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Skip-Correlation for Multi-Power Wireless Carrier SensingRomil Bhardwaj, Krishna Chintalapudi,

and Ramachandran Ramjee, Microsoft Research

https://www.usenix.org/conference/nsdi17/technical-sessions/presentation/bhardwaj

Skip-Correlation for Multi-Power Wireless Carrier Sensing

Romil Bhardwaj, Krishna Chintalapudi, and Ramachandran Ramjee

Microsoft Research

Abstract

Carrier sensing is a key mechanism that enables de-centralized sharing of unlicensed spectrum. However,carrier sensing in its current form is fundamentally un-suitable when devices transmit at different power lev-els, a scenario increasingly common given the diver-sity of Wi-Fi APs in the market and the need for Wi-Fi’s co-existence with new upcoming standards such asLAA/LWA. The primary contribution of this paper is anovel carrier sensing mechanism – skip correlation – thatextends carrier sensing to accommodate multiple trans-mit power levels. Through an FPGA based implementa-tion on the WARP platform, we demonstrate the effec-tiveness of our technique in a variety of scenarios includ-ing support for backward compatibility.

1 IntroductionThe number of public Wi-Fi hotspots worldwide is over50 Million and growing rapidly [11]. Increasingly, manyhot-spots, often deemed “extended range”, transmit atup to 10× higher power than most relatively cheaphome routers. For example, a Cisco Aironet 1570 Se-ries hotspot [1] transmits at the maximum FCC allowedpower of 1W (30dBm) while the Airport Express AP [2]transmits at 100mW (20dBm).

We motivate this paper by asking, “how does a high-power hot-spot affect neighboring low-power APs?” Weemulate this scenario using two identical Wi-Fi APs (TP-LINK Archer C7), 1W-AP and 100mW-AP, with theirtransmit powers set to 1W and 100mW respectively, andconnected to identical laptops, L1 and L100. The APsand their respective clients are placed at two differentnon-line-of-sight locations separated by walls but oper-ate on the same 5 GHz channel 165 with no other APspresent to interfere. First, L100 initiates a TCP down-load through 100mW-AP and 10 seconds later L1 doesthe same through 1W-AP. As seen in Figure 1, as soon asL1 initiates its download, L100’s throughput drops from87Mbps to a few Mbps i.e., L100 nearly starves. OnceL1 finishes, L100 resumes at full throughput.

This starvation occurs when high-power devices don’tsense and back-off to transmissions from low-power de-vices [14]. To avoid collisions, the Wi-Fi standard re-quires devices to sense the channel and ascertain that itis “free”before transmitting. A channel is defined to befree if the ambient power is less than −82dBm, deemedcarrier sensing threshold [9] (CST ). In our experiment,

Figure 1: 100mW-AP starvationFigure 2: Reason forstarvation

100mW-AP received 1W-AP’s transmissions at around-78dBm (> CST) (Figure 2). Since 100mW-AP trans-mitted at 10dB (10×) lower power, 1W-AP received100mW-AP’s transmissions at -88dBm (<CST). Thus,while 100mW-AP sensed 1W-AP’s transmissions andbacked-off, 1W-AP did not sense and yield to 100mW-AP’s transmissions, resulting in near starvation.

In this paper we design a novel carrier sensing mecha-nism, skip-correlation, that addresses the above problemwhile supporting multiple different power levels. Skip-correlation satisfies the following properties:

• Sensing symmetry. A higher power device senses andbacks off to all lower (or equal) power devices thatsense its transmissions; however it does not senseand back off to transmissions from any other de-vice, as this would result in an unnecessary loss inits throughput.

• No collateral damage. Device to device sensing in-teractions that would not have suffered from sensingasymmetry using existing Wi-Fi standard, remain un-affected.

• Simple hardware implementation. Allows easy re-use of existing Wi-Fi carrier sensing digital circuitry.

In Section 2 we show why the first two properties arerequired in multi-power level scenarios to ensure thatwhile higher power devices share equitably, devices thatdo no harm are not adversely affected.Multi-Power Carrier Sensing Threshold Rule. A keyobservation in our paper is that in order to satisfy theabove properties, a sensing device must use a CST valuethat is dynamically determined. Specifically, we showthat a sensing device must use a CST value that de-pends on both, its own transmit power Psense, and that ofthe transmitting device PXmit, as captured by the multi-power CST rule (Eqns 1a, 1b, Section 2). This depen-dence of CST on PXmit poses a key challenge since thesensing device will not know a priori, the identity of thetransmitter or its power, PXmit. Further, as per the Wi-Fi standard, carrier sensing must occur within the first4µs of the packet transmission [19], long before packet

