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.

Press «enter» to see the model of the communication link.  To infer results, try one of the examples below, or your own inputs. To clear results, refresh your browser.

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, and a filter-limited noise bandwidth of 0.1 nm:
    No.L_n = 1e8 «enter»  No.Wa.dl.n = 0.1 «enter»

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, the probe’s transmit aperture is angled to redirect starlight from Alpha Centuari to Earth against a relatively dark background away from the star itself.  To bound the upper limit of performance, the probe’s transmit aperture perfectly conserves the radiance of the Alpha Centauri, which is inferred from its blackbody temperature of 5,790 K.

  1. Set the probe’s transmit aperture to a blackbody temperature of 5,790 K:
    S1.Ra.Th.T = 5790 «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 relatively far from Alpha Centauri, and a filter-limited noise bandwidth of 0.1 nm:
    No.L_n = 1e4 «enter»  No.Wa.dl.n = 0.1 «enter»
  5. Specify an ideal channel capacity of 1 Mbit/yr (this infers the transmit aperture diameter, or the diameter can be specified instead):
    I.C.Miy=1  «enter»

Because the ideal channel capacity is already specified as an input, the key result is the starlight modulator aperture dimensions (S₁.Geom «enter»).