Hybrid Digita-to-Anaog Beamforming for Miimeter-Wave Systems with High User Density Manish Nair, Qasim Zeeshan Ahmed and Huiing Zhu Schoo of Engineering and Digita Arts, University of Kent, Canterbury, CT2 7NT, United Kingdom Emai: {mn307, qahmed and hzhu}@kentacuk Abstract Miimeter-wave (mm-wave) systems with hybrid digita-to-anaog beamforming (D-A BF) have the potentia to fufi 5G traffic demands The capacity of mm- Wave systems is severey imited as each radio frequency (RF) transceiver chain in current base station (BS) architectures support ony a particuar user In order to overcome this probem when high density of users are present, a new agorithm is proposed in this paper This agorithm operates on the principe of seection combining (SC) This agorithm is compared with the state of the art hybrid D-A BF The simuation resuts show that our proposed hybrid D-A BF using SC supports higher density of users per RF chain Furthermore, our proposed agorithm achieves higher capacity than what is achieved by the current hybrid D-A BF systems Index Terms Hybrid beamforming, beamformer, precoder, seection combining, miimeter wave, 3D channe, muti user, interference, MIMO, mobie communications I INTRODUCTION Miimeter-wave (mm-wave) frequencies have the potentia of addressing spectrum scarcity and capacity demands in current ceuar bands [1] Fu scae impementation of digita systems by depoying a radio frequency (RF) transceiver chain per antenna eement is impossibe due to the constraints of cost, power consumption and signa processing compexity imposed by the RF front end and mixed signa components [2] A practica soution wi be to depoy a much smaer number of RF chains where each RF chain can support a arge number of transmit (Tx) antenna eements, resuting in a hybrid digitato anaog (D-A BF) system Therefore, hybrid D-A BF is one of the techniques of reducing the number of RF chains [3], [4], [5] Hybrid D-A BF have been proposed in [6], [7], where the digita beamformer is equivaent to an identity matrix and the anaog beamformer is equivaent to the hermitian of the channe It is aso shown that the overa capacity of the hybrid D-A BF system is imited as compared to the compete digita beamforming (D-BF) system because of the number of RF chains [6] The major drawback in this type of hybrid D-A BF structure is that each RF chain can ony support a particuar user [6] Therefore, the maximum number of users that can be supported by the BS cannot exceed the number of RF chains [6] This wi severey imit mobie capacity in future mm-wave networks especiay in high density user environments ike train stations, stadiums or shopping mas Therefore, new hybrid D-A BF schemes are required, which can support mutipe users by empoying a BS RF chain to achieve simiar capacity gains as promised by the D-BF systems Superposition coding can be appied to the Tx symbos on a singe stream to support mutipe users through a RF chain However, it cannot serve mutipe users simutaneousy as ony a singe 3 dimensiona (3D) beam is formed [8] In this paper, a new hybrid D-A BF agorithm for supporting mutipe users is proposed With this empoyed technique, each user wi have its own separate 3D beam assisting in supporting mutipe users simutaneousy This agorithm is impemented with the hep of seection combining (SC) The SC agorithm is an anaog beamforming (A-BF) technique which modifies the A- BF matrix by designating each and every antenna eement to the seected users The users and antennas are seected depending upon their instantaneous channe state information (CSI) However, the users experience muti-user interference (MUI) from the beamformed signas Therefore, a ow compexity MUI canceing technique is