International Journal of Antennas and Propagation

Volume 2019, Article ID 9764958, 10 pages

https://doi.org/10.1155/2019/9764958

## Downlink Multiuser Hybrid Beamforming for MmWave Massive MIMO-NOMA System with Imperfect CSI

Shaanxi Key Laboratory of Information Communication Network and Security, Xi’an University of Posts and Telecommunications, Xi’an 710121, China

Correspondence should be addressed to Ming Lei; moc.361@21804991gnimiel

Received 29 August 2018; Revised 1 March 2019; Accepted 28 April 2019; Published 13 May 2019

Guest Editor: Khalil Sayidmarie

Copyright © 2019 Jing Jiang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper aims to provide a comprehensive scheme with limited feedback for downlink millimeter wave (mmWave) multiuser multiple-input multiple-output (MIMO) nonorthogonal multiple access (NOMA) system. Based on the feedback of the best beam and the channel quality information (CQI) on this beam, the users are grouped into a cluster having the same or coherent best beam and the maximal CQI-difference. To further reduce the intercluster interference, only the candidate cluster can join the cluster set whose intercluster correlation with the existing clusters is lower than threshold. Based on the results of clustering, mmWave hybrid beamforming is designed. To improve the user experience, each cluster selects the best beam of the user with the higher guaranteed rate requirement as the analog beamforming vector. For digital beamforming, the weak user applies the block diagonalization algorithm based on the strong user’s effective channel to reduce its intracluster interference. Finally, an intracluster power allocation algorithm is developed to maximize the power difference in each cluster which is beneficial to improve the successive interference cancelation (SIC) performance of the strong user. Finally, simulation results show that the proposed MIMO-NOMA scheme offers a higher sum rate than the traditional orthogonal multiple access (OMA) scheme under practical conditions.

#### 1. Introduction

In contrast to the conventional orthogonal multiple access (OMA), nonorthogonal multiple access (NOMA) allows different users to efficiently share the same resources (i.e., time, frequency, space, and code) at different power levels. Exploiting their respective channel gain differences, multiuser signals are separated at receivers by successive interference cancelation (SIC). Thus, it is an important technique for 5G systems which can significantly enhance system capacity and overall spectral efficiency [1–3].

NOMA can flexibly combine other 5G technologies, e.g., MIMO, cognitive radio, cooperative communication, and channel coding [3]. Because MIMO-NOMA systems can significantly increase the number of supportable users and in turn improve the system sum capacity, the research of MIMO-NOMA has been carried out widely [4–7]. Multiple users with distinct channel gains are grouped into MIMO-NOMA clusters. The users in the same cluster are scheduled on NOMA basis. The intracluster interference is mitigated by SIC based on the obvious channel gain difference. Multiple clusters may utilize the multiuser MIMO principles to cancel the intercluster interference. References [4–8] prove that NOMA combined with MIMO techniques could achieve great system performance gains over OMA.

Thanks to the abundant bandwidth resources, millimeter wave (mmWave) frequency becomes a natural choice to achieve Gigabit data rates [9, 10]. The number of supportable users can be more than the number of radio frequency (RF) chains at the same resources by exploiting MIMO-NOMA in mmWave system. On the other hand, the channel of mmWave is highly directional. For mmWave MIMO-NOMA system, the users in a same cluster use the same beam and the different clusters use the distinct different beams. For the users in a same cluster, the obvious power difference in a same beam could assure good SIC performance. For different clusters, the distinct different beams are beneficial to greatly reduce the intercluster inference [11, 12]. Therefore, mmWave MIMO-NOMA can effectively improve the spectral efficiency and cope with the demands of massive connectivity.

Considering mmWave MIMO-NOMA system, [11] analyzes the achievable sum rate of the proposed beamspace MIMO-NOMA in a typical mmWave channel mode, which shows an obvious performance gain compared with the existing beamspace MIMO. Zero-forcing beamforming (ZF-BF) is designed to reduce the interbeam interference in the beamspace. Furthermore, a dynamic power allocation is proposed to maximize the achievable sum rate which contains the intrabeam and interbeam power optimization. Reference [12] proposes a hybrid analog/digital beamforming scheme with a power allocation algorithm aiming to maximize the energy efficiency. Users having a high channel correlation and large channel gain difference are grouped as a cluster. Reference [13] investigates the maximization of the sum rate of the system with clusters of 2-user or more-user. It decomposes the original problem into power and beam gain allocation problems. Reference [14] proposes a hybrid analog/digital beamforming framework to maximize the sum rate and analyzes the effect of beam misalignment on rate performance.

