40 research outputs found
OFDM based Distributed Space Time Coding for Asynchronous Relay Networks
Recently Li and Xia have proposed a transmission scheme for wireless relay
networks based on the Alamouti space time code and orthogonal frequency
division multiplexing to combat the effect of timing errors at the relay nodes.
This transmission scheme is amazingly simple and achieves a diversity order of
two for any number of relays. Motivated by its simplicity, this scheme is
extended to a more general transmission scheme that can achieve full
cooperative diversity for any number of relays. The conditions on the
distributed space time block code (DSTBC) structure that admit its application
in the proposed transmission scheme are identified and it is pointed out that
the recently proposed full diversity four group decodable DSTBCs from precoded
co-ordinate interleaved orthogonal designs and extended Clifford algebras
satisfy these conditions. It is then shown how differential encoding at the
source can be combined with the proposed transmission scheme to arrive at a new
transmission scheme that can achieve full cooperative diversity in asynchronous
wireless relay networks with no channel information and also no timing error
knowledge at the destination node. Finally, four group decodable distributed
differential space time block codes applicable in this new transmission scheme
for power of two number of relays are also provided.Comment: 5 pages, 2 figures, to appear in IEEE International Conference on
Communications, Beijing, China, May 19-23, 200
A Novel Construction of Multi-group Decodable Space-Time Block Codes
Complex Orthogonal Design (COD) codes are known to have the lowest detection
complexity among Space-Time Block Codes (STBCs). However, the rate of square
COD codes decreases exponentially with the number of transmit antennas. The
Quasi-Orthogonal Design (QOD) codes emerged to provide a compromise between
rate and complexity as they offer higher rates compared to COD codes at the
expense of an increase of decoding complexity through partially relaxing the
orthogonality conditions. The QOD codes were then generalized with the so
called g-symbol and g-group decodable STBCs where the number of orthogonal
groups of symbols is no longer restricted to two as in the QOD case. However,
the adopted approach for the construction of such codes is based on sufficient
but not necessary conditions which may limit the achievable rates for any
number of orthogonal groups. In this paper, we limit ourselves to the case of
Unitary Weight (UW)-g-group decodable STBCs for 2^a transmit antennas where the
weight matrices are required to be single thread matrices with non-zero entries
in {1,-1,j,-j} and address the problem of finding the highest achievable rate
for any number of orthogonal groups. This special type of weight matrices
guarantees full symbol-wise diversity and subsumes a wide range of existing
codes in the literature. We show that in this case an exhaustive search can be
applied to find the maximum achievable rates for UW-g-group decodable STBCs
with g>1. For this purpose, we extend our previously proposed approach for
constructing UW-2-group decodable STBCs based on necessary and sufficient
conditions to the case of UW-g-group decodable STBCs in a recursive manner.Comment: 12 pages, and 5 tables, accepted for publication in IEEE transactions
on communication
Generalized Silver Codes
For an transmit, receive antenna system (
system), a {\it{full-rate}} space time block code (STBC) transmits complex symbols per channel use. The well known Golden code is an
example of a full-rate, full-diversity STBC for 2 transmit antennas. Its
ML-decoding complexity is of the order of for square -QAM. The
Silver code for 2 transmit antennas has all the desirable properties of the
Golden code except its coding gain, but offers lower ML-decoding complexity of
the order of . Importantly, the slight loss in coding gain is negligible
compared to the advantage it offers in terms of lowering the ML-decoding
complexity. For higher number of transmit antennas, the best known codes are
the Perfect codes, which are full-rate, full-diversity, information lossless
codes (for ) but have a high ML-decoding complexity of the order
of (for , the punctured Perfect codes are
considered). In this paper, a scheme to obtain full-rate STBCs for
transmit antennas and any with reduced ML-decoding complexity of the
order of , is presented. The codes constructed are
also information lossless for , like the Perfect codes and allow
higher mutual information than the comparable punctured Perfect codes for . These codes are referred to as the {\it generalized Silver codes},
since they enjoy the same desirable properties as the comparable Perfect codes
(except possibly the coding gain) with lower ML-decoding complexity, analogous
to the Silver-Golden codes for 2 transmit antennas. Simulation results of the
symbol error rates for 4 and 8 transmit antennas show that the generalized
Silver codes match the punctured Perfect codes in error performance while
offering lower ML-decoding complexity.Comment: Accepted for publication in the IEEE Transactions on Information
Theory. This revised version has 30 pages, 7 figures and Section III has been
completely revise
Fast-Decodable Asymmetric Space-Time Codes from Division Algebras
Multiple-input double-output (MIDO) codes are important in the near-future
wireless communications, where the portable end-user device is physically small
and will typically contain at most two receive antennas. Especially tempting is
the 4 x 2 channel due to its immediate applicability in the digital video
broadcasting (DVB). Such channels optimally employ rate-two space-time (ST)
codes consisting of (4 x 4) matrices. Unfortunately, such codes are in general
very complex to decode, hence setting forth a call for constructions with
reduced complexity.
