Interference is arguably the most notorious impairment in modern wireless communica- tion systems as it takes over on noise as the first constraint to reliable communications. It is unfortunate however that a general approach to dealing with interference is not known. In this regard, the capacity region of the interference channel (IC) is only known for the case where both receivers experience strong interference [26]. When the interference level is sufficiently strong at the receivers, they are able to decode the im- pairment and subtract it from the received signal without incurring in a rate penalty. Having that as a premise, the authors of [68] demonstrated by adding a relay to the interference channel, that increasing the interference level at the receivers is not always detrimental to the communication process, and on the contrary allows the receivers to have a better view of the interference and decode it. This process is known as inter- ference forwarding (IF) and creates the conditions for decoding the interference at the receivers without incurring in rate penalty. The authors coined the name Interference Channel with a Relay (ICR) for this hybrid model. They also considered a scenario where the intended receiver is not benefited by the relayed message and the unintended receiver only receives interference from the relay, and demonstrated that the rate region is increased, leaving no doubt about the benefit of interference forwarding.
We focus our efforts on studying the benefits of interference forwarding in the cognitive interference channel (CIC) with a relay (CICR). The CIC [6] is a model for unidirec- tional cooperation at the transmitters where one transmitter (cognitive transmitter) is assumed to have noncausal knowledge of the other transmitter’s message (primary transmitter). As opposed to the traditional conception of a cognitive radio (CR), in the CIC both transmitters utilize the channel simultaneously. As the cognitive transmitter has knowledge of both messages, it utilizes its resources to cooperate with the primary user by sending the primary message and also by applying sophisticated encoding tech- niques to eliminate the effect of the interference at its receiver. For a comprehensive account of the CIC the reader is referred to [12]. Figure 5.1 depicts the CICR in the
Figure 5.1: The cognitive interference channel with a relay. The cognitive side is denoted by the subscript 1.
discrete memoryless (DM) case where transmitter 1 is cognitive.
Our model is also motivated by practical applications. On the one hand, it is well known that cooperative communications can provide huge benefits, improving the effi- ciency of the spectrum utilization. On the other hand a secondary system that ideally should not interfere with the primary users can also provide other ways to help the primary users besides the relaying that takes place at the cognitive transmitter. This is achieved in our model by the external relay.
We derive a general achievable rate region for the CICR (in very strong interference) based on superposition coding at the transmitters and block Markov coding [3] at the relay. The relay forwards both users’ messages. We later simplify this general achiev- able scheme into two setups. In the first setup, the relay only conveys the primary user’s signal, which is interference at the cognitive receiver. In the second setup, the relay only conveys the cognitive user’s signal, which turns out as interference at the primary receiver. We characterize the capacity region of both setups in very strong interference under certain conditions, namely when there is no rate penalty for decod- ing both messages at both receivers. As described above, the encoding schemes are as in the CIC in very strong interference and the decoding at the receivers proceeds by backward and simultaneous non-unique decoding. To analyse the benefit due to IF only, we modify both setups by cutting the link from the relay to the receiver that the relayed message is intended to. In this way the relay will only send interference to the unintended receiver. Through this modification we demonstrate that as opposed to the first setup, in the second setup a real benefit of IF is present as the rate region is enlarged compared to the CIC rate region in very strong interference. We also study the case whether the relay should ever allocate power to forward interference if he is able to decode both messages from the transmitters. In the case where the channel is in strong interference but not in very strong interference, we show that allocating part of the relay’s power to forward interference outperforms the achievable rate region obtained by only allocating power to retransmit the intended message. This latter pro- cess is known in this account as message forwarding (MF).
The rest of the chapter is organized as follows: We present the channel model in Sec- tion 5.2. Our main results are in Section 5.3 where we present the general achievable rate region and capacity results for both setups when certain conditions hold. In Sec- tion 5.4 we compute the rate regions in both setups when Gaussian inputs are assumed and compare them with the capacity region of the CIC in strong interference. Rate