Non-orthogonal Multiple Access Based Hybrid Beamforming in 5G mmWave Systems Wei Wu, Danpu Liu Beijing Laboratory of Advanced Information Network Beijing Key Laboratory of Network System Architecture and Convergence Beijing University of Posts and Telecommunications, P.R. China Email:
[email protected],
[email protected]
Abstract—In this paper, we propose a non-orthogonal multiple access(NOMA) based hybrid beamforming design in 5G mmWave systems. The proposed design depends on the known array geometry and incurs a low training and feedback overhead. Our model assumes that each user employs analog-only beamforming while the BS performs hybrid analog and digital beamforming. To achieve a higher sum capacity, multiple users are allowed to share the same beam based on NOMA mechanism. However, the use of analog beamformer from different localized users means that the BS’s digital beamformers are not perfectly aligned with the users’ baseband effective channels and multiple users may be assigned similar or even identical beamformers. In the meantime, a user pairing and power allocation algorithm is proposed to mitigate interference from other beams so as to maximize the sum capacity. Simulation results verify the significant advantage of the proposed scheme in sum capacity.
I. I NTRODUCTION The consolidation of millimeter-wave(mmWave) and massive multiple-input multiple-output (MIMO) systems is regarded as a prospective technique for future 5G mmWave cellular systems because this combination can provide orders of magnitude increase both in available bandwidth and spectrum efficiency [1], [2]. Although large scale antenna arrays with full digital beamforming can yield optimal performance, implementing the same number of transceiver units (TXRUs) is impractical due to the excessive demand on real-time signal processing, high power consumption and high cost at mmWave bands. Therefore, a hybrid digital and analog beamforming (so-called hybrid beamforming) architecture is a more practical solution for 5G mmWave cellular systems since the number of TXRUs is much lower than the number of antennas in this case [3]–[5]. Most of existing work on hybrid beamforming in 5G mmWave systems mainly focus on hybrid precoding design with perfect or partially CSI [3], [5]–[7] and channel estimation [4], [8], [9]. With regard to conventional orthogonal multiple access(OMA, i.e., TDMA, FDMA and CDMA), the number of TXRUs in the base station(BS) can not be less than the total number of TXRUs for all of served users in a multiuser MIMO c 2017 IEEE 978-1-5386-3531-5/17/$31.00
system. Otherwise, the sum capacity is susceptible to degradation due to the time/frequency/code resources allocation. MmWave signals suffer high path loss such that the served users in different locations have strongly different received introduce non-orthogonal multiple access(NOMA) technology into multiuser hybrid beamforming system to improve the sum capacity. NOMA has also been recognized as a key promising technique for future 5G mmWave systems [10]. Unlike conventional OMA, NOMA uses the power domain to serve multiple users in the same time/frequency/code channel, where successive interference cancellation (SIC) is employed at users with better channel conditions [11]. The use of NOMA technology can further improve the performance of MIMO beamforming, and the optimal design of NOMA with beamforming has been investigated in [12]. In this paper, we propose a NOMA based hybrid beamforming in 5G mmWave systems. The proposed design depends on the known array geometry and incurs a low training and feedback overhead. Our model assumes that the each user equips a single TXRU and employs analog-only beamforming while the BS with serval TXRUs performs hybrid analog and digital beamforming. If