Wireless Communication Systems

Wireless Communication Systems

@CS.NCTU

Lecture 10: Rate Adaptation

Frequency-Aware Rate Adaptation (MobiCom’09)

Lecturer: Kate Ching-Ju Lin (林靖茹)

Motivation

• The bandwidth supported in 802.11 is getting wider

⎻ 20MHz in 802.11a/b/g

⎻ 40MHz in 802.11n

⎻ 80-160MHz in 802.11ac

• 802.11 adopts OFDM, which partitions the wideband channel to subcarrier

• Frequency-selective fading

⎻ Different subcarriers experience independent fading due to the multipath effect

⎻ Different frequencies exhibit very different SNRs

⎻ But the transmitter can assign one rate to the entire band

2

Frequency Diversity

• The SNRs of different frequencies can differ by as much as 20dB

• Different receivers prefer different frequencies

3

Frequency-Aware Rate Adaptation and MAC Protocols

Hariharan Rahul

^†

, Farinaz Edalat

^ℵ

, Dina Katabi

^†

, and Charles Sodini

^†

†

Massachusetts Institute of Technology

^ℵ

RKF Engineering Solutions, LLC

ABSTRACT

There has been burgeoning interest in wireless technologies that can use wider frequency spectrum. Technology advances, such as 802.11n and ultra-wideband (UWB), are pushing toward wider fre- quency bands. The analog-to-digital TV transition has made 100- 250 MHz of digital whitespace bandwidth available for unlicensed access. Also, recent work on WiFi networks has advocated discard- ing the notion of channelization and allowing all nodes to access the wide 802.11 spectrum in order to improve load balancing. This shift towards wider bands presents an opportunity to exploit frequency diversity. Specifically, frequencies that are far from each other in the spectrum have significantly different SNRs, and good frequencies differ across sender-receiver pairs.

This paper presents FARA, a combined frequency-aware rate adaptation and MAC protocol. FARA makes three departures from conventional wireless network design: First, it presents a scheme to robustly compute per-frequency SNRs using normal data trans- missions. Second, instead of using one bit rate per link, it en- ables a sender to adapt the bitrate independently across frequencies based on these per-frequency SNRs. Third, in contrast to traditional frequency-oblivious MAC protocols, it introduces a MAC protocol that allocates to a sender-receiver pair the frequencies that work best for that pair. We have implemented FARA in FPGA on a wide- band 802.11-compatible radio platform. Our experiments reveal that FARA provides a 3.1× throughput improvement in comparison to frequency-oblivious systems that occupy the same spectrum.

Categories and Subject Descriptors

C.2.2 [Computer Sys- tems Organization]: Computer-Communications Networks

General Terms

Algorithms, Design, Performance

Keywords

Wireless, Cognitive Radios, Wideband, Rate Adapta- tion, Cross-layer

1 I

NTRODUCTION

Wireless technologies are pushing toward wider frequency bands than the 20 MHz channels employed by existing 802.11 networks.

802.11n already includes a 40 MHz mode that bonds together two 20 MHz bands [23]. Emerging ultra-wideband (UWB) technolo- gies employ hundreds of MHz to support multimedia homes and offices [24, 50, 9, 40]. The FCC has recently permitted unlicensed

Permission to make digital or hard copies of all or part of this work for per- sonal 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 re- publish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee.

MobiCom’09, September 20–25, 2009, Beijing, China.

Copyright 2009 ACM 978-1-60558-702-8/09/09 . . . $10.00.

0 5 10 15 20 25 30

-40 -20 0 20 40

SNR (dB)

Freq (Mhz)

Figure 1: Frequency diversity across 100 MHz of 802.11a spec- trum as observed by two receivers for transmissions from the same sender. The figure shows that the SNRs of different frequen- cies can differ by as much as 20 dB on a single link. Further, different receivers prefer different frequencies.

use of digital TV whitespaces that occupy 100-250 MHz of spectrum vacated by television bands in the analog-to-digital transition [12].

Furthermore, recent empirical studies show that the 802.11 chan- nelization model which limits each node to a single 20 MHz chan- nel can lead to severe load imbalance [19, 28, 37]. They advocate discarding channelization and allowing all nodes to access the en- tire 802.11 spectrum based on demand [19, 37]. This push towards wider bands is further enabled by the constantly lowering prices of high-speed ADC and DAC hardware [38, 31].¹ In particular, today, wireless cards that span over 100 MHz of spectrum can be built us- ing off-the-shelf hardware components [35].

As wireless networks push towards wider bands, we can no longer afford to ignore frequency diversity. Specifically, multipath effects cause frequencies that are far away from each other in the spectrum to experience independent fading. Thus, different frequencies can exhibit very different SNRs for a single sender-receiver pair. Further, the frequencies that show good performance for one sender-receiver pair may be very different than the frequencies that show good per- formance for another pair. Fig. 1 shows empirical measurements of the SNRs across 100 MHz of the 802.11a spectrum, as observed by 2 clients for transmissions from the same AP (see §9 for exper- imental setup). The figure reveals that different frequencies show a difference in SNR of over 20 dB both for a single link and across links. Existing bitrate adaptation and MAC protocols however are frequency-oblivious. They assign the same bitrate to all frequencies and allocate the medium in a time-based manner, ignoring the fact that different frequencies work better for different sender-receiver pairs. Thus, current rate adaptation and MAC protocols can neither deal with the challenge nor exploit the opportunities introduced by the frequency diversity of wide bands or unchannelized 802.11.

1The wider the band, the faster the ADC and DAC have to sample the signal.

