In this paper, the region of SINRs vector for a given user on its assigned sub-carriers (SCs) which corresponds to a given target-rate, is characterized. In doing so, given the user's data rate, the boundary of region of the SINRs vector corresponding to data rate for the user on its assigned SCs is obtained. We show that for a given preference of the user, the point laid on that boundary corresponds to the minimum SINRs vectors for providing the given data rate for the user. Therefore, characterizing the region of SINRs vector corresponding to the target-rate for each users on their assigned SCs and at the same time characterizing the feasible SINRs region on each SCs (which is a traditional problem and addressed already) enable us to study if a given target-rate vector is admissible or not.