A channel coded CP-OFDM interpretation of TZ-OFDM systems

Trailing zero (TZ) OFDM systems replace the cyclic prefix (CP) in OFDM systems by a sequence of zeros. However, this paper shows that a cyclic prefix is still present in TZ-OFDM systems. Indeed, it is shown that a TZ-OFDM system implicitly works by first adding redundancy to the symbols to be transmitted (channel coding) and then adding a cyclic prefix. This paper also proves that the channel coding introduced by the TZ-OFDM system is spectrally balanced, meaning that it maps white noise to (essentially) white noise. This is a desirable property because it is known that any coding scheme which achieves the channel capacity over an unknown multipath channel must be white-like. By introducing the Cramer-Rao bound as a figure of merit, it is shown that there exist channels over which a TZ-OFDM system performs worse than an uncoded OFDM system. The Cramer-Rao bound is also used to explain why using a cyclic prefix is desirable; it allows channels with otherwise unstable inverses to be inverted accurately.