AccuRate: Constellation Based Rate Estimationin Wireless Networks

Souvik SenDuke University

Naveen SanthapuriDuke University

Romit Roy ChoudhuryDuke University

Srihari NelakuditiUniversity of South Carolina

Abstract

This paper proposes to exploit physical layer informationtowards improved rate selection in wireless networks.While existing schemes pick good transmission rates,this paper takes a step further towards computing theoptimal bit rate. The main idea is to capture the chan-nel behavior through symbol level dispersions, and “re-play” these dispersions on different rate encodings ofthe same packet. The “replay” action can be emulatedat the receiver without requiring the transmitter to sendthe packet at every other rate. The maximum success-ful rate is likely to be the optimal rate of the receivedpacket, and assuming that the channel remains coherent,the same rate can be prescribed for the next transmis-sion. We design, implement, and evaluate this idea overa small testbed of USRP hardware and GNURadio soft-ware. Our proposal, called AccuRate, predicts a packet’soptimal rate 95% of times when the packet is receivedcorrectly. When the packet is received in error, AccuRatecomputes its optimal rate with 93% accuracy. In terms ofthroughput, we show that AccuRate improves over thestate-of-the-art scheme SoftRate by around 10%, and isreasonably close to the optimal.

1 Introduction

Rate estimation is an important problem because itdirectly translates to throughput. The difficulty in rateestimation stems from channel fluctuations – the optimalrate quickly becomes stale, requiring a fresh round ofestimation [1–3]. WiFi rate control is performed at thelink layer, and hence, must operate on the granularity ofpackets. Approaches such as ARF [4], RRAA [5], andSampleRate [2] continuously track the success/failureof packets, and employ statistical prediction methods toselect the appropriate rate. To improve responsivenessto channel fluctuations, alternate schemes have exploredthe use of SNR for rate selection. RBAR [6] andOAR [7] were the first-generation schemes that utilizedRTS/CTS to exchange SNR values. However, with

recent consensus to turn off RTS/CTS, new schemes arerecording historical SNRs and deriving a rate-versus-SNR relationship from it [8, 9]. While this improvesperformance, continuously refreshing the SNR for everyrate is often difficult [9]. Moreover, the rate-vs-SNRrelationship changes with different propagation envi-ronments, especially when the channel changes quicklyover time [1]. Therefore, although practical SNR-basedschemes are reasonably good at slower time-scales, theylack the agility to achieve per packet rate adaptaion indynamic wireless environments.

This paper proposes to exploit physical layer informa-tion (such as symbol level dispersion on a constellationspace) to improve the accuracy of rate selection. Weshow that such PHY layer information can be derivedfrom a received packet, and then used to compute theoptimal rate at which that packet should have been trans-mitted. Although the optimal rate is computed in retro-spect, it can be valuable for guiding the transmission rateof subsequent packets. Moreover, symbol level informa-tion can discriminate between losses due to fading andinterference, further assisting in link layer retransmissionstrategies. Our ideas are consolidated into a constella-tion based rate estimation scheme, called AccuRate. Weshow that the improvements from AccuRate are consis-tent over diverse wireless environments.

AccuRate’s main idea is intuitive. Given that the PHYlayer encodes a sequence of bits into a symbol on theconstellation space, AccuRate looks at the dispersionbetween the transmitted and received symbol positions.Small dispersions indicate that the communication linkis strong, and perhaps capable of supporting higher ratesthan the one used. By comparing these dispersions to thepermissible dispersions at different bit rates, AccuRatecan precisely derive the maximum rate the packet couldhave been transmitted at. Even when the packet fails,AccuRate extracts known parts of the packet (preambleand postamble [10]), and estimates the appropriate ratefrom them. Of course, this is a retrospective analysis of

a just-concluded transmission. However, as argued ear-lier, knowing the optimal rate of a received packet is avaluable primitive for rate control algorithms. The Accu-Rate receiver prescribes this rate to the transmitter, whichin turn uses it for the next transmission. So long as thechannel remains coherent between two consecutive pack-ets, AccuRate achieves a near-optimal rate selection ac-curacy.

This paper is not the first to use PHY layer informa-tion towards rate estimation. Recently, authors in [1]proposed SoftRate, a scheme that uses PHY layer con-fidence values to estimate a packet’s bit error rate (BER).By comparing the BER against an empirically generatedlookup table, the transmitter picks a “good” bit rate forsubsequent transmissions. While SoftRate makes a valu-able contribution, we show that there is room for im-provement. Specifically, we show that by directly op-erating on symbol constellations, AccuRate can “jump”to the optimal rate in one step, while eliminating thereliance on empirical measurements. Moreover, Ac-cuRate’s approach scales to arbitrarily high bit rates,and does not require large gaps between the consecutiverates. Experiments performed in a wireless channel sim-ulator [11] (where the channel conditions can be repeatedfor fair comparison) demonstrates that AccuRate reliablyselects the optimal rate. Similar experiments on a pro-totype USRP testbed show consistent throughput gainsunder various wireless environments. Together, theseresults confirm that AccuRate advances the state of theart through PHY-aware rate estimation. AccuRate’s keycontributions can be summarized as follows.

• Identify the opportunity of rate estimation us-ing symbol dispersion at the PHY layer. Weverify our ideas through measurements on theUSRP/GNURadio platform. The findings offer newinsights for further research at the link layer.

• Develop a constellation based rate estimationscheme (AccuRate) that “jumps” to the appro-priate rate. The wireless channel manifests itselfthrough symbol level dispersions. By “replaying”the dispersions on packets at different rates, Accu-Rate is able to identify the best bit rate of a packet.This bit rate is prescribed for future transmissions.

• Implement and evaluate AccuRate on a USRPtestbed, and on a emulation platform composedof USRPs and a wireless channel simulator. Re-sults from 25 hours of testbed experimentationshows consistent improvement in performance overexisting schemes. Emulation results (enabling ex-periments under controllable and repeatable chan-nel conditions) exhibit similar trends.

2 Related Work

Perfect bit rate selection in wireless networks is an elud-ing problem that has been researched extensively in thepast [1, 2, 4–9, 12–18]. Existing schemes have beenbroadly classified as frame-level or SNR-based, and hasbeen well surveyed in [1]. Here, we touch upon only therecent works relevant to AccuRate.

