Resource Allocation for Transmit Hybrid Beamforming in Decoupled Millimeter Wave Multiuser-MIMO Downlink

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1 Receved November 1, 2016, accepted November 23, 2016, date of publcaton December 2, 2016, date of current verson February 25, Dgtal Object Identfer /ACCESS Resource Allocaton for Transmt Hybrd Beamformng n Decoupled Mllmeter Wave Multuser-MIMO Downlnk IRFAN AHMED 1, (Senor Member, IEEE), HEDI KHAMMARI 1, AND ADNAN SHAHID 2, (Member, IEEE) 1 Computer Engneerng Department, Taf Unversty, Ta f 21974, Saud Araba 2 Department of Informaton Technology, Ghent Unversty, 9000 Ghent, Belgum Correspondng author: I. Ahmed (rfan.ahmed@eee.org) Ths work was supported by the Kng Abdulazz Cty for Scence and Technology under Grant PC ABSTRACT Ths paper presents a study on jont rado resource allocaton and hybrd precodng n multcarrer massve multple-nput multple-output communcatons for 5G cellular networks. In ths paper, we present the resource allocaton algorthm to maxmze the proportonal farness (PF) spectral effcency under the per subchannel power and the beamformng rank constrants. Two heurstc algorthms are desgned. The proportonal farness hybrd beamformng algorthm provdes the transmt precoder wth a proportonal far spectral effcency among users for the desred number of rado-frequency (RF) chans. Then, we transform the number of RF chans or rank constraned optmzaton problem nto convex semdefnte programmng (SDP) problem, whch can be solved by standard technques. Inspred by the formulated convex SDP problem, a low-complexty, two-step, PF-relaxed optmzaton algorthm has been provded for the formulated convex optmzaton problem. Smulaton results show that the proposed suboptmal soluton to the relaxed optmzaton problem s near-optmal for the sgnal-to-nose rato SNR 10 db and has a performance gap not greater than 2.33 b/s/hz wthn the SNR range 0 25 db. It also outperforms the maxmum throughput and PF-based hybrd beamformng schemes for sum spectral effcency, ndvdual spectral effcency, and farness ndex. INDEX TERMS Mllmeter-wave, beamformng, 5G, resource allocaton. I. INTRODUCTION Recently, the need for hgh data rates has dramatcally ncreased. The 4G or Long Term Evoluton- Advanced (LTE-A) technology can handle applcatons wth data rates up to several Mbps. Therefore, new moble applcatons that mandate data rates n the range of several Ggabts per second (Gbps) cannot be handled wth such technology. To handle such large data volumes, hgher frequency bands spans from 6 to 95 GHz must be employed [1], [2]. 5G wreless technology wll use these frequency bands whch leads to the emergence of promnent technology by 2020 [3]. Moreover, 5G moble technology shall comply wth predecessor technologes, smlar to LTE-A technology, whch s backward compatble wth prevous generatons [4]. The massve multple-nput multple-output (MIMO) systems permt hgh spectral effcency by usng large antenna arrays at both the transmtter and the recever of a wreless communcaton lnk. The large spectrum avalable n the mllmeter-wave bands presents an emergng alternatve to the tradtonal wreless systems to acheve several fold moble data traffc ncrease. The mllmeter wave (mmwave) systems are desgned to overcome sgnal attenuaton and to provde hgh throughput wreless communcaton lnks. In mmwave systems, the beamformng uses a large antenna arrays to overwhelm path loss wth drectonal transmsson. In Massve MIMO systems, the tradtonal baseband dgtal beamformng (DB) requres one dstnct rado-frequency (RF) chan per antenna. Both beamformng and precodng are done at baseband, however n mmwave systems, the hgh power consumpton and the hgh cost of mxed-sgnal and RF chans led to opt to hybrd beamformng (HB) operatng n the baseband and analog domans. Thus several studes proposed dfferent archtectures amng to reduce the number of RF chans by combnng an analog RF beamformer and a baseband dgtal beamformer. Such technques are known as hybrd beamformng methods IEEE. Translatons and content mnng are permtted for academc research only. Personal use s also permtted, but republcaton/redstrbuton requres IEEE permsson. See for more nformaton. VOLUME 5, 2017

2 Hybrd beamformng methods are devoted to jontly optmze the analog and dgtal beamformers to maxmze the achevable rate. The performances of the dfferent hybrd beamformng algorthms can be compared n lght of power consumpton calculatons and achevable rates. A user schedulng and sub-carrer allocaton algorthm for multuser downlnk MIMO orthogonal frequency dvson multple access (OFDMA) systems wth hybrd analog-dgtal beamformng was proposed n [5]. Such a desgn wth hybrd analog-dgtal beamformng algorthm was desgned to reduce the number of RF chans and Phase Shfters (PS). The subsequent beamformng system should acheve the same performance of a dgtal beamformng that uses the same number of RF chans as the number of antennas of the transmtter. A transcever desgn for maxmzng the spectral effcency of a large-scale MIMO system wth hybrd beamformng archtecture usng a lmted number of RF chans and fnte-resoluton PSs was proposed n [6]. It was shown that for the crtcal case where the number of RF chans s equal to the number of data streams, the performance s close to that of the exhaustve search method. The achevable rate can be mproved sgnfcantly by addng extra RF chans n low-resoluton PS case. A hybrd beamformng structure reported n [7], led to obtan the same performance as the fully-dgtal beamformng scheme f the number of RF chans at each end s greater than or equal to twce the number of data streams. In [8], a dfferent hybrd archtecture replaced the PSs wth swtches at the recever and showed that antenna selecton s preferred n a range of operatng condtons. Ths archtecture of hybrd beamformng was presented for compressed sensng based channel estmaton. An teratve hybrd transcever desgn algorthm based on the nonlnear least-squares formulaton for mmwave MIMO systems was presented n order to reduce the performance gap between the optmal full-baseband and the exstng Orthogonal Matchng Pursut (OMP)-based hybrd transcever desgns n spte of usng a much smaller number of RF chans [9]. A practcal transmtter structure n whch each antenna s only connected to a unque RF chan, was desgned