On the problem of bandwidth partitioning in FDD block-fading single-user MISO/SIMO systems

We report on our research activity on the problem of how to optimally partition the available bandwidth of frequency division duplex, multi-input single-output communication systems, into subbands for the uplink, the downlink, and the feedback. In the downlink, the transmitter applies coherent beamforming based on quantized channel information which is obtained by feedback from the receiver. As feedback takes away resources from the uplink, which could otherwise be used to transfer payload data, it is highly desirable to reserve the right amount of uplink resources for the feedback. Under the assumption of random vector quantization, and a frequency flat, independent and identically distributed block-fading channel, we derive closed-form expressions for both the feedback quantization and bandwidth partitioning which jointly maximize the sum of the average payload data rates of the downlink and the uplink. While we do introduce some approximations to facilitate mathematical tractability, the analytical solution is asymptotically exact as the number of antennas approaches infinity, while for systems with few antennas, it turns out to be a fairly accurate approximation. In this way, the obtained results are meaningful for practical communication systems, which usually can only employ a few antennas.