Outage probability of multiple-input single-output (MISO) systems with delayed feedback

  • Authors:
  • Venkata Sreekanth Annapureddy;Devdutt V. Marathe;T. R. Ramya;Srikrishna Bhashyam

  • Affiliations:
  • Coordinated Science Laboratory, Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign;Indian Institute of Management, Ahmedabad, India;Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai, India;Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai, India

  • Venue:
  • IEEE Transactions on Communications
  • Year:
  • 2009

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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 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.