proposed at the receiver (Rx) From our simuations, it can be observed that the proposed hybrid D-A BF using the SC agorithm achieves superior capacity gains to other hybrid D-A agorithms as proposed in [6], [7] Our proposed hybrid D-A BF agorithm aso accounts for the 3D mm-wave channe for a muti-user system which is generated when panar antenna arrays are depoyed [9], [10] The reminder of this paper is organized as foows In Section II, the system mode is described In Section III, we propose the hybrid D-A BF SC based agorithm In Section IV, the simuation resuts for the mentioned BF techniques are discussed Finay, the paper is concuded in Section V II DESCRIPTION OF THE HYBRID D-A BF SYSTEM Figure 1 Hybrid BF Structure The bock diagram of the hybrid D-A BF system is shown in Fig 1 This structure is preferred as it is common to the current ceuar BS systems [6] Each of the N RF chains is connected to a arge-scae array of M identica antennas The anaysis is carried out considering a downink scenario for the i-th RF chain supporting the k-th user For the i-th RF chain the A-BF is performed over ony M antennas by the anaog beamformer A i As the channe experiences L resovabe mutipath [11], [12], [13], [14], [15], [16], the digita beamformer for the i-th
chain is represented as D i having dimensions ML MLThe compete digita beamformer D is given as: D = diag[d 1,D 2,,D N ], (1) where D accounts for N-RF chains in the BS and is NML NML dimensiona A 3D mm-wave Channe Mode The 3D mm-wave modified Saeh-Vaenzuea (SV) channe impuse response (CIR) for the i-th RF chain and the m-th Tx antenna is given by [17], [18], [19]: h k i,m(t) = = V 1 U 1 v=0 u=0 L 1 α k i,m,uvh k i,m,uvδ(t τ v τ uv ) αi,m,h k k i,m,δ(t τ), (2) where h k i,m, is the k-th user CIR of -th resovabe muti-path for the m-th Tx antenna of the i-th RF chain V denotes the number of custers, U the number of of resovabe muti-paths in one custer, and L = UV is the tota number of resovabe muti-paths at the receiver is reated to u and v by = vu+u In (2) h k i,m,uv = hk i,m,uv represents the fading gain of ejθuv the u-th resovabe muti-path in the v-th custer connecting the m-th antenna in the i-th RF chain to the k-th user τ v is the time-of-arriva (ToA) of the v-th custer and τ uv = uτ denotes the ToA of the u-th resovabe muti-path in the v-th custer In our mm-wave channe, it is assumed that the average power of a muti-path at a given deay is reated to the power of the first resovabe muti-path of the first custer through the foowing reationship [18], [19]: ( Puv k = P00exp k τ ) ( v exp τ ) uv, (3) Ψ ψ where Puv k = P k = h k i,m,uv 2 represents the expected power of the u-th resovabe muti-path in the v-th custer connecting the k-thusertothem-th antenna in the i-th RF BS chain Ψ and ψ are the corresponding power deay constants of the custer and the resovabe muti-path respectivey For the channe mode to be generic, we assume that the deay spread, which is (L 1)τ of the mm-wave channe spans g 1 data bits, satisfying (g 1)N τ (L 1) gn τ, where N τ is the number of time sots per symbo Secondy, we assume that the L number of resovabe mutipath components are randomy distributed, but they are the same over each symbo Due to the wider bandwidth at mm-wave, a the L muti-path components can be resoved at the Rx side [20], [21], and muti-path diversity wi be expoited in the anaog beamformer to significanty improve capacity in our proposed system The CIR experienced by the i-th RF chain and the k-th user is given as: H k i (t) =diag [ H k i,0 (t),hk i,1 (t),,hk i,m 1 (t)], (4) where H k i,m (t) is the L (2L 1) dimensiona Bock-Toepitz tempora CIR convoution matrix associated with the i-th RF chain, m-th Tx antenna and