to optmze the analog and dgtal beamformng matrces for a maxmum achevable rate wth transmt power constrant. For a small antenna array or for a great number of propagaton paths, the performance of such method can be mproved by adjustng analog ampltude to reduce the complexty [10]. A hybrd beamformng based mult-beam transmsson dversty scheme was proposed for a sngle stream transmsson for sngle user MIMO operaton. The proposed structure flexblty permtted to adaptvely adjust the transmsson sgnal accordng to the unfavorable channel characterstcs at hgh frequency bands ncludng mmwave [11]. Compress sensng and matchng pursut are popular approaches to fnd the near optmal precoders and combners. A precodng strategy usng a varant of matchng pursut was consdered to develop an teratve hybrd beamformng algorthm for the sngle user mmwave channel. The proposed soluton assumes only partal channel knowledge at both the base and moble statons n the form of angle of arrval (AoA) knowledge. The presented precodng method utlzes the channel sparsty, recprocty, and the algorthmc concept of bass pursut [12]. For a sngle user beamformng and precodng n mmwave systems wth large arrays, a low hardware complexty precodng soluton consdered the precoder desgn problem as a sparsty constraned least squares problem. The proposed algorthm allows mmwave systems to approach waterfllng capacty [13]. An nclusve survey on the beamformng n mllmeter wave communcatons s presented n [14]. Motvaton: The DB s an optmal precoder for any desgn crteron and channel model [7], [15]. Usng maxmum throughput or proportonal farness (PF) crtera, one can desgn an optmal maxmum throughput dgtal beamformer (MTDB) or PF dgtal beamformer (PFDB). DB based desgns need one RF chan per antenna. Due to the hgher cost and the power consumpton n massve MIMO mmwave communcaton systems (because of large number of RF chans, contanng dgtal to analog converter (DAC), data converter, mxer etc [16]), DB s not feasble for practcal mplementatons. HB s the feasble choce to acheve the acceptable performance. A general approach for hybrd precoders desgn s to maxmze the spectral effcency by mnmzng the Frobenus norm of the dfference between the dgtal precoder and the proposed hybrd precoder usng bass pursut [15], [16]. In most of the aforementoned HB desgns ether the objectve s to mnmze the number of RF chans [5], [8], [9], or to maxmze the throughput for lmted number of RF chans [6], [7], [10], [13], [15]. In a practcal cellular networks, farness among the equally payng users s an utmost mportant deployment and optmzaton crteron. PF s a wdely adopted rado resource allocaton scheme n access networks [17]. There s no such lterature that provdes PF-based hybrd precoder for a desred number of RF chans. PF-based systems wth the choce of number of RF chans gve upper bound on the achevable system PF throughput tradeoff wth captal and runnng costs. To date, the optmal soluton for a gven number of RF chans n HB desgn s stll an open research topc [14], [18]. Objectves: To develop a transmt precoder that maxmzes the PF spectral effcency for a gven number of RF chans and per subchannel power constrant n multuser multcarrer massve MIMO system. Contrbutons: The contrbuton of ths paper s threefold: 1) HB precoder desgn for PF-based resource allocaton for multuser and multcarrer massve MIMO systems. It has been shown that for low sgnal-to-nose rato (SNR) values wth 64 transmt antennas, 8 users wth sngle antenna, and 16 RF chans, the PF hybrd beamformng (PFHB) provdes a comparatve average sum spectral effcency wth respect to maxmum throughput hybrd beamformng (MTHB) wth upto 50% ncrease n farness when the users are 50m apart. 2) We have transformed the non-convex rank-constrant resource allocaton problem to the form of convex VOLUME 5,

3 I. Ahmed et al.: Resource Allocaton for Transmt Hybrd Beamformng n Decoupled Mllmeter Wave Multuser-MIMO Downlnk FIGURE 1. A transmt and receve structure of hybrd beamformng n multcarrer multuser systems. optmzaton problem whch can be solved by standard semdefnte programmng (SDP) technques. In partcular, the non-convex rank constrant has been replaced by 2-norm and trace constrant. The nuclear norm s used as a convex substtute n the objectve functon because t s the convex envelope of the rank. 3) A low complexty, subchannel level PF relaxed optmzaton (PFRO) soluton s presented for feasble mplementatons. It solves the convex optmzaton problem n two steps. The frst step provdes the optmal users combnatons and power allocatons, whereas, the second step extracts the precoder wth the desred number of RF chans. Smulaton results show that PFRO outperforms the MTHB and PFHB n average sum spectral effcency, ndvdual user spectral effcency, and the farness ndex. Ths paper s organzed as follows: In secton II we present the system model. Secton III s about the problem formulaton and performance analyss of hybrd beamformng based on proportonal-far spectral effcency n mmwave MU-MIMO downlnk. Performance evaluaton and comparsons of proposed scheme are provded n secton IV, followed by conclusons n secton V. Notatons: Vectors and matrces are represented by boldface lower-case and upper-case letters, respectvely, other notatons are explaned below: Cm n K tr(a) blkd( ) AT AH E(A) In kak kak2 kakf 172 m n dmensonal complex space Calgraphc letters denote sets Trace of matrx A Block dagonal A transpose A conjugate transpose Expected value of A Identty matrx of sze n n Nuclear norm of matrx A 2-norm of matrx A Frobenus norm of matrx A II. SYSTEM MODEL We consder a multuser MIMO cellular system n whch the enb wth Nt antennas sends Ns data streams to K number of UEs each equpped wth nk antennas as shown n Fg. 1. We denote P Nr as the sum of the antennas on all UEs such that K Nr = k=1 nk. Perfect channel state nformaton (CSI) s assumed at enb and each UE. We use orthogonal frequency dvson multple access (OFDMA) block-based transmsson because ths s the modulaton of choce of modern cellular and wreless local area networks [19]. We assume narrowband block fadng such that each OFDM block contans Ns symbols and Nf subchannels. Then, the OFDM block becomes s1,1 s1,2 s1,nf.... s2,1. s2,2. (1) S= sns 1,Nf sns,1 sns,nf 1 sns,nf We make Ns = K,.e., the number of symbols s equal to the number of UEs. The transmtter uses an NRF Ns dgtal beamformer FDB for each subchannel, followed by an Nt NRF analog beamformer FAB for each subchannel. The sampled transmtted block on subchannel s gven by DB x = FAB F s (2) where x s an Nt 1 column vector and s = [s1,,..., sk, ]T. The transmtted symbol for UE k on subchannel, xk, s a DB DB lnear functon of symbols,.e., xk, = FAB fk, sk,, where fk, s the k th column of FDB. The transmtted OFDM block s x = [x1,..., xnf ]. In general, MIMO channel models fall nto two categores: () analytcal models, and () geometrcal models. Analytcal models descrbe the channel transfer functon matrx, whereas, geometrcal channel models descrbe the physcal propagaton between transmt array and receve array [19]. A. ANALYTICAL CHANNEL MODEL The nput-output relatonshp of the system model s gven by y = Hx + w (3) VOLUME 5, 2017

