JPNT 7(2), 53-59 (2018) https://doi.org/10.11003/JPNT.2018.7.2.53

JPNT

Journal of Positioning, Navigation, and Timing

A Pseudo-Random Beamforming Technique for Time-Synchronized Mobile Base Stations with GPS Signal Woong Son, Bang Chul Jung† Department of Electronics Engineering, Chungnam National University, Daejeon 34134, Korea

ABSTRACT This paper proposes a pseudo-random beamforming technique for time-synchronized mobile base stations (BSs) for multicell downlink networks which have mobility. The base stations equipped with multi-antennas and mobile stations (MSs) are time-synchronized based on global positioning system (GPS) signals and generate a number of transmit beamforming matrix candidates according to the predetermined pseudo-random pattern. In addition, MSs generate receive beamforming vectors that correspond to the beam index number based on the minimum mean square error (MMSE) using transmit beamforming vectors that make up a number of transmit beamforming matrices and wireless channel matrices from BSs estimated via the reference signals (RS). Afterward, values of received signal-to-interference-plus-noise ratio (SINR) with regard to all transmit beamforming vectors are calculated, and the resulting values are then feedbacked to the BS of the same cells along with the beam index number. Each of the BSs calculates each of the sum-rates of the transmit beamforming matrix candidates based on the feedback information and then transmits the calculated results to the BS coordinator. After this, optimum transmit beamforming matrices, which can maximize a sum-rate of the entire cells, are selected at the BS coordinator and informed to the BSs. Finally, data signals are transmitted using them. The simulation results verified that a sum-rate of the entire cells was improved as the number of transmit beamforming matrix candidates increased. It was also found that if the received SINR values and beam index numbers are feedbacked opportunistically from each of the MSs to the BSs, not only nearly the same performance in sum-rate with that of applying existing feedback techniques could be achieved but also an amount of feedback was significantly reduced.

Keywords: GPS time-synchronization, random beamforming, user scheduling, opportunistic feedback

1. INTRODUCTION It is believed to be highly important to manage interference efficiently in order to increase communication capacity in wireless communication networks (Nam et al. 2014). Thus, a number of studies have been conducted on interference management methods using a multi-antenna-based beamforming technology. In particular, as a technology to control interference between multi-users within the cell, a technique of scheduling users and selecting an optimum transmission beamforming matrix which maximizes a Received Oct 25, 2017 Revised Mar 25, 2018 Accepted Mar 26, 2018 †Corresponding Author E-mail: [email protected] Tel: +82-42-821-6580 Fax: +82-42-823-5436

Copyright © The Institute of Positioning, Navigation, and Timing

sum-rate among the multi-transmit beamforming matrix candidates generated with a random method in a single cell environment, has been proposed (Choi et al. 2007). However, the technique has drawbacks that a downlink resource is wasted as a training section is needed in the downlink to select a beamforming matrix between BS and MS, and the feedback overhead with regard to multi-beamforming matrices for user scheduling increases. More recently, interference management techniques have been proposed to combine transmit-receive beamforming technique and user scheduling to improve a sum-rate by minimizing the effect of interference signals at the multi-cell environment (Jung & Shin 2011, Yang et al. 2013, 2017). However, although these technologies take the random beamforming technique into consideration, they did not consider an environment where a relatively small number of MSs are present by utilizing

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54

JPNT 7(2), 53-59 (2018)

Fig. 1.  The system model of a K-cell MIMO downlink cellular network.

multiple beamforming matrix candidates as presented in the aforementioned technique. In order to use the aforementioned random beamforming techniques in a mobile BS environment, time synchronization between mobile BSs is important. In the third generation partnership project long term evolution (3GPP LTE) system that is currently commercialized, the following technologies have been used: technology that arranges uplink and downlink slots in the time domain through time synchronization between BSs or technology that reduces the interference signal effect between cells through cooperation between BSs and improves a sum-rate of MSs that exist at the cell boundaries. The time synchronization between BSs can be implemented using GPS receivers with relatively low complexity and cost (Irmer et al. 2011, Bladsjo et al. 2013). This paper proposes a pseudo-random beamforming technique for time-synchronized mobile BSs suitable for multi-cell downlink networks which have mobility. Each of the mobile BSs generates a number of transmit beamforming matrix candidates pseudo-randomly, and MSs generate a number of receive beamforming vectors that correspond to the transmit beamforming matrix candidates based on the minimum mean square error (MMSE). In addition, the SINR values received using each of the receive beamforming vectors and the beam index numbers are feedbacked to the BSs. Each of the BSs calculates a sum-rate for each of all the transmit beamforming matrix candidates based on the collected information, thereby transmitting it to the BS coordinator. Finally, the BS coordinator selects the optimal transmit beamforming matrix candidate that can maximize a sum-rate of all cells and performs transmission https://doi.org/10.11003/JPNT.2018.7.2.59

using the selected candidate. Out of a number of transmit beamforming matrix candidates, the existing feedback techniques, which feedback SINR values and beam index numbers for all transmit beamforming vectors, require a large amount of feedback information. To solve this problem, an opportunistic feedback technique (Jung et al. 2007) that feedbacked only some of the receive SINR values in descending order was applied to reduce the amount of feedback information significantly. Simulation experiments verified that the nearly same performance in sum-rate can be obtained compared to that of existing feedback technique applied. The present paper is organized as follows: In Section 2, a system model of multi-cell downlink cellular network is presented. Section 3 explains the operation procedure of the proposed pseudo-random beamforming technique for mobile BSs that are time-synchronized. In Section 4, the performance of the proposed technique is verified through computer simulations. In Section 5, conclusions are derived.

2. SYSTEM MODEL The downlink cellular network model consisting of mobile BSs and MSs, which is studied in this paper, is described here. Fig. 1 shows an example of the downlink network where K cells exist. In the system model, mobile BSs, in which Nt antennas are held in each cell, and U MSs having Nr antennas, are present. All BSs are assumed to employ the same frequency during the downlink transmission and have been time-synchronized using GPS signals. The wireless

expressed using Eq. (1). [𝑚𝑚,𝑑𝑑]

𝒚𝒚𝑖𝑖,𝑗𝑗

[𝑖𝑖] 𝑇𝑇

[𝑚𝑚]

= (𝑯𝑯𝑖𝑖,𝑗𝑗 ) 𝑽𝑽𝑖𝑖

[𝑘𝑘 ] 𝑇𝑇

[𝑚𝑚]

𝒙𝒙𝑖𝑖 + ∑𝐾𝐾𝑘𝑘=1,𝑘𝑘 ≠𝑖𝑖 (𝑯𝑯𝑖𝑖,𝑗𝑗 ) 𝑽𝑽𝑘𝑘 𝒙𝒙𝑘𝑘 + 𝒛𝒛𝑖𝑖 ,𝑗𝑗

[𝑖𝑖]& 𝑇𝑇Bang [𝑚𝑚,𝑑𝑑 ] [Jung [𝑖𝑖] 𝑇𝑇 [𝑚𝑚,𝑏𝑏 ] [𝑏𝑏 ] Woong Son Chul Random Beamforming Technique 𝑑𝑑] 55 𝐵𝐵

