Analysis of the error probability of an all digital detector

Several analytical approaches are taken to evaluate the error probability of a digital communications system with a detector implemented as a digital signal processor. Specifically, a binary hypothesis problem is considered, where the reciever consists of a low-pass filter, a sampler, a dynamic range scaling device, an A/D converter, a digitally implemented integrate-and-dump filter and a threshold device. The digital processing for the receiver is done with fixed-point arithmetic. Exact error probability expressions are given for cases overflow and no overflow in the integrate-and-dump filter. Approximate expressions for P//e, which depend upon approximations of the moments of the quantization error, are obtained. The P//e expressions are derived as functions of E//b/N//O, the number of bits in the integrate-and-dump filter output, the number of samples per binary symbol, and the dynamic range scaling factor. Numerical examples illustrating the above analytical approaches are given.