Abstract-Analog-to-digital converters (ADCs) stand for a significant part of the total power consumption in a massive MIMO base station. One-bit ADCs are one way to reduce power consumption. This paper presents an analysis of the spectral efficiency of single-carrier and OFDM transmission in massive MIMO systems that use one-bit ADCs. A closed-form achievable rate, i.e., a lower bound on capacity, is derived for a wideband system with a large number of channel taps that employs low-complexity linear channel estimation and symbol detection. Quantization results in two types of error in the symbol detection. The circularly symmetric error becomes Gaussian in massive MIMO and vanishes as the number of antennas grows. The amplitude distortion, which severely degrades the performance of OFDM, is caused by variations between symbol durations in received interference energy. As the number of channel taps grows, the amplitude distortion vanishes and OFDM has the same performance as single-carrier transmission. A main conclusion of this paper is that wideband massive MIMO systems work well with one-bit ADCs.

Abstract-In massive MIMO, most precoders result in downlink signals that suffer from high PAR, independently of modulation order and whether single-carrier or OFDM transmission is used. The high PAR lowers the power efficiency of the base station amplifiers. To increase power efficiency, low-PAR precoders have been proposed. In this article, we compare different transmission methods for massive MIMO in terms of the power consumed by the amplifiers. It is found that: 1) OFDM and single-carrier transmission have the same performance over a hardened massive MIMO channel and 2) when the higher amplifier power efficiency of low-PAR precoding is taken into account, conventional and low-PAR precoders lead to approximately the same power consumption. Since downlink signals with low PAR allow for simpler and cheaper hardware, than signals with high PAR, therefore, the results suggest that low-PAR precoding with either single-carrier or OFDM transmission should be used in a massive MIMO base station.

Massive multiple-input-multiple-output (MIMO) systems can suffer from coherent intercell interference due to the phenomenon of pilot contamination. This paper investigates a two-layer decoding method that mitigates both coherent and non-coherent interference in multi-cell Massive MIMO. To this end, each base station (BS) first estimates the channels to intracell users using either minimum mean-squared error (MMSE) or element-wise MMSE (EW-MMSE) estimation based on uplink pilots. The estimates are used for local decoding on each BS followed by a second decoding layer where the BSs cooperate to mitigate inter-cell interference. An uplink achievable spectral efficiency (SE) expression is computed for arbitrary two-layer decoding schemes. A closed-form expression is then obtained for correlated Rayleigh fading, maximum-ratio combining, and the proposed large-scale fading decoding (LSFD) in the second layer. We also formulate a sum SE maximization problem with both the data power and LSFD vectors as optimization variables. Since this is an NP-hard problem, we develop a low-complexity algorithm based on the weighted MMSE approach to obtain a local optimum. The numerical results show that both data power control and LSFD improve the sum SE performance over singlelayer decoding multi-cell Massive MIMO systems.

The distortion from massive MIMO (multiple-inputmultiple-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 crosscorrelation 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.

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.

We investigate the performance of wideband massive MIMO base stations that use one-bit ADCs for quantizing the uplink signal. Our main result is to show that the many taps of the frequency-selective channel make linear combiners asymptotically consistent and the quantization noise additive and Gaussian, which simplifies signal processing and enables the straightforward use of OFDM. We also find that single-carrier systems and OFDM systems are affected in the same way by one-bit quantizers in wideband systems because the distribution of the quantization noise becomes the same in both systems as the number of channel taps grows.

The high hardware complexity of a massive mimo base station, which requires hundreds of radio chains, makes it challenging to build commercially. One way to reduce the hardware complexity and power consumption of the receiver is to lower the resolution of the analog-todigital converters (adcs). We derive an achievable rate for a massive mimo system with arbitrary quantization and use this rate to show that adcs with as low as 3 bits can be used without significant performance loss at spectral efficiencies around 3.5 bpcu per user, also under interference from stronger transmitters and with some imperfections in the automatic gain control.

Co-existing wireless systems, which share a common spectrum, need to mitigate out-of-band (OOB) radiation to avoid excessive interference. For legacy systems, OOB radiation is well understood and is commonly handled by digital precompensation techniques. When using large arrays, however, new phenomena and hardware limitations have to be considered. First, signals can be radiated directionally, which might focus the OOB radiation. Second, low-complexity hardware is used for cost reasons, which increases the relative amount of OOB radiation. Given that massive MIMO and millimeter wave communication rely on base stations with a large number of antennas, the spatial behavior of OOB radiation from large arrays will have significant implications for the hardware requirements of future base stations. We show that, if the OOB radiation is beamformed, its array gain is never larger than that of the in-band signal. In many cases, the OOB radiation is close to isotropic even when the in-band signal is highly directive. With the same total radiated power, the OOB radiation from large arrays is therefore never more severe than from a legacy system with the same adjacent-channel-leakage ratio. Further, the OOB radiation is less detrimental than from a legacy system since the high array gain of the in-band signal allows large arrays to radiate less total power than legacy systems. We also show how OOB radiation from large arrays varies with location in static propagation environments and how these effects vanish when averaged over the small-scale fading. Since a higher relative amount of OOB radiation can be tolerated for large arrays, the linearity requirement can be relaxed as compared to legacy systems. Specifically, less stringent linearity requirements on each transmitter makes it possible to build large arrays from low-complexity hardware.This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.