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decoding begins. In Section 3, we consider several al-ternatives that satisfy the Multi-Power CST rule but fallshort in terms of their implementation viability.Skip-Correlation. For carrier sensing, Wi-Fi receiverscorrelate against a standard preamble that is transmittedat the beginning of each packet. The channel is deemedbusy if the correlation value is greater than a thresh-old. Skip-Correlation relies on the property of correla-tion based sensing that doubling the number of samplesused in correlation is equivalent to using a CST that is3dB lower (Section 4). In Skip-correlation, while thehighest power device correlates against the entire pream-ble (to allow for lowest CST value), lower power devicesskip certain parts of the preamble and correlate againstlesser samples. A reverse trend applies to the pream-bles being transmitted – while the lowest power transmit-ter transmits the entire preamble (to allow being sensedby the highest power device), higher power transmit-ters transmit only a part of the preamble. The preambleparts to be transmitted and those to be used in correla-tion while sensing depend on the transmit power of thedevice. These parts are carefully chosen to satisfy theMulti-power CST rule, enabling higher power devices todefer to far away lower power devices (avoiding starva-tion) while simultaneously allowing lower power devicesto not defer to other low pow far away devices (avoidingcollateral damage).Hardware Implementation and Backward Compati-bility. Skip-correlation can be implemented as a minorhardware circuit modification to the popular Schmidl-Cox correlator used in Wi-Fi today and requires onlya few additional delay elements and adders. We haveextended WARP’s existing Wi-Fi implementation to in-corporate skip-correlation (Section 6). We demonstratethat skip correlation implemented on up to 6dB higherpower devices can protect unmodified 100mW devices,thus, supporting backward compatibility. Note that the6dB limitation only applies when backward compatibil-ity is desired. Skip-correlation technique does not havethis limitation when green field preambles are used. Wedemonstrate the effectiveness of skip-correlation for gen-eral multi-power carrier sensing among nodes with 9dBpower difference using a green field preamble(Section 7).Key Difference from Prior Work. Prior related workaccepts the lack of carrier sensing symmetry as a givenand optimizes the overall network by managing the var-ious nodes’ transmit powers, rates and/or CST values(Section 8). However, this won’t work in the earlier sce-nario of an independent hotspot operator impacting thehome AP. In this paper, we take a fundamentally differ-ent approach and ensure carrier sensing symmetry in afully decentralized manner at the physical layer, whileallowing nodes to independently choose their transmitpowers.

Non-Wi-Fi scenarios. Skip-Correlation is a generaltechnique and can be used in non-Wi-Fi scenarios.Sharing with LTE-U, LAA, LWA: New cellular stan-dards such as LTE-U, LAA, and LWA [10] are beingdesigned for unlicensed use alongside Wi-Fi. LAA andLWA use carrier sensing but starvation can occur if a1W LAA/LWA base-station transmits near a home user’s100mW Wi-Fi AP.White Spaces: "White spaces" or unused T.V channelsare available for unlicensed use in the U.S., U.K., Canadaand Singapore [4]. Mobile white space devices, limitedto transmit at up to 100mW, may starve near 1W fixedbase-stations [25].Summary of our contributions.• We propose a new Multi-Power Carrier Sensing

Threshold Rule, that can eliminate starvation for lowpower devices while not causing collateral damage.

• We propose a novel sensing technique – Skip-Correlation – that implements the above sensing ruleand renders itself to a simple implementation.

• We implement skip-correlation on WARP FPGA us-ing a small modification to existing Wi-Fi’s carriersensing circuitry that is backward compatible anddemonstrate its efficacy through testbed experiments.

2 Multi-Power Carrier SensingThreshold Rule

In this section we first derive the multi-power level CSTrule from first principles. Then, to provide intuition, wedemonstrate how not following the rule can lead to un-desirable effects with the help of strawmen alternatives.Sensing Symmetry. Consider devices APH and

Figure 3: Sens-ing Symmetry

APL with transmit powers PHand PL, respectively, wherePH−PL=∆ ≥ 0. The circle inFigure 3 depicts the radius whereAPH ’s transmissions are receivedat -82dBm. If APL uses a CST of-82dBm as per the Wi-Fi standard,it will sense and back-off fromAPH ’s transmissions only whenAPL is inside the circle. Thus, for sensing symmetry,APH should sense APL only when APL transmits fromwithin the circle. When APL is on the circle, APHreceives APL’s transmissions at −82 − ∆. Thus, byusing CST=−82 − ∆dBm, APH ensures that it onlysenses APL when APL senses it and no more.No Collateral Damage. In the previous discussion weassumed that APL used a CST of -82dBm. While thereis nothing sacrosanct about -82dBm, it is the value usedby the widely adopted Wi-Fi standard. More importantly,we must ensure that the performance of lower power de-vices that are not causing sensing asymmetry are unaf-

228 14th USENIX Symposium on Networked Systems Design and Implementation USENIX Association

Figure 4: Example showing need for Multi-power CTS Rule

Links A->D D<-A A->B B->A D<->E B->D D->B B->E E->B E->C C->E A<->C A->E E->A C->D D->CRSS -78 -88 -86 -90 -84 -84 -90 -84 -90 -78 -88 -89 -85 -95 -85 -95

Table 1: RSS in dBm for various links in Example in Figure 4

fected. If we were to decrease (or increase) CST forAPL, it would lead to low power devices unnecessarilybacking off (or colliding) with other low power devices,adversely impacting performance. Thus, when the powerof a sensing device is less than or equal to that of thetransmitting device, we require that the CST value used(e.g, -82dBm) is unchanged, thereby ensuring no collat-eral damage.Multi-Power Carrier Sensing Threshold Rule. Insummary, when device A with power PA senses a trans-mission from another device B with power PB , the CST(in dBm) used by sensing device should be,

CST (PA, PB) =

{ −82 if PA ≤ PB , (1a)

−82− (PA − PB) if PA > PB . (1b)

As seen from Eqn 1a, 1b, CST chosen by the sensingdevice is dynamic and depends both on its own transmitpower and that of the transmitting device. We now showthe need for such dependence through an example andcontrast it against a few schemes that use fixed CST.Multi-Power CST Rule vs Fixed Threshold Straw-men. In our example, there are five APs A, B, C, D,E transmitting at 1W, 400mW, 1W, 100mW, and 100mWrespectively, as shown in Figure 4(a). Solid circles repre-sent distance at which received power from an AP dropto -82dBm. The received powers for each link is pro-vided in Table 1 for reference. Figures 4(b-e) depict theinterference graphs induced due to various carrier sens-ing schemes used. When the arrow points from X to Y, itindicates that Y senses and backs-off from X.Wi-Fi Standard. As seen from Figure 4(b), with stan-dard Wi-Fi, there are only two links that can be sensed,i.e., when A transmits to D and when C transmits toE. Consequently, both 100mW devices D and E nearlystarve due to 1W devices A and C, respectively.

Skip-Correlation. Skip-correlation uses Eqns 1a,1b todecide the CST for each link. Thus, 1W-AP uses CST-92dBm when a 100mW-AP transmits, -86dBm when400mW-AP transmits and -82dBm when a 1W-AP trans-

mits. Similarly, 400mW-AP uses CST -82dBm when a1W-AP or a 400mW-AP transmits and -88dBm when100mW-AP transmits. As seen from Figure 4(c), thisCST choice based on the transmit powers of both de-vices i.e., transmitting and sensing, ensures that the sens-ing symmetry is restored between device pairs (A,D) and(E,C) without effecting any other sensing relationship.

Strawman-I: Preamble Power Equalization. InStrawman-I, all WiFi transmitters somehow ensure thatpreambles are transmitted at the same power of 1W tomake all sensing symmetric.1 This scheme achievessensing symmetry since all nodes are equivalent to 1Wnodes from a sensing perspective. However, now all thelower power devices B, D and E, with their extendedpreamble ranges can sense each other (Figure 4(d)).Consequently, they now back-off unnecessarily to eachother, resulting in reduced overall throughput.

Strawman-II: Lower Fixed CST for Higher PowerDevices. An alternative approach is to make higherpower devices more sensitive to lower power receivers.In this scheme, unlike the Multi-Power CST rule, we usea fixed CST value for ease of implementation. The 1Wand 400mW APs use Eqn 1b to derive a fixed CST thatalways protects the lowest power device i.e., 100mW AP.Thus, A and C use a fixed CST of -92dB (-82-10), B usesa fixed CST of -88dBm (-82-6), while D and E use thestandard CST of -82dBm. This scheme again ensuressensing symmetry since higher power devices will nowalways detect all low power devices. However, due to theextended sensing ranges, now the higher power devicesA,B, and C sense and back off from each other unneces-sarily, resulting in reduced overall capacity.

The above examples demonstrate how using a fixedCST at the receiver or fixed preamble transmit powersat the transmitter causes collateral damage, underminingthe throughput of higher or lower power devices depend-

1While low power 100mW transmitters are typically not equippedwith power amplifiers to transmit at 1W, one could elongate preamblelengths to achieve an equivalent scenario.


Figure 5: CSMA in WiFi

ing on which class of devices they are chosen to protect.A dynamic CST that depends on the transmit power ofboth the sensing and the transmitting device is necessaryto ensure symmetry without causing collateral damage.

