34 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
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
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
A Simple Recursively Computable Lower Bound on the Noncoherent Capacity of Highly Underspread Fading Channels
Real-world wireless communication channels are typically highly underspread: their coherence time is much greater than their delay spread. In such situations it is common to assume that, with sufficiently high bandwidth, the capacity without Channel State Information (CSI) at the receiver (termed the noncoherent channel capacity) is approximately equal to the capacity with perfect CSI at the receiver (termed the coherent channel capacity). In this paper, we propose a lower bound on the noncoherent capacity of highly underspread fading channels, which assumes only that the delay spread and coherence time are known. Furthermore our lower bound can be calculated recursively, with each increment corresponding to a step increase in bandwidth. These properties, we contend, make our lower bound an excellent candidate as a simple method to verify that the noncoherent capacity is indeed approximately equal to the coherent capacity for typical wireless communication applications. We precede the derivation of the aforementioned lower bound on the information capacity with a rigorous justification of the mathematical representation of the channel. Furthermore, we also provide a numerical example for an actual wireless communication channel and demonstrate that our lower bound does indeed approximately equal the coherent channel capacity.The work of T. H. Loh was supported by the 2013 - 2017 Electromagnetics and Time Metrology Programme of the National Measurement Office, an Executive Agency of the U.K. Department for Business, Innovation and Skills, under Projects EMT13018This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/TWC.2016.253167
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A Simple Recursively Computable Lower Bound on the Noncoherent Capacity of Highly Underspread Fading Channels
Real-world wireless communication channels are typically highly underspread: their coherence time is much greater than their delay spread. In such situations it is common to assume that, with sufficiently high bandwidth, the capacity without Channel State Information (CSI) at the receiver (termed the noncoherent channel capacity) is approximately equal to the capacity with perfect CSI at the receiver (termed the coherent channel capacity). In this paper, we propose a lower bound on the noncoherent capacity of highly underspread fading channels, which assumes only that the delay spread and coherence time are known. Furthermore our lower bound can be calculated recursively, with each increment corresponding to a step increase in bandwidth. These properties, we contend, make our lower bound an excellent candidate as a simple method to verify that the noncoherent capacity is indeed approximately equal to the coherent capacity for typical wireless communication applications. We precede the derivation of the aforementioned lower bound on the information capacity with a rigorous justification of the mathematical representation of the channel. Furthermore, we also provide a numerical example for an actual wireless communication channel and demonstrate that our lower bound does indeed approximately equal the coherent channel capacity.The work of T. H. Loh was supported by the 2013 - 2017 Electromagnetics and Time Metrology Programme of the National Measurement Office, an Executive Agency of the U.K. Department for Business, Innovation and Skills, under Projects EMT13018This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/TWC.2016.253167
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
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