I may not have satisfied answer here, but I would like to correct/add some information for the question.
Each carrier in LTE is 15khz so in a calculation i found that useful symbol time = 1/15khz = 66.6666 micro sec
wrt to this
Normal Cyclic Prefix:
Normal Cyclic Prefix length = 4.6875 micro sec. This length applies for symbol 1,2,3,4,5,6 but not for symbol 0.
- For Symbol 0, Cyclic Prefix length = 5.2083 micro sec.(please refer OFDM baseband signal generation section in 3GPP spec 36.211 in which OFDM parameters table mentions about cyclic prefix length)
- so 6 symbol out of 7 has length = 66.6666 + 4.6875 = 71.3541 micro sec
- But for symbol 0, length = 66.6666 + 5.2083 = 71.8749 micro sec
- So total lengh in case of Normal Cyclic Prefix is 71.8749 + (6 * 71.3541) = 499.9995 micro sec(0.4999995)
Extended Cyclic Prefix:
Extended Cyclic Prefix length = 16.6666 micro sec ----so each symbol in this = 66.6666 + 16.6666 = 83.3332 micro sec
and Extended cyclic prefix Slot (6 symbols) duration = 83.3332 * 6 = 499.992 micro sec (0.4999992 millis)
I hope it helps !!