296 research outputs found
A Random Matrix Approach to the Finite Blocklength Regime of MIMO Fading Channels
978-1-4673-2580-6International audienceThis paper provides a novel central limit theorem (CLT) for the information density of the MIMO Rayleigh fading channel under white Gaussian inputs, when the data blocklength n and the number of transmit and receive antennas K and N , respectively, are large but of similar order of magnitude. This CLT is used to derive closed-form upper bounds on the error probability via an input-constrained version of Feinstein's lemma by Polyanskiy et al. and the second-order approximation of the coding rate. Numerical evaluations suggest that the normal approximation is tight for reasonably small values of n, K, N
Delay Performance of MISO Wireless Communications
Ultra-reliable, low latency communications (URLLC) are currently attracting
significant attention due to the emergence of mission-critical applications and
device-centric communication. URLLC will entail a fundamental paradigm shift
from throughput-oriented system design towards holistic designs for guaranteed
and reliable end-to-end latency. A deep understanding of the delay performance
of wireless networks is essential for efficient URLLC systems. In this paper,
we investigate the network layer performance of multiple-input, single-output
(MISO) systems under statistical delay constraints. We provide closed-form
expressions for MISO diversity-oriented service process and derive
probabilistic delay bounds using tools from stochastic network calculus. In
particular, we analyze transmit beamforming with perfect and imperfect channel
knowledge and compare it with orthogonal space-time codes and antenna
selection. The effect of transmit power, number of antennas, and finite
blocklength channel coding on the delay distribution is also investigated. Our
higher layer performance results reveal key insights of MISO channels and
provide useful guidelines for the design of ultra-reliable communication
systems that can guarantee the stringent URLLC latency requirements.Comment: This work has been submitted to the IEEE for possible publication.
Copyright may be transferred without notice, after which this version may no
longer be accessibl
Beta-Beta Bounds: Finite-Blocklength Analog of the Golden Formula
It is well known that the mutual information between two random variables can
be expressed as the difference of two relative entropies that depend on an
auxiliary distribution, a relation sometimes referred to as the golden formula.
This paper is concerned with a finite-blocklength extension of this relation.
This extension consists of two elements: 1) a finite-blocklength channel-coding
converse bound by Polyanskiy and Verd\'{u} (2014), which involves the ratio of
two Neyman-Pearson functions (beta-beta converse bound); and 2) a novel
beta-beta channel-coding achievability bound, expressed again as the ratio of
two Neyman-Pearson functions.
To demonstrate the usefulness of this finite-blocklength extension of the
golden formula, the beta-beta achievability and converse bounds are used to
obtain a finite-blocklength extension of Verd\'{u}'s (2002) wideband-slope
approximation. The proof parallels the derivation of the latter, with the
beta-beta bounds used in place of the golden formula.
The beta-beta (achievability) bound is also shown to be useful in cases where
the capacity-achieving output distribution is not a product distribution due
to, e.g., a cost constraint or structural constraints on the codebook, such as
orthogonality or constant composition. As an example, the bound is used to
characterize the channel dispersion of the additive exponential-noise channel
and to obtain a finite-blocklength achievability bound (the tightest to date)
for multiple-input multiple-output Rayleigh-fading channels with perfect
channel state information at the receiver.Comment: to appear in IEEE Transactions on Information Theor
Low-latency Ultra Reliable 5G Communications: Finite-Blocklength Bounds and Coding Schemes
Future autonomous systems require wireless connectivity able to support
extremely stringent requirements on both latency and reliability. In this
paper, we leverage recent developments in the field of finite-blocklength
information theory to illustrate how to optimally design wireless systems in
the presence of such stringent constraints. Focusing on a multi-antenna
Rayleigh block-fading channel, we obtain bounds on the maximum number of bits
that can be transmitted within given bandwidth, latency, and reliability
constraints, using an orthogonal frequency-division multiplexing system similar
to LTE. These bounds unveil the fundamental interplay between latency,
bandwidth, rate, and reliability. Furthermore, they suggest how to optimally
use the available spatial and frequency diversity. Finally, we use our bounds
to benchmark the performance of an actual coding scheme involving the
transmission of short packets
Minimum Energy to Send Bits Over Multiple-Antenna Fading Channels
This paper investigates the minimum energy required to transmit
information bits with a given reliability over a multiple-antenna Rayleigh
block-fading channel, with and without channel state information (CSI) at the
receiver. No feedback is assumed. It is well known that the ratio between the
minimum energy per bit and the noise level converges to dB as goes
to infinity, regardless of whether CSI is available at the receiver or not.
This paper shows that lack of CSI at the receiver causes a slowdown in the
speed of convergence to dB as compared to the case of
perfect receiver CSI. Specifically, we show that, in the no-CSI case, the gap
to dB is proportional to , whereas when perfect
CSI is available at the receiver, this gap is proportional to . In
both cases, the gap to dB is independent of the number of transmit
antennas and of the channel's coherence time. Numerically, we observe that,
when the receiver is equipped with a single antenna, to achieve an energy per
bit of dB in the no-CSI case, one needs to transmit at least information bits, whereas bits suffice for the case of
perfect CSI at the receiver
Coherent multiple-antenna block-fading channels at finite blocklength
In this paper we consider a channel model that is often used to describe the
mobile wireless scenario: multiple-antenna additive white Gaussian noise
channels subject to random (fading) gain with full channel state information at
the receiver. Dynamics of the fading process are approximated by a
piecewise-constant process (frequency non-selective isotropic block fading).
This work addresses the finite blocklength fundamental limits of this channel
model. Specifically, we give a formula for the channel dispersion -- a quantity
governing the delay required to achieve capacity. Multiplicative nature of the
fading disturbance leads to a number of interesting technical difficulties that
required us to enhance traditional methods for finding channel dispersion.
Alas, one difficulty remains: the converse (impossibility) part of our result
holds under an extra constraint on the growth of the peak-power with
blocklength.
Our results demonstrate, for example, that while capacities of and antenna configurations coincide (under fixed received
power), the coding delay can be quite sensitive to this switch. For example, at
the received SNR of dB the system achieves capacity with
codes of length (delay) which is only of the length required for the
system. Another interesting implication is that for the MISO
channel, the dispersion-optimal coding schemes require employing orthogonal
designs such as Alamouti's scheme -- a surprising observation considering the
fact that Alamouti's scheme was designed for reducing demodulation errors, not
improving coding rate. Finding these dispersion-optimal coding schemes
naturally gives a criteria for producing orthogonal design-like inputs in
dimensions where orthogonal designs do not exist
Diversity versus Multiplexing at Finite Blocklength
A finite blocklenth analysis of the diversity-multiplexing tradeoff is
presented, based on nonasymptotic bounds on the maximum channel coding rate of
multiple-antenna block-memoryless Rayleigh-fading channels.The bounds in this
paper allow one to numerically assess for which packet size, number of
antennas, and degree of channel selectivity, diversity-exploiting schemes are
close to optimal, and when instead the available spatial degrees of freedom
should be used to provide spatial multiplexing. This finite blocklength view on
the diversity-multiplexing tradeoff provides insights on the design of
delay-sensitive ultra-reliable communication links.Comment: Proc. IEEE Int. Symp. Wirel. Comm. Syst. (ISWCS), Aug. 2014, to
appea
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
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