Most of the existing works on mmWave MIMO-NOMA, such as [11–14], have assumed perfect knowledge of channel state information (CSI) at the transmitter, which is difficult to realize in practice. Reference [15] proposes a hybrid precoding scheme based on one-stage feedback, which makes use of all feedback overhead to enable precise beam information and takes advantage of the second-order channel statistics to mitigate multiuser interference. Reference [16] proposes the random beamforming in which base station (BS) broadcasts the random beams and the users with the enough signal strength feed their channel quality information (CQI) back to the BS.

MmWave MIMO-NOMA system with limited feedback has been studied but with limited results. Reference [15] has not yet considered user clustering and the intracluster interference cancelation with limited feedback. Reference [16] reduces the feedback overhead, but the channel measurement is time-consuming and complicated. In this paper, we put forward a comprehensive scheme with imperfect CSI for mmWave MIMO-NOMA system. To reduce the hardware complexity, we apply low RF chains structure at the BS, where the hybrid analog/digital beamforming is considered. The major contributions of this paper can be listed as follows:

(1) The user clustering is designed based on the limited feedback scheme. References [16–21] put forward some feedback designs for MIMO-NOMA, e.g., on bit feedback, the path loss information, and other second-order statistics. Considering mmWave user could acquire the big gain in the specific beam, one-bit feedback or the path loss information is not accurate enough. In this paper, the limited feedback uses the best beam and CQI value based on this beam. The users having the same or adjacent best beam are sorted based on their CQI values, and the users with the maximal CQI-difference are formed a cluster. To further reduce the intercluster interference, the user clustering algorithm applies the intercluster correlation threshold to assure only the cluster with the distinct different beam can join the cluster set. Numerical results prove that it acquires obvious sum rate improvement by adequately exploiting the high directional feature of mmWave.

(2) We propose a novel hybrid analog/digital beamforming algorithm. In general, the users in a same cluster will use the beam of the strong user as the beamforming vector [11, 12]. The beamforming gains are assured to achieve first for the strong users. However, the weak users would require higher data rate. To improve the quality of user experience and the user fairness, for each cluster, we select the beam of the user with the higher rate requirement as the analog beamforming vector. For digital beamforming, the prior work [12] applies ZF-BF to cancel the intercluster interference. For mmWave communication, the distinct different beams cause very little interference as to the sparsity of mmWave channel. In this paper, the digital beamforming is designed for the strong user and the weak user, respectively. The strong user utilizes the singular value decomposition (SVD) of its effective channel to acquire more gains from digital beamforming. Especially, the weak user exploits the block diagonalization (BD) algorithm to mitigate the intracluster interference from the strong user in the same cluster.

(3) As the power difference between the two users in a same cluster increases, not only is the SIC performance of the strong user improved, but also the intracluster interference of the weak user is reduced. So we derive an intracluster power allocation scheme that maximizes the power difference under the users’ quality of service (QoS) requirements. We derive a closed-form optimal power allocation for the two users in a cluster by deriving the exact bounds for the power allocation coefficient region.

(4) Finally, we evaluate the sum rate performance of the downlink MIMO-NOMA system using the proposed beamforming, user clustering and power allocation algorithms. The simulations are done with a wide range of beam correlation thresholds, including the interuser and intercluster thresholds in the user clustering algorithm. Both of the perfect CSI and random selection cases are considered in the simulations. Numerical results also compare the sum rate performances of MIMO-OMA and the proposed MIMO-NOMA and illustrate the significance of the proposed MIMO-NOMA scheme.

The rest of this paper is organized as follows. Section 2 presents the system and channel model of mmWave MIMO-NOMA system. Sections 3, 4, and 5 describe the designs of user clustering, hybrid beamforming and power allocation, respectively. The simulation configuration and results are presented and discussed in Section 6, and finally, Section 7 concludes this paper.

*Notation*. In the reminder of this paper, we use the following notations: and denote the transpose and Hermitian transpose, respectively, denotes the Frobenius norm, and denotes the distribution of circularly symmetric complex Gaussian random variable with mean and covariance .

#### 2. System and Channel Model

Consider a downlink mmWave beamforming NOMA transmission system, in which one BS communicates with clusters. Each cluster consists of multiple single-antenna users. The BS is equipped with antennas and RF chains for reducing the hardware complexity. We consider the fully connected architecture that each RF chain is linked to all antennas by using multiple phase shifters. We assume that the number of clusters served by the BS is equal to that of RF chains . Although each cluster can contain more than two users, we suppose here that there are two users in each cluster for simplicity. This is consistent with the standard implementation of NOMA in long term evolution advanced (LTE-A) as well [22].

