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Proceedings ArticleDOI

Predictable 802.11 packet delivery from wireless channel measurements

30 Aug 2010-Vol. 40, Iss: 4, pp 159-170
TL;DR: It is shown that, for the first time, wireless packet delivery can be accurately predicted for commodity 802.11 NICs from only the channel measurements that they provide, and the rate prediction is as good as the best rate adaptation algorithms for 802.
Abstract: RSSI is known to be a fickle indicator of whether a wireless link will work, for many reasons. This greatly complicates operation because it requires testing and adaptation to find the best rate, transmit power or other parameter that is tuned to boost performance. We show that, for the first time, wireless packet delivery can be accurately predicted for commodity 802.11 NICs from only the channel measurements that they provide. Our model uses 802.11n Channel State Information measurements as input to an OFDM receiver model we develop by using the concept of effective SNR. It is simple, easy to deploy, broadly useful, and accurate. It makes packet delivery predictions for 802.11a/g SISO rates and 802.11n MIMO rates, plus choices of transmit power and antennas. We report testbed experiments that show narrow transition regions (

Summary (4 min read)

1. INTRODUCTION

  • Wireless LANs based on 802.11 are used almost everywhere, from airports to zoos and in urban, suburban and rural areas.
  • For good performance, reliability and coverage, the physical layer settings should match the RF channel over which the wireless signals are sent.
  • Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page.
  • In practice, 802.11 LANs have never used channel measurements as more than a coarse indicator of expected performance.
  • This approach is very effective for slowly varying channels and simple configurations (e.g., a few rates with fixed transmit power and channel) since the best setting will soon be found.

2. MOTIVATION

  • Existing predictions of packet delivery for a given link are based on its Received Signal Strength Indication (RSSI) value.
  • Convolutional coding is applied across the bits for error correction and bits are interleaved to spread them in frequency.
  • Note that the details of single-stream 802.11n differ slightly from 802.11a/g (optimized coding rates and more data subcarriers), but in ways that are not material for their work so that the authors can treat 802.11n as a superset of 802.11a/g. Packet Delivery versus RSSI/SNR.
  • This is consistent with other reported 1We refer to the metric computed from RSSI and noise measurements as the packet SNR, RSSI-based SNR, or simply RSSI.the authors.
  • Many possible factors cause the observed variability for real channels, including NIC calibration, interference, sampling, and multipath.

3. PACKET DELIVERY MODEL

  • The authors goal is to develop a model that can accurately predict the packet delivery probability of commodity 802.11 NICs for a given physical layer configuration operating over a given channel.
  • In practice, the interesting regions for the four effective SNRs do not overlap because at a particular effective SNR value only one modulation will be near the transition from useless (BER ≈0.5) to lossless (BER ≈0).
  • When graphs in this paper are presented with an effective SNR axis, the authors use all four values, each in the appropriate SNR range.
  • Different devices may have different noise figures, a measure of how much signal strength is lost in the internal RF circuitry of the NIC.
  • The transmitter also needs up-to-date CSI: either from feedback or estimated from the reverse path.

4. TESTBEDS

  • The authors conduct experiments using two stationary wireless testbeds deployed in indoor office environments, T1 and T2 (Figure 4).
  • Each testbed covers a single floor of a multi-story building and has a variety of links in terms of maximum supported rate and line-of-sight versus multi-path fading.
  • The authors conduct mobile experiments using laptops that interact with testbed nodes and are configured in the same way.

4.1 Node Configuration

  • Each node is a stationary desktop or portable laptop equipped with an Intel Wi-Fi Link 5300 (iwl5300) a/b/g/n wireless network adapter.
  • They run the Linux 2.6.34 kernel with a modified version of the iwlagn driver [2].
  • The authors use up to three transmit and receive antennas, supporting up to three MIMO streams, and the rates in Table 1 per stream.
  • Each testbed operates on a 5 GHz channel unoccupied in its environment; there was no noticeable interference.

4.2 Measurement Tools

  • The authors hardware enables us to vary the transmit power level from −10 dBm to 16 dBm in steps of 0.5 dB, and divides power equally across streams.
  • These combine to define the per-receive-chain packet SNR : = RSSI (dBm)− Noise (dBm)− AGC (dB) (3) The iwl5300 calculates the quantities RSSI and Noise as the respective sums of average signal strength and average error vector magnitude in each OFDM subcarrier [2].
  • This is exactly the traditional definition of SNR applied to OFDM.
  • The authors configure the NIC to compute this feedback packet for every received frame, rather than just during sounding, and send it up to the driver instead of back to the transmitter.
  • Each channel matrix entry is a complex number, with signed 8-bit resolution each for the real and imaginary parts.

5. PACKET DELIVERY EVALUATION

  • The authors use their testbeds to experimentally evaluate how well their model of §3 predicts packet delivery.
  • This is the fundamental measure of whether the model is useful; good predictions enable applications such as rate adaptation, transmit power control, antenna selection, and channel selection.

5.1 Measurement setup

  • The authors first measure packet delivery for different antenna configurations over a 20 MHz channel on their testbeds.
  • In each test, the authors send 1500 byte packets as constant bit-rate UDP traffic generated by iperf at 2 Mbps for 5 seconds.
  • Note that CSI is measured during the preamble, so it does not depend on the transmit rate.
  • Similarly, 3x3 CSI gives us the channel between each pair of transmit and receive antennas, so it also implicitly contains 1x1 CSI.
  • The above testing gives us ground truth data to probe variation across 200 links, 26 dB of transmit power, four antenna configurations ranging from 1x1 to 3x3, and 8 per stream rates (for 24 rates with up to three streams).

5.2 RSSIs and Multiple Antennas

  • The authors model predicts packet delivery in terms of effective SNR as described in §3.
  • This is simple enough for the 1x1 case of a single transmit and receive antenna: the authors convert the single RSSI value to a packet SNR using Eq. (3), which is then mapped to packet delivery for the transmit rate that is used.
  • The authors first convert the per-antenna RSSIs to SNRs and then sum the SNRs.
  • This is a straightforward choice for a single spatial stream as it corresponds to receiver processing using MRC [8].

5.3 Results

  • To compare their model with RSSI, the authors first analyze their 1x1 measurements to find the transition windows for all of the links in testbed T1.
  • The authors define this to be the effective SNR or packet SNR values over which packet delivery rises from 10% to 90% for any link.
  • While the transitions for the last four rates are inflated with RSSI, they remain tight with effective SNR.
  • The larger significance of narrow transition windows is that, by reducing them enough that they do not overlap, the authors are able to unambiguously predict the highest rate that will work for all links nearly all of the time.
  • They agree with the measured SNRs on a wired link (Figure 1(a)), which strongly suggests that the effective SNR captures the fundamental error characteristics of the link.

