Noncoherent detection in asynchronous multiuser channels

The noncoherent demodulation of multiple differentially phase-shift-keyed signals transmitted simultaneously over an asynchronous code-division multiple-access (CDMA) channel is considered under the white Gaussian background noise regime. A class of bilinear detectors is defined with the objective of obtaining the optimal bilinear detector. The asymptotic efficiency of the bilinear detectors is derived by characterizing the dominant behaviour of error probability functionals of general quadratic detection schemes in the high signal-to-noise ratio regions. The optimality criterion considered is near-far resistance that denotes worst-case asymptotic efficiency over the signal energies and phases which are unknown at the receiver. The optimal bilinear detector is therefore obtained by solving a minimax optimization problem. In the finite packet length case, this detector is shown to be a time-varying multiinput multioutput linear decorrelating filter followed by differential decision logic. In the limit as packet lengths go to infinity, the time-varying decorrelating detector is replaced by a time-invariant multiinput, multioutput decorrelating filter. Several properties of the optimally near-far resistant detector are established. Prominent among these properties are its bit-error rate invariance to the signal energies and phases of the interfering users, thereby alleviating the near-far problem, and its optimality in near-far resistance among all possible detectors, bilinear or otherwise.