# Outage Capacity of the Fading Relay Channel in the Low SNR Regime

### Amir Salman Avestimehr

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/EECS-2006-36

April 7, 2006

### http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-36.pdf

In this thesis we look at the outage capacity of the fading relay channel with half-duplex constraint in the low SNR regime. First we consider the scenario that the channel state information (CSI) is available only at the receiver. In this case we show that a Bursty Amplify-Forward (BAF) protocol is optimal and achieves the max-flow min-cut upper bound on the outage capacity of this network. But as the channel estimation is quite challenging in the low SNR regime we look at the scenario that neither the transmitter nor the receiver know the channel state (non coherent). We show that the outage capacity in this scenario is the same as before, hence the receiver does not need to estimate the channel to get the same rate as before. We also investigate another extreme that the channel state information is available at both the transmitter and the receiver (full CSI). We show that this additional information will just slightly increase the outage capacity while the communication protocol gets quite complicated. Finally we consider two important extensions: one is when we have an average sum power constraint on the source and the relay and we can optimize the power allocated to the source and the relay. The other extension is when we can add more relays to help the source. Here the goal is to understand how much these additional relays are beneficial.

**Advisor:** David Tse

BibTeX citation:

@mastersthesis{Avestimehr:EECS-2006-36, Author = {Avestimehr, Amir Salman}, Title = {Outage Capacity of the Fading Relay Channel in the Low SNR Regime}, School = {EECS Department, University of California, Berkeley}, Year = {2006}, Month = {Apr}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-36.html}, Number = {UCB/EECS-2006-36}, Abstract = {In this thesis we look at the outage capacity of the fading relay channel with half-duplex constraint in the low SNR regime. First we consider the scenario that the channel state information (CSI) is available only at the receiver. In this case we show that a Bursty Amplify-Forward (BAF) protocol is optimal and achieves the max-flow min-cut upper bound on the outage capacity of this network. But as the channel estimation is quite challenging in the low SNR regime we look at the scenario that neither the transmitter nor the receiver know the channel state (non coherent). We show that the outage capacity in this scenario is the same as before, hence the receiver does not need to estimate the channel to get the same rate as before. We also investigate another extreme that the channel state information is available at both the transmitter and the receiver (full CSI). We show that this additional information will just slightly increase the outage capacity while the communication protocol gets quite complicated. Finally we consider two important extensions: one is when we have an average sum power constraint on the source and the relay and we can optimize the power allocated to the source and the relay. The other extension is when we can add more relays to help the source. Here the goal is to understand how much these additional relays are beneficial.} }

EndNote citation:

%0 Thesis %A Avestimehr, Amir Salman %T Outage Capacity of the Fading Relay Channel in the Low SNR Regime %I EECS Department, University of California, Berkeley %D 2006 %8 April 7 %@ UCB/EECS-2006-36 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-36.html %F Avestimehr:EECS-2006-36