6. APPLICATION TO RATE SELECTION

  • The most direct uses of packet delivery predictions are rate adaption, transmit power control, and channel selection.
  • They provide a well-established baseline against which the authors can gauge their performance.
  • The authors goal is to perform as well as the best, already nearoptimal 802.11a/g schemes on their home ground, with a method that has the advantages of simplicity, deployability, and generality.
  • Rate adaptation is an open problem for 802.11n.
  • Most schemes in the literature were not designed for MIMO systems, and none of the ones that were have been tested on real 802.11 channels.

6.1 Rate Selection Algorithms

  • The authors experiment with ESNR, an algorithm based on their model, plus SampleRate [5], the de facto rate selection algorithm in use today, and SoftRate [28], a research algorithm with the best published results.
  • It maintains delivery statistics for different rates to compute the expected airtime to send a packet, including retries.
  • The input to these predictions is the bit error rate (BER) as estimated from side-information provided by the convolutional decoder.
  • ESNR uses their model in a very simple way: given recent channel state information, compute the highest rate configuration that is predicted to successfully deliver packets (PRR > 90%).

6.2 Trace-driven Simulator

  • 7 the authors turn to simulations to compare these algorithms.
  • No algorithm will beat SampleRate by a significant margin on static channels, because it will quickly adapt to the channel.
  • The CSI reflects frequency-selective fading over real, varying 20 MHz MIMO channels that is typically not observed with more narrowband experimentation, e.g., on the USRP.
  • To ensure that ESNR is not given the unrealistic advantage of ground truth CSI, the authors corrupt the CSI at the level of ADC quantization, which typically induces an error of ±1.5 dB in the output effective SNRs.
  • SoftRate estimates the BER directly during decoding.

6.3 Rate Adaptation Results

  • The authors first examine the performance of ESNR for SISO rates.
  • Even in these mobile channels, ESNR holds up very well and tracks Previous-OPT within 10%.
  • Note that packet SNR was observed to fare quite poorly [28] in mobile channels, but since effective SNR reflects actual link quality its estimates are more accurate (§5) and stable (2–3× less variance).
  • Next, the authors compare ESNR with SampleRate and SoftRate in Figure 11 and Figure 12.

8. CONCLUSION

  • Wireless links are easy to understand in theory, but difficult to operate in practice, thus search is used to find the best rates, power levels, or other parameter of interest.
  • The authors model takes as input the RF channel (measured as 802.11 Channel State Information) and predicts whether the link will deliver packets for a wide range of NIC configurations.
  • It uses the notion of effective SNR to handle OFDM over faded links, works for MIMO configurations, and needs no calibration of target links.
  • The authors show that, for the first time, measurements taken by commodity NICs can accurately predict whether links will work over a wide range of rates, transmit power, spatial streams, and antennas settings that have not previously been tested.
  • In contrast, predictions based on RSSI often confuse from two to five rates as the potential best rate to use.

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Predictable 802.11 Packet Delivery from
Wireless Channel Measurements
Daniel Halperin
, Wenjun Hu
, Anmol Sheth
, and David Wetherall
University of Washington
and Intel Labs Seattle
ABSTRACT
RSSI is known to be a fickle indicator of whether a wireless link
will work, for many reasons. This greatly complicates operation
because it requires testing and adaptation to find the best rate, trans-
mit power or other parameter that is tuned to boost performance.
We show that, for the first time, wireless packet delivery can be
accurately predicted for commodity 802.11 NICs from only the
channel measurements that they provide. Our model uses 802.11n
Channel State Information measurements as input to an OFDM re-
ceiver model we develop by using the concept of effective SNR. It
is simple, easy to deploy, broadly useful, and accurate. It makes
packet delivery predictions for 802.11a/g SISO rates and 802.11n
MIMO rates, plus choices of transmit power and antennas. We re-
port testbed experiments that show narrow transition regions (<2 dB
for most links) similar to the near-ideal case of narrowband, fre-
quency-flat channels. Unlike RSSI, this lets us predict the highest
rate that will work for a link, trim transmit power, and more. We use
trace-driven simulation to show that our rate prediction is as good
as the best rate adaptation algorithms for 802.11a/g, even over dy-
namic channels, and extends this good performance to 802.11n.
Categories and Subject Descriptors
C.2.1 [Computer-Communication Networks]: Network Archi-
tecture and Design—Wireless Communication
General Terms
Design, Experimentation
1. INTRODUCTION
Wireless LANs based on 802.11 are used almost everywhere,
from airports to zoos and in urban, suburban and rural areas. Mod-
ern wireless NICs provide a large and growing range of physical
layer configurations to obtain good performance across this range
of environments. With 802.11n, the latest version of the standard
that ships on most laptops, combinations of modulation, coding and
spatial streams offer rates from 6 Mbps to 600 Mbps [1]. Other im-
portant choices include transmit power, channel, and antennas.
For good performance, reliability and coverage, the physical layer
settings should match the RF channel over which the wireless sig-
nals are sent. This is evident in rate adaptation schemes [5, 10, 14,
28] that determine the highest rate for transmission, since a good
scheme has a large effect on throughput. Other work adapts trans-
mit power to reduce co-channel interference [17, 21, 25].
Permission to make digital or hard copies of all or part of this work for
personal or classroom use is granted without fee provided that copies are
not made or distributed for profit or commercial advantage and that copies
bear this notice and the full citation on the first page. To copy otherwise, to
republish, to post on servers or to redistribute to lists, requires prior specific
permission and/or a fee.
SIGCOMM’10, August 30–September 3, 2010, New Delhi, India.
Copyright 2010 ACM 978-1-4503-0201-2/10/08 ...$10.00.
In theory, it is simple to select the physical layer configuration
because this is directly determined by the specifics of the RF chan-
nel. The signal-to-noise ratio (SNR) is the gold standard for per-
formance in narrowband channels. Textbook formulas relate the
error rate of different modulations to the SNR [27]. The best rate or
required transmit power is then simple to compute.
In practice, 802.11 LANs have never used channel measurements
as more than a coarse indicator of expected performance. There
have simply been too many ways in which the observed measure-
ments and actual performance fail to match the predictions of the-
ory. For example, the most accessible channel measurement is re-
ceived signal strength indication (RSSI), which serves as a proxy
for the true SNR. RSSI measurements are samples that may vary
over packet reception, be mis-calibrated, or be corrupted by in-
terference, all of which are known to be issues in practice [6, 10,
22]. Even if RSSI were perfect, it does not reflect the frequency-
selective fading of 802.11 channels, which are not close to narrow-
band. Nor does it account for imperfect receivers that may greatly
degrade performance [3, 10]. Due to these factors, the minimum
RSSI at which a rate starts to work varies by more than 10 dB for
real links [22, 30, 31].
To reconcile these viewpoints, a form of guided search is widely
used in practice to select operating points [21, 24, 29]. Packet de-
livery is simply tested for a rate or transmit power to see how well
it works. If the loss rate is too high, a lower rate (or more power) is
used, otherwise a higher rate (or less power) is tested. SampleRate
is a well-known algorithm of this kind for finding transmit rates [5].
This approach is very effective for slowly varying channels and sim-
ple configurations (e.g., a few rates with fixed transmit power and
channel) since the best setting will soon be found.
However, search becomes less effective as channels change more
quickly and the configuration space becomes more complex. Both
of these factors are trends: 802.11 clients are increasingly used
when they are truly mobile, both walking and in vehicles; and NICs
that are now being deployed with 802.11n depend on multiple an-
tennas, which adds another dimension to and increases the size of
the search space. Also, tuning combinations such as rate and power
is much more complex.
For rate selection, recent work has made headway by measur-
ing symbol-level details of packet reception. In particular, SoftRate
uses the output of soft-Viterbi decoding for each symbol to estimate
the bit error rate (BER) [28]. This allows it to predict the effects on
packet delivery of changing the rate. AccuRate uses symbol er-
ror vectors for the same purpose [23]. However, these methods
are not defined for selecting other useful parameters, such as trans-
mit power, and they do not extend from 802.11a/g to 802.11n, e.g.,
when selecting antennas or numbers of spatial streams.
In this work, we return to the basic problem of using theory to
connect the performance of 802.11 NICs on real links to measured
channels in practice. The opportunity to make progress has arisen
for two reasons. First, 802.11n NICs measure the channel at the
OFDM subcarrier level to support MIMO (multiple antenna) op-
eration. They report this information in a standard Channel State
1

Information (CSI) format [1]. This provides a much richer source
of information than RSSI. Note that this CSI naturally applies to
802.11a/g rates because they are a subset of 802.11n rates. Sec-
ond, modern NICs use OFDM, which gives channel estimates that
are less susceptible to interference than spread spectrum (because
of lower correlation), and are calibrated. Both factors lead to more
meaningful measurements than in the past.
We use the CSI as input to a model of receiver processing that we
develop to predict packet delivery. Our model uses the concept of
an effective SNR for a multi-carrier channel [18], such as OFDM,
in which there are different subcarrier SNRs, plus approximations
for coding, interference between MIMO streams, and decoding al-
gorithms. It requires no per-link calibration and predicts delivery
for a wide range of configurations (including rates, transmit power,
antenna selection, and spatial streams) from a single CSI measure-
ment. We also expect it can be extended to new factors such as
beamforming for even wider applicability in the future.
We make two contributions in this paper. Our main contribution
is to show how to accurately predict the performance of commodity
802.11 OFDM NICs over real links using only the channel mea-
surements that the NIC provides. We believe this to be a first. Our
packet delivery model is evaluated with measurements over two sta-
tionary indoor wireless testbeds built from PCs and 3-antenna In-
tel 802.11a/g/n NICs. For a wide range of configurations, we can
predict whether a link will successfully deliver packets (>90%),
outside of a narrow (<2 dB for most links) uncertainty region that
is similar to behavior over the near-ideal channel of nodes con-
nected by a wire. This lets us consistently predict the best rate
to use over a channel, and perform other tasks such as trim ex-
cess transmit power. In contrast, RSSI often fails to reflect perfor-
mance by a wide enough margin that it does not reliably predict
the best rate or power setting, especially for dense modulation and
higher coding rates (transition >7 dB for 10% of the links). A key
factor in this improvement is the use of effective SNR to capture
frequency-selective fading, which is clearly visible in our testbeds.
No published work has explored effective SNR measures in 802.11
beyond simulation, to the best of our knowledge. Note that our ef-
fective SNR model does not predict the performance of links under
interference. However, our measurements show that its estimate
of interference-free link quality is robust to interfering transmis-
sions 5). We also discuss ways to handle persistent interference.
Our method is practical and can be applied to many classic prob-
lems, including rate adaptation, transmit power tuning, and channel
and antenna selection. While we must leave most of this to future
work, we demonstrate how our model can inform rate adaptation.
Our second contribution is a rate selection algorithm that is as good
as the best 802.11a/g rate adaptation algorithms and extends this
excellent performance to 802.11n. Our algorithm simply uses our
model to predict the highest rate for the channel, repeating to track
the channel over time. We use a trace-driven simulation to compare
it with SampleRate, which is widely used in practice, and SoftRate,
which has the best published performance. Our algorithm tracks
the best rate nearly as well as is possible, even for dynamic mobile
channels. It performs very well for MIMO rates, and supports en-
hancements such as transmit power trimming and antenna selection.
As far as we are aware, there is no other reported work on 802.11n
rate adaptation that is evaluated for real, 802.11 channels, and no
other rate adaptation algorithms that support these enhancements.
In the rest of this paper, we first motivate the need for better de-
livery predictions in §2, and then present our model in §3. Our ex-
perimental testbeds are described in §4, and our model is evaluated
in §5. In §6, we use simulation to study rate selection guided by
our model. §7 discusses related work, and §8 concludes the paper.
Modulation Coding Rate Data Rate (Mbps)
BPSK 1/2 6.5
QPSK 1/2 13.0
QPSK 3/4 19.5
QAM-16 1/2 26.0
QAM-16 3/4 39.0
QAM-64 2/3 52.0
QAM-64 3/4 58.5
QAM-64 5/6 65.0
Table 1: 802.11n single-stream rates.
2. MOTIVATION
Existing predictions of packet delivery for a given link are based
on its Received Signal Strength Indication (RSSI) value. This is
widely available as a proxy for the SNR. We characterize this map-
ping to motivate our research.
802.11 Setting. Our work applies to 802.11a/g/n radios that use
coded Orthogonal Frequency Division Multiplexing (OFDM). 20 or
40 MHz channels are divided into 312.5 kHz bands called subcar-
riers, each of which sends independent data simultaneously. Con-
volutional coding is applied across the bits for error correction and
bits are interleaved to spread them in frequency. Each subcarrier
in a packet is modulated equally, using BPSK, QPSK, QAM-16, or
QAM-64, with 1, 2, 4 or 6 bits per symbol, respectively. The data
rates depend on the combination of modulation and coding.
Our experimental platform uses 802.11n radios that operate on
20 MHz channels. The single-stream 802.11n rates are shown in
Table 1. The main innovation in 802.11n is the use of multiple an-
tennas for spatial multiplexing. By using MIMO processing, multi-
ple streams can be sent at the same time, each at the single-stream
rate, for higher overall rates. Note that the details of single-stream
802.11n differ slightly from 802.11a/g (optimized coding rates and
more data subcarriers), but in ways that are not material for our
work so that we can treat 802.11n as a superset of 802.11a/g.
Packet Delivery versus RSSI/SNR. Textbook analyses of modu-
lation schemes give delivery probability for a single signal in terms
of the signal-to-noise (SNR) ratio [8], typically expressed on a log
scale in decibels. This model holds for narrowband channels with
additive white Gaussian noise. It predicts a sharp transition region
of 1–2 dB over which a link changes from extremely lossy to highly
reliable. This makes the SNR a valuable indicator of performance.
RSSI values reported by NICs give an estimate of the total sig-
nal power for each received packet. From RSSI, the packet SNR
can then readily be computed using NIC noise measurements.
1
We
generated performance curves using SNR for a real 802.11n NIC
over a simple wired link with a variable attenuator and for a sin-
gle transmit and receive antenna. The result is shown for all single
antenna 802.11n rates in Figure 1(a). We observe a characteristic
sharp transition region for packet reception rate (PRR) versus SNR.
This is despite the relatively wide 20 MHz channel, 56 OFDM sub-
carriers, coding and other bit-level operations. This is the behavior
we want from a link metric in order to predict packet delivery.
In contrast, packet delivery over real wireless channels does not
exhibit the same picture. Figure 1(b) shows the measured PRR ver-
sus SNR for three sample rates (6.5, 26, and 65 Mbps) over all wire-
less links in our testbeds, using the same 802.11n NICs. The SNR
of the transition regions can exceed 10 dB, so that some links easily
work for a given SNR and others do not. There is no longer clear
separation between rates. This is consistent with other reported
1
We refer to the metric computed from RSSI and noise measure-
ments as the packet SNR, RSSI-based SNR, or simply RSSI.
2

