models.parkinresearch.com

Communication Link Model

The communication link model represents single-mode electromagnetic propagation from a transmitting aperture to a receiving aperture. For a photon-starved (Poisson) channel with pulse position modulation (PPM), it infers the ideal and hard-decision channel capacities in the presence of noise. Also, the Shannon limit is used to bound the additive white Gaussian noise (AWGN) channel capacity. The model incorporates relativistic corrections to account for Doppler shift and brightening/dimming caused by the transmitter approaching or receding from the receiver at relativistic speed.

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Interstellar laser link from Alpha Centauri to Earth

Based on Parkin, K.L.G, 2020. A Starshot Communication Downlink. arXiv preprint arXiv:2005.08940.

  1. Choose a 4 m diameter aperture that radiates 100 Watts time-average power:
    S1.Ge.D.m = 4 «enter»  S1.Pr.W = 100 «enter»
  2. Specify that the transmitter and receiver are separated by 4.4 lightyears at relative speed of 0.2 c:
    r.ly = 4.4 «enter»  b = 0.2 «enter»
  3. Choose a 30 m diameter receiver and 1250 nm wavelength signal in that frame:
    S2.Ge.D.m = 30 «enter»  S2.W.l.n = 1250  «enter»
  4. Specify a noise spectral radiance that is consistent with a telescope pointing close to but not at Alpha Centauri, 0.1 nm filter-limited noise bandwidth, and a 6 K noise temperature for the superconducting nanowire receiver:
    N.No.L_n = 1e8 «enter»  N.No.Wa.dl.n = 0.1 «enter»  N.Tr = 6 «enter»
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Key results are the ideal Poisson pulse position modulation (PPM) channel characteristics (Ideal «enter») and the hard-decision PPM channel characteristics (Hard «enter»).

Interstellar modulated starlight link from Alpha Centauri to Earth

In this example, an interstellar probe angles a reflector to redirect starlight from Alpha Centuari to Earth against a relatively dark background away from the star itself.  The reflector is covered by a liquid crystal, let’s say, that turns the star’s reflection on and off as needed to send a message. To bound the upper limit of performance, the probe’s reflecting aperture (when turned on) perfectly conserves the radiance of the Alpha Centauri, which is inferred from its blackbody temperature of 5,790 K.

  1. Set the probe’s reflecting aperture to a blackbody temperature of 5,790 K:
    S1.Ra.Th.T = 5790 «enter»
  2. Because power is ‘free’ there is a disadvantage to high peak to average power ratio (it decreases the average power, hence channel capacity), so set 1 bit/pulse (on-off keying), and correspondingly add an extra propagation loss to account for the factor of 2 decrease in average radiated power because the reflector is not radiating half the time:
    H.m = 1 «enter»  L.O.- = 0.5 «enter»
  3. Specify that the transmitter and receiver are separated by 4.4 lightyears at a relative speed of 0.2 c:
    r.ly = 4.4 «enter»  b = 0.2 «enter»
  4. Choose a 30 m diameter receiver and 1250 nm wavelength signal in that frame:
    S2.Ge.D.m = 30 «enter»  S2.W.l.n = 1250  «enter»
  5. Specify a noise spectral radiance that is consistent with a telescope pointing relatively far from Alpha Centauri, 0.1 nm filter-limited noise bandwidth, and a 0.1 K noise temperature for the superconducting receiver:
    N.No.L_n = 1e4 «enter»  N.No.Wa.dl.n = 0.1 «enter»  N.Tr = 0.1 «enter»
  6. Specify a reflector diameter of 4 meters:
    S1.Ge.D.m=4  «enter»
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An upper bound to data transfer rate via on-off keying of redirected starlight from Alpha Centauri turns out to be 1 bit/min (0.5 Mbit/yr).