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On the ultimate limits of chaos-based asynchronous DS-CDMA-I: basic definitions and results

The ultimate limits of chaos-based asynchronous direct-sequence code-division multiple access systems are investigated using the concept of capacity taken from information theory. To this aim, we model the spreading at the transmitter and the sampling of the incoming signal at the receiver with a unique linear multi-input multi-output transfer function. We then assume the existence of a coding/decoding pair that is able to transmit information through this channel with a vanishing error probability. The capacity of the system is then identified with the maximum rate at which such an errorless link may operate. The capacity is a random quantity depending on the spreading sequences and, due to the asynchronism, on the users relative delays and phases. We then compare different spreading strategies [classical m and Gold codes, independent identically distributed (i.i.d.) and chaos-based codes] in terms of expected performance as well as of the probability that one method outperforms another. To ease further analytical investigations that should cope with expectations of logarithms, we measure capacity not only in bits per use but also in codewords per use. Some formal results along with extensive numerical evidence show that this does not alter the performance ranking. Such a ranking shows that chaos-based spreading always outperforms i.i.d. spreading and those trying to mimic it. This aligns with and complements what was already known about the ability of chaos-based techniques of minimizing multiple access interference.