Wireless devices have become an integral part of our everyday lives. Cell-phones, PDA's, Wi-Fi enabled laptops, smart homes and appliances, and automated highway systems are some of the examples of wireless devices and networks in common use. More and more applications and functionalities are constantly being added to these devices, and to support these new applications high data rate communication is required between the wireless devices.;Achieving high data rates with wireless communication is impeded by severe fluctuations in the received signal strength (called fading) due to mobility, the exponential attenuation of signal power with distance (called path loss), and interference due to simultaneous transmissions by different users at the same time or over same frequency band. Two of the promising techniques to mitigate the effects of fading, path loss, and interference are: using multiple antennas at the transmitter and receiver, and employing extra nodes (called relays) in between the transmitter and its receiver to relay the transmitter's message to its receiver.;This dissertation identifies the optimal transmit and receive strategy with multiple antennas that maximizes the transmission capacity of an ad-hoc wireless network. The transmission capacity is defined as the maximum number of transmitter-receiver pairs that can simultaneously communicate under a per transmission quality of service constraint. This dissertation also presents novel relay transmission strategies for multiple antenna equipped relay based communication that achieve near optimal performance, with Shannon capacity and diversity-multiplexing tradeoff (DMT) as the performance metrics. The Shannon capacity is defined as the maximum rate of reliable communication, while the DMT characterizes the maximum diversity gain for a given value of multiplexing gain in a multiple antenna system. DMT is used as the benchmark, since transmission strategies that meet the DMT are guaranteed to leverage both the advantages of multiple antenna systems.
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