SE24 meeting
M61_18R0_SE24
OFCOM, Biel, 5-6 September 2011
Date issued:
02 09 2011
Source:
Silver Spring Networks
Status:
For consideration
Subject:
Clarification of access mechanism mathematics
Password protected:
yes
no
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Summary
This contribution examines the mathematics developed in the draft report and questions the
completeness of certain aspects. It further examines the commentary associated with different
access mechanisms and suggests that there are also omissions here which would offer a more
balanced presentation.
Proposal: For consideration
Background
The draft ECC report on, Improving Spectrum Efficiency in the SRD band, whilst using
experience from principally the 863 to 870 MHz,, will set the direction for years to come in the
use of different access mechanisms in all SRD bands. Given this, SSN believes that the scope
should reflect all nuances of the potential access mechanisms which might be used.
Simon Dunkley
2/9/11
Clarification of access mechanism mathematics
Introduction
Work within WI23 of SE24 is examining mechanisms for maximising the efficiency with which SRD
bands should be used. The draft report from the group emphasises the efficacy of the Listen Before
Talk (LBT) mechanism, but appears to underplay the downsides of the technique as well as
appearing to be based on flawed analysis.
This contribution examines the mathematical basis for the different access mechanisms considered,
highlights the known problems associated with implementing LBT, makes observations of potential
flaws within the draft report and concludes with recommendations for the drafting group.
Mathematics of access mechanisms
The theoretical throughput of various multiple-access mechanisms for packet radio systems was set
out in a seminal paper by Kleinbrook and Tobagi1. This derived the performance of the various
mechanisms from first principles, assuming the channel to be wideband and accessed by pairs of
transmitter/receivers. Various mechanisms were considered, including Pure Aloha, slotted Aloha, 1Persistent CSMA (in effect, LBT) through to Perfect Scheduling.
Aloha
In Aloha systems, as shown in the draft report, the probability of any one packet colliding with
repeated packet transmissions from a second radio is shown below:
PCOLLm  Tm  TN Fm
Where, Fm = repetition frequency of second radio, Tm is the packet length of the second radio and Tn
is the packet length of the wanted packet.
1
Packet Switching in Radio Channels: Part 1 – Carrier Sense Multiple-Access Modes and Their ThroughputDelay Characteristics, Kleinrock & Tobagi, IEEE Transactions on Communications, 1975, vol 23, number 5,
p1400-1416
In the general case, where N radios are competing, the probability of any one packet colliding is:
PCOLL  1  1  2TF 
N 1
Where the duration and frequency of each packet is T and F, respectively.
The aggregate throughput of the channel is:
S = G.e-2G
Where S is the offered load and G is the normalized channel capacity.
The maximum throughout before catastrophic congestion in the channel occurs is 18%.
This work is already included in the report, however, the addition of the diagram clarifies the
derivation of the formulae.
Now if we consider the development of the Listen Before Talk section of the report, there appear to
be some anomalies arising.
Listen Before Talk
The probability of collision can be reduced by sensing the channel before transmitting and, if the
channel is not clear, various strategies can be used before attempting to retransmit.
For CSMA probability of any one packet colliding with repeated packet transmissions from a second
radio is:
Pcoll = (Tr + Td) x Fm
Where Tr is the listening time, Td is the turnaround time and Tlbt is the transmit duration.
For two radio systems, the probability of collision is very low due to the effectiveness of the sensing
mechanism.
When N radios attempt to access the same channel, however, a further collision mechanism arises:
packets that are ‘queued’ (sensed a packet transmission and awaiting retransmission) have an
increased probability of collision, depending on the re-try strategy adopted.
The throughput of the simplest strategy, 1-persistent CSMA can be shown2 to be:
Where:
 is the propagation delay and T is the packet transmission time. S the throughput , G the offered
load and  = /T
As the propagation delay is much shorter than the transmission time, α is typically <<1, and so:
Sth = [G(1 + G) e-G]/[G + e-G]
The maximum throughput before catastrophic congestion in the channel occurs is 53%.
Mixed LBT and Aloha
An environment populated by a mix of radios deploying LBT and Aloha is shown below.
The probability of any one LBT packet colliding with repeated packet transmissions from a second
Aloha radio is:
Total Pcoll =[(Tr +Td + Tlbt) x (1+(Tdc-Tr) x Fdc )] x Fdc
Note: The No Conflict/Conflict period reflect times in which the sensing phase of a potential
transmission occurs.
2
Packet Switching in Radio Channels: Part 1 – Carrier Sense Multiple-Access Modes and Their ThroughputDelay Characteristics, Kleinrock & Tobagi, IEEE Transactions on Communications, 1975, vol 23, number 5,
p1400-1416
Extending this single-packet analysis to the general case for N transmitters using calculations
equivalent to those shown for the previous two cases is analytically challenging, but could be tackled
numerically.