3 Approaches for ImplementingMulti-Power CST Rule

The dependence of CST on the transmit power of thetransmitting device poses a significant challenge, sinceidentity of the transmitter or its transmit power are un-known a priori to the sensing device. To motivate whythis is a hard problem that requires a nuanced solu-tion like skip-correlation, we consider two simpler ap-proaches for implementing Multi-Power CST and showwhy these are not practically viable.Carrier Sensing: A Primer. Carrier Sensing (CS)in Wi-Fi is achieved by transmitting a special signal,preamble, ahead of each packet. During CS, devicescontinuously try to detect presence of this preamble inthe received signal. In Wi-Fi, the preamble used for CSis called the Short Training Sequence (STS) and is 160samples long (8 µs).

Figure 5 depicts how two devices Device1 and De-vice2 might share spectrum using CS. First, both devicesgenerate a random counter. In the example in Figure 5,Device1 and Device2 generate 2 and 3, respectively. Ev-ery 9µs (Wi-Fi slot-width) the devices decrement theircounters. Device1 counts-down to 0 first at the beginningof slot 2 and initiates its transmission. Device2 continuesto listen and detects STS from Device1’s transmissionbefore the end of Slot 2 and backs-off, avoiding a colli-sion. If Device2 is unable to detect STS from Device1before the beginning of slot 3, then its counter wouldhave reached 0 and it would transmit its packet causing apacket collision.

3.1 Using HeadersWe first consider if one can re-use MAC headers to dis-cover the power of the transmitter. Suppose that everydevice maintains a table of transmit powers of all itsneighbors. The listening device can decode the head-ers of the received packet to determine the identity of thetransmitter and looks up the power of the transmissionto make the carrier sensing decision. Alternatively thetransmitting device could add an additional field in theheaders that encodes transmit power information – thiswould avoid the need for the lookup. The key drawback

of these approaches is that they require decoding of head-ers before the back-off decision can be taken.

As discussed earlier, the Wi-Fi standard requires back-off decision be taken within 9µs of the packet trans-mission. The identity of the transmitting device is onlyknown in the MAC header which arrives about 50µs intothe packet transmission.

The fastest way for the transmitter to let the receiverknow of the transmitter’s power level is by adding an ad-ditional power level field in the PHY. The earliest thiscan be done is in the OFDM symbol immediately afterthe LTS (it cannot be added before LTS as LTS is usedfor frequency offset estimation – a necessary step beforedecoding). Thus, the slot-width would have to be at least20µs (LTS + STS + 1 OFDM Symbol).

Why can’t we simply increase the Wi-Fi slot width?Increasing the Wi-Fi slot width to 20µs would resultin more than doubling of the average backoff interval,severely reducing MAC efficiency and overall through-put [19].

3.2 Using Orthogonal PreamblesIn this approach, a unique preamble is assigned to eachpower level. Each of these preambles are orthogonal tothe others and have low cross-correlation properties (likeCDMA codes). Thus, each preamble uniquely encodesthe transmit power level information within itself. A de-vice transmits the preamble corresponding to its trans-mit power level. Listening devices now correlate againstall possible preambles simultaneously using a matched-filter (Appendix B) bank. The bank uses a different CSTfor each correlator given by Eqn 1a, 1b for sensing.

There are two key drawbacks to this approach – highcomplexity of implementation and need for very longpreambles for correctly inferring the power level. SinceSchimdl-Cox is oblivious to the exact preamble transmit-ted, it cannot be used in this scheme as it will be unableto distinguish between the different preambles. As dis-cussed in Section 6.2, for 4 power levels a matched-filterapproach requires over 1500 multipliers while Schimdl-Cox and our proposed scheme Skip-Correlation requiresonly 5. The other drawback arises from the ability todistinguish between different preambles and inferringthe correct preamble through cross-correlation. As wedemonstrate in Appendix C, for 4 power levels, even at128 samples long, the incorrect preamble detections areas high as 14%. Using preambles longer than 128 sam-ples will increase Wi-Fi slot width, resulting in low MACefficiency. Finally, note that these drawbacks are funda-mental to this approach and also apply to other imple-mentations such as Tufvesson [26].

4 Adapting CSTMost Wi-Fi receivers perform carrier sensing by correlat-ing against the Wi-Fi preamble. Skip-correlation relies


on a basic property of correlation-based sensing – dou-bling the number of samples used in correlation is equiv-alent to using a CST that is 3dB lower. In this section weexplain this property and provide a proof sketch (detailedproof in Appendix B) for one specific correlation-basedscheme – Schmidl-Cox detection – commonly used inWi-Fi devices today and that we modify in our imple-mentation2.Schmidl-Cox Preamble Detection Let S(n) be thepreamble of length L samples that is transmitted. The re-ceived signal Srecv(n) received by the sensing device forthe cases when no preamble was transmitted and when apreamble was transmitted is given by Eqns 2a, 2b respec-tively as,

Srecv(n) =

{N(n) no preamble Xmit, (2a)S(n)∗H+N(n) preamble Xmit. (2b)

In Eqns 2a,2b, N(n) is the receiver noise, H is thechannel response that captures how the channel trans-forms the transmitted signal due to effects such as multi-path fading and, ∗ is the convolution operation.

