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This paper discusses the rms error in estimating the bearing of a source with a linear array in a noisy environment. The techniques used are the Cramér-Rao (CR) bound and techniques developed recently by Ziv and Zakai. These new techniques give improved results at low signal-to-noise ratio. Below a certain threshold level of signal-to-noise ratio, the error increases faster than the CR bound predicts. This error is shown to be related to the sidelobe structure of the array. The variation of bearing error with array design is considered.