Outage Probability of Multiuser Relay Networks in Nakagami-m Fading Channels

Abstract-We evaluate the performance of downlink multiuser relay networks (MRNs) equipped with a single amplify-andforward (AaF) relay. A thorough and exact analysis is conducted to analyze the outage probability of MRNs under dissimilar Nakagami-m fading conditions. More specifically, we derive new closed-form expressions for the outage probability and the probability density function (pdf) of the highest end-to-end signalto-noise ratio (SNR) associated with the strongest destination with the single user and Rayleigh fading as special cases. In particular, we provide new results for channel-state information (CSI)-based-gain relaying and fixed-gain relaying. We then demonstrate that the achievable diversity order is equal to either the first-hop fading parameter or the product of the second-hop fading parameter and the number of destinations. Furthermore, we derive compact closed-form expressions for the moments of the highest end-to-end SNR, from which other moment-based measures such as the average SNR and the amount of fading are deduced. Our results highlight the performance improvements offered by opportunistic scheduling and reveal the impact of the relay location with unbalanced hops on the overall performance. Various numerical examples illustrate the proposed analysis

Multi-user Diversity Systems with Application to Cognitive Radio

abstract: This thesis aims to investigate the capacity and bit error rate (BER) performance of multi-user diversity systems with random number of users and considers its application to cognitive radio systems. Ergodic capacity, normalized capacity, outage capacity, and average bit error rate metrics are studied. It has been found that the randomization of the number of users will reduce the ergodic capacity. A stochastic ordering framework is adopted to order user distributions, for example, Laplace transform ordering. The ergodic capacity under different user distributions will follow their corresponding Laplace transform order. The scaling law of ergodic capacity with mean number of users under Poisson and negative binomial user distributions are studied for large mean number of users and these two random distributions are ordered in Laplace transform ordering sense. The ergodic capacity per user is defined and is shown to increase when the total number of users is randomized, which is the opposite to the case of unnormalized ergodic capacity metric. Outage probability under slow fading is also considered and shown to decrease when the total number of users is randomized. The bit error rate (BER) in a general multi-user diversity system has a completely monotonic derivative, which implies that, according to the Jensen's inequality, the randomization of the total number of users will decrease the average BER performance. The special case of Poisson number of users and Rayleigh fading is studied. Combining with the knowledge of regular variation, the average BER is shown to achieve tightness in the Jensen's inequality. This is followed by the extension to the negative binomial number of users, for which the BER is derived and shown to be decreasing in the number of users. A single primary user cognitive radio system with multi-user diversity at the secondary users is proposed. Comparing to the general multi-user diversity system, there exists an interference constraint between secondary and primary users, which is independent of the secondary users' transmission. The secondary user with high- est transmitted SNR which also satisfies the interference constraint is selected to communicate. The active number of secondary users is a binomial random variable. This is then followed by a derivation of the scaling law of the ergodic capacity with mean number of users and the closed form expression of average BER under this situation. The ergodic capacity under binomial user distribution is shown to outperform the Poisson case. Monte-Carlo simulations are used to supplement our analytical results and compare the performance of different user distributions.Dissertation/ThesisM.S. Electrical Engineering 201