Uplink Performance of Time-Reversal MRC in Massive MIMO Systems Subject to Phase Noise

Multi-user multiple-input multiple-output (MU-MIMO) cellular systems with an excess of base station (BS) antennas (Massive MIMO) offer unprecedented multiplexing gains and radiated energy efficiency. Oscillator phase noise is introduced in the transmitter and receiver radio frequency chains and severely degrades the performance of communication systems. We study the effect of oscillator phase noise in frequency-selective Massive MIMO systems with imperfect channel state information (CSI). In particular, we consider two distinct operation modes, namely when the phase noise processes at the $M$ BS antennas are identical (synchronous operation) and when they are independent (non-synchronous operation). We analyze a linear and low-complexity time-reversal maximum-ratio combining (TR-MRC) reception strategy. For both operation modes we derive a lower bound on the sum-capacity and we compare their performance. Based on the derived achievable sum-rates, we show that with the proposed receive processing an $O(\sqrt{M})$ array gain is achievable. Due to the phase noise drift the estimated effective channel becomes progressively outdated. Therefore, phase noise effectively limits the length of the interval used for data transmission and the number of scheduled users. The derived achievable rates provide insights into the optimum choice of the data interval length and the number of scheduled users.Comment: 13 pages, 6 figures, 2 tables, IEEE Transactions on Wireless Communications (accepted

Massive MIMO with Non-Ideal Arbitrary Arrays: Hardware Scaling Laws and Circuit-Aware Design

Massive multiple-input multiple-output (MIMO) systems are cellular networks where the base stations (BSs) are equipped with unconventionally many antennas, deployed on co-located or distributed arrays. Huge spatial degrees-of-freedom are achieved by coherent processing over these massive arrays, which provide strong signal gains, resilience to imperfect channel knowledge, and low interference. This comes at the price of more infrastructure; the hardware cost and circuit power consumption scale linearly/affinely with the number of BS antennas $N$. Hence, the key to cost-efficient deployment of large arrays is low-cost antenna branches with low circuit power, in contrast to today's conventional expensive and power-hungry BS antenna branches. Such low-cost transceivers are prone to hardware imperfections, but it has been conjectured that the huge degrees-of-freedom would bring robustness to such imperfections. We prove this claim for a generalized uplink system with multiplicative phase-drifts, additive distortion noise, and noise amplification. Specifically, we derive closed-form expressions for the user rates and a scaling law that shows how fast the hardware imperfections can increase with $N$ while maintaining high rates. The connection between this scaling law and the power consumption of different transceiver circuits is rigorously exemplified. This reveals that one can make the circuit power increase as $\sqrt{N}$, instead of linearly, by careful circuit-aware system design.Comment: Accepted for publication in IEEE Transactions on Wireless Communications, 16 pages, 8 figures. The results can be reproduced using the following Matlab code: https://github.com/emilbjornson/hardware-scaling-law

Receiver Algorithm based on Differential Signaling for SIMO Phase Noise Channels with Common and Separate Oscillator Configurations

In this paper, a receiver algorithm consisting of differential transmission and a two-stage detection for a single-input multiple-output (SIMO) phase-noise channels is studied. Specifically, the phases of the QAM modulated data symbols are manipulated before transmission in order to make them more immune to the random rotational effects of phase noise. At the receiver, a two-stage detector is implemented, which first detects the amplitude of the transmitted symbols from a nonlinear combination of the received signal amplitudes. Then in the second stage, the detector performs phase detection. The studied signaling method does not require transmission of any known symbols that act as pilots. Furthermore, no phase noise estimator (or a tracker) is needed at the receiver to compensate the effect of phase noise. This considerably reduces the complexity of the receiver structure. Moreover, it is observed that the studied algorithm can be used for the setups where a common local oscillator or separate independent oscillators drive the radio-frequency circuitries connected to each antenna. Due to the differential encoding/decoding of the phase, weighted averaging can be employed at a multi-antenna receiver, allowing for phase noise suppression to leverage the large number of antennas. Hence, we observe that the performance improves by increasing the number of antennas, especially in the separate oscillator case. Further increasing the number of receive antennas results in a performance error floor, which is a function of the quality of the oscillator at the transmitter.Comment: IEEE GLOBECOM 201

EM-Based Estimation and Compensation of Phase Noise in Massive-MIMO Uplink Communications

