17 research outputs found
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
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 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
A Queueing Characterization of Information Transmission over Block Fading Rayleigh Channels in the Low SNR
Unlike the AWGN (additive white gaussian noise) channel, fading channels
suffer from random channel gains besides the additive Gaussian noise. As a
result, the instantaneous channel capacity varies randomly along time, which
makes it insufficient to characterize the transmission capability of a fading
channel using data rate only. In this paper, the transmission capability of a
buffer-aided block Rayleigh fading channel is examined by a constant rate input
data stream, and reflected by several parameters such as the average queue
length, stationary queue length distribution, packet delay and overflow
probability. Both infinite-buffer model and finite-buffer model are considered.
Taking advantage of the memoryless property of the service provided by the
channel in each block in the the low SNR (signal-to-noise ratio) regime, the
information transmission over the channel is formulated as a \textit{discrete
time discrete state} queueing problem. The obtained results show that
block fading channels are unable to support a data rate close to their ergodic
capacity, no matter how long the buffer is, even seen from the application
layer. For the finite-buffer model, the overflow probability is derived with
explicit expression, and is shown to decrease exponentially when buffer size is
increased, even when the buffer size is very small.Comment: 29 pages, 11 figures. More details on the proof of Theorem 1 and
proposition 1 can be found in "Queueing analysis for block fading Rayleigh
channels in the low SNR regime ", IEEE WCSP 2013.It has been published by
IEEE Trans. on Veh. Technol. in Feb. 201
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