Recently, some reduced complexity constructions have been proposed, but they
have mainly been based on different ad hoc methods and have resulted in
isolated examples rather than in a more general class of codes. In this paper,
it will be shown that a family of division algebra based MIDO codes will always
result in at least 37.5% worst-case complexity reduction, while maintaining
full diversity and, for the first time, the non-vanishing determinant (NVD)
property. The reduction follows from the fact that, similarly to the Alamouti
code, the codes will be subsets of matrix rings of the Hamiltonian quaternions,
hence allowing simplified decoding. At the moment, such reductions are among
the best known for rate-two MIDO codes. Several explicit constructions are
presented and shown to have excellent performance through computer simulations.Comment: 26 pages, 1 figure, submitted to IEEE Trans. Inf. Theory, October
201
Construction of Block Orthogonal STBCs and Reducing Their Sphere Decoding Complexity
Construction of high rate Space Time Block Codes (STBCs) with low decoding
complexity has been studied widely using techniques such as sphere decoding and
non Maximum-Likelihood (ML) decoders such as the QR decomposition decoder with
M paths (QRDM decoder). Recently Ren et al., presented a new class of STBCs
known as the block orthogonal STBCs (BOSTBCs), which could be exploited by the
QRDM decoders to achieve significant decoding complexity reduction without
performance loss. The block orthogonal property of the codes constructed was
however only shown via simulations. In this paper, we give analytical proofs
for the block orthogonal structure of various existing codes in literature
including the codes constructed in the paper by Ren et al. We show that codes
formed as the sum of Clifford Unitary Weight Designs (CUWDs) or Coordinate
Interleaved Orthogonal Designs (CIODs) exhibit block orthogonal structure. We
also provide new construction of block orthogonal codes from Cyclic Division
Algebras (CDAs) and Crossed-Product Algebras (CPAs). In addition, we show how
the block orthogonal property of the STBCs can be exploited to reduce the
decoding complexity of a sphere decoder using a depth first search approach.
Simulation results of the decoding complexity show a 30% reduction in the
number of floating point operations (FLOPS) of BOSTBCs as compared to STBCs
without the block orthogonal structure.Comment: 16 pages, 7 figures; Minor changes in lemmas and construction
Low ML-Decoding Complexity, Large Coding Gain, Full-Rate, Full-Diversity STBCs for 2 X 2 and 4 X 2 MIMO Systems
This paper (Part of the content of this manuscript has been accepted for
presentation in IEEE Globecom 2008, to be held in New Orleans) deals with low
maximum likelihood (ML) decoding complexity, full-rate and full-diversity
space-time block codes (STBCs), which also offer large coding gain, for the 2
transmit antenna, 2 receive antenna () and the 4 transmit antenna, 2
receive antenna () MIMO systems. Presently, the best known STBC for
the system is the Golden code and that for the system is
the DjABBA code. Following the approach by Biglieri, Hong and Viterbo, a new
STBC is presented in this paper for the system. This code matches
the Golden code in performance and ML-decoding complexity for square QAM
constellations while it has lower ML-decoding complexity with the same
performance for non-rectangular QAM constellations. This code is also shown to
be \emph{information-lossless} and \emph{diversity-multiplexing gain} (DMG)
tradeoff optimal. This design procedure is then extended to the
system and a code, which outperforms the DjABBA code for QAM constellations
with lower ML-decoding complexity, is presented. So far, the Golden code has
been reported to have an ML-decoding complexity of the order of for
square QAM of size . In this paper, a scheme that reduces its ML-decoding
complexity to is presented.Comment: 28 pages, 5 figures, 3 tables, submitted to IEEE Journal of Selected
Topics in Signal Processin
Asymptotically-Optimal, Fast-Decodable, Full-Diversity STBCs
For a family/sequence of STBCs , with
increasing number of transmit antennas , with rates complex symbols
per channel use (cspcu), the asymptotic normalized rate is defined as . A family of STBCs is said to be
asymptotically-good if the asymptotic normalized rate is non-zero, i.e., when
the rate scales as a non-zero fraction of the number of transmit antennas, and
the family of STBCs is said to be asymptotically-optimal if the asymptotic
normalized rate is 1, which is the maximum possible value. In this paper, we
construct a new class of full-diversity STBCs that have the least ML decoding
complexity among all known codes for any number of transmit antennas and
rates cspcu. For a large set of pairs, the new codes
have lower ML decoding complexity than the codes already available in the
literature. Among the new codes, the class of full-rate codes () are
asymptotically-optimal and fast-decodable, and for have lower ML decoding
complexity than all other families of asymptotically-optimal, fast-decodable,
full-diversity STBCs available in the literature. The construction of the new
STBCs is facilitated by the following further contributions of this paper:(i)
For , we construct -group ML-decodable codes with rates greater than
one cspcu. These codes are asymptotically-good too. For , these are the
first instances of -group ML-decodable codes with rates greater than
cspcu presented in the literature. (ii) We construct a new class of
fast-group-decodable codes for all even number of transmit antennas and rates
.(iii) Given a design with full-rank linear dispersion
matrices, we show that a full-diversity STBC can be constructed from this
design by encoding the real symbols independently using only regular PAM
constellations.Comment: 16 pages, 3 tables. The title has been changed.The class of
asymptotically-good multigroup ML decodable codes has been extended to a
broader class of number of antennas. New fast-group-decodable codes and
asymptotically-optimal, fast-decodable codes have been include