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PAPER
Non-Orthogonal Multiple Access Using Intra-Beam Superposition Coding and SIC in Base Station Cooperative MIMO Cellular Downlink∗ Nobuhide NONAKA† , Student Member, Yoshihisa KISHIYAMA†† , and Kenichi HIGUCHI†a) , Members
SUMMARY This paper extends our previously proposed nonorthogonal multiple access (NOMA) scheme to the base station (BS) cooperative multiple-input multiple-output (MIMO) cellular downlink for future radio access. The proposed NOMA scheme employs intra-beam superposition coding of a multiuser signal at the transmitter and the spatial filtering of inter-beam interference followed by the intra-beam successive interference canceller (SIC) at the user terminal receiver. The intra-beam SIC cancels out the inter-user interference within a beam. This configuration achieves reduced overhead for the downlink reference signaling for channel estimation at the user terminal in the case of non-orthogonal user multiplexing and enables the use of the SIC receiver in the MIMO downlink. The transmitter beamforming (precoding) matrix is controlled based on open loop-type random beamforming using a block-diagonalized beamforming matrix, which is very efficient in terms of the amount of feedback information from the user terminal. Simulation results show that the proposed NOMA scheme with block-diagonalized random beamforming in BS cooperative multiuser MIMO and the intra-beam SIC achieves better system-level throughput than orthogonal multiple access (OMA), which is assumed in LTE-Advanced. We also show that BS cooperative operation along with the proposed NOMA further enhances the cell-edge user throughput gain which implies better user fairness and universal connectivity. key words: non-orthogonal multiple access, superposition coding, successive interference cancellation, downlink, MIMO, base station cooperation
1. Introduction In order to continue to ensure the sustainability of mobile communication services over the next decade, new technology solutions that can respond to future challenges need to be identified and developed [1]. For future radio access in the 2020 era, significant gains in system capacity/efficiency and quality of user experience (QoE) are required in view of the anticipated exponential increase in the volume of mobile data traffic, e.g., beyond 1000-fold in 2020 and beyond compared to 2010. In the 3rd generation mobile communication systems such as W-CDMA and cdma2000, non-orthogonal multiple Manuscript received October 29, 2014. Manuscript revised March 13, 2015. † The authors are with the Department of Electrical Engineering, Graduate School of Science and Technology, Tokyo University of Science, Noda-shi, 278-8510 Japan. †† The author is with NTT DOCOMO, INC., Yokosuka-shi, 2398536 Japan. ∗ The material in this paper was presented in part at the IEEE 80th Vehicular Technology Conference, Vancouver, Canada, September 2014. a) E-mail:
[email protected] DOI: 10.1587/transcom.E98.B.1651
access based on direct sequence-code division multiple access (DS-CDMA) is used in the downlink. Meanwhile, orthogonal multiple access (OMA) based on orthogonal frequency division multiple access (OFDMA) is adopted in the 3.9 and 4th generation mobile communication systems such as LTE [2] and LTE-Advanced [3], [4]. OMA was a reasonable choice for achieving good system-level throughput performance in packet-domain services using channelaware time- and frequency-domain scheduling with simple single-user detection at the receiver. However, for further enhancements of the system efficiency and QoE especially at the cell edge, non-orthogonal multiple access (NOMA) can again be a promising candidate as a wireless access scheme for future radio access. To make NOMA promising, it should be used with advanced transmission/reception techniques such as dirty paper coding (DPC) or a successive interference canceller (SIC) along with superposition coding [5]–[22], which is different from the 3rd generation mobile communication systems. This paper focuses on the use of the SIC. NOMA exploits the new approach of user multiplexing in the power-domain that was not sufficiently utilized in previous generations. An attractive feature of NOMA with the SIC is its ability to optimize the tradeoff between the sum user throughput and user fairness with regard to the achievable user throughput of the respective users. This is because all users can use the overall transmission bandwidth irrespective of the channel conditions in NOMA, while OMA must restrict the bandwidth assignment to the users under poor channel conditions in order to achieve a sufficiently high sum user throughput [5], [14]. This paper focuses on the multiple-input multipleoutput (MIMO) downlink [12], [13], [23], [24]. In the MIMO downlink, the broadcast channel is not degraded [12]. Therefore, superposition coding with the SIC [5], [6] is not optimal and DPC [7] should be used to utilize fully the entire multiuser capacity region [12]. However, DPC is very difficult to implement in practice and is very sensitive to delay in channel state information (CSI) feedback. Furthermore, in order to achieve the multiuser capacity region using DPC, user-dependent beamforming (precoding) must be employed. This results in increased overhead of the (orthogonal) reference signals dedicated to the respective users as the number of multiplexed users is increased beyond the number of transmitter antennas, which, in practice, decreases the throughput gain possible with DPC.
