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In this paper, we will propose a framework for computing detection (Pd) and false alarm (Pfa) probabilities for chip-time differential transmitted-reference (Tc-DTR) receivers over frequency-selective multipath fading channels further impaired by narrow-band interference (NBI). We will show that, when compared to similar non-coherent receiver architectures, Tc-DTR offers an intrinsic robustness to NBI, provided that the direct sequence (DS) signature code is adequately designed to minimize the effect of interference. We will point out that, among various non-coherent receiver schemes, the property of almost completely rejecting NBI via a proper code design is unique to Tc-DTR with DS coding. Guidelines for optimal code and system optimization will also be provided in the present manuscript. Numerical simulations will be shown to substantiate findings and analytical derivations.