Massive MIMO with Optimal Power and Training Duration Allocation

We consider the uplink of massive multicell multiple-input multiple-output systems, where the base stations (BSs), equipped with massive arrays, serve simultaneously several terminals in the same frequency band. We assume that the BS estimates the channel from uplink training, and then uses the maximum ratio combining technique to detect the signals transmitted from all terminals in its own cell. We propose an optimal resource allocation scheme which jointly selects the training duration, training signal power, and data signal power in order to maximize the sum spectral efficiency, for a given total energy budget spent in a coherence interval. Numerical results verify the benefits of the optimal resource allocation scheme. Furthermore, we show that more training signal power should be used at low signal-to-noise ratio (SNRs), and vice versa at high SNRs. Interestingly, for the entire SNR regime, the optimal training duration is equal to the number of terminals.

Power Scaling of Uplink Massive MIMO Systems with Arbitrary-Rank Channel Means

This paper investigates the uplink achievable rates of massive multiple-input multiple-output (MIMO) antenna systems in Ricean fading channels, using maximal-ratio combining (MRC) and zero-forcing (ZF) receivers, assuming perfect and imperfect channel state information (CSI). In contrast to previous relevant works, the fast fading MIMO channel matrix is assumed to have an arbitrary-rank deterministic component as well as a Rayleigh-distributed random component. We derive tractable expressions for the achievable uplink rate in the large-antenna limit, along with approximating results that hold for any finite number of antennas. Based on these analytical results, we obtain the scaling law that the users' transmit power should satisfy, while maintaining a desirable quality of service. In particular, it is found that regardless of the Ricean K-factor, in the case of perfect CSI, the approximations converge to the same constant value as the exact results, as the number of base station antennas, M, grows large, while the transmit power of each user can be scaled down proportionally to 1/M. If CSI is estimated with uncertainty, the same result holds true but only when the Ricean K-factor is non-zero. Otherwise, if the channel experiences Rayleigh fading, we can only cut the transmit power of each user proportionally to 1/√M. In addition, we show that with an increasing Ricean K-factor, the uplink rates will converge to fixed values for both MRC and ZF receivers.

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 colocated 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 phasedrifts, 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 p N, instead of linearly, by careful circuit-aware system design.

Multipair Full-Duplex Relaying with Massive Arrays and Linear Processing

We consider a multipair decode-and-forward relay channel, where multiple sources transmit simultaneously their signals to multiple destinations with the help of a full-duplex relay station. We assume that the relay station is equipped with massive arrays, while all sources and destinations have a single antenna. The relay station uses channel estimates obtained from received pilots and zero-forcing (ZF) or maximum-ratio combining/maximum-ratio transmission (MRC/MRT) to process the signals. To reduce significantly the loop interference effect, we propose two techniques: i) using a massive receive antenna array; or ii) using a massive transmit antenna array together with very low transmit power at the relay station. We derive an exact achievable rate in closed-form for MRC/MRT processing and an analytical approximation of the achievable rate for ZF processing. This approximation is very tight, especially for large number of relay station antennas. These closed-form expressions enable us to determine the regions where the full-duplex mode outperforms the half-duplex mode, as well as, to design an optimal power allocation scheme. This optimal power allocation scheme aims to maximize the energy efficiency for a given sum spectral efficiency and under peak power constraints at the relay station and sources. Numerical results verify the effectiveness of the optimal power allocation scheme. Furthermore, we show that, by doubling the number of transmit/receive antennas at the relay station, the transmit power of each source and of the relay station can be reduced by 1.5dB if the pilot power is equal to the signal power, and by 3dB if the pilot power is kept fixed, while maintaining a given quality-of-service.

On the MIMO Capacity with Residual Transceiver Hardware Impairments

Radio-frequency (RF) impairments in the transceiver hardware of communication systems (e.g., phase noise (PN), high power amplifier (HPA) nonlinearities, or in-phase/quadrature-phase (I/Q) imbalance) can severely degrade the performance of traditional multiple-input multiple-output (MIMO) systems. Although calibration algorithms can partially compensate these impairments, the remaining distortion still has substantial impact. Despite this, most prior works have not analyzed this type of distortion. In this paper, we investigate the impact of residual transceiver hardware impairments on the MIMO system performance. In particular, we consider a transceiver impairment model, which has been experimentally validated, and derive analytical ergodic capacity expressions for both exact and high signal-to-noise ratios (SNRs). We demonstrate that the capacity saturates in the high-SNR regime, thereby creating a finite capacity ceiling. We also present a linear approximation for the ergodic capacity in the low-SNR regime, and show that impairments have only a second-order impact on the capacity. Furthermore, we analyze the effect of transceiver impairments on large-scale MIMO systems; interestingly, we prove that if one increases the number of antennas at one side only, the capacity behaves similar to the finite-dimensional case. On the contrary, if the number of antennas on both sides increases with a fixed ratio, the capacity ceiling vanishes; thus, impairments cause only a bounded offset in the capacity compared to the ideal transceiver hardware case.

