Wireless Communications and Mobile Computing

Volume 2017 (2017), Article ID 9171068, 13 pages

https://doi.org/10.1155/2017/9171068

## Iterative Multiuser Equalization for Subconnected Hybrid mmWave Massive MIMO Architecture

^{1}Instituto de Telecomunicações (IT) and DETI, Universidade de Aveiro, Aveiro, Portugal^{2}Instituto de Telecomunicações (IT) and Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Caparica, Portugal

Correspondence should be addressed to R. Magueta

Received 1 August 2017; Accepted 3 December 2017; Published 20 December 2017

Academic Editor: Patrick Seeling

Copyright © 2017 R. Magueta 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

Millimeter waves and massive MIMO are a promising combination to achieve the multi-Gb/s required by future 5G wireless systems. However, fully digital architectures are not feasible due to hardware limitations, which means that there is a need to design signal processing techniques for hybrid analog-digital architectures. In this manuscript, we propose a hybrid iterative block multiuser equalizer for subconnected millimeter wave massive MIMO systems. The low complexity user-terminals employ pure-analog random precoders, each with a single RF chain. For the base station, a subconnected hybrid analog-digital equalizer is designed to remove multiuser interference. The hybrid equalizer is optimized using the average bit-error-rate as a metric. Due to the coupling between the RF chains in the optimization problem, the computation of the optimal solutions is too complex. To address this problem, we compute the analog part of the equalizer sequentially over the RF chains using a dictionary built from the array response vectors. The proposed subconnected hybrid iterative multiuser equalizer is compared with a recently proposed fully connected approach. The results show that the performance of the proposed scheme is close to the fully connected hybrid approach counterpart after just a few iterations.

#### 1. Introduction

A new generation of cellular network (fifth generation, 5G) is coming, and some innovative technologies are needed to ensure better performance and quality of service (QoS). Two enabling technologies have been considered to meet the QoS requirements for future wireless communication, massive MIMO (mMIMO), and millimeter wave (mmWave) communications [1]. By using mmWave bands, several tens of GHz of bandwidth become available for wireless systems [2], while the mMIMO allows the continued increasing demand of higher data rates for future wireless networks [3]. Comparing the mMIMO with conventional MIMO approaches, the mMIMO can scale up the conventional MIMO by orders of magnitude [4]. A survey on mMIMO, also identified as large-scale MIMO, with channel modelling, applications scenarios, and physical/networking techniques can be seen in [5]. The use of mmWave with mMIMO is very promising, because smaller wavelength compared to conventional communication systems allows the same volume to pack more antennas [6], which means that the terminals can support a large number of antennas.

The mmWave mMIMO combination can be used to exploit new efficient spatial processing techniques, such as beamforming/precoding and spatial multiplexing, at both transmitter and/or receiver terminals [7]. These techniques are different than those used for sub-6 GHz bands due to limitations in hardware [8]. In these systems, it is not practical to have one fully dedicated radio frequency (RF) chain by antenna [9] as in sub-6 GHz conventional MIMO systems [10] due to the power consumption and the high cost of mmWave mixed-signal components. Another issue is the mmWave propagation characteristics, which are quite different from sub-6 GHz because the mmWave channels are not so rich in multipath propagation effects [11, 12], which should be taken into consideration in the techniques design for these systems. To overcome the limitation of the RFs chains number, purely analog beamforming can use phase shifters [8], with some schemes proposed in [13, 14], where statistical channel knowledge is used through phase shifters, to optimally adjust the arrays response in space, applying a beam steering solution.

The performance of the pure-analog techniques is limited by constraints on the amplitudes of phase shifters and due to the phases of the ones quantized. Therefore, analog beamforming is usually limited to single-stream transmission [15]. These limitations are overcome by doing some signal processing at an analog level and the rest at the digital level. These architectures are called hybrid analog/digital architectures and have been addressed in [15, 16]. Precoding and/or combining/equalization designs for single-user systems have been addressed for fully connected hybrid architectures in [17–19]. In these architectures, each of the RF chains is connected to all receive-and-transmit antennas. In [17], a hybrid spatially sparse precoding/combining approach was designed for mmWave mMIMO systems. The spatial structure of mmWave channels was used to transform the single-user multistream precoding and combining scheme into a sparse reconstruction problem. In [18], joint turbo-like beamforming was designed to compute transmit/receiving analog beamforming coefficients; however the digital processing part was not considered. In [19], codebook design approaches were addressed for single-stream transmissions through an analog beamforming structure. For multiuser systems, some beamforming approaches have been proposed for fully connected hybrid architectures [20–22]. The authors of [20] proposed uplink receiving beamforming where they assume only single antenna user-terminals (UTs), and at both stages analog and digital ones dealt with multiuser interference. Reference [21] proposed for the downlink a limited feedback analog/digital two-stage precoding and combining algorithm. Transmit/receiving analog beamforming are jointly computed in the first stage to maximize the power of the desired signal, and then the interference is explicitly mitigated using conventional linear zero-forcing (ZF) precoding in the second stage, that is, in the digital domain. An efficient hybrid iterative block space-time multiuser equalizer was proposed in [22]. This equalizer was designed based on the iterative block decision feedback equalization (IB-DFE) principle [23]. IB-DFE was originally proposed in [24]. It does not need the feedback loop of the channel decoder output, and it can be considered as a low complexity turbo equalizer. IB-DFE has been extended to several scenarios, like diversity scenarios and conventional and cooperative MIMO systems, among many others [25–30].

