Cell-free massive multiple-input multiple-output (mMIMO) networks enhance coverage and spectral efficiency (SE) by distributing antennas across access points (APs) with phase coherence between APs. However, the use of cost-efficient local oscillators (LOs) introduces phase noise (PN) that compromises phase coherence, even with centralized processing. Sharing an LO across APs can reduce costs in specific configurations but cause correlated PN between APs, leading to correlated interference that affects centralized combining. This can be improved by exploiting the PN correlation in channel estimation. This paper presents an uplink orthogonal frequency division multiplexing (OFDM) signal model for PN-impaired cell-free mMIMO, addressing gaps in single-carrier signal models. We evaluate mismatches from applying single-carrier methods to OFDM systems, showing how they underestimate the impact of PN and produce over-optimistic achievable SE predictions. Based on our OFDM signal model, we propose two PN-aware channel and common phase error estimators: a distributed estimator for uncorrelated PN with separate LOs and a centralized estimator with shared LOs. We introduce a deep learning-based channel estimator to enhance the performance and reduce the number of iterations of the centralized estimator. The simulation results show that the distributed estimator outperforms mismatched estimators with separate LOs, whereas the centralized estimator enhances distributed estimators with shared LOs.

The use of up to hundreds of antennas in massive multi-user (MU) multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) poses a complexity challenge for digital predistortion (DPD) aiming to linearize the nonlinear power amplifiers (PAs). While the complexity for conventional time domain (TD) DPD scales with the number of power PAs, frequency domain (FD) DPD has a complexity scaling with the number of user equipments (UEs). In this work, we provide a comprehensive analysis of different state-of-the-art TD and FD-DPD schemes in terms of complexity and linearization performance in both rich scattering and line-of-sight (LOS) channels and with antenna crosstalk. We propose a novel low-complexity FD convolutional neural network (CNN) DPD. We also propose a learning algorithm for any FD-DPDs with differentiable structure. The analysis shows that FD-DPD, particularly the proposed FD CNN, is preferable in LOS scenarios with few users, due to the favorable trade-off between complexity and linearization performance. On the other hand, in scenarios with more users or isotropic scattering channels, significant intermodulation distortions among UEs degrade FD-DPD performance, making TD-DPD more suitable. The proposed learning algorithm allows FD-DPDs to outperform TD-DPD optimized by indirect learning architecture under antenna crosstalk.

Cell-Free massive MIMO networks provide huge power gains and resolve inter-cell interference by coherent processing over a massive number of distributed instead of colocated antennas in access points (APs). Cost-efficient hardware is preferred but imperfect local oscillators in both APs and users introduce multiplicative phase noise (PN), which affects the phase coherence between APs and users even with centralized processing. In this paper, we first formulate the system model of a PN- impaired uplink Cell-Free massive MIMO orthogonal frequency division multiplexing network, and then propose a PN-aware linear minimum mean square error channel estimator and derive a PN- impaired uplink spectral efficiency expression. Numerical results are used to quantify the spectral efficiency gain of the proposed channel estimator over alternative schemes for different receiving combiners.

The frequency and spatial characteristics of nonlin-ear distortion from a MIMO-OFDM (multiple-input multiple-output orthogonal frequency-division multiplexing) basestation with memoryful nonlinear amplifiers (modeled by a generalized memory polynomial) is studied herein. We prove a theorem about a linear representation of the amplified signal from which the nonlinear distortion is obtained. Our measurement results demonstrate that the generalized memory polynomial can provide better accuracy of the nonlinear distortion than the memoryless and memory polynomial models. Furthermore, it is shown that in contrast to the memoryless amplifier, the amplifier with memory can distort the useful linear signal and introduce interference in a wider range of sub carriers. The derived theory is useful to predict how the nonlinear distortion will behave, to analyze the in-band and out-of-band radiation, and to schedule users in the frequency plane to minimize the effect of nonlinear distortion.

