Can I use 在 with 一边... 一边? 我一边吃饭，一边做作业


I do homework while eating


  我一边在吃饭，一边在做作业


I'm doing homework while eating

Is the second sentence correct? Can I use 在 or does 一边...一边 already imply that the action I'm talking about is happening right now?
[一边 (verb A) 一边 (verb B)] indicates  (verb A) and (verb B) are carried out  concurrently. Please read Is the 边～边 the synonym for 一边～一边? for reference
[在 (verb A)] indicates (verb A) is in a progressive tense (in the middle of doing it / in a continuous state of doing it)
Neither structure indicate tense, because Chinese verbs do not inflect between present and past tense. Please read How do you specify past tense for 是? for reference



  我一边在吃饭，一边在做作业


It is not technically wrong, but the more efficient structure to express the same meaning is "我在边吃饭，边做作业" 

[边] 吃饭 [边] 做作业 indicates "eat dinner" (verb A) and "do homework" (verb B) are carried out concurrently

[在] [边吃饭，边做作业] indicates both actions are in a progressive tense (in the middle of doing it / in a continuous state of doing it)