I'm waiting for you = 난 널 기다리고 있어. '~는데' links dependent clause and main clause. 눈이 오는데 차를 몰아도 될까? 내가 TV를 보고 있는데 전화가 왔다. 그 애는 노래는 잘 부르는데 춤은 잘 못춰.

Guni's right. I would say 나 너 기다리고 있어 in daily conversation as we drop ㄴ/은/는 and ㄹ/을/를 a lot. -는데 is sometimes used to suggest you expect a reply or a question about it. For example, if you say 이거 무슨 음식이이에요? 한 번도 먹어본 적 없어요 to mean "What food is this? I haven't eaten it", you're just stating the fact you haven't eaten it. However, if you say 이거 무슨 음식이에요? 한 번도 먹어본 적 없*는데*요 instead, the cook might be intrigued. The cook would wonder what you think of it - if it's delicious or not. -는데 makes the cook think there's something he or she would love to know and feel like asking.

Hi, I'm sorry. I forgot to point this out, it should be 오늘 누나 생일인데, not 오늘 누나 생일은데. Have a great day! ^^