abstract: This dissertation considers two different kinds of two-hop multiple-input multiple-output (MIMO) relay networks with beamforming (BF). First, "one-way" amplify-and-forward (AF) and decode-and-forward (DF) MIMO BF relay networks are considered, in which the relay amplifies or decodes the received signal from the source and forwards it to the destination, respectively, where all nodes beamform with multiple antennas to obtain gains in performance with reduced power consumption. A direct link from source to destination is included in performance analysis. Novel systematic upper-bounds and lower-bounds to average bit or symbol error rates (BERs or SERs) are proposed. Second, "two-way" AF MIMO BF relay networks are investigated, in which two sources exchange their data through a relay, to improve the spectral efficiency compared with one-way relay networks. Novel unified performance analysis is carried out for five different relaying schemes using two, three, and four time slots in sum-BER, the sum of two BERs at both sources, in two-way relay networks with and without direct links. For both kinds of relay networks, when any node is beamforming simultaneously to two nodes (i.e. from source to relay and destination in one-way relay networks, and from relay to both sources in two-way relay networks), the selection of the BF coefficients at a beamforming node becomes a challenging problem since it has to balance the needs of both receiving nodes. Although this "BF optimization" is performed for BER, SER, and sum-BER in this dissertation, the solution for optimal BF coefficients not only is difficult to implement, it also does not lend itself to performance analysis because the optimal BF coefficients cannot be expressed in closed-form. Therefore, the performance of optimal schemes through bounds, as well as suboptimal ones such as strong-path BF, which beamforms to the stronger path of two links based on their received signal-to-noise ratios (SNRs), is provided for BERs or SERs, for the first time. Since different channel state information (CSI) assumptions at the source, relay, and destination provide different error performance, various CSI assumptions are also considered. / Dissertation/Thesis / Ph.D. Electrical Engineering 2012

For this project, the design, implementation, characterization, calibration and possible applications of a multiple transducer stethoscope apparatus were investigated. The multi-transducer sensor array design consists of five standard stethoscope diaphragms mounted to a rigid frame for a-priori knowledge of their relative spatial locations in the x-y plane, with compliant z-direction positioning to ensure good contact and pressure against the subject’s skin for reliable acoustic coupling. When this apparatus is properly placed on the body, it can digitally capture the same important body sounds investigated with standard acoustic stethoscopes; especially heart sounds. Acoustic signal inputs from each diaphragm are converted to electrical signals through microphone pickups installed in the stethoscope connective tubing; and are subsequently sampled and digitized for analysis. With this system, we are able to simultaneously interrogate internal body sounds at a sampling rate of 2 KHz, as most heart sounds of interest occur below 200 Hz. This system was characterized and calibrated by chirp and impulse signal tests. After calibrating the system, a variety of methods for combining the individual sensor channel data to improve the detectability of different signals of interest were explored using variable-delay beam forming. S1 and S2 heart sound recognition with optimized beam forming delays and inter-symbol noise elimination were investigated for improved discernment of the S1 or S2 heart sounds by a user. Also, stereophonic presentation of heart sounds was also produced to allow future investigation of its potential clinical diagnostic efficacy.