Analysis and design of short block OFDM spreading matrices for use on multipath fading channels

We consider the use of block spreading in a multicarrier system to gain diversity advantage when employed over multipath fading channels. The main idea is to split the full set of subcarriers into smaller blocks and spread the data symbols across these blocks via unitary spreading matrices in order to gain multipath diversity across each block at the receiver. We pose the problem of designing the spreading matrix as a finite dimensional optimization problem in which the asymptotic error is minimized. This formulation allows us to find explicit solutions for the optimal spreading matrices. The performance is validated for the uncoded channel as well as for the coded channel employing turbo-iterative decoding. We further demonstrate that suboptimal linear complexity equalization strategies for spread orthogonal frequency division multiplexing (OFDM) do not gain any diversity advantage over traditional diagonal OFDM.