0 5 10 15 20 25 30
0
20
40
60
80
100
Packet−level SNR (dB)
PRR
6.5
13
19.5
26
39
52
58.5
65
(a) A wired 802.11n link with variable attenuation has a
predictable relationship between SNR and packet recep-
tion rate (PRR) and clear separation between rates.
0 5 10 15 20 25 30 35
0
20
40
60
80
100
Measured packet SNR (dB)
PRR
6.5
26
65
(b) Over real wireless channels in our testbeds, the transition
region varies up to 10 dB. This loses the clear separation be-
tween rates (and so only three rates are shown for legibility).
Figure 1: Measured (single antenna) 802.11n packet delivery
over wired and real channels.
measurements that show RSSI does not predict packet delivery for
real links [3, 22, 30, 31].
Impact of Frequency-Selective Fading. Many possible factors
cause the observed variability for real channels, including NIC cal-
ibration, interference, sampling, and multipath. Here, we look at
frequency-selective fading due to multipath, as our experiments
show this to be a major factor.
Multipath causes some subcarriers to work markedly better than
others although all use the same modulation and coding. These
channel details, and not simply the overall signal strength as given
by RSSI, affect packet delivery. Figure 2 illustrates this with the
measured subcarrier SNRs for four different links in our testbed
averaged over a 5-second run. All links are shown at the closest
transmit power level, in steps of 2 dB, to 80% packet delivery when
using the 52 Mbps rate. However, the fading profiles vary signifi-
cantly across the four links. One distribution is quite flat across the
subcarriers, while the other three exhibit frequency-selective fading
of varying degrees. Two of the links have two deeply-faded subcar-
riers that are more than 20 dB down from the peak.
These links harness the received power with different efficien-
cies. The more faded links are more likely to have errors that must
be repaired with coding, and require extra transmit power to com-
pensate. Thus, while the performance is roughly the same, the
most frequency-selective link needs a much higher overall packet
SNR (30.2 dB) than the frequency-flat link (16.5 dB). This differ-
ence of almost 14 dB highlights why RSSI-based SNR does not re-
liably predict performance. Fading and its effects are well-known.
However, it is rare to see data that shows fading for real links and
NICs because it has been difficult to measure.
Impact of multiple streams. The use of multiple antennas adds an-
other dimension to the problem of predicting packet delivery. While
5
15
25
35
45
-28 -14 0 14 28
SNR (dB)
Subcarrier index
PRR 83%, SNR 30.2dB
PRR 78%, SNR 27.1dB
PRR 74%, SNR 18.2dB
PRR 80%, SNR 16.5dB
Figure 2: Channel gains on four links that perform about
equally well at 52 Mbps. The more faded links require larger
RSSIs (i.e., more transmit power) to achieve similar PRRs.
we do not present further motivating data here, we briefly note that
this makes the problem more difficult, not simpler. To begin with,
there is now an RSSI for each receive antenna. This makes it dif-
ficult to know which RSSI or function of RSSIs to use to predict
delivery even when there is a single spatial stream. When multiple
streams are sent simultaneously, they interfere on the channel. The
MIMO processing used to separate them depends on the details of
the channel, and less of the signal will be harnessed if the RF paths
are correlated. This adds variability that exacerbates fading effects.
3. PACKET DELIVERY MODEL
Our goal is to develop a model that can accurately predict the
packet delivery probability of commodity 802.11 NICs for a given
physical layer configuration operating over a given channel. We
want our model to be simple and practical, so that it can be readily
deployed, and to cover a wide range of physical layer configura-
tions, so that it can be applied in many settings and for many tasks.
In particular, the scope of our model is 802.11n including multiple
antenna modes, of which single antenna 802.11a/g is a subset. This
scope is sufficient for many current and future networks. We model
delivery for single packet transmission only, leaving extensions for
interference and spatial reuse to future work.
Model Design. The structure of our model is simple: given 1) the
current state of the RF channel between transmitter and receiver,
and 2) a target physical layer configuration of the NIC, it predicts
whether that link will reliably deliver packets in that configuration.
For the first piece of input, we use 802.11n Channel State In-
formation (CSI). The CSI is a collection of MxN matrices H
s
in
which each describes the RF path (SNR and phase) between all
pairs of N transmit and M receive antennas for one subcarrier s.
It is reported by the NIC in a format specified by the standard [1],
with details in §4.2. An 802.11n NIC can probe a receiver to gather
CSI, or use channel reciprocity to learn CSI from a received packet.
The CSI is a much richer source of information than the RSSI, and
it gives us the opportunity to develop a much more accurate model.
The second form of input is the target physical layer configura-
tion for which we want to predict delivery. This is specified as the
choice of transmit and receive antennas, transmit power level, and
transmit rate (as the combination of modulation, coding, and num-
ber of spatial streams). Other choices, such as beamforming, could
be added in the future. The only restriction is that the CSI includes
the antennas and subcarriers used in the target configuration.
For the model output, we define that the link will work, i.e., will
reliably deliver packets, if we predict 90% packet reception rate.
We do not try to make predictions in the transition region during
which a link changes from lossy to reliable. Predictions there are
3

