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.

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.

Space-Constrained Massive MIMO: Hitting the Wall of Favorable Propagation

The recent development of the massive multiple-input multiple-output (MIMO) paradigm, has been extensively based on the pursuit of favorable propagation: in the asymptotic limit, the channel vectors become nearly orthogonal and interuser interference tends to zero [1]. In this context, previous studies
have considered fixed inter-antenna distance, which implies an increasing array aperture as the number of elements increases. Here, we focus on a practical, space-constrained topology, where an increase in the number of antenna elements in a fixed total space imposes an inversely proportional decrease in the inter-antenna distance. Our analysis shows that, contrary to existing studies, inter-user interference does not vanish in the massive MIMO regime, thereby creating a saturation effect on the achievable rate.

Interacting supernovae and supernova impostors. SN 2007sv: the major eruption of a massive star in UGC 5979

We report the results of the photometric and spectroscopic monitoring campaign of the transient SN 2007sv. The observables are similar to those of Type IIn supernovae, a well-known class of objects whose ejecta interact with pre-existing circumstellar material (CSM). The spectra show a blue continuum at early phases and prominent Balmer lines in emission; however, the absolute magnitude at the discovery of SN 2007sv (M-R=-14.25 +/- 0.38) indicate it to be most likely a supernova impostor. This classification is also supported by the lack of evidence in the spectra of very high velocity material as expected in supernova ejecta. In addition, we find no unequivocal evidence of broad lines of alpha- and/or Fe-peak elements. The comparison with the absolute light curves of other interacting objects (including Type IIn supernovae) highlights the overall similarity with the prototypical impostor SN 1997bs. This supports our claim that SN 2007sv was not a genuine supernova, and was instead a supernova impostor, most likely similar to the major eruption of a luminous blue variable.

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.

Massive stars exploding in a He-rich circumstellar medium - VI. Observations of two distant Type Ibn supernova candidates discovered by La Silla-QUEST

We present optical observations of the peculiar stripped-envelope supernovae (SNe) LSQ12btw and LSQ13ccw discovered by the La Silla-QUEST survey. LSQ12btw reaches an absolute peak magnitude of M-g = -19.3 +/- 0.2, and shows an asymmetric light curve. Stringent pre-discovery limits constrain its rise time to maximum light to less than 4 d, with a slower post-peak luminosity decline, similar to that experienced by the prototypical SN Ibn 2006jc. LSQ13ccw is somewhat different: while it also exhibits a very fast rise to maximum, it reaches a fainter absolute peak magnitude (M-g =-18.4 +/- 0.2), and experiences an extremely rapid post-peak decline similar to that observed in the peculiar SN Ib 2002bj. A stringent pre-discovery limit and an early marginal detection of LSQ13ccw allow us to determine the explosion time with an uncertainty of +/- 1 d. The spectra of LSQ12btw show the typical narrow He I emission lines characterizing Type Ibn SNe, suggesting that the SN ejecta are interacting with He-rich circumstellar material. The He I lines in the spectra of LSQ13ccw exhibit weak narrow emissions superposed on broad components. An unresolved H alpha line is also detected, suggesting a tentative Type Ibn/IIn classification. As for other SNe Ibn, we argue that LSQ12btw and LSQ13ccw likely result from the explosions of Wolf-Rayet stars that experienced instability phases prior to core collapse. We inspect the host galaxies of SNe Ibn, and we show that all of them but one are hosted in spiral galaxies, likely in environments spanning a wide metallicity range.

Massive stars exploding in a He-rich circumstellar medium - V. Observations of the slow-evolving SN Ibn OGLE-2012-SN-006