History based: SampleRate [2] by Bicket adapts trans-mission rate by periodically probing the channel withpackets at various bit rates. The idea is to adapt to chang-ing channel conditions and minimize the overall trans-mission time for the packets. In RRAA [5] the authorspropose faster rate estimation than SampleRate by usingloss information from short frame windows. Frame er-ror history based schemes like SampleRate and RRAAdo not distinguish between fading and collision whichis significant for rate estimation. This class of schemesare also slow to converge, and may not converge at all,if channel conditions change frequently. AccuRate dis-tinguishes between fading and collisions and has a one-packet convergence-time to estimate the best rate sup-ported by the channel.

SNR-based: Two recent SNR-based schemes take across layer approach to perform rate estimation. In[9], Camp and Knightly show that SNR-BER relation-ships change with the operating environment and there-fore need training to operate in a particular environment.They also compare existing SNR-based schemes withSNR-trained schemes to show that trained SNR schemesperform considerably better. In [17], the authors demon-strate the utility of adaptive modulation per frequencyband. The variation of channel characteristics across fre-quency sub-bands accentuates the effect in ultra wideband regimes which will benefit the most from suchschemes. To perform well these schemes need in-situtraining for each environment. AccuRate does not needany training or information about the environment.

Collision vs. Fading: Collision detection has been anarea of active research and lately several schemes havebeen proposed [19–23]. The scheme in COLLIE [20] al-lows a transmitter to distinguish between a fading and acollision loss by having the receiver send back the er-roneously received packet. This allows the sender toidentify the corrupt bits (via comparison with the orig-inal packet), and then analyze the cause of failure by an-alyzing the corruption patterns. Of course, the schemedepends on proper packet reception from the receiver ina timely manner. In [22], the authors propose a way todistinguish between collisions and fading, and adapt ratebased only on the errors due to fading. This scheme isstill history based and suffers from the same patholo-gies associated with other similar schemes. The useof OFDM symbol dispersions was shown in [23] as a

technique to distinguish between collision and fading.Our work goes beyond making this distinction by usingknown dispersions to select the correct rate.

SoftRate: The closest proposal to AccuRate is SoftRate[1], which was the first to exploit PHY layer informationfor rate estimation. We therefore focus on explaining thedifferences between SoftRate and AccuRate. SoftRateachieves high quality rate estimation using a cross layerapproach, but we believe there is room for improvement.Specifically, SoftRate estimates the rate supported by thechannel based on the BER of the received packet. TheBER is an average of SoftPHY confidence values, com-puted from the dispersion of the received symbols fromtheir nearest constellation symbols. SoftRate employs aheuristic to predict the BER at other bit-rates using theBER estimate at a given bit rate1. While this heuristiccan effectively indicate when the rate must decrease tothe next-lower bit rate (or increase to the next-higher bitrate), the ability to jump directly to the best rate is lim-ited. In contrast, AccuRate’s ability to replay the chan-nel distortion on all possible rates facilitates selection ofthe best rate in one step. The replaying mechanism isexpected to scale to bit rates at potentially finer granu-larity. However, unlike SoftRate, the hardware cost andimplementation complexity may be excessive. To bal-ance performance and complexity, one may envision acombination of AccuRate and SoftRate – a topic of fu-ture research.

3 Background and Observations

We present some background material on PHY layerencoding/decoding of bits with different modulationschemes. Building on this understanding, we observethat the extent of signal distortion due to channel fadingis independent of the modulation scheme. We validatethis through USRP/GNURadio measurements, and use itas a pivot for subsequently proposed ideas.

Figure 1: Symbol constellation for 16QAM: (a) Eachsymbol corresponds to a 4-bit sequence. (b) Symbolsreceived after suffering channel-induced dispersions.

1The heuristic exploits the empirical observation that, under a givenSNR, adjacent bit rates experience a factor of 10 difference in BER.

3.1 PHY Layer Symbol ConstellationsThe PHY layer encodes a sequence of bits into a PHYsymbol which is represented by a position on a 2Dcomplex plane called the constellation diagram. Figure1(a) shows an ideal constellation diagram from 16-aryquadrature amplitude modulation (16QAM). If the trans-mitter wishes to send a bit sequence “0000”, it sets theIn-Phase (x-axis) and Quadrature (y-axis) to a value of<−3,−3>. The receiver recovers the I and Q valuesafter demodulation, and plots each symbol on the IQplane. Since the channel distorts the transmitted signals,the received symbol positions get dispersed from theirideal positions. Let ~ri be the received symbol positionand ~si be its ideal symbol position. We define its disper-sion as ~di = ~ri−~si

~si. This is essentially the Error Vector

Magnitude (EVM) [24, 25], but for ease of understand-ing, we refer to it as dispersion. Figure 1(b) shows anexample of the dispersed symbols at the receiver.

To decode the symbols, for each received symbol po-sition, ~ri, the receiver guesses the corresponding idealsymbol position, ~si. A simple method is to pick the sym-bol that is closest to the received symbol position ~ri. Inother words, there is a tile associated with each symbolin the constellation. When a symbol ~si is received cor-rectly, its received position falls within the symbol’s tile,i.e., ~ri ∈ tile(~si). When all the symbols in a packetare received correctly, the corresponding bits will passthe CRC check and the packet is handed to the upperlayer.

With channel fading or interference from nearby trans-missions, the received symbol position ~ri may be quitefar away from the transmitted symbol position ~si. The re-ceived position ~ri may even fall outside the tile of ~si, i.e.,~ri /∈ tile(~si). Then, ~ri will be closer to another symbolposition than ~si, misguiding the receiver to believe thatsome other symbol was transmitted instead of ~si. Thiserror will be caught later when the CRC check on thepacket fails. Of course, channel coding techniques, suchas forward error correction (FEC), may be effective incorrecting some errors in demodulation. If the numberof errors are large, even channel coding may not be ade-quate to recover the packet.