In addition to the fully connected architectures, there are subconnected architectures that allow us to reduce the number of phase shifters from to , when compared with fully connected counterparts, where and are the number of antennas and the number of RF chains [31]. Thus, the power consumption used to excite and to compensate the insertion loss of phase shifters is reduced, and the computational complexity is also lower [31]. There are two types of subconnected architectures, dynamic and fixed [32]. In the dynamic subconnected case, each RF chain can dynamically connect to a different set of antennas, and in the fixed subconnected one, each RF chain is always physically connected to the same set of antennas. Precoding schemes for dynamic subconnected hybrid architectures have been proposed in [32, 33]. Reference [32] uses a relaxation of the mutual information maximization problem to design a technique that adapts the subarray structure according to the channel covariance matrix for frequency selective channels. The authors of [33] proposed a two-step algorithm for single-user narrowband systems that iteratively optimizes the hybrid precoder for spectral efficiency maximization, obtaining an extra data stream via the index of the active antenna set without any extra RF chain. Fixed subconnected hybrid architectures were addressed in [34–37]. In [34], precoder and combiner schemes for narrowband single-user systems are proposed, where a two-layer optimization method jointly exploiting the interference alignment and fractional programming was employed. First, the analog precoder and combiner are optimized via the alternating-direction optimization method, and then the digital precoder and combiner are optimized based on an effective channel matrix. The authors of [35] designed a precoder and a combiner for a wideband single-user system where the overall spectral efficiency is maximized considering a power budget constraint for each subcarrier. The works in [36, 37] are focused on multiuser downlink systems. In [36], the total achievable rate optimization problem with nonconvex constraints is decomposed to a series of subrate optimization problems for each subantenna array, and then an algorithm is implemented to perform a successive interference cancelation-based hybrid precoding. Precoding and combining schemes are performed in [37] for downlink, where virtual path selection maximizes the channel gain of the analog effective channel, and then a zero-forcing precoding in the digital domain is applied to mitigate the interference.

In this manuscript, we propose an efficient hybrid iterative block multiuser equalizer for subconnected mmWave mMIMO systems. The limitation that each RF chain is only physically connected to a subset of antennas makes the design of the proposed subconnected hybrid iterative multiuser equalizer harder than for the fully connected based approaches. To the best of our knowledge, iterative block detection designed for subconnected mmWave mMIMO architectures has not been addressed in the literature. We propose low complexity UTs without access to the Channel State Information (CSI), using a single RF chain and pure-analog random precoding. A time encoder/precoder is applied to guarantee that the transmit signal and thus the noise plus interference at the receiver side are Gaussian distributed. This not only simplifies the receiver optimization problem but also increases the diversity effects on the mmWave mMIMO system. The designed subconnected hybrid equalizer is optimized by using the average bit-error-rate (BER) as a metric. We compute the analog part of the equalizer sequentially over the RF chains using a dictionary built by the array response vectors. Finally, we show that the BER performance of the proposed subconnected hybrid iterative multiuser equalizer tends to the BER performance of a fully connected hybrid equalizer as the number of iterations increases.

This paper is organized as follows. Section 2 presents the subconnected hybrid multiuser mmWave mMIMO system model. Section 3 begins with the description of a channel model for mmWave mMIMO systems, followed by the description of user-terminals (UT) and finally the design of the proposed subconnected hybrid iterative multiuser equalizer. Section 4 shows some BER performance results, and in Section 5, major conclusions are presented.

*Notations*. Matrices are denoted in boldface capital letters and column vectors in boldface lowercase letters. The operations , , , and represent the trace, the conjugate, the transpose, and the Hermitian transpose of a matrix. is the operator that represents the sign of a real number and if is a complex number. It can also be employed elementwise to matrices. The functions and represent the real part and imaginary part of . The functions and , where is a vector and is a square matrix, correspond to a diagonal matrix where the entries of diagonal are equal to and to a vector equal to the diagonal entries of . The element of row and column of matrix is denoted by . The identity matrix is .

#### 2. System Characterization

In this section, we describe the channel model, the UTs, and the receiver signals for the mmWave mMIMO system. We consider a multiuser system with users, each one with transmit antennas, that sends one data stream per time slot to the base station with receiving antennas.

##### 2.1. Channel Model

We consider a -sized block fading channel, that is, a channel that remains constant during a block but varies independently between blocks. The channel follows the clustered sparse mmWave channel model discussed in [17] where is the channel matrix, which contributes the sum of clusters, each one with the contribution of propagation paths. The channel matrix may be expressed to the th user as is a normalization factor, and is the complex gain of the th ray in the th scattering cluster. The functions and represent transmit and receiving antenna element gain for and , that is, the azimuth (elevation) angles of arrival and departure. The vectors and represent the normalized receiving and transmit array response vectors for the corresponding angles. Reference [17] addressed the random distributions used to generate the path gains and the angles of channel, such that .

##### 2.2. User-Terminal Model Description

We assume that each user has only a single RF chain and sends only one data stream per time slot over the transmit antennas, as shown in Figure 1. We also consider that the UTs have no access to CSI, simplifying the overall system design. The analog precoder of th UT at the instant is mathematically modelled by and is physically realized using a vector of analog phase shifters, where all elements of vector have equal norm . Therefore, the analog precoder vector of the th UT at the instant is generated randomly according towhere with and are i.i.d. uniform random variables such that .