c 2015 The Institute of Electronics, Information and Communication Engineers Copyright
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Due to the above reasons, we recently proposed a NOMA scheme with intra-beam superposition coding of multiple user signals and an intra-beam SIC to remove the inter-user interference within a beam due to the superposition coding [18]. In this scheme, the number of reference signals is equal to the number of transmitter antennas, which is the same as in LTE-Advanced assuming OMA, irrespective of the number of non-orthogonally multiplexed users. The scheme effectively utilizes the SIC, which is easier to implement and more robust against channel variation compared to DPC, in the MIMO downlink. This paper extends our previously proposed NOMA scheme to the base station (BS) cooperative MIMO cellular downlink for future radio access. Since the MIMO capacity is increased as the numbers of transmitter and receiver antennas are increased [23], [24], and while the allowable numbers of these antennas per BS and user terminal are limited, employing a combination of BS cooperation and multiuser MIMO is an effective way to enhance the cellular system performance [25]–[27]. For the beamforming matrix control strategy appropriate for the proposed NOMA in a BS cooperative MIMO scenario, we employ block-diagonalized random beamforming [30] in the paper, which is based on random or opportunistic beamforming described in [28] and [29]. Random beamforming is effective in reducing the CSI feedback. The block diagonalization avoids transmission power efficiency loss in a BS cooperative MIMO scenario with random beamforming. We show that the proposed NOMA scheme with BS cooperation achieves better system-level throughput compared to OMA. We also show that the effectiveness of the proposed NOMA scheme is more significant when BS cooperation is assumed since the BS cooperation improves the channel conditions of the cell-edge users, which are appropriate for obtaining a higher non-orthogonal user multiplexing gain. The remainder of the paper is organized as follows. Section 2 describes the proposed NOMA scheme for BS cooperative MIMO downlink. Section 3 presents simulation results on the system-level throughput and a comparison to OMA. Finally, Sect. 4 concludes the paper. 2. Proposed NOMA Scheme 2.1 NOMA Using Intra-Beam Superposition Coding and SIC in BS Cooperative MIMO Downlink Let us assume L cooperating BSs. A set of cooperating BSs is called a cluster. Each BS has M transmitter antennas. We assume OFDM signaling with a cyclic prefix, although we consider non-orthogonal user multiplexing. Therefore, the inter-symbol interference and inter-carrier interference are perfectly eliminated assuming that the length of the cyclic prefix is sufficiently long so that it covers the entire multipath delay spread. There are F frequency blocks and the bandwidth of a frequency block is W Hz. The number of receiver antennas at the user terminal is N. The number of users per cell is K. Thus, the number of users per cluster
Fig. 1
Operational principle of proposed scheme.
is LK. For simplicity, in the following, we describe the proposed scheme at some particular time-frequency block (resource block) f ( f = 1, . . . , F). For multiple time-frequency blocks, the same process is performed independently in principle. In this section, the time index, t, is omitted for simplicity. Figure 1 illustrates the operational principle of the proposed scheme using intra-beam superposition coding at the BS transmitter and an intra-beam SIC [18] at the user terminal receiver (for simplicity, a single BS is illustrated without loss of generality). The set of BSs performs MIMO transmission with B beams, where B = LM. The LM-dimensional b-th (b = 1, . . . , B) transmitter beamforming (precoding) vector at frequency block f is denoted as m f,b . We assume that the multiuser scheduler schedules a set of users, U f,b = {i( f, b, 1), i( f, b, 2), . . . , i( f, b, k( f, b))}, to beam b of frequency block f . Term i( f, b, u) indicates the u-th (u = 1, . . . , k( f, b)) user index scheduled at beam b of frequency block f , and k( f, b) denotes the number of simultaneously scheduled users at beam b of frequency block f . At the BS transmitter, each i( f, b, u)-th user information bit sequence is independently channel coded and modulated. Term si( f,b,u), f,b denotes the coded modulation symbol of user i( f, b, u) at beam b of frequency block f . We assume E[|si( f,b,u), f,b |2 ] = 1. The allocated transmission power for user i( f, b, u) at beam b of frequency block f is denoted as pi( f,b,u), f,b . In the proposed scheme, si( f,b,u), f,b of all k( f, b) users is first superposition coded [5], [6] as intra-beam superposition coding and then multiplied by the transmitter beamforming vector, m f,b . Finally, by accumulating all B beam transmission signal vectors, the LM-dimensional transmission signal vector, x f , at frequency block f is generated as xf =
B b=1
m f,b
k( f,b)
√
pi( f,b,u), f,b si( f,b,u), f,b .
