An analytical framework for noncoherent decision feedbackdetection is introduced while considering nonorthogonal binarymodulation (NBM) over the synchronous Gaussian K-user channel. Followingthe key idea of noncoherent decorrelating decision feedback detection(NC-DDFD) proposed previously, a K-parameter class of NC-DDFDs isdefined. The symmetric energy measure is defined as the worst-case (overusers) asymptotic effective energy for noncoherent detection. Withoutmaking any simplifying assumption about error propagation, the NC-DDFDthat optimizes symmetric energy among the K parameter class of detectorsis derived. Since the NC-DDFD based on the generalized likelihood ratiotest (GLRT) belongs to the K-parameter class of NC-DDFDs, the optimumNC-DDFD outperforms the GLRT based NC-DDFD in symmetric energy. Like thelatter detector, the optimum NC-DDFD does not require the knowledge ofthe energies or phases of any of the users' transmissions. Exactexpressions for symmetric energy and upper and lower bounds for symbolerror rate (SER) and asymptotic effective energies are obtained for theoptimum NC-DDFD. Rules for ordering users are obtained that guaranteethat the optimum NC-DDFD can user-wise outperform a parallel bank ofpost-decorrelative GLRT detectors
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