Two-channel Costas loop tracking performance for UQPSK signals with arbitrary data formats

Previous results on the tracking performance of two-channel Costas-type carrier synchronization loops are generalized and corrected, in order that they may be applied to several mixed-format cases. In particular, the mean-square phase jitter performance of these loops with active arm filters, synchronous or asynchronous symbol clocks, and arbitrary data formats on the two channels is examined. It is demonstrated that for each case, selection of the channel gain ratio, as motivated by the MAP estimation theory, does not guarantee optimum loop tracking performance: in some instances, a conventional single-channel Costas loop would outperform the two-channel version with the MAP choice of gain ratio. 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'. This can, in some cases, improve the performance measure, although in all cases, the two-channel loop will still outperform the single-channel version.