= (𝑯𝑯𝑖𝑖,𝑗𝑗 ) 𝒗𝒗𝑖𝑖

𝑥𝑥 𝑖𝑖 + ∑𝑏𝑏=1,𝑏𝑏≠𝑑𝑑 (𝑯𝑯𝑖𝑖,𝑗𝑗 ) 𝒗𝒗𝑖𝑖

[𝑘𝑘 ] 𝑇𝑇 [𝑚𝑚,𝑏𝑏 ] [𝑏𝑏 ] + ∑𝐾𝐾𝑘𝑘=1,𝑘𝑘≠𝑖𝑖 ∑𝐵𝐵𝑏𝑏=1 (𝑯𝑯𝑖𝑖,𝑗𝑗 ) 𝒗𝒗𝑘𝑘 𝑥𝑥 𝑘𝑘 +

𝒛𝒛𝑖𝑖 ,𝑗𝑗 ,

𝑥𝑥 𝑖𝑖

at the j-th MS of the i-th cell is zi,j~CN(0, N0 INr), and each of the elements is assumed to express thermal noise per receive[ ] [𝐵𝐵] 𝑇𝑇 1 Here, the dataantenna signal vector thatMS. is transmitted fromwhen the 𝑘𝑘-th satisfies 𝒙𝒙𝑘𝑘 = [𝑥𝑥 𝑘𝑘 , … , 𝑥𝑥𝑘𝑘 ] ∈ ℂ k-th of the In addition, theBS BS transmits and the data signal vector power is assumed to be 𝔼𝔼[‖𝒙𝒙𝑖𝑖‖22 ] = 𝑃𝑃. The thermal noise at the 𝑗𝑗-th MS o data signal vector xk using the m-th transmit beamforming i-th cell is 𝒛𝒛𝑖𝑖,𝑗𝑗 ~𝐶𝐶𝐶𝐶(0, 𝑁𝑁0 𝑰𝑰𝑁𝑁𝑟𝑟 ), and each of the elements is assumed to express thermal noise per rec j-th the and thewhen MS𝑘𝑘-th of the cell receives signal antenna of the matrix, MS. In addition, BS i-th transmits data signaldata vector 𝒙𝒙𝑘𝑘 using the 𝑚𝑚-th tran [𝑏𝑏 ] xi[b] via and the b-th transmit vector,data thesignal effective beamforming matrix, the 𝑗𝑗 -th MS of beamforming the 𝑖𝑖-th cell receives 𝑥𝑥 𝑖𝑖 via the 𝑏𝑏-th tran N r×1 [i,m,b] [ ] 𝑖𝑖,𝑚𝑚,𝑏𝑏 channel MS is ∈ vector of i,j beamforming vector, the vector effectivehchannel 𝒉𝒉𝑖𝑖,𝑗𝑗the corresponding ∈ ℂ𝑁𝑁𝑟𝑟×1 of the corresponding MS is expre as shown in Eq. (2). as shown in Eq.expressed (2).

Fig. 2.  Flow chart of the proposed technique.

[ ] 𝑇𝑇

𝑖𝑖,𝑚𝑚,𝑏𝑏 𝒉𝒉𝑖𝑖,𝑗𝑗 ≜ (𝑯𝑯𝑖𝑖,𝑗𝑗𝑖𝑖 ) 𝒗𝒗𝑖𝑖𝑚𝑚,𝑏𝑏 . [



]

[

]

(2)

3. PROPOSED PSEUDO-RANDOM BEAMFORMING TECHNIQUE BASED ON BETWEEN TIME-SYNCHRONIZED 3.COLLABORATION PROPOSED PSEUDO-RANDOM MOBILE BASE STATIONS BEAMFORMING TECHNIQUE BASED ONinCOLLABORATION BETWEEN TIMEThis section detail describes the operation procedure of the pseudo-random beamform technique for time-synchronized mobile BSs that can beBASE applied to the aforementioned system mod SYNCHRONIZED MOBILE STATIONS

Section 2, along with flow chart (Fig. 2). In Section 2, it was assumed that time synchronization already done between BSs using the GPS signal, and the BSs and MSs knew the information regardin channel matrix from the k-th BS to the j-th MS in the i-th cell beamforming This matrix sectioncandidates in detailconsisting describesofthe operation procedure transmit B transmit beamforming vectors generated In addition, each beamforming of the MSs within the cell that is Hi,j[k] ∈ Nt×Nr. Here, it satisfies i, k ∈ {1, …, K} and j ∈ {1,pseudo-random …, U}, ofmethod. the pseudo-random technique forreceives time- the RS broadca BSs obtains a wireless channel matrix from the BS to the MS.

and the channel is independent and identically distributed synchronized mobile BSs that can be applied to the (i.i.d.) with regard to all i, j, k. Since it is quasi-static during the aforementioned systemVector model in Section 2, along with Feedback 3.1 Generation of Receive Beamforming at the MS and Beam Information data signal transmission, the channel coefficient is assumed flow chart (Fig. 2). In Section 2, it was assumed that time An MS generates MB receive beamforming vectors that correspond to the transmit beamform to be an unchangeable constant. However, considering thebased on synchronization was already done between BSs using the(3)GPS vectors the MMSE and wireless channel matrix, as presented in Eq. (Ohwatari et al. 2011 MS environment, once transmit data signals change over signal, and the BSs and MSs knew the information regarding time, it is assumed to change independently. Assuming M transmit beamforming matrix candidates consisting of that M pseudo-random beamforming matrix candidates B transmit beamforming vectors generated via a pseudoconsisting of B(≤Nt) transmit beamforming vectors created random method. In addition, each of the MSs within the using a pseudo-random method are already generated, the cell that receives the RS broadcast by BSs obtains a wireless beam index number of the transmit beamforming matrix channel matrix from the BS to the MS. satisfies m ∈ {1, …, M} and the transmit beamforming index 3.1 Generation of Receive Beamforming Vector at the MS number satisfies b ∈ {1, …, B}. Thus, the m-th transmit and Beam Information Feedback beamforming matrix candidate generated at the k-th BS

satisfies Vk[m] = [vk[m,1], …, vk[m,b], …, vk[m,B]] ∈ Nt×Nt, and the b-th transmit beamforming vector in the candidate satisfies vk[m,b] An MS generates MB receive beamforming vectors that correspond to the transmit beamforming vectors based on ∈ Nt×1. When the k-th BS transmits data signal vector using index numberthe satisfies ∈ {1, … , 𝐵𝐵}. Thus, the 𝑚𝑚-thmatrix transmitcandidate beamforming matrix candidate generated at wireless channel matrix, as presented in Eq. (3) m-th𝑏𝑏 transmit beamforming among the MMSE and [𝑚𝑚] [𝑚𝑚,1] [𝑚𝑚,𝑏𝑏 ] [𝑚𝑚,𝐵𝐵] 𝑁𝑁 ×𝑁𝑁 𝑡𝑡 𝑡𝑡 the 𝑘𝑘-th BS satisfies 𝑽𝑽𝑘𝑘 = [𝒗𝒗𝑘𝑘 , … , 𝒗𝒗𝑘𝑘 matrix , … , 𝒗𝒗candidates ] ∈ ℂ consisting , and the of 𝑏𝑏-th beamforming M transmit B transmit (Ohwatari et al. 2011). beamforming 𝑘𝑘 [𝑚𝑚,𝑏𝑏 ] [m,d] vector in the transmit candidate beamforming satisfies 𝒗𝒗𝑘𝑘 ∈vectors, ℂ𝑁𝑁𝑡𝑡 ×1. When the 𝑘𝑘-thsignal BS transmits signal vector using the the receive vector ydata i,j Nr×1 𝑚𝑚 -th transmit matrix candidate 𝑀𝑀 receives transmit beamforming matrix candidates [𝑚𝑚,𝑏𝑏 ] −1 [𝑖𝑖,𝑚𝑚,𝑏𝑏 ] at the j-th MS of the i-th among cell that the data ∈ beamforming (𝑁𝑁0 𝑰𝑰 𝑁𝑁𝑟𝑟 + 𝑹𝑹𝑖𝑖 ,𝑗𝑗 ) 𝒉𝒉𝑖𝑖,𝑗𝑗 [𝑚𝑚,𝑑𝑑] 𝑁𝑁 ×1 [ ] 𝑚𝑚,𝑏𝑏  𝑟𝑟 consisting of signal 𝐵𝐵 transmit beamforming the receive signal vector 𝒚𝒚 ∈isℂ at the of 𝑗𝑗-th (3) 𝒖𝒖𝑖𝑖,𝑗𝑗MS = , ∀𝑚𝑚, 𝑏𝑏. 𝑖𝑖,𝑗𝑗 d ∈ {1, …,vectors, B}-th transmit via the beamforming vector ] −1 [𝑖𝑖,𝑚𝑚,𝑏𝑏 ] the 𝑖𝑖 -th cell that receives the data signal via the 𝑑𝑑 ∈ {1, … , 𝐵𝐵}-th transmit beamforming vector is ‖(𝑁𝑁0 𝑰𝑰 𝑁𝑁𝑟𝑟 + 𝑹𝑹𝑖𝑖[[,𝑗𝑗𝑚𝑚,𝑏𝑏 𝑚𝑚,𝑏𝑏 ]) −1 𝒉𝒉 [𝑖𝑖,𝑚𝑚,𝑏𝑏 ]‖ 𝑖𝑖,𝑗𝑗 (𝑁𝑁0 𝑰𝑰 𝑁𝑁𝑟𝑟 + 𝑹𝑹𝑖𝑖 ,𝑗𝑗 ) 𝒉𝒉𝑖𝑖,𝑗𝑗 expressed [𝑚𝑚,𝑏𝑏 ] expressed using Eq. (1). using Eq. (1). [𝑚𝑚,𝑑𝑑]

𝒚𝒚𝑖𝑖,𝑗𝑗

=

=

𝒖𝒖

=

,

∀𝑚𝑚, 𝑏𝑏.

