Design and Simplification of Quantize-Forward Relaying in Massive MIMO HetNets Ahmad Abu Al Haija * , Min Dong ‡ , Ben Liang * , Gary Boudreau † , S. Hossein Seyedmehdi † * University of Toronto, Toronto, ON, Canada, † Ericsson Canada, Ottawa, ON, Canada ‡ University of Ontario Institute of Technology, Oshawa, ON, Canada Abstract—To investigate how massive multiple-input multiple- output (MIMO) impacts the data transmission of a dense het- erogeneous network (HetNet), we study its uplink transmission that consists of two users communicating with a macro-cell base station (MCBS) through a small-cell BS (SCBS) with zero-forcing (ZF) detection at each BS. We first analyze the scheme with quantize-forward (QF) relaying at the SCBS and joint decoding (JD) at the MCBS for both users’ messages. To maximize the rate region, we derive the optimal quantization at the SCBS for both users’ data streams and show how they depend on the large-scale fading. We further propose a new scheme that simplifies the QF-JD scheme through Wyner-Ziv (WZ) binning and time division (TD) transmission at the SCBS to allow not only sequential but also separate decoding of each user’s message at the MCBS. For this QF-WZTD scheme, the optimal quantization parameters are identical to that of the QF-JD scheme while the phase durations and power allocation are conveniently optimized as functions of the quantization parameters. Despite its simplicity, the QF-WZTD scheme achieves the same rate region of the QF- JD scheme, making it an attractive option for the fifth-generation HetNets. I. I NTRODUCTION The development of the fifth-generation (5G) cellular net- works aims to drastically improve the spectral efficiency and data rate of current networks to serve an escalating number of connected devices. Hence, some key enabling technologies have been proposed, such as Ultra Dense Networks (UDNs), HetNets, massive MIMO, and full-duplex transmission [1]. In UDNs, the number of user equipments (UEs) is small as compared with the number of SCBSs and MCBSs [2]. Hence, we investigate the uplink transmission in a HetNet as shown in Fig. 1, where two UEs communicate with a MCBS through a SCBS. This uplink channel theoretically resembles the multiple-access relay channel (MARC) [3]. With a single antenna at each node, the rate regions for MARC have been derived for decode-forward (DF) relaying [3], [4] and QF relaying [5]–[7] schemes. In an UDN, the SCBS location is random and can be close the MCBS where QF relaying can outperform DF relaying [8]. Hence, in this paper, we investigate QF relaying in a massive MIMO HetNet. For multi-antenna QF relaying, the quantization resolution at the relay node is the key design problem. This leads to the optimization of the covariance matrix of the quantization noise vector, which is in general non-convex and challenging. Hence, approximate solutions were obtained via iterative numerical methods for one way [9] and two way [10] half-duplex relay channels and cloud radio access network [11]. With massive This work has been funded in part by Ericsson Canada and by the Natural Sciences and Engineering Research Council of Canada. MCBS UE1 Macro cell UE2 SCBS Small cell UE Fig. 1. Uplink transmission in a dense HetNet. MIMO, the quantization problem can be simplified with pos- sible closed-form solutions, avoiding high computational cost and processing delay of the numerical methods. The design simplification with massive MIMO [12] stems from its ability to 1) neglect the small scale fading through channel hardening [13], 2) orthogonalize different user trans- missions through beamforming [14], and 3) approach the optimal performance with simple linear receivers, e.g, zero forcing (ZF) receiver [14]. Consequently, the optimal design of quantization noise covariance may only depend on the large- scale fading of each channel with a complexity that scales with the number of UEs instead of antennas [12, Myth 9]. Since large-scale antenna arrays can be made rather compact, they can be implemented at both MCBS and SCBS [12] [15]. Hence, it is of interest to investigate how massive MIMO simplifies the QF relaying design in a HetNet. This paper has the following contributions: • We consider the uplink transmission of two UEs in a massive MIMO HetNet with ZF detection and analyze the rate region of a QF-JD scheme with QF relaying at the SCBS and JD at the MCBS for both UEs’ messages. To maximize the rate region, we derive the optimal quantization parameters at the SCBS for UEs’ data streams in closed-form, where the number of parameters is equal to the number of UEs instead of antennas, and we show how their values depend on the large-scale fading [12]. • We propose a new QF-WZTD scheme that simplifies QF-JD by deploying not only Wyner-Ziv (WZ) binning at the SCBS [8] but also time division (TD) transmission for each bin index of a UE’s quantized data stream. These two techniques allow the the MCBS to deploy separate and sequential decoding for each bin index, quantization index, and UE message. • We prove that the proposed QF-WZTD scheme has the same rate region and the same optimal quantization parameters as those of the QF-JD scheme, while the optimal TD phase durations and power allocation are conveniently obtained as direct functions of the quantization parameters.