Veniamin I. Morgenshtern

Distributed orthogonalization in large interference relay networks

We study fading interference relay networks where M single-antenna source-destination terminal pairs communicate through a set of K relays using half-duplex two-hop relaying. Two specific protocols are considered, P1 introduced in H. Bolcskei, et al. (2004), H. Bolcskei and R.U. Nabar (2004) and P2 introduced in A.F. Dana and B. Hassibi (2003). P1 relies on the idea of relay partitioning and requires each relay terminal to know one backward and one forward fading coefficient only. P2 requires each relay terminal to know all M backward and M forward fading coefficients and does not need relay partitioning. We prove that in the large-M limit the minimum rate of growth of K for P1 to achieve a strictly positive per source-destination terminal pair capacity is K infin M3 whereas in P2 it is K infin M2. The protocols P1 and P2 are thus found to trade off the number of relay terminals for channel state information (CSI) at the relays; more CSI at the relays reduces the total number of relays needed to achieve a strictly positive per source-destination terminal pair capacity in the large-M limit

Super-Resolution of Positive Sources: The Discrete Setup

In single-molecule microscopy it is necessary to locate with high precision point sources from noisy observations of the spectrum of the signal at frequencies capped by

Information Theory of Underspread WSSUS Channels

f_c

On the Sensitivity of Continuous-Time Noncoherent Fading Channel Capacity

, which is just about the frequency of natural light. This paper rigorously establishes that this super-resolution problem can be solved via linear programming in a stable manner. We prove that the quality of the reconstruction crucially depends on the Rayleigh regularity of the support of the signal; that is, on the maximum number of sources that can occur within a square of side length about

On the sensitivity of noncoherent capacity to the channel model

1/f_c

Noncoherent SIMO pre-log via resolution of singularities

. The theoretical performance guarantee is complemented with a converse result showing that our simple convex program convex is nearly optimal. Finally, numerical experiments illustrate our methods.

The SIMO pre-log can be larger than the SISO pre-log

The chapter focuses on the ultimate limit on the rate of reliable communication through Rayleigh-fading channels that satisfy the wide-sense stationary (WSS) and uncorrelated scattering (US) assumptions and are underspread. Therefore, the natural setting is an information-theoretic one, and the performance metric is channel capacity. The family of Rayleigh-fading underspread WSSUS channels constitutes a good model for real-world wireless channels: their stochastic properties, like amplitude and phase distributions match channel measurement results. The Rayleigh-fading and the WSSUS assumptions imply that the stochastic properties of the channel are fully described by a two-dimensional power spectral density (PSD) function, often referred to as scattering function. The underspread assumption implies that the scattering function is highly concentrated in the delay-Doppler plane. Two important aspects need to be accounted for by a model that aims at being realistic: neither the transmitter nor the receiver knows the realization of the channel; and the peak power of the transmit signal is limited. Based on these two aspects the chapter provides an information-theoretic analysis of Rayleigh-fading underspread WSSUS channels in the noncoherent setting, under the additional assumption that the transmit signal is peak-constrained.

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

The noncoherent capacity of stationary discrete-time fading channels is known to be very sensitive to the fine details of the channel model. More specifically, the measure of the support of the fading-process power spectral density (PSD) determines if noncoherent capacity grows logarithmically with the signal-to-noise ratio (SNR) or slower than logarithmically. Such a result is unsatisfactory from an engineering point of view, as the support of the PSD cannot be determined through measurements. The aim of this paper is to assess whether, for general continuous-time Rayleigh-fading channels, this sensitivity has a noticeable impact on capacity at SNR values of practical interest. To this end, we consider the general class of band-limited continuous-time Rayleigh-fading channels that satisfy the wide-sense stationary uncorrelated-scattering (WSSUS) assumption and are, in addition, under spread. We show that, for all SNR values of practical interest, the noncoherent capacity of every channel in this class is close to the capacity of an additive white Gaussian noise channel with the same SNR and bandwidth, independently of the measure of the support of the scattering function (the 2-D channel PSD). Our result is based on a lower bound on noncoherent capacity, which is built on a discretization of the channel input-output relation induced by projecting onto Weyl-Heisenberg sets. This approach is interesting in its own right as it yields a mathematically tractable way of dealing with the mutual information between certain continuous-time random signals.

A lower bound on the noncoherent capacity pre-log for the MIMO channel with temporally correlated fading

We establish a lower bound on the noncoherent capacity pre-log of a temporally correlated Rayleigh block-fading single-input multiple-output (SIMO) channel. Surprisingly, when the covariance matrix of the channel satisfies a certain technical condition related to the cardinality of its smallest set of linearly dependent rows, this lower bound reveals that the capacity pre-log in the SIMO case is larger than that in the single-input single-output (SISO) case.The noncoherent capacity of stationary discrete-time fading channels is known to be very sensitive to the fine details of the channel model. More specifically, the measure of the set of harmonics where the power spectral density of the fading process is nonzero determines if capacity grows logarithmically in SNR or slower than logarithmically. An engineering-relevant problem is to characterize the SNR value at which this sensitivity starts to matter. In this paper, we consider the general class of continuous-time Rayleigh-fading channels that satisfy the wide-sense stationary uncorrelated-scattering (WSSUS) assumption and are, in addition, underspread. For this class of channels, we show that the noncoherent capacity is close to the AWGN capacity for all SNR values of practical interest, independently of whether the scattering function is compactly supported or not. As a byproduct of our analysis, we obtain an information-theoretic pulse-design criterion for orthogonal frequency-division multiplexing systems.

Capacity pre-log of SIMO correlated block-fading channels

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 ≥ 2Q − 1 and the channel correlation matrix satisfies mild technical conditions. The main technical tool used to prove our result is Hironakas celebrated theorem on resolution of singularities in algebraic geometry.