Spread spectrum signals have been used for secure communications for several decades. Nowadays, they are also widely used outside the military domain, especially in Code Division Multiple Access (CDMA) systems. Due to their low probability of interception, these signals increase the difficulty of spectrum surveillance. Direct-Sequence Spread Spectrum transmitters (DS-SS) use a periodical pseudo-random sequence to modulate the baseband signal before transmission. In the context of spectrum surveillance, the pseudo-random sequence used by the transmitter is unknown (as well as other transmitter parameters such as duration of the sequence, symbol frequency and carrier frequency). Hence, in this context, a DS-SS transmission is very difficult to detect and demodulate, because it is often below the noise level. In this paper, we propose a method for estimating the spreading waveform without prior knowledge on the transmitter. Only the period of the pseudo-random sequence is assumed to have been estimated (this can be done using cyclostationarity analysis). Our method is based on eigenanalysis techniques. We show that the spreading sequence can be recovered from the first and the second eigenvectors. This property provides a way to estimate the spreading sequence. Experimental results are given to illustrate the performances of the method and show that a good estimation can be obtained even when the signal is far below the noise level.