Granted this works only for active radar-guided missiles, but those can easily be detected by their radar shining right at you. Maybe all the missiles in sci-fi are radar-guided?
Others have already commented, but normal surveillance radar is like a spotlight from the tower. It goes around and scans the area. If they determine that you are important, the radar can "lock on" to you which means that it will no longer scan around but would shine the light on you constantly.
If they want to shoot at you, they turn on another even stronger more focused light to improve accuracy.
Military today have ability to detect enemy targetting radars and when they lock on so having such a thing in SciFi does not seem strange to me.
Ah sorry I misunderstood your comment. I thought you wanted to say it was obvious for the target to know. Haha yes a notification protocol would be a weird thing to have. It would be gamed the millisecond things went beyond friendly warnings.
The same way they do now: by detecting whatever the attacker is using to sense and target them. Today, that's usually radar. In sci-fi, maybe it's tachyon beams or something.
Aside from detecting any guidance signal the trajectory changing towards them is a giveaway that it is homing and not just a dumb projectile that they are in the path of.
even if the missile isn't using active guidance (ie laser/radar), it's pretty easy to detect anything with an engine in space. there aren't a lot of other explanations for a small object on an intercept course for your ship at high acceleration.
I'm not sure if this is true, if the missile is coming head on. If it is made in a stealthy way, the "head" of the missile could obscure the engine area and make the plume invisible to the target. Having low RCS alongside with hidden plume could make a passively targetted missile relatively stealthy to the target.
Ofcourse, anyone with enough offset to the target would be able to easily detect the engine and thermal release but the target could be unaware.
Another method to hide it is if missile uses some kind of obstacle in order to accelerate behind, for example you fire your missiles and they accelerate when a moon or a planet break line of sight from the target to the missiles. This would make their acceleration burn invisible to the target and could get them very close without being noticed.
if you're curious about this topic, I highly recommend checking out the webpage linked in the sibling comment, "There Ain't No Stealth in Space" if you're curious about this topic.
tl;dr: it's exceedingly difficult to hide anything that consumes power in space. the rcs thrusters would either be too weak to achieve the delta v to hit the target, or the friction from the thrust against the nozzle would unstealth the missile. even the radiation from the onboard computer would likely stand out against the cosmic background. a missile like you describe could potentially evade current detection systems, but would almost certainly be detected by any civilization where ship-to-ship space combat is feasible. and not in a handwavy future tech way, but just from extrapolating current tech. I highly recommend checking out that page. it makes for a great read.
I've read it and mostly agree. The article even talks about the "solution" I mentioned (they call it cold plate). Stealth in space is impossible if you use constraints they used (solar system coverage with sensors and need to hide a ship with life support).
What I've talked more is about a missile. Missile can fly "cold", it could even be multistage so that after it's acceleration burn it can drop of a hot lower stage and continue to the target completely cold. If you add a cold plate and "terrain masking" you could effectively use a missile stealthily. Ofcourse if there is a full system sensor coverage this is not possible, but I've said that in my initial comment as well. You may be able to hide the heat from your target, but not from everyone.