3.2 Relation between Transmission Rateand Symbol Constellation Density

For ease of explanation, let us ignore channel coding fornow and assume that each symbol encodes the actualbits from the packet. Observe that a higher transmis-sion rate is realized by encoding a longer bit-sequenceon a symbol. Thus, if one increases the length of the se-quence from 2 to 4 bits per-symbol, the constellation di-agram must also accommodate a greater number of sym-bols (from 4QAM to 16QAM). In other words, the den-

Q

I

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I

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Figure 2: Symbol density increases with increasing data rates (BPSK, QPSK (or 4QAM), 16QAM, 64QAM).

sity of symbols in the constellation diagram increases athigher rates as shown in Fig. 2. Since increased den-sity implies shorter distance between neighboring sym-bols, the received packet is more susceptible to errors athigher rates when the channel is weak. Figure 3 confirmsthis by showing that the maximum tolerable BPSK error(|si − ri|) can be twice that of QPSK (or 4QAM), andfour times that of 16QAM. This well-known observationwill underlie the design of AccuRate.

BPSK

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Figure 3: Lower rates can tolerate higher magnitude ofsymbol dispersion

3.3 Relation between Dispersion due toChannel Fading and Bit Rate

We now demonstrate that symbol dispersion is not influ-enced by the modulation scheme (or transmission rate),and is only a function of the channel. We transmit datafrom a static USRP sender to a static USRP receiver us-ing 2, 4, 16, and 64 QAM. We maintain as much coher-ence in the channel as possible (by keeping the physicalenvironment static), and transmit small packets repeat-edly using different modulation schemes in a round robinmanner. For every received symbol, we calculate its dis-persion from the correct constellation symbol2. Figure 4plots the CDF of symbol dispersion magnitude for eachmodulation scheme for packets transmitted in one round.

2The correct constellation symbol is known because the transmittedpacket is known in our experiments. Thus, even when a packet fails,we can still compute the correct dispersions.

Almost-identical curves provide evidence that the disper-sions are independent of the symbol constellation, andtherefore the transmission rate. More detailed experi-mental evidence is presented in [25].

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Figure 4: CDF of symbol dispersion magnitude for pack-ets transmitted with different modulation schemes. Notall packets were received correctly, but their dispersionscould be computed offline using the (known) transmittedpacket.

These observations enable us to model the channel be-havior based on the dispersion of known symbols at thereceiver. The receiver can then conduct a what-if analysisby “replaying” the channel on a packet encoded at differ-ent rates. For instance, Fig. 5(a) shows the dispersionof symbols when a packet was transmitted using 4QAM.Given that the dispersion is independent of the modu-lation, the receiver can check whether a higher modu-lation such as 16QAM with denser constellation couldhave tolerated the same level of dispersion. In otherwords, 16QAM is feasible if all the received symbols ineach 4QAM quadrant can be accommodated in a smaller16QAM tile (drawn with dashed grids) as in Fig. 5(b).The original 16QAM grid, as shown in Fig. 7 has beenshifted and superimposed on Fig. 5(b) for the purposeof demonstration. In this example, 16QAM is not feasi-ble since some received symbols spill out of their correcttile. More generally, this shows that the outcome of a16QAM transmission may be predicted without actuallytransmitting the packet over the air. Repeating this overall possible bit rates will reveal the best possible rate for

-1 -0.7 0.7 1

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Figure 5: Receiver checks if QPSK (4QAM) packetcould have sustained higher bit rate (16QAM).

this just-received packet3. Such a retrospective analysiscan guide us in subsequent rate control decisions. Thedetails on how this hindsight is leveraged is described inthe following sections.

4 Determining The Optimal TransmissionRate in Retrospect

We now explain how a receiver can determine from areceived packet, what could have been the optimal rate,for transmitting that packet. A high level schematic ofthe procedure is depicted in Fig. 6. We present the ratecomputation method for three cases: (1) when the packetis received successfully, (2) when the packet fails due tofading, and (3) when the packet fails due to interference.We support our basic claims with measurements from theUSRP testbed.

4.1 In Case of Successful Packet ReceptionLet us first consider the case where a packet is suc-cessfully received. Since all the bits are decoded cor-rectly, the receiver is aware of all the transmitted sym-bols. Hence, it can compute the dispersion ~di, between

3The what-if analysis with “replay” operation is applicable evenwith channel coding as discussed later in Section 4.1.1

Figure 6: Flowchart of determining the optimal rate inretrospect.

each transmitted symbol position ~si and received sym-bol position ~ri. Assuming N symbols in the packet, thechannel can then be characterized by ~D, a sequence ofdispersions, i.e., ~D = {~d1, ~d1, · · · ~dN}. Now, supposethe packet was transmitted at a bit rate of R. Given thatit was received successfully, it is clear that the symbol-constellation density corresponding to R can tolerate thedispersion ~D. Now the question is what is the highestrate, R∗ (≥ R), at which the transmission would havebeen successful over a channel with dispersion sequence~D.

Note that, as argued before, ~D is independent of themodulation used by the transmitter, i.e., the i’th sym-bol gets dispersed by ~di regardless of whether that sym-bol is from the constellation of BPSK, QPSK, 16QAM,or 64QAM. Consequently, the receiver can analyze theoutcome of different modulations without requiring thetransmitter to explicitly send the packet once per eachmodulation. The procedure to check whether a transmis-sion at a higher modulation would be successful is as fol-lows. For each symbol i, we apply the dispersion vector~di on its ideal position ~si in the constellation space andcheck if the resulting symbol position would still be cor-rectly decoded. If that position happens to be closer tosome other constellation point (i.e., in some other tile),this constellation is too dense for this dispersion. Inthis manner, the most-dense constellation is chosen inwhich, for each symbol i, ~di is completely contained inthe same tile. Figure 7 illustrates this checking opera-tion – a symbol received through BPSK modulation isbeing tested against a 4QAM and 16QAM constellation.In this example, the channel-induced dispersion can betolerated by a 4QAM symbol, whereas a 16QAM sym-bol will not be decoded correctly as it’s received positionfalls in the wrong tile. Ignoring error coding, this impliesthat 16QAM is an inappropriate rate for transmitting this

packet. However, 4QAM may prove to be suitable, pro-vided all the symbols in the packet passes this test suc-cessfully.

di

di

di

si

ri

si

ri

si

ri

Figure 7: Computing the appropriate rate at which thispacket reception would have been successful. In this caseBPSK and QPSK will be successful where as 16QAMwill not.

