Weak Signal Communication

Hams operate with a maximum power level of 1.5 kW. While you can do a lot with 1,500 watts... it's far weaker than even an average Class A commercial broadcaster. Many hams have turned this on it's ear and operate QRP... 5 watts or less. Squeezing signal from the noise in that arena requires favorable conditions and some serious technical know-how. There are three primary way to approach this largely self-imposed impediment. More here.

1. Coherent CQ
2. QRSS
3. Specialized Digital Signal Modes

Coherent CQ is technique centered around a bit rate often called a "clock rate."  This uses precisely calibrated transmitters which key at a very stable and specific rate. This consistency allows receivers to use extremely narrow-band filtering.  While the transmission rate is very slow, the super narrow-band filtering improves  the signal to noise ratio making the technique workable.  This can also be used with DSP. 

QRSS is another slow speed QRS CW mode used with narrow-band filtering. But this is not based on signal coherence. This uses extremely long time intervals with element lengths of 10 to 30 seconds or longer. FSCW, DFCW, BPSK and  WOLF are digital modes that can be used within the QRSS arena.
A number software programs can aid implementation, see below. More here.

• Argo http://www.sdradio.eu/weaksignals/argo/index.html 
• Spectran http://www.sdradio.eu/weaksignals/spectran.html 
• Spectrum Lab http://www.qsl.net/dl4yhf/spectra1.html 

 Specialized Digital Signal Modes are an even bigger area to get into because there are numerous digital solutions of varying efficacy. Open Source types of Weak Signal Communication Software inclulde WSJT, MAP65, WSPR, and WSJT-X. All of them require SDR hardware, a SSB transceiver and a PC.Most of them can run on Linux, OSX, and FreeBSD. More here and here.