In the phased-array radar (PAR) signals from each antenna are transmitted at the same carrier frequency, which yields narrowly focused only angle dependent beampattern. In contrast, in the frequency-diverse-array (FDA) radar signals from antenna array are generally transmitted at linearly increasing frequencies that yields range, time, and angle dependent beampattern. Reported literature on FDA radar missed the contribution of path-differences in the signal model due to the antenna array elements, which may lead to misleading results. In this work, incorporating missed path-differences, the signal model of FDA radar is corrected. Using the corrected signal model, it is shown that the instantaneous beampattern depends on the number of transmit antenna and average beampattern depends on the product of frequency-offset and pulse-duration. Moreover, to illuminate the desired region-of-interest for longer dwell time, discrete-Fourier-transform based low-complexity algorithm is proposed. In contrast to the conventional FDA radar's 'S' shaped beampattern, the beampattern of the proposed algorithm changes linearly with range. Simulation results compare the performance of our proposed algorithm with the existing ones and show the superiority of our proposed algorithm.Index Terms-Frequency-diverse-array radars, Linear and non-linear frequency offset, Time and range dependent beampattern, Discrete-Fourier-transform.