09-07-2012, 12:03 PM
Systematic Design of Unitary Space–Time Constellations
[attachment=27241]
INTRODUCTION
RECENT theoretical treatments have shown that communication
systems that employ multiple antennas can have
very high channel capacities, especially in Rayleigh flat-fading
environments [5], [16], [9]. In [5], a constructive approach to
achieving some of this capacity is proposed under the assumption
that the receiver knows the complex-valued Rayleigh fading
coefficients. Under the same assumption, [14] presents a trellisbased
approach for designing space–time codes, and [15] gives
a space–time signaling method based on orthogonal designs.
However, the known-channel assumption may not be realistic in
a rapidly changing fading environment or with a large number
of transmitter antennas.
FOURIER-BASED CONSTRUCTION
In this section we present a Fourier-based construction of a
constellation of unitary space–time signals. Section III-A gives
the intuition behind the construction, which has a block-circulant
signal correlation structure. Section III-B then proves that
this construction yields all constellations having a block-circulant
correlation structure.
We make no claim for the optimality of circulant correlation
structure. However, this structure has the advantage that it significantly
simplifies the design process.
EQUIVALENT ALGEBRAIC CONSTRUCTION
The constellation construction described in the previous section
can also be viewed algebraically, and in this section we
create a constellation of signals by mapping a linear block code
into complex signal matrices. The code is over the ring of integers
modulo- and the number of codewords is equal to the
number of desired signals . We will relate to shortly, and
we begin by describing the construction for transmitter
antenna.
CONCLUSIONS
Unitary space–time modulation is appropriate for flat-fading
conditions where nobody knows the propagation coefficients.
It requires the design of relatively large constellations of matrix-
valued signals according to a criterion that differs markedly
from the traditional maximum-Euclidean-distance criterion.We
have introduced new design algorithms that easily produce large
constellations of these signals in a systematic manner, by successive
rotations of an initial signal. This entails the imposition
of a circulant correlation structure on the constellation. Further
research is needed to determine if significant improvements are
possible by relaxing this structure.
[attachment=27241]
INTRODUCTION
RECENT theoretical treatments have shown that communication
systems that employ multiple antennas can have
very high channel capacities, especially in Rayleigh flat-fading
environments [5], [16], [9]. In [5], a constructive approach to
achieving some of this capacity is proposed under the assumption
that the receiver knows the complex-valued Rayleigh fading
coefficients. Under the same assumption, [14] presents a trellisbased
approach for designing space–time codes, and [15] gives
a space–time signaling method based on orthogonal designs.
However, the known-channel assumption may not be realistic in
a rapidly changing fading environment or with a large number
of transmitter antennas.
FOURIER-BASED CONSTRUCTION
In this section we present a Fourier-based construction of a
constellation of unitary space–time signals. Section III-A gives
the intuition behind the construction, which has a block-circulant
signal correlation structure. Section III-B then proves that
this construction yields all constellations having a block-circulant
correlation structure.
We make no claim for the optimality of circulant correlation
structure. However, this structure has the advantage that it significantly
simplifies the design process.
EQUIVALENT ALGEBRAIC CONSTRUCTION
The constellation construction described in the previous section
can also be viewed algebraically, and in this section we
create a constellation of signals by mapping a linear block code
into complex signal matrices. The code is over the ring of integers
modulo- and the number of codewords is equal to the
number of desired signals . We will relate to shortly, and
we begin by describing the construction for transmitter
antenna.
CONCLUSIONS
Unitary space–time modulation is appropriate for flat-fading
conditions where nobody knows the propagation coefficients.
It requires the design of relatively large constellations of matrix-
valued signals according to a criterion that differs markedly
from the traditional maximum-Euclidean-distance criterion.We
have introduced new design algorithms that easily produce large
constellations of these signals in a systematic manner, by successive
rotations of an initial signal. This entails the imposition
of a circulant correlation structure on the constellation. Further
research is needed to determine if significant improvements are
possible by relaxing this structure.