In Schmidl-Cox detection, S(n) comprises two iden-tical halves i.e., S(i) = S(i + L

2 ). As the transmissionpasses through the channel, each of its halves are effectedby the channel in exactly the same way and are expectedto be identical. Consequently, the receiver correlates twoconsecutive L

2 length windows of the received signal as,

C =

∣∣∣∣∣∣∣i=L

2∑i=1

Srecv(i)Srecv(i+L

2)

∣∣∣∣∣∣∣2

(3)

A high correlation value (C > Cth) indicates that apreamble was transmitted and the channel is deemedbusy. The advantage of using Schmidl-Cox is that it isrobust to multi-path effects in the channel.Detection Probability depends on Product of Re-ceived Signal Strength and Correlation Length. TheWi-Fi standard specifies that a signal at -82dBm mustbe detected with a probability 90% or higher [9]. Re-ceiver noise induces variability in the correlation valueC. Choosing a low Cth will result in a high detectionprobability, but also increased false detection rate i.e.,concluding that there is a preamble when there is in factonly noise. Cth is usually calibrated such that the de-tection probability is 90% (or some higher value) whenthe received signal strength is at -82dBm. Appendix Bdescribes in detail, how to choose Cth. As shown in Ap-pendix B, for the operating regime of typical Wi-Fi re-ceivers, the preamble detection probability is governedby a χ2

1 distribution with mean,

µ(C) ≈ (LES)2/4 (4)

where ES is received signal strength of the preamble.Eqn 4 implies that the probability distribution and hence

2The property holds for other correlation based schemes as well.

Figure 6: A Skip Correlation Examplethe detection probability remain approximately unalteredif the product LES is kept the same.Adapting CST by changing L. Suppose that when thereceived preamble’s signal strength isES = -82dBm andthe number of preamble samples used for correlation isL, then preambles are detected with 90% probability. Byusing 2L samples for correlation instead of L, the samedetection probability would be achieved when ES is at -85dBm (half of -82dBm). Thus, Eqn 4 can be interpretedas doubling the number of samples used in the correla-tion will allow detection at a received signal strength 3dBlower with the same detection probability i.e., loweringthe CST by 3dB.

5 Skip-CorrelationIn this section we describe our proposed scheme – Skip-Correlation – that implements carrier sensing accordingto the Multi-Power CST rule. Our scheme reuses Wi-Fi’s preamble (STS) and most of Wi-Fi’s carrier sensingcircuits while adding very little extra circuitry.

We first provide the reader intuition for skip-correlation using an example. Then we formally describeskip-correlation for N arbitrary power levels, followedby a proof of how it satisfies the Multi-Power CST rule.

PSense

PXmit 20dBm 23dBm 26dBm 29dBm

L (CST) L (CST) L (CST) L (CST)20dBm 2γ (-82) 2γ (-82) 2γ (-82) 2γ (-82)23dBm 4γ (-85) 2γ (-82) 2γ (-82) 2γ (-82)26dBm 8γ (-88) 4γ (-85) 2γ (-82) 2γ (-82)29dBm 16γ (-91) 8γ (-88) 4γ (-85) 2γ (-82)

Table 2: Number of samples used in correlation (L) andCST (in dBm) for all combinations of power levels

5.1 A Skip-Correlation ExampleFigure 6 depicts an example with four different powerlevels 20, 23, 26, 29dBm with corresponding parts of thepreamble transmitted and correlated against. The entirepreamble is 16γ samples long with two identical halvesof 8γ samples to allow Schmidl-Cox detection. We as-sume that γ is chosen such that the correlation lengthof 2γ samples corresponds to a CST of -82dBm, i.e., it


provides a 90% detection probability when the receivedsignal strength is -82dBm.

