This thesis explores the optimal node placement for linear Gaussian multiple relay networks of an arbitrary size and with one source-destination pair. Consider the the low attenuation regime (path loss exponent less than 3/2). Under the condition that the minimum achievable rate from source to destination is maintained, we derive upper bounds of node placement with the incoherent and coherent coding schemes, and examine the optimal power assignment related to the node placement with the coherent coding scheme. We prove that the farthest distance between two adjacent nodes is bounded even for an infinite total number of relay nodes, and closed-form formulas of the bounds are derived for both the coding schemes. Furthermore, the distance from the source to the destination is of the same order as the total number of nodes, given the path loss exponent greater than one half under the incoherent coding scheme and the path loss exponent greater than 1 with coherent relaying with interference subtraction coding scheme. Conditioned on a conjecture based on the simulation results, we also provide heuristic upper bounds, which are a little tighter than the strictly proved bounds. The bounds provided in this thesis can serve as a helpful guideline for the relay extension problem in practical network implementation.

This thesis explores the optimal node placement for linear Gaussian multiple relay networks of an arbitrary size and with one source-destination pair. Consider the the low attenuation regime (path loss exponent less than 3/2). Under the condition that the minimum achievable rate from source to destination is maintained, we derive upper bounds of node placement with the incoherent and coherent coding schemes, and examine the optimal power assignment related to the node placement with the coherent coding scheme. We prove that the farthest distance between two adjacent nodes is bounded even for an infinite total number of relay nodes, and closed-form formulas of the bounds are derived for both the coding schemes. Furthermore, the distance from the source to the destination is of the same order as the total number of nodes, given the path loss exponent greater than one half under the incoherent coding scheme and the path loss exponent greater than 1 with coherent relaying with interference subtraction coding scheme. Conditioned on a conjecture based on the simulation results, we also provide heuristic upper bounds, which are a little tighter than the strictly proved bounds. The bounds provided in this thesis can serve as a helpful guideline for the relay extension problem in practical network implementation.