A Base Station (BS) includes an apparatus capable of performing an offset adjustment for a Mobile Station (MS). The BS can determine an offset mean value of the MS using a previously estimated offset of the MS if UpLink (UL) data received from the MS does not exist. The BS determines whether to transmit an unsolicited ranging response message (Unsolicited RNG-RSP) using the offset mean value of the MS. If transmitting the Unsolicited RNG-RSP, the BS transmits the MS the Unsolicited RNG-RSP including an offset adjustment value for the MS.