(1)
u=1
The transmission power allocation constraint is represented as k( f,b) u=1
pi( f,b,u), f,b = pb ,
B b=1
pb = ptotal ,
(2)
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where pb is the transmission power of beam b and ptotal is the total transmission power per frequency block. We assume that pb and ptotal are identical for all beams at all frequency blocks in the paper. The set of pi( f,b,u), f,b of all users in U f,b is denoted as P f,b . The N-dimensional received signal vector of user i( f, b, u) at frequency block f , yi( f,b,u), f , is represented as yi( f,b,u), f = Hi( f,b,u), f x f + wi( f,b,u), f = Hi( f,b,u), f
B
k( f,b )
√
m f,b
pi( f,b ,u ), f,b si( f,b ,u ), f,b +wi( f,b,u), f ,
u =1
b =1
(3) where Hi( f,b,u), f is the N× LM-dimensional channel matrix between the set of BSs within a cluster and user i( f, b, u) at frequency block f and wi( f,b,u), f denotes the receiver noise plus inter-cluster interference vector at frequency block f . In the proposed scheme, the user terminal first performs spatial filtering to suppress the inter-beam interference. Assuming that user i( f, b, u) uses the N-dimensional spatial filtering vector, vi( f,b,u), f,b , to receive beam b of frequency block f , the scalar signal after the spatial filtering, zi( f,b,u), f,b , is represented as zi( f,b,u), f,b = vi(Hf,b,u), f,b yi( f,b,u), f = vi(Hf,b,u), f,b Hi( f,b,u), f m f,b
k( f,b)
√
pi( f,b,u ), f,b si( f,b,u ), f,b
u =1
+vi(Hf,b,u), f,b Hi( f,b,u), f
B b =1 b b
k( f,b )
m f,b
√
pi( f,b ,u ), f,b si( f,b ,u ), f,b
u =1
+vi(Hf,b,u), f,b wi( f,b,u), f .
(6) Thus, among users to which beam b of frequency block f is allocated, the channel after the spatial filtering is a degraded single-input single-output (SISO) channel, and the equivalent normalized channel gain of user i( f, b, u) becomes gi( f,b,u), f,b . We apply the intra-beam SIC to signal zi( f,b,u), f,b in order to remove the inter-user interference within a beam. A single stage SIC using codeword-based signal decoding [5], [6] is implemented. Based on information theory, the optimality of the single stage SIC using codewordbased signal decoding along with superposition coding is proven from the viewpoint of the achievable capacity region in the SISO downlink (i.e., broadcast channel). Similar to the SISO downlink [5], [8]–[10], the optimal order of decoding in the intra-beam SIC is in the order of the increasing normalized channel gain, gi( f,b,u), f,b . Based on this order, any user can correctly decode the signals of other users whose decoding order comes before that user for the purpose of interference cancellation. Thus, user i( f, b, u) can remove the inter-user interference from user i( f, b, u ) whose gi( f,b,u ), f,b is lower than gi( f,b,u), f,b . As a result, the instantaneous throughput of user k (k = 1, . . . , LK) at beam b of frequency block f assuming that the scheduler schedules user set U f,b with allocated transmission power set P f,b is represented as R f,b (k|U f,b , P f,b ) = ⎛ ⎞ ⎧ ⎟⎟⎟ ⎪ ⎜⎜⎜⎜ ⎪ ⎪ ⎟⎟⎟ p g ⎪ k, f,b k, f,b ⎪ ⎪W log2 ⎜⎜⎜⎜1+ ⎟⎟ , k ∈ U f,b ⎨ ⎜ ⎜⎝ , gk, f,b p j, f,b +1 ⎟⎟⎠ ⎪ ⎪ ⎪ ⎪ j∈U f,b ,g j, f,b >gk, f,b ⎪ ⎪ ⎩0, k U
(4)
In the paper, we assume that vi( f,b,u), f,b is calculated based on the minimum mean squared error (MMSE) criteria due to its optimality in the sense that the MMSE filtering maximizes the signal-to-interference-plus-noise ratio (SINR) of the filter output. The second and third terms of (4) are the interbeam interference and receiver noise plus inter-cluster interference observed at the spatial filtering output, respectively. By normalizing the aggregated power of the inter-beam interference and receiver noise plus inter-cluster interference to be one, (4) can be rewritten as zi( f,b,u), f,b = k( f,b) √ √ gi( f,b,u), f,b pi( f,b,u ), f,b si( f,b,u ), f,b +qi( f,b,u), f,b ,