Digital predistortion (DPD) is a method commonly used to compensate for the nonlinear effects of power amplifiers (sPAs). However, the computational complexity of most DPD algorithms becomes an issue in the downlink of massive multi-user (MU) multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM), where potentially up to several hundreds of PAs in the base station (BS) require linearization. In this paper, we propose a convolutional neural network (CNN)-based DPD in the frequency domain, taking place before the precoding, where the dimensionality of the signal space depends on the number of users, instead of the number of BS antennas. Simulation results on generalized memory polynomial (GMP)-based PAs show that the proposed CNN-based DPD can lead to very large complexity savings as the number of BS antenna increases at the expense of a small increase in power to achieve the same symbol error rate (SER).

We propose an over-the-air digital predistortion optimization algorithm using reinforcement learning. Based on a symbol-based criterion, the algorithm minimizes the errors between downsampled messages at the receiver side. The algorithm does not require any knowledge about the underlying hardware or channel. For a generalized memory polynomial power amplifier and additive white Gaussian noise channel, we show that the proposed algorithm achieves performance improvements in terms of symbol error rate compared with an indirect learning architecture even when the latter is coupled with a full sampling rate ADC in the feedback path. Furthermore, it maintains a satisfactory adjacent channel power ratio.

neural networks (NNs) for multiple hardware impairments mitigation of a realistic direct conversion transmitter are impractical due to high computational complexity. We propose two methods to reduce the complexity without significant performance penalty. First, propose a novel NN with shortcut connections, referred to as shortcut real-valued time-delay neural network (SVDEN), where trainable neuron-wise shortcut connections are added between the input and output layers. Second, we implement a NN pruning algorithm that gradually removes connections corresponding to minimal weight magnitudes in each layer. Simulation and experimental results show that SVDEN with pruning achieves better performance for compensating frequency-dependent quadrature imbalance and power amplifier nonlinearity than other NN-based and Volterra-based models, while requiring less or similar complexity.

We consider a discrete memoryless cloud radio access network in which K users communicate with a remote destination through 2 relays in a cascade. The relays are oblivious in the sense that they operate without knowledge of the users’ codebooks. We focus on a scenario where the first and second relays are connected through a finite-capacity error-free link, while the second relay is connected to the remote destination via an infinite-capacity link. We establish the capacity region in this case, and show that it is achieved via a compress-and-forward scheme with successive decoding. Finally, the extension to Gaussian networks is discussed.

In line-of-sight (LOS) massive MIMO, there is a nonnegligible probability that the channel vectors of some users become correlated. In these correlated scenarios, nonlinear precoders can be used instead of linear precoders at the cost of high computational complexity. To reduce the complexity of nonlinear precoders, hybrid linear and nonlinear precoders have been suggested in 5G New Radio (NR). In this paper, we find the probability that there is at least one pair of correlated users and we find the average number of correlated users. We propose a hybrid linear and nonlinear precoder (HLNP) with max-min power control for which the served users are divided into two groups. By employing a proposed modified Tomlinson-Harashima Precoding (THP), we design and combine the transmit vectors of the two groups such that inter-group interference is removed. Simulation results show that by employing HLNP instead of zero-forcing, the required transmit power to assure a given average block error rate (BLER) with 95% probability is reduced. For a 64-antennas BS, when modified THP is used for 3 out of 10 users in HLNP, the transmit power is reduced by up to 4.70 dB to assure an average BLER of 10−2using 16QAM and 64QAM constellations with NR low-density parity-check codes.

Tracking the nonlinear behavior of an RF power amplifier (PA) is challenging. To tackle this problem, we build a connection between residual learning and the PA nonlinearity, and propose a novel residual neural network structure, referred to as the residual real-valued time-delay neural network (R2TDNN). Instead of learning the whole behavior of the PA, the R2TDNN focuses on learning its nonlinear behavior by adding identity shortcut connections between the input and output layer. In particular, we apply the R2TDNN to digital predistortion and measure experimental results on a real PA. Compared with neural networks recently proposed by Liu et at. and Wang et at., the R2TDNN achieves the best linearization performance in terms of normalized mean square error and adjacent channel power ratio with less or similar computational complexity. Furthermore, the R2TDNN exhibits significantly faster training speed and lower training error.

