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Linear least squares estimation (LLSE) techniques can provide an effective means of suppressing narrow-band interference in direct sequence (DS) spread-spectrum systems. In the results presented here, analytical expressions for bit error rate are derived for two DS spread-spectrum systems under the conditions of either tone or narrowband Gaussian interference. It is shown that the most common LLSE filter design can lead to performance inferior to that of various other filter designs. However, results are also presented demonstrating that an LLSE filter design motivated by the structure of the maximum-likelihood receiver leads to consistently superior performance. The performance of a system using this new design criterion is compared with that of an approximation to the maximum-likelihood (ML) receiver for the tone interference model and with that of the exact ML receiver for the Gaussian interference. Finally, it is shown that the bit error rate estimate obtained from application of a Gaussian approximation for the test statistic is overly pessimistic for the systems studied here.