Pulse-amplitude modulation (PAM) is extended to two and four dimensions by means of a nonlinear, memoryless mapping to obtain pulse-amplitude-and-phase modulation (PAPM). This modulation requires either the same bandwidth as double-sideband PAM or twice as much but yields a signal-to-noise ratio (SNR) improvement factor similar to that of FM with considerably less sacrifice of spectral occupancy. Several signal-space mappings are investigated for Gaussian data. Expressions for output SNR are derived in terms of a linear error above threshold and an anomalous threshold-producing error. PAPM is compared with various modulation techniques in terms of power and bandwidth requirements. The degradations in output SNR caused by carrier phase, carrier amplitude, and sample timing reference errors are evaluated so that requirements for demodulator design can be specified.

This paper examines codes for four-dimensional (4-D) modulation and their performance for digital transmission. The signals are defined byMpoints inside a sphere in four-dimensional Euclidian space. Three classes of 4-D codes are presented, and an algorithm is given which yields good 4-D codes of any length. Bounds on symbol error probability are plotted versus symbol-energy-to-noise-density ratio. The performance is shown to exceed that of amplitude- and-phase modulation in two independent two-dimensional channels.

A class of quaternary codes is described, and an algorithm for generating the codes is given. The codes have properties that make them useful for radar applications: 1) their auto-correlation consists of a single pulse, 2) their length can be any power of two, 3) each code can be paired with another code (its mate) of the same class in such a way that the crosscorrelation of mates is identically zero, 4) coded waveforms can be generated in a simple network the number of whose elements is proportional to the base-2 logarithm of the code length, and 5) the same network can be readily converted to a matched filter for the coded waveform.

article Free AccessAnalogue Study of Electron Trajectories Authors: Benjamin F. Logan Massachusetts Institute of Technology, Cambridge, Mass. Massachusetts Institute of Technology, Cambridge, Mass.View Profile , George R. Welti Massachusetts Institute of Technology, Cambridge, Mass. Massachusetts Institute of Technology, Cambridge, Mass.View Profile , George C. Sponsler Massachusetts Institute of Technology, Cambridge, Mass. Massachusetts Institute of Technology, Cambridge, Mass.View Profile Authors Info & Claims Journal of the ACMVolume 2Issue 1pp 28–41https://doi.org/10.1145/320789.320793Published:01 January 1955Publication History 8citation417DownloadsMetricsTotal Citations8Total Downloads417Last 12 Months9Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF