8.4 Power Allocation Games in Parallel Interference Relay Channels 229 where Z k N(0, N k ), k {1, 2, r}, represents the Gaussian complex noise in band (q) (q) (q) and, for all (k, ) K 2 , h k is the channel gain between S k and D , h kr is the (q) channel gain between S k and R, and h rk is the channel gain between R and D k in band (q). As far as the channel state information (CSI) is concerned, we always assume coherent communications for each transmitter­receiver pair (S k , D k ), but at the transmitters, the information assumptions will be context-dependent. The single- user decoding (SUD) will always be assumed at D 1 and D 2 . At the relay, the implemented reception scheme will depend on the protocol (q) assumed. The expressions of the signals transmitted by the relay, X r , q {1, . . . , Q}, will also depend on the relay protocol and will therefore also be explained in the corresponding sections. So far, we have not mentioned any power constraint on the (q) signals X r . We also assume that the relay implements a fixed power allocation (q) (q) policy between the Q available bands (E|X r | 2 = P r , q {1, . . . , Q}). As in Maric et al. (2008) and Sahin and Erkip (2007a, b), the relay is assumed to operat e in the full-duplex mode. In what follows, the existence of an NE solution for the non-cooperative power allocation game where the transmitters are assisted by several relaying nodes is (q) (q)