Linear-Complexity Models for Wireless MAC-to-MAC Channels

Wireless local area networks suffer from frequent bit-errors that result in Medium Access Control (MAC) layer packet drops. Bandwidth and media quality constraints of real-time applications necessitate analysis and modeling at the "MAC-to-MAC wireless channel." In this paper, we propose and evaluate stochastic models for the 802.11b MAC-to-MAC bit-error process. We propose an Entropy Normalized Kullback-Leibler (ENK) measure to accurately evaluate the performance of the models. We employ this measure to demonstrate that the traditional full-state Markov chains of order-10 and order-9 are required for accurate representation of the channel at 2 and 5.5 Mbps, respectively. However, the complexity of this modeling paradigm increases exponentially with respect to the order. For many real-time and non-real-time applications, which require (or could benefit significantly from) accurate modeling, the high complexity of full-state high-order Markov models makes them impractical or virtually ineffective. Thus, we propose two new linear-complexity models, which we refer to as the short-term energy model (SEM) and the zero-crossing model (ZCM). These models, which constitute the most important contribution of this paper, constrain the complexity to increase linearly with the model order. We illustrate that the linear-complexity models, while yielding orders of magnitude reduction in complexity, provide a performance comparable to that of the exponential complexity full-state models. Within the linear-complexity context, we illustrate that the zero-crossing model perform better than its short-term energy counterpart. Finally, for varying window sizes and due to its low complexity, we show that the zero-crossing model can be adapted in real-time. Such an adaptive model provides accurate channel modeling and characterization for rate adaptive applications. [PUBLICATION ABSTRACT]