Dissecting OFDM: the independent roles of the cyclic prefix and the IDFT operation

An orthogonal frequency-division multiplex (OFDM) system encodes each block of data by first performing an inverse discrete Fourier transform operation and then adding a cyclic prefix. This letter uses the Cramer-Rao bound (CRB) to study the roles of these two operations. The main result is that a cyclic prefix allows almost all channels, including channels with otherwise unstable inverses, to be inverted accurately and moreover, it is the most efficient way of achieving this stability.