Waves have been over-simplified as sinusoidal in physics since Newton and in mathematics since Euler, but even ripples on water diminish in wavelength gradually but indefinitely. Resonance in an "imperfect oscillator" with changing natural frequency conversely requires successive wave cycles with periods changing at the same rate. We have rigorous mathematical basis and observational evidence beyond 5σ, a threshold still awaited for the Higgs boson, for a continuum of propagation modes fundamentally new to science that satisfy the imperfect resonance, characterised by a specific rate of change of frequency with travel time, β, in units of (dimensionless) fractional change per second.

The modes provide aliases of all signals, regardless of waveform and modulation, at frequencies changed by the mode rate β times travel time r/c from their sources. We have PCT patents recently issued in China and the US, with other jurisdictions pending, for these modes and their reception with imperfect oscillators, and are working on prototype design.

Consider that GPS signals come from satellites orbiting 20,200 km overhead. The distance at horizon is even greater, and they are easily jammed (or spoofed) with cheap devices sold online. GPS access is the first casualty in war, as vividly demonstrated in Ukraine. Disc-shaped antennas currently being deployed by militaries are able to distinguish a jammer on ground or water surface by direction from the overhead satellites, but helpless against jamming from the air, and unwieldy for drones.

Now consider a receiver tuning to our modes with β ±10/s. The aliases of a jammer at 10 m appear at just 525 Hz shifts, at 1575,420,000±425 Hz, and those of an airborne jammer at 10 km (33,000 ft), at 525 kHz shifts, at 1575,489,486 and 1575,945,140 Hz. But the satellite L1 arrives at specific shifts of -βr/c = ±10/s x 67 ms = ±0.67, at 1575.42(1±0.67) = 475 MHz or 2.675 GHz. Our receiver's 400M and 2.6G antennas would be deaf to jamming and spoofing! (For comparison, the satellite and aircraft Dopplers would be under 5 kHz.)

We modify ONLY the radio frequency (RF) down-conversion to make the local oscillator imperfect in the above sense, and correct the received signal for time scale, as the modulation arrives at 1/3rd speed at 475 MHz and 3x speed at 2.675 GHz. There's no change at the GPS satellites or uplink, or after down-conversion at the receiver. Our receiver-only concept and modification apply identically to non-GPS communication. A drone with our modification in its ~$10 RF front-end chip will look no different but would be electronically invincible. Airline navigation and communication would be similarly protected, and satellite interference similarly bypassed for radio astronomy. Most external interferences would be suppressed, improving performance, even for cellphones and WiFi..

With GPS as showcase, we expect our receiver-only technology will proliferate by demand from aircraft navigation and comms to emergency services and even to 5g devices and smart watches, through licensing to equipment manufacturers and RF front-end chip vendors.