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In this paper, we propose a new blind subspace-based signature waveform estimation technique for direct-sequence code division multiple-access (DS-CDMA) communication systems operating in the presence of unknown wide-sense stationary interference. Unlike the existing algorithms, the proposed technique requires just a single receive antenna and is applicable to the case of arbitrary transmitted symbol constellations. Necessary and sufficient conditions for identifiability of the proposed technique are derived. For practical scenarios where the data covariance matrix is estimated using a finite number of samples, a closed form expression for the mean-squared error (MSE) of the estimated channel is obtained. For the high signal-to-interference ratio (SIR) regime and Gaussian interference, an approximation of the MSE expression is also derived and the effects of different parameters on the performance of the proposed algorithm are analyzed. Numerical examples validate our analytical results.