Key Features of FARA

• Allow a receiver to measure the SNR of each sub-channel

• Instead of assigning the same rate to the

entire band, allows each sub-channel to pick the optimal rate matching its SNR

4

Frequency-Aware Rate Adaptation and MAC Protocols

Hariharan Rahul

^†

, Farinaz Edalat

^ℵ

, Dina Katabi

^†

, and Charles Sodini

^†

†

Massachusetts Institute of Technology

^ℵ

RKF Engineering Solutions, LLC

ABSTRACT

There has been burgeoning interest in wireless technologies that can use wider frequency spectrum. Technology advances, such as 802.11n and ultra-wideband (UWB), are pushing toward wider fre- quency bands. The analog-to-digital TV transition has made 100- 250 MHz of digital whitespace bandwidth available for unlicensed access. Also, recent work on WiFi networks has advocated discard- ing the notion of channelization and allowing all nodes to access the wide 802.11 spectrum in order to improve load balancing. This shift towards wider bands presents an opportunity to exploit frequency diversity. Specifically, frequencies that are far from each other in the spectrum have significantly different SNRs, and good frequencies differ across sender-receiver pairs.

This paper presents FARA, a combined frequency-aware rate adaptation and MAC protocol. FARA makes three departures from conventional wireless network design: First, it presents a scheme to robustly compute per-frequency SNRs using normal data trans- missions. Second, instead of using one bit rate per link, it en- ables a sender to adapt the bitrate independently across frequencies based on these per-frequency SNRs. Third, in contrast to traditional frequency-oblivious MAC protocols, it introduces a MAC protocol that allocates to a sender-receiver pair the frequencies that work best for that pair. We have implemented FARA in FPGA on a wide- band 802.11-compatible radio platform. Our experiments reveal that FARA provides a 3.1× throughput improvement in comparison to frequency-oblivious systems that occupy the same spectrum.

Categories and Subject Descriptors

C.2.2 [Computer Sys- tems Organization]: Computer-Communications Networks

General Terms

Algorithms, Design, Performance

Keywords

Wireless, Cognitive Radios, Wideband, Rate Adapta- tion, Cross-layer

1 I

NTRODUCTION

Wireless technologies are pushing toward wider frequency bands than the 20 MHz channels employed by existing 802.11 networks.

802.11n already includes a 40 MHz mode that bonds together two 20 MHz bands [23]. Emerging ultra-wideband (UWB) technolo- gies employ hundreds of MHz to support multimedia homes and offices [24, 50, 9, 40]. The FCC has recently permitted unlicensed

Permission to make digital or hard copies of all or part of this work for per- sonal 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 re- publish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee.

MobiCom’09, September 20–25, 2009, Beijing, China.

Copyright 2009 ACM 978-1-60558-702-8/09/09 . . . $10.00.

0 5 10 15 20 25 30

-40 -20 0 20 40

SNR (dB)

Freq (Mhz)

Figure 1: Frequency diversity across 100 MHz of 802.11a spec- trum as observed by two receivers for transmissions from the same sender. The figure shows that the SNRs of different frequen- cies can differ by as much as 20 dB on a single link. Further, different receivers prefer different frequencies.

use of digital TV whitespaces that occupy 100-250 MHz of spectrum vacated by television bands in the analog-to-digital transition [12].

Furthermore, recent empirical studies show that the 802.11 chan- nelization model which limits each node to a single 20 MHz chan- nel can lead to severe load imbalance [19, 28, 37]. They advocate discarding channelization and allowing all nodes to access the en- tire 802.11 spectrum based on demand [19, 37]. This push towards wider bands is further enabled by the constantly lowering prices of high-speed ADC and DAC hardware [38, 31].¹ In particular, today, wireless cards that span over 100 MHz of spectrum can be built us- ing off-the-shelf hardware components [35].

As wireless networks push towards wider bands, we can no longer afford to ignore frequency diversity. Specifically, multipath effects cause frequencies that are far away from each other in the spectrum to experience independent fading. Thus, different frequencies can exhibit very different SNRs for a single sender-receiver pair. Further, the frequencies that show good performance for one sender-receiver pair may be very different than the frequencies that show good per- formance for another pair. Fig. 1 shows empirical measurements of the SNRs across 100 MHz of the 802.11a spectrum, as observed by 2 clients for transmissions from the same AP (see §9 for exper- imental setup). The figure reveals that different frequencies show a difference in SNR of over 20 dB both for a single link and across links. Existing bitrate adaptation and MAC protocols however are frequency-oblivious. They assign the same bitrate to all frequencies and allocate the medium in a time-based manner, ignoring the fact that different frequencies work better for different sender-receiver pairs. Thus, current rate adaptation and MAC protocols can neither deal with the challenge nor exploit the opportunities introduced by the frequency diversity of wide bands or unchannelized 802.11.

1The wider the band, the faster the ADC and DAC have to sample the signal.

54Mb/s

6Mb/s

SNR-based Adaptation

• Maintain a SNR-to-rate lookup table

• The sender transmits few symbols at the lowest bit-rate for all sub-channels

• The receiver selects the highest rate for each sub-

channel corresponding to the SNR of that sub-channel

⎻ Discard the sub-channels if SNR is too low to support the

lowest rate

₅

where H

i

is the channel, x

i

[k ] is the k

^th

transmitted signal sam- ple in subband i , and n

i

[k ] is the corresponding noise sample. The receiver knows H

i

for all subbands because it is estimated using known OFDM symbols in the preamble [20]. In the case of a pi- lot subband, x

i

[k ] is also known at the receiver since pilot subbands contain a known data sequence. As a result, the receiver can estimate the noise samples, n

i

[k ], and the noise power, N

₀

, as:

n

i

[k ] = y

i

[k ] − H

ⁱ

x

i

[k ] (4) N

₀

= E

_{i ,k}

(n

ⁱ

[k ]

²

) (5) where the function E (.) is the mean computed using all pilot bits across all symbols in the data packet.

