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 pre-compensation 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 to upkeep the same received signal-to-noise ratio.

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.

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.

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(amp;lt;amp;lt; 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.

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.

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 constantenvelope constraints.

Massive MIMO (multiple-input–multiple-output) is a multi-antenna technology for cellular wireless communication, where the base station uses a large number of individually controllable antennas to multiplex users spatially.  This technology can provide a high spectral efficiency.  One of its main challenges is the immense hardware complexity and cost of all the radio chains in the base station.  To make massive MIMO commercially viable, inexpensive, low-complexity hardware with low linearity has to be used, which inherently leads to more signal distortion.  This thesis investigates how the degenerated linearity of some of the main components—power amplifiers, analog-to-digital converters (ADCs) and low-noise amplifiers—affects the performance of the system, with respect to data rate, power consumption and out-of-band radiation. The main results are: Spatial processing can reduce PAR (peak-to-average ratio) of the transmit signals in the downlink to as low as 0B; this, however, does not necessarily reduce power consumption.  In environments with isotropic fading, one-bit ADCs lead to a reduction in effective signal-to-interference-and-noise ratio (SINR) of 4dB in the uplink and four-bit ADCs give a performance close to that of an unquantized system.  An analytical expression for the radiation pattern of the distortion from nonlinear power amplifiers is derived.  It shows how the distortion is beamformed to some extent, that its gain never is greater than that of the desired signal, and that the gain of the distortion is reduced with a higher number of served users and a higher number of channel taps.  Nonlinear low-noise amplifiers give rise to distortion that partly combines coherently and limits the possible SINR.  It is concluded that spatial processing with a large number of antennas reduces the impact of hardware distortion in most cases.  As long as proper attention is paid to the few sources of coherent distortion, the hardware complexity can be reduced in massive MIMO base stations to overcome the hardware challenge and make massive MIMO commercial reality.

Storskaliga fleranvändar-MIMO-system, med hundratals basstationsantenner, studeras med allt större intresse både inom akademin och industrin. En anledning är att sådana system kan betjäna flera enantennsanvändare samtidigt över samma tids-frekvens-resurs med fleranvändarförkodning. Det innebär högre datahastigheter och bättre spektral effektivitet. En annan anledning är att basstationens energiförbrukning förväntas avta linjärt med antalet antenner tack vare den ökade antennförstärkningen. För att möjliggöra den stora ökningen av antalet antenner, måste priset per antenn, med dess sändtagarkedja, vara lågt. Vore det möjligt att tillverka basstationsantenner av billiga, massproducerade mobiltelefonskomponenter, som effektförstärkare utan avancerad linearisering, då skulle storskalig fleranvändar-MIMO kunna bli verklighet.

Effektförstärkare i mobiltelefoner är generellt anpassade att ha hög verkningsgrad och har, i och med detta, kraftigt olinjära överföringsegenskaper. Det är fördelaktigt att sända signaler med lågt toppvärde genom sådana effektförstärkare, för att undvika svår distortion och för att maximera verkningsgraden genom att endast använda en liten avbackning från arbetspunkten. Konventionellt förkodade signaler har tyvärr högt toppvärde (ca. 10 dB). Detta arbete har undersökt en av Mohammed m.fl. (2013a) föreslagen förkodning för storskalig MIMO som resulterar i sändarsignaler med lågt toppvärde. Det visas att denna förkodning ger signaler med ett toppvärde på 4 dB, och att toppvärdet kan göras godtyckligt litet genom att dessutom begränsa fasvariationen. Ju mer fasen begränsas, desto lägre blir emellertid antennförstärkning. Till exempel om fasvariationen begränsas till π/2, sänks toppvärdet till 2,6 dB, men 2-3 dB högre sändareffekt behövs för att bibehålla samma prestanda eller, likvärdigt, så måste basstationen utrustas med 1,6-2,0 gånger fler antenner. Kontinuerlig fasmodulering som ett sätt att få sändarsignaler med konstant envelopp har studerats kort. Lågtoppvärdesförkodning, där sändarsignalerna ligger innanför en cirkel, föreslås som ett sätt att minska den erfodrade sändareffekten utan att öka toppvärdet märkvärt (<4,5 dB) relativt Mohammeds m.fl. förkodning. Förkodningsalgoritmen som utvecklades för detta fastnade dock i lokala minima, vilket försämrade dess prestanda. Sändareffekten kunde därför endast minskas lite grand (<1 dB) vid höga datahastigheter.

En preliminär länkbudget baserad på en enkel effektförstärkarmodell har visat att, med fullständig kanalkännedom och i frekvensplatt fädning, skulle lågtoppvärdesförkodning kunna minska energiförbrukningen med 33 % jämfört med konventionell, linjär förkodning i en basstation med 100 antenner. Analysen antyder att olineariserade klass AB mobiltelefonseffektförstärkare kan vara ett alternativ för storskalig fleranvändar-MIMO-basstationer.