Extended phase-shift keying

A fundamental conceptual gap in angle modulation theory that has been around for a long time is filled. Unification of the angle modulations FM, PM, FSK, and PSK is achieved by exposing the duality between FM and PM, and particularly between FSK and PSK, with the additional observation that FSK is digital-FM and PSK is digital-PM. In order for this duality to hold unversally, it is shown that PSK must possess a modulation index similar to that of analog FM. This unlimited modulation index for PSK is a new concept in angle modulation theory, and this extension of known PSK modulation is called extended PSK (EPSK). Four angle demodulation methods are proposed for EPSK. Computer simulations of EPSK signals are performed for the purpose of measuring and characterizing the power-spectral-densities (PSDs) of these new signals. Experiments verify the computer results. A form of Carson's rule for estimating the bandwidth of EPSK signals is derived from Carson's rule for FM.; It is shown that known results on the probability density of the modulo-2{dollar}pi{dollar} noise-phase are not useful for characterizing the phase noise (not modulo-2{dollar}pi{dollar}) at the output of an extended phase demodulator with white Gaussian noise at the input, with or without signal present. With a new extended noise-phase model, it is shown that the threshold effect is due to an enhancement of the additive noise because of the nonlinearity of the phase component of the cartesian-to-polar transformation. This enhancement of the noise is manifest in the appearance of two effects, called clicks and doublets in the literature. An initial approach toward a click removal signal processor (CRSP) shows an 8dB reduction in the SNR at which the onset of errors due to clicks occurs.; Simulation of one EBPSK signal to determine bit-error rate (BER) performance, when demodulated using the MLSE algorithm, confirms that the minimum-attainable BER does change as the modulation factor is varied. A minimum BER occurs at a modulation factor around p = 1.25 for the raised-cosine pulse, which is greater than the phase shift for standard BPSK. Thus, extended PSK is required to achieve this BER minimum.