Interpolation noise in a hard-limited beamformer
J. W. Young · The Journal of the Acoustical Society of America · 1983
Beamforming typically requires sampling of individual hydrophone outputs at a rate substantially higher than Nyquist for bandpass processes. One approach to minimizing the sampling rate is the use of an interpolation filter for reconstruction of intermediate sample values [R. G. Pridham and R. A. Mucci, J. Acoust. Soc. Am. 63, 425–434 (1978)]. In principle, the required samples can be determined without error from the Nyquist rate samples since the latter contain complete information on the band-limited element signal. When the element signals are hard-limited, all amplitude information is lost and errors are introduced into the interpolation process. Information in a hard-limited signal (HLS) is contained in the zero-crossing times. Basically, sampling a HLS obliterates the information necessary to determine exact zero-crossing times between sample values. In this paper, we present an analysis of the mean square error (interpolation noise) associated with estimating the values of the HLS at intermediate times. We compute the increase in beam noise power due to this error and show that this imposes a limit on our ability to perform adaptive null steering with such an array.