  We investigate the effect of feedback delay on the outage probability of
multiple-input single-output (MISO) fading channels. Channel state information
at the transmitter (CSIT) is a delayed version of the channel state information
available at the receiver (CSIR). We consider two cases of CSIR: (a) perfect
CSIR and (b) CSI estimated at the receiver using training symbols. With perfect
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 show that BF-IC is close
to optimal for low SNR and USPA is close to optimal at high SNR. With imperfect
CSIR, we obtain an upper bound on the outage probability with USPA and BF-IC.
Results show that the loss in performance due to imperfection in CSIR is not
significant, if the training power is chosen appropriately.
