Interference management in wireless networks

The world is going wireless, and the availability of high-speed ubiquitous wireless connectivity is being taken for granted. Along with high bandwidth consuming applications such as high-definition video, mobile devices such as smartphones and tablets are becoming omnipresent. The legacy wireless systems are not designed to meet such an exponential growth in the demand for wireless connectivity. To meet both short- and long-term demands, we need to develop methods to maximize the spectral efficiency of existing wireless systems, and also understand the fundamental limits of various architectures to guide the design of future wireless networks. Breaking the interference barrier is an important step in achieving higher throughput in both cellular and ad-hoc wireless networks. Towards this end, there has been a renewed interest in information-theoretic studies of Gaussian interference channels in recent years. The technique used by almost all legacy systems to handle interference in wireless networks is to separate the users signals as much as possible using the available time, frequency and spatial dimensions, and then to treat the residual interference as noise. We refer to this technique as simply treating interference as noise. In the first part of the dissertation, we consider the following two problems: (1) Suppose we restrict the strategy to treating interference as noise, then what is the best achievable sum-rate? (2) How sub-optimal is this strategy compared to the best possible strategy? Both of these problems have been widely studied for over three decades, and yet they remain open. We solve both of these problems under certain conditions on the channel parameters which are satisfied when the interference levels are low compared to the signal levels. In such a low interference regime, we show that the best sum-rate achievable with treating interference as noise is a solution to a convex maxmin optimization problem, and therefore the optimal transmit strategies and the corresponding best sum-rate can be efficiently computed using standard convex optimization algorithms. We also show that the corresponding best sum-rate is indeed equal to the sum capacity, thus proving that treating interference as noise is the best strategy in the low interference regime. In the second part of the dissertation, we obtain insights into the problem of interference channel with coordinated multi-point (CoMP) transmission and reception, where the transmitters cooperate to jointly transmit the messages, and the receivers cooperate to jointly receive the messages. The advanced cellular systems such as LTE-Advanced are likely to use CoMP as the physical layer interference management technique to enhance the capacity. Since determining the exact capacity of wireless systems is a difficult problem, often the coarser metric of degrees of freedom (DoF) is used to obtain first-order insights at high SNRs. We provide some insights into the benefits of CoMP by studying the DoF of interference channel with CoMP transmission and reception as a function of the transmit and receive cooperation orders