Out-of-Band Radiation from Antenna Arrays Clarified

Non-linearities in radio-frequency (RF) transceiver hardware, particularly in power amplifiers, cause distortion in-band and out-of-band. Contrary to claims made in recent literature, in a multiple-antenna system this distortion is correlated across the antennas in the array. A significant implication of this fact is that out-of-band emissions caused by non-linearities are beamformed, in some cases into the same direction as the useful signal.Comment: IEEE Wireless Communications Letters, 2018, to appea

Spatial Characteristics of Distortion Radiated from Antenna Arrays with Transceiver Nonlinearities

The distortion from massive MIMO (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

Impact of Spatial Filtering on Distortion from Low-Noise Amplifiers in Massive MIMO Base Stations

In massive MIMO 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 SINR 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

Channel Estimation in Massive MIMO under Hardware Non-Linearities: Bayesian Methods versus Deep Learning

This paper considers the joint impact of non-linear hardware impairments at the base station (BS) and user equipments (UEs) on the uplink performance of single-cell massive MIMO (multiple-input multiple-output) in practical Rician fading environments. First, Bussgang decomposition-based effective channels and distortion characteristics are analytically derived and the spectral efficiency (SE) achieved by several receivers are explored for third-order non-linearities. Next, two deep feedforward neural networks are designed and trained to estimate the effective channels and the distortion variance at each BS antenna, which are used in signal detection. We compare the performance of the proposed methods with state-of-the-art distortion-aware and -unaware Bayesian linear minimum mean-squared error (LMMSE) estimators. The proposed deep learning approach improves the estimation quality by exploiting impairment characteristics, while LMMSE methods treat distortion as noise. Using the data generated by the derived effective channels for general order of non-linearities at both the BS and UEs, it is shown that the deep learning-based estimator provides better estimates of the effective channels also for non-linearities more than order three.Comment: 14 pages, 10 figures, to appear in IEEE Open Journal of the Communications Societ

Impact of Power Amplifier Nonlinearities in Multi-user Massive MIMO Downlink

In this paper, we investigate the impact of power amplifier (PA) nonlinear distortion in pre-coded multi-user large antenna or massive MIMO downlink systems. First, detailed signal and system models are derived for the received signal at single-antenna user equipment (UE) under channel-aware linear precoding in the base-station combined with behavioral models for the individual PA units, covering both single-carrier and multi-carrier modulation schemes. Based on the derived models, it is shown that the PA induced nonlinear distortion can also combine coherently in the channel, depending on the relative differences between the phase characteristics of the different PA units and the corresponding distortion terms. Furthermore, it is also shown that the impact of nonlinear PAs and the resulting linear and nonlinear multi-user interference, quantified in terms of the received signal-to- interference-plus-noise ratio (SINR), is largely dependent on the effective or observable linear gain in the UE receiver demodulation stage. By observing only the instantaneous direct linear gain, the PA induced nonlinear distortion has a substantial impact on the effective SINR, even if very large number of TX antennas is adopted relative to the number of spatially multiplexed UEs. On the other hand, if the statistically averaged linear gain can be observed, the impact of nonlinear PAs is far less severe. These findings give thus new insight, not only to the core impact of nonlinear PAs in massive MIMO systems but also to the downlink reference signal design, radio frame design and radio resource management in time, in order to facilitate the estimation of the statistically averaged linear gains in the receivers within the scheduled transmission and processing blocks