On Asynchronous Interference Channels

The first part of the thesis studies a decentralized network of separate transmitterreceiver (Tx-Rx) pairs. The users are asynchronous meaning there exists a mutual delay between their transmitted codewords. Each Tx stays silent permanently after it sends its codeword. The channel from each Tx to each Rx is modelled by a static and nonfrequency selective coefficient followed by additive white Gaussian noise. Each Tx sends a preamble sequence before transmitting its codeword to ensure its affiliated Rx knows the exact arrival time for the codeword. The network being decentralized, different users are unaware of each other’s preamble sequences. As such, the receivers can not determine the exact positions of interference bursts. We introduce a learning technique based on piecewise-linear regression where it is shown how each Rx successfully estimates the number of interferers, the coefficients of the channels carrying interference and the mutual delays. The estimates for the mutual delays are not perfect, however, they are reliable enough to guarantee successful decoding of the codewords. The second part of the thesis addresses a centralized Gaussian interference channel of two Tx-Rx pairs under stochastic data arrival (GIC-SDA). The information bits arrive at the transmitters according to independent and asynchronous Bernoulli processes (TxTx asynchrony). The transmissions are asynchronous (Tx-Rx asynchrony) in the sense that a Tx immediately sends a codeword to its Rx when there are enough information bits gathered in its buffer. Such immediate style of transmission is in contrast to the TxRx synchronous style discussed in [20]. In a setting where the transmitters only know the statistics of Tx-Tx asynchrony, it is shown how each user designs its codebook rate in order to maximize the probability of successful decoding at the receivers. An achievable region is characterized for the codebook rates in a two-user GIC-SDA under the requirements that the transmissions be immediate and the receivers treat interference as noise. This region is described as the union of uncountably many polyhedrons and is in general disconnected and non-convex due to infeasibility of time sharing. Special attention is given to the symmetric case where closed-form expressions are developed for the achievable codebook rates.