993 research outputs found
On the Sensitivity of Noncoherent Capacity to the Channel Model
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.Comment: To be presented at IEEE Int. Symp. Inf. Theory 2009, Seoul, Kore
On the Sensitivity of Continuous-Time Noncoherent Fading Channel Capacity
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 in 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, underspread.
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 AWGN
channel with the same SNR and bandwidth, independently of the measure of the
support of the scattering function (the two-dimensional 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 (WH) 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.Comment: final versio
Oversampling Increases the Pre-Log of Noncoherent Rayleigh Fading Channels
We analyze the capacity of a continuous-time, time-selective, Rayleigh
block-fading channel in the high signal-to-noise ratio (SNR) regime. The fading
process is assumed stationary within each block and to change independently
from block to block; furthermore, its realizations are not known a priori to
the transmitter and the receiver (noncoherent setting). A common approach to
analyzing the capacity of this channel is to assume that the receiver performs
matched filtering followed by sampling at symbol rate (symbol matched
filtering). This yields a discrete-time channel in which each transmitted
symbol corresponds to one output sample. Liang & Veeravalli (2004) showed that
the capacity of this discrete-time channel grows logarithmically with the SNR,
with a capacity pre-log equal to . Here, is the number of
symbols transmitted within one fading block, and is the rank of the
covariance matrix of the discrete-time channel gains within each fading block.
In this paper, we show that symbol matched filtering is not a
capacity-achieving strategy for the underlying continuous-time channel.
Specifically, we analyze the capacity pre-log of the discrete-time channel
obtained by oversampling the continuous-time channel output, i.e., by sampling
it faster than at symbol rate. We prove that by oversampling by a factor two
one gets a capacity pre-log that is at least as large as . Since the
capacity pre-log corresponding to symbol-rate sampling is , our result
implies indeed that symbol matched filtering is not capacity achieving at high
SNR.Comment: To appear in the IEEE Transactions on Information Theor
Calculation of Mutual Information for Partially Coherent Gaussian Channels with Applications to Fiber Optics
The mutual information between a complex-valued channel input and its
complex-valued output is decomposed into four parts based on polar coordinates:
an amplitude term, a phase term, and two mixed terms. Numerical results for the
additive white Gaussian noise (AWGN) channel with various inputs show that, at
high signal-to-noise ratio (SNR), the amplitude and phase terms dominate the
mixed terms. For the AWGN channel with a Gaussian input, analytical expressions
are derived for high SNR. The decomposition method is applied to partially
coherent channels and a property of such channels called "spectral loss" is
developed. Spectral loss occurs in nonlinear fiber-optic channels and it may be
one effect that needs to be taken into account to explain the behavior of the
capacity of nonlinear fiber-optic channels presented in recent studies.Comment: 30 pages, 9 figures, accepted for publication in IEEE Transactions on
Information Theor
A Mobile Wireless Channel State Recognition Algorihm: Introduction, Definition, and Verification - Sensing for Cognitive Environmental Awareness
This research includes mobile wireless systems limited by time and frequency dispersive channels. A blind mobile wireless channel (MWC) state recognition (CSR) algorithm that detects hidden coherent nonselective and noncoherent selective processes is verified. Because the algorithm is blind, it releases capacity based on current channel state that traditionally is fixed and reserved for channel gain estimation and distortion mitigation. The CSR algorithm enables cognitive communication system control including signal processing, resource allocation/deallocation, or distortion mitigation selections based on channel coherence states. MWC coherent and noncoherent states, ergodicity, stationarity, uncorrelated scattering, and Markov processes are assumed for each time block. Furthermore, a hidden Markov model (HMM) is utilized to represent the statistical relationships between hidden dispersive processes and observed receive waveform processes. First-order and second-order statistical extracted features support state hard decisions which are combined in order to increase the accuracy of channel state estimates. This research effort has architected, designed, and verified a blind statistical feature recognition algorithm capable of detecting coherent nonselective, single time selective, single frequency selective, or dual selective noncoherent states. A MWC coherence state model (CSM) was designed to represent these hidden dispersive processes. Extracted statistical features are input into a parallel set of trained HMMs that compute state sequence conditional likelihoods. Hard state decisions are combined to produce a single most likely channel state estimate for each time block. To verify the CSR algorithm performance, combinations of hidden state sequences are applied to the CSR algorithm and verified against input hidden state sequences. State sequence recognition accuracy sensitivity was found to be above 99% while specificity was determined to be above 98% averaged across all features, states, and sequences. While these results establish the feasibility of a MWC blind CSR algorithm, optimal configuration requires future research to further improve performance including: 1) characterizing the range of input signal configurations, 2) waveform feature block size reduction, 3) HMM parameter tracking, 4) HMM computational complexity and latency reduction, 5) feature soft decision combining, 6) recursive implementation, 7) interfacing with state based mobile wireless communication control processes, and 8) extension to wired or wireless waveform recognition
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
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
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