𝑖𝑖,𝑗𝑗 [𝑚𝑚,𝑏𝑏 ] −1 [𝑖𝑖,𝑚𝑚,𝑏𝑏 ] [‖𝑚𝑚,𝑏𝑏 𝑹𝑹𝑖𝑖 ,𝑗𝑗is generated ) 𝒉𝒉𝑖𝑖,𝑗𝑗 at ‖the 𝑗𝑗-th MS of the 𝑖𝑖-th cell, (𝑁𝑁]0∈𝑰𝑰 𝑁𝑁ℂ𝑟𝑟 𝑁𝑁+𝑟𝑟×1 The receive beamforming vector 𝒖𝒖 𝑇𝑇 𝑇𝑇 [𝑖𝑖] [𝑚𝑚] [𝑘𝑘 ] [𝑚𝑚] u [m,b] ∈ Nr×1 is generated The receive 𝑖𝑖,𝑗𝑗 beamforming vector (𝑯𝑯𝑖𝑖,𝑗𝑗 ) 𝑽𝑽𝑖𝑖 𝒙𝒙𝑖𝑖 + ∑𝐾𝐾𝑘𝑘=1,𝑘𝑘 ≠𝑖𝑖 (𝑯𝑯𝑖𝑖,𝑗𝑗 ) 𝑽𝑽𝑘𝑘 𝒙𝒙𝑘𝑘 + 𝒛𝒛𝑖𝑖 ,𝑗𝑗 [𝑚𝑚,𝑏𝑏 ] i,j 𝑁𝑁 ×𝑁𝑁 𝑟𝑟 𝑟𝑟 is expressed as shown ℂunit-norm. has a unit-norm. Here, at thethe interference matrix 𝑹𝑹𝑖𝑖,𝑗𝑗 [𝑚𝑚,𝑏𝑏 j-th MS 𝒖𝒖ofcovariance the] ∈i-th it has∈aat 𝑟𝑟×1 isand [𝑖𝑖] 𝑇𝑇 [𝑚𝑚,𝑑𝑑] [𝑑𝑑] [𝑖𝑖] 𝑇𝑇 (4). [𝑚𝑚,𝑏𝑏 ] [𝑏𝑏receive ] ℂ𝑁𝑁cell, generated the 𝑗𝑗-th MSHere, of thethe 𝑖𝑖-th cell, The beamforming vector 𝐵𝐵 𝑖𝑖,𝑗𝑗 (𝑯𝑯𝑖𝑖,𝑗𝑗 ) 𝒗𝒗𝑖𝑖 𝑥𝑥 𝑖𝑖 + ∑𝑏𝑏=1,𝑏𝑏≠𝑑𝑑 (𝑯𝑯𝑖𝑖,𝑗𝑗 ) 𝒗𝒗𝑖𝑖 𝑥𝑥 𝑖𝑖  Nr×Nr [m,b] interference covariance matrix R[𝑚𝑚,𝑏𝑏 i,j ] ∈ 𝑁𝑁𝑟𝑟 ×𝑁𝑁𝑟𝑟is expressed as ∈ ℂ is expressed as shown has a unit-norm. Here, the interference covariance matrix 𝑹𝑹 𝑇𝑇 𝑖𝑖,𝑗𝑗 [𝑘𝑘 ] [𝑚𝑚,𝑏𝑏 ] [𝑏𝑏 ] [𝑚𝑚,𝑏𝑏 ] [𝑚𝑚,𝑏𝑏 ] [𝑚𝑚,𝑏𝑏 ] 𝐻𝐻 [𝑖𝑖,𝑚𝑚,𝑏𝑏 ] [𝑖𝑖,𝑚𝑚,𝑏𝑏 ] 𝐻𝐻 shown + ∑𝐾𝐾𝑘𝑘=1,𝑘𝑘≠𝑖𝑖 ∑𝐵𝐵𝑏𝑏=1 (𝑯𝑯𝑖𝑖,𝑗𝑗 ) 𝒗𝒗𝑘𝑘 𝑥𝑥 𝑘𝑘 + 𝒛𝒛(4). (1) 𝑖𝑖 ,𝑗𝑗 , 𝑹𝑹𝑖𝑖,𝑗𝑗 in=Eq. 𝔼𝔼 [(4). 𝒚𝒚𝑖𝑖,𝑗𝑗 (𝒚𝒚𝑖𝑖,𝑗𝑗 ) ] − 𝒉𝒉𝑖𝑖,𝑗𝑗 (𝒉𝒉𝑖𝑖 ,𝑗𝑗 ) − 𝑁𝑁0 𝑰𝑰𝑁𝑁𝑟𝑟 .

(3)

(3)

and it

in Eq. and it

in Eq. (4)

(1)  [𝑚𝑚,𝑏𝑏 ] [ ] [ ] 𝐻𝐻 [𝑖𝑖,𝑚𝑚,𝑏𝑏 ] [𝑖𝑖,𝑚𝑚,𝑏𝑏 ] 𝐻𝐻 [𝑚𝑚,𝑏𝑏 ] [𝒚𝒚𝑖𝑖,𝑗𝑗𝑚𝑚,𝑏𝑏 (𝒚𝒚𝑖𝑖,𝑗𝑗𝑚𝑚,𝑏𝑏 ) ] − 𝒉𝒉𝑖𝑖,𝑗𝑗 Here, the data signal vector that is transmittedAssuming from thereception at𝑹𝑹𝑖𝑖,𝑗𝑗 = 𝔼𝔼 (𝒉𝒉 )beamforming − 𝑁𝑁0 𝑰𝑰𝑁𝑁𝑟𝑟 . (4) 𝑖𝑖 ,𝑗𝑗 the 𝑗𝑗-th MS of the 𝑖𝑖-th cell using the transmit vectors 𝒖𝒖𝑖𝑖,𝑗𝑗(4), 𝑇𝑇 [1] [𝐵𝐵] Nt×1 [1] [B] T 𝑁𝑁 ×1 𝑡𝑡 Here, the datak-th signal thatxkis=transmitted BS𝑀𝑀𝑀𝑀 satisfies 𝒙𝒙signal = [𝑥𝑥 𝑘𝑘values , … , 𝑥𝑥with ∈ ℂ to ,the transmit beamforming vectors can be calculated using Eq. (5). BSvector satisfies , and the data [xk , …, xkfrom ] ∈ the 𝑘𝑘-th 𝑘𝑘SINR 𝑘𝑘 ] regard receive [𝑚𝑚,𝑏𝑏 ] 2 ‖2 ] and the data signal power is assumed to be[‖x 𝔼𝔼 [‖ 𝒙𝒙 = 𝑃𝑃. The thermal noise at the 𝑗𝑗-th MS of MS the Assuming reception at the 𝑗𝑗-th of the 𝑖𝑖-th cell j-th usingMS theoftransmit vectors 𝒖𝒖𝑖𝑖,𝑗𝑗 , P. vectorvector power is assumed to be ] = The thermal noise Assuming reception at the the i-thbeamforming cell using the ‖ 𝑖𝑖 2 i 2

