Outage probabilities and single-hop throughput are two important performance metrics that have been evaluated for certain specific types of wireless networks. However, there is a lack of comprehensive results for larger classes of networks, and there is no systematic approach that permits the convenient comparison of the performance of networks with different geometries and levels of randomness. The uncertainty cube is introduced to categorize the uncertainty present in a network. The three axes of the cube represent the three main potential sources of uncertainty in interference-limited networks: the node distribution, the channel gains (fading), and the channel access scheme (set of transmitting nodes). For the performance analysis, a new parameter, the so- called spatial contention, is defined. It measures the slope of the outage probability in an ALOHA network as a function of the transmit probability p at p = 0. Outage is defined as the event that the signal-to-interference ratio (SIR) is below a certain threshold in a given time slot. It is shown that the spatial contention is sufficient to characterize outage and throughput in large classes of wireless networks, corresponding to different positions on the uncertainty cube. Existing results are placed in this framework, and new ones are derived. Further, interpreting the outage probability as the SIR distribution, the ergodic capacity of unit-distance links is determined and compared to the throughput achievable for fixed (yet optimized) transmission rates.
This case is studied in @cite_6 . The characteristic function of the interference is determined to be Note that their notation is adapted to ours. Also, a small mistake in [Eqn. (18)] net:Sousa90 is corrected here.
@cite_6
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1Consider an additive Gaussian noise channel affected by an additive interference sequence, taken from a given codebook, which is known non-causally at the transmitter (e.g., via prior decoding). It is known that in this case optimal performance is attained by Dirty Paper Coding, which treats the interference signal as unstructured. In other words, for this example, the knowledge of the specific interferer's codebook at the decoder is not useful in terms of capacity. In this paper, two variations of this basic scenario are presented in which treating interference as unstructured is instead generally suboptimal. In the first case, a second encoder of the source message is present in the system that is not aware of the interferer's sequence, and source and interference messages are uncorrelated; In the second case, the sources encoded by the informed transmitter and interferer are correlated (and an uninformed encoder may or may not be present). Results are given in terms of conditions for achievability for both discrete and Gaussian models of the scenarios discussed above, and corroborated by numerical results. Optimal strategies are also identified in special cases. The conclusions herein point to the importance of exploiting the interfererence structure in multiterminal and source-channel coding scenarios.