Multi-element array signal reconstruction with adaptive least-squares algorithms

For a mechanical antenna system with a perfect parabolic reflector surface of diameter D the antenna gain is proportional to (D/λ_c)², where λ_c denotes the received carrier wavelength. However, for a practical system an increase in D/λ_c is also associated with a decrease in antenna efficiency due to the imperfect reflector surface. Since the antenna efficiency is a very sensitive function of the RMS surface deviation or effectively ofD/λ_c, the loss in efficiency can more than offset the increase in directivity. The loss in efficiency results owing to the dispersion of the signal in the focal plane, with the result that only a fraction of the available signal power is collected by the focal feed. A configuration wherein several feeds are placed in the focal plane of the antenna is considered so as to capture all the available power. However, the signal phase and amplitude at the outputs of the various feeds vary randomly with time owing to the time-varying deformation of the reflector surface induced, for example, by vibrational modes set up by gravitational or thermal fields or wind. Coherent signal combining techniques based on an adaptive least-squares algorithm are investigated for nearly optimally and adaptively combining the outputs of these feeds. The performances of the two proposed versions of the least-squares algorithm are evaluated by simulations. It is shown for the example considered that both the adaptive least-squares algorithms are capable of offsetting most of the loss in the antenna gain incurred owing to reflector surface deformations.