Shared Wideband Transmit Antenna Arrays: Optimal Pattern Synthesis and Spatio-Temporal Delta-Sigma Modulation

Title of Dissertation: Shared Wideband Transmit Antenna Arrays: Optimal Pattern Synthesis and Spatio-Temporal Delta-Sigma Modulation Dan P. Scholnik, Doctor of Philosophy, 2006 Dissertation directed by: Dr. Tulay Adali, Professor Computer Science and Electrical Engineering Dr. Jeffrey O. Coleman Naval Research Laboratory The use of a single transmit array to simultaneously performmultiple independent functions requires an architecture with an elusive combination of high power, linearity, and wide bandwidth. A promising approach is delta-sigma modulation, which achieves high linearity by spectrally shaping the errors from a low-resolution quantizer away from the signal band. Delta-sigma modulation can potentially provide high power as well when combined with appropriate power driver electronics, but the bandwidth requirements can only be met with extreme clock rates. The clock rate can be reduced by jointly shaping quantization noise in temporal and spatial frequency. The spatio-temporal delta-sigma modulator introduced here reduces required clock rates by taking advantage of spatial oversampling, either by adding array elements or by taking advantage of the inherent spatial oversampling at the lower operating frequencies of wideband arrays. The loop filter in the spatio-temporal delta-sigma modulator is the key to the design, and it is shown how second-order cone programming (SOCP, an efficient form of convex optimization) can be used to optimize the resulting signal-to-noise ratio subject to stability and computability constraints. The choice of computability constraint is shown to have a strong effect on both the resulting system performance and on the ease of parallel implementation. Once a linear architecture is assumed, then custom optimization of transmit array patterns offers a great deal of flexibility. Although narrowband pattern synthesis is wellstudied, wide-bandwidth arrays pose a more challenging design problem. In a conventional wideband array beam steering is done using time delays, resulting in a beamwidth that is proportional to frequency, and a mainlobe frequency response that shows undesired angledependent effects. It is shown that placing an FIR filter at each element of an array allows the direct control of such metrics as directivity, efficiency, gain, peak and mean-square sidelobe levels, polarization, and mainlobe frequency-response flatness. These metrics are formulated for wideband arrays and optimized using SOCP. The system model and the derivations are general enough to admit almost any array architecture, including arbitrary element locations, nonuniform element responses, and multiple polarizations.