Modulated Data Signals Research Articles

Passband Timing Recovery in an All-Digital Modem Receiver

The performance of conventional modem receivers, where adaptive equalization is achieved by a digital transversal filter with tap gains spaced at the symbol interval, depends critically on the choice of the sampling phase. In this paper, a digital timing recovery loop is described and analyzed in the case of passband quadrature amplitude modulated data signals. Under conditions likely to be encountered on actual voiceband communication channels, the clock phase derived is shown to prevent spectral nulls and to accurately approximate the optimum timing phase for an infinite equalizer. Computer simulations show that the proposed system is capable of fast timing acquisition.

Error performance of p.s.k. and f.f.s.k. subcarrier data demodulators

The error performance of filter threshold and integrate and dump demodulators is calculated, for phase shift key (p.s.k.) and fast frequency shift key (f.f.s.k) modulated data signals. A review is given of existing theory and techniques and some material is presented on f.f.s.k. demodulators.

On the design of gradient algorithms for digitally implemented adaptive filters

The effect of digital implementation on the gradient (steepest descent) algorithm commonly used in the mean-square adaptive equalization of pulse-amplitude modulated data signals is considered. It is shown that digitally implemented adaptive gradient algorithms can exhibit effects which are significantly different from those encountered in analog (infinite precision) algorithms. This is illustrated by considering the often quoted result of stochastic approximation that to achieve the optimum rate of convergence in an adaptive algorithm the step size should be proportional to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/n</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> is the number of iterations. On closer examination one finds that this result applies only when <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> is large and is relevant only for analog algorithms. It is shown that as the number of iterations becomes large one should not continually decrease the step size in a digital gradient algorithm. This result is a manifestation of the quantization inherent in any digitally implemented system. A surprising result is that these effects produce a digital residual mean-square error that is minimized by making the step size as large as possible. Since the analog residual error is minimized by taking small step sizes, the optimum step-size sequence reflects a compromise between these competing goals. The performance of a time-varying gain sequence suggested by stochastic approximation is contrasted with the performance of a constant step-size sequence. It is shown that in a digital environment the latter sequence is capable of attaining a smaller residual error.

Phase-Shift-Keyed Signal Detection with Noisy Reference Signals

This paper derives and graphically illustrates the performance characteristics of Phase-Shift-Keyed communication systems where the receiver's phase reference is noisy and derived from the observed waveform by means of a narrow-band tracking filter (a phase-locked loop). In particular, two phase measurement methods are considered. One method requires the transmission of an auxiliary carrier (in practice, this signal is usually referred to as the sync subcarrier). This carrier is tracked at the receiver by means of a phase-locked loop, and the output of this loop is used as a reference signal for performing a coherent detection. The second method is self-synchronizing in that the reference signal is derived from the modulated data signal by means of a squaring-loop. The statistics (and their properties) of the differenced-correlator outputs are derived and graphically illustrated as a function of the signal-to-noise ratio existing in the tracking filter's loop bandwidth and the signal-to-noise ratio in the data channel. Conclusions of these results as well as design trends are presented.