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 linearcomplexity 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.