Thus, every received packet allows the receiver to obtain a new SNR measurement for each OFDM subband. The receiver maintains a time weighted moving average of the SNR in each subband, which it updates on the reception of a data packet.

A few points are worth noting:

(a) What happens when the data packet is corrupted (i.e. does not pass the checksum test)? Even when the packet is corrupted, the receiver can still compute an accurate estimate of the per-subband SNRs. This is because the receiver can compute the average received power, regardless of whether the packet is corrupted or not. Further- more, the receiver can still obtain an accurate estimate of the noise power since this only requires the pilots which are known, and sent at BPSK, which is the most robust modulation rate and hence al- low synchronization and packet recovery even at low SNRs. Thus, FARA can get accurate estimates of the per-subband SNRs from ev- ery captured packet, including corrupted packets.

(b) How accurate are FARA’s SNR estimates? We note that since FARA has access to the PHY layer, it can collect accurate SNR estimates. In particular, traditional estimates of the SNR use RSSI readings, which measure the received power of a few samples at the beginning of the packet (i.e., the AGC gain) [6], or infer the SNR using just the correlation of header symbols in the preamble of the packet [49]. In contrast, FARA exploits the known pilot bits to ac- curately estimate the noise power and utilize it in its SNR compu- tation. Furthermore, FARA computes its signal and noise estimates over the whole packet and not just a few samples at the beginning of the packet, which allows it to obtain more stable estimates.

(c) Do different choices of bitrate affect the accuracy of FARA’s SNR estimation? OFDM data subbands use a different modulation scheme depending on the choice of bitrate. The modulation scheme in a subband, however, does not affect our per-subband SNR esti- mate. The estimation of SNR involves only the measured power in each subband and hence can be performed on any packet indepen- dent of the modulation and coding schemes used by the transmitter.

6 F ^REQUENCY -A ^WARE R ^ATE A ^DAPTATION

The goal of rate adaptation is to determine the highest bitrate that a channel can sustain at any point in time. Traditional 802.11 rate adaptation schemes are frequency-oblivious, and use the same modulation scheme and coding rate across all frequencies. Thus, they cannot exploit the frequency diversity present across the 802.11 spectrum. In contrast, FARA exploits this frequency diversity via a frequency-aware rate adaptation scheme that picks different bitrates for different frequencies depending on their SNRs.

6.1 PHY Architecture

In 802.11, a particular bit rate implies a single modulation scheme and code rate over all OFDM subbands in the entire packet. For

… 011010 …

… 011010 …

subband n Modu-

late IFFT

OFDM Transmitter Side

ADC subband 1

FFT

OFDM Receiver Side Code &

Interleave

Demodu- late

Decode &

Deinterleave

subband n subband 1

DAC

(a) Schematic of 802.11 PHY

… 011010 …

… 011010 …

IFFT

OFDM Transmitter Side

ADC FFT

OFDM Receiver Side

Modulate DAC

Code & Interleave Decode & Deinterleave

Demodulatie

(b) Schematic of FARA-enabled 802.11 PHY

Figure 3: OFDM PHY semantics with and without FARA. In FARA-enabled devices, the choice of modulation and FEC code rate is done independently for each OFDM subband.

Minimum Required SNR Modulation Coding

<3.5 dB Suppress subband

3.5 dB BPSK 1/2

5.0 dB BPSK 3/4

5.5 dB 4-QAM 1/2

8.5 dB 4-QAM 3/4

12.0 dB 16-QAM 1/2

15.5 dB 16-QAM 3/4

20.0 dB 64-QAM 2/3

21.0 dB 64-QAM 3/4

Table 1: Minimum required SNR for a particular modulation and code rate (i.e., bitrate). Table is generated offline using the WiGLAN radio platform by running all possible bit rates for the whole operational SNR range. The SNR field refers to the minimum SNR required to maintain the packet loss rate below 1% (see §9 for experimental setup).

example, a bitrate of 24 Mbps corresponds to 16-QAM modula- tion scheme and a half-rate code. 802.11 has 4 possible modulation schemes (BPSK, 4-QAM, 16-QAM, and 64-QAM), and 3 possible code rates (1/2, 2/3, and 3/4). In current 802.11, a transmitter imple- ments a particular bitrate by first taking the input bit stream, passing it to the convolutional coder, and puncturing to achieve the desired coding rate. The bits are then interleaved, modulated and striped over the OFDM subbands, as shown in Fig. 3(a). The process is reversed on the receiver as shown in the figure.

FARA makes a few modifications to the existing 802.11 PHY layer, as shown in Fig. 3(b). Specifically, FARA employs the same set of modulation schemes and code rates supported by the existing 802.11. However, it allows each OFDM subband to pick a modu- lation scheme and a code rate that match its SNR, independently from the other subbands. Note that this design does not require addi- tional modulation/demodulation or coding/decoding modules in the PHY layer. In particular, since we use standard 802.11 modulation and coding options, we only need to buffer the samples and process them through the same pipeline.

