Asymptotic Analysis of Wireless Systems with Rayleigh Fading

Citation

Rao, Chaitanya Kumar (2007) Asymptotic Analysis of Wireless Systems with Rayleigh Fading. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/YYD6-VP11. https://resolver.caltech.edu/CaltechETD:etd-04252007-122857

Abstract

This thesis looks at ways to improve either the reliability or the rate at which we can successfully transmit information over Rayleigh-fading wireless communication channels.

We study four wireless schemes, the first in the low signal-to-noise ratio (SNR) regime, the remaining three at high SNR. The analysis provides insights that apply to more general SNRs.

Firstly we investigate a point-to-point multiple antenna link at low SNR. At low SNR channel estimates can be unreliable, and therefore we assume the channel is unknown to both transmitter and receiver. Adopting a block-fading model we find the mutual information between transmitter and receiver up to second order in the SNR. The expression is valid for input distributions with regular behavior of fourth- and sixth-order moments, in particular most practical schemes. Subject to input-signal constraints, we determine the optimal signaling to maximize this mutual information.

We undertake high SNR analysis by finding the diversity-multiplexing gain trade-off of three further wireless systems with fading. Using techniques from existing works we find the optimal diversity-multiplexing gain trade-off for an M by N multiple antenna system with R single antenna relays. This uses a two-stage protocol in which the source first transmits to relays, then the relays multiply their received signal by a unitary matrix, before forwarding the result to the receiver. The trade-off is found to be equal to that of a multiple-input multiple-output (MIMO) link with R transmit and min{M,N} receive antennas.

Next we consider a network with two source-destination pairs (an interference channel) and establish relationships between the rate and diversity achievable by certain schemes. We show through two more schemes how cooperation amongst the nodes achieves a higher diversity, but with a reduced rate of the system. These schemes can easily be generalized from two to m source-destination pairs.

A final scheme is considered where n relay nodes are added to the m source-destination pairs, which act to cancel interference in an aim to increase diversity. The outage behavior of this scheme is analyzed and it is shown that for sufficiently many relay nodes, a diversity linear in n can be obtained.

Thesis Files