The invention relates to 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 with at least one common transmission channel which is available for access to several terminals, wherein the base station is provided for controlling the access to the common transmission channel, wherein the terminals are provided for sending at least an access signal to the base station for the purpose of obtaining access to the common transmission channel, and wherein at least two different start moments can be assigned to the terminals for transmitting their respective access signals.