On the Sum-Rate Capacity of Gaussian X Channels

Abstract

Interference caused by the reception of unintended signals at the receivers is a major source of performance bottleneck limiting the capacity of wireless communication systems. An interesting model to study the effect of interference in communication systems is the two?user interference channel (IC), consisting of two point?to?point links which interfere with each other. By allowing messages on all the links of the IC, we obtain the X channel (XC), i.e., both transmitters have an independent message for each receiver, for a total of four messages in the channel. In this sense, the XC is a generalization of the IC. A related channel model, the Z channel (ZC), is obtained from the XC by removing one of the four links and its corresponding message. A defining feature of most modern wireless communication systems is the use of multiple antennas at some or all of the terminals. In the first part of the thesis, we study three related MIMO channels, namely, the Gaussian MIMO IC, the Gaussian MIMO ZC, and the Gaussian MIMO XC, which are obtained as the MIMO counterparts of the single?antenna channels mentioned earlier. We first derive a sum?rate outer bound for the MIMO ZC and compare it with existing bounds in the literature. We also characterize the sum?rate capacity of the MIMO ZC under certain channel conditions. We then study the sum?rate of the Gaussian MIMO XC. We propose a new sum?rate outer bound for the MIMO XC by utilizing the sum?rate outer bound for the MIMO ZC. Subsequently, we derive another outer bound for the MIMO XC by assuming receiver cooperation and deriving the worst noise covariance matrix for the resulting two?user multiple?access channel. We later compare the above two outer bounds for the MIMO XC with some achievable schemes found in the literature and show that the second outer bound is close to the achievable scheme at low to medium SNRs, while the first outer bound is closer at high SNRs. Next, we consider some ramifications of the above results for the MIMO IC. In the second part of the thesis, we study two related channel models, the Gaussian many?to?one X channel and the Gaussian one?to?many X channel, which are obtained as special cases of the general multi?user X channel, with a single antenna at each transmitter and receiver. The many?to?one XC can be described as an XC with 搈any?to?one� connectivity. In the many?to?one XC, communication links exist between all transmitters and one of the receivers, along with a communication link between each transmitter and its corresponding receiver. On the other hand, the one?to?many XC can be described as an XC with 搊ne?to?many� connectivity, and can be obtained by reversing the roles of the transmitters and receivers in the many?to?one XC and vice versa. For the above two channels, we formulate transmission strategies that involve using Gaussian codebooks and treating interference from a subset of transmitters or interference at a subset of receivers as noise. We use sum?rate as the criterion of optimality for evaluating the strategies. We obtain sufficient channel conditions under which the strategies are either sum?rate optimal or within a gap from an outer bound. In the process, sum?rate capacity is characterized in some subregions of the many?to?one and one?to?many XC. We also identify a region in which the many?to?one XC can be operated as a many?to?one IC without loss of sum?rate, and further show that, in this region, the sum?rate capacity can be characterized to within one bit per user. Lastly, we consider some implications of the above results for the many?to?one IC. We formulate transmission strategies for the many?to?one IC and obtain channel conditions under which the strategies achieve sum?rate capacity. A region where the sum?rate capacity can be characterized to within one bit per user is also identified.