Christopher Mollén

Uplink Performance of Wideband Massive MIMO With One-Bit ADCs

Analog-to-digital converters (ADCs) stand for a significant part of the total power consumption in a massive multiple-input multiple-output (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 orthogonal-frequency-division-multiplexing (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 employ 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.

One-bit ADCs in wideband massive MIMO systems with OFDM transmission

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.

Out-of-band radiation measure for MIMO arrays with beamformed transmission

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.

Waveforms for the Massive MIMO Downlink: Amplifier Efficiency, Distortion and Performance

In massive multiple-input multiple-output (MIMO), most precoders result in downlink signals that suffer from high peak-to-average ratio (PAR), independently of modulation order and whether single-carrier or orthogonal frequency-division multiplexing (OFDM) transmission is used. The high PAR lowers the power efficiency of the base-station amplifiers. To increase the power efficiency, low-PAR precoders have been proposed. In this paper, 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.

Spatial Characteristics of Distortion Radiated From Antenna Arrays With Transceiver Nonlinearities

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.

Achievable uplink rates for massive MIMO with coarse quantization

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-to-digital 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.

Out-of-Band Radiation from Large Antenna Arrays

The OOB radiation from large arrays with nonlinear hardware has a different radiation pattern than the beamformed in-band signal. This is the main difference between the OOB radiation from large arrays and from well-studied legacy systems. Beamforming might focus the OOB radiation in certain directions but also significantly reduce the total power that has to be transmitted. For cost and power-consumption reasons, large arrays might have to be built from low-complexity hardware without advanced precompensation for linearization, which increases the relative amount of OOB radiation. Given that large arrays will be used in future base stations, a correct understanding of the OOB radiation is crucial to specify appropriate linearity requirements for the hardware. We show that the OOB radiation from large arrays varies little between coherence times; it is isotropic in many cases; and when it is beamformed, it is directed toward the served user in a very narrow beam with an array gain equal to or less than that of the in-band signal. We draw the conclusion that, compared to legacy systems, less stringent linearity requirements can be used in many systems with large arrays by virtue of the lower transmit power needed

Multiuser MIMO precoding with per-antenna continuous-time constant-envelope constraints

A transmission scheme for the multiuser MIMO downlink, where the transmit signal from each antenna has constant envelope and a limited bandwidth, is proposed in order to enable the use of highly efficient, nonlinear amplifiers at the base station. To evaluate its performance, an achievable rate is derived and the necessary transmit power of the proposed scheme is computed for a system with 40 antennas that serves 4 users at data rates around 1 bpcu. For this system and 40% excess 30 dB-bandwidth, approximately 3 dB more transmit power is required to achieve the same sum-rate as without the constant-envelope constraints.

Frequency-domain interpolation of the zero-forcing matrix in massive MIMO-OFDM

We consider massive multiple input multiple output (MIMO) systems with orthogonal frequency division multiplexing (OFDM) that use zero-forcing (ZF) to combat interference. To perform ZF, large dimensional pseudo-inverses have to be computed. In this paper, we propose a discrete Fourier transform (DFT)-interpolation-based technique where substantially fewer ZF matrix computations have to be done with very little deterioration in data rate compared to computing an exact ZF matrix for every subcarrier. We claim that it is enough to compute the ZF matrix at L(≪ N) selected subcarriers where L is the number of resolvable multipaths and N is the total number of subcarriers and then interpolate. The proposed technique exploits the fact that in the massive MIMO regime, the ZF impulse response consists of L dominant components. We benchmark the proposed method against full inversion, piecewise constant and linear interpolation methods and show that the proposed method achieves a good tradeoff between performance and complexity.

Performance analysis of (TDD) massive MIMO with Kalman channel prediction

In massive MIMO systems, which rely on uplink pilots to estimate the channel, the time interval between pilot transmissions constrains the length of the downlink. Since switching between up- and downlink takes time, longer downlink blocks increase the effective spectral efficiency. We investigate the use of low-complexity channel models and Kalman filters for channel prediction, to allow for longer intervals between the pilots. Specifically, we quantify how often uplink pilots have to be sent when the downlink rate is allowed to degrade by a certain percentage. To this end, we consider a time-correlated channel aging model, whose spectrum is rectangular, and use autoregressive moving average (ARMA) processes to approximate the time-variations of such channels. We show that ARMA-based predictors can increase the interval between pilots and the spectral efficiency in channels with high Doppler spreads. We also show that Kalman prediction is robust to mismatches in the channel statistics.