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.

Over time, wireless technology advancements in the field of communications have been attracting every individual to turn into a wireless user. To accommodate the increasing number of users and to avoid the problem of spectrum scarcity, the concept of Cognitive Radio Network (CRN) has been developed. Cognitive Radio (CR) is an intelligent radio which efficiently detects and allocates the spectrums of primary licensed users (PUs) to the secondary unlicensed users (SUs). The SUs can utilize these spectrums as long as they do not cause harmful interfere to the PUs. Interference may occur because of the following reasons: misdetection of spectrum availability, the high transmission power of SU when both SU and PU are present in the same channel at the same time. In order to avoid interference, the radio has to have a very accurate spectrum sensing method, transmit power at SU should be constrained by the peak interference power of PU and the CR should continuously sense the presence of PUs. To increase the wireless coverage area and reliability of CRN, a new technology called Cooperative Cognitive Radio Network (CCRN), which is a combination of CRN and cooperative communications was developed. A CCRN not only increases the reliability and wireless coverage area of CR but also improves the overall performance of the system. In this context, the main objective of this research work is to evaluate the outage performance of a CCRN in an environment where fading and shadowing also come into the picture and to study the importance of relay networks in CRN. To fulfill the objectives of this research work, a two-hop decode-and-forward CCRN is considered. The recently introduced κ − µ shadowed fading channel is employed over the CCRN to generate a realistic environment.  In order to implement such system as a whole, a deep literature study is performed beforehand. Analytical expressions for the Probability Density Function (PDF) and Cumulative Distribution Function (CDF) of the Signal-to-Noise Ratio (SNR) are obtained. The analytical expressions and simulation results for Outage Probability (OP) are obtained and compared under different fading parameters. The importance of a multiple-relay system in CRN is presented. From the results obtained in this research work, we can conclude that the OP decreases with increase in allowable peak interference power at the PU. The transmit power at SU should always be constrained by the peak interference power at the PU to avoid interference. The overall system performance increases with increasing number of relays.