4 where x = [x 1,..., x Nf ] T s the transmt sgnal vector, H = blkd(h 1,...H Nf ) s the system channel matrx, w C N f N r 1 s the nose vector, and y = [y 1,..., y Nf ] T s the receve sgnal vector. The receved sgnal y on the th subchannel can be obtaned from (3) as y = H x + w (4) where H = [H 1,,..., H K, ] T C N r N t s the channel matrx wth H k, = [h 1,k,..., h nk,k] T, x s gven n (2), and y = [y 1,,..., y K, ] T. On the th subchannel, the j th UE receves the sum of all transmtted sgnals for K UEs over ts MIMO channel H as y = K H x k, + w (5) k=1 where y s an n j 1 vector, H C n j N t s the MIMO channel matrx whch s defned n the next subsecton. We denote the rank of the channel matrx H by r, where 0 r mn(n j, N t ),. In matrx form, the above equaton s gven as y = H x + w (6) The n k N f receved sgnal at the k th UE s gven by y k = [H k,1 F AB 1 FDB 1 s 1,..., H k,nf F AB N f F DB N f s Nf ]F 1 + w k, where H k, C n k N t s the random MIMO channel between enb and UE k for the th subchannel, x = F AB F DB s s N t 1 transmt sgnal vector, F 1 s the nverse fast fourer transform (IFFT) matrx of sze N f, and w k CN (0, σ 2 ) s the N f 1 vector of addtve whte Gaussan nose (AWGN) of whch each element follows complex normal dstrbuton wth zero mean and varance σ 2. Combnng the sgnals for all UEs n a K dmensonal receved sgnal vector y = [y 1,..., y K ], we get the system equaton as (7) y = HF AB F DB SF 1 + w, (8) The FFT operaton at the UE k transforms the receved sgnal nto frequency doman as ý k = [H k,1 F AB 1 FDB 1 s 1,..., H k,nf F AB N f F DB N f s Nf ] + w k F. (9) B. GEOMETRICAL CHANNEL MODEL Due to the hgh free-space pathloss characterstc at mmwave frequences, mmwave propagaton leads to lmted spatal scatterng. In addton, the large tghtly-packed antenna arrays that are characterstc of mmwave transcevers lead to hgh levels of antenna correlaton. Ths combnaton of sparse scatterng and tghtly packed antenna arrays makes many of the statstcal fadng dstrbutons (e.g., d Raylegh fadng model) used n tradtonal MIMO analyss naccurate for mmwave channel modelng. Therefore, we adopt a narrowband channel representaton, based on the extended Saleh- Valenzuela model, whch accurately captures the mathematcal structure present n mmwave channels [7], [20]. For smplcty, we assume that each scatterng cluster around the transmtter and recever contrbutes a sngle propagaton path [13]. Geometrcal channel model descrbes the physcal propagaton between transmt array and receve array. Due to near optcal lne-of-sght (LOS) wave propagaton at mm- Wave frequences, the mmwave channels are expected to have lmted scatterng, say, L. The mmwave MIMO channel matrx wth N t transmt and N r receve antennas, can be modeled as H = N t N r ρl L α l a t (φ t,l )a H r (φ r,l), (10) l=1 where α l represents the complex gan of the l th path wth..d. CN (0, 1) and ρ s the dstance dependent pathloss between transmtter and recever s taken from [21]. Moreover, a t and a r are the transmt and receve steerng vectors, respectvely. The varables φ t,l [0, 2π) and φ r,l [0, 2π) are the l th path s azmuth angles (boresght angles n the transmt array and receve array) of departure and arrval, respectvely. The steerng vectors are gven by a t (φ t,l ) = 1 Nt [a t,1 (φ t,l ),..., a t,nt (φ t,l )] (11) a r (φ r,l ) = 1 Nr [a r,1 (φ r,l ),..., a r,nr (φ r,l )] (12) The elements of transmt and receve steerng vectors are gven by a t, (φ t,l ) = e jωτ,t,l =e j2π( 1) d t λ sn(φ t,l), a r, (φ r,l ) = e jωτ,r,l =e j2π( 1) dr λ sn(φ r,l), =1, 2,..., N t (13) =1, 2,..., N r (14) where λ s the wavelength, ω = 2π λ, τ s the beamformng delay, and d t and d r are the antenna spacng at the enb and UE, respectvely. III. PROBLEM FORMULATION In ths secton we defne our optmzaton problem. Our objectve s to maxmze the cell user farness-aware spectral effcency through jont resource allocaton and hybrd beamformng. The spectral effcency (bts/s/hz) of the UE k on the subchannel s gven by R k, = log 2 (1 + γ k, ), (15) Ɣ where Ɣ s the SNR gap between Shannon capacty and the performance obtaned by the employed modulaton and codng scheme n practcal wreless channel. For M-QAM modulaton and target bt error rate of Pe, Ɣ = (2/3)ln(5Pe) [22]. The receved sgnal-to-nterference-and-nose rato (SINR) γ k, at the UE k on the subchannel s gven as γ k, = h k, F AB f DB k, 2 j =k h k,f AB f DB 2 + σ 2 (16) VOLUME 5,

5 where E [ h k, 2 F] = N t N r ρ k, wth ρ k, = P t,k, /P r,k,. The overall precodng [ vector ] f B k, = F AB f DB k, provdes the power constrant as E f B k, 2 F = 1 such that the average N t N r receved power at UE k on subchannel s gven by [ ] [ ] E h k, 2 F E f B k, 2 F = 1 ρ k, (17) Ths average receved power s obtaned through P r,k, = P t,k, ρ k,, where P t,k, s the transmt power allocated to the symbol of UE k on subchannel. The well known Proportonal Far (PF) algorthm ams to maxmze the logarthmc utlty functon k log R k, where R k s the long-term data rate of the user k. Ths objectve s known as proportonal far crtera. Ths s equvalent to maxmze the k R k(t)/ R k where R k (t) s total data transmtted to user k at tme t [23], [24]. In order to acheve balance tradeoff between throughput and farness, we use PF based spectral effcency maxmzaton. We defne per user proportonal farness metrc as U(f B k, ) = R k,(t),, k, (18) R k, (t) where R k, (t) s average spectral effcency (movng