Trading rate versus diversity in space-time-frequency block coding schemes

This paper presents space-time-frequency (STF) designs applied to a MIMO-OFDM system. The basic idea is to make use of frequency diversity in combination with spatial diversity for reducing the number of antennas. The problem is that the use of additional diversity (given that we stick to complex orthogonal codes) has an impact on the spectral efficiency. This impact can be overcome by an increase of the modulation order, and the increase of diversity must compensate for the drawbacks coming from this higher order. The situation is first explained through a simple combination of Alamouti schemes, resulting in a global rate of 1/2. This scheme provides the same diversity as the 4-antenna Tarokh code of same rate. We then show how the scheme can be modified in order to better see the impact of the diversity in a coded transmission. Finally, we illustrate that such schemes can be useful in a two transmit antenna setting, since, in the lower rate mode of IEEE 802.11a standard, they provide better performance than the Alamouti scheme, while the Tarokh scheme would require 4 antennas. Other consequences are highlighted : (i) such schemes are not useful for higher order modulations, (ii) frequency does not always bring as much diversity as space in practical situations, depending on the channel model.