The widespread availability of antenna arrays and the capability to independently control signal emissions from each antenna make transmit signal design increasingly important for radar and wireless communication systems. In the first part of this work, we develop the framework for a MIMO radar transmit scheme which trades of waveform diversity for beampattern directivity. Time-division beamforming consists of a linear precoder that provides direct control of the transmit beampattern and is able to form multiple transmit beams in a single pulse. The MIMO receive ambiguity function, which incorporates the receiver structure, reveals a space and delay-Doppler separability that emphasizes the importance of the transmit-receive beampattern and single-input single-output (SISO) ambiguity function. The second part of this work focuses on channel estimation for massive MIMO systems. As the size of arrays increase, conventional channel estimation techniques no longer remain practical. In current systems, training sequences probe wireless channels in orthogonal directions to obtain channel state information for block fading channels. The training overhead becomes signicant as the number of transmit antennas increases, thereby creating a need for alternative channel estimation techniques. In this work, we relax the orthogonal restriction on the sounding vectors and introduce a feedback channel to enable closed-loop sounding vector design. A probability of misalignment framework is introduced, which provides a measure to sequentially design sounding vectors.
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