Recently, the use of coherent space-frequency coding in orthogonal frequency-division multiplexing (OFDM)-based frequency-selective multiple-input multiple-output (MIMO) fading channels has been proposed. Acquiring knowledge of the fading coefficients in a MIMO channel is already very challenging in the frequency-flat (fast) fading case. In the frequency-selective case, this task becomes significantly more difficult due to the presence of multiple paths, which results in an increased number of parameters to be estimated. In this paper, we address code design for noncoherent frequency-selective MIMO-OFDM fading links, where neither the transmitter nor the receiver knows the channel. We derive the code design criteria, quantify the maximum achievable diversity gain, and provide explicit constructions of full-diversity (space and frequency) achieving codes along with an analytical and numerical performance assessment. We also demonstrate that unlike in the coherent case, noncoherent space-frequency codes designed to achieve full spatial diversity in the frequency-flat fading case can fail completely to exploit not only frequency diversity but also spatial diversity when used in frequency-selective fading environments. We term such codes "catastrophic.".
['Moritz Borgmann', 'Helmut Bölcskei']
Noncoherent space-frequency coded MIMO-OFDM