On the capacity of Gaussian interference channels

In a multiuser wireless communication system, the transmitters communicate with their intended receivers while generating interference to any unintended receivers. Interference, and the way to deal with it, is a central issue in the physical layer design of wireless networks. Among various multiuser systems, the interference channel (IC) is the simplest model that captures the essence of interference. Despite decades of intense research effort, the capacity region of IC remains unknown except for a few special cases. The focus of this thesis is on Gaussian IC. In particular, we examine how interference affects the fundamental performance limits and provide insights on how interference should be treated for various Gaussian interference channel models under different operating conditions. We start with inner bounds of Gaussian ICs, including scalar Gaussian interference channel (GIC), multiple-input single-output (MISO) IC, and multiple-input multiple-out (MIMO) IC. For the scalar GIC, we investigate the use of Sato\u27s modified frequency multiplexing (FDM) idea and obtain the largest computable rate region with cardinality bounds on the number of sub-bands. For the MISO IC, which is more complex than the scalar IC, we obtain the achievable rate region under the assumption of single-user detection at all receivers. Our results indicate that simple transmitter beamforming is optimal to achieve the largest rate region for a two-user MISO IC. For the MIMO IC, an even more complex model than MISO IC, we focus on the study of its achievable sum rate. The results show that superposition encoding with sequential decoding achieves a sum rate that is larger than the FDM sum rate at all interference power levels, a sharp contrast to the scalar case. We then introduce new outer bounds on the capacity region of Gaussian IC. The sum-rate capacity of GIC under the so-called noisy interference is obtained, which constitutes a breakthrough in our understanding of GIC with weak interference. Perhaps more significantly, we show that the sum-rate capacity of GIC with noisy interference is achieved by treating interference as noise at each receiver. Finally, we extend the capacity results of a simple scalar GIC to more complex networks. They include a parallel GIC where several transceiver pairs communicate over parallel GICs and we characterize the conditions under which treating interference as noise at all receivers is optimal. The fundamental result about the concavity of sum capacity as a function of signal power allows us to extend the result to parallel Gaussian broadcast channels and parallel Gaussian multiple access channels. The optimal power allocation scheme also generalizes the classic water filling approach to the single user parallel channels. Our second generalization involves MIMO IC where we derive sufficient conditions to achieve the noisy-interference sum-rate capacity of MIMO IC. In addition, the sum-rate capacity of MIMO Z interference channel (ZIC) and capacity region of MIMO IC with strong interference are also obtained that generalize existing known results for the scalar GIC