|vi(Hf,b,u), f,b Hi( f,b,u), f m f,b |2 ⎫. gi( f,b,u), f,b = ⎧ B ⎪ ⎪ ⎪ ⎪ H 2 ⎪ ⎪ ⎪ ⎪ p |v H m | ⎨ ⎬ b i( f,b,u), f,b i( f,b,u), f f,b =1,b b ⎪ ⎪ b ⎪ ⎪ ⎪ H H ⎪ ⎪ ⎩+vi( f,b,u), f,b E[wi( f,b,u), f wi( f,b,u), f ]vi( f,b,u), f,b ⎪ ⎭
(5)
u =1
where qi( f,b,u), f,b denotes the sum of the inter-beam interference, receiver noise, and inter-cluster interference terms after normalization (thus, E[|qi( f,b,u), f,b |2 ] = 1). Term gi( f,b,u), f,b is represented as
(7)
f,b
2.2
Block-Diagonalized Random Beamforming
In general, any kind of LM × LM-dimensional beamforming matrix determination criteria can be applied to the proposed NOMA scheme using the intra-beam superposition coding and SIC described in the previous subsection. In the paper, we employ open loop-based random beamforming [28], [29]. Random beamforming is effective in reducing the CSI feedback. We note that in [21], the combination of the closed loop-type beamforming and the proposed NOMA scheme is investigated. Figure 2 shows the operational flow of random beamforming. First, the BS randomly determines B beamforming vectors without the aid of feedback information from the user terminals. Then, the BS transmits the downlink reference signals before the actual data transmission. The number of reference signals equals the number of beams, B,
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m f,b,l = 0, for l (b − 1)/M + 1.
(9)
With (9), the overall beamforming matrix, M f , is blockdiagonalized and is represented as ⎤ ⎡ O ⎥⎥ ⎢⎢⎢ M f,1 · · · ⎥ ⎢⎢ .. ⎥⎥⎥⎥ , .. M f = ⎢⎢⎢⎢ ... (10) . . ⎥⎥⎥ ⎢⎣ ⎦ O · · · M f,L
Fig. 2
Operational flow of random beamforming.
and the respective reference signals are beamformed using the respective predetermined beamforming vectors. By using the b-th reference signal, the estimate of Hk, f m f,b is obtained at user terminal k. Using the estimate of Hk, f m f,b for all B beams, the spatial filtering vector, vk, f,b , is calculated. With vk, f,b and the estimate of Hk, f m f,b , the equivalent channel gain, gk, f,b , is measured using (6). For user k, SINR of beam b at frequency block f becomes SINRk, f,b = gk, f,b pb (note that this SINR does not include the intra-beam interference). User k feeds back SINRk, f,b to the serving BS. The BS performs multiuser scheduling based on the reported SINRk, f,b . Actual data transmission for the set of scheduled users is performed using the predetermined beamforming vectors. Since the random beamforming only requires the SINR feedback, the feedback overhead can be reduced compared to closed loop-type beamforming such as the codebook-based or explicit channel feedback-based approaches. Although the beamforming vectors are determined independently of the user channel conditions, when the number of candidate users for scheduling is sufficiently large, we can expect that the randomly selected beamforming vector would be matched to the channel of some user with high probability. As for the random beamforming matrix generation, we apply a block-diagonalized random beamforming matrix for BS cooperative MIMO aiming at improving the power efficiency, which was recently proposed in [30]. The LM × LM-dimensional overall random beamforming matrix at frequency block f can be written as M f = m f,1 · · · m f,LM ⎤ ⎡ ⎢⎢⎢m f,1,1 · · · m f,LM,1 ⎥⎥⎥ ⎢⎢ .. ⎥⎥⎥⎥ , .. = ⎢⎢⎢⎢ ... (8) . . ⎥⎥⎥ ⎢⎣ ⎦ m f,1,L · · · m f,LM,L where M-dimensional vector m f,b,l is the beamforming vector used at BS l for beam b at frequency block f . The proposed block-diagonalized beamforming matrix assumes that (l − 1)M + 1 to lM beams are transmitted from BS l only. Thus,
