A full diversity constellation, that is, a set of unitary matrices whose differences have nonzero determinant, is a design criterion for codes with good performance using differential unitary space-time modulation. Fixed-point free groups and the infinite groupSU(2) have been used to produce full diversity unitary group constellations. In this paper, we present a new Bruhat decomposition design for constructing full diversity unitary space-time constellations for any number of antennas. They are constructed from cosets of a unitary diagonal subgroupD, and our design has a particularly simple structure for the case where the number of transmitter antennas is prime. We also consider the extension of these constellation designs for an even number of transmitter antennas by replacingDwith a Hamiltonian constellation. Some examples of proposed constellations for two to six transmitter antennas are given. Simulations show that our proposed constellations perform well in unknown Rayleigh fading channel.

This correspondence presents a construction of affine reflection group codes. The solution to the initial vector and nearest distance problem is presented for all irreducible affine reflection groups of rank n ges 2, for varying stabilizer subgroups. We use a detailed analysis of the geometry of affine reflection groups to produce a decoding algorithm which is equivalent to the maximum-likelihood decoder, yet whose complexity depends only on the dimension of the vector space containing the codewords, and not on the number of codewords. We give several examples of the decoding algorithm, both to demonstrate its correctness and to show how, in small rank cases, it may be further streamlined by exploiting additional symmetries of the group.

Diversity sum, which is calculated from the Frobenius norm of the difference of two distinct elements in a signal constellation, is the significant parameter to predict a unitary space–time constellation having good performance in low signal-to-noise ratio (SNR). In this correspondence, we propose a method to compute the diversity sum of a unitary group constellation using a character table. Our proposed analysis is simple, requiring only a lookup of the character table. We illustrate our method for the finite special linear groups$SL_{2}$, and compare codes with high diversity sum against fixed point free groups at low SNR. We also introduce the notion of a faithful group constellation, that is, one whose diversity sum is greater than$0$. Faithful group constellations may be obtained from any nontrivial character of a group. We describe the method to do so in this correspondence and illustrate it with the example of the finite projective special linear group${\rm PSL}_{2}$.

A closed-form upper bound is presented for the average pairwise error probabilities (PEP) of space–time codes for a keyhole channel. It is derived from the exact conditional PEP for given fading channel coefficients using a moment generating function-based approach. Simulation results are included for varying numbers of antennas that affirm that the proposed PEP serves as a tight bound for codes in a keyhole channel.

In this correspondence, we propose new unitary space-time constellation designs with high diversity products. Our Hamiltonian and product constellations are based on Slepian's group codes, and can be used for any number of antennas and any data rate. Our Hamiltonian constellations achieve the theoretical upper bound of diversity product when the number of transmitter antennas is even and the cardinality of the signal constellation is less than or equal to 5. Many of our Hamiltonian and product constellations outperform, and have higher diversity products than, the best known designs in the literature. These include orthogonal designs, dicyclic groups, cyclic groups, parametric codes, numerical approaches, nongroup designs, Cayley codes, TAST codes and some constellations obtained from fixed-point free groups.

In this paper, we propose new full diversity unitary space-time codes based on Hamiltonian constellation designs. Our proposed constellations can be used for any number of antennas and for any data rate. For two transmitter antennas, the constellations are constructed from cyclic group codes. For a larger number of transmitter antennas, the design employs the direct sum of 2 times 2 Hamiltonian matrices and roots of unity. We give some examples of proposed constellations, and also show that they outperform known design techniques in the literature

Full diversity signal constellations for any numbers of transmitter antennas and for any orders which are constructed from 2/spl times/2 Hamiltonian matrices are investigated in this paper. The diversity product of a 2/spl times/2 Hamiltonian constellation equals one half of the Euclidean distance between two points in C/sup 2/. By considering the transformation from R/sup 4/ to C/sup 2/, the idea of group codes is used to construct a high diversity product constellation for any order L. The (L,4) cyclic group codes are considered to obtain L 4-dimensional codewords for group codes. We show that our 2/spl times/2 Hamiltonian constellations have higher diversity product than orthogonal and diagonal constellation designs. We extend our construction to the general case for any numbers of transmitter antennas M>2 by using a direct sum of 2/spl times/2 Hamiltonian matrices for M even, and a direct sum of 2/spl times/2 Hamiltonian matrices with the L/sup th/ roots of unity for M odd. It is shown that these constellations outperform cyclic groups and some of those obtained using fixed-point free groups.

This paper proposes new unitary space-time constellation designs with high diversity products for any number of antennas and any rate based on Slepian's group codes. Many of our Hamiltonian and product constellations have the best known diversity products in the literature, and outperform all other constellation designs.

In this paper, we present a new design of constructing full diversity unitary constellations using differential space-time modulation for any number of transmitter and receiver antennas. These constellations are constructed from a Bruhat decomposition which allows us to choose disjoint nonoverlapping cosets of a unitary diagonal subgroup in such a way that full diversity is preserved. Simulations show that our Bruhat constellations perform well in unknown Rayleigh fading channel.