Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for modulating and demodulating transpositional modulated (TM) signals. One aspect features a method of modulating a carrier signal that include the actions of generating a TM signal by generating a sinusoidal signal, and modulating the sinusoidal signal based on a data signal to provide the TM signal. Inserting the TM signal into a carrier signal to provide a TM modulated carrier signal. Modulating the TM modulated carrier signal with a non-TM signal to provide a combined signal. Transmitting the combined signal.