A base station receives multiple first signals from multiple mobile terminals over a first radio channel (e.g., a RACH, a CPCH, etc.). Multiple acknowledgement signals are generated for transmission over an acquisition indication channel (AICH) during a same access time slot. Each acknowledgement signal is responsive to one of the mobile terminals and includes a signature sequence of bits associated with the first signal received from that mobile terminal. An AICH transmission power profile is determined for the access time slot. If the AICH transmission power profile exceeds a predetermined maximum transmission power parameter, then a first portion of the an AICH transmission power profile is adjusted. Thereafter, the acknowledgement signals are transmitted over the AICH in accordance with the adjusted AICH transmission power profile.