Looking at the US$4.01 NXP MKW01Z128 that Bill Paul mentioned. This chip’s RF interface is really interesting because it can transmit license-free as low as 290 MHz (1.03 m) at up to 600 kbps. It has 128 KiB of Flash and 16 KiB of RAM and a 48 MHz Cortex-M0, sucking 16 mA when actively receiving (and up to 95 mA when transmitting) at 1.8 to 3.6 volts. It's targeted at last-mile metering and wireless sensor networks.
Its power output is -18 to 17 dBm (50 mW!) and its sensitivity is -120 dBm (a femtowatt!) and so it occurred to me that maybe we should measure solid angles in dB. In this case, without further amplification, the receive antenna needs to capture signal over -137 dB (or more) of the sphere around an isotropic transmit antenna.
(The -120 dBm is dependent on lowering the communication rate to 1200 bps.)
A half-wave dipole antenna, the ideal, would be 516 mm long for 290 MHz; it gives you 2.15 dBi of “antenna gain”, so you get down to a solid angle of -139 dB, and it captures signal over about 0.2 m², I think. This subtends -139 dB of solid angle at about 1000 km.
That’s pretty impressive — two such chips can communicate over 1000 km with nothing between them but half-wave dipoles, and furthermore without a license.
On Spaceship Earth, though, it’s a little tricky to have nothing between them, and 1000 km is far too short for moonbounce. If you were to use a 30 dBi dish antenna to transmit, that would get you to about 30 000 km, which isn’t even all the way around Spaceship Earth; if you use another one to receive, that gets you to 900 000 km, which is far enough for moonbounce — but then you only have about 3 dB of headroom, and the moon sucks most of that up; typical moonbounce path losses are around 240 dB.
The 315 MHz UHF unlicensed (ultra-low-power/short-range device in US and Japan, not ITU) frequency band it uses (which extends down to 290 mHz, at the top of the VHF band) is mostly used by garage door openers, keyless car openers, and whatnot. It should have reasonable building penetration, better than cellphone signals.
E-skip ionospheric propagation apparently doesn’t reach 290 MHz (250 MHz seems to be the limit), but it might be subject to tropospheric ducting from atmospheric temperature inversions, and to transequatorial propagation, and otherwise is limited to 3570 m √(h/m) line-of-sight radio horizon. Reaching 1000 km with 3570 m √(h/m) would require a stratospheric balloon or drone at 79 km altitude. A terrestrial structure like my office at about 60 m only has a line of sight of around 30 km. (Probably all the people remotely unlocking their cars would provide too much interference, but maybe not.) Totally unsurprising structures like trees might be only 10 m tall, and thus have a line of sight up to about 10 km.
Tropospheric ducting, if it’s possible, has the additional advantage that the strength of radio waves trapped in the atmospheric duct only drops off as the reciprocal of distance, rather than its square.
If you were to try to do something cute and moonbouncelike, maybe you could use a mountain. For example, a few kilometers from Las Cruces, Organ Needle reaches 2700 m above sea level, while Las Cruces itself is at only 1200 m. A dish (or radome) pointed at Organ Needle would effectively transmit isotropically from 1500 m, giving it a line-of-sight range of over 100 km, as long as the reflected power was high enough.
16 mA × 3.6 V / 48 MHz works out to about a nanojoule per instruction. 95 mA × 3.6 V / 600 kbps works out to 570 nJ per bit.
17 mA at 1.8 volts is roughly the power supplied by the solar cell from a solar calculator, and just about at the right voltage already; two such cells in series with a capacitor ought to provide plenty of power for the device as long as it’s only transmitting with a relatively light duty cycle.