An arrangement, method, and access point (AP) in a wireless telecommunication network for providing a user terminal (UT) with access to the network utilizing a contention-based, multi-access uplink channel. The AP includes Nrx receive antennas, where Nrx>1, for receiving simultaneous uplink transmissions from a number of UTs, wherein the number of UTs transmitting on a given slot is less than or equal to Nrx. The AP sends power-control commands to the UTs to control the transmit power of each of the UTs to provide received signals of equal average power at the AP. The AP also instructs each UT to select its transmission data rate based on a noise level at the AP, so as to achieve a desired level of reliability. An MMSE receiver without successive interference cancellation receives the packets transmitted from the UTs and separately demodulates and decodes the packets received from each user terminal.