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Multihop Channel Modeling


Multi-hop networks, such as ad-hoc, sensor, and mesh networks, suffer from inaccurate physical layer models. In this project, we address the model for shadowing. We propose to jointly model shadowing between link pairs of a multihop ad-hoc network as correlated random variables. The improved multihop channel model allows more realistic analysis and simulation of ad-hoc networks.


Traditionally, channel models assume that shadowing on different links are independent. For example, the path-loss exponent model says that path loss on link (i,j), L_{i,j} , is given by

L_{i,j} = L_0 + 10 n_p \log_{10} \frac{\| z_i - z_j\|}{\Delta_0} + Z_{i,j}

where L_0 is the path loss at a reference distance \Delta_0, z_i and z_j are the positions of nodes i and j, n_p is the path loss exponent (it would be 2 in free space), and Z_{i,j} is the fading loss.

The independence assumption is that \{Z_{i,j}\} for all link pairs (i,j) are independent. This is a strong simplifying assumption, because radio links that are geographically proximate will pass through similar environments and thus will experience correlation. Two such proximate links are shown in Fig. (1). The presence of the environment effects both links a and b similarly. Consequently, the shadow fading experienced by the links will be correlated.

Fig. 1 Motivation for link correlation

Related Research

Multi-hop routing is used as a form of diversity -- if one link fails, another link or set of links is chosen to complete the path from source to destination. In this sense, multi-hop routing is similar to other diversity schemes used in wireless communications. All diversity schemes are limited by correlation in channels. In fact, Molisch [2002] showed that limitation in capacity of the MIMO system when considering correlated shadowing. Further, correlation in shadowing was identified as the key feature that influence the system performance in indoor WLAN [Butterworth, 2002].


Early shadow fading correlation in multihop ad-hoc network have been reported [Patwari, 2002]. The main challenge in that study was the limited measurement set. Essentially, statistical characterization of sensor network measurements would require a large number of networks of the identical geometry, but measured in the same environment, but in different places. For example, identical networks in multiple different office environments. In reality, it is difficult to get access to so many different places, and to deploy networks of the identical geometry. Also, each network deployment of 16 sensors would require 16x15=240 measurements, and an office environment may not be static by the time these 240 measurements are complete for a network, if measurements are done serially.


Instead, we conduct large number of measurements in parallel using a specially-developed sensor network. Further, rather than switch places, we randomly change the environment. We conduct a large number of tests, deploying mica2 sensors in a 4x4 square grid. Each sensor node is 4 feet (1.2m) apart. The nodes are programed with a specific NesC/TinyOS code. The mica2 sensor motes have the capability to measure the RSS of the received signal which is a measurement of both shadowing and other types of fading. We use 10 cardboard boxes covered with aluminum foil to make them effective radio wave reflectors. The boxes are placed randomly in the grid, (but not on top of sensors).

Fig. 2 Showing one of the measurement setup with boxes covered with aluminum foil and placed randomly in the grid

NesC/TinyOS module

The application requires to make a large number of pairwise measurements. The MAC of each sensor node is implemented as a TDMA. Each sensor node listen to transmitting sensor node when it is not transmitting and records RSS values with the transmitting sensor node. Each sensor node is given a separate node ID and its time slot is determined by its ID. Each sensor node also transmits the RSS values it has measured. Apart from the deployed sensor nodes, there is a receiver base connected to a laptop for recording the data. The receiver base is similar to the deployed sensor node with the difference that it does not transmit.

In order to reduce the effects of small scale or multipath fading, we divide the frequency band of mica2 into 16 slots separated by 2 MHz, more than coherence bandwidth. Sensor nodes hop over these frequency bands and RSS values are collected at each center frequency.

After a complete cycle, the laptop has stored all pair-wise frequency-averaged RSS values measured in the sensor network. This NesC/TinyOS code is available upon request.

Current Status

Currently, measurements collected over different measurement setup are being analyzed for shadowing correlation. Various different types of correlation functions are being considered. Future development will be posted here shortly.

Nesh Model Implementations

The Matlab code for calculating shadowing correlation is available online. Please visit NeSh model for instructions and download.


  • Piyush Agrawal
  • Neal Patwari
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Page last modified on April 07, 2008, at 01:34 PM MST