In this thesis, we study the capacity and achievable rates for multi-antenna and multi-carrier diamond relay channels. In an N-relay diamond channel, source transmits messages to the destination with the help of $N$ relays, and there is no direct link between the source and the destination. We first analyze the 2-relay multiple-input multiple-output (MIMO) Gaussian diamond channel. In this channel, the source, destination and the relays are assumed to have multiple antennas. We show that a multihopping decode-and-forward with multiple access (MDF-MAC) protocol achieves rates within a constant gap from capacity when a channel parameter Delta is greater than zero. We also identify the transmit covariance matrices to be used by each relay in the multiple-access (MAC) state of the MDF-MAC protocol.


We then study the M-relay diamond relay channel with multicarrier transmission. We propose new decode-and-forward (DF) protocols for this channel based on selection of 2 relays from the network of M relays. The DF protocols proposed for the case of multicarrier transmission are motivated by the gap results we obtained for the 2-relay MIMO diamond relay channel. The protocol for the M-relay case is an extension of the 2-relay case using appropriate relay selection. We then propose another new decode-and-forward (DF) protocol called Greedy Successive Relaying (GSR) protocol for the M-relay multicarrier diamond relay channel. The GSR protocol uses two states and the relays are partitioned into two sets, A and B. In the first state of the GSR protocol, the relays in A will receive messages from the source while the relays in B will transmit messages to the destination. In the second state, the role of the relays will be reversed i.e. the relays in A will be transmitting to the destination while the relays in B will be receiving from the source. The GSR protocol takes advantage of: (1) successive relaying to overcome the half-duplex limitation, and (2) greedy subcarrier allocation across relays to exploit the available diversity from all the relays. The proposed GSR protocol performs significantly better than the existing protocols.


Finally, we study the multicarrier diamond channel with two destinations. We propose a successive relaying decode-and-forward protocol for the half-duplex 2-relay 2-destination multicarrier channel. The proposed protocol performs significantly better than existing protocols and achieves sum rates close to the cutset upper bound. We also prove that the linear program that describes the cutset upper bound for sum capacity is optimized using only 3 of the 4 possible states of the half-duplex network. Of these 3 states, successive relaying uses the two states in which one of the relays is receiving from the source while the other relay is transmitting to the destinations.