Locally optimum rank detection of known signals under a weakly depende
nt noise model is considered in this paper. The weakly dependent noise
model is known to be useful for modeling inter-user interference, whi
ch is important in the synthesis and analysis of mobile communication
systems. For good weak-signal detection performance under any specifie
d noise probability density function, the locally optimum detector is
derived based on signs and ranks of the observation. It is also shown
that the locally optimum rank detector has the same asymptotic perform
ance as the locally optimum rank detector which uses the actual values
of the observations.