In this paper, we present a technique to model and linearize a multi-antenna transmitter using only a small set of observation receivers that perform over-the-air measurements. We assume that the transmitter suffers from distortion due to power amplifier (PA) nonlinearities but not from crosstalk. By avoiding the use of an observation receiver in every transmitter branch, the hardware complexity and cost of multi-antenna transmitters can be reduced. First, equations are developed to extract PA models from observation receivers. Based on the extracted PA models, predistorters can then be identified for every transmit branch. We present simulation results that demonstrate that it is indeed possible to model and linearize a set of PAs using only one single observation receiver.

In massive multiple-input-multiple-output base stations, power consumption and cost of the low-noise amplifiers (LNAs) can be substantial because of the many antennas. We investigate the feasibility of inexpensive, power efficient LNAs, which inherently are less linear. A polynomial model is used to characterize the nonlinear LNAs and to derive the second-order statistics and spatial correlation of the distortion. We show that, with spatial matched filtering (maximum-ratio combining) at the receiver, some distortion terms combine coherently, and that the signal-to-interference-and-noise ratio of the symbol estimates therefore is limited by the linearity of the LNAs. Furthermore, it is studied how the power from a blocker in the adjacent frequency band leaks into the main band and creates distortion. The distortion term that scales cubically with the power received from the blocker has a spatial correlation that can be filtered out by spatial processing and only the coherent term that scales quadratically with the power remains. When the blocker is in free-space line-of-sight and the LNAs are identical, this quadratic term has the same spatial direction as the desired signal, and hence cannot be removed by linear receiver processing.

The distortion from massive multiple-input multiple-output base stations with nonlinear amplifiers is studied and its radiation pattern is derived. The distortion is analyzed both in-band and out-of-band. By using an orthogonal Hermite representation of the amplified signal, the spatial cross-correlation matrix of the nonlinear distortion is obtained. It shows that, if the input signal to the amplifiers has a dominant beam, the distortion is beamformed in the same way as that beam. When there are multiple beams without any one being dominant, it is shown that the distortion is practically isotropic. The derived theory is useful to predict how the nonlinear distortion will behave, to analyze the out-of-band radiation, to do reciprocity calibration, and to schedule users in the frequency plane to minimize the effect of in-band distortion.

We investigate the uplink throughput achievable by a multiple-user (MU) massive multiple-input multiple-output (MIMO) system, in which the base station is equipped with a large number of low-resolution analog-to-digital converters (ADCs). Our focus is on the case where neither the transmitter nor the receiver have any a priori channel state information. This implies that the fading realizations have to be learned through pilot transmission followed by channel estimation at the receiver, based on coarsely quantized observations. We propose a novel channel estimator, based on Bussgang's decomposition, and a novel approximation to the rate achievable with finite-resolution ADCs, both for the case of finite-cardinality constellations and of Gaussian inputs, that is accurate for a broad range of system parameters. Through numerical results, we illustrate that, for the 1-bit quantized case, pilot-based channel estimation together with maximal-ratio combing, or zero-forcing detection enables reliable multi-user communication with high-order constellations, in spite of the severe nonlinearity introduced by the ADCs. Furthermore, we show that the rate achievable in the infinite-resolution (no quantization) case can be approached using ADCs with only a few bits of resolution. We finally investigate the robustness of low-ADC-resolution MU-MIMO uplink against receive power imbalances between the different users, caused for example by imperfect power control.

The spatial characteristics of the out-of-band radiation that a multiuser MIMO system emits, due to its power amplifiers (modeled by a polynomial model) being nonlinear, are studied by deriving an analytical expression for the continuous-time cross-correlation of the transmit signals. It is shown that, at any spatial point and on any frequency, the received power averaged over many channel realizations from a MIMO base station is the same as from a SISO base station when the two radiate the same amount of power. For a specific channel realization however, the received power can deviate from this average. We show that the deviations from the average are small in a MIMO system with multiple users and that the deviations can be significant with only one user. Using an ergodicity argument, we conclude that out-of-band radiation is less of a problem in massive MIMO, where precoding and array gain let us reduce the total radiated power compared to SISO systems. The requirements on spectral regrowth can therefore be relaxed in MIMO systems without causing more total out-of-band radiation.