Optimum transmission strategies for the Gaussian one-to-many interference network

We study the Gaussian one-to-many interference network which is obtained as a special case of a general interference network, where only one transmitter generates interference in the network. We allow transmission of messages on all the links of the network. This communication model is different from the corresponding one-to-many interference channel. We formulate two transmission strategies for the above network, which involve using Gaussian codebooks and treating interference as noise at a subset of the receivers. We use sum-rate as the criterion of optimality for evaluating the strategies. For the first strategy, we characterize the sum-rate capacity under certain channel conditions, while for the second strategy, we derive a sum-rate outer bound and characterize the gap between the outer bound and the achievable sum-rate of the strategy. Next, we show that the solution approach for the second strategy has applications to the cascade Gaussian Z network, a network consisting of parallel point-to-point links, where each transmitter except the last has a communication link to the adjacent receiver. Lastly, we illustrate the regions corresponding to the derived channel conditions for each strategy.