We present optical observations of the peculiar Type Ibn supernova (SN Ibn) OGLE-2012-SN-006, discovered and monitored by the Optical Gravitational Lensing Experiment-IV survey, and spectroscopically followed by Public ESO Spectroscopic Survey of Transient Objects (PESSTO) at late phases. Stringent pre-discovery limits constrain the explosion epoch with fair precision to JD = 245 6203.8 +/- 4.0. The rise time to the I-band light-curve maximum is about two weeks. The object reaches the peak absolute magnitude M-I = -19.65 +/- 0.19 on JD = 245 6218.1 +/- 1.8. After maximum, the light curve declines for about 25 d with a rate of 4 mag (100 d)(-1). The symmetric I-band peak resembles that of canonical Type Ib/c supernovae (SNe), whereas SNe Ibn usually exhibit asymmetric and narrower early-time light curves. Since 25 d past maximum, the light curve flattens with a decline rate slower than that of the Co-56-Fe-56 decay, although at very late phases it steepens to approach that rate. However, other observables suggest that the match with the Co-56 decay rate is a mere coincidence, and the radioactive decay is not the main mechanism powering the light curve of OGLE-2012-SN-006. An early-time spectrum is dominated by a blue continuum, with only a marginal evidence for the presence of He I lines marking this SN type. This spectrum shows broad absorptions bluewards than 5000 angstrom, likely O II lines, which are similar to spectral features observed in superluminous SNe at early epochs. The object has been spectroscopically monitored by PESSTO from 90 to 180 d after peak, and these spectra show the typical features observed in a number of SN 2006jc-like events, including a blue spectral energy distribution and prominent and narrow (v(FWHM) approximate to 1900 km s(-1)) He I emission lines. This suggests that the ejecta are interacting with He-rich circumstellar material. The detection of broad (10(4) km s(-1)) O I and Ca II features likely produced in the SN ejecta (including the [OI] lambda lambda 6300,6364 doublet in the latest spectra) lends support to the interpretation of OGLE-2012-SN-006 as a core-collapse event.

Massive stars exploding in a He-rich circumstellar medium - IV. Transitional Type Ibn supernovae

We present ultraviolet, optical and near-infrared data of the Type Ibn supernovae (SNe) 2010al and 2011hw. SN 2010al reaches an absolute magnitude at peak of M-R = -18.86 +/- 0.21. Its early light curve shows similarities with normal SNe Ib, with a rise to maximum slower than most SNe Ibn. The spectra are dominated by a blue continuum at early stages, with narrow P-Cygni He I lines indicating the presence of a slow-moving, He-rich circumstellar medium. At later epochs, the spectra well match those of the prototypical SN Ibn 2006jc, although the broader lines suggest that a significant amount of He was still present in the stellar envelope at the time of the explosion. SN 2011hw is somewhat different. It was discovered after the first maximum, but the light curve shows a double peak. The absolute magnitude at discovery is similar to that of the second peak (M-R = -18.59 +/- 0.25), and slightly fainter than the average of SNe Ibn. Though the spectra of SN 2011hw are similar to those of SN 2006jc, coronal lines and narrow Balmer lines are clearly detected. This indicates substantial interaction of the SN ejecta with He-rich, but not H-free, circumstellar material. The spectra of SN 2011hw suggest that it is a transitional SN Ibn/IIn event similar to SN 2005la. While for SN 2010al the spectrophotometric evolution favours a H-deprived Wolf-Rayet progenitor (of WN-type), we agree with the conclusion of Smith et al. that the precursor of SN 2011hw was likely in transition from a luminous blue variable to an early Wolf-Rayet (Ofpe/WN9) stage.

The death of massive stars - II. Observational constraints on the progenitors of Type Ibc supernovae

The progenitors of many Type II core-collapse supernovae (SNe) have now been identified directly on pre-discovery imaging. Here, we present an extensive search for the progenitors of Type Ibc SNe in all available pre-discovery imaging since 1998. There are 12 Type Ibc SNe with no detections of progenitors in either deep ground-based or Hubble Space Telescope archival imaging. The deepest absolute BVR magnitude limits are between -4 and - 5 mag. We compare these limits with the observed Wolf-Rayet population in the Large Magellanic Cloud and estimate a 16 per cent probability that we have failed to detect such a progenitor by chance. Alternatively, the progenitors evolve significantly before core-collapse or we have underestimated the extinction towards the progenitors. Reviewing the relative rates and ejecta mass estimates from light-curve modelling of Ibc SNe, we find both incompatible with Wolf-Rayet stars with initial masses >25 M⊙ being the only progenitors. We present binary evolution models that fit these observational constraints. Stars in binaries with initial masses ≲ 20 M⊙ lose their hydrogen envelopes in binary interactions to become low-mass helium stars. They retain a low-mass hydrogen envelope until ≈104 yr before core-collapse; hence, it is not surprising that Galactic analogues have been difficult to identify.

