2,089 research outputs found
Maximum Rate of Unitary-Weight, Single-Symbol Decodable STBCs
It is well known that the Space-time Block Codes (STBCs) from Complex
orthogonal designs (CODs) are single-symbol decodable/symbol-by-symbol
decodable (SSD). The weight matrices of the square CODs are all unitary and
obtainable from the unitary matrix representations of Clifford Algebras when
the number of transmit antennas is a power of 2. The rate of the square
CODs for has been shown to be complex symbols per
channel use. However, SSD codes having unitary-weight matrices need not be
CODs, an example being the Minimum-Decoding-Complexity STBCs from
Quasi-Orthogonal Designs. In this paper, an achievable upper bound on the rate
of any unitary-weight SSD code is derived to be complex
symbols per channel use for antennas, and this upper bound is larger than
that of the CODs. By way of code construction, the interrelationship between
the weight matrices of unitary-weight SSD codes is studied. Also, the coding
gain of all unitary-weight SSD codes is proved to be the same for QAM
constellations and conditions that are necessary for unitary-weight SSD codes
to achieve full transmit diversity and optimum coding gain are presented.Comment: accepted for publication in the IEEE Transactions on Information
Theory, 9 pages, 1 figure, 1 Tabl
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
Design of fully diverse multiple-antenna codes based on Sp(2)
Fully diverse constellations, i.e., sets of unitary matrices whose pairwise differences are nonsingular, are useful in multiple-antenna communications, especially in multiple-antenna differential modulation, since they have good pairwise error properties. Recently, group theoretic ideas, especially fixed-point-free (fpf) groups, have been used to design fully diverse constellations of unitary matrices. Here we construct four-transmit-antenna constellations appropriate for differential modulation based on the symplectic group Sp(2). They can be regarded as extensions of Alamouti's celebrated two-transmit-antenna orthogonal design which can be constructed from the group Sp(1). We further show that the structure of Sp(2) codes lends itself to efficient maximum-likelihood (ML) decoding via the sphere decoding algorithm. Finally, the performance of Sp(2) codes is compared with that of other existing codes including Alamouti's orthogonal design, a 4/spl times/4 complex orthogonal design, Cayley differential unitary space-time codes and group-based codes
Representation theory for high-rate multiple-antenna code design
Multiple antennas can greatly increase the data rate and reliability of a wireless communication link in a fading environment, but the practical success of using multiple antennas depends crucially on our ability to design high-rate space-time constellations with low encoding and decoding complexity. It has been shown that full transmitter diversity, where the constellation is a set of unitary matrices whose differences have nonzero determinant, is a desirable property for good performance. We use the powerful theory of fixed-point-free groups and their representations to design high-rate constellations with full diversity. Furthermore, we thereby classify all full-diversity constellations that form a group, for all rates and numbers of transmitter antennas. The group structure makes the constellations especially suitable for differential modulation and low-complexity decoding algorithms. The classification also reveals that the number of different group structures with full diversity is very limited when the number of transmitter antennas is large and odd. We, therefore, also consider extensions of the constellation designs to nongroups. We conclude by showing that many of our designed constellations perform excellently on both simulated and real wireless channels
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
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