How to select the date of SAR products over an area to form mosaic in order to do crop classification?

My aim is to do crop classification over large scale area and as result, I need to do mosaic, so the question is there any restrict or limitation on the date of the products to form the mosaic and how? please

I think this is a logical question. There is no technical limit which prevents you from mosaicing images of different dates, but if the SAR images are acquired from dates which represent different stages of crop development you will inevitably have transitions between your images.
Another point is that crops are sensitive to looking direction and incidence angles. So whenever you mosaic images of different tracks, keep in mind that the backscattering mechanisms can change over such large areas.

Lastly, the main information of SAR data for crop classification lies in the multi-temporal observation of longer time series.

I highly recommend these resources on agricultural mapping with SAR data:

so what about if we just do the classification for every product and then do mosaic to construct large scale crop classification

this depends on the type of classification. If you work with thresholds you will get different results between the products, for example. But if you follow a supervised approach, you might be more lucky.

I got this reply from professor Franz Meyer. what I understood from this is that he wants me to divide the entire large scale area into pieces 100x100 km area. Then do the classification for every area and mosaic them. so the question that I have now is that,should I use MGRS as projection system during the terrain correction

this is a good question. Without having thought about your problem too deeply, I would suggest to mosaic only along-track for now then tile up your area into slightly overlapping 100x100km tiles (e.g., following the MGRS grid). Then you can form stacks that preserve the full temporal fidelity for every 100x100km tile and can analyze the data pixel by pixel to derive agriculture metrics. I would mosaic derived agriculture variables at the very end I guess. At least during certain phases of the crop growth period, RCS can vary rapidly and mosaicking data from different dates at the data level may remove some of this information.

ABraun, could you please elaborate on this if possible

I think he means that you work on subsets based on the MGRS grid.
This does not necessarily require your data to be projected in UTM. Especially as your data covers more than one UTM zone I suggest to stick with WGS84 (EPSG:4326) during the terrain correction.

@ABraun Thank you very much, the link you provided is not Available.

the link works for me acutally
Please try the main page: > Resources > Agriculture