V-OFDM: On Performance Limits over Multi-Path Rayleigh Fading Channels

As a bridge of connecting orthogonal frequency division multiplexing (OFDM) with single-carrier frequency domain equalization (SC-FDE) techniques, Vector OFDM (V-OFDM) provides significant flexibility in system design. This paper presents an analytical study of V-OFDM over multi-path fading channels. Our goal is to investigate the diversity gain and coding gain of each vector block (VB) in V-OFDM so as to ultimately reveal its performance limits over fading channel. By using algebraic number theory tools, we rigorously prove for the first time that a majority of VBs in V-OFDM can surely realize the diversity gain of min {M, G}, where M is the length of each VB, and G is the total number of channel taps. Furthermore, some specific VBs, whose length equals the total number of channel taps, can not only harvest the maximum diversity gain but also achieve the maximum coding gain. It is further demonstrated that, even though VBs fail to benefit from additional diversity gain when M exceeds G, they can enjoy significantly increased coding gains. Our analysis concludes that it is preferable to choose the length of VBs to be equal to the number of channel taps in consideration of both overall system performance and computational complexity.