6.2 Mapping Subband SNRs to Optimal Bitrates

The receiver needs to map the average SNR in each subband to

the optimal bitrate for that band. To do so, the receiver uses an SNR

characterization table like the one in Table 1 that lists the minimum

SNR required for a particular combination of modulation and cod-

Rx-based Adaptation

• The receiver is in charge of

⎻ Measuring the channel

⎻ Selecting the rate

⎻ Responding to the AP

• To decrease the feedback overhead, embed the rate information in ACK

• Perform some optimization to reduce the size of the embedded information

6

FARA in Frequency-Aware MAC

• Further combine FARA with the frequency-aware MAC protocol to leverage frequency diversity

• Instead of communicating with one receiver at a time, serve N (2-5) receivers concurrently

⎻ Randomly select N receivers with queued packets

⎻ Assign each sub-channel to a proper receiver

⎻ All the N receivers occupy the entire band

7

Frequency-Aware Rate Adaptation and MAC Protocols

Hariharan Rahul^†, Farinaz Edalat^ℵ, Dina Katabi^†, and Charles Sodini^†

†Massachusetts Institute of Technology ^ℵRKF Engineering Solutions, LLC

ABSTRACT

There has been burgeoning interest in wireless technologies that can use wider frequency spectrum. Technology advances, such as 802.11n and ultra-wideband (UWB), are pushing toward wider fre- quency bands. The analog-to-digital TV transition has made 100- 250 MHz of digital whitespace bandwidth available for unlicensed access. Also, recent work on WiFi networks has advocated discard- ing the notion of channelization and allowing all nodes to access the wide 802.11 spectrum in order to improve load balancing. This shift towards wider bands presents an opportunity to exploit frequency diversity. Specifically, frequencies that are far from each other in the spectrum have significantly different SNRs, and good frequencies differ across sender-receiver pairs.

This paper presents FARA, a combined frequency-aware rate adaptation and MAC protocol. FARA makes three departures from conventional wireless network design: First, it presents a scheme to robustly compute per-frequency SNRs using normal data trans- missions. Second, instead of using one bit rate per link, it en- ables a sender to adapt the bitrate independently across frequencies based on these per-frequency SNRs. Third, in contrast to traditional frequency-oblivious MAC protocols, it introduces a MAC protocol that allocates to a sender-receiver pair the frequencies that work best for that pair. We have implemented FARA in FPGA on a wide- band 802.11-compatible radio platform. Our experiments reveal that FARA provides a 3.1× throughput improvement in comparison to frequency-oblivious systems that occupy the same spectrum.

Categories and Subject Descriptors C.2.2 [Computer Sys- tems Organization]: Computer-Communications Networks General Terms Algorithms, Design, Performance

Keywords Wireless, Cognitive Radios, Wideband, Rate Adapta- tion, Cross-layer

1 INTRODUCTION

Wireless technologies are pushing toward wider frequency bands than the 20 MHz channels employed by existing 802.11 networks.

802.11n already includes a 40 MHz mode that bonds together two 20 MHz bands [23]. Emerging ultra-wideband (UWB) technolo- gies employ hundreds of MHz to support multimedia homes and offices [24, 50, 9, 40]. The FCC has recently permitted unlicensed

Permission to make digital or hard copies of all or part of this work for per- sonal 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 re- publish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee.

MobiCom’09, September 20–25, 2009, Beijing, China.

Copyright 2009 ACM 978-1-60558-702-8/09/09 . . . $10.00.

0 5 10 15 20 25 30

-40 -20 0 20 40

SNR (dB)

Freq (Mhz)

Figure 1: Frequency diversity across 100 MHz of 802.11a spec- trum as observed by two receivers for transmissions from the same sender. The figure shows that the SNRs of different frequen- cies can differ by as much as 20 dB on a single link. Further, different receivers prefer different frequencies.

use of digital TV whitespaces that occupy 100-250 MHz of spectrum vacated by television bands in the analog-to-digital transition [12].

Furthermore, recent empirical studies show that the 802.11 chan- nelization model which limits each node to a single 20 MHz chan- nel can lead to severe load imbalance [19, 28, 37]. They advocate discarding channelization and allowing all nodes to access the en- tire 802.11 spectrum based on demand [19, 37]. This push towards wider bands is further enabled by the constantly lowering prices of high-speed ADC and DAC hardware [38, 31].¹ In particular, today, wireless cards that span over 100 MHz of spectrum can be built us- ing off-the-shelf hardware components [35].

As wireless networks push towards wider bands, we can no longer afford to ignore frequency diversity. Specifically, multipath effects cause frequencies that are far away from each other in the spectrum to experience independent fading. Thus, different frequencies can exhibit very different SNRs for a single sender-receiver pair. Further, the frequencies that show good performance for one sender-receiver pair may be very different than the frequencies that show good per- formance for another pair. Fig. 1 shows empirical measurements of the SNRs across 100 MHz of the 802.11a spectrum, as observed by 2 clients for transmissions from the same AP (see §9 for exper- imental setup). The figure reveals that different frequencies show a difference in SNR of over 20 dB both for a single link and across links. Existing bitrate adaptation and MAC protocols however are frequency-oblivious. They assign the same bitrate to all frequencies and allocate the medium in a time-based manner, ignoring the fact that different frequencies work better for different sender-receiver pairs. Thus, current rate adaptation and MAC protocols can neither deal with the challenge nor exploit the opportunities introduced by the frequency diversity of wide bands or unchannelized 802.11.

1The wider the band, the faster the ADC and DAC have to sample the signal.

assign to the blue receiver

assign to the green receiver

Performance

• Compare with SampleRate in 20MHz and 100MHz channel

8 80

100 120 140 160 180 200

ate (Mbps)

SampleRate FARA

0 20 40 60 80

A1 A2 A3 A4 A5 B1 B2 B3 B4 C1 C2 C3 C4 D1 D2 D3 D4

Rate

Location

(a) Frequency-aware rate adaptation for a 100 MHz channel

10 15 20 25 30 35

Rate (Mbps)

SampleRate FARA

0 5 10 15 20 25 30 35

A1 A2 A3 A4 A5 B1 B2 B3 B4 C1 C2 C3 C4 D1 D2 D3 D4

Rate (Mbps)

Location

SampleRate FARA

(b) Frequency-aware rate adaptation for a 20 MHz channel

Figure 11: FARA Rate Adaptation: FARA’s frequency-aware rate adaptation achieves higher throughput than SampleRate’s frequency-oblivious rate adaptation at all locations, with gains vary- ing from 1.4× to 3.6× for a 100 MHz wide channel, and 1.1× to 1.5×for the 20 MHz channel.

