## 1 Introduction
However, the presence of non-ideal devices in real implementations brings in several error sources that may affect the performance of the algorithms under study. In particular, real phase shifter implementations introduce phase errors whose magnitude was studied in [14; 15], and non-ideal combiners introduce power losses that were characterized, for instance, in [16]. The effect of hardware-constrained base stations in massive MIMO systems was extensively analyzed in [17], where a scaling law of the increase of some particular imperfections with the number of antennas was provided. In addition, hardware constraints impose practical limitations that should be desirably considered in the algorithms design. This was highlighted in [18; 19], which propose constant envelope precoders suitable for the use of power-efficient RF power amplifiers as a constraint to avoid the problems of such non-ideal amplifiers with their inherent non-linear behaviour. Overall, it is of paramount importance to consider the effect of hardware impairments and other practical limitations when analyzing the system performance achieved by massive MIMO cellular systems. Motivated by the lack of concluding results on the mmW multi-cell performance of ABF, this paper provides a thorough assessment of ABF schemes for MU single-stream transmission under realistic channel conditions in the lower edge of the mmW frequency band. In particular, a carrier frequency of 28 GHz is considered, which, although it does not strictly belong to the mmW band (defined from 30 and 300 GHz), it has been widely adopted by industry as a mmW frequency, as any other frequency above 10 GHz [20]. To this end, exhaustive system simulations have been conducted, assuming a multi-cell deployment in which the channel is accurately emulated and there is a coexistence of users with very different channel conditions. The main objective is to complement existing theoretical studies by assessing under which conditions ABF schemes can approach the performance of fully-digital precoders. In addition, the performance of the analog schemes with inter-beam interference in the system (i.e., when multiple users are simultaneously scheduled) is also investigated. Simulation results with ideal assumptions on aspects such as the timely availability of channel state information (CSI), ideal phase-shifters and combiners for ABF and lack of per-antenna power constraints (PAPC) will be contrasted with results including more realistic assumptions on these aspects. More specifically, the following realistic assumptions were selected and analyzed:  
* outdated CSI at the transmitters;
* PAPC in the precoding design;
* Inaccuracy errors caused by real phase shifters;
* Losses introduced by real combiners. The rest of the paper is organized as follows. Section 2 details the system model and multi-antenna schemes assessed in this work, namely fully-digital and analog schemes. Section 3 describes the simulation assumptions and includes the performance evaluation with ideal assumptions. Sections 4 and 5 are devoted to the performance evaluation including practical limitations and hardware impairments, respectively. Finally, Section 6 draws the main findings of the paper.