what's the baseband FFT size of LTE? In standard of 3GPP LTE physical layer(3GPP TS 36.211), the FFT size for baseband signal generation for both Dl and UL is 2048 and CP size is also determined. However there is a table in several resources said we have different FFT and CP size. E.g.

http://lteuniversity.com/ask_the_expert/f/59/t/405.aspx

How is it possible?
Read the book 4G Lte Advanced by Stefan Parkvall and Eric Dahlman. According to the book,
FFT size of 2048, with a corresponding sampling rate of 30.72 MHz, is suitable for the wider LTE carrier bandwidths, such as bandwidths of the order of 15 MHz and above. However, for smaller carrier bandwidths, a smaller FFT size and a correspondingly lower sampling rate can very well be used.(Lowering the sample rate simplifies the implementation in dual-mode HSPA/LTE terminals)

Also,nothing forbids the implementation of an OFDM modulator as a set of parallel modulators, 
Also, nothing prevents the use of a larger IFFT size, for example a size-2048 IFFT size, even in the case of a smaller number of OFDM subcarriers.

Tcp= 160·Ts and Tcpe=512.Ts. Change in CP induces change in the total number of REs(6X12, instead of 7X12). Note that #sub carriers remain 12 in both cases and FFT size is dependent on BW allocated which is expressed in #sub carriers.