OFDM
Demodulator
Deinterleaver
Convolutional
Decoder
Descrambler
(0)
Received
signal
MIMO Stream
Separation
Separated signals
for each spatial stream
(1)
Scrambled,
coded bits
(3)
(2)
Scrambled,
interleaved,
coded bits
(4)
Scrambled bits
(5)
Received
bitstream
Packet
processing
Figure 3: The 802.11n MIMO-OFDM decoding process. MIMO receiver separates the RF signal (0) for each spatial stream (1).
Demodulation converts the separated signals into bits (2). Bits from the multiple streams are deinterleaved and combined (3) followed
by convolutional decoding (4) to correct errors. Finally, scrambling that randomizes bit patterns is removed and the packet is
processed (5).
Modulation Bits/Symbol (k) BER
k
(ρ)
BPSK 1 Q
2ρ
QPSK 2 Q
ρ
QAM-16 4
3
4
Q
p
ρ/5
QAM-64 6
7
12
Q
p
ρ/21
Table 2: Bit error rate as a function of the symbol SNR ρ for
narrowband signals and OFDM modulations. Q is the standard
normal CDF.
likely to be variable, and simply knowing when the link starts to
work is useful information in practice.
802.11 Packet Reception. The model must account for the action
of the 802.11 receiver on the received signal. This is a complex pro-
cess described in many pages of the 802.11n specification [1]. Our
challenge is to capture it well enough with a fairly simple model.
We begin by describing the main steps involved (Figure 3).
First, MIMO processing separates the signals of multiple spatial
streams that have been mixed by the channel. As wireless chan-
nels are frequency-selective, this operation happens separately for
each subcarrier. The demodulator converts each subcarrier’s sym-
bols into the bits of each stream from constellations of several dif-
ferent modulations (BPSK, QPSK, QAM-16, QAM-64). This hap-
pens in much the same way as demodulating a narrowband channel.
The bits are then deinterleaved to undo an encoding that spreads
errors that are bursty in frequency across the data stream. A paral-
lel to serial converter combines the bits into a single stream. For-
ward error correction at any of several rates (1/2, 2/3, 3/4, and 5/6)
is then decoded. Finally, the descrambler exclusive-ORs the bit-
stream with a pseudorandom bitmask added at the transmitter to
avoid data-dependent deterministic errors.
Modeling Delivery. We build our model up from narrowband de-
modulation. Standard formulas summarized in Table 2 relate SNR
(denoted ρ) to bit-error rate (BER) for the modulations used in
802.11 [8]. CSI gives us the SNR values (ρ
s
) to use for each sub-
carrier. For a SISO system, ρ
s
is given by the single entry in H
s
.
In OFDM, decoding is applied across the demodulated bits of
subcarriers. If we assume frequency-flat fading for the moment,
then all the subcarriers have the same SNR. The link will behave
the same as in our wired experiments in which RSSI reflect real
performance and it will be easy to make predictions for a given SNR
and modulation combination. We can use Figure 1(a) to measure
the fixed transition points between rates and thus make our choice.
Frequency-selective fading complicates this picture as some weak
subcarriers will be much more likely to have errors than others that
are stronger. To model a link in this case, we turn to the notion of an
effective SNR. This is defined as the SNR that would give the same
error performance on a narrowband channel [18]. For example,
the links in Figure 2 will have effective SNR values that are nearly
equal because they perform similarly, even though their RSSIs are
spread over 15 dB.
The effective SNR is not simply the average subcarrier SNR; in-
deed, assuming a uniform noise floor, that average is indeed equiv-
alent to the packet SNR derived from the RSSI. Instead, the effec-
tive SNR is biased towards the weaker subcarrier SNRs because it
is these subcarriers that produce most of the errors. If we ignore
coding for the moment, then we can compute the effective SNR by
averaging the subcarrier BERs and then finding the corresponding
SNR. That is:
BER
eff,k
=
1
52
X
BER
k
(ρ
s
) (1)
ρ
eff,k
= BER
1
k
(BER
eff,k
) (2)
We use BER
1
k
to denote the inverse mapping, from BER to SNR.
We have also called the average BER across subcarriers the effec-
tive BER, BER
eff
. SoftRate estimates BER using internal receiver
state [28]. We compute it from channel measurements instead.
Note that the BER mapping and hence effective SNR are func-
tions of the modulation (k). That is, unlike the RSSI, a particular
wireless channel will have four different effective SNR values, one
describing performance for each of the modulations. In practice, the
interesting regions for the four effective SNRs do not overlap be-
cause at a particular effective SNR value only one modulation will
be near the transition from useless (BER 0.5) to lossless (BER
0). When graphs in this paper are presented with an effective SNR
axis, we use all four values, each in the appropriate SNR range.
For 802.11n, we also model MIMO processing at the receiver.
To do this we need to estimate the subcarrier SNRs for each spa-
tial stream from the channel state matrix H
s
. Although the stan-
dard does not specify receiver processing, we assume that a Min-
imum Mean Square Error (MMSE) receiver is used. It is compu-
tationally simple, optimal and equivalent to Maximal-Ratio Com-
bining (MRC) for a single stream, and near optimal for multiple
streams. All of these make it a likely choice in practice. The SNR
of the i
th
stream after MMSE processing for subcarrier s is given
by ρ
s,i
= 1/Y
ii
1, where Y =
H
H
s
H
s
+ I
1
for i [1, N ]
and N xN identity matrix I [27]. For MIMO, the model computes
the effective BER averaged across both subcarriers and streams.
Coding interacts with the notion of effective SNR in a way that
is difficult to analyze. One challenge is that the ability to correct
bit errors depends on the position of the errors in the data stream.
To sidestep this problem, we rely on the interleaving that random-
izes the coded bits across subcarriers and spatial streams. Assum-
ing perfect interleaving and robust coding, bit errors in the stream
should look no different from bit errors for flat channels (but at a
4