the k-th user, given by (5) at the bottom of the page Finay, H k i (t) wi aso be a tempora matrix be of dimension ML M(2L 1) The k-th user 3D BFgainαi,m,uv k = αk i,m, for every Tx antenna eement of the i-th RF chain is given in (6) F Rx,V and F Rx,H are the Rx beam pattern for the vertica (V) and horizonta (H) poarizations, respectivey F Tx,i,V and F T x,i,h are the Tx beam pattern for the i-th RF chain are the initia random phases for vertica (VV), cross (VH, HV), and horizonta poarizations (HH) for the resovabe muti-path κ m is the intra-custer Rician K-factor associated with the m-th Tx antenna custer [10] θ and φ are the eevation and azimuth ange-of-arriva (AoA), respectivey Finay, θ,m and φ,m are the eevation and azimuth ange-of-departure (AoD) of the -th resovabe mutipath and m-th Tx antenna in the i-th RF chain φ VV,φ VH,φ HV,φ HH B Received Symbos of Hybrid D-A BF The L sampes of received signa at the k-th user from the i-th RF chain is expressed as: where y k i (t) =H k i (t)a i (t)d i x k i (t)+n k i (t), (7) x k i (t) = [ x k i,0 (t),xk i,1 (t),,xk i,m 1 (t)] T are the ML 1 dimensiona transmitted uncorreated data symbos to the k-th user from the i-th RF chain x k i,m (t) = [x k i,m (t),xk i,m (t 1),,xk i,m (t L +1)]are the L symbo sampes for a the resovabe muti-paths, corresponding to the m-th Tx antenna in the i-th chain BF design wi be discussed in detai in the foowing section n k i (t) is modeed as independent and identica distributed (iid) compex Gaussian random noise with zero mean and a variance of σi 2 for the k-th user The signa to noise ratio (SNR) of the i-th RF chain is denoted by γ i and is given as [22]: γ i (D i,a i (t),h k H k i i (t)) = γ (t)a i (t)d i x k i (t) 2 0 σi 2, (9) where γ 0 is the average input SNR Maximizing this SNR wi ead to improved system capacity (in bit per second per Hz) for (8) h k i,m,0(t) h k i,m,1(t) h k i,m,l 1(t) 0 0 H k 0 h k i,m,0(t 1) h k i,m,1(t 1) h k i,m,l 1(t 1) 0 i,m(t) = 0 0 h k i,m,0(t L +1) h k i,m,1(t L +1) h k i,m,l 1(t L +1) α k i,m, = [ FRx,V (φ,θ ) F Rx,H(φ,θ ) ] T [ e jφvv κ 1 m e jφhv κ 1 m e jφvh e jφhh ] [FT ] x,i,v (φ,m,θ,m ) F T x,i,h(φ,m,θ,m ) (5) (6)
the k-th user associated with the i-th RF chain, and cacuated as [22]: C k i =og 2 [1 + γ i (D i,a i (t),h k i (t))] (10) Let us now proceed towards designing the BF matrices which maximize the SNR of the i-th RF chain III BEAMFORMER DESIGN FOR HYBRID D-A BF In this section, a type of hybrid D-A BF is considered for supporting a high density of users in mm-wave systems In the separate design of hybrid D-A BF as proposed in [6] - [7], the anaog beamformer A i = H H i / H i F is equa to the normaized hermitian of the channe H i F is the Frobenius norm of the channe The digita beamformer, D i = I is an identity matrix of size L The BF matrix in this case is simpy a matched fiter (MF) as A i D i = H H i / H i F However, high user density environment cannot be supported by this method Therefore, the SC agorithm is proposed A Hybrid D-A BF with Seection Combining (SC) In SC agorithm, M antenna eements in the i-th RF chain have to be aocated to K users K represents the tota number of users in a high user density environment, that have to be supported by the i-th RF chain such that K M The aocation of antenna eements is based on the cacuation of expected power of the 3D mm-wave modified SV channe of every user For the m-th antenna eement in the i-th RF chain, the channe power associated with the k-th user is cacuated as foows: L 1 p k i,m = h k i,m, 2 (11) This process is repeated for a the K users for the m-th antenna eement The m-th antenna is then assigned to that user which has the maximum power: k m =argmax k K { p 0 i,m,p 