Angular resolution of sensor arrays for signals with a bandwidth larger than zero

For sinusoidal waves with bandwidth zero, the classical formula epsilon = (k)(lambda)/L = kc/fL is obtained for the resolution angle of a sensor array with aperture L. Waves with the time variation of a rectangular pulse of duration delta T yield epsilon = 2Kc/(Delta f)(L)(Square root of P/P sub N), where P/P sub N is the signal-to-noise ratio and Delta f = 1/2(Delta T) is the nominal bandwidth of the pulse. Hence, the resolution angle epsilon can be reduced by increasing the signal power as well as by increasing the array length L or the bandwidth Delta f. This is pertinent to radar and underwater acoustic beam-forming.