Performance analysis of LTE downlink system using relay-based selective transmission
Personal and Ubiquitous Computing
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The relay channel consists of a transmitter input $x_{1}$, a relay input $x_{2}$, a relay output $y_{2}$ , and a receiver output $y_{3}$. In this paper, we establish the capacity of three new classes of semi-deterministic relay channels: 1) a class of degraded semi-deterministic relay channels, 2) a class of semi-deterministic orthogonal relay channels, and 3) a class of semi-deterministic relay channels with relay-transmitter feedback. For the first class of relay channels, the output of the relay $y_{2}$ depends on a deterministic function of the transmitter's input $x_{1}$, i.e., on $s=f_{1}\left (x_{1}\right )$, rather than on $x_{1}$ directly. In addition, the relay channels satisfy the condition that $S \rightarrow \left (X_{2},Y_{2}\right ) \rightarrow Y_{3}$ forms a Markov chain for all input probability distributions $p\left (x_{1},x_{2}\right )$. Hence, the first class of relay channels includes, but is strictly not limited to, the class of degraded relay channels previously considered by Cover and El Gamal. The partial decode-and-forward strategy achieves the capacity of the class of degraded semi-deterministic relay channels. Next, we consider the class of semi-deterministic orthogonal relay channels where there are orthogonal channels from the relay to the receiver and from the transmitter to the receiver. In addition, the output of the relay $y_{2}$ is a deterministic function of $x_{1}$, $x_{2}$ and $y_{3}$ , i.e., $y_{2}=f_{4}\left (x_{1},x_{2},y_{3}\right )$. The class of semi-deterministic orthogonal relay channels is a generalization of the class of deterministic relay channels considered by Kim. The compress-and-forward strategy achieves the capacity of the class of semi-deterministic orthogonal relay channels. For the third class of relay channels, there is a causal and noiseless feedback from the relay to the transmitter. In addition, similar to the second class of relay channels, the output of the relay $y_{2}$ is a deterministic function of $x_{1}$, $x_{2}$, and $y_{3}$ . Both the generalized strategy of Gabbai and Bross and the hash-and-forward strategy of Kim achieve the capacity of the class of semi-deterministic relay channels with relay-transmitter feedback.