# Multiuser Equalizer for Hybrid Massive MIMO mmWave CE-OFDM Systems
###### Abstract  
This paper considers a multiuser broadband uplink massive multiple input multiple output (MIMO) millimeter-wave (mmWave) system. The constant envelope orthogonal frequency division multiplexing (CE-OFDM) is adopted as a modulation technique to allow an efficient power amplification, fundamental for mmWave based systems. Furthermore, a hybrid architecture is considered at the user terminals (UTs) and base station (BS) to reduce the high cost and power consumption required by a full-digital architecture, which has a radio frequency (RF) chain per antenna. Both the design of the UT's precoder and base station equalizer are considered in this work. With the aim of maximizing the beamforming gain between each UT and the BS, the precoder analog coefficients are computed as a function of the average angles of departure (AoD), which are assumed to be known at the UTs. At the BS, the analog part is derived by assuming a system with no multi-user interference. Then, a per carrier basis nonlinear/iterative multi-user equalizer, based on the iterative block decision feedback equalization (IB-DFE) principle is designed, to explicitly remove both the multi-user and residual inter carrier interferences, not tackled in the analog part. The equalizer design metric is the sum of the mean square error (MSE) of all subcarriers, whose minimization is shown to be equivalent to the minimization of a weighted error between the hybrid and the full digital equalizer matrices. The results show that the proposed hybrid multi-user equalizer has a performance close to the fully digital counterpart. CE-OFDM; hybrid analog/digital architectures; massive MIMO; mmWave communications; nonlinear equalizer +
Footnote †: journal: Applied  
due to the small wavelengths inherent to these bands, we can pack these hundreds of antennas in the same volume of sub-6 GHz systems [4]. Although, mMIMO mmWave systems are very promising, they still face some difficulties such as: the mmWave mMIMO channels tend to be more correlated [5; 6; 7]; the power consumption of some hardware components of radio frequency (RF) chains, such as analog-to-digital converters (ADCs), digital-to-analog converters (DACs), mixers, power amplifiers, is higher; and the cost of some hardware components of the referred RF chains is also higher. Therefore, new techniques that consider the specific characteristics of the channel and hardware constraints should be explored. There are three major architectures that can be explored. The first one, it is the use of low-resolution DACs/ADCs. However, the performance degradation at high signal-to-noise ratio (SNR) regions is substantial [8]. The second one, it is the use of only one RF chain, i.e., a fully analog architecture. However, this limits the achievable performance, and therefore it is usually employed in single-stream transmissions [9]. Finally, the other technique is the use of hybrid analog-digital architectures. In these systems, the number of RF chains is lower than the number of antennas employed at both the user terminals (UTs) and base station (BS), reducing the cost and the power consumption. This is the architecture followed in this paper and in the last years several transmit and receive hybrid beamforming approaches have been proposed [10; 11; 12; 13; 14; 15; 16; 17; 18], as discussed in Section 1.1. The use of mmWave bands allows larger bandwidths, but considering orthogonal frequency division multiplexing (OFDM) modulation, this leads to a higher number of subcarriers. Therefore, the use of OFDM, which is very efficient to mitigate the effects of inter-symbol interference (ISI) in frequency selective channels, results in a signal with high amplitude fluctuations, making the large peak-to-average power ratio (PAPR) a problem, which should be taken into account for mmWave mMIMO systems [19]. A high PAPR results in strong nonlinear distortions caused by the power amplifier [20], degrading the system performance.