where M × M-dimensional matrix M f,l = [m f,(l−1)M+1,l . . . m f,lM,l ] represents the set of beamforming vectors for beams (l − 1)M + 1 to lM, which are transmitted only from BS l. We assume that M f,l is a randomly generated unitary matrix. Therefore, M f is also a unitary matrix. By using the block-diagonalized random beamforming matrix with the appropriate user scheduling, the wasted transmission power consumed at a BS far from the scheduled user is suppressed. Since each of the beams is dedicated to a particular BS, the dynamic beam selection process includes dynamic BS selection (switching) based on the instantaneous CSI (SINRk, f,b ) feedback. 3. 3.1
Simulation Results Simulation Assumption
We evaluate the distribution of the user throughput in a multi-cell downlink. Table 1 gives the simulation parameters. These parameters basically follow the evaluation assumptions by the 3GPP [31]. We assume a cluster with L = 7 cooperating BSs. The seven-cluster model (one center cluster and six surrounding (interfering) clusters) is assumed. The inter-site (BS) distance is 0.5 km. The number of users per cell, K, is parameterized from 3 to 50. The locations of the user terminals in each cell are randomly assigned with a uniform distribution. The values for W and F are set to 180 kHz and 24, respectively (the overall transmission bandwidth is 4.32 MHz). The BS transmission power is 43 dBm. The transmission power per beam is assumed to be the same for all frequency blocks. Terms M and N are set to two. We assume an omni-directional antenna pattern without considering the vertical antenna pattern. We take into account the distance-dependent path loss with the decay factor of 3.76, lognormal shadowing with the standard deviation of 8 dB and 0.5-correlation among sites, and 6-path Rayleigh fading with the rms delay spread of 1 μs and the maximum Doppler frequency of 5.55 Hz. The receiver noise power density of the user terminal is −169 dBm/Hz. In NOMA, the scheduler can allocate a beam of a certain frequency block to more than one user simultaneously. In the paper, we use the proportional fair (PF)-based multiuser beam allocation along with the power allocation to the respective users scheduled for the same beam. PF-based resource allocation [32], [33] is known to achieve a good tradeoff between system efficiency and user fairness by maximizing the product of the user throughput among users. From [14], [16], [18], and [34], we use the following
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Simulation parameters.
set U are sorted in the order of the increasing equivalent normalized channel gain. The k-th sorted user index is denoted as π(k). The transmission power of user π(k) is set to pπ(k), f,b = αpπ(k−1), f,b ,
multiuser resource (beam and power) allocation policy. The user throughput of user k at time t when scheduling user set U f,b (t) and power set P f,b (t) are applied at time t is defined as T (k; t) = T (k; t − 1) ⎫ ⎧ ⎪ ⎪ B F ⎪ ⎪ ⎪ 1⎪ ⎬ ⎨ + ⎪ R (t), P (t); t −T (k; t−1) k|U . ⎪ f,b f,b f,b ⎪ ⎪ ⎪ ⎪ tc ⎩ ⎭ f =1 b=1
(11) Term t denotes the time index representing a subframe index. Parameter tc defines the time horizon for throughput averaging. We assume tc of 100 with the subframe length of 1 ms in the following evaluation (thus 100-ms average user throughput is measured). Term R f,b (k|U f,b (t), P f,b (t); t) is the instantaneous throughput of user k in beam b of frequency block b at time instance t assuming U f,b (t) and P f,b (t), which is calculated using (7). The resource allocation policy for beam b of frequency block f selects user set U f,b (t) and allocation power set P f,b (t) at time t according to the following criteria. γ f,b (U, P; t) =
LK R f,b (k|U, P; t) k=1
T β (k; t − 1)
.
