Soft-decision equalization techniques for frequency selective MIMO channels

Multi-input multi-output (MIMO) technology is an emerging solution for high data rate wireless communications. We develop soft-decision based equalization techniques for frequency selective MIMO channels in the quest for low-complexity equalizers with BER performance competitive to that of ML sequence detection. We first propose soft decision equalization (SDE), and demonstrate that decision feedback equalization (DFE) based on soft-decisions, expressed via the posterior probabilities associated with feedback symbols, is able to outperform hard-decision DFE, with a low computational cost that is polynomial in the number of symbols to be recovered, and linear in the signal constellation size. Building upon the probabilistic data association (PDA) multiuser detector, we present two new MIMO equalization solutions to handle the distinctive channel memory. With their low complexity, simple implementations, and impressive near-optimum performance offered by iterative soft-decision processing, the proposed SDE methods are attractive candidates to deliver efficient reception solutions to practical high-capacity MIMO systems. Motivated by the need for low-complexity receiver processing, we further present an alternative low-complexity soft-decision equalization approach for frequency selective MIMO communication systems. With the help of iterative processing, two detection and estimation schemes based on second-order statistics are harmoniously put together to yield a two-part receiver structure: local multiuser detection (MUD) using soft-decision Probabilistic Data Association (PDA) detection, and dynamic noise-interference tracking using Kalman filtering. The proposed Kalman-PDA detector performs local MUD within a sub-block of the received data instead of over the entire data set, to reduce the computational load. At the same time, all the inter-ference affecting the local sub-block, including both multiple access and inter-symbol interference, is properly modeled as the state vector of a linear system, and dynamically tracked by Kalman filtering. Two types of Kalman filters are designed, both of which are able to track an finite impulse response (FIR) MIMO channel of any memory length. The overall algorithms enjoy low complexity that is only polynomial in the number of information-bearing bits to be detected, regardless of the data block size. Furthermore, we introduce two optional performance-enhancing techniques: cross- layer automatic repeat request (ARQ) for uncoded systems and code-aided method for coded systems. We take Kalman-PDA as an example, and show via simulations that both techniques can render error performance that is better than Kalman-PDA alone and competitive to sphere decoding. At last, we consider the case that channel state information (CSI) is not perfectly known to the receiver, and present an iterative channel estimation algorithm. Simulations show that the performance of SDE with channel estimation approaches that of SDE with perfect CSI.

Soft Lewis acid catalyzed cycloisomerization of oxo-alkynes and enynes

In the literature, some transition metal salts have been used as soft Lewis acids to activate alkynes toward nucleophilic attack. For example, Pt(II), Au(I) and Pd(II) catalysts can catalyze cycloisomerization reactions of alkynyl compounds to give a variety of cyclic products. In order to expand the scope of these reactions, in chapter 2 of this dissertation, several alkynyl epoxides were isomerized to cyclic allyl vinyl ethers using PtCl2 as the catalyst. Three of these allyl vinyl ethers were hydrolyzed to 2-hydroxymorpholine derivatives and two were converted to piperidine derivatives by thermal Claisen rearrangement. In order to find more benign and inexpensive catalysts for these types of reactions, in chapter 3 of this dissertation, BiCl3 was used to catalyze the isomerization of eight enynes to pyrrolidine derivatives. This reaction was normally catalyzed by expensive noble metal catalysts, such as Pd(II), Pt(II) and Au(I). All the cyclic products are valuable intermediates in the synthesis of bioactive molecules, these soft Lewis acid catalyzed cycloisomerization may find applications in the synthesis of bioactive molecules.