average) over a past wndow of length T w = 1/α [25], as R k, (t) = αr k, (t 1) + (1 α) R k, (t 1), (19) We consder the system that can select the subsets of UEs on dfferent subchannels to maxmze the utlty functon. For K number of UEs n the system the enb can select from 1 to K UEs on subchannel. Then, there are a total of 2 K possble UEs combnatons on subchannel. Snce the possble ndependent spatal layers are upper bounded by mn(n t, N r ) and we assume N r < N t, therefore ϕ,l {1, 2,..., K} for l = 1, 2,..., 2 K denotes the l th UE assgnment set on subchannel, contanng the ndces of a set of UEs. The spectral effcency of UE k on subchannel s gven by R k, = χ,l log 2 (1 + γ k, ), (20) Ɣ where χ,l {0, 1} s a bnary decson varable such that t s equal to one f an UE combnaton l s selected on subchannel, otherwse t s equal to zero. Now we formulate our optmzaton problem for jont resource allocaton and precoders desgn wth the objectve to maxmze the utlty functon as max f B k, :k ϕ,l N f U =1 l=1 k ϕ,l ( ) f B k, subject to C1 : tr(f DB H F AB H F AB F DB ) P, C2 : rank(f AB F DB ) N RF, C3 : χ,l = 1. (21) l L where L s a set of all possble consecutve 1 s from 1 to 2 K 1,,e., L = {2 1 1, 2 2 1,..., 2 K 1}. To the extent of the authors knowledge, no general soluton to the above optmzaton problem (21) exsts n the lterature. In order to make the problem tractable we apply the tme sharng technques of [26] to make the objectve functon convex. We use the pseudo user concept of [27] for each users assgnment set. It has been shown that for systems wth large number of subchannels, lke n the mmwave frequency band, the tme sharng technques such that the bnary decson varable χ,l can take any real value between 0 and 1, has zero dualty gap [28], [29]. IV. PROPOSED SOLUTION The mult-users MIMO system n the network provdes a number of opportuntes, such as spatal multplexng, transmt or receve dversty gan, mult-user dversty, beamformng. These benefts come wth tradeoff among them. In ths paper, we present resource allocaton algorthm to maxmze the PF spectral effcency under the per subchannel power and the beamformng rank constrants as shown n (21). A. USERS CHANNEL DECOUPLING At each transmsson slot, the enb decdes on the subchannel allocaton and the transmt beamformers for the downlnk. In mult-user massve MIMO transmsson more than one UE share a certan subchannel. In ths case, zero-forcng (ZF) lnear block dagonal technque [30] can be used to spatally separate the UEs whch creates decoupled channels for all the UEs. Zero-forcng s a suboptmal but low complexty approach wthn the lnear precoders class. It performs very well n the hgh SNR regme or as the multuser dversty ncreases, the probablty of matchng users wth spatally compatble channels grows [18], [31], [32]. Moreover, wth the ntroducton of large antenna arrays, such that N t N r has shown that zero-forcng beamformng can acheve up to 98% of the non-lnear drty paper codng (DPC) capacty [33]. In order to make ths paper self-contaned, we descrbe the block dagonalzaton brefly. For smplcty, frst we consder the downlnk transmsson over one subchannel. If there are K UEs on subchannel, then the downlnk channel on ths subchannel s expressed as N r N t matrx H = [H T 1,,..., HT K, ]T (22) For UE j, we defne the followng (N r n j ) N t channel matrx H = [HT 1,,..., HT j 1,, HT j+1,,..., HT K, ]T (23) Let the rank of H be denoted by r, then the nullspace of H has dmenson N t r n j. Performng the SVD of each user s channel matrx on subchannel leads to the followng H = U V H = U [V (1) V (0) ] H, (24) where U and V are the untary matrces. The columns of U are the left sngular vectors of H, the columns of V are the rght sngular vectors of H, and s a dagonal matrx n whch the dagonal entres are the sngular values of H. In the last equalty of (24), V (1) holds the frst r 174 VOLUME 5, 2017

6 rght sngular vectors of H and V (0) contans the N t r sngular vectors of H whch are n the nullspace of H. The columns of V (0) are best suted for UE j beamformng vector f B because they wll provde zero nterference at other UEs. Usually V (0) contans more number of columns than the n j, therefore we use some lnear combnatons of the columns of V (0) to make at most n j columns. [ ] H V (0) 0 [ ] = U V (1) 0 0 V (0), (25) where H V (0) gves the matrx wth columns as the lnear combnatons of the columns of V (0). The rght hand sde of the equaton s the SVD of H V (0), where s r r dagonal matrx and V (1) represents the r sngular vectors wth nonzero sngular values of H V (0). The transmt beamformng matrx f B = H V (0) maxmzes the UE j spectral effcency wthout any nter-ue nterference. The transmt beamformng matrx for subchannel s defned as F B = [f B 1,,..., fb K, ]P1/2, (26) where f B H f B = I, 1 j K and P s a block dagonal matrx whose elements scale the power allocated to each nterference-free vrtual subchannel for all UEs. For a partcular UE some vrtual spatal subchannels may not be used whch s ndcated by the zero values of the dagonal elements of P k, matrx. The pre-processed receved sgnal at UE k on subchannel s gven by ỹ k, = H k, x k, + w k, = H k, f B k, P1/2 k, s k, + w k, = k, P 1/2 k, s k, + w k, (27) It can be seen that the data streams for each UE are decoupled. The UE k spectral effcency on subchannel under block dagonal constrant s gven by R k, = χ,l log 2 I + 2 k, P k, (28) Ɣ B. PROPORTIONAL FAIRNESS HYBRID BEAMFORMING The proposed user schedulng and subchannel allocaton algorthm s based on [5], wth the am to maxmze the PF spectral effcency subjected to the per subchannel power and transmt beamformng matrx rank constrants as gven n (21). There s no general soluton to the problem n (21). The PFHB algorthm maxmzes the PF spectral effcency for a fxed power per subchannel and a gven rank constrant. We express the PFHB precodng matrx as a product of analog and dgtal beamformng matrces (F B = F AB (N t N RF ) FDB,(N RF K) ). Frst we obtan the user set for each subchannel that maxmzes the PF spectral effcency. The non-selected users gve zero column vector n the precodng matrx for each subchannel. For the selected users per subchannel, we form a combned block dagonal zero-forcng precodng matrx whch s known as practcal, low complexty, near optmal precodng [15], [34]. Then, the