Power Density Spectrum of the Product of Two Time-Displaced Versions of a Maximum Length Binary Pseudonoise Signal

An analytical expression for the power density spectrum of the product of two time-displaced versions of a maximum-length binary pseudonoise signal is derived. This expression is valid for any value of the pseudorandom sequence length. This provides a possibility for evaluating the effect of correlator self-noise on the serial synchronization decision circuitry of the spread-spectrum receiver for all possible values of the time difference between the pseudonoise modulation on the carrier and the pseudonoise waveform generated at the receiver.