I would like to model a transmitter and received pair, both sampling at the same bandwidth (not clock synchronized), where there are a number of reflectors. The time delay due to the reflectors can be a non-integer multiple of the receiver resolution (1 / sampling bandwidth), and I would like to accurately model that.
This means that if I take the transmitted signal at the nominal sample rate, and sum a bunch of time-delayed versions of the signal (with the time delay equal to the difference in time it takes light to travel the direct path and the reflected path), this will be inaccurate because the time delays will be quantized to the sampling period, which is too coarse.
Obviously I can upsample and then do the sum of the upsampled discrete-time signals, which will decrease the quantization error of the time delay. But I'm wondering if there's a way to model the received digital signal without any quantization error. In other words, I'd like to model the continuous-time reflections.
I'm modeling this for a RADAR application, so I'd like the model to be phase-accurate. I'm assuming that each reflector can be modeled by the distance to the transmitter and the receiver, and some real-valued attenuation constant. Is this assumption accurate for RADAR applications? I'm also assuming that the received signal is a sum of time-delayed signals with time-delay and attenuation from the reflector's distances and attenuation constant. Is this accurate for RF, or do I need to account for a discrete phase jump at each reflection?