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 includes the operations of generating a non-transpositional modulation (non-TM) signal from a first data signal, where the non-TM signal has a frequency spectrum that occupies a bandwidth. Generating a TM signal by generating a modulation from a second data signal, and shifting the modulation signal in frequency to an upper or lower sideband in the frequency spectrum of the non-TM signal which lies within the bandwidth of the non-TM signal, and where the power of the first modulated signal is less than a power of the non-TM signal. Combining the non-TM signal with the TM signal on a common carrier signal to provide a combined signal. Transmitting the combined signal.