A wireless network with at least one base station and a plurality of associated terminals for the exchange of payload data and control data and at least one common transmission channel which is available for access to several terminals is described. The base station is configured to control access to the common transmission channel and the terminals are configured to send at least an access signal to the base station for the purpose of obtaining access to the common transmission channel. Different start moments and different preambles can be assigned to the terminals for transmitting their respective access signals.