{U ∗f,b (t), P∗f,b (t)} = arg max γ f,b (U, P; t). {U,P}
(12)
(14)
with a sum power constraint. Parameter α (0 < α ≤ 1) controls the system efficiency and user fairness. As α decreases, the system tends to allocate more power to the users experiencing worse channel conditions and vise versa. For each candidate set of users, U, we perform power allocation using (14) first and then calculate the resource allocation metric, γ f b (U, P; t), to find the optimal U. The fixed transmission power control method using (14) has another practical merit; this method does not require feedback of the power information allocated to the respective users via the downlink control signaling. Refer to [16] for more details regarding power allocation strategies along with scheduling. The delay time of the SINR feedback signal from the user terminals in random beamforming and scheduling processes is set to zero in the following evaluation to assess the basic performance of the proposed NOMA scheme. Refer to, e.g., [36] regarding the impact of the SINR feedback delay in general random beamforming and scheduling processes on the system-level throughput. The user throughput is calculated based on the Shannon formula with the maximum limit of 6 b/s/Hz (corresponding to 64QAM). We assumed the perfect channel estimation and SINR feedback, which result in the perfect SIC procedure, for simplicity. Thus, there is no residual interference and no decoding error during the SIC process. Note that the performance of the proposed NOMA in a case with channel estimation and SINR feedback errors is investigated in [22]. The maximum number of non-orthogonally multiplexed users per beam of each frequency block, Nmax , is parameterized from 1 to 4. In the resource allocation, all possible user sets U, where |U| ≤ Nmax , are examined and the user set achieving the highest resource allocation metric is selected. The Nmax of one corresponds to OMA as in LTE and LTE-Advanced. In the following, we use the following system-level throughput measures for performance evaluation. • Sum user throughput per cell
(13)
Term γ f,b (U, P; t) is the resource allocation metric for user set U and power set P, and the combination of U and P that maximizes the resource allocation metric is selected in principle. Here, β (β ≥ 0) is the weighting factor introduced in [35]. The β of one corresponds to pure PF resource allocation and a β of greater than one tends to achieve better user fairness at the cost of reduced system efficiency. However, the joint optimization of U and P in (13) is computationally complex [16]. Therefore, we employ a fixed (channel-independent) transmission power control method [16] in the following evaluation. At beam b of frequency block f , we assume that the users in candidate user
Assuming that the throughput of user k is T (k), the sum user throughput per cell is defined as 1 T (k). L k=1 LK
Sum user throughput per cell =
(15)
The sum user throughput per cell is a typical measure of capacity in evaluating LTE and LTE-Advanced [2], [3], [31]. • Cell-edge user throughput The user throughput value at the cumulative probability of 5% is defined as the cell-edge user throughput [31]. The cell-edge user throughput is a typical measure of the QoE at
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Fig. 4 Fig. 3
Sum user throughput per cell as a function of K.
Geometric mean user throughput as a function of α.
the cell edge and user fairness in evaluating LTE and LTEAdvanced [2], [3], [31]. • Geometric mean user throughput The geometric mean user throughput is defined as ⎛ LK ⎞1/LK ⎜⎜⎜ ⎟⎟ ⎜ Geometric mean user throughput = ⎜⎝ T (k)⎟⎟⎟⎠ . k=1
(16) Fig. 5
The geometric mean user throughput is a good system performance measure that simultaneously takes into account the system efficiency and user fairness. The resource allocation using PF criteria maximizes the geometric mean user throughput. 3.2 Simulation Results Figure 3 shows the geometric mean user throughput as a function of α. In the figure, Nmax is parameterized from one to four and K and β are set to 30 and 1.0, respectively. As α increases from zero, the system tends to allocate more power to the users experiencing good channel conditions, which contributes to the system efficiency mainly by increasing the throughput of the users near the BS. However, since the cell-edge user throughput tends to decrease at the same time, there is a best α value. From the viewpoint of the geometric mean user throughput, the best α value is approximately 0.1 under the simulation assumptions. This best α value indicates that a large power gap is effective in NOMA for enhancing the system performance, since the BS can select the user set comprising cell-edge and cell-interior users. By increasing Nmax from one, the geometric mean user throughput is significantly increased, while it tends to be saturated beyond Nmax = 3. This means that most of the NOMA gain is obtained with a relatively small Nmax such as 2 or 3. The geometric mean user throughput in BS cooperation is significantly higher than that for no BS cooperation. In the following evaluation, the α value is set so that the geometric mean user throughput is maximized for the respective system conditions based on pre-performed computer simulations.
Cell-edge user throughput as a function of K.
