12,621 research outputs found
Towards the Optimal Amplify-and-Forward Cooperative Diversity Scheme
In a slow fading channel, how to find a cooperative diversity scheme that
achieves the transmit diversity bound is still an open problem. In fact, all
previously proposed amplify-and-forward (AF) and decode-and-forward (DF)
schemes do not improve with the number of relays in terms of the diversity
multiplexing tradeoff (DMT) for multiplexing gains r higher than 0.5. In this
work, we study the class of slotted amplify-and-forward (SAF) schemes. We first
establish an upper bound on the DMT for any SAF scheme with an arbitrary number
of relays N and number of slots M. Then, we propose a sequential SAF scheme
that can exploit the potential diversity gain in the high multiplexing gain
regime. More precisely, in certain conditions, the sequential SAF scheme
achieves the proposed DMT upper bound which tends to the transmit diversity
bound when M goes to infinity. In particular, for the two-relay case, the
three-slot sequential SAF scheme achieves the proposed upper bound and
outperforms the two-relay non-orthorgonal amplify-and-forward (NAF) scheme of
Azarian et al. for multiplexing gains r < 2/3. Numerical results reveal a
significant gain of our scheme over the previously proposed AF schemes,
especially in high spectral efficiency and large network size regime.Comment: 30 pages, 11 figures, submitted to IEEE trans. IT, revised versio
Optimal space-time codes for the MIMO amplify-and-forward cooperative channel
In this work, we extend the non-orthogonal amplify-and-forward (NAF)
cooperative diversity scheme to the MIMO channel. A family of space-time block
codes for a half-duplex MIMO NAF fading cooperative channel with N relays is
constructed. The code construction is based on the non-vanishing determinant
criterion (NVD) and is shown to achieve the optimal diversity-multiplexing
tradeoff (DMT) of the channel. We provide a general explicit algebraic
construction, followed by some examples. In particular, in the single relay
case, it is proved that the Golden code and the 4x4 Perfect code are optimal
for the single-antenna and two-antenna case, respectively. Simulation results
reveal that a significant gain (up to 10dB) can be obtained with the proposed
codes, especially in the single-antenna case.Comment: submitted to IEEE Transactions on Information Theory, revised versio
A bounded degree SOS hierarchy for polynomial optimization
We consider a new hierarchy of semidefinite relaxations for the general
polynomial optimization problem on a
compact basic semi-algebraic set . This hierarchy combines some
advantages of the standard LP-relaxations associated with Krivine's positivity
certificate and some advantages of the standard SOS-hierarchy. In particular it
has the following attractive features: (a) In contrast to the standard
SOS-hierarchy, for each relaxation in the hierarchy, the size of the matrix
associated with the semidefinite constraint is the same and fixed in advance by
the user. (b) In contrast to the LP-hierarchy, finite convergence occurs at the
first step of the hierarchy for an important class of convex problems. Finally
(c) some important techniques related to the use of point evaluations for
declaring a polynomial to be zero and to the use of rank-one matrices make an
efficient implementation possible. Preliminary results on a sample of non
convex problems are encouraging
Feynman-Kac formula for Levy processes and semiclassical (Euclidean) momentum representation
We prove a version of the Feynman-Kac formula for Levy processes and
integro-differential operators, with application to the momentum representation
of suitable quantum (Euclidean) systems whose Hamiltonians involve
L\'{e}vy-type potentials. Large deviation techniques are used to obtain the
limiting behavior of the systems as the Planck constant approaches zero. It
turns out that the limiting behavior coincides with fresh aspects of the
semiclassical limit of (Euclidean) quantum mechanics. Non-trivial examples of
Levy processes are considered as illustrations and precise asymptotics are
given for the terms in both configuration and momentum representations
A Comparison of CP-OFDM, PCC-OFDM and UFMC for 5G Uplink Communications
Polynomial-cancellation-coded orthogonal frequency division multiplexing
(PCC-OFDM) is a form of OFDM that has waveforms which are very well localized
in both the time and frequency domains and so it is ideally suited for use in
the 5G network. This paper analyzes the performance of PCC-OFDM in the uplink
of a multiuser system using orthogonal frequency division multiple access
(OFDMA) and compares it with conventional cyclic prefix OFDM (CP-OFDM), and
universal filtered multicarrier (UFMC). PCC-OFDM is shown to be much less
sensitive than either CP-OFDM or UFMC to time and frequency offsets. For a
given constellation size, PCC-OFDM in additive white Gaussian noise (AWGN)
requires 3dB lower signal-to-noise ratio (SNR) for a given bit-error-rate, and
the SNR advantage of PCC-OFDM increases rapidly when there are timing and/or
frequency offsets. For PCC-OFDM no frequency guard band is required between
different OFDMA users. PCC-OFDM is completely compatible with CP-OFDM and adds
negligible complexity and latency, as it uses a simple mapping of data onto
pairs of subcarriers at the transmitter, and a simple weighting-and-adding of
pairs of subcarriers at the receiver. The weighting and adding step, which has
been omitted in some of the literature, is shown to contribute substantially to
the SNR advantage of PCC-OFDM. A disadvantage of PCC-OFDM (without overlapping)
is the potential reduction in spectral efficiency because subcarriers are
modulated in pairs, but this reduction is more than regained because no guard
band or cyclic prefix is required and because, for a given channel, larger
constellations can be used
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