Can we do cyclic prefix with zeros in OFDM rather than with samples from end of the ofdm symbol?
There are two major approaches for cyclic extension in OFDM systems - CP (cyclic prefix) and ZP (zero padding, also called Trailing Zeros, TZ). Generally they show the same performance, I mean in AWGN or Fading channel. CP method is the simplest one so it is preferred in the most cases. ZP approach leads to slightly less transmission power level for obvious reason. Doppler performance is the same. The main idea of using ZP as I understood is the existence of equalization techniques for combating spectral nulls that is the major problem of OFDM equalizers. I can't explain this technique because I haven't modeled or implemented it, but you can search some articles in the Web. In one of the article it stands that for CP the simple equalizer exists but symbol recovery isn't guaranteed. But for ZP symbol recovery is guaranteed with complexity of equalizer increasing. I think it is the ckear idea. But I suppose it leads to some matrix subspace algorithms e.g. SVD, so it can be too difficult to implement. I've heard ZP is popular in hydroacoustic OFDM techniques of equalization so you can also refer to this topic. 

Hope it helps.