Capacity of SIMO and MISO Phase-Noise Channels with Common/Separate Oscillators

In multiple antenna systems, phase noise due to instabilities of the radio-frequency (RF) oscillators, acts differently depending on whether the RF circuitries connected to each antenna are driven by separate (independent) local oscillators (SLO) or by a common local oscillator (CLO). In this paper, we investigate the high-SNR capacity of single-input multiple-output (SIMO) and multiple-output single-input (MISO) phase-noise channels for both the CLO and the SLO configurations. Our results show that the first-order term in the high-SNR capacity expansion is the same for all scenarios (SIMO/MISO and SLO/CLO), and equal to $0.5\ln (\rho)$, where $\rho$ stands for the SNR. On the contrary, the second-order term, which we refer to as phase-noise number, turns out to be scenario-dependent. For the SIMO case, the SLO configuration provides a diversity gain, resulting in a larger phase-noise number than for the CLO configuration. For the case of Wiener phase noise, a diversity gain of at least $0.5 \ln(M)$ can be achieved, where $M$ is the number of receive antennas. For the MISO, the CLO configuration yields a higher phase-noise number than the SLO configuration. This is because with the CLO configuration one can obtain a coherent-combining gain through maximum ratio transmission (a.k.a. conjugate beamforming). This gain is unattainable with the SLO configuration.Comment: IEEE Transactions on Communication

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

ML Detection in Phase Noise Impaired SIMO Channels with Uplink Training

The problem of maximum likelihood (ML) detection in training-assisted single-input multiple-output (SIMO) systems with phase noise impairments is studied for two different scenarios, i.e. the case when the channel is deterministic and known (constant channel) and the case when the channel is stochastic and unknown (fading channel). Further, two different operations with respect to the phase noise sources are considered, namely, the case of identical phase noise sources and the case of independent phase noise sources over the antennas. In all scenarios the optimal detector is derived for a very general parametrization of the phase noise distribution. Further, a high signal-to-noise-ratio (SNR) analysis is performed to show that symbol-error-rate (SER) floors appear in all cases. The SER floor in the case of identical phase noise sources (for both constant and fading channels) is independent of the number of antenna elements. In contrast, the SER floor in the case of independent phase noise sources is reduced when increasing the number of antenna elements (for both constant and fading channels). Finally, the system model is extended to multiple data channel uses and it is shown that the conclusions are valid for these setups, as well.Comment: (To appear in IEEE Transactions on Communications, 2015), Contains additional material (Appendix B. T-slot Detectors

Distributed Massive MIMO in Cellular Networks: Impact of Imperfect Hardware and Number of Oscillators

Distributed massive multiple-input multiple-output (MIMO) combines the array gain of coherent MIMO processing with the proximity gains of distributed antenna setups. In this paper, we analyze how transceiver hardware impairments affect the downlink with maximum ratio transmission. We derive closed-form spectral efficiencies expressions and study their asymptotic behavior as the number of the antennas increases. We prove a scaling law on the hardware quality, which reveals that massive MIMO is resilient to additive distortions, while multiplicative phase noise is a limiting factor. It is also better to have separate oscillators at each antenna than one per BS.Comment: First published in the Proceedings of the 23rd European Signal Processing Conference (EUSIPCO-2015) in 2015, published by EURASIP. 5 pages, 3, figure

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 Systems with Non-Ideal Hardware: Energy Efficiency, Estimation, and Capacity Limits

The use of large-scale antenna arrays can bring substantial improvements in energy and/or spectral efficiency to wireless systems due to the greatly improved spatial resolution and array gain. Recent works in the field of massive multiple-input multiple-output (MIMO) show that the user channels decorrelate when the number of antennas at the base stations (BSs) increases, thus strong signal gains are achievable with little inter-user interference. Since these results rely on asymptotics, it is important to investigate whether the conventional system models are reasonable in this asymptotic regime. This paper considers a new system model that incorporates general transceiver hardware impairments at both the BSs (equipped with large antenna arrays) and the single-antenna user equipments (UEs). As opposed to the conventional case of ideal hardware, we show that hardware impairments create finite ceilings on the channel estimation accuracy and on the downlink/uplink capacity of each UE. Surprisingly, the capacity is mainly limited by the hardware at the UE, while the impact of impairments in the large-scale arrays vanishes asymptotically and inter-user interference (in particular, pilot contamination) becomes negligible. Furthermore, we prove that the huge degrees of freedom offered by massive MIMO can be used to reduce the transmit power and/or to tolerate larger hardware impairments, which allows for the use of inexpensive and energy-efficient antenna elements.Comment: To appear in IEEE Transactions on Information Theory, 28 pages, 15 figures. The results can be reproduced using the following Matlab code: https://github.com/emilbjornson/massive-MIMO-hardware-impairment

Information-theoretic analysis of MIMO channel sounding

The large majority of commercially available multiple-input multiple-output (MIMO) radio channel measurement devices (sounders) is based on time-division multiplexed switching (TDMS) of a single transmit/receive radio-frequency chain into the elements of a transmit/receive antenna array. While being cost-effective, such a solution can cause significant measurement errors due to phase noise and frequency offset in the local oscillators. In this paper, we systematically analyze the resulting errors and show that, in practice, overestimation of channel capacity by several hundred percent can occur. Overestimation is caused by phase noise (and to a lesser extent frequency offset) leading to an increase of the MIMO channel rank. Our analysis furthermore reveals that the impact of phase errors is, in general, most pronounced if the physical channel has low rank (typical for line-of-sight or poor scattering scenarios). The extreme case of a rank-1 physical channel is analyzed in detail. Finally, we present measurement results obtained from a commercially employed TDMS-based MIMO channel sounder. In the light of the findings of this paper, the results obtained through MIMO channel measurement campaigns using TDMS-based channel sounders should be interpreted with great care.Comment: 99 pages, 14 figures, submitted to IEEE Transactions on Information Theor