam, Figure (c-polar plot) and (d) present dual beam with Frostbeamformer IV CONCLUSIONS This paper has presented a novel multiple beamforming system model and architecture for massive MIMO system and applications to DVB-NGH and mmWave 5G systems In this system, we have been using some robust optimum criteria to exploit the channel and minimize the inter-user interference among the cells The system has combined cylindrical array antenna multiple beamforming architecture with spatial multiplexing The results of this ongoing research have shown that it is possible to achieve reality and reliability and a certain performance based-on MATLAB simulations for some channel propagation models In the next research, we investigate the proposed system with FD-MIMO mode to unite AAS, 3D beamforming, and spatial multiplexing to deliver efficient spectrum utilization while increasing network capacity Acknowledgment: This work was supported in part by the Ministry of Science and Technology under the project number NDT.32.ITA/17 REFERENCES [1] David Vargas; Gozálvez Serrano, D.; David Gomez-Barquero; Cardona Marcet, N., “MIMO for DVB-NGH, the next generation mobile TV broadcasting”, IEEE Communications Magazine 51(7):130-137 doi:10.1109/MCOM.2013.6553689, 2013 [2] Jong Gyu Oh1 , Yong Ju Won1 , Jin Seop Lee1 , Yong-Hwan Kim2, Jong Ho Paik3 and Joon Tae Kim, “A study of development of transmission systems for next-generation terrestrial K UHD and HD convergence broadcasting”, EURASIP Journal on Wireless Communications and Net (2015) 2015:128 [3] S Cioni, A Vanelli-Coralli, and G.E Corazza, “Analysis and Performance of MIMO-OFDM in Mobile Satellite Broadcasting Systems”, IEEE Communications Society, IEEE Globecom 2010 proceedings [4] Yue Zhang, C Zhang, J Cosmas, K K Loo, T Owens, R D Di Bari, Y Lostanlen, and M Bard, “Analysis of DVB-H Network Coverage With the Application of Transmit Diversity”, IEEE TRANSACTIONS ON BROADCASTING, VOL 54, NO 3, SEPTEMBER 2008 [5] Tan, W., Assimonis, S D., Matthaiou, M., Han, Y., Jin, S., & Li, X., “Analysis of different planar antenna arrays for mmWave massive MIMO systems”, IEEE Vehicular Technology Conference (VTC) Institute of Electrical and Electronics Engineers (IEEE) DOI: 10.1109/VTCSpring.2017.8108586, 2017 Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san CNTT, 11 - 2018 93 Công nghệ thông tin [6] David Schnaufer Bror Peterson, “Delivering 5G mmWave fixed wireless access”, EDN Network, September 28, 2017 [7] Chandane.E.R, M M Pawar, “DVB Enhancement by using MIMO-OFDM”, International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014, ISSN 2229-5518, pp 50-53 [8] WY Zou, Y Wu, COFDM: an overview IEEE Trans Bro 41 (1), –8 (1995) [9] Bror Peterson and David Schnaufer, “5G Fixed Wireless Access Array and RF Front-End Trade-Offs”, MICROWAVE JOURNAL, FEBRUARY 2018 [10] Theodore S Rappaport, Yunchou Xing, George R MacCartney, “Overview of Millimeter Wave Communications for Fifth-Generation (5G) Wireless Networks-with a focus on Propagation Models”, IEEE Transactions on Antennas and Propagation, Special Issue on 5G, Nov 2017 [11] Wonil Roh, Ji-Yun Seol, JeongHo Park, Byunghwan Lee, Jaekon Lee, Yungsoo Kim, Jaeweon Cho, and Kyungwhoon Cheun, “Millimeter-Wave Beamforming as an Enabling Technology for 5G Cellular Communications: Theoretical Feasibility and Prototype Results”, IEEE Communications Magazine, February 2014, pp 106-113 [12] Daniele Pinchera, Marco Donald Migliore, Fulvio Schettino and Gaetano Panariello, “Antenna Arrays for Line-Of-Sight Massive MIMO: Half Wavelength Is Not Enough”, Electronics 2017, 6, 57; doi:10.3390/electronics6030057 [13] YanLi, Xiaodong Ji, DongLiang, and Yuan Li, “Dynamic Beamforming for Three-Dimensional MIMO Technique in LTE-Advanced Networks”, International Journal of Antennas and Propagation Volume 2013, Article ID 764507, http://dx.doi.org/10.1155/2013/764507, 2013 [14] T Bai, R Vaze, and R W Heath, Jr., “Analysis of Blockage Effects on Urban Cellular Networks”, IEEE Trans Wireless, 2014 [15] Yue Rong, Y.C Eldar and A.B Gershman, “Performance tradeoffs among beamforming approaches”, Proceed 4th IEEE Workshop on Sensor Array and Multichannel Processing, 2006 [16] M R Akdeniz, Y Liu, M K Samimi, S Rangan, T S Rappaport, et al., “Millimeter wave channel modeling and cellular capacity evaluation,” IEEE J Sel Areas Comm., vol 32, no 6, pp 1164-1179, Apr 2014 [17] Yonina C.Eldar, “Minimax MSE Estimation of Deterministic Parameters With Noise Covariance Uncertainties”, IEEE Trans Signal Processing, Vol 54, No 1, 2006 94 L T Tan, N H Trung, T T Kien, “Robust multiple … cylindrical antenna arrays.” Nghiên cứu khoa học công nghệ [18] Ming Zhang, Anxue Zhang, Qingqing Yang, “Robust Adaptive Beamforming Based on Conjugate Gradient Algorithms”, IEEE Transactions on Signal Processing, Volume: 64, Issue: 22, pp: 6046 – 6057, 2016 [19] Sergiy A.V., Alex B.G and Zhi-Quan Luo, “Robust Adaptive Beamforming Using Worst-Case Performance Optimization: A Solution to the Signal Mismatch Problem”, IEEE Trans Signal Pro., Vol 51, No 2, 2013 TÓM TẮT HỆ THỐNG ĐỊNH HƯỚNG BỀN VỮNG ĐA BÚP SĨNG QUY MƠ LỚN DỰA TRÊN MẢNG ANTEN TRỤ Nhu cầu truyền tải dịch vụ tốc độ cao gia tăng cho hệ thống không dây hệ hệ thống thông tin di động hệ thứ (5G) truyền hình kỹ thuật số mặt đất cầm tay hệ (DVB-NGH) Truyền dẫn nhiều đầu vào nhiều đầu quy mô lớn (Massive MIMO) kỹ thuật hứa hẹn để đáp ứng nhu cầu tốc độ truyền dẫn cao Hệ thống Massive MIMO hỗ trợ phân tập bậc cao, tăng tốc độ liệu hiệu phổ cao Bài báo đề xuất kiến trúc hệ thống định hướng đa búp sóng với tiêu chí tối ưu bền vững để khai thác phân tập kênh giảm thiểu giao thoa người dùng tế bào Hệ thống sử dụng ăng ten mảng hình trụ kết hợp kiến trúc định hướng đa búp sóng với ghép kênh khơng gian Các kết mô theo phương pháp Monte-Carlo điều kiện khác minh chứng hiệu phương pháp đề xuất Từ khóa: MIMO quy mơ lớn; Định hướng đa búp sóng; Anten mảng; Ghép kênh khơng gian Nhận ngày 28 tháng 06 năm 2018 Hoàn thiện ngày 09 tháng 10 năm 2018 Chấp nhận đăng ngày 05 tháng 11 năm 2018 Địa chỉ: 1Đại học Bách Khoa Hà Nội; Viện KH-CNQS * Email: trung.nguyenhuu@hust.edu.vn Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san CNTT, 11 - 2018 95 ... Frostbeamformer IV CONCLUSIONS This paper has presented a novel multiple beamforming system model and architecture for massive MIMO system and applications to DVB-NGH and mmWave 5G systems In this system, ... other antenna types such as patch antennas, etc., taking into account the corresponding gain functions 2.3 Optimum beamforming for proposed multiple beamforming system The proposed multiple beamforming. .. Communications for Fifth-Generation (5G) Wireless Networks-with a focus on Propagation Models”, IEEE Transactions on Antennas and Propagation, Special Issue on 5G, Nov 2017 [11] Wonil Roh, Ji-Yun