Title :
On the power spectral density of self-synchronizing scrambled sequences
Author :
Fair, I.J. ; Bhargava, V.K. ; Wang, Q.
Author_Institution :
Dept. of Electr. Eng., Tech. Univ. Nova Scotia, Halifax, NS, Canada
fDate :
7/1/1998 12:00:00 AM
Abstract :
We derive a closed-form expression for the power spectral density of amplitude/phase-shift keyed bit sequences randomized through self-synchronizing scrambling when the source sequence is a stationary sequence of statistically independent bits. In addition to the dependence on the symbol pulse shape, duration, and the signal space values with which symbols are represented, we show that the power spectral density is dependent only on the probability of logic ones in the source bit stream, the period of the impulse response of the scrambling shift register, and the number of logic ones in this period. Our results confirm that optimum randomization results with use of primitive scrambling polynomials and poorest randomization occurs with “two-tap” polynomials of the form xD+1
Keywords :
amplitude shift keying; binary sequences; phase shift keying; polynomials; probability; random processes; spectral analysis; synchronisation; amplitude-shift keyed bit sequences; closed-form expression; impulse response period; logic ones probability; phase-shift keyed bit sequences; power spectral density; primitive scrambling polynomials; scrambling shift register; self-synchronizing scrambled sequences; signal space values; source bit stream; stationary source sequence; statistically independent bits; symbol duration; symbol pulse shape; two-tap polynomials; Closed-form solution; Decoding; Frequency synchronization; Polynomials; Probabilistic logic; Probability; Pulse shaping methods; Shape; Shift registers; Statistical analysis;
Journal_Title :
Information Theory, IEEE Transactions on