1 i,m,,p K 1 i,m }, (12) where argmax cacuates the maximum vaue This process is repeated M times unti a the M antennas are aocated to the S users where S K The remaining (K S) users are not supported It is cear that SC agorithm aocates non-contiguous antenna eements to the respective users Therefore, the users wi experience MUI from the beamformed signas generated from antenna eements that are aocated to other users Interference from the undesired beamformed signas can be eiminated at every user by a set of receive BF weights It is assumed that the SC antenna aocation information is avaiabe at the receiver For exampe, consider a scenario in which the number of antenna eements in the i-th RF chain is M = 4, the tota number of singe antenna users to be supported by this i-th RF chain is S = 3, and where the SC antenna aocation for the i-th RF chain that foows the pattern as shown in Fig 2 In this scenario, antenna m 0 is aocated to user s 0 ; m 1 and m 3 to s 2 ; and m 2 to s 1 As shown in the figure, A-BF A SC i (t) is performed over each of the M antennas, where as MUI suppression is impemented by Figure 2 SC Antenna Aocation for the i-th RF chain the weights w s at the s-th user The A-BF matrix A SC i (t), as depicted in Fig 2 is given by: A SC i H 0 i,0h (t)/ H 0 i,0 F H 2 i,1h (t)/ H 2 i,1 (t) =diag F H 1 i,2h (t)/ H 1 i,2 F, (13) H 2 i,3h (t)/ H 2 i,3 F where H s i,m (t) represents the CIR from the m-th Tx antenna to the s-th user as was defined in (5) Now et us examine the case of user s 2 The received signa at s 2 can be represented as: i (t) = w 2 H 2 i,1(t)a SC i (t)x i (t)+w 2 H 2 i,3(t)a SC i (t)x i (t) + w 2 H 2 i,0(t)a SC 2 i (t)x i (t) + w 2 Hi,2(t)A i (t)x i (t) }{{}}{{} Interference from user s 0 Interference from user s 1 + w 2 n i,2 (t) (14) y s2 In (14), x i (t) = [x 0 i,0 (t),x2 i,1 (t),x1 i,2 (t),x2 i,3 (t)]t is the ML 1 symbo vector for the i-th chain, where x s i,m (t) = [x s i,m (t),xs i,m (t 1),,xs i,m (t L +1)]is the L 1 symbo vector assigned to the m-th antenna that is aocated to the s-th user by the SC agorithm n i,2 (t) is the iid compex Gaussian random noise for the user s 2 with a variance of σi,2 2 {H 2 i,m (t)asc i (t)} is the ML ML signa received at s 2 after anaog preprocessing at the Tx and channe conditioning given by (15) at the top of the foowing page In (15) h 2 i,m, (t) is the -th resovabe muti-path at time instant t as defined previousy The 1 ML Rx-BF seection weights w 2 = [0, 1, 0, 1], where the 0 s and 1 s are L dimensiona, operating on {H 2 i,m (t)asc i (t)}, wi cance the MUI from the unwanted beamformed signas that are generated by antenna eements aocated to the other users by the SC agorithm It can be observed that the pattern of zeros foow the MUI s from the respective antenna eements which need to be eiminated D i is identity simiar to [6], [7] The weights for the other users for mitigating MUI can be simiary derived as w 0 = [1, 0, 0, 0] and w 1 = [0, 0, 1, 0] respectivey, and can be extended for any SC antenna aocation In this way, the receiver compexity can be reduced significanty because processing is moved to the Tx side To satisfy the tota power constraint the signa power of the i-th RF chain is: 1 M M 1 m=0 s=0 S 1 p s i,m σi 2 γ i (16) Finay, the SNR for the i-th RF chain and the s-th user for the
