arXiv subjects

Erwin Riegler

Publications and source records attributed to Erwin Riegler.

29 records · Page 2Linked to original sources

arXiv2013

Capacity Pre-Log of Noncoherent SIMO Channels via Hironaka's Theorem

We find the capacity pre-log of a temporally correlated Rayleigh block-fading SIMO channel in the noncoherent setting. It is well known that for block-length L and rank of the channel covariance matrix equal to Q, the capacity pre-log in the SISO case is given by 1-Q/L. Here, Q/L can be interpreted as the pre-log penalty incurred by channel uncertainty. Our main result reveals that, by adding only one receive antenna, this penalty can be reduced to 1/L and can, hence, be made to vanish in the large-L limit, even if Q/L remains constant as L goes to infinity. Intuitively, even though the SISO channels between the transmit antenna and the two receive antennas are statistically independent, the transmit signal induces enough statistical dependence between the corresponding receive signals for the second receive antenna to be able to resolve the uncertainty associated with the first receive antenna's channel and thereby make the overall system appear coherent. The proof of our main theorem is based on a deep result from algebraic geometry known as Hironaka's Theorem on the Resolution of Singularities.

cs.IT↗

arXiv2013

A Lower Bound on the Noncoherent Capacity Pre-log for the MIMO Channel with Temporally Correlated Fading

We derive a lower bound on the capacity pre-log of a temporally correlated Rayleigh block-fading multiple-input multiple-output (MIMO) channel with T transmit antennas and R receive antennas in the noncoherent setting (no a priori channel knowledge at the transmitter and the receiver). In this model, the fading process changes independently across blocks of length L and is temporally correlated within each block for each transmit-receive antenna pair, with a given rank Q of the corresponding correlation matrix. Our result implies that for almost all choices of the coloring matrix that models the temporal correlation, the pre-log can be lower-bounded by T(1-1/L) for T <= (L-1)/Q provided that R is sufficiently large. The widely used constant block-fading model is equivalent to the temporally correlated block-fading model with Q = 1 for the special case when the temporal correlation for each transmit-receive antenna pair is the same, which is unlikely to be observed in practice. For the constant block-fading model, the capacity pre-log is given by T(1-T/L), which is smaller than our lower bound for the case Q = 1. Thus, our result suggests that the assumptions underlying the constant block- fading model lead to a pessimistic result for the capacity pre-log.

cs.IT↗

arXiv2012

Simultaneous Distributed Sensor Self-Localization and Target Tracking Using Belief Propagation and Likelihood Consensus

We introduce the framework of cooperative simultaneous localization and tracking (CoSLAT), which provides a consistent combination of cooperative self-localization (CSL) and distributed target tracking (DTT) in sensor networks without a fusion center. CoSLAT extends simultaneous localization and tracking (SLAT) in that it uses also intersensor measurements. Starting from a factor graph formulation of the CoSLAT problem, we develop a particle-based, distributed message passing algorithm for CoSLAT that combines nonparametric belief propagation with the likelihood consensus scheme. The proposed CoSLAT algorithm improves on state-of-the-art CSL and DTT algorithms by exchanging probabilistic information between CSL and DTT. Simulation results demonstrate substantial improvements in both self-localization and tracking performance.

cs.NI↗

arXiv2012

On the Capacity of Large-MIMO Block-Fading Channels

We characterize the capacity of Rayleigh block-fading multiple-input multiple-output (MIMO) channels in the noncoherent setting where transmitter and receiver have no a priori knowledge of the realizations of the fading channel. We prove that unitary space-time modulation (USTM) is not capacity-achieving in the high signal-to-noise ratio (SNR) regime when the total number of antennas exceeds the coherence time of the fading channel (expressed in multiples of the symbol duration), a situation that is relevant for MIMO systems with large antenna arrays (large-MIMO systems). This result settles a conjecture by Zheng & Tse (2002) in the affirmative. The capacity-achieving input signal, which we refer to as Beta-variate space-time modulation (BSTM), turns out to be the product of a unitary isotropically distributed random matrix, and a diagonal matrix whose nonzero entries are distributed as the square-root of the eigenvalues of a Beta-distributed random matrix of appropriate size. Numerical results illustrate that using BSTM instead of USTM in large-MIMO systems yields a rate gain as large as 13% for SNR values of practical interest.

cs.IT↗

arXiv2012

Message-Passing Algorithms for Channel Estimation and Decoding Using Approximate Inference

We design iterative receiver schemes for a generic wireless communication system by treating channel estimation and information decoding as an inference problem in graphical models. We introduce a recently proposed inference framework that combines belief propagation (BP) and the mean field (MF) approximation and includes these algorithms as special cases. We also show that the expectation propagation and expectation maximization algorithms can be embedded in the BP-MF framework with slight modifications. By applying the considered inference algorithms to our probabilistic model, we derive four different message-passing receiver schemes. Our numerical evaluation demonstrates that the receiver based on the BP-MF framework and its variant based on BP-EM yield the best compromise between performance, computational complexity and numerical stability among all candidate algorithms.