9.3 Gains of Frequency-Aware Rate Adaptation

Now that we have established the existence of frequency diversity, its stability which makes it amenable to be harnessed by a rate adap- tation protocol, and the robustness of the mapping from SNR to op- timal bitrate, we measure the experimental gains from a frequency- aware rate adaptation protocol.

Method. Again we use the topology in Fig. 6. We fix the sender in location tx and randomly pick a receiver location. We repeat the experiment for all receiver locations shown in Fig. 6. For each loca- tion, we compare two schemes. The first is FARA’s frequency-aware rate adaptation as described in §6. The second uses SampleRate [5], a well known rate adaptation scheme that assigns the same bitrate to all subbands. Each run lasts for ten minutes, and is repeated five times. We look at the benefit of frequency-aware adaptation for two scenarios: a standard 20 MHz 802.11 channel, and a wide 100 MHz channel.

Results. Fig. 11 shows that FARA’s frequency-aware rate adap- tation achieves significantly higher throughput than a frequency- oblivious algorithm such as SampleRate. Specifically, for a stan- dard 20 MHz channel, a frequency-aware rate adaptation scheme increases the throughput by 1.24×. These gains become even higher as we move to wide and bonded channels, where FARA’s rate adap- tation improves the average throughput by 2.1× over SampleRate.

The throughput gain is larger for receivers with worse channels.

For example, some of the worse receivers experience a through- put gain that is as high as 3.5×. This is due to FARA’s ability to avoid bad frequency bands. Specifically, SampleRate’s frequency- oblivious rate adaptation experiences significant errors from sub-

0 0.2 0.4 0.6 0.8 1

0 0.5 1 1.5 2 2.5 3 3.5

Fraction of clients

Gain FARA CSMA MAC

FARA MAC

Figure 12: Gains from a Frequency-aware Architecture:The fig- ure plots two CDFs. The dashed line is the CDF of the ratio of client throughput under FARA to its throughput in traditional 802.11 networks which use SampleRate and CSMA MAC. The solid line is the CDF of the ratio of client throughput under FARA with a CSMA MAC and traditional 802.11 with SampleRate and CSMA.

The CDFs show that FARA provides on average 3× throughput gain.

70% of the gain comes from FARA’s frequency-aware rate adapta- tion, and 30% is due to its frequency-aware MAC protocol.

bands that have very low SNRs and hence cannot support even the lowest transmission rate. To compensate for such bad subbands, SampleRate has to drastically lower its average transmission rate and increase coding across all subbands. In contrast, FARA suppresses subbands with less than 3.5 dB SNR and does not need to reduce the rate of every subband to compensate for the extra errors from such bad subbands.

Also, the throughput gain for NLOS channels is typically higher than the gain for LOS channels, because these channels see higher frequency diversity due to the greater prevalence of multiple paths with similar attenuation. Interestingly, location A2 shows significant throughput gain even though it has a LOS channel to tx, because it is within a passage that provides multiple opportunities for reflected waves that together create significant frequency diversity.

9.4 Gains of Frequency-Aware MAC

We now examine the throughput improvement provided by a frequency-aware MAC over a frequency-oblivious MAC.

Method. We again use the topology in Fig. 6. We collect mea- surements by transmitting from node tx to four random receiver nodes. We consider only four concurrent receivers because we have a total of five radio boards (including the transmitter). However, we can experiment with various scenarios by choosing different receiver sets. We run the experiment 10 times for each set of receivers, and repeat for a variety of receiver sets. We compare two MAC pro- tocols: first, a frequency-oblivious CSMA MAC, where a sender checks whether the medium is available and transmits the packet at the head of its queue, and second, FARA’s frequency-aware MAC as described in §7. Note that FARA transmits four packets in every frame and hence has less medium sensing overhead. Thus, to ensure that the differences between the two MACs are due only to frequency diversity, and not medium access overhead, we allow the sender to transmit its packets without waiting for an idle medium. This opti- mization favors the baseline MAC, and is possible because we have only a single sender in each experiment. Note that both FARA and the CSMA MAC use the same spectrum of 100 MHz.

Results. Fig. 12 plots the CDFs of the ratio of the throughput in FARA to the throughput in traditional 802.11 which uses Sam-

80 100 120 140 160 180 200

ate (Mbps)

SampleRate FARA

0 20 40 60 80

A1 A2 A3 A4 A5 B1 B2 B3 B4 C1 C2 C3 C4 D1 D2 D3 D4

Rate

Location

(a) Frequency-aware rate adaptation for a 100 MHz channel

10 15 20 25 30 35

Rate (Mbps)

SampleRate FARA

0 5 10 15 20 25 30 35

A1 A2 A3 A4 A5 B1 B2 B3 B4 C1 C2 C3 C4 D1 D2 D3 D4

Rate (Mbps)

Location

SampleRate FARA

(b) Frequency-aware rate adaptation for a 20 MHz channel

Figure 11: FARA Rate Adaptation: FARA’s frequency-aware rate adaptation achieves higher throughput than SampleRate’s frequency-oblivious rate adaptation at all locations, with gains vary- ing from 1.4× to 3.6× for a 100 MHz wide channel, and 1.1× to 1.5×for the 20 MHz channel.