N t N RF analog matrx F AB s obtaned by selectng N RF domnant left sngular vectors of SVD(F B ). Fnally, for fxed F AB, we fnd F DB for each subchannel that maxmzes the PF utlty. The operaton of the PFHB algorthm s as follows: Gven the nput parameters n lne 1 of Algorthm 1 t starts wth ntalzaton phase havng two sets: an empty set of UEs K on subchannel and a set of UEs to be scheduled K t. In MU-MIMO OFDM systems, when N t > K k=1 n k, each subchannel can be spatally allocated to varous UEs. For each subchannel, the nner whle loop (lne 21) runs for K tmes. Each tme, the sum of the utlty functon wth UEs n set K plus the utlty functon of each UE k K t s evaluated n lne 10. Lne 11 selects k whch maxmzes the utlty functon. Update the F B and U(F B )updated. If U(F B )updated s greater than or equal to the last U(F B )last then the selected UE k s added n the set K and removed from the set K t. Store the updated values of U(F B )updated and U(F B )last and repeat the loop for k = 2, 3,..., K t. On the ext of whle loop (8-24) we wll have the UEs n the set K that maxmzes the utlty functon n (21). After fnshng for all subchannels, the overall transmt beamformng matrx F B s formed by horzontal concatenaton of all F B ( = {1, 2,..., N f }). In lne 26, F B s checked for the rank constrant; f t s less than or equal to N RF then F AB and F DB are obtaned from the QR-decomposton of F B. But f the rank constrant s not satsfed, then arrange the F B n descendng order and take the frst mn number of F B that gves rank(f B ) N RF. The analog beamformng matrx F AB s obtaned through the frst N RF number of left sngular vectors of F B as shown n lnes 34 and 35. To fnd the dgtal beamformng matrx F DB, repeat the algorthm from lne 8 to 28 by usng updated channel matrx H = H (Nr N t )F AB (N t N RF ). C. OPTIMAL SOLUTION USING SEMIDEFINITE PROGRAMMING In ths subsecton, we transform our problem to the form of convex optmzaton problem where we can use the standard semdefnte programmng (SDP) technques to get the optmal soluton for the relaxed problem. In the optmzaton problems wth convex objectve functons and constrants except the non-convex rank constrant, t s generally desred to keep the rank of matrx smaller than a gven value. For these problems, the nuclear norm often serves as a convex substtute for the rank because t s the convex envelop of the rank [35]. Our optmzaton problem n (21) wth nuclear norm penalty becomes mn ξ,f B k, :k ϕ,l N f U =1 l=1 k ϕ,l ( ) f B k, + ξ F subject to C1 : tr(f DB H F AB H F AB F DB ) P, C2 : rank(f AB F DB ) N RF C3 : l=1 χ,l 1, C4 : F 0, (29) VOLUME 5,

7 Algorthm 1 PFHB Resource Allocaton Algorthm 1: Inputs 2: K t : Number of UEs to be scheduled 3: N f : Number of subchannels 4: K : Number of UEs to be scheduled on subchannel 5: N RF : Number of RF chans 6: Intalzaton 7: K t = {1,..., K t }, U(F B )last = 0, K = {}, {Resource allocaton to maxmze the PF spectral effcency} 8: whle N f do 9: whle k K t do 10: Compute U(F B ) = U(FB ) + U(fB k, ), k K t 11: k = arg max k {U(F B )} 12: Update F B and U(F B )update wth UE k 13: 14: f U(F B )updated U(F B )last then K = K {k } 15: K t = K t {k } 16: U(F B )last = U(F B )updated 17: k : else 19: break 20: end f 21: end whle 22: χ,l = 1 23: : end whle 25: Stack the beamformng matrces F B = [F B 1,..., FB N f ] 26: f rank(f B ) N RF then 27: (F AB, F DB ) = QRdecomposton(F B ) 28: End of Algorthm 29: else 30: U(F B ) ordered = sort(u(f B ), descendng) 31: whle length(u(f B )ordered ) do 32: F B = horzontalstack(f B) 33: f rank(f B ) N RF then 34: SVD(F B ) = U V H 35: F AB = U(:, 1 : N RF ) 36: break 37: end f 38: : end whle 40: end f 41: Repeat lne 8 to 28 42: Output 43: F B = [F B 1,..., FB N f ] 44: [K 1,..., K Nf ] where F = F B F BH and the parameter ξ 0. We replace the rank constrant by convex nequalty constrant to force the rank to be at most the desred value. The followng lemma replaces the rank constrant by convex constrant that ensures the desred upper lmt on rank for any nonzero matrx F. Lemma 1: Gven nteger q wth N t /2 < q < N t. Let F = F B F BH, whch s an N t N t symmetrc semdefnte matrx, satsfes r F 2 tr(f) 0, where q 1 < r q, then ether rank(f) q, or F = 0. Proof: If F = 0, the constrant s already satsfed. Consder the case when F = 0. Assume σ 1 σ 2... σ Nt 0 be the ordered sngular values of F. Usng the defntons of the matrx nduced 2-norm and trace [35], the constrant can then be wrtten as rσ 1 N t =1 σ 0, and t follows that: rσ 1 rσ 1 (N t q)σ 1 + (N t q)σ 1 (r N t + q)σ 1 + N t =q+1 N t =q+1 N t =q+1 σ σ q j=1 q j=1 (σ 1 σ ) qσ q Both terms on left hand sde of the last nequalty are postve, therefore left hand sde s strctly postve, whch then requres permssble values of σ 1 to σ q, and thus rank(f) q. Ths constrant n (29) yelds convex optmzaton problem n standard form as mn ξ,f B k, :k ϕ,l N f U =1 l=1 k ϕ,l ( ) f B k, + ξ F subject to C1 : tr(f DB H F AB H F AB F DB ) P, C2 : r F 2 tr(f) 0 C3 : l=1 χ,l 1, C4 : F 0, (30) Ths s a convex semdefnte programmng (SDP) problem whch can be solved by the standard SDP technques. Before applyng the SDP technque we need to fnd the optmal value of parameter ξ. It can be obtaned by frst fndng the dual of problem (30) and then mnmzng over the Lagrangan as shown n [36]. If the constrant C2 ndvdually holds for all subchannels, then, the optmzaton problem can be transformed to subchannel level whch reduces the computatonal complexty from O(2 N f K ) to O(N f 2 K ). Subchannel level C2 s not tractable, therefore, we splt the problem nto two subproblems and solve n next secton. D. PROPORTIONAL FAIRNESS RELAXED OPTIMIZATION (PFRO): A SUBOPTIMAL SOLUTION We propose a subchannel level two step heurstc algorthm PFRO; nspred by the optmzaton problem n (30). We relaxed the objectve functon n (30) by removng ξ F. It has been shown [36] that for better performance, the value of the parameter ξ should be postve and close to zero, so that, we can safely transform the objectve functon n (30) to σ j σ j 176 VOLUME 5, 2017