4.1.1 Error Correction with Channel Coding

We now introduce the role of channel coding in rate com-putation. Briefly, channel coding helps in error correc-tion by including redundant bits in the packet. Somesymbols may fall in the incorrect tile on the constellation,but channel coding may still be able to correct them. Thisimplies that coding can allow for a denser constellation,at the expense of a larger packet size. The net result is anew intermediate rate between the sparse and the denseconstellation. To clarify with an example from 802.11g,4QAM results in 24Mbps. However, data rate 18Mbpscan be achieved if the 4QAM modulation is combinedwith a 3/4 coding scheme. Thus, channel coding allowsfor additional data rates, offering finer-grained choices tothe rate selection algorithm.

With coding, our goal then is to precisely identify thebest <modulation, coding> tuple at which this packetwould have been successful. For this, the receiver con-siders every higher modulation scheme, and computesthe fraction of symbols that would have been in error.Note that the higher the modulation, the more the num-ber of errors, and the larger the number of redundant bits.Suppose a modulation M1 needs 3/4 coding to correcterrors and a higher modulation M2 requires more redun-dant 1/2 coding. Let R1 and R2 be the rates correspond-ing to M1 and M2 respectively. Then, the effective rates(after accounting for the overhead due to coding) wouldbe 3

4R1 and 12R2. The higher effective rate is then chosen

as the best rate in retrospect, i.e.,R∗ = max(34R1,

12R2).

Besides offering bit rates at finer granularity, channelcoding also allows for precisely computing the symboldispersions. If a packet is known to pass the CRC check,the exact dispersion can be computed for all the symbolsin that packet. These dispersions can then be recordedand replayed on higher-rate packet encodings to estimatethe best bit rate. Observe that a packet may be success-ful even if some replayed dispersion causes the symbol tofall in an incorrect tile – channel coding may absorb theseerrors, similar to over-the-air reception. In other words,

so long as the dispersions are precisely known, the re-playing operation is no different from an actual transmit-receive operation. As will be clear from Section 5.2, eventhe same hardware chain may be reused for both the ac-tual reception and the replayed operation. This impliesthat, as long as a packet is received correctly, AccuRatecan retrospectively compute its optimal bit rate, and useit for the subsequent transmission.

4.2 In Case of Packet Loss due to Fading

Let us now consider the case where a packet is not re-ceived correctly, and the receiver has to find the smallestrate reduction that would have resulted in a successfulreception. This is more challenging because, unlike theabove case, the receiver does not know the actual trans-mitted symbol ~si for every received symbol position ~ri.Since the packet failed the CRC check, some ~ri musthave been outside the tile of the correct symbol ~si andinside the tile of some other symbol. The receiver doesnot know which of the symbols are incorrectly decodedand so it can not precisely compute for each symbol thedispersion ~di caused by the channel.

Fortunately, each packet starts with a preamble, a glob-ally known sequence of bits, that the receiver uses todetect and synchronize onto a newly arriving signal.The receiver can utilize the preamble to estimate disper-sion [26]. Suppose the preamble consists of k symbolsand their computed dispersions are ~dpre

1 , ~dpre2 , · · · , ~dpre

k .We subject this sequence of k dispersions to the wholepacket, i.e., we compute the dispersion for i’th symbolin the packet as ~di = ~d

prei%k. Given this set of ~di vectors,

we try to estimate the optimal rateR∗ using the same ap-proach as described earlier.

The preamble’s symbol dispersions will only capture thechannel behavior in the earlier parts of the packet. If thechannel changes over time, the later changes will remainunquantified. Therefore, to better cope with channel vari-ations, a postamble [10] may be inserted at the end of thepacket. Suppose the postamble also consists of k sym-bols and their dispersions are ~d

post1 , ~d

post2 , · · · , ~dpost

k .Given the original packet size of N symbols, and a ran-domly generated packet of N or more symbols, we sub-ject the ith symbol in the random packet to a dispersion~di, computed as follows: If i < N

2 , then ~di = ~dprei%k, else

~di = ~dposti%k . The rationale is that the preamble is a bet-

ter representative of the first half of the original packetduration, while the postamble is better for the rest of theduration. Also, when the random packet is encoded at alower rate, the number of symbols increase. The postam-ble is likely to be a better estimate of the channel forthese symbols as well. Once again, based on ~di vectorsobtained thus, we try to estimate the optimal rate of the

packet, R∗. The overhead of postamble would be jus-tifiable if that leads to throughput improvements due tobetter rate estimation.

4.3 In Case of Packet Loss due to Interfer-ence and Fading

Rate selection must be approached somewhat differentlywhen interference is the cause of packet failure. Underinterference only, the transmitter should ideally backoffand transmit at the same rate. Under both interferenceand fading, the ideal approach is to backoff but transmitat a rate that accounts for the channel’s fading compo-nent. We approach this problem by looking at both thepreamble and the postamble. The presence of a preambleand postamble in a packet offers multiple “glimpses” intohow the channel varied during packet reception. Becauseboth preamble and postamble are known, the receivercomputes their respective dispersion vector sequences~Dpre and ~Dpost. Using statistical methods, we com-pute the similarity of these sequences (detailed in Section6). If there was no interference, ~Dpre and ~Dpost wouldbe similar and the loss is attributed to fading. Other-wise, depending on whether the interference overlappedwith the preamble or postamble, ~Dpre or ~Dpost wouldexhibit a higher dispersion than the other. If rate mustbe selected only in response to channel fading, then wemust select R∗ based on min( ~Dpre, ~Dpost). Of course,when the interference overlaps with both the preambleand the postamble, ~Dpre and ~Dpost will be similar, andour approach will incorrectly select a lower-than-optimalrate. Also, if the interfering packet is small enough tofit within the preamble and postamble of a transmission,AccuRate will fail to prescribe backoff although it willstill estimate the rate induced by fading alone. One wayto alleviate this problem is to insert known ”midambles”in different parts of the packet thereby allowing for mul-tiple glimpses into the channel behavior. We discussthese possibilities in section 7.