Phase noise (PN) is a major disturbance in MIMO systems, where the contribution of different oscillators at the transmitter and the receiver side may degrade the overall performance and offset the gains offered by MIMO techniques. This is even more crucial in the case of massive MIMO, since the number of PN sources may increase considerably. In this work, we propose an iterative receiver based on the application of the expectation-maximization algorithm. We consider a massive MIMO framework with a general association of oscillators to antennas, and include other channel disturbances like imperfect channel state information and Rician block fading. At each receiver iteration, given the information on the transmitted symbols, steepest descent is used to estimate the PN samples, with an optimized adaptive step size and a threshold-based stopping rule. The results obtained for several test cases show how the bit error rate and mean square error can benefit from the proposed phase-detection algorithm, even to the point of reaching the same performance as in the case where no PN is present{\color{black}, offering better results than a state-of-the-art alternative}. Further analysis of the results allow to draw some useful trade-offs respecting final performance and consumption of resources.Comment: Submitted to IEEE Transactions on Communication

Reciprocity Calibration for Massive MIMO: Proposal, Modeling and Validation

This paper presents a mutual coupling based calibration method for time-division-duplex massive MIMO systems, which enables downlink precoding based on uplink channel estimates. The entire calibration procedure is carried out solely at the base station (BS) side by sounding all BS antenna pairs. An Expectation-Maximization (EM) algorithm is derived, which processes the measured channels in order to estimate calibration coefficients. The EM algorithm outperforms current state-of-the-art narrow-band calibration schemes in a mean squared error (MSE) and sum-rate capacity sense. Like its predecessors, the EM algorithm is general in the sense that it is not only suitable to calibrate a co-located massive MIMO BS, but also very suitable for calibrating multiple BSs in distributed MIMO systems. The proposed method is validated with experimental evidence obtained from a massive MIMO testbed. In addition, we address the estimated narrow-band calibration coefficients as a stochastic process across frequency, and study the subspace of this process based on measurement data. With the insights of this study, we propose an estimator which exploits the structure of the process in order to reduce the calibration error across frequency. A model for the calibration error is also proposed based on the asymptotic properties of the estimator, and is validated with measurement results.Comment: Submitted to IEEE Transactions on Wireless Communications, 21/Feb/201

On the Impact of Phase Noise in Communication Systems –- Performance Analysis and Algorithms

The mobile industry is preparing to scale up the network capacity by a factor of 1000x in order to cope with the staggering growth in mobile traffic. As a consequence, there is a tremendous pressure on the network infrastructure, where more cost-effective, flexible, high speed connectivity solutions are being sought for. In this regard, massive multiple-input multiple-output (MIMO) systems, and millimeter-wave communication systems are new physical layer technologies, which promise to facilitate the 1000 fold increase in network capacity. However, these technologies are extremely prone to hardware impairments like phase noise caused by noisy oscillators. Furthermore, wireless backhaul networks are an effective solution to transport data by using high-order signal constellations, which are also susceptible to phase noise impairments. Analyzing the performance of wireless communication systems impaired by oscillator phase noise, and designing systems to operate efficiently in strong phase noise conditions are critical problems in communication theory. The criticality of these problems is accentuated with the growing interest in new physical layer technologies, and the deployment of wireless backhaul networks. This forms the main motivation for this thesis where we analyze the impact of phase noise on the system performance, and we also design algorithms in order to mitigate phase noise and its effects. First, we address the problem of maximum a posteriori (MAP) detection of data in the presence of strong phase noise in single-antenna systems. This is achieved by designing a low-complexity joint phase-estimator data-detector. We show that the proposed method outperforms existing detectors, especially when high order signal constellations are used. Then, in order to further improve system performance, we consider the problem of optimizing signal constellations for transmission over channels impaired by phase noise. Specifically, we design signal constellations such that the error rate performance of the system is minimized, and the information rate of the system is maximized. We observe that these optimized constellations significantly improve the system performance, when compared to conventional constellations, and those proposed in the literature. Next, we derive the MAP symbol detector for a MIMO system where each antenna at the transceiver has its own oscillator. We propose three suboptimal, low-complexity algorithms for approximately implementing the MAP symbol detector, which involve joint phase noise estimation and data detection. We observe that the proposed techniques significantly outperform the other algorithms in prior works. Finally, we study the impact of phase noise on the performance of a massive MIMO system, where we analyze both uplink and downlink performances. Based on rigorous analyses of the achievable rates, we provide interesting insights for the following question: how should oscillators be connected to the antennas at a base station, which employs a large number of antennas