8 one n (31). The constrant C1 s smply lmts the subchannel level power allocaton to each user wthn the avalable power per subchannel. The transformed rank constrant n C2 s realzed by Eckart-Young theorem [37] of low rank approxmaton n the second step of algorthm. In constrant C3, the relaxaton on χ,l has been removed and χ,l becomes a bnary varable. The resultant mxed nteger optmzaton problem s not convex because of the nteger constrant. The global optmal of such a mxed nteger optmzaton problem requres the combnaton of conventonal convex optmzaton algorthm wth an exhaustve search. In the frst step, we solve the followng convex optmzaton problem by frst convertng (see Appendx A) t nto a mxed nteger dscplned convex programmng (MIDCP) and then usng CVX [38] wth MOSEK solver [39]. max p k,,χ,l l=1 subject to C1: k ϕ,l U(f B k, ) C2: K p k, P, k=1 l=1 χ,l = 1, C3: p k, 0, k,. (31) where χ,l and p k, are the optmzaton varables. The output χ,l provdes the optmal users combnaton l on the subchannel, and p k, allocates the subchannel power P among the selected users to maxmze the PF spectral effcency. In lne 13, we determne the precodng vector for UE k on subchannel wth the help of the bnary selecton varable χ,l. The bnary varable χ,l corresponds to the optmal users set ϕ,l. In bnary form l can be wrtten as l = [l1,...l K ] where the bnary dgt lk = 1 f the user k s n the selected users set ϕ,l. Then, the precoder of UE k on subchannel s gven by { f B k, = f B k, for lk = 1, 0 for lk = 0. (32) The precodng matrx for subchannel s calculated n lne 14. In lne 15, 16, the average spectral effcency has been calculated for the nput of cvxoptmzaton functon n the next teraton. In the second step, the overall precodng matrx F B s obtaned by stackng the precodng matrces of all subchannels n lne 19. The rank of F B s checked aganst the nput N RF. If t s greater than N RF, then, low rank approxmaton [37] s used to ensure the rank constrant. Fnally, the analog and dgtal beamformng matrces are obtaned from QR-decomposton as shown n lnes 21 to 23. In practcal mplementatons, the dgtal beamformng can be realzed at the baseband frequency whereas, the analog beamformng can be mplemented by usng low cost phase shfters (PSs) at the RF frequency. In order to realze the analog beamformng wth analog phase shfters, we need a constant magntude beamformng matrx. Ths can be obtaned from followng lemma: Lemma 2: For a matrx A C m n, any element a mn can be represented by the sum of two unt magntude vectors, gven that 2a max a mn 2a max, where a max = max {a mn}. m,n Proof: The complex matrx element can be wrtten as a mn = a mn e jφ mn (33) 2a max snce 2a max a mn 2a max, we can have cos θ mn = a mn (34) 2a max usng Euler dentty, cos θ mn = ejθ mn + e jθ mn (35) 2 comparng (34) and (35) and then substtutng a mn 2a max n (33), we get a mn = 1 2 (e j(φ mn+cos 1 ( amn 2amax )) + e j(φ mn cos 1 ( amn 2amax ))) (36) Lemma 2 enables the practcal mplementaton of the evaluated analog beamformng matrces n Algorthms 1 and 2. E. COMPLEXITY ANALYSIS In ths subsecton, we provde the complexty analyss of Algorthms 1 and 2. The complexty of the exhaustve search algorthm for the soluton of the optmal hybrd beamformng wth PF n (21) even after the users channel decouplng n subsecton IV-A s O(2 KN f ). Before gong nsde of algorthms complexty we explan the complextes of some commonly used mathematcal operatons. The complexty of SVD, rank, QR decomposton and pseudo-nverse of a matrx of dmenson m n s O(mn(mn 2, m 2 n)), and for a matrx multplcaton of matrces of dmensons m n and n p s O(mnp) [40]. From Algorthm 1, we can observe that the complexty of PFHB comes from the followng parts: From lne 8-22, there are two nested whle loops,.e., N f loop and K loop. Wth K loop we calculate the utlty functon U, therefore, the complexty s O(N t N f K). Lne 26 contans the rank of matrx F B wth complexty O(Nt 2KN f ) (assumng KN f > N t ). Lne 27 s subchannel-wse QR decomposton therefore t has the complexty O(K 2 N t ). Lne 30 contans subchannel-wse sortng of the utlty functon wth complexty O(N f log N f ). Fnally, lnes gve rank and SVD wth complexty O(mn(N t (K) 2, Nt 2 K)) where s the number of subchannels that gves rank(f B ) N RF. Usng the rules of constant factors, polynomals, and exponental bg-oh expressons [41, Ch. 3], we sum up the overall complexty of the PFHB algorthm as O(N 2 t KN f ). In Algorthm 2 the complexty contrbutng factors are: lnes 8-11 contan channel matrx, zero forcng beamformng matrx (pseudonverse), and CNR wth complexty O(N t ). In lne 12, we use CVX for subchannel level optmal soluton VOLUME 5,

9 Algorthm 2 PF Relaxed Optmzaton (PFRO) Resource Allocaton Algorthm 1: Inputs 2: K: Number of UEs to be scheduled 3: N f : Number of subchannels 4: K : Number of UEs to be scheduled on subchannel 5: N RF : Number of RF chans 6: Intalzaton 7: K = {1,..., K}, K = {}, {Step 1:Resource allocaton to maxmze the PF spectral effcency} 8: whle N f do 9: Compute H usng (10) CN {0, 1} are generated for channel coeffcents. The transmt antenna array s ULA wth antenna spacng d = λ/2. Channel matrx s generated by usng (10). We assume nfnte resoluton PS. It should be noted that the MTDB and PFDB graphs n the smulaton results are to show the performance of an deal non-feasble fully dgtal precoder as a reference. Smulatons are averaged over 100 channel realzatons for each subchannel. 10: Compute zero forcng beamformng matrx F B 11: Compute carrer-to-nose rato CNR 12: Compute [χ,l, p k, ] = cvxoptmzaton(p, K, CNR, R (t)) (see Appendx A) 13: Compute f B k, usng (32) 14: F B = [f B 1,,..., fb K, ] 15: Compute spectral effcency R (t) = log 2 (1+p CNR ) 16: Update average spectral effcency R (t) = αr (t 1) + (1 α) R (t 1) 17: : end whle {Step 2: Rank constrant realzaton} 19: Stack the beamformng matrces F B = [F B 1,..., FB N f ] 20: f rank(f B ) N RF then 21: (F AB, F DB ) = QRdecomposton(F B ) 22: F AB = F AB (:, 1 : N RF ), F AB C N t N RF 23: F DB = F DB (1 : N RF, :), F DB C N RF (N f K) 24: End of Algorthm 25: else 26: SVD(F B ) = U V H 27: = dag(σ 1,..., σ NRF, 0,...0) 28: F B = U V 29: go to lne 21 30: end f that has the worse-case complexty O(N f 2 K ) (wth exhaustve search method). Lnes have O(1) except lne 15 whch has complexty O(log K). Lne 20, 21, and 26 contan rank, QR decomposton, and SVD, respectvely, for those the complexty s O(N 2 t KN f ). To sum up, the overall complexty of the PFRO algorthm s O(N f 2 K ). In summary, the sub-optmal PF-based hybrd beamformng algorthm PFHB has the