is $e^{-\rho r}$ where $\rho > 0$. This is a simple model used for tractability (see [@firouzabadi-martins08optimal-node-placement], [@appuswamy-etal10relay-placement-deterministic-line]) and [@altman-etal11greec-cellular Section $2.3$] for prior work assuming exponential path-loss). However, for propagation scenarios involving randomly placed scatterers (as would be the case in a dense urban environment, or a forest, for example) analytical and experimental support has been provided for the exponential path-loss model (a discussion has been provided in Section \[subsection:motivation-for-exponential-path-loss\]). We also discuss in Section \[subsection:insights\_for\_power\_law\_from\_exponential\] how the insights obtained from the results for exponential path-loss can be used for power-law path-loss (power gain at a distance $r$ is $r^{-\eta}$, $\eta>0$). Deployment with other path-loss models is left in this paper as a possible future work.

Under exponential path-loss, the channel gains and power gains in the line network become multiplicative, e.g., $h_{i,i+2}=h_{i,i+1}h_{i+1,i+2}$ and $g_{i,i+2}=g_{i,i+1}g_{i+1,i+2}$ for $i \in \{0,1,\cdots,N-1\}$.

We discuss in Section \[subsection:shadowing-fading\] how shadowing and fading can be taken care of in our model, by providing a fade- margin in the power at each transmitter.

Motivation for the Sum Power Constraint {#subsec:sum_power_constraint}
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In this paper we consider the sum power constraint $\sum_{i=0}^{N}P_{i}=P_{T}$ (in mW) over the source and the relays. This constraint has the following motivation. 