Spatial and Temporal Power Allocation for MISO Systems with Delayed Feedback

We determine the minimum outage probability of multiple-input single-output (MISO) channels in the presence of delayed feedback. Channel state information at the transmitter (CSIT) is a delayed version of the perfect channel state information available at the receiver (CSIR). Under a short-term power constraint, we determine: (a) the outage probability for beamforming with imperfect CSIT (BF-IC) analytically, and (b) the optimal spatial power allocation (OSPA) scheme that minimizes outage numerically. Results show that, for delayed CSIT, BF-IC is close to optimal for low SNR and uniform spatial power allocation (USPA) is close to optimal at high SNR. Similarly, under a long-term power constraint, we determine the outage probability for BF-IC with temporal power control and compare it with USPA with temporal power control.