Envelope Fluctuation Statistics of Filtered PSK and Other Digital Modulations

Radio signals derived using constant-envelope digital modulations (e.g., PSK, FSK and variations thereon) are impervious to the nonlinear characteristics of high-power RF amplifiers such as TWT's. However, constant-envelope modulations that must be heavily filtered to meet spectrum emission requirements, or intrinsically spectrumefficient modulations such as Quadrature Partial Response Signaling (QPRS), exhibit envelope fluctuations that render them vulnerable to amplifier nonlinearities. This paper describes a study, based on the use of Monte Carlo computer simulations, of the RF envelope variations associated with different digital modulations. Simulations and statistical analyses of these variations have been conducted for both filtered PSK and QPRS. The PSK category includes such special cases as Staggered Quaternary PSK (SQPSK); Minimum Shift Keying (MSK);
L
-ary PSK with cosine rolloff shaping (divided equally between transmitter and receiver); and linear phase modulation using shaped (nonrectangular) baseband pulses. The primary fluctuation measure used in the study is the dynamic range, in decibels, between the 10th and 90th percentiles of the RF envelope. This quantity,
D
, is presented for the various modulations considered and for various types of transmit filtering, with filter bandwidth-to-symbol rate ratio treated as a variable. The numerical results show the tradeoff between envelope constancy and spectrum efficiency among the most widely used digital radio approaches. For QPRS modulations,
D
is typically in the range 11-16 dB; for heavily filtered PSK modulations, the range of
D
lies roughly 6 dB lower, but other sources of distortion are more prominent.