Synthetic-Aperture Radar Based on Nonsinusoidal Functions: IX -Array Beam Forming

Abstract
For sinusoidal waves with bandwidth zero, one obtains the classical formula ϵ = κNL = kc//spl conint/L for the resolution angle of a sensor array, where L is the length of the array, λ the wavelength, /spl conint/the frequency, and c the phase velocity of the wave, while κis a constant whose value is usually chosen to be 1. Waves with the time variation of a rectangular pulse of duration ▵T yield the resolution angle ϵ = 2Kc/▵/spl conint/ P/P /sub N/, where P/P/sub N/ is the signal-to-noise ratio and ▵/spl conint/ = 1/2▵T the nominal bandwidth of the pulse; the same result holds for coded pulse sequences, such as Barker codes or complementary codes, if the main lobe of their auto-correlation function has the shape of a triangle with rise time ▵T. Hence, the resolution angle e can be reduced by increasing the signal power, as well as by increasing the array length L or the bandwidth ▵f. For sinusoidal waves, an increase of the signal power brings no reduction of the resolution angle. The trade between signal power and frequency bandwidth is of interest whenever the attenuation increases rapidly with frequency, e.g., in high-resolution all-weather radar or in underwater acoustic beam forming.