On the power spectral density of certain digitally modulated signals with applications to code despreading

Techniques for deriving the power spectral density (PSD) of certain digitally modulated signals that are more general and easier to use than other similar methods are developed. These techniques are especially well suited for deriving the PSD of signal-product waveforms with arbitrary modulating pulse shapes. This is done by decomposing the PSD expression into two factors, one depending solely on the underlying sequences and the other depending only on the pulse shapes. General formulas are derived and, for some cases, they are expressed in terms of the discrete Fourier transform of appropriately defined sequences and the Fourier transform of the modulating pulse shape. Applications where these expressions would be useful include bit and code synchronizers, delay-and-multiply-type of detectors, and spread-spectrum and code-division multiple-access systems, either at radio or at optical frequencies