Nt1310 Unit 4 Lab Report

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Suppose we have a single-hop RCS where there is one AF relay that amplifies the signal received from a transmitter and forwards it to a receiver. Assume that the transmitter sends over the transmitter-to-relay channel a data symbol ${s_k}$, from a set of finite modulation alphabet, $S={S_1, S_2,ldots,S_{cal A}}$, where ${cal A}$ denotes the size of the modulation alphabet. The discrete-time baseband equivalent signal received by the relay, $z_k$, at time $k$ is given by
z_k = h_{1,k}s_k + n_{1,k},~~~~for~~k=1,2,ldots,M label{relaySignal} end{equation} where $n_{1,k}sim {cal N}_c(0,sigma_{n1}^2)$ is a circularly-symmetric complex Gaussian noise added by the transmitter-to-relay channel, $h_{1,k}$ denotes the transmitter-to-relay channel, and
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The AF relay can be designed to have a fixed or varying amplification gain, $A_k$. In this paper, without any loss of generality, we assume $A_k$ to be fixed and known and the variance of the two additive noises to be equal, $sigma_{n1}^2 =sigma_{n2}^2 =sigma_{n}^2$.

section{Channel Models} label{sChModel} We consider several channel models based on which we develop different data detection algorithms. The first channel model, which we denote by emph{Channel $1.1$}, assumes that the transmitter-to-relay and the relay-to-receiver channels are quasi-static channels whose values remain constant for the duration of a whole frame length $M$. However, it is assumed that the channel values vary randomly from frame-to-frame according to circularly-symmetric complex Gaussian processes, $h_{1,k}= h_{1}sim {cal N}_c(0,sigma_{h1}^2)$ and $h_{2,k}=h_{2}sim {cal N}_c(0,sigma_{h2}^2)$.

The second channel model,
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However, the cascade of the transmitter-to-relay and the relay-to-receiver channels, $h_{1} imes h_{2}$, are combined and represented by a single channel, $h$. Such representation leads to estimation of fewer parameters. It is to be noted that the real and imaginary components of $h$ have Laplace marginal pdfs. Details of the derivation of the statistical characteristics of $h$ is given in Section ef{sChmodel1.2}. The third channel model, represented by emph{Channel 2.1}, assumes $h_{1,k}$ and $h_{2,k}$ are time-varying circularly-symmetric complex Gaussian channels that take different values at every instant of $k$. We model the time-variations of each of the channels by a first-order Gaussian autoregressive process whose parameters are selected in such a way that their autocorrelation values match to the autocorrelation of the fading process of their corresponding channels.

The fourth channel model,

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