2 i-th cell is 𝒛𝒛𝑖𝑖,𝑗𝑗 ~𝐶𝐶𝐶𝐶(0, 𝑁𝑁0 𝑰𝑰𝑁𝑁𝑟𝑟 ), and each of the elements is assumed express thermal noise receive [ ] 𝐻𝐻 [𝑖𝑖,𝑚𝑚,𝑏𝑏 ] vectors can be calculated using Eq. (5). 𝑀𝑀𝑀𝑀toreceive SINR values withper regard to the transmit |(𝒖𝒖𝑖𝑖,𝑗𝑗𝑚𝑚,𝑏𝑏beamforming | ) 𝒉𝒉𝑖𝑖,𝑗𝑗 ] antenna of the MS. In addition, when the 𝑘𝑘-th BS transmits data signal vector 𝒙𝒙𝑘𝑘 using the 𝑚𝑚-th[𝑚𝑚,𝑏𝑏 transmit , ∀𝑚𝑚, 𝑏𝑏. (5) 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖,𝑗𝑗 = [𝑏𝑏 ] [𝑚𝑚,𝑏𝑏 ] 𝐻𝐻 [𝑚𝑚,𝑏𝑏 ] 𝐻𝐻 [𝑖𝑖,𝑚𝑚,𝑏𝑏 [𝑚𝑚,𝑏𝑏 ]2 [http://www.ipnt.or.kr 𝑚𝑚,𝑏𝑏 ] beamforming matrix, and the 𝑗𝑗 -th MS of the 𝑖𝑖-th cell receives data signal 𝑥𝑥 𝑖𝑖 via the 𝑏𝑏-th transmit (𝒖𝒖𝑖𝑖,𝑗𝑗 |)(𝒖𝒖(𝑁𝑁 𝑹𝑹𝑖𝑖,𝑗𝑗 ] | ) 𝒖𝒖𝑖𝑖,𝑗𝑗 0 𝑰𝑰 ) 𝑁𝑁𝑟𝑟 + 𝒉𝒉 [𝑖𝑖,𝑚𝑚,𝑏𝑏 ] 𝑖𝑖,𝑗𝑗 𝑖𝑖,𝑗𝑗 [𝑚𝑚,𝑏𝑏 ] beamforming vector, the effective channel vector 𝒉𝒉𝑖𝑖,𝑗𝑗 ∈ ℂ𝑁𝑁𝑟𝑟×1 of the corresponding MS is expressed = , ∀𝑚𝑚, 𝑏𝑏. (5) 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑖𝑖,𝑗𝑗 [𝑚𝑚,𝑏𝑏 ] 𝐻𝐻 [𝑚𝑚,𝑏𝑏 ] [𝑚𝑚,𝑏𝑏 ] as shown in Eq. (2). Using the same method, all MSs feedback and beam index numbers to the BSs (𝒖𝒖𝑖𝑖,𝑗𝑗𝑀𝑀𝑀𝑀) receive (𝑁𝑁0 𝑰𝑰 𝑁𝑁𝑟𝑟SINR + 𝑹𝑹𝑖𝑖,𝑗𝑗values ) 𝒖𝒖𝑖𝑖,𝑗𝑗 in the same cell.

‖(𝑁𝑁0 𝑰𝑰 𝑁𝑁𝑟𝑟 + 𝑹𝑹𝑖𝑖 ,𝑗𝑗 [𝑚𝑚,𝑏𝑏 ]

The receive beamforming vector 𝒖𝒖𝑖𝑖,𝑗𝑗

)

∈ ℂ𝑁𝑁𝑟𝑟×1 is generated at the 𝑗𝑗-th MS of the 𝑖𝑖-th cell, and it [𝑚𝑚,𝑏𝑏 ]

unit-norm. Here,56 the interference covariance JPNT 7(2), 53-59 (2018) matrix 𝑹𝑹𝑖𝑖,𝑗𝑗 [𝑚𝑚,𝑏𝑏 ]

𝑹𝑹

[𝑚𝑚,𝑏𝑏 ]

‖

𝒉𝒉𝑖𝑖,𝑗𝑗

[𝑚𝑚,𝑏𝑏 ] 𝐻𝐻

∈ ℂ𝑁𝑁𝑟𝑟 ×𝑁𝑁𝑟𝑟 is expressed as shown in Eq.

−1 [𝑖𝑖,𝑚𝑚,𝑏𝑏[𝑖𝑖,𝑚𝑚,𝑏𝑏 ] [𝑖𝑖,𝑚𝑚,𝑏𝑏 ] 𝐻𝐻 (𝒉𝒉 ] ) −

] −]𝒉𝒉 = 𝔼𝔼 [𝒚𝒚 (𝑁𝑁(𝒚𝒚𝑰𝑰 + )𝑹𝑹 [𝑚𝑚,𝑏𝑏 )

𝒉𝒉

𝑁𝑁0 𝑰𝑰𝑁𝑁 .

(4)

𝑖𝑖,𝑗𝑗 𝑖𝑖,𝑗𝑗𝑟𝑟 𝑖𝑖,𝑗𝑗 𝑖𝑖,𝑗𝑗 𝑖𝑖 ,𝑗𝑗 𝑟𝑟 0 𝑁𝑁 𝑖𝑖 ,𝑗𝑗 u [m,b] [𝑚𝑚,𝑏𝑏 ] 𝑖𝑖,𝑗𝑗 SINR(3) value is the largest during the downlink transmission transmit vectors SINR i,j , MB receive 𝒖𝒖beamforming = , ∀𝑚𝑚, 𝑏𝑏.values −1 𝑖𝑖,𝑗𝑗 [𝑚𝑚,𝑏𝑏 ] [𝑖𝑖,𝑚𝑚,𝑏𝑏 ] ‖(𝑁𝑁transmit ‖ vectors can be with regard to the using ) 𝒉𝒉𝑖𝑖,𝑗𝑗 [𝑚𝑚,𝑏𝑏 ]beam index numbers and receive SINR values collected 0 𝑰𝑰 𝑁𝑁𝑟𝑟 + 𝑹𝑹𝑖𝑖 ,𝑗𝑗beamforming Assuming reception at the 𝑗𝑗-th MS of the 𝑖𝑖-th cell using the transmit beamforming vectors 𝒖𝒖𝑖𝑖,𝑗𝑗 , With regard to a number of transmit beamforming candidates, each of the BSs selects a set of from that are present inmatrix the same cell. Thus, assuming calculated using Eq. (5). eceive SINR values with regard to the transmit beamforming vectors can be calculated using Eq. (5).MSs MSs whose receive SINR value is the largest during the downlink transmission using beam index [𝑚𝑚,𝑏𝑏 ] 𝑁𝑁 ×1 MS of 𝑖𝑖-th cell, andvalues it i-th The receive beamforming vector 𝒖𝒖𝑖𝑖,𝑗𝑗 ∈ ℂ 𝑟𝑟 is generated at the 𝑗𝑗-th m-th that the BS performs using the cell. numbers andthereceive SINR collected from MSs transmission that are present in the same Thus, assuming 2] 𝐻𝐻 [ [𝑚𝑚,𝑏𝑏 𝑁𝑁 ×𝑁𝑁 [ ] ] 𝑟𝑟 𝑟𝑟 𝑚𝑚,𝑏𝑏 𝑖𝑖,𝑚𝑚,𝑏𝑏 transmit beamforming matrix, an achievable sum-rate atanthe that the 𝑖𝑖-th BS performs transmission using the 𝑚𝑚-th transmit beamforming matrix, achievable sum∈ ℂ is expressed as shown in Eq. a unit-norm. Here, the interference covariance 𝑹𝑹 −1 |(𝒖𝒖𝑖𝑖,𝑗𝑗 matrix | 𝑖𝑖,𝑗𝑗 ) 𝒉𝒉 [𝑚𝑚,𝑏𝑏 ] [𝑖𝑖,𝑚𝑚,𝑏𝑏 ]  𝑖𝑖-th cell can be calculated via Eq. (8). [𝑚𝑚,𝑏𝑏 ] (𝑁𝑁0 𝑰𝑰 𝑁𝑁𝑟𝑟 + 𝑹𝑹𝑖𝑖 ,𝑗𝑗 )𝑖𝑖,𝑗𝑗 𝒉𝒉𝑖𝑖,𝑗𝑗 rate∀𝑚𝑚, at the (5) i-th [𝑚𝑚,𝑏𝑏= ] cell can be calculated via Eq. (8). , 𝑏𝑏. (5) 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝐻𝐻 𝑖𝑖,𝑗𝑗

