The problem of interference management is considered in the context of a linear interference network that is subject to long term channel fluctuations due to shadow fading. The fading model used is one where each link in the network is subject independently to erasure with probability p. It is assumed that each receiver in the network is interested in one unique message, which is made available at M transmitters. Optimal schemes from a Degrees of Freedom (DoF) viewpoint are analyzed for the setting of no erasures, and new schemes are proposed with better average DoF performance at higher probabilities of erasure. Additionally, for M=1, the average per user DoF is characterized for every value of p, and optimal message assignments are identified. For M>1, it is first established that there is no strategy for assigning messages to transmitters in networks that is optimal for all values of p. The optimal cooperative zero-forcing scheme for M=2 is then identified, and shown to be information-theoretically optimal when the size of the largest subnetwork that contains no erased links is at most five.
We study an interference network where equally-numbered transmitters and receivers lie on two parallel lines, each transmitter opposite its intended receiver. We consider two short-range interference models: the "asymmetric network," where the signal sent by each transmitter is interfered only by the signal sent by its left neighbor (if present), and a "symmetric network," where it is interfered by both its left and its right neighbors. Each transmitter is cognizant of its own message, the messages of the @math transmitters to its left, and the messages of the @math transmitters to its right. Each receiver decodes its message based on the signals received at its own antenna, at the @math receive antennas to its left, and the @math receive antennas to its right. For such networks we provide upper and lower bounds on the multiplexing gain, i.e., on the high-SNR asymptotic logarithmic growth of the sum-rate capacity. In some cases our bounds meet, e.g., for the asymmetric network. Our results exhibit an equivalence between the transmitter side-information parameters @math and the receiver side-information parameters @math in the sense that increasing decreasing @math or @math by a positive integer @math has the same effect on the multiplexing gain as increasing decreasing @math or @math by @math . Moreover---even in asymmetric networks---there is an equivalence between the left side-information parameters @math and the right side-information parameters @math . Cognitive radio promises a low-cost, highly flexible alternative to the classic single-frequency band, single-protocol wireless device. By sensing and adapting to its environment, such a device is able to fill voids in the wireless spectrum and can dramatically increase spectral efficiency. In this paper, the cognitive radio channel is defined as a two-sender, two-receiver interference channel in which sender 2 obtains the encoded message sender 1 plans to transmit. We consider two cases: in the genie-aided cognitive radio channel, sender 2 is noncausally presented the data to be transmitted by sender 1 while in the causal cognitive radio channel, the data is obtained causally. The cognitive radio at sender 2 may then choose to transmit simultaneously over the same channel, as opposed to waiting for an idle channel as is traditional for a cognitive radio. Our main result is the development of an achievable region which combines Gel'fand-Pinkser coding with an achievable region construction for the interference channel. In the additive Gaussian noise case, this resembles dirty-paper coding, a technique used in the computation of the capacity of the Gaussian multiple-input multiple-output (MIMO) broadcast channel. Numerical evaluation of the region in the Gaussian noise case is performed, and compared to an inner bound, the interference channel, and an outer bound, a modified Gaussian MIMO broadcast channel. Results are also extended to the case in which the message is causally obtained.