Channel Modeling Approach Based on the Concept of Degradation Level Discrete-Time Markov Chain: UWB System Case Study

In this work an approach to obtain an accurate high level channel model based on Discrete-Time Markov Chain, useful in some simulation context, is provided. In particular, this model is based on the concept of error trace analysis and on the degradation level of given observation windows: an observation window is fixed and the degradation level of the link, the Packet Error Rate (PER) relative to the specific window, is evaluated. This approach is useful for any wireless transmission scheme, but in our work, we apply it to the Ultra Wideband (UWB) system. Many researchers have already treated UWB channel modeling. However, to the best of our knowledge, all the proposed channel models work at the physical level investigating only some aspects of channel interaction. It has been shown through a comparative analysis, based on the occurrence of correctly and wrongly received packets, that the degradation level approach is more accurate than the classic Gilbert-Elliot model, the 3rd order Markov model and the Markov-based Trace Analysis (MTA) model.

I. Introduction

The classic channel modeling approach models the phenomena of wireless channel through an impulse response, so it can work only at the physical level and is, therefore, not suitable to work at the packet level. This is not a trivial problem, especially if one also wants to investigate the higher levels of ISO/OSI architecture: in fact, in this case, a model describing the trend of wrong packets in time and the signal corruption at the physical layer is not needed. For this purpose, in this work an approach based on Discrete-Time Markov Chain (DTMC) [1], [2], [3] is proposed in order to model the wireless channel. We call this new approach Degradation Level - DTMC (DL-DTMC). In accordance with [4], it can be observed that channel characterization can be captured by a packet error trace, but in contrast to [4] in this analysis the concept of degradation level [5] is introduced: the single packet is not analyzed, but a time window is fixed and the degradation level of the link which is the Packet Error Rate (PER) computed relative to the specific time window, is evaluated. This approach increases the number of states with respect to the simple Gilbert-Elliott (G-E) model [2], but here it is shown that it improves the accuracy of the model: in particular it will be shown that it is convenient to add new states (also increasing the time window duration) to the DTMC until the utility of the last added state is null. Furthermore, a procedure, to obtain a specific model for a given wireless system, data rate, scenario (that is Line of Sight, LOS, or No-Line of Sight, NLOS) and average noise power level starting from data collected by simulation is described. In this work, we apply our approach to Ultra Wideband (UWB) systems [6]. General approaches for the channel modeling of UWB networks, taking into account multipath fading, shadowing and path loss are considered in [7], [8] and in many other works, but all these models work at the bit level. In [9] an UWB packet level channel modeling was proposed, but, in this work, the authors modeled the PER variation due to people shadowing as a Finite-State Markov Chain (FSMC), so, respect to our work, other channel aspects were treated. Instead, our goal is to obtain, through degradation level analysis, a packet level model for the UWB channel capturing the multipath fading effects. In the following related work is described in Section II. Then, in Section III, some notions about DTMC and trace analysis will be given and our model will be described in detail; the UWB system case study with some examples will be described in Section IV; finally, in Section V a performance evaluation will be made, comparing our model with the G-E, 3rd order Markov and Markov-based Trace Analysis (MTA) models and in the last Section the conclusions will be summarized.