𝒖𝒖𝑖𝑖,𝑗𝑗 [𝑚𝑚,𝑏𝑏 ] 𝑹𝑹𝑖𝑖,𝑗𝑗 =

= [𝑚𝑚,𝑏𝑏] , ] ∀𝑚𝑚, 𝑏𝑏. (3) [𝑚𝑚,𝑏𝑏 ] [𝑚𝑚,𝑏𝑏 −1 [𝑖𝑖,𝑚𝑚,𝑏𝑏 ] (𝒖𝒖‖𝑖𝑖,𝑗𝑗 ) (𝑁𝑁0 𝑰𝑰[𝑁𝑁𝑚𝑚,𝑏𝑏 +] 𝑹𝑹 ) 𝒖𝒖𝑖𝑖,𝑗𝑗 𝐵𝐵 ‖[𝑖𝑖,𝑚𝑚,𝑏𝑏] 𝐻𝐻 𝑹𝑹]𝑖𝑖 ,𝑗𝑗𝑟𝑟𝐻𝐻 ) 𝑖𝑖,𝑗𝑗[𝒉𝒉𝑖𝑖,𝑚𝑚,𝑏𝑏 (𝑁𝑁 0 𝑰𝑰 [𝑚𝑚,𝑏𝑏 ] 𝑁𝑁𝑟𝑟 + [𝑚𝑚,𝑏𝑏 𝑖𝑖,𝑗𝑗 ] [𝑚𝑚] [𝑚𝑚,𝑏𝑏 ]  𝔼𝔼 [𝒚𝒚𝑖𝑖,𝑗𝑗 (𝒚𝒚𝑖𝑖,𝑗𝑗 ) ] − 𝒉𝒉𝑖𝑖,𝑗𝑗 (𝒉𝒉𝑖𝑖 ,𝑗𝑗 ) − 𝑁𝑁0 𝑰𝑰𝑁𝑁𝑟𝑟 . (4) [𝑙𝑙𝑙𝑙𝑙𝑙2 (1matrix )]. of the BSs 𝑅𝑅 = ∑ 𝑆𝑆𝑆𝑆𝑆𝑆𝑅𝑅𝑖𝑖,𝑗𝑗 each (8)of + 𝑚𝑚𝑚𝑚𝑚𝑚 (8) selects a set Withnumbers regard totoa the number of transmit beamforming candidates, 𝑖𝑖 1≤𝑗𝑗≤𝑈𝑈 g the same method, all MSs feedback 𝑀𝑀𝑀𝑀 receive SINR values and beam index BSs [𝑚𝑚,𝑏𝑏 ] 𝑏𝑏=1 𝑁𝑁 ×1 MSs whose receive SINR value is the largest during the downlink transmission using beam index 𝑟𝑟 Usingvector the same all feedback ∈ℂ is MSs generated at theMB 𝑗𝑗-threceive MS of SINR the 𝑖𝑖-th cell, and it ] receive 𝒖𝒖𝑖𝑖,𝑗𝑗 method, eThe same cell. beamforming [𝑚𝑚,𝑏𝑏 numbers and receive SINR values collected from MSs that are present in the same cell. Thus, assuming Assuming at the MSin ofsum-rate thenumbers 𝑖𝑖-th cell transmit beamforming vectors 𝒖𝒖BSs [𝑚𝑚,𝑏𝑏 ]the [𝑚𝑚] This study reception analyzed performance of using the entire the amount of feedback 𝑖𝑖,𝑗𝑗 ,calculate achievable sum-rates with regard 𝑁𝑁cell ×𝑁𝑁the values and𝑗𝑗-th beam index the BSs same cell. to the all backhole link 𝑟𝑟in 𝑟𝑟and ∈ ℂ is expressed as shown in Eq. unit-norm. Here, the interference covariance matrix 𝑹𝑹to through calculate achievable sum-rates using with regard to all 𝑚𝑚 andbeamforming feedback 𝑅𝑅𝑖𝑖 matrix, 𝑖𝑖,𝑗𝑗feedback thatbeBSs the 𝑖𝑖-th BS performs the 𝑚𝑚-th transmit an achievable sumreceivewhen SINRexisting values with regard and to thethe transmit beamforming vectors can calculated using Eq. transmission (5). mation feedback opportunistic techniques were applied. Let us [m] thethe BS coordinator. R This study analyzed performance in sum-ratetorate of entire m and feedback through the backhole link to the BS the 𝑖𝑖-th me that the number of bits required for quantizing the receive SINR values is at defined ascell 𝑄𝑄. can be calculated via Eq. i(8). 2