Figures 4 and 5 show the sum user throughput per cell and cell-edge user throughput as a function of the number of users per cell, K, respectively. We tested the cases with Nmax of one and two. Term β is set to 1.0. From Fig. 4, NOMA using Nmax = 2 significantly increases the sum user throughput per cell compared to OMA for the wide range of K up to 50. Figure 5 shows a clear gain in the cell-edge user throughput by increasing Nmax from 1 to 2. The throughput gains for the cell-edge user throughput by using the proposed NOMA scheme assuming Nmax = 2 relative to OMA when K= 30 are approximately 19% and 16% for the cases with and without BS cooperation, respectively. The reason why the cell-edge user throughput gain is increased with BS cooperation can be understood as follows. The proposed NOMA can allocate a wider transmission bandwidth to the respective users than can OMA, which results in better user throughput in principle. We assume that ψk and pk are the allocated bandwidth and transmission power, respectively, to user k. The throughput of user k, R(k), can be expressed as gk pk R(k) = ψk log2 1 + , (17) ψk (gk ηk + nk ) where gk is the channel gain. Terms gk ηk and nk are the power density of intra-beam interference after the SIC process and the aggregated power density of the receiver noise, inter-cell interference, and inter-beam interference, respectively, at the receiver of user k. We note that the definitions of these symbols are valid only for this explanation and it can be slightly different in other parts of the paper. Equa-
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tion (17) suggests that R(k) increases as ψk increases. However, when gk is very low, which may occur at the cell edge, R(k) can be approximated as gk pk gk pk log2 e = log2 e. R(k) ≈ ψk · (18) ψk (gk ηk +nk ) (gk ηk +nk ) Thus, an increase in ψk does not contribute to an increase in R(k). The BS cooperation in the proposed NOMA scheme increases the effective gk of cell-edge users via dynamic BS selection. We assume that g˜ k is the channel gain of user k normalized by its average, which is exponentially distributed with unit mean due to Rayleigh fading. In the ideal case where the averages of the normalized channel gain of user k among L BSs are identical, with dynamic BS selection L among L BSs, the g˜ k at the selected BS becomes l=1 1/l times on average. This is a selection diversity effect. Therefore, the expansion effect of the allocation bandwidth per user by using the proposed NOMA compared to OMA can contribute to an increase in cell-edge user throughput more efficiently. Figure 5 also indicates that the cell-edge user throughput gain by using BS cooperation relative to the case without BS cooperation is increased as K increases. This is due to the effect of dynamic BS selection in the scenario where the resource allocation per user is limited. We note that as Nmax increases in the proposed NOMA, the required K value for obtaining a sufficiently saturated sum user throughput is increased. An explanation regarding this with simple modeling is as follows. When we employ the PF-based resource allocation, roughly said, the scheduler selects the users with the highest g˜ k among K candidate users. In the proposed NOMA, the best Nmax users are selected simultaneously. Assuming the exponential distribution of g˜ k , the probability density function of g˜ k of the selected d-th best user (d = 1, . . . , Nmax ) is represented as d−1 ∂ K −kg fd (g) = e (1 − e−g )K−k . (19) k ∂g k=0
Therefore, the g˜ k of the selected d-th best user becomes Gd times on average, where Gd is given by ∞
Gd = 0
g · fd (g)dg =
K 1 k=d
k
.
(20)
This is a selection diversity effect during the scheduling and is called the multiuser diversity gain. The multiuser diversity gain increases as K increases. From (20), we see that the proposed NOMA requires more candidate users, K, for scheduling to achieve a sufficient multiuser diversity gain for the second to Nmax -th best users, compared to OMA, where Nmax = 1. Figure 6 shows the user throughput gain when using the proposed NOMA under various conditions regarding BS cooperation for the respective user coverage positions. The value of the user coverage position corresponds to the cumulative probability of the user throughput. Therefore, roughly
Fig. 6
User throughput gain.
said, the user coverage position of 0 indicates the boundary of the cell or cluster and that of 1 indicates the vicinity of the BS. The number of users per cell, K, and β are set to 30 and 1.0, respectively. The throughput gain of the proposed NOMA relative to OMA is always higher than one. This means that the proposed NOMA improves the system performance regardless of the user position. We see that the cell-edge user throughput gain is especially significant, which means improvement in the user fairness. The sum and cell-edge user throughput levels for NOMA with BS cooperation are increased by approximately 4% and 56%, respectively, compared to those for NOMA without BS cooperation. This means that the user fairness of NOMA is improved through BS cooperation. This is because of the dynamic BS selection as a part of the beam selection enhancing the throughput of users near the cell edge. The sum and celledge user throughput levels using NOMA with BS cooperation are increased by approximately 51% and 83%, respectively, compared to that using OMA without BS cooperation. For the same conditions regarding the BS cooperation, almost the same user throughput gain with NOMA compared to OMA is observed for both cases with and without BS cooperation. We note that the proposed NOMA achieves significantly high throughput gain at user coverage positions of higher than around 0.8, thus in the vicinity of the BS. The users in such a region experience very good channel conditions. Therefore, even with a very small power assignment, these users can achieve high user throughput with the SIC. Since the remaining large fraction of BS transmission power can be used by the other users, scheduling these users under very good channel conditions does not significantly degrade the throughput of other users in NOMA and this kind of resource allocation is effectively achieved using PF-based resource allocation.
