Receive Response Design Compensating Direction-Dependent Impulse Responses of UWB Antennas

We demonstrated that the ultra-wideband (UWB) waveforms may not only have different amplitudes for different directions but also different waveform shapes for both transmit and receive antennas. When designing the receive filter response, these direction-dependent antenna impulse responses need to be considered. Taking account of the relative orientations of both transmit and receive antennas, a metric that maximizes the average received signal to noise ratio is defined. To make the maximization problem mathematically tractable, one upper-bound of the metric is chosen to for applying variational calculus. The solution is a linear combination of all incoming waveforms weighted by their relative probability of occurence. For practical purpose, a best-candidate solution is also obtained through numerical search. The results are illustrated for the diamond antenna, which is a potential UWB antenna. The search process also reveals that a large percentage of the candidate waveforms can provide close performance to the linear combination solution, while some candidates provide poor performances and should therefore be avoided in practice.