Why we use 1536 point FFT for 15 MHz bandwidth, when we can use 1024 point FFT, as in bandwidth of 15 MHz we have only 900 subcarriers.
The LTE standard requires different FFT sizes for different bandwidths:
And all the parameters have to fit together, as shown in:
"LTE parameters have been chosen such that FFT lengths and sampling rates are easily obtained for all operation modes while at the same time ensuring the easy implementation of dual-mode devices with a common clock reference."
Note that in the above link, the 15 MHz bandwidth has 901 subcarriers and 635 guard subcarriers.
Also see this post: