Cooperative Distributed Beamforming With Outdated CSI and Channel Estimation Errors

Abstract

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 The acquisition of perfect CSI is disturbed by outdated CSI and channel estimation errors.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 It is shown that outdated CSI seriously degrades the performance, and therefore, the outage probability is bounded and no diversity is achieved.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 However, even when CSI is outdated, it is shown that the asymptotic outage decreases as the number of relays K increases, where the logarithm of the outage probability decreases at the rate of K log K. This paper shows that, when the destination re-estimates the current CSI for decoding, the effect of outdated CSI is greatly mitigated and consequently achieves a diversity gain of one.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expression is very tight even in low-to-moderate SNR regimes.Index Terms-Cooperative relaying, distributed beamforming, outdated CSI, channel estimation errors, minimum mean square error, outage probability, diversity order.

Outage Analysis of Partial Relay Selection Schemes with Feedback Delay and Channel Estimation Errors in Nonidentical Rayleigh Fading Channels

“…The source and the relays transmit training signals orthogonally, and then the minimum-mean-square-error-(MMSE-) estimated channels at the relays and the destination are given by [12][13][14]…”

Outage Performance of Selective Dual-Hop MIMO Relaying with OSTBC and Transmit Antenna Selection in Rayleigh Fading Channels

“…Fig. 7 shows the outage performances for the channels with low correlation when The first and second hop channel matrices with feedback delay are modeled by [17,18].…”

Adaptive Distributed Beamforming for Relay Networks Based on Local Channel State Information

“…For distributed beamforming algorithms, assumption of global CSI at each node is not practical. (19) for RSB, (32), (36) (38) for CMB are adaptive solutions for relay networks based on local CSI only. However, as a compromise, the global parameter y[n] has to be broadcasted back to the relay nodes, which incurs extra power consumption.…”

“…Define the weight vector error e r,w [n] = w o − w r [n]. Substituting it into (19) and taking the expectation of both sides, we have…”

“…With partial CSI, [18] proposed a worstcase optimization robust algorithm against the error in relay to destination coefficients with the consideration that the source to relay coefficient could be estimated more accurately. In [19], a robust distributed beamforming algorithm is presented by considering not only the channel estimation error, but also the CSI outdate factor. Another robust scheme was proposed in [20] for source to relay transmission based on a relay network with each node equipped with an antenna array.…”