the traditonal OMA is used, the maximum number of users simultaneously served by the BS can not be larger than the number of BS TXRUs. In our design, multiple users are allowed to share the same beam by the use of NOMA mechanism. However, the use of analog beamformer from different localized users means that the BS’s digital beamformers are not perfectly aligned with the users’ baseband effective channels and multiple users may be assigned similar or even identical beamformers. In the meantime, a user pairing and power allocation scheme is proposed to mitigate interference from other beams and guarantee improved sum capacity. Notation: A is a matrix, a is a vector, a is a scalar, and A is a set. |a| and ]a are the magnitude and phase of the complex number a. tr(A), AT , AH , A† , kAk1 , kAkF , A [r, :] , A [:, c] and A [r, c] denote the trace, transpose, conjugate transpose, pseudo inverse, 1-norm, Frobenius norm, the rth row,
Cluster 1 UE1,1 UE1,2
Cluster 2 UE2,1 UE2,2
factors for two users, and αm,1 +αm,2 = 1. On the downlink, theBS applies a M ×M digital baseband precoder, BB FBB = f1BB , f2BB , . . . , fM , followed by an NBS × M RF analog RF precoder, FRF = f1RF , f2RF , . . . , fM . The transmitted signal is therefore given by x = FRF FBB s,
Cluster M UEM,1
BS
UEM,2
Figure 1. NOMA based hybrid beamforming system
(1)
where s = [s1 , s2 , · · · , sm , · · · sM ] is the M × 1 vector P IM and P is of transmit symbols, such that E[ssH ] = M the average total transmitted power. FRF is implemented 2 with analog phase shifters, i.e., |FRF [r, c]| = 1/NBS , and the transmitter’s total power constraint is enforced 2 by normalizing FBB such that kFRF FBB kF = M . In the mth cluster, rm,1 and rm,2 are the received signals of the strong user and the weak user, respectively, and which be modeled as rm,i = Hm,i
M X
BB FRF fm sm + nm,i for i = 1, 2, (2)
m=1
Figure 2. Multiuser hybrid beamforming architecture
the cth column and the element in the rth row and the cth column of A, respectively. II. S YSTEM MODEL AND P ROBLEM FORMULATION A. System model Consider the mmWave system shown in Fig.1. A BS with MBS TXRUs and NBS antennas is assumed to communicate with K users. The K users in a cell are divided into M clusters and each user is equipped with NUE antennas as depicted in Fig.2. The number of users in a cluster can be more than two, but we will assume here that each cluster has two users for the sake of simplicity, i.e., K = 2M . Further, we focus on the multiuser beamforming case in which the BS communicates with each cluster via only one analog beam. In this case, 2M users can be supported by M clusters and M beams in K users. Therefore,the maximum number of clusters that can be simultaneously served by the BS equals the number of BS TXRUs, i.e., M ≤ MBS . For simplicity, we will also assume that the BS will use M out of the MBS available TXRUs to serve the M clusters. Among two users in a cluster, the user near (or far) the BS having a larger (or smaller) channel gain is defined as a strong (or weak) user. The transmitting signal of mth cluster consists of the signals of the strong and weak √ √ users, i.e., sm = αm,1 sm,1 + αm,2 sm,2 , where sm,1 and sm,2 are the signals for the strong and weak users, respectively, αm,1 and αm,2 are the power allocation
where Hm,1 and Hm,2 denote the matrix of complex channel gains from the antennas of the BS to the strong and weak user antennas in the mth cluster, respectively, and nm,i ∼ N (0, σ 2 I) is the Gaussian noise corrupting the received signal. At the ith UE in the mth cluster, the analog RF combiner wm,i is used to process the received signal rm,i : H ym,i = wm,i Hm,i
M X
BB H FRF fm sm + wm,i nm,i
m=1
(3)
