Asymptotic Performance of Linear Receivers in MIMO Fading Channels

Linear receivers are an attractive low-complexity alternative to optimal processing for multi-antenna MIMO communications. In this paper we characterize the information-theoretic performance of MIMO linear receivers in two different asymptotic regimes. For fixed number of antennas, we investigate the limit of error probability in the high-SNR regime in terms of the Diversity-Multiplexing Tradeoff (DMT). Following this, we characterize the error probability for fixed SNR in the regime of large (but finite) number of antennas. As far as the DMT is concerned, we report a negative result: we show that both linear Zero-Forcing (ZF) and linear Minimum Mean-Square Error (MMSE) receivers achieve the same DMT, which is largely suboptimal even in the case where outer coding and decoding is performed across the antennas. We also provide an approximate quantitative analysis of the markedly different behavior of the MMSE and ZF receivers at finite rate and non-asymptotic SNR, and show that while the ZF receiver achieves poor diversity at any finite rate, the MMSE receiver error curve slope flattens out progressively, as the coding rate increases. When SNR is fixed and the number of antennas becomes large, we show that the mutual information at the output of a MMSE or ZF linear receiver has fluctuations that converge in distribution to a Gaussian random variable, whose mean and variance can be characterized in closed form. This analysis extends to the linear receiver case a well-known result previously obtained for the optimal receiver. Simulations reveal that the asymptotic analysis captures accurately the outage behavior of systems even with a moderate number of antennas.Comment: 48 pages, Submitted to IEEE Transactions on Information Theor

Living at the Edge: A Large Deviations Approach to the Outage MIMO Capacity

Using a large deviations approach we calculate the probability distribution of the mutual information of MIMO channels in the limit of large antenna numbers. In contrast to previous methods that only focused at the distribution close to its mean (thus obtaining an asymptotically Gaussian distribution), we calculate the full distribution, including its tails which strongly deviate from the Gaussian behavior near the mean. The resulting distribution interpolates seamlessly between the Gaussian approximation for rates $R$ close to the ergodic value of the mutual information and the approach of Zheng and Tse for large signal to noise ratios $\rho$. This calculation provides us with a tool to obtain outage probabilities analytically at any point in the $(R, \rho, N)$ parameter space, as long as the number of antennas $N$ is not too small. In addition, this method also yields the probability distribution of eigenvalues constrained in the subspace where the mutual information per antenna is fixed to $R$ for a given $\rho$. Quite remarkably, this eigenvalue density is of the form of the Marcenko-Pastur distribution with square-root singularities, and it depends on the values of $R$ and $\rho$.Comment: Accepted for publication, IEEE Transactions on Information Theory (2010). Part of this work appears in the Proc. IEEE Information Theory Workshop, June 2009, Volos, Greec

Absorption spectra of Q 0000-263 and Q 1442+101

Studying the Lyman-alpha forest allows us to trace the cosmological distribution of matter through time, and may reveal insights into important questions such as the onset of galaxy formation. An equation for determining the number of Lyman-alpha absorption lines per redshift per rest equivalent in the Lyman-alpha forest is given. For a nonevolving population of clouds gamma = 1 for q(sub 0) = 0, and gamma = 0.5 for q(sub 0) = 0.5. A detailed study of the Lyman-alpha forests of Q 1442+101 at z(sub em) = 3.54 and Q 0000-263 at z(sub em) = 4.11

A big-data spatial, temporal and network analysis of bovine tuberculosis between wildlife (badgers) and cattle

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Colors and K-Band Counts of Extremely Faint Field Galaxies

We combine deep K-band (Keck) with V- and I-band (NTT) observations of two high-Galactic latitude fields, surveying a total of ~2 sq. arcmin. The K-band galaxy counts continue to rise above K=22, reaching surface densities of few x 10^5 per sq. degree. The slope for the counts is (d log(N) per mag per sq. degree) = 0.23 +/- 0.02 between K=18-23, consistent with other deep K surveys. The numbers of galaxies in each mag bin is about two times greater than the galaxy counts of Djorgovski et al. (1995). The optical and near infrared magnitudes of all objects detected in the V+I+K image are discussed in the context of grids of isochrone synthesis galaxy evolutionary models (Bruzual & Charlot 1993, 1995). The colors of most of the observed galaxies are consistent with a population drawn from a broad redshift distribution. A few galaxies at K=19-20 are red in both colors (V-I>3; I-K>2), consistent with being early-type galaxies having undergone a burst of star formation at z>5 and viewed at z~1. At K>20, we find ~8 ``red outlier'' galaxies with I-K>4 and V-I<2.5, whose colors are difficult to mimic by a single evolving or non-evolving stellar population at any redshift. They are likely either low-metallicity, dusty dwarf galaxies, or old galaxies at high redshift (z>1.2). Their surface density is several per square arcminute, which is so high that they are probably common objects of low luminosity $L<L_*$.Comment: 28 pages, 9 Figures (2 Plates), uses aaspp4.sty. The complete paper (including large figures and the plates) are available via anonymous ftp at ftp://coma.berkeley.edu/pub/lmoustakas/ . To appear in the Astrophysical Journal, Feb 1 1997, vol. 47

A Dark Census: Statistically Detecting the Satellite Populations of Distant Galaxies

In the standard structure formation scenario based on the cold dark matter paradigm, galactic halos are predicted to contain a large population of dark matter subhalos. While the most massive members of the subhalo population can appear as luminous satellites and be detected in optical surveys, establishing the existence of the low mass and mostly dark subhalos has proven to be a daunting task. Galaxy-scale strong gravitational lenses have been successfully used to study mass substructures lying close to lensed images of bright background sources. However, in typical galaxy-scale lenses, the strong lensing region only covers a small projected area of the lens's dark matter halo, implying that the vast majority of subhalos cannot be directly detected in lensing observations. In this paper, we point out that this large population of dark satellites can collectively affect gravitational lensing observables, hence possibly allowing their statistical detection. Focusing on the region of the galactic halo outside the strong lensing area, we compute from first principles the statistical properties of perturbations to the gravitational time delay and position of lensed images in the presence of a mass substructure population. We find that in the standard cosmological scenario, the statistics of these lensing observables are well approximated by Gaussian distributions. The formalism developed as part of this calculation is very general and can be applied to any halo geometry and choice of subhalo mass function. Our results significantly reduce the computational cost of including a large substructure population in lens models and enable the use of Bayesian inference techniques to detect and characterize the distributed satellite population of distant lens galaxies.Comment: 21 pages + appendices, 7 figures. v2: Some derivations streamlined, extended appendices. Matches version published in PR