4.4 Experimental ValidationThe above approach, AccuRate, raises a few obviousquestions about its feasibility and performance. How ac-curately can a receiver determine the optimal rate in ret-rospect? Is the preamble sufficient or the postamble alsonecessary for estimating the rate in case of packet lossdue to fading? To answer these questions, we conductedexperiments on a Rayleigh fading channel simulator [11]and a real testbed. The evaluation setting is described indetail in Section 6. Briefly, in the simulator we froze thechannel parameters for a Rayleigh fading model in GNU-Radio and computed the ideal rate R̂ (by transmitting atall rates). Next, we allowed the receiver to determine theoptimal rate R∗ from the received packet under identicalchannel conditions. We repeated this experiment with

different channel parameters and transmit powers. Over-all, we compared R̂ and R∗ for more than 2000 pack-ets. Fig. 8(a) shows the comparison by plotting the dif-ference between R∗ and R̂ rate levels (e.g., successive802.11 bit rates such as 24 Mbps and 18 Mbps are sep-arated by 1 rate level). These results indicate that whenthe packets are received correctly, R∗ = R̂ for every in-stance. Even with preamble alone, AccuRate can deter-mine the rate correctly in 80% of the cases, and the ad-dition of postamble improves the accuracy to 95%. Thepostamble samples help AccuRate better estimate wire-less channel coefficients using symbol dispersion. Weobserved similar results over a real wireless channel be-tween a USRP/GNURadio transmitter and receiver pair– Fig. 8(b) shows these results.

The above description and supporting results offer rea-son to believe that symbol dispersion information gath-ered from a received packet can be used to estimate thepacket’s optimal rate. Considering that the channel co-herence time is expected to be in the order of multiplepackets, the receiver can prescribe the same rate for thesubsequent transmission. One could argue that the op-timal rate for the previous packet may not be optimalfor the next packet or may even cause packet loss. Butnote that every rate adaptation scheme has to speculatethe future channel conditions based on the past measure-ments. Any scheme that is not overly conservative andattempts to extract the best throughput from the channelruns the risk of packet loss. However, since our approachis based on fine grain information about the channel, thenext packet has a reasonable chance of succeeding at theprescribed rate. In the following section, we gather ourideas into a single Constellation Based Rate estimationprotocol, called AccuRate.

5 AccuRate Protocol and Implementation

5.1 ProtocolThe AccuRate module is located at the boundary ofthe PHY and MAC layer. For every outgoing frame,AccuRate concatenates it with a postamble. Upon re-ception of this packet, the AccuRate receiver performsthe following checks and reacts accordingly. If thepacket is correctly received, AccuRate estimates the besttransmission rate, and piggybacks it in the acknowledg-ment (ACK). If the packet is incorrectly received (mean-ing that the preamble was decoded but the CRC checkfailed), AccuRate triggers an interference-detection op-eration. Learning that the failure was not due to interfer-ence, AccuRate estimates the appropriate rate using onlythe pre/postambles [1], and conveys this back througha negative acknowledgment (NACK). However, if inter-ference was the cause of failure, AccuRate performs rateestimation using either the interference-free preamble orpostamble, depending on which exhibits lower symbol

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Figure 8: Accuracy of determining the optimal rate in retrospect: (a) simulation; (b) test bed. The x-axis is expressedin rate levels, where two successive 802.11 rates are assumed to have a rate level difference of one. The AccuRate-correct-packets and AccuRate-pre+postamble curves overlap. These results correspond to channel conditions withfading but without interference (impact of interference on AccuRate is evaluated in Section 6). The optimal rate in thetestbed scenario is determined by sending a train of small packets at all possible rates. (details in Section 6.1)

.

dispersion. AccuRate conveys this fading-induced ratein the NACK, but also instructs the transmitter to back-off according to regular 802.11. In the worst case, ifthe packet’s preamble itself is non-decodable, AccuRatecannot perform any rate prediction. The transmitter doesnot receive any ACK/NACK, and retransmits the packetas per the 802.11 specifications. In all other cases, thetransmitter adopts AccuRate’s rate and backoff prescrip-tions, and prepares accordingly for the next transmissionto the same receiver.

5.2 ImplementationAccuRate builds on the OFDM codebase for theUSRP/GNU-Radio platform. We adopt the publiclyavailable building blocks of SoftRate (like the BCJRdecoder [27]) for building AccuRate. This facilitates aplatform for fair comparison between the two. 802.11a/gspecified modulation schemes and channel coding ratesare used (Table 1) in an attempt to emulate 802.11 likescenarios. The transmitter encodes the data using astandard rate-1/2 convolutional encoder, and appliespuncturing to achieve varying code rates. The bandwidthis fixed at 20 MHz for GNURadio simulations and at2 MHz for testbed experiments. We have incorporateda Rayleigh fading channel simulator [11] into theGNURadio codebase. The OFDM implementation usesan FFT length of 1024, with 394 occupied tones, 8 pilottones and a cyclic prefix of length 256.

Figure 9 presents the block diagram for AccuRate’s im-plementation in GNURadio. SoftRate is also shown as acomparison point, especially because the two schemesuse very similar modules. In SoftRate, an incomingpacket is demodulated and passed through the BCJR

decoder. The output of the BCJR decoder comprisesthe data bits and their respective confidence values.These are passed through a BER computation module,resulting in the actual packet and its single BER. TheSoftRate estimation algorithm runs in the “Select Rate”module, which picks the packet’s rate by comparing theBER against a BER-Rate relationship curve. The finaloutput, R∗

SoftRate, is SoftRate’s prescribed rate.

We note that AccuRate uses a similar module chain witha few augmentations. When the over-the-air packet ar-rives, AccuRate measures the symbol level dispersionsfrom the demodulator and stores it in the Build Disper-sion Model module. This module uses the correctly re-ceived packet to calculate the accurate per-symbol dis-persion4. In addition, a random packet is generatedand encoded at different rates (R1, R2, ...Rn). Symbolsfrom each rate-encoded packet are then subjected to therecorded dispersions, and the output is passed throughthe demodulator. Although Figure 9 shows the opera-tions in parallel (incurring an additional hardware cost),we use a single chain in our GNURadio implementationand iterate over all possible rate encodings (imposing ahigher processing latency). The output of the demodula-tor, denoted Demod, is fed into the BCJR decoder. Theoutput bits are collected into a frame and checked forCRC (the confidence values are not used in AccuRate).If the CRC check passes at that rate, AccuRate deems thecorresponding rate to be successful. AccuRate picks themaximum of all successful rates, and prescribes it for thesubsequent transmission.

4If the over-the-air packet failed, the dispersion sequence is suitablybuilt from the preamble and postamble only.

