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The effect of fading, channel inversion, and threshold scheduling on ad hoc networks (0707.3584v1)

Published 24 Jul 2007 in cs.IT and math.IT

Abstract: This paper addresses three issues in the field of ad hoc network capacity: the impact of i)channel fading, ii) channel inversion power control, and iii) threshold-based scheduling on capacity. Channel inversion and threshold scheduling may be viewed as simple ways to exploit channel state information (CSI) without requiring cooperation across transmitters. We use the transmission capacity (TC) as our metric, defined as the maximum spatial intensity of successful simultaneous transmissions subject to a constraint on the outage probability (OP). By assuming the nodes are located on the infinite plane according to a Poisson process, we are able to employ tools from stochastic geometry to obtain asymptotically tight bounds on the distribution of the signal-to-interference (SIR) level, yielding in turn tight bounds on the OP (relative to a given SIR threshold) and the TC. We demonstrate that in the absence of CSI, fading can significantly reduce the TC and somewhat surprisingly, channel inversion only makes matters worse. We develop a threshold-based transmission rule where transmitters are active only if the channel to their receiver is acceptably strong, obtain expressions for the optimal threshold, and show that this simple, fully distributed scheme can significantly reduce the effect of fading.

Citations (325)

Summary

  • The paper demonstrates that threshold-based scheduling significantly increases ad hoc network capacity by leveraging multi-user diversity and maintaining acceptable outage probabilities.
  • The paper employs stochastic geometry to derive tight bounds on outage probability and transmission capacity under varying network conditions.
  • The paper finds that while channel inversion improves link fairness, it reduces overall network capacity by increasing interference across the network.

Evaluating the Impact of Channel Fading, Channel Inversion, and Threshold Scheduling on Ad Hoc Networks

The paper in focus offers a meticulous examination of ad hoc network capacity in relation to three pivotal phenomena: channel fading, channel inversion power control, and threshold-based scheduling. It endeavors to delineate how these elements, independently and collectively, modulate the potential maximum number of concurrent successful transmissions, the so-called transmission capacity (TC), while maintaining acceptable outage probability levels.

Analytical Approach

The methodology capitalizes on tools from stochastic geometry to derive asymptotically tight bounds on outage probability (OP) and transmission capacity. Stochastic geometry allows a fundamental understanding of the impact of random network parameters such as node distance and channel gain, providing a framework that can be applied over large-scale networks characterized by homogeneous Poisson point processes.

Channel Fading and Scheduling Mechanisms: Traditional fading degrades network capacity without any channel state information (CSI). This degradation emanates from signal variations due to multipath and shadowing effects. Two strategies are posed for their amelioration: channel inversion and threshold-based scheduling, which solely necessitate pairing coordination without external node communication. Threshold scheduling activates transmission only if the channel to the receiver surpasses a certain threshold, which introduces multi-user diversity, proving to significantly increase the network's throughput.

Channel Inversion and Its Detriments: An interesting insight presented is that channel inversion, while beneficial for individual link reliability and fairness by offering uniform signal reception across different channel conditions, results in reduced total network capacity. This reduction arises from increased interference levels, as all transmitters attempt to normalize their received power, thus inadvertently increasing interference across weaker links.

Key Findings and Conclusions

The research finds threshold-based scheduling provides substantial increases in capacity, reaching levels akin to networks only susceptible to path-loss but not fading. This fully distributed mechanism straightforwardly exploits multi-user diversity without requiring high computational loads or extensive coordination.

The paper's results are robust, substantiated by deriving bounds on the distribution of interference, SINR levels, and fundamentally, the expressions of transmission capacity under different network configurations and channel conditions. Importantly, by contrasting scenarios with and without channel inversion, the findings stress that, surprisingly, channel inversion should be deployed judiciously as its fairness benefits do not offset its adverse impact on overall network capacity.

Practical and Theoretical Implications

From a practical standpoint, this evidence suggests that for ad hoc networks, employing threshold-based scheduling is advantageous over simply attempting to normalize channel conditions through inversion power control. This aligns with the desire for efficient, scalable network operations, especially in scenarios where infrastructure support is minimal or absent, as in mobile ad hoc networks (MANETs).

Theoretically, the paper offers a clear articulation of how changes in fading and shadowing characteristics due to environmental conditions can be methodically addressed to maintain optimal performance. The demonstrated tightness of bounds provides a reliable basis for future enhancements and evalutation of similar mechanisms in varying deployments, including cognitive radio and opportunistic spectrum usage scenarios.

Future Directions

Future research spurred by these insights may delve into dynamic and adaptive threshold scheduling, possibly driven by real-time network analytics. Another promising direction is examining the synergy between scheduling approaches considered and emerging interference management techniques like interference alignment or advanced signal processing.

Ultimately, this paper underscores a nuanced landscape where simplistic power control measures must be re-evaluated in favor of more strategic scheduling and network management techniques that capitalize on inherent channel variabilities to maximize network throughput and efficiency. It leaves potential for extending the stochastic geometric approach to encompass more complex, heterogeneous network topologies and richer channel models.