Abstract
We investigate the joint effects of feedback delay and channel estimation errors (CEE) over Nakagami- m fading channels for two-hop amplify-and-forward (AF) relaying systems with transmit beamforming (TB) and relay selection (RS). We derive new closed-form expressions for the system outage performance including the exact analysis and informative high SNR asymptotic approximations, which indicate that TB feedback delay reduces the achievable diversity order to one, regardless of Nakagami- m fading parameters. Whereas RS delay reduces the diversity order to a case without relay selection and CEE merely result in coding gain loss, numerical results verify the theoretical analysis and illustrate that the outage performance is more sensitive to the TB feedback delay.
Highlights
Transmit beamforming (TB) and relay selection (RS) are regarded as two promising techniques for multiple-antenna multiple-relay assisted networks to achieve full spatial diversity and have been investigated intensively [1]
We look into the high SNR regime and derive the asymptotic expression for the outage probability, which enables the characterization of the joint effect of TB feedback delay, RS delay, channel estimation quality order, Nakagami-m fading parameters, the number of antennas and relays on the achievable diversity order, and array gain of the system
It can be clearly seen from the figure that analytical and simulated outage probability curves match excellently, which confirm the accuracy of our mathematical analysis and the tightness of the asymptotic analysis as well as the lower bound in high SNR regime
Summary
Transmit beamforming (TB) and relay selection (RS) are regarded as two promising techniques for multiple-antenna multiple-relay assisted networks to achieve full spatial diversity and have been investigated intensively [1]. To achieve coherent beamforming for a maximal ratio transmission or select one or a set of relays for signal forwarding, perfect knowledge of channel state information (CSI) is required at the transmitter, which is probably unavailable because of practical limitations such as feedback delay and channel estimation errors (CEE). The effects of feedback delay on the performance of a two-hop TB and amplify-and-forward (AF) relay network with and without interference over Rayleigh-fading channels are investigated in [2, 3], respectively. Most existing related works limited their analysis to either single-relay or single-antenna systems and do not yet consider TB and RS simultaneously or investigate the joint effect of outdated and imprecise CSI. Numerical results verify the theoretical analysis and illustrate the decremental effects of feedback delay and CEE on the system performance
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