Net degrees of freedom of recent schemes for the MISO BC with delayed CSIT AND finite coherence time

Abstract

Most techniques designed for the multi-input single-output (MISO) Broadcast Channel (BC) require accurate current channel state information at the transmitter (CSIT) which is not a realistic assumption because of feedback delay. A novel approach by Lee and Heath, space-time interference alignment, proves that in the underdetermined (overloaded) MISO BC with N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> transmit antennas and K = N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> +1 users N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> (sum) Degrees of Freedom (DoF) are achievable if the feedback delay is not too big, thus disproving the conjecture that any delay in the feedback necessarily causes a DoF loss. We explain this approach a bit more succinctly and evaluate the net DoF that this scheme can be expected to yield in a realistic system by taking into account the cost of CSIT acquisition (training and feedback). We term the resulting scheme ST-ZF, referring to the use of Space-Time Zero Forcing precoding. The net DoF comparison with TDMA-ZF, MAT-ZF and MAT shows that ST-ZF is also of interest in practice.