Cooperative Distributed Beamforming With Outdated CSI and Channel Estimation Errors

This paper investigates the effect of imperfect channel state information (CSI) on the outage performance of cooperative distributed beamforming (DBF). The acquisition of perfect CSI is disturbed by outdated CSI and channel estimation errors. Decode-and-forward relays are considered with individual power constraints at each relay. Considering a training-and-feedback strategy to acquire CSI, a closed-form approximate expression for outage probability and the achievable diversity gain are first provided under Rayleigh fading channels. Numerical observations verify that the approximation is very tight. It is shown that outdated CSI seriously degrades the performance, and therefore, the outage probability is bounded and no diversity is achieved. Conversely, channel estimation errors cause slight performance degradation, and full diversity order is still achievable. However, even when CSI is outdated, it is shown that the asymptotic outage decreases as the number of relays K increases, where the logarithm of the outage probability decreases at the rate of K log K. This paper shows that, when the destination re-estimates the current CSI for decoding, the effect of outdated CSI is greatly mitigated and consequently achieves a diversity gain of one. To re-estimate the current CSI with small overhead, the beamformed training sequence (BFTS) strategy is proposed, in which a new closed-form formula for minimum-mean-square-error estimation is presented using Gaussian approximation. Numerical results verify that the outage performance with the proposed BFTS scheme is close to that of a perfect estimation. A closed-form outage expression of DBF with the proposed BFTS scheme is also presented under an assumption of high-signal-to-noise ratio (SNR), but the expression is very tight even in low-to-moderate SNR regimes.