50 ft
Figure 4: Our indoor 802.11n testbeds, T1 and T2. T1 consists of 10 nodes spread over 8 100 square feet, and T2 consists of 11 nodes
spread over 20 000 square feet. The nodes are placed to ensure a large number of links between them, a variety of distance between
nodes, and diverse scattering characteristics.
8
12
16
20
24
-28 -14 0 14 28
SNR (dB)
Subcarrier index
BPSK
QPSK
QAM-16
QAM-64
Packet SNR
Subcarrier SNRs
Figure 5: Sample faded link showing the packet SNR and ef-
fective SNRs for different modulations. BPSK has the lowest
effective SNR, but it needs less energy to decode.
lower SNR). Thus our estimate of the effective BER in Eq. (1) will
accurately reflect the uncoded error performance of the link. Our
algorithm now proceeds as in the case of a flat-fading channel de-
scribed above: we take the computed effective SNR value and use
the measurements from a flat-fading link (Figure 1(a)) to determine
transmission success or failure. As in CHARM [10], we support
different packet lengths with different SNR thresholds.
Note that this procedure differs from the typical approach of
simulation-based analyses [11, 15, 19], that instead map the un-
coded BER estimate such as we compute to a coded BER esti-
mate by means of a simple log-linear approximation. They then
use the coded BER estimate, and the length of the target transmis-
sion, to directly compute the packet delivery rate of the link. We
believe our method of thresholding the effective SNR is better be-
cause it directly accommodates variation in the receiver implemen-
tation. Different devices may have different noise figures, a measure
of how much signal strength is lost in the internal RF circuitry of
the NIC. They may implement soft Viterbi decoders with more or
fewer soft bits for their internal state, or indeed might do hard de-
coding instead. A receiver could use the optimal Maximum Like-
lihood MIMO decoder that has exponential complexity for small
constellations like BPSK, but revert to the imperfect but more ef-
ficient MMSE at higher modulations. All of these can be easily
expressed, albeit maybe approximately, as (perhaps modulation-
dependent) shifts in the effective SNR thresholds. In contrast, chang-
ing these parameters in the simulation approach involves changing
the internals of the calculation.
Protocol Details. Effective SNR calculations can be performed by
either receiver or transmitter, and each has advantages. For it to
make decisions, the transmitter must know the receiver’s thresholds
for the different rates; these are fixed for a particular model of NIC
and can be shared once, e.g., during association. The transmitter
also needs up-to-date CSI: either from feedback or estimated from
the reverse path. Alternately, the receiver can request rates and se-
lect antennas directly using the new Link Adaptation Control field
of any 802.11n QoS packet [1, §7.1.3.5a]. This obviates sending
CSI, but the calculation instead requires that the transmitter share
its spatial mappings, i.e. how it maps spatial streams to transmit an-
tennas. These are likely to change less frequently than the channel,
if at all. Finally, when operating in either mode with fewer trans-
mit streams than antennas, the transmitter must occasionally send a
short probe packet with all antennas to measure the full CSI.
Summary and Example. Combining the above steps, our model
consists of the following: 1) CSI is obtained and a test config-
uration is chosen; 2) the MMSE expression is used to compute
per-stream, subcarrier SNRs from the CSI for the test number of
streams; 3) the effective SNR is computed from the per-stream,
subcarrier SNRs for the test modulation; and 4) the effective SNR
is compared against the pre-determined threshold for the test mod-
ulation and coding to predict whether the link will deliver packets.
As an example, Figure 5 shows the CSI for a SISO link (steps 1–
2) as a fading profile across subcarriers, with the computed effective
SNRs for all modulations (step 3). These effective SNRs are com-
pared with pre-determined thresholds (step 4, see §5) to correctly
predict that the best working rate will be 39 Mbps. Note that these
effective SNRs are well below the RSSI-based packet SNR that is
biased towards the stronger subcarriers (note the logarithmic y-axis
scale). This link does a poor job of harnessing the received power
because it is badly faded, so its RSSI is a poor predictor of rate.
Applications can use this model to find useful configurations
without sending packets to test them. For example, the highest rate
can be predicted by running the model for all candidate rates and
selecting the best working rate. Alternatively, we could predict the
minimum transmit power to support a rate.
4. TESTBEDS
We conduct experiments using two stationary wireless testbeds
deployed in indoor office environments, T1 and T2 (Figure 4). T1
consists of 10 nodes spread over 8 100 square feet. T2 is less dense
by comparison with 11 nodes over 20 000 square feet. Each testbed
covers a single floor of a multi-story building and has a variety of
links in terms of maximum supported rate and line-of-sight versus
multi-path fading. We conduct mobile experiments using laptops
that interact with testbed nodes and are configured in the same way.
5

Citations
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22 Jan 2011
TL;DR: The measurement setup comprises the customized versions of Intel's close-source firmware and open-source iwlwifi wireless driver, userspace tools to enable these measurements, access point functionality for controlling both ends of the link, and Matlab scripts for data analysis.
Abstract: We are pleased to announce the release of a tool that records detailed measurements of the wireless channel along with received 802.11 packet traces. It runs on a commodity 802.11n NIC, and records Channel State Information (CSI) based on the 802.11 standard. Unlike Receive Signal Strength Indicator (RSSI) values, which merely capture the total power received at the listener, the CSI contains information about the channel between sender and receiver at the level of individual data subcarriers, for each pair of transmit and receive antennas.Our toolkit uses the Intel WiFi Link 5300 wireless NIC with 3 antennas. It works on up-to-date Linux operating systems: in our testbed we use Ubuntu 10.04 LTS with the 2.6.36 kernel. The measurement setup comprises our customized versions of Intel's close-source firmware and open-source iwlwifi wireless driver, userspace tools to enable these measurements, access point functionality for controlling both ends of the link, and Matlab (or Octave) scripts for data analysis. We are releasing the binary of the modified firmware, and the source code to all the other components.

1,354 citations


Cites methods from "Predictable 802.11 packet delivery ..."

  • ...It works on up-to-date Linux operating systems: in our testbed we use Ubuntu 10.04 LTS with the 2.6.36 kernel....

    [...]

