ON THE POWER SPECTRAL DENSITY OF SELF-SYNCHRONIZING SCRAMBLED SEQUENCES

We derive a closed-form expression for the power spectral density of a mplitude/phase-shift keyed bit sequences randomized through self-synch ronizing scrambling when the source sequence is a stationary sequence of statistically independent bits, In addition to dependence on the sy mbol pulse shape, duration, and the signal space values with which sym bols are represented,,ve show that the power spectral density is depen dent only on the probability of logic ones in the source bit stream, t he period of the impulse response of the scrambling shift register, an d the number of logic ones in this period, Our results confirm that op timum randomization results with use of primitive scrambling polynomia ls and poorest randomization occurs with ''two-tap'' polynomials of th e formx(D) + 1.