H 2 i,0(t)h 0 i,0(t) H / H 0 i,0 F H 2 i,m(t)a SC H 2 i (t) = diag i,1(t)h 2 i,1(t) H / H 2 i,1 F H 2 i,2(t)h 1 i,2(t) H / H 1 i,2 F = H 2 i,3(t)h 2 i,3(t) H / H 2 i,3 F diag L 1 L 1 L 1 h2 i,0,(t)h 0 i,0,(t) / H 0 i,0 F h2 i,0,(t 1)h 0 i,0,(t 1) / H 0 i,0 F h2 i,0,(t L +1)h 0 i,0,(t L +1) / H 0 i,0 F h2 i,1,(t) 2 / H 2 i,1 F h2 i,1,(t 1) 2 / H 2 i,1 F L 1 h2 i,1,(t L +1) 2 / H 2 i,1 F h2 i,2,(t)h 1 i,2,(t) / H 1 i,2 F h2 i,2,(t 1)h 1 i,2,(t 1) / H 1 i,2 F h2 i,2,(t L +1)h 1 i,2,(t L +1) / H 1 i,2 F h2 i,3,(t) 2 / H 2 i,3 F h2 i,3,(t 1) 2 / H 2 i,3 F L 1 h2 i,3,(t L +1) 2 / H 2 i,3 F (15) SC agorithm is cacuated as foows [22]: γ i (w s,d i,a SC i (t),h s i (t)) = M sγ 0 M (σ2 i,sw H s ) 1 w H s H s i (t) A SC i (t)d i D H i A SC H i (t) H sh i (t)w s, (17) where M s is the number of antennas aocated to the s-th user and σi,s 2 is the corresponding iid noise variance IV SIMULATION RESULTS Tabe I 3D MM-WAVE MODIFIED SV CHANNEL PARAMETERS [10] Description Unit Vaue Inter-custer inter-arriva rate 1/ns 021 Intra-custer inter-arriva rate 1/ns 077 Inter-custer decay factor ns 419 Intra-custer decay factor ns 107 Sma-scae fading RMS db 126 Inter-custer Rician K-factor db -10 Intra-custer Rician K-factor db -10 In this section, beam pattern and the capacity performance of two different kinds of hybrid D-A BF agorithms are investigated SC based hybrid D-A BF is compared with the separate hybrid D-A BF proposed in [6], [7] The parameters for generating the 3D mm-wave modified SV channe mode are mentioned in Tabe-I [10] Perfect channe knowedge or CSI [23], [24], [25], [26], [27], [28], [29], [30], [31], [32] is assumed between the Tx antennas and Rx antenna Two different environments are considered in our simuations In the first environment perfect ine-of-sight (LoS) is avaiabe Whie, in the second environment, mutipath are present, and the number of resovabe mutipath is assumed to be 15 A uniform panar array of M =16 16 antennas is considered Fig 3 indicates that by using the SC agorithm to design the hybrid D-A BF system, the capacity increases when the number of users per RF chain increases This is because with a arger number of users, the number of resovabe mutipath in the mm-wave channe increases which are combined using A-BF to improve the SNR at the respective users In this way, muti-path diversity has been expoited in our mm- Wave system This is observed in the curves with K = 8 users and L =15resovabe mutipath per Tx antenna custer attaining the upper bound as compared to the singe user case with L =15resovabe mutipath K =8users per RF chain in a BS is chosen to represent a high user density scenario in mm-wave systems However, capacity gains from mutipath diversity wi be offset by the power constraint in the i-th RF chain, and it wi tend to saturate From this figure, it can aso be observed that the SC agorithm outperforms the separate hybrid D-A BF design Substantia gains in terms of performance are achieved by using our agorithm Fig 4 in the foowing page pots the beam patterns generated by the M =16 16 panar BS antenna array in the i-th RF chain Fig 4a shows the pattern for a singe user, with separate hybrid D-A BF design as in [6], [7] Fig 4b shows the pattern generated for a second and a third user in addition to the first user for the same RF chain using the SC agorithm Capacity (b/s/hz) 10 3 10 2 10 1 10 0 8 Users: 15 Mutipaths 2 Users: 15 Mutipaths 1 User with LoS 1 User with 15 Mutipaths 10-1 LoS 2 Users with LoS: SC 2 Users with 15 Mutipaths: SC 8 Users with 15 Mutipaths: SC 10-2 -30-20 -10 0 10 20 30 SNR (db) Figure 3 Capacity of the proposed hybrid D-A BF systems as a function of SNR Resuts are reported for a downink mmwave system with M =16 16 BS antennas from SNR of 30dB to 30dB The simuated environment incudes both a singe LoS channe and L =15muti-path