9.3 Gains of Frequency-Aware Rate Adaptation

Now that we have established the existence of frequency diversity, its stability which makes it amenable to be harnessed by a rate adap- tation protocol, and the robustness of the mapping from SNR to op- timal bitrate, we measure the experimental gains from a frequency- aware rate adaptation protocol.

Method. Again we use the topology in Fig. 6. We fix the sender in location tx and randomly pick a receiver location. We repeat the experiment for all receiver locations shown in Fig. 6. For each loca- tion, we compare two schemes. The first is FARA’s frequency-aware rate adaptation as described in §6. The second uses SampleRate [5], a well known rate adaptation scheme that assigns the same bitrate to all subbands. Each run lasts for ten minutes, and is repeated five times. We look at the benefit of frequency-aware adaptation for two scenarios: a standard 20 MHz 802.11 channel, and a wide 100 MHz channel.

Results. Fig. 11 shows that FARA’s frequency-aware rate adap- tation achieves significantly higher throughput than a frequency- oblivious algorithm such as SampleRate. Specifically, for a stan- dard 20 MHz channel, a frequency-aware rate adaptation scheme increases the throughput by 1.24×. These gains become even higher as we move to wide and bonded channels, where FARA’s rate adap- tation improves the average throughput by 2.1× over SampleRate.

The throughput gain is larger for receivers with worse channels.

For example, some of the worse receivers experience a through- put gain that is as high as 3.5×. This is due to FARA’s ability to avoid bad frequency bands. Specifically, SampleRate’s frequency- oblivious rate adaptation experiences significant errors from sub-

0 0.2 0.4 0.6 0.8 1

0 0.5 1 1.5 2 2.5 3 3.5

Fraction of clients

Gain FARA CSMA MAC

FARA MAC

Figure 12: Gains from a Frequency-aware Architecture:The fig- ure plots two CDFs. The dashed line is the CDF of the ratio of client throughput under FARA to its throughput in traditional 802.11 networks which use SampleRate and CSMA MAC. The solid line is the CDF of the ratio of client throughput under FARA with a CSMA MAC and traditional 802.11 with SampleRate and CSMA.

The CDFs show that FARA provides on average 3× throughput gain.

70% of the gain comes from FARA’s frequency-aware rate adapta- tion, and 30% is due to its frequency-aware MAC protocol.

bands that have very low SNRs and hence cannot support even the lowest transmission rate. To compensate for such bad subbands, SampleRate has to drastically lower its average transmission rate and increase coding across all subbands. In contrast, FARA suppresses subbands with less than 3.5 dB SNR and does not need to reduce the rate of every subband to compensate for the extra errors from such bad subbands.

Also, the throughput gain for NLOS channels is typically higher than the gain for LOS channels, because these channels see higher frequency diversity due to the greater prevalence of multiple paths with similar attenuation. Interestingly, location A2 shows significant throughput gain even though it has a LOS channel to tx, because it is within a passage that provides multiple opportunities for reflected waves that together create significant frequency diversity.

9.4 Gains of Frequency-Aware MAC

We now examine the throughput improvement provided by a frequency-aware MAC over a frequency-oblivious MAC.

Method. We again use the topology in Fig. 6. We collect mea- surements by transmitting from node tx to four random receiver nodes. We consider only four concurrent receivers because we have a total of five radio boards (including the transmitter). However, we can experiment with various scenarios by choosing different receiver sets. We run the experiment 10 times for each set of receivers, and repeat for a variety of receiver sets. We compare two MAC pro- tocols: first, a frequency-oblivious CSMA MAC, where a sender checks whether the medium is available and transmits the packet at the head of its queue, and second, FARA’s frequency-aware MAC as described in §7. Note that FARA transmits four packets in every frame and hence has less medium sensing overhead. Thus, to ensure that the differences between the two MACs are due only to frequency diversity, and not medium access overhead, we allow the sender to transmit its packets without waiting for an idle medium. This opti- mization favors the baseline MAC, and is possible because we have only a single sender in each experiment. Note that both FARA and the CSMA MAC use the same spectrum of 100 MHz.

Results. Fig. 12 plots the CDFs of the ratio of the throughput in FARA to the throughput in traditional 802.11 which uses Sam-

location location

100MHz 20MHz

Throughput gain is especially large as

the band is wider

Wireless Communication Systems

@CS.NCTU

Lecture 10: Rate Adaptation

Predictable 802.11 Packet Delivery from Wireless Channel Measurements (SIGCOMM’10)

Kate Ching-Ju Lin ( 林靖茹)

Motivation

• Again, different frequencies experience different channel condition à frequency-selective

• Why not FARA?

⎻ Need hardware modification

10

Frequency-Aware Rate Adaptation and MAC Protocols

Hariharan Rahul

^†

, Farinaz Edalat

^ℵ

, Dina Katabi

^†

, and Charles Sodini

^†

†

Massachusetts Institute of Technology

^ℵ

RKF Engineering Solutions, LLC

ABSTRACT

There has been burgeoning interest in wireless technologies that can use wider frequency spectrum. Technology advances, such as 802.11n and ultra-wideband (UWB), are pushing toward wider fre- quency bands. The analog-to-digital TV transition has made 100- 250 MHz of digital whitespace bandwidth available for unlicensed access. Also, recent work on WiFi networks has advocated discard- ing the notion of channelization and allowing all nodes to access the wide 802.11 spectrum in order to improve load balancing. This shift towards wider bands presents an opportunity to exploit frequency diversity. Specifically, frequencies that are far from each other in the spectrum have significantly different SNRs, and good frequencies differ across sender-receiver pairs.

