On the Calculation of Squaring Loss in Costas Loops with Arbitrary Arm Filters

The calculation of the optimum performance of suppressed carrier receivers with Costas loop tracking is directly related to evaluating the loop's so-called squaring loss. Recent work by the author and others presented specific numerical results for this loss when the input data were biphase-
L
(Manchester coded) and the Costas loop arm filters were of the
n
-pole Butterworth type. These results were largely obtained by numerical integration on a digital computer. This paper presents a partial fraction expansion technique for arriving at closed form expressions for squaring loss for Costas loops with arbitary arm filters and NRZ as well as Manchester coded data. Specific closed form results are given for one and two pole Butterworth filters as examples.