lowest complexty O(N 2 t KN f ), whereas, the relaxed optmal algorthm PFRO shows a sgnfcant performance mprovement at the cost of exponental complexty n K, as O(N f 2 K ). V. SIMULATION RESULTS In the smulaton setup, number of subchannels N f s 64 and ndependent Raylegh dstrbuted complex random varables FIGURE 2. Average sum spectral effcency per subchannel. A. SUM SPECTRAL EFFICIENCY Fg. 2, system level average sum spectral effcency (ASSE) per subchannel s shown. The SNR s vared from 0 to 25dB, where SNR = N f P. The number of users K K t σ 2 t s 8, nose power densty s 174dBm/Hz, and the subchannel bandwdth s 5MHz. Snce the complex channel coeffcents are..d Raylegh dstrbuted wth zero mean and varance 1, and zero forcng precodng s employed wth ρ k, = 1, k,. It can be seen that at low SNR values all HB schemes are close to each other. The proposed PFHB algorthm gves lower sum spectral effcency as compared to the MTHB of [18]. The relaxed suboptmal soluton PFRO shows the superorty over the MTHB of [18] and proposed PFHB because PFRO algorthm uses optmal users combnaton and optmal power allocaton per subchannel. Fg. 2 also shows that the proposed PFRO scheme s nearoptmal, snce the sum spectral effcency gap s less than 2.33bps/Hz for all SNR values 0 25dB and the requred SNR gap between the optmal PFDB and the proposed PFRO to acheve the same sum spectral effcency s wthn 2dB, where PFDB s obtaned from Algorthm 1 by settng N RF = N t. B. INDIVIDUAL USER SPECTRAL EFFICIENCY In practcal scenaros, users are at the dfferent dstances from the enb and have dfferent average receved SNRs. Fg. 3 shows the ndvdual spectral effcency when users are placed at gradually ncreasng dstances from the enb. The transmt power s fxed at 45dBm. The maxmum throughput based MTDB and MTHB gve hgh spectral effcency to closer users but the edge users suffer from the low or zero value, 178 VOLUME 5, 2017

10 TABLE 1. Smulaton Parameters FIGURE 3. Indvdual spectral effcency when K t = 8 users are placed at dfferent dstances from enb. whereas, the PF-based PFDB, PFRO and PFHB try to acheve the best tradeoff between spectral-effcency and farness. The PFDB ndvdual spectral effcency even reaches the MTDB for some users but sum spectral effcency s always less than the MTDB. The PFRO provdes hgher ndvdual user spectral effcency than PFHB and more unform spectral effcency dstrbuton to the users wth dfferent dstances (average receved SNR) as compared to the MTDB and MTHB schemes. The PFDB has best tradeoff between throughput and farness but at the cost of large number of RF chans and power consumpton. FIGURE 5. Jan s farness ndex. C. FAIRNESS We analyze the performance of the algorthms n terms of farness usng Jan s farness ndex [42]. Jans farness ndex (JFI) has been wdely used as a measure of farness n communcaton systems, whch s defned as ( Kk=1 ) 2 R k JFI = K K k=1 R 2 k (37) FIGURE 4. Spectral effcency comparson of schemes wth varous nter-user dstances. Fg. 4 shows the sum spectral effcency of dfferent schemes wth varous nter-users dstances and coverage areas. For example, wth nter-users dstance of 20m, each user has a dstance of 20m wth each other, such that the farthest user has a dstance of 20 K t (160m radus coverage area when K t = 8) from the enb. The sum spectral effcency of two deal schemes (MTDB and PFDB) s hgh as expected. Among the three practcal hybrd beamformng schemes, the PFRO performs better than MTHB and PFHB for all nteruser dstances. In PFRO, the sum spectral effcency for 400m radus coverage area s greater than the sum spectral effcency of 160m radus coverage area n PFHB. where R k s the k th users average throughput. As shown n the Fg. 5, PFDB has the hghest farness ndex among all DB and HB schemes, because of the PF-based resource allocaton and the expensve dgtal beamformng. Among the three HB technques, the proposed PFRO outperforms the other schemes. Snce, the farness among users depends on the slope of the ndvdual users throughput, therefore, PFRO and PFHB exhbt approxmately the same performance n farness ndex as shown n Fg. 5. Agan, at very small nter-user dstances the PFRO, PFHB and MTHB have same performance but at large nter-user dstances, PFRO and PFHB provde hgh farness among users. D. PERFORMANCE OF ALGORITHMS We analyze the performance of proposed algorthms by calculatng the tme-elapsed for the sum spectral effcency VOLUME 5,

11 of Fg 6 and Fg. 7 reveals the large computaton tme of the Algorthm 2 as compared to the Algorthm 1. The optmal soluton to the problem n (30) has exponental complexty both n number of subchannels and number of users. The proposed soluton to the PFRO uses CVX to fnd the optmal users combnaton per subchannel and the power allocaton for the selected users, and the domnant component of the executon tme s due to the cvxoptmzaton() functon n lne 12 of Algorthm 2. FIGURE 6. Algorthm 1 tme elapsed for sum spectral effcency wth dfferent values of K t and N f, when average SNR = 20dB. VI. CONCLUSIONS In ths paper, we present resource allocaton algorthms (PFHB and PFRO) to maxmze the proportonal farness spectral effcency under the per subchannel power and the transmt beamformng rank constrants. The PFHB algorthm provdes the PF-based hybrd precodng matrx for requred number of RF chans. Then, we transform the number of RF chans or rank constraned optmzaton problem nto convex semdefnte programmng problem whch can be solved by standard technques. Inspred by the convex SDP problem we present PFRO algorthm. It has been shown that the proposed PFRO scheme provdes near-optmal sum spectral effcency. The performance gap s less than 2.33bps/Hz and 2dB n terms of sum spectral effcency and requred SNR, respectvely, to acheve the same performance. The proposed PFRO provdes better performance n sum spectral effcency, ndvdual spectral effcency, and farness ndex among other HB desgns. FIGURE 7. Algorthm 2 tme elapsed for sum spectral effcency wth dfferent values of K t and N f, when average SNR = 20dB. evaluaton wth dfferent values of the number of users and the number of subchannels n Fg. 6 and Fg. 7. Algorthms 1 and 2 are desgned n such a way that ensures ther termnaton n two teratons at the most. In Algorthm 1, SVD(F B ) n lne 34 and the selecton of the frst N RF left sngular