Full-diversity STBCs for block-fading channels from cyclic codes

Abstract

Viewing an n-length vector over F(q/sup m/) (the finite field of q/sup m/ elements) as an m/spl times/n matrix over F/sub q/, by expanding each entry of the vector with respect to a basis of F(q/sup m/) over F/sub q/, the rank weight of the n-length vector over F(q/sup m/) is the rank of the corresponding m/spl times/n matrix over F/sub q/. Using the appropriate discrete Fourier transform (DFT), it is known that, under some conditions, n-length cyclic codes over F(q/sup m/), (n|q/sup m/-1 and m/spl les/n), have full-rank (=m). Using this result, we obtain designs for full-diversity space time block codes (STBCs) suitable for block-fading channels from n length cyclic codes over F(q/sup m/). These STBCs are suitable for m transmit antennas over signal sets matched to F/sub q/, where q=2 or q is a prime of the form 4k+1, (k=1, 2, ...). We also present simulation results which illustrate the performance of a few of these STBCs and show that our codes perform better than the well known codes for block-fading channels.