The modified cramer-rao bound for channel estimation in quantize-and-forward cooperative systems

The quantize-and-forward (QF) cooperative protocol can effectively be used to combat fading in systems using half-duplex relay terminals. While the outage behavior of the QF protocol has been extensively investigated, few research has been performed on the impact of imperfect channel estimates. In this contribution, a lower bound (LB) on the estimation error is obtained for a one-hop relaying channel with data quantization at the relay. To this purpose the modified Cramer-Rao (MCRB) bound is calculated, which, compared to the true Cramer-Rao bound (CRB), is a looser and computationally less complex bound that converges to the CRB in the high signal-to-noise ratios. By using a general system model for the relay channel, the obtained results can be utilized to benchmark a wide variety of systems

The modified Cramer-Rao bound for channel estimation in quantize-and-forward cooperative systems

The quantize-and-forward (QF) cooperative protocol can effectively be used to combat fading in systems using half-duplex relay terminals. While the outage behavior of the QF protocol has been extensively investigated, few research has been performed on the impact of imperfect channel estimates. In this contribution, a lower bound (LB) on the estimation error is obtained for a one-hop relaying channel with data quantization at the relay. To this purpose the modified Cramer-Rao (MCRB) bound is calculated, which, compared to the true Cramer-Rao bound (CRB), is a looser and computationally less complex bound that converges to the CRB in the high signal-to-noise ratios. By using a general system model for the relay channel, the obtained results can be utilized to benchmark a wide variety of systems

Lower bounds on the estimation performance in low complexity quantize-and-forward cooperative systems

Cooperative communication can effectively mitigate the effects of multipath propagation fading by using relay channels to provide spatial diversity. A relaying scheme suitable for half-duplex devices is the quantize-and-forward (QF) protocol, in which the information received from the source is quantized at the relay before being forwarded to the destination. In this contribution, the Cramer-Rao bound (CRB) is obtained for the case where all channel parameters in a QF system are estimated at the destination. The CRB is a lower bound (LB) on the mean square estimation error (MSEE) of an unbiased estimate and can thus be used to benchmark practical estimation algorithms. Additionally, the modified Cramer-Rao bound (MCRB) is also presented, which is a looser but computationally less complex bound. An importance sampling technique is developed to speed up the computation of the MCRBs, and the MSEE performance of a practical estimation algorithm is compared with the (M)CRBs. We point out that the parameters of the source-destination and relay-destination channels can be accurately estimated but that inevitably the source-relay channel estimate is poor when the instantaneous SNR on the relay-destination channel is low; however, in this case, the decoder performance is not affected by the inaccurate source-relay channel estimate

The Cramer-Rao Bound for channel estimation in block fading amplify-and-forward relaying networks

In this paper, we express the Cramer-Rao Bound (CRB) for channel coefficient and noise variance estimation at the destination of an Amplify-and- Forward (AF) based cooperative system, in terms of the a posteriori expectation of the codewords. An algorithm based on factor graphs can be applied in order to calculate this expectation. As the computation of the CRB is rather intensive, the modified CRB (MCRB), which is a looser bound, is derived in closed form. It can be shown that the MCRB coincides with the CRB in the high signal-to-noise ratio (SNR) limit and to that end the CRB/MCRB ratio is simulated in case of uncoded and convolutional encoded transmission

Maximum-likelihood channel estimation in block fading amplify-and-forward relaying networks

Several diversity techniques have been proposed to counteract the effect of fading on the error performance of wireless networks. A recent and promising technique, which achieves spatial diversity without increased hardware demands, is cooperative communication, involving other terminals in the network that relay the information broadcasted by the source terminal to the destination terminal. In literature several cooperative protocols have been studied under the simplifying assumption that all channel state information is available at the destination. In this paper, we use the space-alternating generalized expectation-maximization (SAGE) algorithm to perform codeaided iterative channel estimation from the broadcasted signals in an Amplify-and-Forward protocol, and investigate the resulting error performance