Abstract
Achievable rates and resource allocation strategies for imperfectly known fading relay channels are studied. It is assumed that communication starts with the network training phase in which the receivers estimate the fading coefficients. Achievable rate expressions for amplify-and-forward and decode-and-forward relaying schemes with different degrees of cooperation are obtained. We identify efficient strategies in three resource allocation problems: (1) power allocation between data and training symbols, (2) time/bandwidth allocation to the relay, and (3) power allocation between the source and relay in the presence of total power constraints. It is noted that unless the source-relay channel quality is high, cooperation is not beneficial and noncooperative direct transmission should be preferred at high signal-to-noise ratio (SNR) values when amplify-and-forward or decode-and-forward with repetition coding is employed as the cooperation strategy. On the other hand, relaying is shown to generally improve the performance at low SNRs. Additionally, transmission schemes in which the relay and source transmit in nonoverlapping intervals are seen to perform better in the low-SNR regime. Finally, it is noted that care should be exercised when operating at very low SNR levels, as energy efficiency significantly degrades below a certain SNR threshold value.
Highlights
In wireless communications, deterioration in performance is experienced due to various impediments such as interference, fluctuations in power due to reflections and attenuation, and randomly-varying channel conditions caused by mobility and changing environment
The least amount of energy required to send one information bit reliably is given by Eb/N0 = signal-to-noise ratio (SNR)/(C(SNR)) where C(SNR) is the channel capacity in bits/symbol. (Note that Eb/N0 is the bit energy normalized by the noise power spectral level N0.) In our setting, the capacity will be replaced by the achievable rate expressions and the resulting bit energy, denoted by E(b,U)/N0, provides the least amount of normalized bit energy values in the worst-case scenario and serves as an upper bound on the achievable bit energy levels in the channel
We have assumed that the source-destination, source-relay, and relay-destination channels are not known by the corresponding receivers a priori, and transmission starts with the training phase in which the channel fading coefficients are learned with the assistance of pilot symbols, albeit imperfectly
Summary
Deterioration in performance is experienced due to various impediments such as interference, fluctuations in power due to reflections and attenuation, and randomly-varying channel conditions caused by mobility and changing environment. In [10], under again the assumption of the availability of CSI at the receiver and transmitter, optimal dynamic resource allocation methods in relay channels are identified under total average power constraints and delay limitations by considering delay-limited capacities and outage probabilities as performance metrics. In [11], resource allocation schemes in relay channels are studied in the low-power regime when only the receiver has perfect CSI. To the best of our knowledge, performance analysis and resource allocation strategies have still not been sufficiently addressed for imperfectlyknown relay channels in an information-theoretic context by considering rate expressions. We note that Avestimehr and Tse in [23] studied the outage capacity of slow fading relay channels They showed that Bursty Amplify-Forward strategy achieves the outage capacity in the low-SNR and low outage probability regime. The proofs of the achievable rate expressions are relegated to the appendix
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