Information theoretic limits of cognition and cooperation in wireless networks

In this thesis, we introduce and study the information theoretic limits of cognition, or asymmetric transmitter cooperation, in wireless channels. We consider multi-user channels in which the messages of some transmitters are known in a non-causal fashion (prior to transmission) to other transmitters, but not vice-versa. This asymmetry in message knowledge and resulting asymmetric transmitter cooperation is what we call cognition. Besides being of theoretical interest as its own result, asymmetric transmitter cooperation may be motivated as a novel way in which cognitive radios may opportunistically exploit secondary spectrum licensing. We frame cognition as a strict information theoretic problem whereby we are able to quantify the potential benefits to both nodes of different capabilities when this asymmetry in message knowledge is properly exploited. We study three different cognitive channels in three main chapters.; Chapter 2 considers the cognitive channel: two interfering point-to-point channels in which one cognitive transmitter knows both its own message as well as that of the primary transmitter. We prove an achievable rate region which combines two intuitive strategies: the cognitive transmitter could reinforce the message of the primary transmitter or code so as to mitigate interference from the primary transmitter. We extend the results to a Gaussian cognitive channel. This allows us to visualize and compare the cognitive achievable rate region to those of other related Gaussian noise channels. We provide an alternative formulation of the Gaussian cognitive channel achievable region which illustrates the connection to Gaussian multiple-input multiple-output broadcast channels.; Chapter 3 considers cognitive multiple-access channels. These channels consist of a (q → 1) channel in which all transmitters have a function of the messages of another (p → 1) channel, but not vice versa. Achievable rate regions, outer bounds are derived for the discrete channel, which are then applied to the Gaussian noise channel.; Chapter 4 considers a cognitive X-channel: a two transmitter, two receiver channel in which four messages, one from each transmitter to each receiver, are to be transmitted. We demonstrate an achievable rate region for the cognitive X-channel in which a codeword is the non-causally known side-information at the second transmitter. We use this achievable rate region to evaluate the multiplexing gains of the cognitive and cognitive X-channels in Gaussian noise.