Adaptive transmit beamforming based on channel state information (CSI) is a key feature in next generation wireless cellular systems. However, CSI available for adaptation is imperfect due to feedback delay and estimation errors. In this work, we analyze the outage performance of maximum eigen-mode beamforming with imperfect CSI. First we analyze the outage probability in terms of the correlation coefficient ¿ between the CSI available at the transmitter (CSIT) and the CSI available at the receiver (CSIR). The analysis shows that feedback delay leads to significant degradation at medium and high signal-to-noise ratios (SNR). Furthermore, the effect of delay can be overcome only if ¿ tends to one with increasing SNR. Then, we study whether linear minimum mean squared error (MMSE) prediction can achieve the required behavior in ¿. The length of the prediction filter required is numerically evaluated and shown to increase with SNR. Finally, the asymptotic diversity order is analyzed as a function of the rate at which 1 - ¿ approaches 0 as the SNR ¿ ¿. Results show that for 1 - ¿ proportional to SNR-1, the asymptotic diversity order remains unaltered.

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 longterm 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.

Antenna selection in Multiple-Input-Multiple-Output (MIMO) systems preserves diversity gain while significantly reducing hardware complexity. However, imperfect Channel State Information (CSI) affects performance. In this paper, we first analyze the performance of a MIMO system employing antenna selection at the transmitter and Maximal Ratio Combining (MRC) at the receiver in the presence of feedback delay and channel estimation errors. Then, we determine whether channel prediction can compensate for the effect of feedback delay. Outage probability is analyzed as a function ofρ, the correlation coefficient between the CSI used at the receiver for decoding (CSIR) and the CSI used at the transmitter for selection (CSIT). Analytical results show that the effect of feedback delay is more significant than the effect of estimation error. In order to overcome the effect of delay,ρshould increase with SNR. For a given SNR, the length of the Linear Minimum Mean Square Error (LMMSE) prediction filter required is calculated and shown to increase with SNR. Finally, we determine the asymptotic diversity order as a function of the feedback quality. Results show that if1 - ρ ∝ SNR-1, the diversity order with imperfect CSI is same as that with perfect CSI.