For each of the 16 transmitter power level (PXmit) andsensing device power level (PSense) combinations, Ta-ble 2 lists the number of preamble samples used for cor-relation (L) and the corresponding CST (in dBm) usedby the sensing device. One can verify that all 16 combi-nations satisfy the Multi-power CST rule. As seen fromTable 2, CST is reduced only for 6/16 scenarios (markedas bold) by the necessary amount dictated by the Multi-Power CST rule to eliminate starvation but remains at-82dBm for the rest 10/16 scenarios to avoid collateraldamage. We now describe three combinations (gray cellsin Table 2) to provide intuition.20dBm transmitting, 20dBm sensing. While the 20dBmtransmitter transmits all 16γ samples (T1 and T1’), the20dBm sensing node only correlates 2γ samples (R1 andR1’). Thus, the 20dBm sensing device uses a CST of-82dBm as desired.20dBm transmitting, 29dBm sensing. The 29dBm re-ceiver correlates against all 16γ samples (R7 and R7’)i.e., 8 times more samples than the 20dBm receiver. Asdiscussed in Section 4, this means that the CST for thispair is 8 times (9dB) lower than -82dBm or -91dBm.23dBm transmitting, 26dBm sensing. The 23dBm trans-mitter transmits preamble parts T2 and T2’. The 26dBmreceiver correlates against pieces R4-R6 and R4’-R6’.T2 and T2’, however, do not overlap with R6 and R6’.Thus no preamble samples are transmitted for R6 andR6’ to correlate upon. Consequently, correlation occursonly over the 4γ samples R4, R5, R4’ and R5’. Thus, theCST for this pair is 2 times (3dB) lower than -82dBm or-85dBm.

5.2 Notation UsedWe now outline the notation used for describing the partsof preambles to be transmitted and correlated against fora general scenario with N power levels.

• The Preamble : The entire preamble has L samplesand is denoted by S = [S1,S2, · · · ,SL] with its lefthalf SLH identical to its right half SRH .

• Transmitted Preamble: The preamble transmitted bya device with power level P comprising multiplepieces is denoted by SXmitP with its right and lefthalves as SXmit,LHP and SXmit,RHP .

• Correlated Preamble: The preamble correlatedagainst is denoted by SRecvP comprising SRecv,LHP

and SRecv,RHP as its identical left and right halves.• Preamble Part: A part of the preamble from sample

index i to j is denoted as S[i, k] = [Si,Sj , · · · ,Sk].• Union : C = A ∪ B, indicates that a preamble C

contains pieces from both preambles A and B.

Figure 7: Skip Correlation for P1 < P2 < · · · < PN

• Intersection: A ∩B denotes pieces that are commonto both A and B.

5.3 Arbitrary Transmit PowersIn this section we describe Skip-Correlation for generalscenarios where devices may choose from N distinctpower levels P1 < P2 < · · · < PN .

For the following discussion, we assume that any sub-part of the preamble with γ samples along with its identi-cal copy e.g.,S[1, γ] and S[L2 + 1, L2 + γ], ensures detec-tion at -82 dBm (or some other standard specified value).The entire preamble S has L = 2γ PN

P1samples with its

first half identical to its second half. Figure 7 depicts thefirst half of the preambles transmitted and correlated byvarious devices (the second half is identical).Preamble Transmission. A device with transmit powerPk transmits SXmit,LHPk

comprising the first γ PN

Pkof the

preamble and its copy in the second half i.e.,

SXmit,LHPk

= S

[1, γ

PN

Pk

](5)

This ensures that devices of all power levels transmit thesame amount of total preamble energy of 2γPN .Preamble Reception. A device with transmit powerlevel Pk correlates against k different pieces of thepreamble in the left half captured in SRecv,LHPk

and itsshifted copy in the second half, i.e.,

SRecv,LHPk

= S[1, γ] ∪i=k−1⋃i=1

S

[γ

PN

Pk−i+1, γ

PN

Pk−i+1+ λk,i

](6a)

λk,i = Pkγ

(1

Pk−i−

1

Pk−i+1

)(6b)

The first piece is S[1, γ]. The rest k − 1 pieces, havelengths λk,i, i = 1, · · · , k − 1 starting at sample numberγ PN

Pk−i+1.

Proof of Correctness. When a device transmits at apower level Pi to a device with transmit power level Pk,the following properties P1 and P2 always hold,


Figure 8: High Level View of Changes between Stan-dard Schmidl-Cox and Skip-Correlation

• P1 : if Pi ≥ Pk the correlation is only againstS[1, γ], which is 2γ samples corresponding to a CSTof -82dBm.

• P2 : if Pi < Pk the number of preamble samplescorrelated at the receiving device (in SXmitPi

∩SRecvPk)

is 2Pk

Piγ – corresponding to a CST that is Pk

Pilower

than -82dBm i.e.,−82−(PkdB−PidB) in log-scale.

Thus, CST used in skip-correlation matches the Multi-Power CST rule. The proof of these properties is pro-vided in Appendix A.

6 Design and ImplementationSchmidl-Cox detection is typically implemented on anASIC in the Wi-Fi card as a digital circuit. Skip-Correlation can be realized through a minor modifica-tion of Schmidl-Cox. Hence, we start by describing howSchimdl-Cox correlation is implemented and then ex-plain how to modify it to implement Skip-Correlation.

