Two-Channel Costas Loop Tracking Performance for UQPSK Signals with Arbitrary Data Formats

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Abstract
This paper generalizes and corrects previous results on the tracking performance of two-channel Costas-type carrier synchronization loops. In particular, the mean-square phase jitter performance of these loops is evaluated when the data formats on the two channels are arbitrary. Particular attention is given to the case where the loops contain active arm filters with or without hard limiters following them. For each case, it is demonstrated that selection of the channel gain ratio, as motivated by MAP estimation theory, does not guarantee optimum loop tracking performance. In fact, it is shown that, in some instances, a conventional single-channel Costas loop will outperform the two-channel version with the MAP choice of gain ratio. Instead, it is suggested that the gain ratio be chosen to directly minimize the mean-square phase tracking jitter which is equivalent to minimizing the loop's "squaring loss." When this is done, it is shown that, in some cases, one can obtain significant improvement in this performance measure. In all cases, however, the two-channel loop will now outperform the single-channel version.

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