Tracking Performance of Costas Loops with Hard-Limited In-Phase Channel

It is becoming increasingly popular in the design of suppressed carrier receivers, which employ Costas loops for earrier reconstruction, to hard-limit the output of the in-phase channel. Doing so allows replacement of the analog multiplier, which forms the loop error signal, with a chopper-type device which typically exhibits much less dc offset. The false lock behavior of such a hard-limited loop was recently investigated and shown to be quite different from that of the conventional Costas loop without the hard limiter. This paper presents the companion, analysis of the tracking performance of the hard-limited loop and assesses the penalty, if indeed it is a penalty rather than an improvement, in this performance relative to the conventional Costas loop with an analog third multiplier. In particular, for the case of arm filters and NRZ data, the squaring loss (or equivalently the linear loop tracking jitter) is evaluated and illustrated as a function of the ratio of arm filter bandwidth to data rate and data signal-to-noise ratio. Superimposed on these numerical results will be the corresponding ones for the conventional Costas loop. As a finale, the equivalence in operation of the Costas loop with hard-limited in-phase channel and a baseband modulation carrier reconstruction loop referred to as a demod/ remod loop is discussed.