Date of Award

Fall 2011

Degree Type


Degree Name

Master of Applied Science (MASc)


Electrical and Computer Engineering


Jian-Kang Zhang


Dongmei Zhao, Kon Max Wong



Committee Member

Dongmei Zhao, Kon Max Wong


In this thesis, noncoherent cooperative amplify-and-forward (AF) half-duplex relay systems and wireless communication systems equipped with a single transmitter antenna and multiple receiver antennas (SIMO) are considered, in which perfect channel information is unavailable at the destination end. For the AF half-duplex relay systems, the use of the least square error (LSE) receiver is proposed for detection. By using perturbation theory on the eigenvalues, an asymptotic formula of pairwise error probability for the LSE detector is derived. The result shows that the full diversity gain function mimics coherent cooperative AF half-duplex relay systems, whereas the coding gain function mimics noncoherent multi-inputs multi-outputs (MIMO) systems.

In order to design full diversity noncoherent signals for both systems, a novel concept called a uniquely factorable constellation (UFC) is proposed in this thesis. It is proved that such a UFC design guarantees the unique blind identification of channel coefficients and transmitted signals in a noise-free case for the SIMO channel by only processing two received signals, as well as full diversity with the noncoherent maximum likelihood (ML) receiver in a noisy case. By using the Lagrange's four-square theorem, an algorithm is developed to efficiently and effectively design various sizes of energy-efficient unitary UFCs to optimize the coding gain. In addition, a closed-form optimal energy scale is found to maximize the coding gain for the unitary training scheme based on the commonly-used quadrature amplitude modulation (QAM) constellations.

McMaster University Library