Minimum outage probability transmission with imperfect feedback for MISO fading channels
IEEE Transactions on Wireless Communications
Optimum power control over fading channels
IEEE Transactions on Information Theory
Limiting performance of block-fading channels with multiple antennas
IEEE Transactions on Information Theory
Space-time transmit precoding with imperfect feedback
IEEE Transactions on Information Theory
Fading channels: how perfect need "perfect side information" be?
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Capacity and power allocation for fading MIMO channels with channel estimation error
IEEE Transactions on Information Theory
Beamforming in MISO systems: empirical results and EVM-based analysis
IEEE Transactions on Wireless Communications
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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 better for low SNR and USPA is better 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.