The error rate exponent of a collision resolution algorithm for underwater acoustic local area networks
Authors: Brady David 
Published: October 2005

There is growing interest in the development of underwater acoustic local area networks for long-term and real-time telemetering of data from ocean-bottom instrumentation. Due to the large propagation delay of the underwater acoustical channel and the finite energy supply of battery powered, ocean-bottom nodes, network protocols designed for radio-based local area networks (LANs) are inappropriate for narrow-band, underwater acoustic LANs and would yield large expected packet delays and low throughput. It has been demonstrated that incorporating interference suppression techniques into protocol design increase throughput and decrease network delay in underwater acoustic local area networks, at the expense of a modest increase in central receiver complexity. These techniques allow simultaneous packet transmissions from cochannel, asynchronous network nodes, and provides the receiver with an algorithm to resolve the packet collisions, often without retransmission. The standard benchmark for comparing such collision resolution techniques is the probability of bit error of a collided packet in the low thermal noise regime. In the additive white Gaussian noise channel with binary phase-shift keying modulation, the logarithm of the bit error rate of the kth packet behaves as −ηkSNRk/2 for sufficiently low background noise, where ηk is the asymptotic multiuser efficiency (AME) of the given collision resolution algorithm, and SNRk is the received signal-to-background-noise ratio from the corresponding transmitter.

Thus, ηk is an attenuation of the SNR required for interference cancellation, and provides a simple yet precise means of comparing collision resolution algorithms. To date, this parameter is only known for the following collision resolution techniques in the two-user, asynchronous AWGN channel: maximum likelihood sequence detection, decorrelating detection, linear MMSE detection, and conventional detection. In this talk the error rate exponent for a class of collision resolution algorithms will be presented. This class includes those techniques that estimate and subtract multiple-access interference (MAI) by using tentative data decisions, and includes the two-stage detectors with both conventional or decorrelated tentative decisions. The error rate exponent for this class will be shown to quantify the following conclusions: (1) strong users will suffer from subtractive interference cancellation through error propagation, (2) the AME for a sufficiently weak user rises rapidly to that of the optimum sequence receiver for sufficiently strong interference, but (3) some detectors in this class tend to have low near-far resistance. It will be shown that while the asymptotic multiuser efficiency of two-stage detection with decorrelated tentative decisions dominates that of the decorrelating detector for a wide range of relative energies, the near-far resistances of these detectors exhibit a reverse ordering. More importantly, the asymptotic multiuser efficiencies for this class of detectors clearly indicate regions for which a given user should avoid updating tentative decisions and suggest combinations of the above receivers to improve single-user performance.