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better sum and cell-edge user throughput levels compared to OMA, which is assumed in LTE-Advanced. The effect of the proposed NOMA is more significant when BS cooperation is assumed, since the BS cooperation improves the channel conditions of the cell-edge users, which is appropriate for obtaining a higher non-orthogonal user multiplexing gain. The sum and cell-edge user throughput gains from NOMA in BS cooperation are approximately 51% and 83%, respectively, compared to OMA without BS cooperation. References Fig. 7
Sum and cell-edge user throughput as a function of β.
Figure 7 shows the sum user throughput per cell and cell-edge user throughput as a function of β. We assume BS cooperation in this figure. In addition to performance of the NOMA with Nmax of 2, OMA with β of 1 is also plotted for the performance comparison. K is set to 30. From Fig. 7, the sum user throughput of NOMA is reduced as β increases. Meanwhile, the cell-edge user throughput is increased as β increases, and that value is maximized at approximately β of 3.0. This is because the scheduler tends to allocate a large amount of resources to the cell-edge users when β is relatively large. The proposed NOMA maintains a higher sum user throughput and the proposed NOMA greatly enhances the cell-edge user throughput compared to OMA until β is greater than 2.4. The throughput gains for the sum and celledge user throughput by using the proposed NOMA scheme assuming β = 1.0 relative to OMA are approximately 39% and 19%, respectively. Furthermore, the throughput gain for the cell-edge user throughput by using the proposed NOMA scheme assuming β = 2.4 compared to OMA is approximately 65%, while the sum user throughput of NOMA remains the same as that for OMA. 4. Conclusion Aiming at further enhancement of the system efficiency and cell-edge user experience for future radio access, this paper proposed an extended NOMA scheme for the BS cooperative multiuser MIMO downlink. The first feature of the proposed NOMA scheme is the use of intra-beam superposition coding and an intra-beam SIC for non-orthogonal multiuser multiplexing within a beam. This brings about effective use of the receiver SIC and avoids increasing the overhead of the downlink orthogonal reference signals dedicated to the respective users when the number of multiplexed users is increased beyond the number of transmitter antennas. The second feature is the application of block-diagonalized random beamforming for determining the beamforming matrix. With the appropriate resource allocation (scheduling and power control) strategy, random beamforming effectively achieves a high spatial multiplexing gain along with multiuser diversity with limited CSI feedback. Based on simulation results, we show that the proposed NOMA in BS cooperative multiuser MIMO simultaneously achieves
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Nobuhide Nonaka received the B.E. degree from Tokyo University of Science, Noda, Japan in 2013. His research interest is in the area of base station cooperative MIMO and nonorthogonal multiple access technologies.
Yoshihisa Kishiyama received his B.E., M.E., and Dr. Eng. degrees from Hokkaido University, Sapporo, Japan in 1998, 2000, and 2010, respectively. In 2000, he joined NTT DOCOMO, INC. He has been involved in research and development for 4G/5G mobile broadband technologies and physical layer standardization in 3GPP. He is currently a Senior Research Engineer of 5G Laboratory in NTT DOCOMO, INC. His current research interests include 5G radio access technologies such as massive MIMO/beamforming, non-orthogonal multiple access (NOMA), and so on. He was a recipient of the International Telecommunication Union (ITU) Association of Japan Award in 2012.
Kenichi Higuchi received the B.E. degree from Waseda University, Tokyo, Japan, in 1994, and received the Dr.Eng. degree from Tohoku University, Sendai, Japan in 2002. In 1994, he joined NTT Mobile Communications Network, Inc. (now, NTT DOCOMO, INC.). While with NTT DOCOMO, INC., he was engaged in the research and standardization of wireless access technologies for wideband DS-CDMA mobile radio, HSPA, LTE, and broadband wireless packet access technologies for systems beyond IMT-2000. In 2007, he joined the faculty of the Tokyo University of Science and currently holds the position of Associate Professor. His current research interests are in the areas of wireless technologies and mobile communication systems, including advanced multiple access, radio resource allocation, inter-cell interference coordination, multiple-antenna transmission techniques, signal processing such as interference cancellation and turbo equalization, and issues related to heterogeneous networks using small cells. He was a co-recipient of the Best Paper Award of the International Symposium on Wireless Personal Multimedia Communications in 2004 and 2007, a recipient of the Young Researcher’s Award from the IEICE in 2003, the 5th YRP Award in 2007, the Prime Minister Invention Prize in 2010, and the Invention Prize of Commissioner of the Japan Patent Office in 2015. He is a member of the IEICE and IEEE.