R*

AccuRate

R*SoftRate

Mod/Encode

Channel

BCJR

DecoderBER

Select

Rate

BER-Rate

Build

Random

Packet

Build

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Model

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at rate r1

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at rate rn

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at r1

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at rn

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SoftRate

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Correct bits

Figure 9: Block diagram of AccuRate

Table 1: 802.11 Modulation and coding used in Accu-Rate (20Mhz channel)

Modulation Coding 802.11 rate (implemented?)BPSK 1/2 6 Mbps (yes)BPSK 3/4 9 Mbps (yes)QPSK 1/2 12 Mbps (yes)QPSK 3/4 18 Mbps (yes)

16QAM 1/2 24 Mbps (yes)16QAM 3/4 36 Mbps (yes)64QAM 2/3 48 Mbps (no)64QAM 3/4 54 Mbps (yes)

6 Evaluation

6.1 Methodology

We faced two challenges while evaluating AccuRate. (1)The wireless channel changes over time making it diffi-cult to determine what could have been the optimal ratefor a given transmission. (2) The high latency incurredin procuring RF samples from the USRP front-endmakes it impractical to evaluate AccuRate in realtime.In view of these, we make two approximations in ourexperimentation methodology. First, we incorporate aRayleigh fading simulator into the GNURadio codebase.The simulator [11] employs the same USRP/GNURadiotransmitter and receiver, only connects them througha loopback configuration. Packets flow out of the

transmitter, and instead of advancing through the wire-less channel, they are made to flow through simulatedchannel conditions. The output of the channel simulatoris presented to the receiver which then executes regulardemodulation/decoding. Since the simulated channelconditions can be forced to remain unchanged, weare able to compare the optimal bit rate for a giventransmission against those prescribed by AccuRate andother schemes.

Our second approximation is designed to test the perfor-mance of AccuRate over real wireless channels. To thisend, we repeatedly transmitted trains of packets, eachtrain comprising of 7 short packets (each 200 bytes) atincreasing bit rates. Assuming that the channel is co-herent for the duration of the packet train, we determinethe optimal transmission rateR∗ by recording the highestbit rate successful in that train. Now, AccuRate picks arandom packet in the first train, predicts the optimal ratefor that packet R∗

AccuRate. The operation is performedoffline – the difference between R∗ and R∗

AccuRate char-acterizes AccuRate’s rate selection accuracy. Moreover,the packet corresponding to R∗

AccuRate in the next trainis also selected, as if that’s the transmission that Accu-Rate would have executed. This packet’s transmission atR∗

AccuRate is then used to predict the subsequent trans-mission rate, and so on. The throughput is computedbased on the success/failure of the packets selected ineach train. SoftRate’s performance is also compared in

these settings. Thus, while simulators provide faithfulcomparisons under approximate channel models, packet-train based evaluations attempt to achieve the converse.We believe that together, these experiments provide a faircomparison between AccuRate, SoftRate, and the Opti-mal rate selection algorithms.

6.2 Performance ResultsWe have designed experiments to answer the followingkey questions about the performance of AccuRate. (1)What is AccuRate’s rate estimation accuracy comparedto the optimal rate and other existing schemes? (2)How does the accuracy vary under different channelconditions? (3) How well does AccuRate discriminatebetween fading and interference? How does interferenceaffect rate selection? (4) What is the accuracy of rate es-timation based on preamble and postamble dispersions?

To understand AccuRate’s performance against existingschemes, we also evaluate SoftRate and SNR-based rateestimation. SNR-based rate uses the SNR feedback topick the transmission bit rate. The SNR-rate relationshipis derived a priori from a wide range of empirical mea-surements on USRP/GNURadios.

Rate Selection AccuracyWe evaluated the accuracy of rate estimation by Accu-Rate and other schemes in both slow fading (walking)and fast fading (driving) scenarios as described below.

Slow Fading: We induced slow fading by movingthe USRP transmitter on a wheeled chair, while it istransmitting to a fixed USRP receiver. We transmitted500 packet trains where each train has one packet perrate. We repeat this experiment 10 different times andthus resulting in a total of 5000 packet transmissionsper each bit rate. Figure 10(a) shows the results ofthese testbed experiments by plotting the CDF of theestimation accuracy. A negative value of the differencebetween estimated rate and optimal rate indicates under-selection and a positive value indicates overselection.AccuRate selects the optimal rate nearly 95% of thetime, which is around 10% and 20% better than SoftRateand SNR-based scheme respectively. We also conductedsimulations by setting the channel parameters to reflectslow fading. In this case, as shown in Figure 10(b),AccuRate is always optimal and again performs betterthan the other two schemes. Based on these results, weconclude that AccuRate estimates the rate with highaccuracy under slow fading.To get a sense of how well the predicted rate by Accu-Rate tracks the optimal rate in a time varying channel,we take a closer look at AccuRate rate selection. Weplot the AccuRate rate and optimal rate at each point fora 300 train snapshot in Figure 11. Clearly, AccuRate

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Figure 10: Rate selection accuracy under slow-fadingmobility: a) Testbed vs (b) Simulation results. The X-axis shows the difference in discrete rate levels.

tracks the optimal rate curve reasonably well.

Fast Fading: Doppler effects at vehicular speeds causefast fading in wireless channels. We examine Accu-Rate’s performance by simulating such conditions in theRaleigh Fading channel simulator for GNURadio [11].This simulator implements detailed channel modelsincluding multipath. The inputs (and outputs) to thissimulator are drawn from (and sent to) GNURadio. Thesystem parameters are configured to emulate variouschannel coherence conditions. Doppler Shift is variedbetween 400Hz to 4KHz, translating to channel coher-ence time of 1ms to 100 µs. This captures the range ofmobile channel conditions. We sent 25000 packets ofsize 700 bytes for each Doppler Shift. The channel isreplayed for every scheme for performance comparison.

We present the rate selection accuracy for each schemeunder varying channel coherence time in Table 3. Weshow only the accurate and over-selection percentagesand omit the under-selection percentages (which canbe inferred as they total 100%) for clarity. SNR-basedschemes underestimate or overestimate the rate in

Coherence Time1ms 500µs 200µs 100µs

Scheme Accuracy Over-Select Accuracy Over-Select Accuracy Over-Select Accuracy Over-SelectAccuRate 98% 1% 98% 1% 97% 2% 95% 3.1%SoftRate 83% 0% 86% 6% 78% 4% 80% 14%

SNR 79% 14% 57% 21% 60% 24% 54% 18%

Table 2: Rate selection accuracy under various fading conditions (simulated).