Self-regulated Shocks in Massive Star Binary Systems

In an early-type, massive star binary system, X-ray bright shocks result from the powerful collision of stellar winds driven by radiation pressure on spectral line transitions. We examine the influence of the X-rays from the wind-wind collision shocks on the radiative driving of the stellar winds using steady-state models that include a parameterized line force with X-ray ionization dependence. Our primary result is that X-ray radiation from the shocks inhibits wind acceleration and can lead to a lower pre-shock velocity, and a correspondingly lower shocked plasma temperature, yet the intrinsic X-ray luminosity of the shocks, L X, remains largely unaltered, with the exception of a modest increase at small binary separations. Due to the feedback loop between the ionizing X-rays from the shocks and the wind driving, we term this scenario as self-regulated shocks. This effect is found to greatly increase the range of binary separations at which a wind-photosphere collision is likely to occur in systems where the momenta of the two winds are significantly different. Furthermore, the excessive levels of X-ray ionization close to the shocks completely suppress the line force, and we suggest that this may render radiative braking less effective. Comparisons of model results against observations reveal reasonable agreement in terms of log (L X/L bol). The inclusion of self-regulated shocks improves the match for kT values in roughly equal wind momenta systems, but there is a systematic offset for systems with unequal wind momenta (if considered to be a wind-photosphere collision).

Sum-Rate and Power Scaling of Massive MIMO Systems with Channel Aging

This paper investigates the achievable sum-rate of massive multiple-input multiple-output (MIMO) systems in the presence of channel aging. For the uplink, by assuming that the base station (BS) deploys maximum ratio combining (MRC) or zero-forcing (ZF) receivers, we present tight closed-form lower bounds on the achievable sum-rate for both receivers with aged channel state information (CSI). In addition, the benefit of implementing channel prediction methods on the sum-rate is examined, and closed-form sum rate lower bounds are derived. Moreover, the impact of channel aging and channel prediction on the power scaling law is characterized. Extension to the downlink scenario and multi-cell scenario are also considered. It is found that, for a system with/without channel prediction, the transmit power of each user can be scaled down at most by 1= p M (where M is the number of BS antennas), which indicates that aged CSI does not degrade the power scaling law, and channel prediction does not enhance the power scaling law; instead, these phenomena affect the achievable sum-rate by degrading or enhancing the effective signal to interference and noise ratio, respectively.

A Tractable Approach to Uplink Spectral Efficiency of Two-Tier Massive MIMO Cellular HetNets

This letter investigates the uplink spectral efficiency (SE) of a two-tier cellular network, where massive multiple-input multiple-output macro base stations are overlaid with dense small cells. Macro user equipments (MUEs) and small cells with single user equipment uniformly scattered are modeled as two independent homogeneous Poisson point processes. By applying stochastic geometry, we analyze the SE of the multiuser uplink at a macro base station that employs a zero-forcing detector and we obtain a novel lower bound as well as its approximation. According to the simple and near-exact analytical expression, we observe that the ideal way to improve the SE is by increasing the MUE density and the base station antennas synchronously rather than increasing them individually. Furthermore, a large value of path loss exponent has a positive effect on the SE due to the reduced aggregated interference.

Cell Coverage Optimization for the Multicell Massive MIMO Uplink

We investigate the cell coverage optimization problem for the massive multiple-input multiple-output (MIMO) uplink. By deploying tilt-adjustable antenna arrays at the base stations, cell coverage optimization can become a promising technique which is able to strike a compromise between covering cell-edge users and pilot contamination suppression. We formulate a detailed description of this optimization problem by maximizing the cell throughput, which is shown to be mainly determined by the user distribution within several key geometrical regions. Then, the formulated problem is applied to different example scenarios: for a network with hexagonal shaped cells and uniformly distributed users, we derive an analytical lower bound of the ergodic throughput in the objective cell, based on which, it is shown that the optimal choice for the cell coverage should ensure that the coverage of different cells does not overlap; for a more generic network with sectoral shaped cells and non-uniformly distributed users, we propose an analytical approximation of the ergodic throughput. After that, a practical coverage optimization algorithm is proposed, where the optimal solution can be easily obtained through a simple one-dimensional line searching within a confined searching region. Our numerical results show that the proposed coverage optimization method is able to greatly increase the system throughput in macrocells for the massive MIMO uplink transmission, compared with the traditional schemes where the cell coverage is fixed.