Journal ArticleDOI
TL;DR: In this article, a deep-learning-based indoor fingerprinting system using channel state information (CSI) is presented, which includes an offline training phase and an online localization phase.
Abstract: With the fast-growing demand of location-based services in indoor environments, indoor positioning based on fingerprinting has attracted significant interest due to its high accuracy. In this paper, we present a novel deep-learning-based indoor fingerprinting system using channel state information (CSI), which is termed DeepFi. Based on three hypotheses on CSI, the DeepFi system architecture includes an offline training phase and an online localization phase. In the offline training phase, deep learning is utilized to train all the weights of a deep network as fingerprints. Moreover, a greedy learning algorithm is used to train the weights layer by layer to reduce complexity. In the online localization phase, we use a probabilistic method based on the radial basis function to obtain the estimated location. Experimental results are presented to confirm that DeepFi can effectively reduce location error, compared with three existing methods in two representative indoor environments.

761 citations

Journal ArticleDOI
TL;DR: In this article, the authors survey the channel state information (CSI) in 802.11 a/g/n and highlight the differences between CSI and RSSI with respect to network layering, time resolution, frequency resolution, stability, and accessibility.
Abstract: The spatial features of emitted wireless signals are the basis of location distinction and determination for wireless indoor localization. Available in mainstream wireless signal measurements, the Received Signal Strength Indicator (RSSI) has been adopted in vast indoor localization systems. However, it suffers from dramatic performance degradation in complex situations due to multipath fading and temporal dynamics.Break-through techniques resort to finer-grained wireless channel measurement than RSSI. Different from RSSI, the PHY layer power feature, channel response, is able to discriminate multipath characteristics, and thus holds the potential for the convergence of accurate and pervasive indoor localization. Channel State Information (CSI, reflecting channel response in 802.11 a/g/n) has attracted many research efforts and some pioneer works have demonstrated submeter or even centimeter-level accuracy. In this article, we survey this new trend of channel response in localization. The differences between CSI and RSSI are highlighted with respect to network layering, time resolution, frequency resolution, stability, and accessibility. Furthermore, we investigate a large body of recent works and classify them overall into three categories according to how to use CSI. For each category, we emphasize the basic principles and address future directions of research in this new and largely open area.

704 citations

01 Jan 2014
TL;DR: This article surveys the new trend of channel response in localization and investigates a large body of recent works and classify them overall into three categories according to how to use CSI, highlighting the differences between CSI and RSSI.
Abstract: The spatial features of emitted wireless signals are the basis of location distinction and determination for wireless indoor localization. Available in mainstream wireless signal measurements, the Received Signal Strength Indicator (RSSI) has been adopted in vast indoor localization systems. However, it suffers from dramatic performance degradation in complex situations due to multipath fading and temporal dynamics. Break-through techniques resort to finer-grained wireless channel measurement than RSSI. Different from RSSI, the PHY layer power feature, channel response, is able to discriminate multipath characteristics, and thus holds the potential for the convergence of accurate and pervasive indoor localization. Channel State Information (CSI, reflecting channel response in 802.11 a/g/n) has attracted many research efforts and some pioneer works have demonstrated submeter or even centimeter-level accuracy. In this article, we survey this new trend of channel response in localization. The differences between CSI and RSSI are highlighted with respect to network layering, time resolution, frequency resolution, stability, and accessibility. Furthermore, we investigate a large body of recent works and classify them overall into three categories according to how to use CSI. For each category, we emphasize the basic principles and address future directions of research in this new and largely open area.

612 citations


Cites background or methods from "Predictable 802.11 packet delivery ..."

  • ...Since current off-the-shelf CSIs are only available with Intel 5300 NIC and the modified driver [Halperin et al. 2010], it poses a challenge to employ CSIs on mobile handhelds....

    [...]

  • ...Leveraging the off-the-shelf Intel 5300 NIC and a modified driver, a group of sampled versions of CFRs within the WiFi bandwidth are revealed to upper layers in the format of Channel State Information (CSI) [Halperin et al. 2010]....

    [...]

  • ...In 802.11 a/g/n standards, channel response can be partially extracted from off-the-shelf OFDM receivers in the format of Channel State Information (CSI), which reveals a set of channel measurements depicting the amplitudes and phases of every subcarrier [Halperin et al. 2010]....

    [...]

  • ...DOI: http://dx.doi.org/10.1145/2543581.2543592...

    [...]

  • ...In fact, this sample version of CFR has been employed in recent adaptive wireless communication systems to improve reliability [Halperin et al. 2010] and throughput [Bhartia et al. 2011], as well as for precise indoor localization on off-the-shelf platforms [Wu et al. 2012; Sen et al. 2012a; Sen et…...

    [...]

Proceedings ArticleDOI
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TL;DR: Splicer, a software-based system that derives high-resolution power delay profiles by splicing the CSI measurements from multiple WiFi frequency bands is presented and a set of key techniques to separate the mixed hardware errors from the collected CSI measurements are proposed.
Abstract: Power delay profiles characterize multipath channel features, which are widely used in motion- or localization-based applications. Recent studies show that the power delay profile may be derived from the CSI traces collected from commodity WiFi devices, but the performance is limited by two dominating factors. The resolution of the derived power delay profile is determined by the channel bandwidth, which is however limited on commodity WiFi. The collected CSI reflects the signal distortions due to both the channel attenuation and the hardware imperfection. A direct derivation of power delay profiles using raw CSI measures, as has been done in the literature, results in significant inaccuracy. In this paper, we present Splicer, a software-based system that derives high-resolution power delay profiles by splicing the CSI measurements from multiple WiFi frequency bands. We propose a set of key techniques to separate the mixed hardware errors from the collected CSI measurements. Splicer adapts its computations within stringent channel coherence time and thus can perform well in presence of mobility. Our experiments with commodity WiFi NICs show that Splicer substantially improves the accuracy in profiling multipath characteristics, reducing the errors of multipath distance estimation to be less than $2m$. Splicer can immediately benefit upper-layer applications. Our case study with recent single-AP localization achieves a median localization error of $0.95m$.

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"Predictable 802.11 packet delivery ..." refers background or methods in this paper

  • ...This is a straightforward choice for a single spatial stream as it corresponds to receiver processing using MRC [8]....

    [...]

  • ...Textbook analyses of modulation schemes give delivery probability for a single signal in terms of the signal-to-noise (SNR) ratio [8], typically expressed on a log scale in decibels....

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  • ...This is a straightforward choice for a single spatial stream as it corresponds to receiver processing using MRC [8]....

