# Deep Learning based NDA Channel Estimation

I was wondering if it is possible to use Deep Learning to estimate the Channel Impulse Response for NDA synchronization?

I understand Deep Learning is not normally used for regression problems but I believe you can approximate it as a classification problem if you make your channel tap magnitudes discrete.

I'm not completely sure how NN would be built since you would have the number of SoftMax functions equal to the number of channel taps along with each channel tap having a set of classification values it could take on.

To remove phase and frequency offset dependence you could take the magnitude of the received complex signal and as an assumption assume the tap with the greatest magnitude is real and positive.

• what's NDA in this context? – Marcus Müller Dec 28 '19 at 18:39
• "I understand Deep Learning is not normally used for regression" um, it basically only is: The commonly known "is there a cat in this picture" classification is just finding a minimum-error-probability regression in the slightly higher-dimensional data space. – Marcus Müller Dec 28 '19 at 18:40
• I recommend you look behind the buzzwords and company presentations and consider things like the "universal approximation theorem": it's the mathematical basis for all neural networks, as it (basically) says that you can approximate (i.e. find a regression) an arbitrary smooth function by neural networks. Basically, all the Deep Learning applications you know are regressions! – Marcus Müller Dec 28 '19 at 18:42
• Normally it's used for classification tasks and not regression tasks and it is trained to output a probability among the given classes. NDA means not having a training sequence. In theory you could discretize the channel impulse responses and phase offsets and train. number of classes would be quite large though, the training data would be easy to get - you just generate it in matlab or python or what ever. Deep Learning could also be applied to timing estimation, etc. – FourierFlux Dec 29 '19 at 2:46
• As I tried to explain, your classification is a regression. What does the abbreviation "NDA" stand for? Again, look behind the buzzword: "Deep Learning" is really not a new thing, but just finding a low-dimensional representation (e.g. a probability vector in a classification problem) for a high-dimensional piece of data (e.g. an image). High-dimensional data -> low-count parameter set for a function == regression. Your Deep Learning classificator is just a regression finder. – Marcus Müller Dec 29 '19 at 9:33