This paper presents FARA, a combined frequency-aware rate adaptation and MAC protocol. FARA makes three departures from conventional wireless network design: First, it presents a scheme to robustly compute per-frequency SNRs using normal data trans- missions. Second, instead of using one bit rate per link, it en- ables a sender to adapt the bitrate independently across frequencies based on these per-frequency SNRs. Third, in contrast to traditional frequency-oblivious MAC protocols, it introduces a MAC protocol that allocates to a sender-receiver pair the frequencies that work best for that pair. We have implemented FARA in FPGA on a wide- band 802.11-compatible radio platform. Our experiments reveal that FARA provides a 3.1× throughput improvement in comparison to frequency-oblivious systems that occupy the same spectrum.

Categories and Subject Descriptors

C.2.2 [Computer Sys- tems Organization]: Computer-Communications Networks

General Terms

Algorithms, Design, Performance

Keywords

Wireless, Cognitive Radios, Wideband, Rate Adapta- tion, Cross-layer

1 I

NTRODUCTION

Wireless technologies are pushing toward wider frequency bands than the 20 MHz channels employed by existing 802.11 networks.

802.11n already includes a 40 MHz mode that bonds together two 20 MHz bands [23]. Emerging ultra-wideband (UWB) technolo- gies employ hundreds of MHz to support multimedia homes and offices [24, 50, 9, 40]. The FCC has recently permitted unlicensed

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0 5 10 15 20 25 30

-40 -20 0 20 40

SNR (dB)

Freq (Mhz)

Figure 1: Frequency diversity across 100 MHz of 802.11a spec- trum as observed by two receivers for transmissions from the same sender. The figure shows that the SNRs of different frequen- cies can differ by as much as 20 dB on a single link. Further, different receivers prefer different frequencies.

use of digital TV whitespaces that occupy 100-250 MHz of spectrum vacated by television bands in the analog-to-digital transition [12].

Furthermore, recent empirical studies show that the 802.11 chan- nelization model which limits each node to a single 20 MHz chan- nel can lead to severe load imbalance [19, 28, 37]. They advocate discarding channelization and allowing all nodes to access the en- tire 802.11 spectrum based on demand [19, 37]. This push towards wider bands is further enabled by the constantly lowering prices of high-speed ADC and DAC hardware [38, 31].¹ In particular, today, wireless cards that span over 100 MHz of spectrum can be built us- ing off-the-shelf hardware components [35].

As wireless networks push towards wider bands, we can no longer afford to ignore frequency diversity. Specifically, multipath effects cause frequencies that are far away from each other in the spectrum to experience independent fading. Thus, different frequencies can exhibit very different SNRs for a single sender-receiver pair. Further, the frequencies that show good performance for one sender-receiver pair may be very different than the frequencies that show good per- formance for another pair. Fig. 1 shows empirical measurements of the SNRs across 100 MHz of the 802.11a spectrum, as observed by 2 clients for transmissions from the same AP (see §9 for exper- imental setup). The figure reveals that different frequencies show a difference in SNR of over 20 dB both for a single link and across links. Existing bitrate adaptation and MAC protocols however are frequency-oblivious. They assign the same bitrate to all frequencies and allocate the medium in a time-based manner, ignoring the fact that different frequencies work better for different sender-receiver pairs. Thus, current rate adaptation and MAC protocols can neither deal with the challenge nor exploit the opportunities introduced by the frequency diversity of wide bands or unchannelized 802.11.

1The wider the band, the faster the ADC and DAC have to sample the signal.

Traditional SNR-based Adaptation

• SNR-based rate adaptation is usually inaccurate because we

⎻ Assume frequency-flat fading

⎻ Select the bit-rate based on “ average SNR” across subcarriers

• However, this will over-estimate the channel quality because

⎻ A packet will fail to pass the CRC check even if only a few bits are in error due to frequency-selective

fading

Traditional model: Packet SNR

• Traditional theory well maps the channel condition (SNR) to the corresponding bit-error rate (BER)

⎻ e.g., in BPSK

⎻ But, this only work for a narrow band channel

• The average SNR over all sub-carriers is not a good representation of a wideband channel

⎻ Why? The channel condition is not a linear function

⎻ The losses in a few subcarriers would lead to packet errors

12

BER = Q

✓ d

_min

p 2N

₀

◆

= Q( p

2SN R)

Traditional model: Packet SNR

• Packet SNR: Average power of a link / Noise power

• Due to frequency-selective fading, a link could have a higher packet SNR, but also have a high bit-error rate

13

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 reception 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 between rates (and so only three rates are shown for legibility).

Figure 1: Measured (single antenna) 802.11n packet delivery over wired and real channels.

into 312.5 kHz bands called subcarriers, each of which sends independent data simultaneously. 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. Convolutional coding is applied across the bits for error correction. The data rates depend on the combination of modulation and coding.

Our experimental platform uses 802.11n radios over 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 antennas for spatial multiplexing. By using MIMO processing, multiple streams can be sent and received at the same time, each at the single-stream rate, for higher overall rates. Note that the details of 802.11a/g di↵er slightly from single-stream 802.11n, 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 anal- yses of modulation schemes give delivery probability for a single signal in terms of the signal-to-noise (SNR) ra- tio [8], typically expressed on a log scale in decibels.

This model holds for narrowband channels with addi- tive white Gaussian noise. It predicts a sharp transition region of SNR over which a link changes from extremely

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 per- form about equally well at 52 Mbps. The faded links have larger RSSIs.

lossy to highly reliable. This makes the SNR a valuable indicator of performance.

RSSI values reported by NICs give an estimate of the total signal and noise power of a received packet. From it, the SNR can then readily be computed using NIC noise measurements. We generated performance curves using SNR for a real 802.11n NIC over a simple wired link with a variable attenuator and for a single transmit and receive antenna. The result is shown for all sin- gle antenna 802.11n rates in Figure 1(a). We observe a characteristic sharp transition region for packet recep- tion rate (PRR) versus SNR. This is despite the rela- tively wide channel (with 56 OFDM subcarriers), coding and other bit-level operations. This is the behavior we want 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 versus SNR for three sample rates (6.5, 26, and 65 Mbps) over all wireless 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 measurements that show RSSI does not predict packet delivery for real links [3, 19, 27, 28].

