The N-Phase Digital Tanlock Loop for Tracking Suppressed-Carrier N-ary PSK Signals

Abstract

In this paper, the performance of an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> -phase digital tanlock loop (DTL) in the presence of phase error disturbance is studied. The <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> phase DTL is a digital loop for tracking suppressed-carrier <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> -ary phaseshift keyed (PSK) signals. It has linear phase characteristics in the modulo- <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2\pi/N</tex> sense as a result of using the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\tan^{-1}[.]</tex> function in the phase error detector. We first obtain the probability density function of phase error of the phase detector output and verify it by computer simulation. Then, we consider the optimum bandwidths of the bandpass filters in the loop that yield the minimum variance of the phase error. Also, the finite word length effect on the performance of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> -phase DTL is investigated by computer simulation. In addition, the performance of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> -phase DTL is compared to that of the digital <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> -phase <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I-Q</tex> loop which has sinusoidal phase characteristics. It has been found that the first-order Nphase DTL has wider lock range than the first-order <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> -phase <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I-Q</tex> loop in the absence of noise.