The Output Pdf of a Polarity Coincidence Correlation Detector

Abstract

Further, the linearized &fiC as a function of C1 is d(Qf/ dC1IC I = X Cl, giving, from (3), Noicw , Cl /(2, i id). ( I Now, the totalO2, incorporating (IO) and (9) into (6), is SMOPASS Y.~~~~(t) |~~~~F FI LW lEM I0) } t E F ig. 1 . Correlator block diagram . 02 -[rr/(R2A)] [AI(MRA)] f te(t) dt + rel(MR2A) (11) or, in Laplace transform notation,This last expression shows the system of Fig. I to be an approximation to a second-order PLL, as shown in Fig. 3. R.L. KIRLIN University of Wyoming Laramie, Wyo. 82071 References [11 J.K. Holmes, "Performance of a first-order transition sampling digital phase-locked loop using random walk models," IEEE Abstract A general expression is derived for the probability density function of the output of a cross correlator, the inputs of which are assumed to consist of clipped sine waves of similar frequency plus uncorrelated, stationary Gaussian noise. The correlator output is shown to be a piecewise linear function of the random phase difference between the two input processes; hence, the density function for the correlator output is obtained by a relatively simple transformation from the probability density function of the random phase difference.

On the Use of Polarity Coincidence Correlation Techniques for Differential Phase-Shift-Keyed Demodulation

“…Recently though, Andrews [ 2 ] derived the output probability density function for a polarity coincidence correlation detector with sinusoidal inputs with additive narrow-band Gaussian noise. This probability density function has provided a basis here for the analysis of the probability of error for a DPSK demodulator using polarity coincidence correlation techniques.…”