𝐻𝐻 SINR and thethe amount of feedback information existing coordinator. Each of the MSscell feedbacks maximum of 𝑀𝑀 corresponding [receive [𝑖𝑖,𝑚𝑚,𝑏𝑏 ] value andwhen 𝑚𝑚,𝑏𝑏 ] 𝐻𝐻a total 𝐵𝐵 [𝑚𝑚,𝑏𝑏 ] [𝑚𝑚,𝑏𝑏 ] |(𝒖𝒖 [𝑚𝑚,𝑏𝑏 ] 𝐻𝐻) 𝒉𝒉 [𝑖𝑖,𝑚𝑚,𝑏𝑏|] [𝑖𝑖,𝑚𝑚,𝑏𝑏 ] 3.3 Selection of Optimal Transmit Beamforming Matrix at the BS Coordinator 𝑖𝑖,𝑗𝑗 𝑖𝑖,𝑗𝑗 [ ] 𝑹𝑹𝑖𝑖,𝑗𝑗index = 𝔼𝔼 𝒚𝒚 (𝒚𝒚 ) (𝒉𝒉 ) − 𝑁𝑁 𝑰𝑰 . (4) − 𝒉𝒉 mit beamforming feedback vector numbers from the 𝑚𝑚-th transmit beamforming matrix candidate when [𝑚𝑚,𝑏𝑏 ] 0 𝑁𝑁 [𝑚𝑚] [ ] and the feedback were 𝑖𝑖,𝑗𝑗 opportunistic 𝑖𝑖,𝑗𝑗 𝑖𝑖,𝑗𝑗 𝑖𝑖 ,𝑗𝑗 techniques 𝑟𝑟 = , ∀𝑚𝑚, 𝑏𝑏. (5) 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 [𝑙𝑙𝑙𝑙𝑙𝑙2 (1 + 𝑚𝑚𝑚𝑚𝑚𝑚 𝑆𝑆𝑆𝑆𝑆𝑆𝑅𝑅𝑖𝑖,𝑗𝑗𝑚𝑚,𝑏𝑏 )]. 𝑅𝑅 = ∑ (8) 𝐻𝐻 𝑖𝑖,𝑗𝑗 ng feedback technique is applied. Thus, the number of feedback bits required per MS is expressed as 𝑖𝑖 [𝑚𝑚,𝑏𝑏 ] [𝑚𝑚,𝑏𝑏 ] [𝑚𝑚,𝑏𝑏 ] 1≤𝑗𝑗≤𝑈𝑈 3.3 Selection of Optimal Transmit Beamforming Matrix at The BSfor coordinator selects the beam index ̂ of the optimal transmit beamforming matrix applied. Let us(𝒖𝒖 assume bits required ) that (𝑁𝑁0 𝑰𝑰the 𝑹𝑹𝑖𝑖,𝑗𝑗 ) 𝒖𝒖of 𝑏𝑏=1 number 𝑚𝑚 𝑁𝑁𝑟𝑟 +number 𝑖𝑖,𝑗𝑗 𝑖𝑖,𝑗𝑗 n in Eq. (6). [𝑚𝑚,𝑏𝑏 ] a sum-rate of the entire cell among 𝑀𝑀 transmit beamforming matrix candidates based Assuming reception at the 𝑗𝑗-ththe MSreceive of the SINR 𝑖𝑖-th cell usingisthe transmit beamforming vectors 𝒖𝒖𝑖𝑖,𝑗𝑗 BS, Coordinator the Q. can maximize quantizing values defined asthat [𝑚𝑚] feedbacks it to the BSs. onbe theindex achievable sum-rates collected at each cell as presented in Eq. (9) and then BSs calculate achievable eceive SINRmethod, values with regard to the transmit beamforming vectors can calculated using Eq. (5). ng the same all MSs feedback 𝑀𝑀𝑀𝑀 receive SINR values and beam numbers to the BSs = 𝑀𝑀(𝑙𝑙𝑙𝑙𝑙𝑙the + 𝑄𝑄) . (6) sum-rates with regard to all 𝑚𝑚 and feedback 𝑅𝑅𝑖𝑖 through the backhole link 2 𝐵𝐵 maximum Each of the MSs𝐹𝐹𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 feedbacks receive SINR to the BS coordinator. he same cell. 𝐾𝐾 2transmit value performance and a total of corresponding Thea BS coordinator selects the beam[𝑚𝑚index number m̂ of the This study analyzed in M sum-rate the entire cell isbeamforming and the amount of selects feedback When the opportunistic feedback technique proposed in ]this study applied, each MS ] [𝑚𝑚,𝑏𝑏 ] 𝐻𝐻of[𝑖𝑖,𝑚𝑚,𝑏𝑏 |(𝒖𝒖opportunistic | 𝑚𝑚 ̂ = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 [∑ ]. Coordinator (9) 𝒉𝒉𝑖𝑖,𝑗𝑗 feedback rmation whenSINR existing feedback the techniques wereand applied. Let 𝑘𝑘 BS 𝑖𝑖,𝑗𝑗 )the 3.3 Selection of aOptimal Beamforming Matrix at 𝑅𝑅 the mum receive value from theand 𝑚𝑚-th transmit beamforming matrix candidate total ofTransmit 𝑀𝑀us transmit vector index from m-th transmit beamforming optimal beamforming matrix that can maximize a sum[𝑚𝑚,𝑏𝑏 ] numbers 1≤𝑚𝑚≤𝑀𝑀 = vector , ∀𝑚𝑚, 𝑏𝑏. the as (5) 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑘𝑘=1 𝐻𝐻 ume that the numberbeamforming of bits𝑖𝑖,𝑗𝑗required for quantizing the receive SINR values is defined 𝑄𝑄. sponding transmit index numbers. Each MS feedbacks only predetermined [ ] [ ] [ ] 𝑚𝑚,𝑏𝑏 when existing 𝑚𝑚,𝑏𝑏feedback 𝑚𝑚,𝑏𝑏 matrix candidate technique is rate of the entire cell among M transmit beamforming matrix (𝒖𝒖maximum )order (𝑁𝑁0receive 𝑰𝑰 𝑁𝑁𝑟𝑟SINR + 𝑹𝑹SINR ) 𝒖𝒖 The BS coordinator selects the beam index number 𝑚𝑚 ̂ of the optimal transmit beamforming matrix Each of the feedbacks the value andthea number total of of 𝑀𝑀 corresponding 𝑖𝑖,𝑗𝑗 𝑖𝑖,𝑗𝑗values. 𝑖𝑖,𝑗𝑗Thus, ber of 𝑛𝑛(< 𝑀𝑀)MSs feedbacks in descending of feedback bits 3.4 Data Transmission applied. Thus, the number of feedback bits required per MS candidates based oncell theamong achievable sum-rates collectedmatrix at each that canmatrix maximize a sum-rate entire 𝑀𝑀 transmit beamforming candidates based smitper beamforming vectorasindex numbers from the 𝑚𝑚-th transmit beamforming candidate when of the red MS is expressed shown in Eq. (7). on the achievable sum-rates collected at each cell as presented in Eq. (9) and then feedbacks it to the BSs. technique is applied. Thus, the number of feedback bits required per MS is expressed as gting thefeedback same method, all MSs feedback 𝑀𝑀𝑀𝑀 receive SINR values and beam index numbers to the BSs is expressed as shown in Eq. (6). cell assignal presented intoEq. (9) and then feedbacks it totransmit the BSs.beamforming The BSs transmit data vectors the downlink using the optimal matrix same cell.(6). wn in Eq. (7) 𝐹𝐹𝑚𝑚𝑚𝑚𝑚𝑚−𝑛𝑛−𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 = 𝑛𝑛(𝑙𝑙𝑙𝑙𝑙𝑙2 𝑀𝑀𝑀𝑀 + 𝑄𝑄). delivered from the BS coordinator. When the 𝑗𝑗-th MS of the 𝑖𝑖-th cell receives a data signal through the 𝑑𝑑𝐾𝐾 This study analyzed performance in sum-rate of the entire cell and the amount of feedback [𝑚𝑚]  th transmit beamforming vector of the optimal transmit beamforming matrix, post-processing of the mation when existing feedback and the opportunistic feedback techniques were applied. Let us ( ) (6) (9) 𝑚𝑚 ̂ = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 [∑ 𝑅𝑅 ]. (9) 𝐹𝐹 = 𝑀𝑀 𝑙𝑙𝑙𝑙𝑙𝑙 𝐵𝐵 + 𝑄𝑄 . (6) example, assuming that the number 𝑀𝑀 of𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 transmit beamforming candidates is signals 16, the can number 𝐵𝐵 ofusing Eq. (10). 2 𝑘𝑘 received be done 1≤𝑚𝑚≤𝑀𝑀 me the numbervectors of bits required forupquantizing the beamforming receive SINR values as the 𝑄𝑄. number 𝑄𝑄 𝑘𝑘=1 mitthat beamforming that make the transmit matrix isis defined four, and feedback technique proposed in this MS Each ofthe theopportunistic MSs the maximum value andisa applied, total of each 𝑀𝑀per corresponding sWhen to represent the feedbacks quantized SINR is six, thereceive numberSINR 𝐹𝐹𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 of study feedbacks required MS selects is 16 ×a 𝑇𝑇 [𝑚𝑚̂,𝑑𝑑] [𝑚𝑚 [𝑚𝑚 ̂,𝑑𝑑] ̂,𝑑𝑑] When the opportunistic feedback proposed 3.4candidate Data Transmission mit beamforming vector index numbers fromtransmit the 𝑚𝑚-th transmittechnique beamforming matrix imum receive SINR value from the 𝑚𝑚-th beamforming matrix and a =total ofof𝑀𝑀) 𝒚𝒚𝑖𝑖,𝑗𝑗 ̃𝐹𝐹candidate (𝒖𝒖when 𝑖𝑖,𝑗𝑗 𝑖𝑖,𝑗𝑗 2 4 + 6) = 128 bits when applying the existing technique, whereas the number 𝑦𝑦 𝑚𝑚𝑚𝑚𝑚𝑚−𝑛𝑛−𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 3.4[𝑚𝑚 Data 𝑇𝑇 ng feedback technique isMS applied. Thus, the number bits required per MS expressed as 𝑇𝑇 Transmission esponding transmit beamforming vector index numbers. Each MS feedbacks only theis predetermined inper this study is(𝑙𝑙𝑙𝑙𝑙𝑙 applied, a the maximum back bits required is 4 × + of 6) feedback =MS 48 selects bits when opportunistic feedback [𝑖𝑖] 𝑇𝑇 [𝑚𝑚 [𝑚𝑚 [𝑖𝑖] 𝑇𝑇 [𝑚𝑚 ̂ ,𝑑𝑑] ̂,𝑑𝑑] [𝑑𝑑] ̂,𝑑𝑑] ̂,𝑏𝑏 ] [𝑏𝑏 ] 2 16 × 4 each 𝐵𝐵 = (𝒖𝒖 ) (𝑯𝑯vectors 𝑥𝑥𝑖𝑖downlink + (𝒖𝒖𝑖𝑖,𝑗𝑗using ) ∑the 𝑥𝑥𝑖𝑖 (𝑯𝑯transmit BSsof transmit data signal optimal matrix n in Eq. (6). predetermined 𝑏𝑏=1,𝑏𝑏≠𝑑𝑑 mber of 𝑛𝑛(< 𝑀𝑀) feedbacks in descending orderthe ofisSINR Thus, the The number feedback 𝑖𝑖,𝑗𝑗 bits 𝑖𝑖,𝑗𝑗 ) 𝒗𝒗𝑖𝑖to the 𝑖𝑖,𝑗𝑗 ) 𝒗𝒗𝑖𝑖 beamforming nique whose number 𝑛𝑛 of feedbacks four isvalues. applied. receive SINR value from m-th transmit beamforming 𝑇𝑇 When the 𝑗𝑗-th MS 𝑇𝑇 delivered from the BS coordinator. 𝑖𝑖-th uired per MS is expressed as shown in Eq. (7). [𝑚𝑚 [𝑘𝑘]of𝑇𝑇the [𝑚𝑚 ] cell [𝑏𝑏 ] receives [𝑚𝑚 ̂ ,𝑑𝑑] ̂,𝑏𝑏 ̂,𝑑𝑑] a data signal through the 𝑑𝑑𝐾𝐾 𝐵𝐵 ∑data ) ∑ 𝒗𝒗𝑘𝑘beamforming 𝑥𝑥𝑘𝑘to+the (𝒖𝒖downlink ) 𝒛𝒛𝑖𝑖,𝑗𝑗 .using + (𝒖𝒖 𝑏𝑏=1 (𝑯𝑯 The BSs transmit signal matrix of2M corresponding transmit 𝑖𝑖,𝑗𝑗 𝑖𝑖,𝑗𝑗 ) vectors 𝑖𝑖,𝑗𝑗 th transmit beamforming vector of𝑘𝑘=1,𝑘𝑘≠𝑖𝑖 the optimal transmit matrix, post-processing of the 𝐹𝐹𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐a=total 𝑀𝑀(𝑙𝑙𝑙𝑙𝑙𝑙 𝐵𝐵 + 𝑄𝑄) . (6) User Scheduling at BSs candidate and (10) received signals can be done using Eq. (10). ( ) = 𝑛𝑛 𝑙𝑙𝑙𝑙𝑙𝑙 𝑀𝑀𝑀𝑀 + 𝑄𝑄 . (7) 𝐹𝐹 beamforming vector index numbers. Each MS feedbacks only the optimal transmit beamforming matrix delivered from the 𝑚𝑚𝑚𝑚𝑚𝑚−𝑛𝑛−𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 2 When the opportunistic feedback technique proposed in this study is applied, each MS selects a i-th cellbyreceives BS to coordinator. When of the the predetermined number of n(
quantized SINR is six, the number F_conv of feedbacks required per MS is 16×(log24+6) = 128 bits when applying the existing technique, whereas the number Fmax-n-SINR of feedback bits required per MS is 4×(log216×4+6) = 48 bits when the opportunistic feedback technique whose predetermined number n of feedbacks is four is applied.