Figure 4 Normaized beam pattern for M = 16 16 panar array using separate hybrid D-A BF design and SC (a) Beam pattern of the origina user in Separate Hybrid D-A BF Design The anguar ocation of the user is at θ =0 from the y-z pane φ =30 from the x-z pane, and, (b) Hybrid D-A BF design using SC The combined beam patterns for the 3 users The anguar ocation of the 1-st user is unchanged, where as that of the 2-nd user is θ =45 from the y-z pane φ =45 from the x-z pane, and that of the 3-rd user is θ =0 from the y-z pane φ =90 from the x-z pane The beam directivity is reduced in SC It can be observed from Fig 4b that whie SC achieves user separation, the directivity of the beams are reduced This is because the number of antenna eements aocated per user is reduced, and at the same time, seection combining does not design the D-BF matrix, keeping it as identity as in the case of separate hybrid D-A BF design In our simuations, the number of BS antenna array eements is chosen considering the processing and bandwidth imitations of the massive mutipeinput mutipe-output (MIMO) architectures V CONCLUSION In this paper, a new agorithm which operates on the principe of SC has been proposed for hybrid D-A BF based mm- Wave system From our based agorithm, it is possibe to support more than a singe user per RF chain This agorithm has a significant impact when higher density of users are present and the particuar RF chain had to support mutipe users From our simuations, it has been seen that our proposed hybrid D-A BF using SC achieves higher capacity as compared to the known hybrid D-A BF and supports higher density of users per RF chain ACKNOWLEDGEMENT This work has received funding from the EU s Horizon 2020 Programme under Grant Agreement No 643297 (RAPID 5G) REFERENCES [1] S Sun, T Rappaport, R Heath, A Nix, and S Rangan, MIMO for Miimeter-Wave Wireess Communications: Beamforming, Spatia mutipexing, or Both, IEEE Communications Magazine, vo 52, no 12, pp 110 121, December 2014 [2] A Akhateeb, J Mo, N Gonzaez-Precic, and R Heath, MIMO Precoding and Combining Soutions for Miimeter-Wave Systems, IEEE Communications Magazine, vo 52, no 12, pp 122 131, December 2014 [3] M Crocco and A Trucco, Design of Superdirective Panar Arrays With Sparse Aperiodic Layouts for Processing Broadband Signas via 3-D Beamforming, IEEE/ACM Transactions on Audio, Speech, and Language Processing, vo 22, no 4, pp 800 815, Apri 2014 [4] T E Bogae and L B Le, Beamforming for mutiuser massive mimo systems: Digita versus hybrid anaog-digita, in 2014 IEEE Goba Communications Conference, Dec 2014, pp 4066 4071 [5] O Auhaibi, Q Z Ahmed, C Pan, and H Zhu, Capacity Maximisation for Hybrid Digita-to-Anaog Beamforming mm-wave Systems, to appear in IEEE Goba Communications Conference (GLOBECOM 16), Dec 2016 [6] S Han, C-L I, Z Xu, and C Rowe, Large-Scae Antenna Systems with Hybrid Anaog and Digita Beamforming for Miimeter Wave 5G, IEEE Communications Magazine, vo 53, no 1, pp 186 194, January 2015 [7] W Roh, J-Y Seo, J Park, B Lee, J Lee, Y Kim, J Cho, K Cheun, and F Aryanfar, Miimeter-Wave Beamforming as an Enabing Technoogy for 5G Ceuar Communications: Theoretica Feasibiity and Prototype Resuts, IEEE Communications Magazine,vo 52,no2,pp 106 113, February 2014 [8] H T Do and S Y Chung, Linear beamforming and superposition coding with common information for the gaussian mimo broadcast channe, IEEE Transactions on Communications, vo 57, no 8, pp 2484 2494, Aug 2009 [9] A Akhateeb, O E Ayach, G Leus, and R Heath, Hybrid Precoding for Miimeter Wave Ceuar Systems with Partia Channe Knowedge, in 2013 Information Theory and Appications Workshop (ITA), Feb 2013, pp 1 5 [10] H Xu, V Kukshya, and T Rappaport, Spatia and Tempora Characteristics of 60-GHz Indoor Channes, IEEE Journa on Seected Areas in Communications, vo 20, no 3, pp 620 630, Apr 2002 [11] H Zhu and J Wang, Chunk-based resource aocation in ofdma systems - 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