84 research outputs found
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
PRACTICAL QUANTIZE-AND-FORWARD SCHEMES FOR THE FREQUENCY RELAY CHANNEL
International audienceWe consider static and quasi-static relay channels in which the source-destination and relay-destination signals are assumed to be orthogonal and thus have to be recombined at the destination. We propose cheap relaying schemes that are optimized from the knowledge of the signal-to-noise ratios (SNRs) of the source-relay and relay-destination channels at the relay. For this purpose the scheme under investigation is assumed to be scalar and have to minimize the mean square error between the source signal and its reconstructed version at the destination. We propose a quantize-and-forward (QF) scheme, which is a generalization of techniques based on joint source-channel coding. To further improve the receiver performance when the source-relay SNR is relatively poor we propose a Maximum Likelihood detector (MLD) designed for the QF protocol
Grassmannian Beamforming for MIMO Amplify-and-Forward Relaying
In this paper, we derive the optimal transmitter/ receiver beamforming
vectors and relay weighting matrix for the multiple-input multiple-output
amplify-and-forward relay channel. The analysis is accomplished in two steps.
In the first step, the direct link between the transmitter (Tx) and receiver
(Rx) is ignored and we show that the transmitter and the relay should map their
signals to the strongest right singular vectors of the Tx-relay and relay-Rx
channels. Based on the distributions of these vectors for independent
identically distributed (i.i.d.) Rayleigh channels, the Grassmannian codebooks
are used for quantizing and sending back the channel information to the
transmitter and the relay. The simulation results show that even a few number
of bits can considerably increase the link reliability in terms of bit error
rate. For the second step, the direct link is considered in the problem model
and we derive the optimization problem that identifies the optimal Tx
beamforming vector. For the i.i.d Rayleigh channels, we show that the solution
to this problem is uniformly distributed on the unit sphere and we justify the
appropriateness of the Grassmannian codebook (for determining the optimal
beamforming vector), both analytically and by simulation. Finally, a modified
quantizing scheme is presented which introduces a negligible degradation in the
system performance but significantly reduces the required number of feedback
bits.Comment: Submitted to IEEE Journal of Selected Areas in Communications,
Special Issue on Exploiting Limited Feedback in Tomorrows Wireless
Communication Network
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