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GN

UR

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Rat

e

Packet Number

Testbed

Optimal RateCBAR Estimated Rate

Figure 11: Close-up of AccuRate rate selection under time varying channel.

around 40% of the cases when the coherence time isless than 1ms. This is due to the changes in SNR-BERrelationship with the change in coherence time. Also,SNR is calculated only during the preamble which doesnot capture the entire packet duration. The accuracy ofAccuRate and SoftRate remains relatively consistentacross different coherence times, though AccuRate stilloutperforms SoftRate by around 12%. This is an effectof fast-changing channel conditions, requiring a rateestimation scheme to jump multiple levels in one step.AccuRate executes these jumps effectively.

Interference Detection and Rate Selection: Rateestimation under interference is a challenging problem.A receiver must first detect that there is interference. Itshould then estimate the dispersion due to fading aloneto determine the best rate for the packet under fading.Existing schemes have focused on discriminating be-tween fading and interference, and have proposed tobackoff when losses are due to interference. AccuRatetries to characterize fading even in case of interferencelosses [1], and account for fading alone in rate prescrip-tion. To evaluate these capabilities, we first evaluateAccuRate’s accuracy in detecting interference, followedby rate selection under both interference and fading.Interference Detection AccuracyIn our experiment, we varied the position and power ofthe transmitter and interferer to obtain various realistictopologies. As a result, the SINR varies from 0 to12 dB. We ensured that the primary link has highpacket delivery probability (≥ 0.9) in the absence ofinterference. Now, under interference, we considered

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Figure 12: Interference detection accuracy for differenttransmission bit-rates

the packets that failed the CRC check. We compute thesymbol dispersion distributions Dpre and Dpost for thepreamble and postamble of the CRC-failed packet. Weattribute the loss to interference if these distributionsare not “similar”. Two distributions are declared similarif more than 50% of samples of one distribution fallswithin three sigma limits of the other distribution (wemodel the dispersions with a Gaussian distribution).Figure 12 presents the detection accuracy results forvarying transmission rates. AccuRate’s interferencedetection accuracy is slightly lower than SoftRate forlow bit rates. This is because low bit rates can toleratehigh dispersion and therefore dispersions of preamble

and postamble tend to be similar even in case of aloss with interference. On the other hand, AccuRateperforms much better than SoftRate at higher rates andaccurately diagnoses loss in more than 95% cases.

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Figure 13: Rate prescription accuracy in the presence ofinterference: (a) SoftRate; (b) AccuRate.

Rate Estimation Accuracy with InterferenceWhen interference is detected by AccuRate, it estimatesthe rate supported by the channel under fading alonebased on the lower of the dispersion values amongpreamble and postamble. Fig. 13 compares the ratesprescribed by SoftRate and AccuRate with the optimalrates. In the presence of interference, SoftRate’s estima-tion of the rate supported by the channel is not optimalin 20% to 30% of the cases. Whenever SoftRate failsto identify interference, it computes a conservative rate.AccuRate does not perform well at lower rates either (asexplained above), but is still better than SoftRate. Onthe other hand, AccuRate performs quite well at highertransmission rates as it prescribes the best rate in above92% cases. These results show that AccuRate is quiterobust under varying channel conditions with slow/fastfading and with/without interference.

ThroughputThe projection of effective rate selection on the link’sthroughput is of interest. Figure 14 compares thethroughput between AccuRate, SoftRate, and SNR-based rate estimation. The simulation results in Figure14(a) are obtained for varying channel coherence times.As expected, all schemes suffer performance degrada-tion with shorter coherence times. However, AccuRate’sability to pick the optimal rate from correctly receivedpackets permits the subsequent packet to succeed aswell. This is a positive feedback that results in goodperformance, particularly because a large fraction of thepackets are received correctly. SoftRate outperformsSNR-based rate selection, but still remains below theAccuRate throughput.

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Figure 14: Throughput comparison under (a) simulatedslow fading channels, (b) walking experiments on theUSRP/GNURadio testbed.Figure 14(b) shows the throughput comparison fromtestbed experiments (the receiver was moved with walk-ing speeds). We briefly summarize the experimentmethodology here. Recall that 7 short back-to-backpackets (called a packet-train) are being repeatedly trans-mitted to determine the optimal rate during each train.For a packet-train Ti, say packet j’s rate was estimated

by AccuRate, denoted as R∗ij . Now, for packet-train

Ti+1, the short packet that was transmitted at rate R∗ij is

selected. Observe that, when running as a full system,this is the packet that AccuRate would have transmit-ted. Now, if R∗

ij was an incorrect estimate, this packetin Ti+1 would be received in error, implying that Ac-cuRate would have to make the next estimate based onthis erroneous packet. Continuing this process, we com-pute the number of packets successfully received at thereceiver, and the total time incurred for their transmis-sions. The throughput for SoftRate and SNR-based-Rate are also computed as above. The Optimal through-put is computed based on the highest achievable rate ineach packet-train. Evidently, AccuRate consistently out-performs SoftRate and SNR, except in a few occasionswhere the performances are comparable. On average,AccuRate achieves 87% of the optimal throughput pos-sible while SoftRate accomplishes 75%. We summarizeby observing that SoftRate leaves a small room for im-provement, and AccuRate makes that room even smaller.

Efficacy of Pre/Postamble based ModelsWhen packets are received erroneously, recall that Ac-cuRate uses only the known preamble and postamble tomodel the channel-induced dispersion. This is clearlyan approximation and will cause sub-optimal rate esti-mation. Moreover, the postamble is an additional over-head, and hence, reducing its size is of interest. Fig-ure 15 illustrates the performance of rate estimation withpreambles and two different-sized postambles. In thesimulation results (Figure 15(a)), the performance withpreamble alone achieves around 80% accuracy, 12% rateover-selection, and 8% under-selection. Including halfthe postamble improves the accuracy to around 89%,while the preamble and the postamble together can offernearly 98% accuracy. Of course, in the testbed results(Figure 15(b)), the rate estimation accuracy degrades be-cause the pre/postambles may not always capture the dy-namism of the wireless channel. Thus, while estimatingthe rate of the received packet, AccuRate may be opti-mistic about the channel fluctuations, thereby selectinghigher rates. However, we still find that the degradationis slight. When the preamble and postamble are bothused, rate over-selection is around 5%, and accuracy is94%. We note that the testbed experiments are performedfor walking scenarios. We believe that in exchange forthe postamble overhead, a 5% over-selection and a 94%rate estimation accuracy is a decent tradeoff. Note thatwith correct reception of the packet, rate estimation ac-curacy increases further.

