Signal processing architectures for direct acquisition of spread spectrum signals using long codes. Techniques are described for achieving a high of parallelism, employing code matched filter banks and other hardware sharing. In one embodiment, upper and lower sidebands are treated as two independent signals with identical spreading codes. Cross-correlators, in preferred embodiments, are comprised of a one or more banks of CMFs for computing parallel short-time correlations (STCs) of received signal samples and replica code sequence samples, and a means for calculating the cross-correlation values utilizing discrete-time Fourier analysis of the computed STCs. One or more intermediate quantizers may optionally be disposed between the bank of code matched filters and the cross-correlation calculation means for reducing word-sizes of the STCs prior to Fourier analysis. The techniques described may be used with BOC modulated signals or with any signal having at least two distinct sidebands.