The phoenix is a mythological bird that comes to us from Ancient Egypt; it bursts into flame when it dies. From that flame it is reborn, young and strong again, to live another 500 year lifetime. It has represented rebirth and renewed vigor in Western society since the Roman Empire convinced Egypt that becoming a Roman province was the best way to go. When the United States Congress decided to scrap NASA's SETI and HRMS programs in 1993 on the basis of being too expensive, the SETI Institute re-birthed the search for extraterrestrial intelligence from the ashes of their short-sighted and narrow-minded attitude in the form of Project Phoenix.
Project Phoenix seeks to find nearby extraterrestrial civilizations. It operates on the basis of trying to find evidence of extraterrestrial intelligences we might conceivably communicate with in the comparatively near future. Within a few hundred years rather than many thousands. Instead of searching whole sections of the night sky, it focuses on sun-like stars within 200 light years of our own. Around 1000 stars in all, attempting to detect communications, whether deliberately aimed towards us or not. It is not an easy task, even if there is an extraterrestrial civilization on a planet circling one of these stars and they did actually transmit a message towards us.
The problems are manifold. Project Phoenix does not have access to sufficient radio telescopes for long enough periods to monitor each of the stars more than at very infrequent intervals. Even if possible extraterrestrials sent a message aimed towards our solar system, the likelihood that we would be listening at the appropriate time is small. The only radio message we have sent, from Arecibo in 1974, was three minutes long. So if they are anything like ourselves, the likelihood that they would transmit towards us is exceedingly small and even if they did, if we wanted to hear it we would need to be constantly listening!
That one broadcast message aimed at extraterrestrial civilizations, way back in 1974, was aimed at the M13 globular star cluster some 21000 light years away. If we are anything to go by then we need to expect that we will have to detect their own internal communications rather than anything aimed at us. We have absolutely no idea whether that is even possible!
Numerous science fiction stories have alien invaders arriving above Earth having detected our electromagnetic communications signals, but while many science fiction books have some validity in science, few if any Hollywood movies do and those based on such a premise certainly do not! The Arecibo broadcast was a very strong directional transmission intended to traverse intergalactic space. Most of our communications these days are targeted up to satellites and then beamed down from them. Broadcast signals by their very nature dissipate rapidly over distance. Is it likely that such signals might cross interstellar distances? Are they likely to even get to the edge of our solar system without distorting so much that they are indistinguishable from background noise?
Project Phoenix is a noble and worthy effort; finding out we have comparatively close neighbors, or any at all, would be profound and shake our societies to their bedrocks. Nevertheless, even if every single one of those 1000 star systems has a civilization as technologically advanced as our own, do NOT presume that Project Phoenix, even if it lives the 500 years of the mythological bird, will actually be able to detect even one of them. I realize this is not what most people, interested enough to read an article under this topic, wish to know. And, who knows, we may be lucky; we may find a near neighbor and soon. The reality though, is that it will take a long time; but what would not trying say about us as a species?