# Communication Link Calculator

Calculate link budgets for microwave and laser communications. Infer transmit power, aperture size, channel capacity, and many others.

The communication link model represents single-mode electromagnetic propagation from a transmitting aperture to a receiving aperture. It can be used to calculate the link budget between a satellite and ground station while incorporating real-world losses in a way that is consistent with the IEEE 145-2013 standard.

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 **⏎** to see the model. Try your own inputs or the examples below. Refresh your browser to clear results.

## Satellite downlink to a fixed ground station

Real-world antennas are imperfect, their feed systems have losses and their beams radiate as if from a different area than the physical one. Mathematical self-consistency requires careful attention to which piece of physics pertains to which aperture area: the physical area, the effective area taking illumination efficiency into account, or the effective area taking illumination and radiation efficiencies into account.

In the context of a satellite downlink, these relationships are illustrated in the example below. The illumination efficiency is fundamentally an area efficiency, whereas the radiation efficiency is fundamentally a power efficiency.

- Let’s specify a minimum elevation link geometry: A satellite in geostationary orbit Geom.H = 35786
**⏎**transmits toward a zero-altitude ground station that sees the satellite at its minimum elevation of 15° above the horizon it would see if it were on the surface of a sphere with Earth’s center as its origin Geom.e = 15**⏎**. The model infers the path length of the link Geom.D**⏎**to be 40,000 km. - Specify the ground station: A 3 m diameter parabolic dish S2.Geom.Dh.m = 3
**⏎**receives a carrier whose low edge-of-band frequency is 8 GHz S2.Wave.BL.f.GHz = 8**⏎**and bandwidth is 250 MHz S2.Wave.df.MHz = 250**⏎**. The model infers an arithmetic center frequency S2.Wave.f.GHz**⏎**of 8.125 GHz. Also, for such an X-band dish pointing at 15° elevation, the system noise temperature might be estimated to be Ts = 225**⏎**K. - Specify the satellite’s antenna: A 2 m diameter parabolic dish S1.Geom.Dh.m = 2
**⏎**. - Specify the channel: This will be an AWGN channel with a raw bit error rate of 1E-5 BERAWGN-BPSK-QPSK = 1E-5
**⏎**and QPSK modulation whose spectral efficiency is 2 bit/s/Hz Rb/df = 2**⏎**. The model infers a 1.1 Gbit/s ideal AWGN channel capacity which is 47% utilized, and a carrier to noise ratio of 18. It has also inferred an ideal-case transmit power of 2.8 Watts — how do inefficiencies affect that transmit power? - Specify efficiencies: The satellite’s parabolic dish transmitter has 80% illumination efficiency S1.ha = 0.8
**⏎**, and 90% radiation efficiency S1.hr = 0.9**⏎**and impedance mismatch efficiencies S1.M1 = 0.9**⏎**S1.M2 = 0.9**⏎**, bringing the overall antenna efficiency to 72%. The ground station’s parabolic dish receiver is similar, S2.ha = 0.8**⏎**S2.hr = 0.9**⏎**S2.M1 = 0.9**⏎**S2.M2 = 0.9**⏎**. Also included are 3 dB of atmospheric attenuation losses L.Absorption = -3**⏎**, 0.5 dB pointing loss on the receiver L.PointingRx = -0.5**⏎**, and 0.5 dB jitter loss on the transmitter L.JitterTx = -0.5**⏎**. Consequently, the power that the satellite’s transponder needs to make available S1.Pa**⏎**rises to 25 Watts. The model has computed the various powers, gains, directivities and areas labeled in the diagram above.

## Interstellar laser link from Alpha Centauri to Earth

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

- Specify the transmitter: A 4 m diameter aperture S1.Geom.Dh.m = 4
**⏎**that radiates 100 Watts time-average power S1.Pr.W = 100**⏎**. - Specify that the transmitter and receiver are separated by 4.4 lightyears r.ly = 4.4
**⏎**at 0.2 c relative speed Rel.b = 0.2**⏎**. - Specify the receiver: A 30 m diameter aperture S2.Geom.Dh.m = 30
**⏎**that receives a 1250 nm wavelength signal (measured in the receiver’s rest frame) S2.Wave.l.nm = 1250**⏎**. The model infers that the transmitted wavelength S1.Wave.l.nm**⏎**must be 1020 nm. - Specify a noise spectral radiance that is consistent with a telescope pointing close to but not at Alpha Centauri, N.Noise.Ln = 1E8
**⏎**, 0.1 nm filter-limited noise bandwidth N.Noise.Wave.dl.nm = 0.1**⏎**, and 6 K noise temperature for the superconducting nanowire receiver N.Tr = 6**⏎**.

Key results are the ideal Poisson pulse position modulation (PPM) channel characteristics Ideal **⏎** and the hard-decision PPM channel characteristics Hard **⏎**.

## 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.

- Set the probe’s reflecting aperture to a blackbody temperature of 5,790 K:

S1.Ra.Th.T = 5790 «enter» - 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» - 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» Re.b = 0.2 «enter» - 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» - 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» - Specify a reflector diameter of 4 meters:

S1.Ge.D.m=4 «enter»

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).