# Receiver and transmitter in RF/optic satellite communication: distance vs data rate v2

The first version of this question is here.

I have read the article "Optical communications work best over relatively short distances in space." by Toyoshima, M., Leeb, W., Kunimori, H. and Takano, here

I have a big doubts about how distance affects to data rate. In RF system, the data rate will decrease if we increase a distance between a transmitter and receiver. I think I can explain it with the beam becomes wider.

In the article Mr Toyoshima wrote "for space applications over long distances, RF systems achieve greater maximum data rates than optical communications systems."

If we have a satellite in LEO and a ground station, the distance will be <1000 km, beam width < 20 m....in this case, I think, laser communication wins.

If we have GEO-to ground station or inter-satellite Link, will optic win?

PS Honestly I am writing this post and thinking about it...I don't understand if my conclusion is correct...

One basic characteristic of optical systems is that the electrical power of the signal is proportional to the square of the received optical power. This is in contrast to RF systems, where the electrical power of the signal is proportional to the received RF power. The received optical power is inversely proportional to the square of the link distance, so the signal-to-noise ratio of optical systems degrades more quickly over increasing distance than with RF systems.6 We examined two optical systems and one RF system, and concluded that optical systems are more suitable for communicating over a relatively shorter distances in space than RF systems.

66N. Morimoto, T. Toda, T. Takano, Study of Application Fields of Lightwave Communications in Space, 22nd ISTS Symposium, 2000. Figure 1. Maximum data rates for optical and RF communication systems versus link distance. GEO stands for geostationary earth orbit, and arrows show distances to GEO, Moon, and Mars.

• This is a great follow-up question! I'll take a look at Toyoshima et al. later today. Thanks!
– uhoh
Sep 23, 2021 at 6:25
• The main difference is that is is almost impossible to scale up the receiver for an optical comms system, and almost trivial to scale up an RF receiver to arbitrary size. Sep 23, 2021 at 6:37
• @uhoh how do we regulate optical spectrum? i didnt find any regulation as for RF Sep 23, 2021 at 7:02
• If we have a satellite in LEO and a ground station, the distance will be <1000 km, beam width < 20 m. Do you have a source for that assumption? In my opinion it seems to be too optimistic.
– Uwe
Sep 23, 2021 at 10:51
• fyi I've just asked Are direct conversion optical receivers being looked at for future deep-space communication? and reused your reference.
– uhoh
Feb 9, 2022 at 10:32

This is interesting!

At first I thought that optical communication always wins because the $$\lambda/d$$ for a 30 cm diameter telescope at 850 nm is about 350,000 whereas for a 3 meter dish on a deep space spacecraft at 8 GHz or 32 GHz Ka band is only 80 or 320. That factor of 1000 in $$\lambda/d$$ is a factor of a million in signal strength at the other end, or 60 dB.

That multiplicative factor of a million goes a long way, but the problem is that the current detection schemes for radio and optical are very different.

A radio receiver/detector couples the electric field of the incoming wave into a voltage and that squared, divided by the amplifier's impedance is a power ($$V^2/R$$).

In other words, the received radio power is also the power in the detection circuit, that we compare to the noise equivalent power (NEP) of the amplifier, which will be about $$k_B T \times \Delta f$$ where $$k_B$$ is the Boltzmann constant.

The signal to noise ratio (S/N) is just the ratio of the received power to the noise equivalent power of the receiver front end.

Let's say we are running at the very edge with a S/N = 1. If the received power drops by a factor of 10 (distance is $$\sqrt{10}$$ further) then we have to cut $$\Delta f$$ also by a factor of 10 to maintain the same S/N.

### Photon signal detection

Right now the standard method of converting an optical signal into an electrical signal is to use some kind of photodiode. Most photons that get into the photodiode are absorbed and produce an electron-hole pair. These are collected as an electrical current.

The number of pairs produced and thus the current is proportional to the indcident optical power, okay so far, but the electrical power in the amplifier is equal to the current squared divided by the impedance! ($$I^2R$$)

This means that the electrical power we must compare to the NEP is proportional to the square of the optical power!

Thus once one opens the hood on this problem, one sees that the power collected by the antenna is only half the problem; the method of conversion to electrical signals is so different for optical vs radio that at some very far distance radio may be able to win using conventional detection technology.

### But what about UN-conventional detection technology?

There are a few things to consider that can make optical communication's future at extremely large distances brighter.

Exceeding classical capacity limit in quantum optical channel (also researchgate) is reference #8 in Toyoshima et al.

The amount of information transmissible through a communications channel is determined by the noise characteristics of the channel and by the quantities of available transmission resources. In classical information theory, the amount of transmissible information can be increased twice at most when the transmission resource (e.g. the code length, the bandwidth, the signal power) is doubled for fixed noise characteristics. In quantum information theory, however, the amount of information transmitted can increase even more than twice. We present a proof-of-principle demonstration of this super-additivity of classical capacity of a quantum channel by using the ternary symmetric states of a single photon, and by event selection from a weak coherent light source. We also show how the super-additive coding gain, even in a small code length, can boost the communication performance of conventional coding technique.

Also, since detectors can count individual photons and record their exact arrival time to picosecond precision and some lasers can generate picosecond pulses at micro' and nano-second intervals, there is a lot of opportunity to use the time structure to help boost S/N in a way that is not possible with radio waves, since counting individual radio photons is far more challenging.

For more on that, see

• does the beam size affect to data rate? Sep 23, 2021 at 11:48
• @Adil.Kolenko Yes! What affects maximum data rate (assuming we efficiently use some bandwidth $\Delta f$ is the ratio of signal power in the amplifier to the noise effective power (NEP). If a transmitter has fixed power, then the wider it is, the less is received by a fixed antenna size.
– uhoh
Sep 23, 2021 at 22:27
• beam is increased, data rate is decreased, right? Beam of laser is increased if the distanze is increased. Sep 24, 2021 at 6:38
• @Adil.Kolenko yes, if a beam gets wider, the power per unit area is lower, so the maximum data rate will be lower. Yes.
– uhoh
Sep 24, 2021 at 7:14
• capacity is a max data rate, isnt? can I say the capacity of laser communication is about 100 Gbps (μLCT™100 LASER COMMUNICATION TERMINAL - SpaceMirco )? Oct 4, 2021 at 7:16