Optimization based expanded dictionary adaptive antenna array modeling for far field low frequency propagation

Leveraging existing multi-frequency antenna arrays for purposes they were not originally designed would greatly improve the benefits of such systems. For example, the use of arrays of small antennas with novel waveforms may produce low frequency signals in the far field that are not possible using single antennas and classical waveforms. In particular, we propose to investigate the formation of low frequency signals using a combination of several small wide-band antennas, radiating localized signal forms. We seek to represent an arbitrary low frequency wave signal as a linear combination of localized Hermite functions and compactly supported Wavelet basis functions from several families. We will investigate the design of wavelets with optimal shifts, dilations and amplitudes. The use of a dictionary of different basis functions will allow us to represent arbitrary sinusoids accurately with a small amount of antennas. In order to pick the optimal weights in the linear combination with compactly supported functions, we will investigate the use of iteratively reweighted least squares and moving average approaches. Antenna array weights will be optimized per desired constraints such as maximal signal to noise ratio and minimal variance. Applications of our designs to time reversal detection will be demonstrated.