On the downlink, the BS applies an baseband beamforming followed by an RF beamforming . The sampled transmitted signal is thereforewhere , is the vector of transmitted symbols in which and denote the signals for the 1-th and 2-th in the -th cluster, respectively. Similarly, and stand for the power allocation coefficients for the two users in the -th cluster. is the power allocated to the -th cluster.

The received signal of the -th user in the -th cluster can be represented as follows:where is the vector that represents the mmWave channel of the -th user in the -th cluster. denotes additive white complex Gaussian noise. Moreover, the second term is the intercluster interference from other clusters. Without loss of generality, for each cluster, we assume that where . Following this, the 1-th and 2-th are defined as the strong user and weak user in each cluster, respectively.

Due to the limited scattering in mmWave channel, we adopt a well-established geometric channel model with scatterers [23, 24]. We assume that each scatterer contributes a single propagation path from the BS to user. Then, the channel can be expressed as where the first and second terms denote the line-of-sight (LoS) component and non-line-of-sight (NLoS) components of the -th user in the -th cluster, respectively. denotes the distance from the BS to the -th user in the -th cluster. and are the path loss exponents corresponding to the LoS and NLoS paths, respectively. where denotes the complex gain of the -th path between the BS and the* i*-th user in the* l*-th cluster. is the -th path’s normalized direction, whereas is the antenna array steering vector with respect to . If we assume a uniform linear array (ULA) is used at the BS, can be written as [25]where is related to the angle of departure as [26]. denotes the distance between antenna elements and denotes the signal wavelength satisfying at mmWave frequencies.

#### 3. User Clustering

Appropriately selecting two users which are served in a cluster can help improve the performance of NOMA multiuser beamforming. On the one hand, the big difference of the channel gains can improve SIC performance of the users with high channel gains and reduce the intracluster interference of the users with low channel gains. On the other hand, the beamforming vector is shared by all users in the same cluster. If the channels of those users in a same cluster are highly correlated, the beamforming vectors can acquire the definite array gains and properly cancel the intercluster interference from other clusters. Reference [4] proposed a clustering algorithm selecting user-pair having a high channel correlation and large channel gain difference as set in the same cluster, which requires full CSI. However, the full CSI feedback to the BS is not feasible in practice due to prohibitively high feedback overhead. So we propose a user clustering algorithm with limited feedback information, which only requires the indexes of the best beams and the channel quality information (CQI) values.

The index of the best beam and the user’s CQI are measured and sent back as follows. In the first stage, the BS broadcasts pilot signals on the every vector in the beamforming codebook. In the second stage, each user chooses the best beam and measures the CQI with this beamforming vector. At last, the user sends the index of the best beam and CQI to the BS. The best beam of the* i*-th user can be selected according to the following criterion as [27]where represents the beamforming codebook with size (i.e., feedback bits) and consists of the steering vectors . They have the same form of the array response vector in (4). is the beamforming vector selected from .

As discussed in [24, 28], the effect of LoS component is dominant in mmWave channels, compared to those of NLoS components. Therefore, the above mmWave channel model in (3) can be simplified as where the subscript 0 of the LoS component is omitted for the simplification of notation. Then, the effective channel gain of the user on the beam in (5) can be expressed aswhere is the predefined normalized direction of . is the Fejér kernel, which goes to zero quickly when increases. Therefore, based on the criterion in (5), the normalized direction of the selected beam has the least difference from in the codebook. This means that the normalized direction of each user can be approximately the normalized direction of its selected beam. The correlation of the selected beam between user and user can be rewritten asBased on the above beam correlation expression in (8) and channel expression in (6), the channel correlation between users and user can be simplified aswhere denotes the channel correlation between user and user . (a) follows from that and are approximately and based on the above analysis, respectively. So the correlation between the users’ channels can be replaced with the correlation between their selected beams .

CQI is an indicator carrying information about the channel condition. In LTE, considering a single BS system, the received SNR for each user can be written as [29]where is the transmit power and is the power of received noise and interference. The measured SNR is then mapped to a discrete CQI value using a chipset vendor specific mapping table [30]. Because the positive correlation between channel gain and CQI value, we will just calculate the difference of CQI values between users instead of their channel gain difference.

It is proved in [8] that the more users are admitted to a cluster, the lower is the achieved sum rate, which illustrates the tradeoff between the sum rate and maximum number of admitted users. Considering the tradeoff, we assume that each cluster admits 2 users. Based on the above analysis, a limited feedback downlink MIMO-NOMA user clustering algorithm is described in Algorithm 1, in which the number of clusters and each cluster contains 2 users.