cs.IT↗

arXiv2012

Merging Belief Propagation and the Mean Field Approximation: A Free Energy Approach

We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al. We show that the message passing fixed-point equations obtained with this combination correspond to stationary points of a constrained region-based free energy approximation. Moreover, we present a convergent implementation of these message passing fixedpoint equations provided that the underlying factor graph fulfills certain technical conditions. In addition, we show how to include hard constraints in the part of the factor graph corresponding to belief propagation. Finally, we demonstrate an application of our method to iterative channel estimation and decoding in an orthogonal frequency division multiplexing (OFDM) system.

cs.IT↗

arXiv2011

Receiver Architectures for MIMO-OFDM Based on a Combined VMP-SP Algorithm

Iterative information processing, either based on heuristics or analytical frameworks, has been shown to be a very powerful tool for the design of efficient, yet feasible, wireless receiver architectures. Within this context, algorithms performing message-passing on a probabilistic graph, such as the sum-product (SP) and variational message passing (VMP) algorithms, have become increasingly popular. In this contribution, we apply a combined VMP-SP message-passing technique to the design of receivers for MIMO-ODFM systems. The message-passing equations of the combined scheme can be obtained from the equations of the stationary points of a constrained region-based free energy approximation. When applied to a MIMO-OFDM probabilistic model, we obtain a generic receiver architecture performing iterative channel weight and noise precision estimation, equalization and data decoding. We show that this generic scheme can be particularized to a variety of different receiver structures, ranging from high-performance iterative structures to low complexity receivers. This allows for a flexible design of the signal processing specially tailored for the requirements of each specific application. The numerical assessment of our solutions, based on Monte Carlo simulations, corroborates the high performance of the proposed algorithms and their superiority to heuristic approaches.

stat.ML↗

arXiv2011

Capacity Pre-Log of SIMO Correlated Block-Fading Channels

We establish an upper bound on the noncoherent capacity pre-log of temporally correlated block-fading single-input multiple-output (SIMO) channels. The upper bound matches the lower bound recently reported in Riegler et al. (2011), and, hence, yields a complete characterization of the SIMO noncoherent capacity pre-log, provided that the channel covariance matrix satisfies a mild technical condition. This result allows one to determine the optimal number of receive antennas to be used to maximize the capacity pre-log for a given block-length and a given rank of the channel covariance matrix.

cs.IT↗

arXiv2011

Noncoherent SIMO Pre-Log via Resolution of Singularities

We establish a lower bound on the noncoherent capacity pre-log of a temporally correlated Rayleigh block-fading single-input multiple-output (SIMO) channel. Our result holds for arbitrary rank Q of the channel correlation matrix, arbitrary block-length L > Q, and arbitrary number of receive antennas R, and includes the result in Morgenshtern et al. (2010) as a special case. It is well known that the capacity pre-log for this channel in the single-input single-output (SISO) case is given by 1-Q/L, where Q/L is the penalty incurred by channel uncertainty. Our result reveals that this penalty can be reduced to 1/L by adding only one receive antenna, provided that L \geq 2Q - 1 and the channel correlation matrix satisfies mild technical conditions. The main technical tool used to prove our result is Hironaka's celebrated theorem on resolution of singularities in algebraic geometry.

cs.IT↗

arXiv2009

On the Achievability of Interference Alignment in the K-User Constant MIMO Interference Channel

Interference alignment in the K-user MIMO interference channel with constant channel coefficients is considered. A novel constructive method for finding the interference alignment solution is proposed for the case where the number of transmit antennas equals the number of receive antennas (NT = NR = N), the number of transmitter-receiver pairs equals K = N + 1, and all interference alignment multiplexing gains are one. The core of the method consists of solving an eigenvalue problem that incorporates the channel matrices of all interfering links. This procedure provides insight into the feasibility of signal vector spaces alignment schemes in finite dimensional MIMO interference channels.

cs.IT↗

arXiv2002

Toric complete intersections and weighted projective space

It has been shown by Batyrev and Borisov that nef partitions of reflexive polyhedra can be used to construct mirror pairs of complete intersection Calabi--Yau manifolds in toric ambient spaces. We construct a number of such spaces and compute their cohomological data. We also discuss the relation of our results to complete intersections in weighted projective spaces and try to recover them as special cases of the toric construction. As compared to hypersurfaces, codimension two more than doubles the number of spectra with $h^{11}=1$. Alltogether we find 87 new (mirror pairs of) Hodge data, mainly with $h^{11}\le4$.

math.AG↗