Data Transmission by Combined AM and PM

Theoretical investigations of the performance of combined amplitude and phase modulation systems have been reported on by C. R. Cahn 1 (1960), J. C. Hancock and R. W. Lucky 2 (I960).. Lucky and Hancock 3 (1962), and more recently by M. Leiter and M. P. Talbot 4 (1967). These investigators found that, on the additive white Gaussian channel, combined AM and PM yields a better error rate at fixed signal-to-noise ratio than PM or AM alone when the number of total levels is ^ 8. Here we rigorously establish these claims for a practical system. Instead of using linear matched filter detection (Ref. 2), we use differential or coherent phase detection to estimate the phase and a conventional envelope detector to estimate the amplitude. While theoretically optimum signal locations in two-dimensional space are generally not quantized but subject only to fixed power limitation, we consider practical signal sets which are quantized. 2399 2400 T H E BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1971 The questions we answer in this paper are the following: Given an AMevel system and the facility to use L amplitudes and M phases such that N = LM, what is the value of L, and consequently M, such that the error rate is smallest for a fixed amount of S / N when signaling over the bandlimited additive Gaussian channel? How does this combined modulation scheme compare with only PM or AM at fixed S/N? How efficient is this modulation scheme in terms of attainable bits per cycle of bandwidth at fixed error rate? And finally how close can these theoretical results be realized in the laboratory with actual hardware?