This paper describes the performance of the all digital data transition tracking loop (DTTL) with coherent and noncoherent sampling using nonlinear theory. The effects of few samples per symbol and of non-commensurate sampling and symbol rates are addressed and analyzed for perfectly square pulses as well as filtered pulses. Their impact on the probability density and variance of the phase error are quantified through computer simulations. It is shown that the performance of the all-digital DTTL approaches its analog counterpart when the sampling and symbol rates are noncommensurate (i.e., the number of samples per symbol is irrational). The phase error variance for an even number of samples per symbol is also shown to degrade compared to an odd number of samples per symbol.>

Four different arraying schemes applicable to deep space communications are discussed and analyzed. These include symbol stream combining (SSC), baseband combining (BC), carrier arraying (CA) and full spectrum combining (FSC). In addition, sideband aiding (SA) is also included and compared. Moreover, combinations of these schemes are introduced and discussed such as carrier arraying with sideband aiding and baseband combining (CA/SA/BC) or carrier arraying with symbol stream combining (CA/SSC), just to name a few. Complexity versus performance is traded off throughout the paper and benefits to the reception of existing spacecraft signals are discussed.>

The performance of a QPSK (quadrature phase-shift keying) lock detector is described, taking into account the degradation due to carrier phase jitter. Such an analysis is necessary for accurate performance prediction purposes in scenarios where both the loop SNR is low and the estimation period is short. The derived formulas are applicable to several QPSK loops and are verified using computer simulations.>

Previous analyses of lock detector algorithms for Costas loops have ignored the effects of the inherent correlation between samples of the phase error process. In this work, analysis and simulations are used to quantify the effects of phase correlation on lock detection for the 'square law' and 'absolute value' type detectors. Results which depict the lock detection probability as a function of loop signal-to-noise ratio for a given false alarm rate are obtained. It is shown that the square law detector experiences less degradation due to phase jitter than the absolute value detector and that the degradation in detector signal-to-noise ratio is more pronounced for squarewave than for sinewave signals.>