In a UMTS system, the AICH is arranged to send, in addition to signals acknowledging that a preamble (164) from a mobile (12) is at an acceptable strength, further signals (171, 176) acknowledging message signals (168, 178) from the mobile. Preferably the further signal (171) is a negative acknowledgement signal, indicating that a message (168) is corrupted. Application of the invention avoids the involvement of layer (2) in message acknowledgement.