TY - JOUR

T1 - Locally Diverse Constellations from the Special Orthogonal Group

AU - Karpuk, David A.

AU - Hollanti, Camilla

PY - 2016/6/1

Y1 - 2016/6/1

N2 - To optimize rotated multidimensional constellations over a single-input single-output Rayleigh fading channel, a family of rotation matrices is constructed for all dimensions which are a power of 2. This family is a one-parameter subgroup of the group of rotation matrices, and is located using a gradient descent scheme on this Lie group. The parameter defining the family is chosen to optimize the cutoff rate of the constellation. The optimal rotation parameter is computed explicitly for low signal-to-noise ratios. These rotations outperform full-diversity algebraic rotations in terms of cutoff rate at low signal-to-noise ratio (SNR) and bit error rate at high SNR in dimension n = 4. However, a quadrature amplitude modulation (QAM) constellation rotated by such a matrix lacks full diversity, in contrast with the conventional wisdom that good signal sets exhibit full diversity. A new notion of diversity, referred to as local diversity, is introduced to attempt to account for this behavior. Roughly, a locally fully diverse constellation is fully diverse only in small neighborhoods. A local variant of the minimum product distance is also introduced and is shown experimentally to be a superior predictor of constellation performance than the minimum product distance in dimension n = 4.

AB - To optimize rotated multidimensional constellations over a single-input single-output Rayleigh fading channel, a family of rotation matrices is constructed for all dimensions which are a power of 2. This family is a one-parameter subgroup of the group of rotation matrices, and is located using a gradient descent scheme on this Lie group. The parameter defining the family is chosen to optimize the cutoff rate of the constellation. The optimal rotation parameter is computed explicitly for low signal-to-noise ratios. These rotations outperform full-diversity algebraic rotations in terms of cutoff rate at low signal-to-noise ratio (SNR) and bit error rate at high SNR in dimension n = 4. However, a quadrature amplitude modulation (QAM) constellation rotated by such a matrix lacks full diversity, in contrast with the conventional wisdom that good signal sets exhibit full diversity. A new notion of diversity, referred to as local diversity, is introduced to attempt to account for this behavior. Roughly, a locally fully diverse constellation is fully diverse only in small neighborhoods. A local variant of the minimum product distance is also introduced and is shown experimentally to be a superior predictor of constellation performance than the minimum product distance in dimension n = 4.

KW - capacity

KW - cutoff rate

KW - full diversity

KW - Lie groups

KW - non-uniform constellations

KW - Rayleigh fading channel

KW - rotated constellations

UR - http://www.scopus.com/inward/record.url?scp=84976315625&partnerID=8YFLogxK

U2 - 10.1109/TWC.2016.2541668

DO - 10.1109/TWC.2016.2541668

M3 - Article

AN - SCOPUS:84976315625

VL - 15

SP - 4426

EP - 4437

JO - IEEE Transactions on Wireless Communications

JF - IEEE Transactions on Wireless Communications

SN - 1536-1276

IS - 6

M1 - 7433476

ER -