Average Link Rate Analysis over Finite Time Horizon in a Wireless Network
Bodepudi, Sai Nisanth
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Instantaneous and ergodic rates are two of the most commonly used metrics to characterize throughput of wireless networks. Roughly speaking, the former characterizes the rate achievable in a given time slot, whereas the latter is useful in characterizing average rate achievable over a long time period. Clearly, the reality often lies somewhere in between these two extremes. Consequently, in this work, we define and characterize a more realistic N-slot average rate (achievable rate averaged over N time slots). This N-slot average rate metric refines the popular notion of ergodic rate, which is defined under the assumption that a user experiences a complete ensemble of channel and interference conditions in the current session (not always realistic, especially for short-lived sessions). The proposed metric is used to study the performance of typical nodes in both ad hoc and downlink cellular networks. The ad hoc network is modeled as a Poisson bipolar network with a fixed distance between each transmitter and its intended receiver. The cellular network is also modeled as a homogeneous Poisson point process. For both these setups, we use tools from stochastic geometry to derive the distribution of N-slot average rate in the following three cases: (i) rate across N time slots is completely correlated, (ii) rate across N time slots is independent and identically distributed, and (iii) rate across N time slots is partially correlated. While the reality is close to third case, the exact characterization of the first two extreme cases exposes certain important design insights.
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