Massive MIMO Systems with Hardware-Constrained Base Stations

Massive multiple-input multiple-output (MIMO) systems are cellular networks where the base stations (BSs) are equipped with unconventionally many antennas. Such large antenna arrays offer huge spatial degrees-of-freedom for transmission optimization; in particular, great signal gains, resilience to imperfect channel knowledge, and small inter-user interference are all achievable without extensive inter-cell coordination. The key to cost-efficient deployment of large arrays is the use of hardware-constrained base stations with low-cost antenna elements, as compared to today's expensive and power-hungry BSs. Low-cost transceivers are prone to hardware imperfections, but it has been conjectured that the excessive degrees-of-freedom of massive MIMO would bring robustness to such imperfections. We herein prove this claim for an uplink channel with multiplicative phase-drift, additive distortion noise, and noise amplification. Specifically, we derive a closed-form scaling law that shows how fast the imperfections increase with the number of antennas.

Impact of Residual Transmit RF Impairments on Training-Based MIMO Systems

Radio-frequency (RF) impairments, which intimately exist in wireless communication systems, can severely limit the performance of multiple-input-multiple-output (MIMO) systems. Although we can resort to compensation schemes to mitigate some of these impairments, a certain amount of residual impairments always persists. In this paper, we consider a training-based point-to-point MIMO system with residual transmit RF impairments (RTRI) using spatial multiplexing transmission. Specifically, we derive a new linear channel estimator for the proposed model, and show that RTRI create an estimation error floor in the high signal-to-noise ratio (SNR) regime. Moreover, we derive closed-form expressions for the signal-to-noise-plus-interference ratio (SINR) distributions, along with analytical expressions for the ergodic achievable rates of zero-forcing, maximum ratio combining, and minimum mean-squared error receivers, respectively. In addition, we optimize the ergodic achievable rates with respect to the training sequence length and demonstrate that finite dimensional systems with RTRI generally require more training at high SNRs than those with ideal hardware. Finally, we extend our analysis to large-scale MIMO configurations, and derive deterministic equivalents of the ergodic achievable rates. It is shown that, by deploying large receive antenna arrays, the extra training requirements due to RTRI can be eliminated. In fact, with a sufficiently large number of receive antennas, systems with RTRI may even need less training than systems with ideal hardware.

Electron-impact rotational excitation of the carbon monosulphide (CS) molecule

Rotational excitation of the carbon monosulphide (CS) molecule by thermal electron-impact is studied using the molecular R-matrix method combined with the adiabatic-nuclei-rotation (ANR) approximation. Rate coefficients are obtained for electron temperatures in the range 5-5000 K and for transitions involving levels up to J = 40. It is confirmed that dipole allowed transitions (Delta J = 1) are dominant and that the corresponding rate coefficients exceed those for excitation by neutrals by at least five orders of magnitude. As a result, the present rates should be included in any detailed population model of CS in sources where the electron fraction is larger than similar to 10(-5), in particular in diffuse molecular clouds and interstellar shocks.

Degradation of carbon disulphide (CS2) in soils and groundwater from a CS2 -contaminated site

This study is the first investigation of biodegradation of carbon disulphide (CS₂) in soil that provides estimates of degradation rates and identifies intermediate degradation products and carbon isotope signatures of degradation. Microcosm studies were undertaken under anaerobic conditions using soil and groundwater recovered from CS₂-contaminated sites. Proposed degradation mechanisms were validated using equilibrium speciation modelling of concentrations and carbon isotope ratios. A first-order degradation rate constant of 1.25 × 10-2 h-1 was obtained for biological degradation with soil. Carbonyl sulphide (COS) and hydrogen sulphide (H₂S) were found to be intermediates of degradation, but did not accumulate in vials. A 13C/12C enrichment factor of -7.5 ± 0.8 ‰ was obtained for degradation within microcosms with both soil and groundwater whereas a 13C/12C enrichment factor of -23.0 ± 2.1 ‰ was obtained for degradation with site groundwater alone. It can be concluded that biological degradation of both CS2-contaminated soil and groundwater is likely to occur in the field suggesting that natural attenuation may be an appropriate remedial tool at some sites. The presence of biodegradation by-products including COS and H₂S indicates that biodegradation of CS₂ is occurring and stable carbon isotopes are a promising tool to quantify CS₂ degradation.

The role of lipids and protein kinase Cs in the pathogenesis of diabetic retinopathy

Diabetic retinopathy is one of the most common complications of diabetes and is a major cause of new blindness in the working-age population of developed countries. While the exact pathogenic basis of this condition remains ill defined, it is clear that hyperglycaemia is a critical factor in its aetiology. Protein kinase C (PKC) activation is one of the sequelae of hyperglycaemia and it is thought to play an important role in the development of diabetic complications. This review questions the currently held dogma that PKC stimulation in diabetes is solely mediated through the overproduction of palmitate and oleate enriched diacylglycerols. Blood glucose concentrations are closely tracked by changes in the levels of free fatty acids and these, in addition to oxidative stress, may account for the aberrant activation of PKCs in diabetes. Little is known about why PKCs fail to downregulate in diabetes and efforts should be directed towards acquiring such information. Considerable evidence implicates the PKCbeta isoform in the pathogenesis of diabetic retinopathy, but other isoforms may also be of relevance. In addition to PKCs, it is evident that novel diacyglycerol-activated non-kinase receptors could also play a role in the development of diabetic complications. Therapeutic agents have been developed to inhibit specific PKC isoforms and PKCbeta antagonists are currently undergoing clinical trials to test their toxicity and efficacy in suppressing diabetic complications. The likely impact of these drugs in the treatment of diabetic patients is considered.