Impact of Frequency-Selective Fading. Many pos- sible factors cause the observed variability for real chan- nels, including NIC calibration, interference, sampling, and multipath. Here, we look at frequency-selective fad- ing due to multipath, as our experiments show this to be a major factor.

Multipath causes some subcarriers work markedly bet- ter than others. These channel details, and not sim- ply the overall signal strength as given by RSSI, af- fect packet delivery. Figure 2 illustrates this with the measured subcarrier gains for four di↵erent links in our testbed averaged over a 5-second run. All links deliver approximately 80% of the packets at 52 Mbps, but the fading profiles vary significantly across the four links.

One distribution is quite flat across the subcarriers. The other three exhibit frequency-selective fading, with two

3

Packet SNR

Errors

Effective SNR (ESNR)

• Can we find a metric that can be used to

⎻ Represent a wideband channel

⎻ Estimate the BER of the whole packet

• Average SNR vs. Effective SNR

⎻ Total power of a link vs. Useful power of a link

14

à Effective SNR (ESNR)

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 reception 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 between rates (and so only three rates are shown for legibility).

Figure 1: Measured (single antenna) 802.11n packet delivery over wired and real channels.

into 312.5 kHz bands called subcarriers, each of which sends independent data simultaneously. 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. Convolutional coding is applied across the bits for error correction. The data rates depend on the combination of modulation and coding.

Our experimental platform uses 802.11n radios over 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 antennas for spatial multiplexing. By using MIMO processing, multiple streams can be sent and received at the same time, each at the single-stream rate, for higher overall rates. Note that the details of 802.11a/g di↵er slightly from single-stream 802.11n, 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 anal- yses of modulation schemes give delivery probability for a single signal in terms of the signal-to-noise (SNR) ra- tio [8], typically expressed on a log scale in decibels.

This model holds for narrowband channels with addi- tive white Gaussian noise. It predicts a sharp transition region of SNR over which a link changes from extremely

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 per- form about equally well at 52 Mbps. The faded links have larger RSSIs.

lossy to highly reliable. This makes the SNR a valuable indicator of performance.

RSSI values reported by NICs give an estimate of the total signal and noise power of a received packet. From it, the SNR can then readily be computed using NIC noise measurements. We generated performance curves using SNR for a real 802.11n NIC over a simple wired link with a variable attenuator and for a single transmit and receive antenna. The result is shown for all sin- gle antenna 802.11n rates in Figure 1(a). We observe a characteristic sharp transition region for packet recep- tion rate (PRR) versus SNR. This is despite the rela- tively wide channel (with 56 OFDM subcarriers), coding and other bit-level operations. This is the behavior we want 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 versus SNR for three sample rates (6.5, 26, and 65 Mbps) over all wireless 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 measurements that show RSSI does not predict packet delivery for real links [3, 19, 27, 28].

Impact of Frequency-Selective Fading. Many pos- sible factors cause the observed variability for real chan- nels, including NIC calibration, interference, sampling, and multipath. Here, we look at frequency-selective fad- ing due to multipath, as our experiments show this to be a major factor.

Multipath causes some subcarriers work markedly bet- ter than others. These channel details, and not sim- ply the overall signal strength as given by RSSI, af- fect packet delivery. Figure 2 illustrates this with the measured subcarrier gains for four di↵erent links in our testbed averaged over a 5-second run. All links deliver approximately 80% of the packets at 52 Mbps, but the fading profiles vary significantly across the four links.

One distribution is quite flat across the subcarriers. The other three exhibit frequency-selective fading, with two

3

Packet SNR

Effective SNR

Effective SNR (ESNR)

• Benefits

⎻ Can accurately estimate the packet delivery rate of packets

⎻ Pick a single bit-rate that maximizes the packet delivery rate or the effective throughput in a wideband channel

• How to calculate?

⎻ Reuse the theoretical channel model derived in the textbook

⎻ Find the expected BER of a link

⎻ Then, convert it back to the effective SNR

15

narrow-band SNR narrow-band BER

effective SNR packet BER

Effective BER and Effective SNR

• First calculate the average BER of a selected modulation k across all subcarriers i

• Convert it back to the effective SNR

16

ESNR

_k

= BER

_k ¹

(BER

_e↵,k

)

BER

_k^-1

(): the inverse function BER

_k

()

BER

_e↵,k

= 1 N

X BER

_k

(SNR

_i

)

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

( )

BPSK 1 Q ⌅

2

QPSK 2 Q ⌅

QAM-16 4

³₄

Q ⇣p

/5 ⌘

QAM-64 6

₁₂⁷

Q ⇣p

/21 ⌘

Table 2: Bit error rate as a function of the symbol SNR 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 ) to bit-error rate (BER) for the modulations used in 802.11 [8]. CSI gives us the SNR values (

s

) to use for each sub- carrier. For a SISO system,

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

(

s

) (1)

eff,k

= BER

_k ¹

(BER

_eff,k

) (2)

We use BER

_k ¹

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

s,i

= 1/Y

ii

1, where Y = H

_s^H

H

s

+ I

¹

for i ⇤ [1, N]

and NxN 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

162

ESNR-based Rate Adaptation

• ESNR can be thought of the equivalent SNR of a wideband flat-fading channel

• Hence, now we are able to use ESNR to find the optimal rate by looking up the SNR-to-rate mapping table

17