ACHIEVABLE RATES FOR GAUSSIAN CHANNELS WITH MULTIPLE RELAYS

Multiple-input-multiple-output (MIMO) channels are extensively proposed as a means to overcome the random channel impairments of wireless communications. Based upon placing multiple antennas at both the transmitter and receiver sides of the communication, their virtues are twofold. On the one hand, they allow the transmitter to code across antennas to overcome unknown channel fading. On the other hand, they permit the receiver to sample the signal on the space domain. This operation, followed by the coherent combination of samples, increases the signal-to-noise ratio at the input of the detector and provides large capacity, and reliability, gains. Nevertheless, equipping wireless handsets with multiple antennas is not always possible or worthwhile. Mainly, due to size and cost constraints, respectively. For these cases, the appropriate manner to exploit multi-antenna processing is by means of relaying. This consists of a set of wireless relay nodes assisting the communication between a set of single-antenna sources and a set of single-antenna destinations. With the aid of relays, indeed, MIMO channels can be mimicked in a distributed way. However, the exact channel capacity of single-antenna communications with relays (and how this scheme performs with respect to the equivalent MIMO channel) is a long-standing open problem. To it we have devoted this thesis. In particular, the present dissertation aims at studying the capacity of Gaussian channels when assisted by multiple, parallel, relays. Two relays are said to be parallel if there is no direct link between them, while both have direct link from the source and towards the destination. We focus on three well-known channels: the point-to-point channel, the multiple-access channel and the broadcast channel, and study their performance improvement with the aid of relays. Throughout the dissertation, the following assumptions are made (unless otherwise stated): i) full-duplex operation at the relays, ii) transmit and receive channel state information available at all network nodes, and iii) time-invariant, frequency-flat fading.