Beamforming Illustrations

This report progressively considers two classes of beamforming problems. In the first, the desired characteristics of the sensor array are known and the array design and filter taps are chosen to achieve the desired performance. In the second, the array must adapt to noise and interfering signals, so received data is used to get an optimum response. The illustrations ultimately show that the data dependent algorithms are very sensitive to noise variations and in order to outperform simple data independent methods, a signal modeling approach should be used. ARRAY BASICS The signals that arrive at arrayed antennas differ from sensor to sensor due to the different distances the signal must propagate. In the case of a narrowband signal, these differences are manifested in the phase variations of the carrier signal. Figure 1 illustrates the effect of a linear equispaced sensor geometry on the phase of the received signals. Signals received at adjacent sensors travel a difference in distance of dcos(q) which corresponds to a phase difference o