# Complex-Valued Phase Transmittance RBF Neural Networks for Massive MIMO-OFDM Receivers
## 1 Introduction  
In recent years, with the increasing demand for the real-time processing of big data, the Internet of Things (IoT), and 4K video streaming, technologies to increase area throughput [1] in base station (BS) coverage and hotspot tiers [2] have become increasingly important. In general, the system throughput can be improved by three independent factors: the number of BSs, bandwidth, and spectral efficiency. While the number of base stations is a complicated variable to handle, there are substantial bandwidths in the millimeter wavelength (mmWave) bands that could be employed for BS hotspot tiers. On the other hand, as objects and human bodies easily block mmWaves, increasing the spectral efficiency (SE) of BS coverage tiers arises as a potential solution for wide-area coverage. In order to increase SE, advanced techniques are necessary to use the available BSs and bandwidth more efficiently. In view of this, both BSs and user equipment (UE) currently operate with multiple antennas and orthogonal frequency-division multiplexing (OFDM) [3, 4, 5] to increase spectral efficiency. Multicarrier modulation schemes, such as OFDM, have been widely employed in digital communications systems due to their low susceptibility to intersymbol interference (ISI) [6, 7, 8, 9]. OFDM divides the channel bandwidth into \(K\) orthogonal subcarriers [10]. The serial stream at a high data rate applied to the OFDM input is first converted to multiple parallel low transmission rate sub-streams. Each of the \(K\) parallel sub-streams modulates one of the \(K\) subcarriers. In this way, the OFDM symbol duration is \(K\) times longer than the symbol duration of the equivalent single carrier system, thus avoiding ISI [11]. Anotherimportant characteristic of OFDM systems is that multiple users can be multiplexed in frequency, using \(K\) subcarriers. Multiple-input and multiple-output (MIMO) technologies use multiple antennas on the transmitter and receiver sides, increasing the wireless channel capacity without extra bandwidth, extra power transmission, or both [11]. Usually, as BSs have more computational power than UEs, a larger number of antennas is applied at the transmitter. In this context, when the number of antennas exceeds the number of users, the term massive MIMO (mMIMO) is frequently used. Generally, mMIMO systems operate with 16 or more antennas in BSs. In addition, the uplink can be composed of one or more UEs, where the former characterizes a single-user mMIMO (SU-mMIMO) [12] and the latter a multi-user mMIMO (MU-mMIMO) [13]. For 6G technologies, ultra-massive MIMO (UM-MIMO) schemes have been explored to support data throughputs of Terabits [14]. MIMO and mMIMO communications are broadly implemented either by beamforming, space-time block codes (STBC), or both [15; 16]. While beamforming techniques (either analog, digital, or hybrid [17]) may be more attractive to BSs, because of the necessity of many transmitting antennas, STBC, on the other hand, is feasible for use in both downlink and uplink connections. The combination of OFDM and MIMO is a major trend in mobile communication systems [18; 19; 20; 21; 22], such as 5G and next-generations, which are based on the so-called MIMO-OFDM and mMIMO-OFDM approaches [23]. Nonetheless, digital communication systems over wireless channels may suffer severe signal degradations due to multipath propagation, additive white Gaussian noise (AWGN) [24; 25], and Doppler effects [26]. Moreover, another frequent impairment in OFDM systems is signal distortion, characterized by the PAPR (peak-to-average power ratio), due to nonlinearities at the high-power transmitter amplifier [27; 28]. Since nonlinear impairments usually degrade the performance of linear filters, the search for robust nonlinear filters at the receiver is essential to circumvent this issue [11; 27; 29].