7 Deficiencies, Ongoing Work

AccuRate is promising but not yet ready for full-scaledeployment. We discuss some of the deficiencies anddirections of ongoing work.

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Figure 15: Efficacy of pre/postamble based dispersionmodels for (a) simulation, and (b) testbed. Simulationsconfigured with slow fading channels, while testbed re-sults are from walking experiments.

(1) Pre/Postambles produce inaccurate channelmodeling. When a received packet fails the CRCcheck, AccuRate extracts only the (BPSK modulated)preamble and postamble to model the channel-induceddispersions. These dispersions are replicated to forma packet-long dispersion sequence, and “replayed” onpackets at other rates. Clearly, this is an approximationand does not capture channel variations that may haveoccurred between the preamble and the postamble.Naturally, AccuRate’s selection accuracy deviates fromthe optimal. One way to address this issue could beto introduce midambles in the packets, i.e., knownsymbols that are interspersed with the actual datasymbols. Midambles will offer additional “glimpses”into the channel’s behavior, allowing for a better channeldispersion model. We are investigating the potentialbenefits of midambles as a part of our ongoing work.

(2) Overhead of ambles. Postambles and midamblesare overheads introduced by AccuRate. This overheadcan be viewed as the price of improved rate estimation

accuracy (for erroneously received packets). If thisoverhead is deemed unacceptable (perhaps for shorterpackets), we plan to test a few other ideas. First, the 4pilot tones used for equalization in each OFDM symbolmay be used to replace the post/midambles. These tonesare known, and may serve AccuRate well for estimatingdispersions. Second, we observe that SoftRate doesnot rely on the post/midambles; instead they utilize theconfidence values of all (correct or incorrect) symbols.We envisage that when the packet has failed, Softratecould be triggered to pick reasonably good rates. Whenthe packet is received correctly, AccuRate could predictthe optimal rate. Such a fusion of the two schemes islikely to be better than any one.

(3) Implementation complexity. Our primary focuswhile designing AccuRate has been on estimating theoptimal bit rate, unconstrained by the complexity andcost of its implementation. In practice, the hardwarecost and the implementation complexity will be high.We intend to optimize for these factors in our futurework. However, even if cost and complexity can be side-stepped, AccuRate will still need to meet the latencyconstraints of IEEE 802.11 (i.e., the rate estimationprocess must complete with SIFS time window of 9us).This may be a concern even when implemented inhardware. However, we observe that several componentsof AccuRate, as organized in Figure 9, are amenableto pipelining and speculative operation. For instance,while the symbols are being received, one may speculatecorrect packet reception and form the dispersion vectorfrom the already-received symbols. This dispersionvector can be ”replayed” on a random packet, and hence,the ”replay” operation can be pipelined with the actualover-the-air reception. Since this packet is assumed tobe correct, replaying needs to be performed only for bitrates that are higher than the packet’s actual transmissionbit rate. The replay operation can easily be performed atleast as fast as the actual reception (potentially using thesame hardware), and hence, the SIFS constraint can bemet for correctly received packets.

To account for the case of packet failure, the dispersionscan be modeled from the preamble alone, and replayedin a parallel hardware pipeline. This will also meet thetiming constraints, but at the expense of less accuratedispersion model. While using the postamble willimprove this model, its implementation may violatetiming constraints because the receiver will have towait till the end of packet reception to perform thereplay. To address this concern, we envisage tradingoff hardware cost, interference-detection accuracy, orper-packet overhead. (1) By incurring a greater cost, thereceiver could incorporate a ”bank” of replay chains.Once the postamble arrives at the end of the packet, thereceiver could model the dispersion, and replay themconcurrently on symbols from the tail of the packet.

(2) If this hardware cost is unacceptable, an alternativecould be to move the postamble earlier in the packet.An earlier postamble will model the dispersion in time,which can then be replayed on the symbols arrivingover-the-air. At the risk of not detecting interferencethat arrives during the tail end of the packet, the earlypostamble may reduce hardware cost and meet thedesired time constraints. (3) Another alternative couldbe to include a midamble in addition to the postamble,which elongates the packet but aids in both accurate andtimely rate estimation, and interference detection.

In summary, even if network processors operate at thesame speed as wireless reception, it may be possible tomeet timing constraints through speculation and pipelin-ing. Depending on the outcome of the final CRC check,the corresponding replay thread can be used. Of course,if processor speed exceeds that of wireless reception, thecost, complexity, and accuracy, is likely to improve infavor of AccuRate. A more careful investigation of thisspace is a topic of future research.

8 Conclusion

This paper asks the question, for any received packet, canwe determine the optimal rate at which the packet shouldhave been transmitted. This information is valuable be-cause the optimal rate can help the link layer with im-pending rate selection. In an attempt to answer this ques-tion, we propose AccuRate, a constellation based rateestimation scheme. AccuRate exploits symbol level in-formation to characterize the channel’s distortion on theincoming packet, and then “replays” this distortion onother rate-encodings of the same packet. The maximumrate that succeeds is deemed as the optimal rate. Whensuch a retrospective method is used to decide on impend-ing transmission rates, we find that AccuRate achieveshigher throughput than SoftRate. The performance is of-ten close to the optimal when time-separation betweenpackets are small and the transmissions are in static orslow-moving scenarios. Our ongoing work is simultane-ously focussed on extending AccuRate to high mobilityenvironments, while also making the protocol viable interms of hardware cost and complexity.

9 Acknowledgement

We sincerely thank our shepherd Hari Balakrishnan, aswell as the anonymous reviewers, for their valuable feed-back on this paper. We also thank Mythili Vutukurufor her invaluable help with SoftRate implementation.We are also grateful to NSF for partially funding thisresearch through the following grants – CNS-0448272,CNS-0917020, CNS-0916995, and CNS-0747206.

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