Transmission of random access preamble structures within a cellular wireless network is based on the use of cyclic shifted constant amplitude zero autocorrelation (“CAZAC”) sequences to generate the random access preamble signal. A pre-defined set of sequences is arranged in a specific order. Within the predefined set of sequences is an ordered group of sequences that is a proper subset of the pre-defined set of sequences. Within a given cell, up to 64 sequences may need to be signaled. In order to minimize the associated overhead due to signaling multiple sequences, only one logical index is transmitted by a base station serving the cell and a user equipment within the cell derives the subsequent indexes according to the pre-defined ordering. Each sequence has a unique logical index. The ordering of sequences is identified by the logical indexes of the sequences, with each logical index uniquely mapped to a generating index. When a UE needs to transmit, it produces a second sequence using the received indication of the logical index of the first sequence and an auxiliary parameter and then produces a transmission signal by modulating the second sequence.