Outage Probability of Multiple-Input Single-Output (MISO) Systems with Delayed Feedback

TL;DR

This paper analyzes how feedback delay impacts outage probability in MISO channels, comparing beamforming with imperfect CSIT and uniform power allocation under different power constraints.

Contribution

It provides analytical and numerical results on outage probabilities with delayed CSIT and CSIR, highlighting near-optimal strategies at different SNR regimes.

Findings

BF-IC is near optimal at low SNR with delayed CSIT.

USPA is near optimal at high SNR.

Imperfect CSIR causes minimal performance loss with proper training power.

Abstract

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.