Optimal resource allocation in the downlink/uplink of single-user MISO/SIMO FDD systems with limited feedback

Consider a single-user FDD system with multiple antennas at the BS and a single antenna at the user. We assume that the BS performs coherent transmission and reception in the downlink and uplink, respectively. To this end, downlink resources are employed to estimate the downlink channel at the user, while uplink resources are used to estimate the uplink channel at the BS and to relay a quantized version of the downlink channel estimate back to the BS. The transmit CSI for the downlink is estimated, quantized, outdated and affected by feedback errors, while the receive CSI for the uplink is just estimated. Besides the well-known tradeoff between the training and data payload in a one-way system, in a two-way system like a downlink/uplink FDD system, there is an additional tradeoff between both links due to the feedback. We consider the resource allocation of the downlink and uplink jointly taking into account the feedback and imperfect CSI. As a figure of merit we employ the sum of the downlink and uplink capacities.