1. doc.: IEEE 802.15-<doc# >
<month year>
doc.: IEEE <doc# >
Sept 2009
Project: IEEE P Working Group for Wireless Personal Area Networks (WPANs)
Submission Title: Path Selection Diversity for SUN networks
Date Submitted: Sept 17, 2009
Source: Steve Shearer, Independent
Address: Pleasanton, CA, USA
Voice: (408) , FAX: [], Shearer_inc @ yahoo.com
Re: [ g] TG4g Call for Proposals
Abstract: This presentation analyses the potential EbN0 gains that a Mesh network may offer because of the fact that it is able to communicate on the “best-of –N” paths to its neighbors
Purpose: Technical Proposal to be discussed by IEEE TG4g
Notice: This document has been prepared to assist the IEEE P It is offered as a basis for discussion and is not binding on the contributing individual(s) or organization(s). The material in this document is subject to change in form and content after further study. The contributor(s) reserve(s) the right to add, amend or withdraw material contained herein.
Release: The contributor acknowledges and accepts that this contribution becomes the property of IEEE and may be made publicly available by P
Steve Shearer (Independent)
<author>, <company>

2. doc.: IEEE 802.15-<doc# > Steve Shearer Sept 2009
<month year>
doc.: IEEE <doc# >
Sept 2009
Path Selection Diversity An aspect of Mesh networks that may explain increased performance
Steve Shearer
Sept 2009
Steve Shearer (Independent)
<author>, <company>

3. Sept 2009
Introduction
Meshed networks appear to work quite well in a SUN application
Intuitive logic indicates that the ability to choose “good” channels should result in better performance
This presentation is an attempt validate this observed effect with some theory
Mesh networks are very complex analytically
we believe this analysis provides some theoretical insight to one aspect that may account for the increased performance that is often reported
Steve Shearer (Independent)

4. Criteria for Successful Message Delivery
Sept 2009
Traditionally the criteria for successful message delivery is “successful message delivery between node A and node B”
In a Mesh network the criteria for successful message delivery is “successful message delivery from node A to any one of its neighbors, node B, or node C, or node……”
The latter is clearly a less stringent requirement than the former, so one might expect that it is easier to be successful
Steve Shearer (Independent)

5. Sept 2009
Some assumptions
A number of meshed nodes are in reasonable proximity with one another
Distances between nodes are relatively similar so there is no appreciable difference in propagation attenuation between links
Natural RF scattering causes spatial nulls, but no appreciable ISI
Channel conditions are stationary
Link quality is Rayleigh distributed in a geographical sense
Assume that the communicating node has some way to determine which of the N links has the best quality1
(1) There are potentially several ways to do this reasonably effectively including, using prior history, “sounding bursts” and/or combinations of other methods
Steve Shearer (Independent)

6. Calculation of Effective EbN0
Sept 2009
Calculation of Effective EbN0
Let us assume that the instantaneous bit energy to noise ratio for the link is
We know that is a Rayleigh distributed variable, in the Geographical sense, so the the pdf of is
Consider the probability , that falls below some threshold which would correspond to a communication outage, then
Steve Shearer (Independent)

7. Calculation of Effective EbN0
Sept 2009
Calculation of Effective EbN0
We can find the Probability Density Function defined by the derivative
And then it is easy to calculate the “Effective Energy to Noise Ratio when N neighbors are available” , by integrating …
Conveniently, it can be shown that the above expression reduces to the simple sum
Effective Energy to Noise Ratio when N = neighbors are available
Steve Shearer (Independent)

8. Illustration of Effective EbN0 improvement
Sept 2009
A simulation was set up to present N channel qualities to the communicating node, and allowing it to choose the best
Best of [RV1] – equivalent to single path Psuedo Static simulation
Best of [RV1, RV2] – two available neighbors
etc…
Best of [RV1, RV2, ….RVN] – N neighbors
This was repeated many times and the effective channel quality was computed for each value of N
The graph compares the simulated results with the theory
And shows that significant improvement in effective EbN0 is achieved as the number of neighbors increases
Steve Shearer (Independent)

9. Changing PDF of Channel Quality
Sept 2009
Changing PDF of Channel Quality
Examination of the PDF’s for each value of N is interesting
N=1 is the standard Rayleigh distribution
For N=3 it can be seen that the region of outage is significantly diminished
As N increases, the PDF significantly changes its shape and rapidly moves away from the origin
For N=5, there is essentially zero probability that the channel quality is 0
These effects will have a huge impact on BER to be seen later
Steve Shearer (Independent)

10. Sept 2009
Examination of BER
Knowing the expression for probability of bit error for a particular demodulator , in AWGN would enable us to calculate the probability of bit error Pe in the newly defined diversity scheme as follows
But the math is quite tedious 
So a standard MSK simulation was used to obtain some results for illustrative purposes using :-
a non-coherent demodulator
A Psuedo Static channel, modified to provide the “best-of” approach described earlier
Characteristics of the demodulator
New PDF of the selection diversity scheme
Steve Shearer (Independent)

11. Sept 2009
Simulation results
Note the familiar Pseudo Static result N=1 for a point-to-point link
Gradient is 10e-1 per 10 dB indicating diversity order 1
For a mesh network, where there is a choice of neighbors, the gradient of the BER curve steadily increases
For N=2, the gradient doubles indicating diversity order 2
Etc…
And there are significant EbN0 gains
In the case where 5 neighbors are available the graph shows an improvement of nearly 18dB in overall system performance
(at a BER of 10e-3)
Steve Shearer (Independent)

12. Sept 2009
Conclusion
This note illustrates some of the performance gains that are inherent in Mesh networks
The basic concept is applicable to all modulation types, OFDM, FSK and DSSS
It strongly suggests that Mesh networks may not always be strictly noise limited
And it may explain why uncoded systems appear to work so well in some cases
Steve Shearer (Independent)

13. Sept 2009
Thank You
Questions
Steve Shearer (Independent)