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Estimating the signal direction of arrival (DOA) using a compact system is of great interest in various civil, military, airborne, and communication applications. The signal DOA can be estimated using the arriving delays at multiple collocated sensors. In this paper, the Cramer-Rao bound (CRB) of the DOA estimation based on measuring the time difference of arrival by N pairs of collocated sensors is derived. Then, the optimum sensor arrangement for minimizing the DOA estimation error is obtained and finally a discrete Fourier transform-based solution for estimating the signal DOA is presented. Using computer studies, it is observed that the proposed estimator is unbiased and its mean square error almost coincides with the CRB.