156 research outputs found
The Noncoherent Rician Fading Channel -- Part I : Structure of the Capacity-Achieving Input
Transmission of information over a discrete-time memoryless Rician fading
channel is considered where neither the receiver nor the transmitter knows the
fading coefficients. First the structure of the capacity-achieving input
signals is investigated when the input is constrained to have limited
peakedness by imposing either a fourth moment or a peak constraint. When the
input is subject to second and fourth moment limitations, it is shown that the
capacity-achieving input amplitude distribution is discrete with a finite
number of mass points in the low-power regime. A similar discrete structure for
the optimal amplitude is proven over the entire SNR range when there is only a
peak power constraint. The Rician fading with phase-noise channel model, where
there is phase uncertainty in the specular component, is analyzed. For this
model it is shown that, with only an average power constraint, the
capacity-achieving input amplitude is discrete with a finite number of levels.
For the classical average power limited Rician fading channel, it is proven
that the optimal input amplitude distribution has bounded support.Comment: To appear in the IEEE Transactions on Wireless Communication
The Noncoherent Rician Fading Channel -- Part II : Spectral Efficiency in the Low-Power Regime
Transmission of information over a discrete-time memoryless Rician fading
channel is considered where neither the receiver nor the transmitter knows the
fading coefficients. The spectral-efficiency/bit-energy tradeoff in the
low-power regime is examined when the input has limited peakedness. It is shown
that if a fourth moment input constraint is imposed or the input
peak-to-average power ratio is limited, then in contrast to the behavior
observed in average power limited channels, the minimum bit energy is not
always achieved at zero spectral efficiency. The low-power performance is also
characterized when there is a fixed peak limit that does not vary with the
average power. A new signaling scheme that overlays phase-shift keying on
on-off keying is proposed and shown to be optimally efficient in the low-power
regime.Comment: To appear in the IEEE Transactions on Wireless Communication
Capacity of The Discrete-Time Non-Coherent Memoryless Gaussian Channels at Low SNR
We address the capacity of a discrete-time memoryless Gaussian channel, where
the channel state information (CSI) is neither available at the transmitter nor
at the receiver. The optimal capacity-achieving input distribution at low
signal-to-noise ratio (SNR) is precisely characterized, and the exact capacity
of a non-coherent channel is derived. The derived relations allow to better
understanding the capacity of non-coherent channels at low SNR. Then, we
compute the non-coherence penalty and give a more precise characterization of
the sub-linear term in SNR. Finally, in order to get more insight on how the
optimal input varies with SNR, upper and lower bounds on the non-zero mass
point location of the capacity-achieving input are given.Comment: 5 pages and 4 figures. To appear in Proceeding of International
Symposium on Information Theory (ISIT 2008
Short Packets over Block-Memoryless Fading Channels: Pilot-Assisted or Noncoherent Transmission?
We present nonasymptotic upper and lower bounds on the maximum coding rate
achievable when transmitting short packets over a Rician memoryless
block-fading channel for a given requirement on the packet error probability.
We focus on the practically relevant scenario in which there is no \emph{a
priori} channel state information available at the transmitter and at the
receiver. An upper bound built upon the min-max converse is compared to two
lower bounds: the first one relies on a noncoherent transmission strategy in
which the fading channel is not estimated explicitly at the receiver; the
second one employs pilot-assisted transmission (PAT) followed by
maximum-likelihood channel estimation and scaled mismatched nearest-neighbor
decoding at the receiver. Our bounds are tight enough to unveil the optimum
number of diversity branches that a packet should span so that the energy per
bit required to achieve a target packet error probability is minimized, for a
given constraint on the code rate and the packet size. Furthermore, the bounds
reveal that noncoherent transmission is more energy efficient than PAT, even
when the number of pilot symbols and their power is optimized. For example, for
the case when a coded packet of symbols is transmitted using a channel
code of rate bits/channel use, over a block-fading channel with block
size equal to symbols, PAT requires an additional dB of energy per
information bit to achieve a packet error probability of compared to
a suitably designed noncoherent transmission scheme. Finally, we devise a PAT
scheme based on punctured tail-biting quasi-cyclic codes and ordered statistics
decoding, whose performance are close ( dB gap at packet error
probability) to the ones predicted by our PAT lower bound. This shows that the
PAT lower bound provides useful guidelines on the design of actual PAT schemes.Comment: 30 pages, 5 figures, journa
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
High-SNR Capacity of Wireless Communication Channels in the Noncoherent Setting: A Primer
This paper, mostly tutorial in nature, deals with the problem of
characterizing the capacity of fading channels in the high signal-to-noise
ratio (SNR) regime. We focus on the practically relevant noncoherent setting,
where neither transmitter nor receiver know the channel realizations, but both
are aware of the channel law. We present, in an intuitive and accessible form,
two tools, first proposed by Lapidoth & Moser (2003), of fundamental importance
to high-SNR capacity analysis: the duality approach and the escape-to-infinity
property of capacity-achieving distributions. Furthermore, we apply these tools
to refine some of the results that appeared previously in the literature and to
simplify the corresponding proofs.Comment: To appear in Int. J. Electron. Commun. (AE\"U), Aug. 201
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
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