Problems with CSMA/LBT
Hidden Terminals and Exposed Nodes
Kleinbrook and Tobagi3 noted how ‘Hidden Terminals …badly degrade’ the theoretical performance
of CSMA systems, and proposed the use of a ‘Busy Tone Channel’ for a ‘single station environment’ –
essentially a handshaking , channel reservation protocol. This protocol has been developed and
included in standards such as IEEE802.11 in the form of RTS/CTS (Request to Send/Clear to Send).
Problems still exist, however, with collisions between RTS/CTS messages.
Furthermore, a population of independent devices, such as SRDs, does not have a central node
capable of coordinating the handshaking mechanism.
Finally, dependent on the activity threshold chosen, ‘Exposed Nodes’ can be needlessly prevented
from transmitting by on-going exchanges. This can be explained by considering a victim transmitreceiver pair and an exposed node which is closer to the victim transmitter. The exposed node is
sufficiently far from the victim receiver, but prevented from transmitting by the nearer victim
transmitter.
Adaptive Frequency Agility (AFA) will suffer similar problems as it relies on detection of distant
transmitters before deciding whether to move to another channel.
Activity threshold
In a noisy, ISM band, determining whether a channel is in use by another user or suffering
interference from an industrial system is difficult. Furthermore, setting of the threshold will affect
the proportion of devices that suffer by becoming ‘Hidden Terminals’ (threshold ‘too’ low) or
‘Exposed Nodes’ (threshold ‘too’ high).
In bands such as the 2.4GHz ISM band, relatively long-range systems (such as WiFi) can coexist with
short-range systems (such as Bluetooth). The short-range systems happily operate in a locally higher
noise environment without causing disruption to the WiFi system. Imposition of LBT on the short
range device would destroy its operation.
Cost
LBT technology is relatively expensive to deploy, and is inappropriate for transmit-only devices that,
by definition, have no receiver.
Observations of draft report
Incomplete mathematical treatment
3
Packet Switching in Radio Channels: Part 2 – The hidden terminal problem in carrier sense multiple-access
and the busy tone solution, Kleinrock & Tobagi, IEEE Transactions on Communications, 1975, vol 23, number 5,
p1400-1416
The theoretical treatment of Aloha systems is complete, concluding with maximum theoretical
throughput of the channel.
The LBT treatment appears to be incomplete. The analysis ends at the consideration of two
competing systems, only. The resultant formula, therefore, neglects the probability of ‘queued’
packets colliding when they attempt to re-transmit.
The LDC vs LBT appears to make the same omission. The performance and behaviour of a mixed
LDC/LBT system is difficult to predict and does not appear to be tractable using traditional
techniques.
Spread sheet documentation and assumptions
The spread sheet that accompanies the report does not appear to be well documented, making
interpretation of the results difficult. It appears, however, to utilise – for the LBT case – the
probability of two systems only colliding, thereby ignoring collisions of re-tries and inflating the
apparent effectiveness of the technique. It is also not clear what channel loading is used.
Efficacy of LBT
The diagram below4 shows a comparison of the throughput achieved for various techniques. The
maximum throughput of Aloha is 18% compared to a theoretical maximum of 53% for 1-persistent
CSMA. However, considering the discussion above which examines the limitations of LBT, it is
unlikely that the theoretical maximum for 1-persistent CSMA would be achieved. Thus it is
questionable whether LBT offers enhanced performance.
Frequency Hopping
Section 3.2.5 of the draft report states that, ‘For two FHSS systems sharing the same band (or for one
FHSS and one fixed frequency) the collision probabilities are exactly as derived in section 3.1.1’. This
understates significantly the power of frequency hopping and the possibilities for equitable sharing
and spectrum efficiency.
4
Packet Switching in Radio Channels: Part 1 – Carrier Sense Multiple-Access Modes and Their ThroughputDelay Characteristics, Kleinrock & Tobagi, IEEE Transactions on Communications, 1975, vol 23, number 5,
p1400-1416
Silver Spring Networks in its radio systems operating around the world is able to support high
densities of devices in urban areas, typically 5000 end nodes to one WAN Access Point, within the
busy 902-928MHz band using frequency hopping. Individual data link rates of 100kbits/s are
achieved in a band that is used for both long- and short-range communications.
No form of active channel sensing is used, with transmitters moving to the next pseudo-random
channel after transmitting each packet. The traffic experienced by an Access Point typically causes
an occupation within the band of less than 0.1% for a typical payload of 200 octets when the traffic
is spread evenly across the 83 channels.
Conclusions
Work in the draft report to date appears to contain significant omissions within the mathematics
that cast doubt over the results of the calculations to determine the effectiveness of the LBT
mechanism.
Work within the WI23 drafting group should acknowledge the short comings of using LBT in SRD
bands.
Maximising the spectral efficiency of the band is but one factor in the choice of technologies that
might be deployed. Other factors include: effectiveness of any access mechanism; cost of devices
and their deployment; future flexibility for innovation around any existing scheme.
Frequency Hopping is a good mechanism for an efficiently and effectively sharing of the spectrum
and the report should reflect this.