Derivation of Gardner's Timing-Error Detector from the Maximum Likelihood Principle

In a recent paper [1], Gardner described a new timing-error detector for sampled receivers. The detector derives timing information without decision direction from a BPSK or QPSK signal sampled at rate
2/T
(symbol interval
T
). We will show how this detector can be derived from the maximum likelihood principle, and thus give insight into the nature of the algorithm.