columns as analog beamformng matrx n lne 35 ensure the algorthm termnaton n the second teraton. In Algorthm 2, low rank approxmaton n lnes 26, 27, and 28 guarantees the end of algorthm. Wthn the teraton, the complexty of the algorthms depend on the number of subchannels and the number of users, as dscussed n the subsecton IV-E. It can be seen n Fg. 6 that the tme-elapsed of Algorthm 1 s lnear functon of the number of users for a fxed number of subchannels and vce versa (lnear functon of number of subchannels for fxed number of users). Ths valdates the complexty evaluated n the subsecton IV- E. Fg. 7 seconds the concluded complexty for Algorthm 2 n subsecton IV-E,.e., the computaton tme ncreases lnearly wth number of subchannels for the fxed number of users, and t ncreases exponentally wth the number of users for the fxed number of subchannels. The comparson APPENDIX A PROBLEM FORMULATION FOR CVX CVX s a Matlab-based modelng framework for convex optmzaton. The user challengng part of CVX s to transform the optmzaton problem nto the dscplned convex programmng (DCP). In our transformaton, the nputs are the number of users K, carrer-to-nose rato CNR, per subchannel power P, and the prevous average spectral effcency R_t_1. The outputs are p and X. The utlty functon n (31) whch s defned n (18) contans multplcaton of optmzaton varables whch s aganst the DCP ruleset defned n [38]. In order to express the objectve functon n CVX format, we use the technque avalable at [43] to wrte the spectral effcency functon n lne 10 of below code. The sum of logarthmc functon s replaced by the geometrc functon n lne 9. 1 L=2^K-1; 2 x=de2b(1:2^k-1, left-msb ); 3 CNRx=CNR_repmat.*x; 4 q_t_1=2.^(r_t_1); 5 cvx_begn 6 cvx_solver mosek 7 varables p(l,k) q(l,k) 8 varable X(L,1) bnary 9 maxmze(sum(geo_mean(q,2))) 180 VOLUME 5, 2017

12 10 q <= (1 + CNRx.* mn(p,p*repmat (X,1,K)))./q_t_1; 11 p>=zeros(l,k) 12 sum(sum(p,2))<=p 13 sum(x)==1 14 cvx_end REFERENCES [1] G. Bochechka and V. Tkhvnsky, Spectrum occupaton and perspectves mllmeter band utlzaton for 5G networks, n Proc. ITU Kaledoscope Acad. Conf. Lvng Converg. World-Impossble Standards, Sant Petersburg, Russa, 2014, pp [2] W. Roh et al., Mllmeter-wave beamformng as an enablng technology for 5G cellular communcatons: Theoretcal feasblty and prototype results, IEEE Commun. Mag., vol. 52, no. 2, pp , Feb [3] Part 11: Wreless LAN Medum Access Control (MAC) and Physcal Layer (PHY) Specfcatons Amendment 3: Enhancements for Very Hgh Throughput n the 60 GHz Band, IEEE Standard ad, Dec [4] GSMA. LTE- About Us. accessed on Oct. 22, [Onlne]. Avalable: [5] T. E. Bogale, L. B. Le, and A. Haghghat, User schedulng for massve MIMO OFDMA systems wth hybrd analog-dgtal beamformng, n Proc. IEEE Int. Conf. Commun., London, U.K., Jun. 2015, pp [6] F. Sohrab and W. 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13 I. Ahmed et al.: Resource Allocaton for Transmt Hybrd Beamformng n Decoupled Mllmeter Wave Multuser-MIMO Downlnk [43] M. Grant. (2016). CVX Forum: How to Express Ths Objectve Functon n CVX. [Onlne]. Avalable: IRFAN AHMED (M 10 SM 16) receved the B.E. degree n electrcal engneerng and the M.S. degree n computer engneerng from the Unversty of Engneerng and Technology, Taxla, Pakstan, n 1999 and 2003, respectvely, and the Ph.D. degree n telecommuncaton engneerng from the Bejng Unversty of Posts and Telecommuncatons, Bejng, Chna, n He was a Post-Doctoral Fellow wth Qatar Unversty from 2010 to 2011, where he was nvolved n two research projects, wreless mesh networks wth Purdue Unversty, USA, and rado resource allocaton for LTE wth Qtel. He was also nvolved n Natonal ICT Pakstan funded research project Desgn and Development of MIMO and Cooperatve MIMO Test-Bed wth Iqra Unversty, Islamabad, Pakstan, from 2008 to He s currently an Assocate Professor wth Taf Unversty, KSA. He has authored over 25 nternatonal publcatons. Hs research nterests nclude wreless LAN medum access control protocol desgn and analyss, cooperatve communcatons, MIMO communcatons, performance analyss of wreless channels, energy constraned wreless networks, cogntve rado networks, and rado resource allocaton. Dr. Ahmed served as the Sesson Char of the IEEE WIRELESS COMMUNICATIONS, Networkng and Moble Computng conference held n Shangha, Chna, n 2007, and the IEEE ICC He s an actve Revewer of the IEEE, Sprnger, and Elsever journals, and conferences. He s an Assocate Edtor of the IEEE Access journal. ADNAN SHAHID (M 15) receved the B.Eng. and M.Eng. degrees n computer engneerng wth communcaton specalzaton from the Unversty of Engneerng and Technology, Taxla, Pakstan, n 2006 and 2010, respectvely, and the Ph.D. degree n nformaton and communcaton engneerng from Sejong Unversty, South Korea, n From 2007 to 2012, he was a Lecturer n electrcal engneerng wth the Department of Natonal Unversty of Computer and Emergng Scences, Pakstan. From 2012 to 2015, he was a Ph.D. Research Assstant wth Sejong Unversty. In 2015, he was a Post-Doctoral Researcher wth Yonse Unversty, South Korea. From 2015 to 2016, he was wth the Department of Computer Engneerng, Taf Unversty, Saud Araba. He s currently a Post-Doctoral Researcher wth Mnds/IBCN, Department of Informaton Technology, Unversty of Ghent, Belgum. He s coordnatng and actvely nvolved n the research actvtes of the research project ewine funded by the European Commsson under the Horzon2020 Program. He actvely nvolved n varous research actvtes. He was a recpent of the prestgous BK 21 plus Postdoc Program at Yonse Unversty. He s servng as an Assocate Edtor of the IEEE Access Journal. Hs research nterests nclude the next generaton wreless communcaton and networks wth prme focus on resource management, nterference management, cross-layer optmzaton, self-organzng networks, small cell networks, devce to devce communcatons, machne to machne communcatons, and 5G wreless communcatons. HEDI KHAMMARI receved the B.Eng. and M.Eng. degrees n electrcal engneerng wth automatc control specalzaton, and the Ph.D. degree n electrcal engneerng from the Tuns Unversty, Tuns, n 1988, 1990, and 1999, respectvely. He s currently an Assocate Professor wth the Department of Computer Engneerng, College of Computers and Informaton Technology, Taf Unversty, Saud Araba. 182 VOLUME 5, 2017