A case-control study. First, if there was a suspicion that the phones caused cancer, it would not be ethical to randomly assign some people to use them. Second, brain cancer is rare so it would take huge numbers of participants in an experiment to result in even a few cases of brain cancer. Smoking is an interacting variable. Placebo effect is the biggest problem.
Ecological validity is a problem.
Confounding variable is preferred form of exercise. People hospitalized for other reason may have been in ill health the previous year, which may have caused them to give up coffee. Randomization helps to rule out confounding variables.