for i = 1, 2 and m = 1, 2, . . . , M, where wm,i using analog phase shifters, i.e., 2 |wm,i [r, c]| = 1/NUE , is NUE × 1 combining vector. In this paper, we consider a narrowband blockfading channel model. To incorporate features of mmWave characteristics, the channel coefficients are generated according to 3GPP TR 38.900 [13] and 3GPP TR 36.897 [14]. The 3D MIMO channel model support 2D antenna array to perform elevation beamforming via vertical dimension. Antenna panels with 2D uniform planar array(UPA) model is assumed in our research. B. Problem formulation As seen in (3), each user in a cluster will experience intra-cluster interference from other users in the same cluster and inter-cluster interference from other users in different clusters. For the ith user of the mth cluster, intra-cluster interference can be expressed as H BB √ αm,i sm,i . (4) Iintra m,i = wm,i Hm,i FRF fm With advantage of NOMA, it is easy to manage intracluster interference. On the one hand, the message to the
weak user is allocated more transmission power, which ensures that this user can detect its message directly by treating the strong user’s information as noise. On the other hand, the strong user needs to first detect its partner(weak user)’s information and then to subtract this information from its observation before decoding its own message, using SIC. Therefore, an appropriate power allocation scheme in a cluster is needed. For the users of the mth cluster, inter-cluster interference can be expressed as X H Iinter FRF f`BB s` . (5) m,i = wm,i Hm,i `6=m
Without considering intra-cluster interference and TXRUs constraints, the the optimal digital linear precoder to maximize signal-to-interference-plus-noise ratio (SINR) is known only as iterative solutions [15]. A practical approach requiring little training and feedback overhead is presented in [5]. The main idea of this approach is to employ jointly Tx-Rx analog beamforming to maximize the desired signal power of each user, neglecting the resulting interference among users in the first stage, and apply zero-forcing beamforming(ZFBF) based on the baseband effective channels for eliminating interference. In ZFBF with M TXRUs, the digital precoding vector, f`BB , need to satisfy the following condition: ¯ m f`BB = 0 for ` 6= m, h (6) H ¯ m = wm where h Hm FRF denotes user’s baseband effective channel and 1 ≤ `, m ≤ M . However, in our NOMA based hybrid beamforming system, each user with different received beams in a cluster share the same transmitted beam from BS, with the result that it can not be used for the conventional two stage hybrid beamforming design in [5]. In another words, the transmitter needs to determine which baseband effective channels of the two users in the cluster to be used to apply ZFBF. When ZFBF is based on the strong users’ baseband effective channels, strong users will not receive any interference. Otherwise, it is unhelpful when the strong users with heavy intercluster interference perform SIC to decode intra-cluster interference. Thus, in order to perform SIC correctly, we generate the ZFBF matrix based on the beseband effective channels of the strong users as follow: ¯† = H ¯ H (H ¯H ¯ H )−1 , FBB = H (7) ¯ T1,1 , h ¯ T2,1 , · · · , h ¯ T ]T . Further, with the ¯ = [h where H M,1 optimal user pairing scheme, the inter-cluster interference affecting the weak user could be partly reduced or completely eliminated. Based on the above analysis, the SINR of strong user and weak user in the mth cluster can be written as follow: BB 2 αm,1 P ¯ hm,1 fm (8) , SINRm,1 = M σ2
SINRm,2 BB 2 hm,2 fm αm,2 P ¯ , = 2 P ¯ BB 2 + P hm,2 flBB + M σ 2 hm,2 fm αm,1 P ¯ l6=m
(9) ¯ m,i = wH Hm,i FRF for i = 1, 2 and m = where h m,i 1, 2, . . . , M . The sum capacity of the NOMA based hybrid beamforming (NOMA-HBF)system is then NHB Rsum =
M X
(log (1 + SINRm,1 ) + log (1 + SINRm,2 )).