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Journal Article
TL;DR: Govindan et al. as mentioned in this paper performed a large-scale measurement of packet delivery in dense wireless sensor networks and found that packet de-livery performance is important for energy-constrained networks.
Abstract: Understanding Packet Delivery Performance In Dense Wireless Sensor Networks ∗ Computer Science Department University of Southern California Los Angeles, CA 90089-0781 Jerry Zhao Computer Science Department University of Southern California Los Angeles, CA 90089-0781 Ramesh Govindan zhaoy@usc.edu ABSTRACT Wireless sensor networks promise fine-grain monitoring in a wide variety of environments. Many of these environ- ments (e.g., indoor environments or habitats) can be harsh for wireless communication. From a networking perspec- tive, the most basic aspect of wireless communication is the packet delivery performance: the spatio-temporal charac- teristics of packet loss, and its environmental dependence. These factors will deeply impact the performance of data acquisition from these networks. In this paper, we report on a systematic medium-scale (up to sixty nodes) measurement of packet delivery in three different environments: an indoor office building, a habitat with moderate foliage, and an open parking lot. Our findings have interesting implications for the design and evaluation of routing and medium-access protocols for sensor networks. ramesh@usc.edu spectrum under use, the particular modulation schemes un- der use, and possibly on the communicating devices them- selves. Communication quality can vary dramatically over time, and has been reputed to change with slight spatial displacements. All of these are true to a greater degree for ad-hoc (or infrastructure-less) communication than for wire- less communication to a base station. Given this, and the paucity of large-scale deployments, it is perhaps not surpris- ing that there have been no medium to large-scale measure- ments of ad-hoc wireless systems; one expects measurement studies to reveal high variability in performance, and one suspects that such studies will be non-representative. Wireless sensor networks [5, 7] are predicted on ad-hoc wireless communications. Perhaps more than other ad-hoc wireless systems, these networks can expect highly variable wireless communication. They will be deployed in harsh, inaccessible, environments which, almost by definition will exhibit significant multi-path communication. Many of the current sensor platforms use low-power radios which do not have enough frequency diversity to reject multi-path prop- agation. Finally, these networks will be fairly densely de- ployed (on the order of tens of nodes within communica- tion range). Given the potential impact of these networks, and despite the anecdotal evidence of variability in wireless communication, we argue that it is imperative that we get a quantitative understanding of wireless communication in sensor networks, however imperfect. Our paper is a first attempt at this. Using up to 60 Mica motes, we systematically evaluate the most basic aspect of wireless communication in a sensor network: packet delivery. Particularly for energy-constrained networks, packet de- livery performance is important, since that translates to net- work lifetime. Sensor networks are predicated using low- power RF transceivers in a multi-hop fashion. Multiple short hops can be more energy-efficient than one single hop over a long range link. Poor cumulative packet delivery per- formance across multiple hops may degrade performance of data transport and expend significant energy. Depending on the kind of application, it might significantly undermine application-level performance. Finally, understanding the dynamic range of packet delivery performance (and the ex- tent, and time-varying nature of this performance) is impor- tant for evaluating almost all sensor network communication protocols. We study packet delivery performance at two layers of the communication stack (Section 3). At the physical-layer and in the absence of interfering transmissions, packet de- Categories and Subject Descriptors C.2.1 [Network Architecture and Design]: Wireless communication; C.4 [Performance of Systems]: Perfor- mance attributes, Measurement techniques General Terms Measurement, Experimentation Keywords Low power radio, Packet loss, Performance measurement 1. INTRODUCTION Wireless communication has the reputation of being no- toriously unpredictable. The quality of wireless communica- tion depends on the environment, the part of the frequency ∗ This work is supported in part by NSF grant CCR-0121778 for the Center for Embedded Systems. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. SenSys’03, November 5–7, 2003, Los Angeles, California, USA. Copyright 2003 ACM 1-58113-707-9/03/0011 ... $ 5.00.

1,330 citations

Frequently Asked Questions (17)
Q1. What have the authors contributed in "Predictable 802.11 packet delivery from wireless channel measurements" ?

The authors show that, for the first time, wireless packet delivery can be accurately predicted for commodity 802. 11 NICs from only the channel measurements that they provide. The authors report testbed experiments that show narrow transition regions ( < 2 dB for most links ) similar to the near-ideal case of narrowband, frequency-flat channels. Unlike RSSI, this lets us predict the highest rate that will work for a link, trim transmit power, and more. The authors use trace-driven simulation to show that their rate prediction is as good as the best rate adaptation algorithms for 802. 

The authors have also shown that effective SNR can be implemented on commodity NICs and evaluated it over real wireless channels with mobile and fixed clients. 

Modern wireless NICs provide a large and growing range of physical layer configurations to obtain good performance across this range of environments. 

It uses the notion of effective SNR to handle OFDM over faded links, works for MIMO configurations, and needs no calibration of target links. 

Many rate adaptation algorithms have been proposed that use packet delivery statistics [5, 29], RSSI-based packetSNR [6, 10], or symbol-level details of packet reception [23, 28] to adapt to varying channel conditions. 

Their model uses the concept of an effective SNR for a multi-carrier channel [18], such as OFDM, in which there are different subcarrier SNRs, plus approximations for coding, interference between MIMO streams, and decoding algorithms. 

At each reduced transmit power level, the authors estimate the best supported rate on a link based on appropriate thresholds, and continue the reduction if the original rate is sustained. 

This is one of the largest potential weaknesses of this technique, because effective SNR is based on measurements taken only during the packet preamble. 

If the authors ignore coding for the moment, then the authors can compute the effective SNR by averaging the subcarrier BERs and then finding the corresponding SNR. 

Then the authors collect packet reception rate (PRR) statistics for all 8 rates using 1, 2, and 3 spatial streams as the authors vary the power between −10 dBm and 16 dBm in steps of 2 dB. 

Except for extremely low and high SNRs, nearly all SNRs have at least two and up to five different rates as suitable choices for the best rate. 

The authors conclude that the mere presence of interference does not completely invalidate effective SNR values, and thus transient interference will not cause wild swings in transmit rate. 

The authors convert CSI to effective SNR in a way that better matches the equal modulation and power allocation used by 802.11n and offer a better API for practical use. 

To understand how transition windows map to packet delivery predictions, the authors analyze their measurements for the highest supported rate (PRR≥ 90%) for each link and all NIC settings. 

Their example in §5 suggests that, with a good predictive model, the authors can directly and confidently select a reduced transmit power without degrading link performance. 

To show that this trimming is tight, the authors also consider trimming towards slightly lower thresholds (Effective SNR− 0.5 dB, solid line). 

The authors also varied the transmit power of the node designated as the interferer from low to high to induce a large range of interfering channels.