6.1 Skip-Correlation Circuit DesignThe block-diagram of Schmidl-Cox detector is providedin Figure 8. The received signal is a sequence of complexsamples with I (real) and Q (imaginary) parts. D(x)blocks are delay elements that introduce a delay of xsamples and usually implemented using FIFO of depthx elements. The complex conjugate multiply block takestwo complex samples s(i) and s(i + L

2 ) to perform theoperation s(i)′s(i + L

2 ), where ′ denotes the complexconjugate operation. The real and imaginary parts fromthe complex conjugate multiplier are each fed into anrunning sum block (described later in this section) thatmaintains the sum of the last L2 samples. Finally, the realand imaginary parts of the running sum are squared andadded to be compared against the threshold Cth.The only change required to implement Skip-Correlationis to replace the running-sum (RS) block of Schmidl-Coxby a running sum of parts (RSP in Figure 8).Circuit for Running Sum used in Schmidl-Cox The

Figure 9: Running sum block in Schmidl-Cox withHistory Length x.

running sum over the past x samples in Schmidl-Cox isimplemented by the following equation,

sum(i+ 1) = [s(i+ 1)− s(i− x)] + sum(i) (7)

The circuit implementation for a running sum RS(x) isprovided in Figure 9. A-B block subtracts B from A,and this case produces s(i + 1) − s(i − x) and

∑is an

accumulator that continuously adds its inputs.Circuit for Running Sum of Parts in Skip-Correlator.The circuit for running sum of preamble parts is funda-mentally the sum of several running sums, one for eachpiece of the preamble and is given in Figure 10. Usingthe same notation used in Section 5.3, for a device withpower level Pk the Skip-Correlator is a cascade of k run-ning sum blocks and delay elements. The only exceptionis PN which correlates the entire preamble and is simplyRS(L2 ).

6.2 Circuit ComplexityIn this section we analyze the circuit complexity ofimplementing the Skip-Correlator and the orthogonalpreambles proposal (Section 3.2) and compare themagainst Schmidl-Cox. Since multipliers and adders con-stitute the most expensive elements in these circuits wemeasure complexity by the number of multipliers andadders required.Schmidl-Cox. In the overall Schmidl-Cox circuit thereis one complex conjugate multiplication (3 multipliersand 4 adders [17]), two RS blocks (2 adders in each),two multipliers for squaring real and imaginary parts andfinally another adder – a total of 5 multipliers and 9adders.Skip-Correlation With N power levels. The onlychange in implementing the Skip-Correlator is the RSPblock. A receiver with power level Pk has 2k RS blocks(each with 2 adders). Thus, the complexity is given by5 multipliers and 4k+5 adders. The device at PN−1 willhave the greatest complexity at 5 multipliers and 4N + 1adders. For 4 power levels this corresponds to 5 multi-pliers and 17 adders.Orthogonal Preambles - Multiple Matched Filters.Unlike Schmidl-Cox, correlation against a matched filter(Appendix B ) cannot be implemented using a runningsum. Thus, it requires L complex multipliers for com-puting each of L products and finally L

2 adders for com-puting the sum of the products using a binary tree. Two


Figure 10: Circuit for Running Sum of Parts in Skip-Correlator.

multipliers are needed for squaring the real and imagi-nary parts and finally an adder to compute C. This addsup to 4.5L + 1 adders and 3L + 2 multipliers. If thereare N power levels, there will be N matched filters inthe correlation bank leading to 3NL+ 2 multipliers and4.5NL + 1 adders. As shown in Section B, for N = 4,we will need L = 128 in order to achieve a false positiverate < 10−3. Thus, the circuit for orthogonal preambleswill need over 1500 multipliers and 2300 adders. Thisdemonstrates that implementing the orthogonal pream-ble approach is not practically viable and has at least twoorders of magnitude higher complexity.

6.3 Implementation on WARP

Figure 11: Green Field and Backward Compatible Skip-Correlation Preambles Transmitted by Various Nodes

The WARP software defined radio platform providesan implementation of Wi-Fi with Schmidl-Cox correla-tion for CS. We modified this Schimdl-Cox as shownin Figure 8 to implement a four power level skip-correlation.Correlation Lengths Used. Wi-Fi standard requires thatcarrier sensing be performed within the first 4µs [19] ofthe 9µs slot. Since most modern day commercial Wi-Firadios have a noise floor of -91dBm or less [3, 7, 8], weconsider 0dB SNR as corresponding to -91dBm. Thus,9dB SNR corresponds to -82dBm. As discussed onSection B, at 9dB SNR, L = 8 samples suffices forSchmidl-Cox to give a false positive rate below 10−6;thus for our Skip-Correlation we choose γ = 4. The fullpreamble length for supporting 9dB power difference isL = 8 ∗ 2 ∗ γ = 64. Thus, we use only 64 of the 160samples of the WiFi STS for skip-correlation sensing.Skip-Correlation Green Field Preambles. Figure 11depicts the Green Field preambles used for transmitting

for each of the four different power levels. Note that Wi-Fi has other preambles (e.g., LTS, MIMO preambles etc.)that come after the STS – these are unaffected and hencenot shown. In our design we reuse the WiFi-STS as muchas possible. Only the highlighted parts of the STS pream-ble are used for carrier sensing in skip-correlation. Therest of the preamble is used for other functions such asAGC gain estimation and DC-offset correction. In ourtrials we found that it was necessary for the even the100mW device required a gap of 16 samples between itstwo halves. This is because, in absence of the gap, multi-path from previous samples distorts the second half. Thisaddition of zeros requires changing the delay elementD(L2 ) in Figure 8 to D