m=1
(10)
III. P ROPOSED NOMA BASED H YBRID B EAMFORMING DESIGN In this section, our main objective is to efficiently design hybrid beamforming to maximize the sum capacity of the system. Before the hybrid beamforming design, a user pairing scheme is proposed to suppress intracluster and inter-cluster interference and guarantee that BS’s digital beamformers are well aligned with the users’ baseband effective channels. After that, we propose a power allocation scheme to further reduce intra-cluster interference and ensure proper working of NOMA. A. User Pairing As the analysis in the subsection II-B, intra-cluster and inter-cluster interferences affecting the weak user in NOMA-HBF depend on which users are selected in a cluster. Therefore, the interference can be reduced by properly selecting two users being served in a cluster from among K total users. The best way to reduce interference is to select optimal user pairing via exhaustive search to maximize the sum capacity. However, this approach is infeasible before beam sweeping between BS and UEs and channel sounding in practice. Given the practical difficulties associated with applying the exhaustive search scheme, we propose a low complexity user pairing algorithm to to reduce the interferences. The following Proposition and Remark show some insights about how to efficiently design user pairing to reduce the interferences. Proposition 1: To reduce intra-cluster interferences experienced by the weak user, it is necessary that gaindifference between the baseband effective channels of strong user and weak user after jointly beam Tx-Rx sweeping should be large, i.e., ¯ hm,1 > ¯ hm,2 for m = 1, 2, · · · M . Proof: Assuming that the baseband effective chan ¯ nel gain between the two users is large, i.e., hm,1 > ¯ hm,2 , than P rm,1 > P rm,2 , where P rm,1 and P rm,2 are the power of the two users’ received signals without power allocation, respectively. NOMA system with SIC
processing scheme will allocate less power to the strong user and more power to the weak user. Intra-cluster interferences experienced by the weak user is reduced because the power of strong user’s signal decreases. Further, it is helpful for the strong user to perform SIC by decoding the increasing interfering signal from the weak user. Proposition 2: To reduce inter-user interferences experienced by the weak user, it is necessary that the baseband effective channels of the strong user and the weak ¯ m,1 ≈ ch ¯ m,2 user should be are highly correlated, i.e., h for m = 1, 2, · · · M . Proof: Assuming the baseband effective channels ¯ m,1 of the strong and weak user in the mth cluster, h ¯ m,2 are highly correlated, i.e., h ¯ m,1 ≈ ch ¯ m,2 , and h ¯ m,1 f BB = 0 for ` 6= m, where c is constant. While h ` ¯ m,2 f BB ≈ 0 for ` 6= m. Hence,inter-cluster interference h ` experienced by the weak user could be well suppressed by sharing the ZFBF vector for the strong users. It means that the higher the correlation between the two user’s baseband effective channels in each cluster, the more the inter-cluster interference can be reduced. Remark 1: Proposition 1 is stated for baseband effective channels after jointly beam sweeping between BS and UEs. In an actual commutation system, we only need to compare the gains of the original channels among different users,since beamforming gain via beam sweeping is almost no difference in the same channel environment and system configuration. Pathloss is the main factor effecting the gain-difference between the baseband effective channels of users. Remark 2: The solution given in Proposition 2 is an ideal case after jointly beam sweeping between BS and UEs. However, it is hard to acquire the baseband effective channels before user pairing because all of users in a cluster share the same transmit beam. Owing to the double-directional characteristic of mmWave MIMO channel, the directions of the baseband effective channels are mainly effected by AoA(ZoA) and AoD(ZoD). If each user applying an beam wk? target to |wkH Hk | maximization, wk? H Hk could describe the directionality of the baseband equivalent channel, because BS apply the same beam and different AoD(ZoD) to different users. Therefore, we only need to compare correlation between wk? H Hk of different users. According to Proposition1, 2 and Remark 1, 2, the proposed user pairing algorithm must select two users that have a large channel gain-difference and a high correlation in each cluster. Firstly, the k total users are divided into two groups with M = K/2 users via channel gain comparison, i.e., G1 and G2 , where G1 and G2 denote the group of strong users and weak users respectively. Secondly, considering a limited feedback system, beam sweeping with finite resolution codebooks is uti-
? lized in UE side to optimize best analog combiner wm,i for m = 1, 2, · · · , M and i = 1, 2. According to the criterion of 1-norm maximization of wm,i H Hm,i , the ? design of combiner wm,i for each user can be obtained by solving
H
maximize wm,i Hm,i 1
2
subject to |wm,i [r, c]| = 1/NUE
(11)
m = 1, 2, . . . , M, i = 1, 2. The beam codebooks that can be used include beamsteering codebook [4], IEEE 802.15.3c codebook [16], DFT codebookn[17] and so on. Assuming o wm,i ∈ Cm,i , m,i m,i m,i where Cm,i = c1 , c2 , · · · cNbeam is the codebook set of the mth UE in the ith group, we just need to sort H Hm,i k1 ’s in the descending order and then all k cm,i n ? select the first beam as wm,i . Finally, select users from the group G1 and G2 for pairing via correlation comparison. Defined user’s temporary ˆ tmp , channel after beam sweeping as h m,i ? ˆ tmp = (wm,i h )H Hm,i . m,i
(12)
Thus, the correlation between mth user in group G1 and lth user in group G2 can be written as tmp tmp H h ˆ ˆ h m,1 l,2 . (13) Cor {(m, 1) , (l, 2)} = ˆ tmp h ˆ tmp h m,1 l,2 The overall algorithm for user pairing is summarized in in Algorithm 1. Algorithm 1 can be divided into three steps in general. Note that the complexities of user grouping in step 1, beam sweeping in step 2 and user pairing in step 3 are O (2M ), O (2M |Cm,i |), O 21 M 2 , respectively, where |Cm,i | denotes the number of beams of Cm,i . Thus, the total complexity is only O M 2 . Therefore, the proposed user pairing algorithm will only effectuate a low level of complexity compared with exhaustive searching, whose complexity is O (M !). Further, beam sweeping with finite resolution codebooks also incurs a low training and feedback overhead design. B. Hybrid beamforming design After user pairing processing in Algorithm 1, K = 2M users are divided into M clusters, where each cluster includes a strong user and a weak user. Further, all of the ˆ tmp analog RF combiner wm,i and temporary channel h m,i are solved by beam sweeping in UE side. We define an overall temporary channel for strong users given by ˆ tmp , h ˆ tmp , · · · , h ˆ tmp ], ˆ tmp = [h H 1 1,1 2,1 M,1
(14)
then the overall baseband effective channel for strong ¯1 = H ˆ tmp FRF . users is H 1 Regardless of the phase constraint, it is obvious from the fact that, by using Schwartz’s inequality, the optimum RF precoder FRF is simply given by the matched filtering
Algorithm 1 Proposed User Pairing Algorithm Input: Cm,i , UE beam codebooks Step 1: User grouping via channel gain comparison Sort K user in descending order by kHk kF Set the first M (M = K/2) users as a group, G1 Set the last M users as a group, G2 Step 2: Beam sweeping in UE side For each group Gi , i = 1, 2 For each user m, m = 1, 2, . . . , M ? that solve UE (m, i) select wm,i
? H wm,i = arg max wm,i Hm,i 1 ∀wm,i ∈Cm,i
ˆ tmp , UE (m, i) estimates temporary channel h m,i tmp ? H ˆ h m,i = (wm,i ) Hm,i End for each user End for each group Step 3: User pairing via correlation comparison For each user m in group G1 ,m = 1, 2, . . . , M UE (m, 1) selects UE(`, 2) as a partner that solve ˆ tmp ˆ tmp H hm,1 (h`,2 ) (`, 2) = arg max(`,2)∈G2 hˆtmp hˆtmp | m,1 || `,2 | Delete UE (`, 2) from group G2 End for each user
Algorithm 2 Proposed Hybrid Beamforming Algorithm ˆ tmp , temporary channel for strong users Input: h m,1 Step 1: EGT precoding in RF domain For each strong user (m, 1), m = 1, 2, · · · , M ˆ tmp UE (m, 1) feeds back its temporary channel h m,1 to the BS End for each strong user ˆ tmp H BS set FRF [r, c] = √N1 ej·](H1 ) [r,c] BS ˆ tmp , h ˆ tmp , · · · , h ˆ tmp ] ˆ tmp = [h where H 1 1,1 2,1 M,1 Step 2: ZF beamforming in baseband domain ¯1 BS compute baseband effective channel H tmp ¯ ˆ where H1 = H1 FRF −1 ¯H ¯ 1H ¯H BS designs FBB = H 1 (HBB 1 ) fm BB BS normalize fm = kFRF f BB k m
F
beamforming (OMA-HBF) system. The formulation is as follows NHB NHB maximize Rm,1 + Rm,2 αm,1
NHB OHB subject to Rm,2 ≥ 0.5Rm,2 ,
(17)
0 ≤ αm,1 ≤ 1 ˆ tmp , H 1
matrix to the temporary channel which is also called maximum ratio transmission (MRT) precoding. Under the constraint of phase-only RF precoding, the equal gain transmission (EGT) precoding is proved to be the best approach [6], by setting FRF [r, c] = √
1 ˆ tmp H ej·](H1 ) [r,c] . NBS
(15)
After beam sweeping in UE side and EGT preocoding in BS side, a low dimensional baseband effective channel ¯ 1 for strong users is constructed with given analog H precoding matrix FRF and combing vector wm,1 , m = 1, 2, · · · , M . Based on this effective channel, the BS zero-forcing digital precoder is defined similarly as (7) †
¯H ¯ ¯ H −1 , FBB = H¯1 = H 1 (H1 H1 )
(16)
In summary, the proposed hybrid beamforming algorithm is given in Algorithm 2. C. Power allocation Since a TXRU simultaneously supports two users selected by the user pairing and hybrid beamforming algorithm in a cluster, the total transmit power of a TXRU should be divided among two users. In this case, the intra-cluster inference can be changed by the power allocation scheme such that sum capacity of system may be reduced. For the sake of fairness, we propose a power allocation scheme which maximizes the sum capacity while keeping the weak user’s rate is equal to or greater than that of a conventional OMA based hybrid
NHB NHB where Rm,1 and Rm,2 are the capacity of the strong and the weak users in the mth cluster, respectively. OHB Rm,2 is the capacity of the weak user if the weak user would be supported by OMA hybrid beamforming. The definition are as follow: NHB Rm,1 = log (1 + SINRm,1 ) NHB Rm,2 = log (1 + SINRm,2 ) ! BB 2 P um,2 Hm,2 GRF gm,2 OHB Rm,2 = log 1 + M σ2
(18)
where SINRm,1 and SINRm,2 are defined in (8) (9), um,2 , GRF and gm,2 are analog combing vector, analog beamforming matrix and digital beamforming vector of the weak user if the weak user would be supported by OMA hybrid beamforming, respectively. Solving the optimization problem (17) by KKT conNHB dition, αm,1 has the optimal solution while Rm,2 = OHB 0.5Rm,2 . It can be obtained √ M σ2 ? q αm,1 = BB 2 + M σ 2 P P uH m,2 Hm,2 GRF gm,2 q √ BB 2 − M σ 2 + P uH M σ2 m,2 Hm,2 GRF gm,2 − 2 H H BB P wm,2 m,2 FRF fm P H 2 wm,2 Hm,2 FRF f BB + M σ 2 l •
l6=m
BB 2 + M σ 2 P uH m,2 Hm,2 GRF gm,2 (19)
? Because αm,1 ≥ 0 in (17), it should be satisfy the condition H BB 2 ε = wm,2 Hm,2 FRF fm + M σ2 X 2 H wm,2 Hm,2 FRF flBB +
1
0.8
l6=m
X 2 H wm,2 Hm,2 FRF flBB + M σ 2 )
(20)
0.6 CDF
−(
l6=m
r
P H BB 2 + 1 ≥ 0. u Hm,2 GRF gm,2 M σ 2 m,2 When ε < 0, the total transmit power of a cluster is allocated to the weak user. Thus, the strong user can not be serviced. Therefore, (20) must be satisfied before the proposed power allocation scheme can be applied. If two users selected by the user pairing and hybrid beamforming algorithms satisfy (20), the power will be allocated to the two users according to the proposed scheme, so that these two users will be supported by a single TXRU.
0.4
•
0.2
NOMA-HBF OMA-HBF
0 0
20
40
60 80 100 Sum Capacity [bps/Hz]
120
140
Figure 3. CDF of the sum capacity for the NOMA-HBF and OMAHBF systems
IV. S IMULATION R ESULTS 1
0.8
0.6 Strong users
CDF
In this section, we evaluate the performance for the proposed NOMA-HBF system. We consider a singlecell system in which the BS, with NBS = 256(16 × 16) antennas and P = 44 dBm, is located at the center of the 0.5 × 0.5 km2 square area. UEs are randomly deployed within the BS’s coverage with a minimum BS-UE distance of 10m. Each user is equipped with NUE = 16(4 × 4) antennas and 2-D DFT codebook. Hence, the corresponding CSI feedback is 4 bits. The system bandwidth is 10 MHz and the noise density at the receiver is -169dBm/Hz. The channel model is based on 3GPP TR 38.900 [13] and 3GPP TR 36.897 [14], where an Umi NLOS scenario with center frequency 28GHz is considered. Fig.3 shows the cumulative distribution function (CDF) of the sum capacity for the NOMA-HBF and the conventional OMA-HBF systems when BS server 8 users with 4 TXRUs. The NOMA-HBF system improves the sum capacity compared to the conventional multiuser BF system. Fig.4 shows the CDF of the sum capacity of the weak users and strong users for the NOMA-HBF and OMA-HBF systems. The weak user capacity is almost the same for both NOMA-HBF and OMA-HBF systems. That means the capacity of the weak user is guaranteed by the proposed power allocation scheme, while the capacity of the strong user is significantly enhanced in NOMA-HBF. Fig.5 shows the sum capacity achieved by NOMAHBF and OMA-HBF systems with different number of users. As the number of users increases, the sum capacities of both the NOMA-BF and OMA-HBF increase owing to the multiuser diversity gain. Nevertheless, the capacities of NOMA-HBF are always approximately twice of OMA-HBF’s capacities. Fig.6 shows sum capacity of
Weak users
0.4
NOMA-HBF(Weak users) OMA-HBF(Weak users) NOMA-HBF(Strong users) OMA-HBF(Strong users)
0.2
0 0
20
40 60 80 Sum Capacity [bps/Hz]
100
120
Figure 4. CDF of the sum capacity of the weak users and strong users for the NOMA-HBF and OMA-HBF systems
weak users and strong users achieved by NOMA-HBF and OMA-HBF systems with different number of users. Similarly, the weak user’s capacity is also the same for both NOMA-HBF and OMA-HBF systems. V. C ONCLUSION In this paper, we proposed a NOMA-HBF system designed to improve sum capacity. The proposed NOMAHBF system increases the number of supportable users with limited TXRUs. In addition, by applying the proposed pairing and hybrid beamforming algorithms, effective power allocation, we were able to reduce the intracluster and inter-cluster interferences.
300
Sum Capacity [bps/Hz]
250
200
150
100 NOMA-HBF
50
OMA-HBF 0 8
12
16
20 24 User Number [#]
28
32
Figure 5. Sum capacity achieved by NOMA-HBF and OMA-HBF systems with different number of users 300 NOMA-HBF(Strong users) NOMA-HBF(Weak users) OMA-HBF(Strong users) OMA-HBF(Weak users)
Sum Capacity [bps/Hz]
250
200
Strong users
150
100
50 Weak users 0 8
12
16
20 24 User Number [#]
28
32
Figure 6. Sum capacity of weak users and strong users achieved by NOMA-HBF and OMA-HBF systems with different number of users
ACKNOWLEDGMENT This work was funded by the China National 863 Project under Grant 2014AA01A705 and the NSFC under Grant 61271257. R EFERENCES [1] A. L. Swindlehurst, E. Ayanoglu, P. Heydari, and F. Capolino, “Millimeter-wave massive MIMO: the next wireless revolution?” IEEE Communications Magazine, vol. 52, no. 9, pp. 56–62, 2014. [2] W. Roh, J.-Y. Seol, J. Park, B. Lee, J. Lee, Y. Kim, J. Cho, K. Cheun, and F. Aryanfar, “Millimeter-wave beamforming as an enabling technology for 5G cellular communications: theoretical feasibility and prototype results,” IEEE Communications Magazine, vol. 52, no. 2, pp. 106–113, 2014. [3] O. El Ayach, S. Rajagopal, S. Abu-Surra, Z. Pi, and R. W. Heath, “Spatially sparse precoding in millimeter wave mimo systems,” IEEE Transactions on Wireless Communications, vol. 13, no. 3, pp. 1499–1513, 2014.
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