Asymptotic error probability analysis of quadratic receivers in Rayleigh-fading channels with applications to a unified analysis of coherent and noncoherent space-Time receivers
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 addition, it is proved that for any given nonzero received signal, the unique blind identification of both the equivalent channel and the transmitted signals in a noise-free case is equivalent to full diversity with the LSE detector in a Gaussian noise environment. 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 iv maximum likelihood (ML) receiver in a noisy case. By using the Lagrange’s foursquare 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. Based on the signal design criterion and UFCs established in this thesis, the systematic designs of noncoherent full diversity unitary constellations for the noncoherent SIMO systems and the noncoherent AF half-duplex protocol with three nodes are proposed. We also derive the closed-form decision rule for the generalized likelihood ratio test (GLRT) receiver for the relay systems. Comprehensive computer simulations show that error performance of the unitary UFC designed in this thesis is superior to those of the differential schemes, the optimal unitary training schemes presented in this thesis and the signal-to-noise ratio (SNR) efficient training schemes using the QAM constellation for the SIMO systems, which, thus far, performs the best error performance in current literatures. Computer simulations also demonstrate that error performance of the unitary diagonal distributed space-time block codes proposed in this thesis outperforms those of the differential codes and the optimally precoded training schemes for the relay systems.