ser Scheduling at BSs

3.2 User Scheduling at BSs With regard to a number of transmit beamforming matrix candidates, each of the BSs selects a set of MSs whose receive https://doi.org/10.11003/JPNT.2018.7.2.59

𝐻𝐻 [𝑚𝑚 ̂ ,𝑑𝑑]

+𝐾𝐾 (𝒖𝒖𝑖𝑖,𝑗𝑗 𝐵𝐵

) 𝒛𝒛𝑖𝑖,𝑗𝑗

(10)

[𝑚𝑚 ̂ ,𝑏𝑏 ]

𝑅𝑅 = ∑ ∑ [𝑙𝑙𝑙𝑙𝑙𝑙2 (1 + 𝑚𝑚𝑚𝑚𝑚𝑚 𝑆𝑆𝑆𝑆𝑆𝑆𝑅𝑅𝑘𝑘,𝑗𝑗 )] . The 𝑠𝑠𝑠𝑠𝑠𝑠 first term refers to a desired 1≤𝑗𝑗≤ 𝑈𝑈 signal with data that 𝑘𝑘=1 𝑏𝑏=1 should be received by the MS, the second and third terms denote the intra-cell interference signal and inter-cell interference signal. The last term means the post-processed thermal noise that follows the CN(0, 1) distribution. An achievable sum-rate of the entire cell can be calculated via Eq. (11) if the finally proposed pseudo-random beamforming technique based on cooperation between time-synchronized mobile BSs is applied to the K-cell MIMO

(11)

𝑇𝑇 [𝑚𝑚 ̂ ,𝑑𝑑]

+ (𝒖𝒖𝑖𝑖,𝑗𝑗

[ ] 𝑇𝑇

[

] [ ]

[

] 𝑇𝑇

𝑘𝑘 𝑚𝑚 ̂,𝑏𝑏 𝑏𝑏 𝑚𝑚 ̂,𝑑𝑑 𝐵𝐵 ) ∑𝐾𝐾 𝑥𝑥𝑘𝑘 + (𝒖𝒖𝑖𝑖,𝑗𝑗 ) 𝒛𝒛𝑖𝑖,𝑗𝑗 . 𝑘𝑘=1,𝑘𝑘≠𝑖𝑖 ∑ 𝑏𝑏=1 (𝑯𝑯𝑖𝑖,𝑗𝑗 ) 𝒗𝒗𝑘𝑘

(10)

The first term refers to a desired signal with data that should be received by the MS, the second and Woong third terms denote the intra-cell interference signal and inter-cell interference signal. The last termSon & Bang Chul Jung Random Beamforming Technique 57 means the post-processed thermal noise that follows the 𝐶𝐶𝐶𝐶(0,1) distribution. An achievable sum-rate of the entire cell can be calculated via Eq. (11) if the finally proposed seudo-random beamforming technique based on cooperation between time-synchronized mobile BSs is downlink network.network. pplied to the 𝐾𝐾-cell MIMO downlink



𝐾𝐾

𝐵𝐵

[𝑚𝑚 ̂ ,𝑏𝑏 ]  𝑅𝑅𝑠𝑠𝑠𝑠𝑠𝑠 = ∑ ∑ [𝑙𝑙𝑙𝑙𝑙𝑙2 (1 + 𝑚𝑚𝑚𝑚𝑚𝑚 𝑆𝑆𝑆𝑆𝑆𝑆𝑅𝑅𝑘𝑘,𝑗𝑗 )] . 𝑘𝑘=1 𝑏𝑏=1

1≤𝑗𝑗≤ 𝑈𝑈

(11)

(11)

