Optimum design of near-field sensor arrays

A sensor array having invariant signal-to-noise (SNR) gain over a wide band of frequencies is desirable, even essential, in communication. The design of sensor arrays with frequency invariant (FI) gain has been involved in several investigations. We attain a frequency-variable white noise gain constraint by approximating the constant gain contours in the plane of frequency/wavelength and white noise gain by a piecewise polynomial function, which reduces gain variation with frequency within the lower and middle portions of the design band. Meanwhile, we slightly decrease the sensor spacing, which reduces gain variation within the upper portion of the band, so that gain variation over a 10:1 design band is limited to 1 dB without increasing the sensor number. We perform the design of the equally-spaced array prescribed by J.G. Ryan and R.A. Goubran (see IEEE Trans. Speech Audio Processing, vol.8, no.2, p.173-6, 2000), in order to compare our design result with their´s, and conduct the design of a space-tapered array with FI gain, leading to a result with more generality. We discuss the array´s gain improvement, robustness to errors and capability of distance discrimination, and illustrate the trade-off between them.