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A method of transmitting information in interstellar space at superluminal,or $> c$, speeds is proposed. The information is encoded as phase modulation ofan electromagnetic wave of constant intensity, i.e. fluctuations in the rate ofenergy transport plays no role in the communication, and no energy istransported at speed $>$ c. Of course, such a constant wave can ultimately lastonly the duration of its enveloping wave packet. However, as a unique featureof this paper, we assume the source is sufficiently steady to be capable ofemitting wave packets, or pulses, of size much larger than the separationbetween sender and receiver. Therefore, if a pre-existing and enduring waveenvelope already connects the two sides, the subluminal nature of theenvelope's group velocity will no longer slow down the communication, which isnow limited by the speed at which information encoded as phase modulationpropagates through the plasma, i.e. the phase velocity $v_p > c$. The methodinvolves no sharp structure in either time or frequency. As a working example,we considered two spaceships separated by 1 lt-s in the local hot bubble.Provided the bandwidth of the extra Fourier modes generated by the phasemodulation is much smaller than the carrier wave frequency, the radiocommunication of a message, encoded as a specific alignment between the carrierwave phase and the anomalous (modulated) phase, can take place at a speed inexcess of light by a few parts in 10$^{11}$ at $\nu\approx 1$~GHz, and higherat smaller $\nu$.

Superluminal transmission of phase modulation information by a long macroscopic pulse propagating through interstellar space