4. SIMULATION RESULTS This section analyzes the results of computer simulations on the proposed pseudo-random beamforming technique for time-synchronized mobile BSs, which were conducted in various system environments. Fig. 3 shows the sum-rate per cell according to the increase in the number of MSs within the cell at an environment where three cells are present. The number of transmit antennas at each of the BSs is four, the number of receive antennas in the MS is two, the number of transmit beamforming vectors that make up the transmit beamforming matrix candidate is four, and signal-to-noise ratio (SNR) is 0 dB. The sumrate is improved due to the similar effect of increase in the number of MSs within the cell as the number of transmit beamforming matrix candidates increases. In addition, when users feedback receive SINR values and beam index numbers, the best performance is achieved when applying the existing feedback technique. However, when the opportunistic feedback technique is applied, nearly the same sum-rate with that using the existing feedback technique can be obtained, as the number of MSs within the cell or the number of pre-determined feedbacks increases since only the predetermined number of feedbacks in descending order of receive SINR values is feedbacked. Fig. 4 shows a sum-rate per cell when the number of antennas in the MS is four in the system parameters in Fig. 3. If the number of receive antennas in the MS increases, a receive SINR value at the MS can be improved effectively. Thus, a sumrate per cell can be improved more rapidly if the opportunistic feedback technique is applied. Fig. 5 shows the sum-rate per cell according to the increase in SNR at an environment where three cells are present. The number of transmit antennas at each of the BSs is four, the number of receive antennas in the MS is two, the number of transmit beamforming vectors that make up the transmit beamforming matrix candidate is four, and the number of MSs within the cell is 20. As the SNR increases, a sum-rate per cell increases. When the opportunistic feedback technique is applied, a sum-rate per cell is improved more steeply as the number of feedbacks increases. Fig. 6 shows a sum-rate per cell when the number of antennas in the MS is four in the system parameters in Fig. 5. As the number of receive antennas in the MS increases, the

Fig. 3.  Sum-rates versus the number of MSs when K = 3, Nt = B = 4 and Nr = 2.

Fig. 4.  Sum-rates versus the number of MSs when K = 3, Nt = B = 4 and Nr = 4.

Fig. 5.  Sum-rates versus SNR when K = 3, Nt = B = 4 and Nr = 2.

receive SINR value is improved effectively at the MS. Thus, when the opportunistic feedback technique is applied, a sum-rate per cell is improved more steeply, which is similar http://www.ipnt.or.kr

58

JPNT 7(2), 53-59 (2018)

Fig. 6.  Sum-rates versus SNR when K = 3, Nt = B = 4 and Nr = 4.

technique for time-synchronized mobile BSs that combined the opportunistic feedback technique, and analyzed the performance in various environments. In particular, mobile BSs that are time-synchronized using GPS signals generate a number of pseudo-random transmit beamforming matrix candidates, and MSs generate receive beamforming vectors that can maximize the receive SINR value based on MMSE in response to the transmit beamforming vectors that make up the transmit beamforming matrix. Based on the above operation results, the MSs feedback receive SINR and beam index numbers to the BSs. However, the exiting feedback technique requires a large amount of feedbacks. However, this increasing feedback amount can be reduced by applying the opportunistic feedback technique. The simulation experiment results verified the reduction in feedback information amount while maintaining a sum-rate achieved at the existing feedback technique if the opportunistic feedback was applied to the proposed technique. However, it is more effective to utilize the existing method that feedbacks the maximum SINR value with regard to all the pseudorandom beamforming matrices than using the opportunistic feedback method in an environment where a downlink data sum-rate is more important than reducing the uplink feedback overhead.

ACKNOWLEDGMENTS

Fig. 7.  Feedback overhead versus the number of transmit beamforming candidates when B = 4 and Q =6.

to shown in the above. Fig. 7 shows the number of feedback bits required per MS according to the number of transmit beamforming matrix candidates when the existing feedback and opportunistic feedback techniques are applied in the proposed pseudo-random beamforming technique. The number of beamforming vectors that make up the transmit beamforming matrix candidate is four, and the number of bits required to quantize the receive SINR value is six. As the number of the transmit beamforming matrix candidates increases, an increase in an amount of feedback information in the opportunistic feedback technique is relatively slowed down, compared to that of existing feedback technique.

5. CONCLUSIONS This paper proposed the pseudo-random beamforming https://doi.org/10.11003/JPNT.2018.7.2.59

This work has been supported by the National GNSS Research Center program of Defense Acquisition Program Administration and Agency for Defense Development.

REFERENCES Bladsjo, D., Hogan, M., & Ruffini, S. 2013, Synchronization aspects in LTE small cells, IEEE Commun. Magazine, 51, 70-77. https://doi.org/10.1109/MCOM.2013.6588653 Choi, W., Forenza, A., Andrews, J. G., & Heath, Jr., R. W. 2007, Opportunistic space-division multiple access with beam selection, IEEE Trans. Commun., 55, 2371-2380. https://doi.org/10.1109/TCOMM.2007.910702 Irmer, R., Droste, H., Marsch, P., Grieger, M., Fettweis, G., et al. 2011, Coordinated Multipoint : concepts, performance, and field trial results, IEEE Commun. Magazine, 49, 102-111. https://doi.org/10.1109/ MCOM.2011.5706317 Jung, B. C., Ban, T. W., Choi, W., & Sung, D. K. 2007, Capacity analysis of simple and opportunistic feedback schemes in OFDMA systems, in Proc. of ISCIT, Sydney,

Woong Son & Bang Chul Jung Random Beamforming Technique 59

NSW, Australia, pp.203-205. https://doi.org/10.1109/ ISCIT.2007.4392013 Jung, B. C. & Shin, W.-Y. 2011, Opportunistic interference alignment for interference-limited cellular TDD uplink, IEEE Commun. Letters, 15, 148-150. https://doi.org/ 10.1109/LCOMM.2011.121310.101439 Nam, W., Bai, D. W., Lee, J., & Kang, I. 2014, Advanced interference management for 5G cellular networks, IEEE Commun. Magazine, 52, 52-60. https://doi.org/ 10.1109/MCOM.2014.6815893 Ohwatari, Y., Miki, N., Asai, T., Abe, T., & Taoka, H. 2011, Per for mance of advance d re ceiver employing interference rejection combining to suppress intercell interference in LTE-advanced downlink, in Proc. of IEEE VTC Fall, San Francisco, CA, USA, pp.1-7. https:// doi.org/10.1109/VETECF.2011.6093196 Yang, H. J., Shin, W.-Y., Jung, B. C., & Paulraj, A. 2013, Opportunistic interference alignment for MIMO interfering multiple-access channels, IEEE Trans. Wireless Commun., 12, 2180-2192. https://doi.org/ 10.1109/TWC.2013.032113.120673 Yang, H. J., Shin, W.-Y., Jung, B. C., Suh, C., & Paulraj, A. 2017, Opportunistic downlink interference alignment for multi-cell MIMO networks, IEEE Trans. Wireless Commun., 16, 1533-1548. https://doi.org/10.1109/ TWC.2017.2647942

Department of Electronics Engineering, Chungnam National University, Daejeon, Korea. His research interests include 5G mobile communication systems, statistical signal processing, opportunistic communications, compressed sensing, interference management, interference alignment, random access, relaying techniques, deviceto-device networks, innetwork computation, and network coding. Dr. Jung was the recipient of the Fifth IEEE Communication Society AsiaPacific Outstanding Young Researcher Award in 2011. He was also the recipient of the Bronze Prize of Intel Student Paper Contest in 2005, the First Prize of KAIST’s Invention Idea Contest in 2008, the Bronze Prize of Samsung Humantech Paper Contest in 2009. He has been selected as a winner of the Haedong Young Scholar Award in 2015, which is sponsored by the Haedong Foundation and given by the Korea Institute of Communications and Information Science (KICS).

Woong Son received the B.S. and M.S. degrees in electronics engineering from Chungnam National University, Daejeon, South Korea, in 2015 and 2017, respectively. He is currently a Ph. D student of Chungnam National University, Daejeon, South Korea. His research interests include 5G mobile communication systems, multiple antenna systems, beamforming, interference management, etc. Bang Chul Jung received the B.S. degree in electronics engineering from Ajou University, Suwon, South Korea, in 2002, and the M.S. and Ph.D. degrees in electrical and computer engineering from KAIST, Daejeon, Korea, in 2004 and 2008, respectively. He was a Senior Researcher/Research Professor with the KAIST Institute for Information Technology Convergence, Daejeon, Korea, from January 2009 to February 2010. From March 2010 to August 2015, he was a Faculty member with Gyeongsang National University, Tongyeong, Korea. He is currently an Associate Professor with the http://www.ipnt.or.kr