10 research outputs found
Capacity of Underspread Noncoherent WSSUS Fading Channels under Peak Signal Constraints
We characterize the capacity of the general class of noncoherent underspread
wide-sense stationary uncorrelated scattering (WSSUS) time-frequency-selective
Rayleigh fading channels, under peak constraints in time and frequency and in
time only. Capacity upper and lower bounds are found which are explicit in the
channel's scattering function and allow to identify the capacity-maximizing
bandwidth for a given scattering function and a given peak-to-average power
ratio.Comment: To be presented at IEEE Int. Symp. Inf. Theory 2007, Nice, Franc
Information Theory of underspread WSSUS channels
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
Noncoherent Capacity of Underspread Fading Channels
We derive bounds on the noncoherent capacity of wide-sense stationary
uncorrelated scattering (WSSUS) channels that are selective both in time and
frequency, and are underspread, i.e., the product of the channel's delay spread
and Doppler spread is small. For input signals that are peak constrained in
time and frequency, we obtain upper and lower bounds on capacity that are
explicit in the channel's scattering function, are accurate for a large range
of bandwidth and allow to coarsely identify the capacity-optimal bandwidth as a
function of the peak power and the channel's scattering function. We also
obtain a closed-form expression for the first-order Taylor series expansion of
capacity in the limit of large bandwidth, and show that our bounds are tight in
the wideband regime. For input signals that are peak constrained in time only
(and, hence, allowed to be peaky in frequency), we provide upper and lower
bounds on the infinite-bandwidth capacity and find cases when the bounds
coincide and the infinite-bandwidth capacity is characterized exactly. Our
lower bound is closely related to a result by Viterbi (1967).
The analysis in this paper is based on a discrete-time discrete-frequency
approximation of WSSUS time- and frequency-selective channels. This
discretization explicitly takes into account the underspread property, which is
satisfied by virtually all wireless communication channels.Comment: Submitted to the IEEE Transactions on Information Theor
Unified Capacity Limit of Non-coherent Wideband Fading Channels
In non-coherent wideband fading channels where energy rather than spectrum is
the limiting resource, peaky and non-peaky signaling schemes have long been
considered species apart, as the first approaches asymptotically the capacity
of a wideband AWGN channel with the same average SNR, whereas the second
reaches a peak rate at some finite critical bandwidth and then falls to zero as
bandwidth grows to infinity. In this paper it is shown that this distinction is
in fact an artifact of the limited attention paid in the past to the product
between the bandwidth and the fraction of time it is in use. This fundamental
quantity, called bandwidth occupancy, measures average bandwidth usage over
time. For all signaling schemes with the same bandwidth occupancy, achievable
rates approach to the wideband AWGN capacity within the same gap as the
bandwidth occupancy approaches its critical value, and decrease to zero as the
occupancy goes to infinity. This unified analysis produces quantitative
closed-form expressions for the ideal bandwidth occupancy, recovers the
existing capacity results for (non-)peaky signaling schemes, and unveils a
trade-off between the accuracy of approximating capacity with a generalized
Taylor polynomial and the accuracy with which the optimal bandwidth occupancy
can be bounded.Comment: Accepted for publication in IEEE Transactions on Wireless
Communications. Copyright may be transferred without notic
Eigenvalue Estimates and Mutual Information for the Linear Time-Varying Channel
We consider linear time-varying channels with additive white Gaussian noise.
For a large class of such channels we derive rigorous estimates of the
eigenvalues of the correlation matrix of the effective channel in terms of the
sampled time-varying transfer function and, thus, provide a theoretical
justification for a relationship that has been frequently observed in the
literature. We then use this eigenvalue estimate to derive an estimate of the
mutual information of the channel. Our approach is constructive and is based on
a careful balance of the trade-off between approximate operator
diagonalization, signal dimension loss, and accuracy of eigenvalue estimates.Comment: Submitted to IEEE Transactions on Information Theory This version is
a substantial revision of the earlier versio
Low SNR Capacity of Noncoherent Fading Channels
Discrete-time Rayleigh fading single-input single-output (SISO) and
multiple-input multiple-output (MIMO) channels are considered, with no channel
state information at the transmitter or the receiver. The fading is assumed to
be stationary and correlated in time, but independent from antenna to antenna.
Peak-power and average-power constraints are imposed on the transmit antennas.
For MIMO channels, these constraints are either imposed on the sum over
antennas, or on each individual antenna. For SISO channels and MIMO channels
with sum power constraints, the asymptotic capacity as the peak signal-to-noise
ratio tends to zero is identified; for MIMO channels with individual power
constraints, this asymptotic capacity is obtained for a class of channels
called transmit separable channels. The results for MIMO channels with
individual power constraints are carried over to SISO channels with delay
spread (i.e. frequency selective fading).Comment: submitted to IEEE I
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Quantum information processing approaches in classical systems
The engineering problem of building scalable quantum computers has prompted the development of a rich theory modeling the evolution of quantum systems as well as techniques to preserve quantum information in the presence of noise. Such techniques offer systems-level approaches to the problem of robustly encoding and preserving information and, as a result, see applicability in a wide variety of architectures for computing systems. In this thesis, we visit the mathematical underpinnings of quantum information and apply strategies inspired by quantum information processing to two non-quantum systems to demonstrate advantage. We first describe the construction of a quantum emulation device, an analog electronic system with the same mathematical structure as a gate-based quantum computer, and introduce novel time-domain information encoding methods to increase the computational capacity of the device. We confirm the sustained performance of the improved system by successfully transforming emulated states by randomly selected quantum gates. We then visit similarities between quantum information processing and signal processing in the noncoherent wireless communication setting, the latter being an environment characterized by a lack of instantaneous channel knowledge. We describe the theoretical underpinnings of the noncoherent communication environment from both an information theoretic and signal processing perspective. This leads us to propose a multi-antenna space-time code construction based on a family of quantum error correcting codes known as stabilizer codes. For this code, we derive the optimal decoder in Rayleigh and Ricean fading and benchmark the its performance against coherent and differential coding at comparable rates.Electrical and Computer Engineerin