(L2 + 16

). However, even with

zeros, skip-correlation carrier sensing occurs within first80 samples (4µs).Skip-Correlation Backward Compatible Preambles.Given the large number of 100mW legacy devices, wewant Skip-correlation to work in a backward compat-ible mode in the presence of legacy 100mW devices.Through experimental trials we found that several legacyphones and low power routers did not work with theGreen Field Preamble shown in Figure 11. Our trialsindicated that many legacy devices require additional2-3 contiguous STS sequences within the first 4µs tofunction correctly. We guess that, these devices takelonger time for AGC stabilization and DC-offset correc-tion. Thus, our Backward Compatible WiFi STS pream-ble (Figure 11), introduces 3 additional STS sequenceswithin the first 4µs. However, with this change we canonly support up to 6dB power diversity. Thus, in our thismode we choose only three power levels 20dBm, 23dBmand 26dBm.

7 Testbed ResultsWe first present experimental results demonstrating theeffectiveness of skip-correlation in a backward compat-ibility setting with legacy low power Wi-Fi routers andsmartphones, for power differences of up to 6dB. Wethen present a detailed analysis of how skip-correlationensures symmetry when four power levels spanning 9dBin power difference co-exist. All experiments were con-ducted on an unused 20 MHz Wi-Fi channel in the 5 GHzband.

7.1 Backward Compatibility ExperimentsIn this section, we use the three settings shown in Fig-ure 12 to answer the question: how well does skip-correlation work in the presence of legacy Wi-Fi APs andphones?


+3dB

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Figure 12: Experimental setup with legacy Wi-Fi devices

In all the experiments, we use a mix of off-the-shelfTP-Link Archer C7 APs and WARP APs, each associ-ated with one smartphone, and performing an iperf udpdownload to the smartphone (tcp results are qualitativelysimilar). The Archer C7 APs use auto-rate and MIMO(2X2) while the WARP APs are set to operate at a fixedPHY rate of 6 Mbps. Each node is only aware of itsown configured transmit power and has no explicit infor-mation about the transmit power or other information ofany other nodes. In isolation, the TP-Link client gets anaverage UDP throughput of 86 Mbps while the WARPclients get an average UDP throughput of 4.4 Mbps.

In the first setting (Figure 12(a)), there are 3 APs and3 smartphones, where one of the APs is TP-Link ArcherC7 router and the other two APs are WARP devices. Thetwo WARP APs act as high power APs with 3dB higherpower than the TP-Link AP. The nodes are placed suchthat, when all APs run the standard Wi-Fi, the WARPnodes are unable to sense the TP-Link AP while the TP-Link AP can sense the WARP nodes. Further, the WARPnodes are able to sense each other. At time t = 0s, theTP-Link AP starts the download to its client and at timet = 20s, the two high-power WARP APs start their re-spective downloads. Finally, at t = 180s, the high-powerAPs stop their download.

The results without and with skip-correlation areshown in Figures 13 and 14, respectively. The y-axison the left shows the throughput for clients connected tothe fixed rate WARP AP while the y-axis on the rightshows the throughput for client(s) connected to TP-LinkAP. With standard Wi-Fi, one can clearly see in Figure 13that the client connected to TP-Link AP nearly starves –0.94 Mbps average throughput whenever the high powerWARP APs are in operation while the WARP clients eachget about 2.15Mbps (or about half the time-share). WithSkip-correlation, the starvation is eliminated in Figure 14and the three nodes share approximately equally in time– the low power client gets an average throughput of24 Mbps (28% of 86 Mbps, about one-third) while theclients connected to WARP get 1.4 Mbps each on aver-age (32% of 4.4 Mbps, about one-third).

The second experiment (Figure 12(b)) also has threeAPs but with three different power levels: the TP-LinkAP is the low power AP and the two WARP APs are at3dB and 6dB higher power, respectively. The nodes areplaced such that, when all APs run the standard Wi-Fi,the lower power APs are able to sense the higher powerAPs, but not vice-versa. At time t = 0s, the TP-LinkAP starts the download to its client and at time t = 20s,the two higher power WARP APs start their respectivedownloads. