Research

I’m a recovering academic and lapsed mathematician with an engineering background. My Ph.D. (incomplete) research explored the application of large deviations theory to calculate the asymptotic error rate of certain decision problems in wireless communications.

Research Interests

My research interests and areas of expertise include:

• Information Theory
• Detection and Estimation Theory
• Decision Theory
• Queuing Theory and Networks
• Stochastic System Simulation and Markov Chain Monte Carlo
• Probability and Measure Theory
• Source and Channel Coding
• Cryptography and Number Theory

Selected Papers

• A MAP blind bit-rate detector for variable-gain multiple-access systems (2003)

  • Davis E., Beaulieu N.C., and Rollins M. A MAP blind bit-rate detector for variable-gain multiple-access systems IEEE Trans. Commun. 51 6 880-884 2003.
  • Link (paywalled)
  • Abstract: A maximum a posteriori blind bit-rate detector is derived for a fixed frame-length multiple-access system which employs variable-gain transmitter power and repetition encoding. Blind bit-rate detectors are derived for the additive white Gaussian noise channel and for the slowly fading Nakagami-m channel, assuming infinite depth interleaving at the smallest bit rate. The performances of the detectors are assessed for different frame lengths, signal-to-noise ratios, and fading conditions.

• Asymptotic Results in PSK Modulation Classification

  • This draft paper condenses some of the key results of the PhD thesis. You can read it here.
  • Abstract: Two asymptotic results in modulation classification are presented. First, a consideration of the noiseless case motivates a lower bound on misclassification probability. Contrary to central limit theorem approximations, the error probability does not go to zero as the signal-to-noise ratio goes to infinity for a fixed number of samples, but is bounded from below by a nonzero error floor if the constellations under different hypotheses have signal points in common. Second, Chernoff information, Bhattacharyya distance and Kullback-Liebler distances are calculated for phase-shift keying modulation classification problems. Simulation results show the utility of Chernoff and Bhattacharyya bounds for phase-shift keying modulation classification. It is shown that the Chernoff information is a valuable performance measure for modulation classification, both asymptotically and for a finite number of observations.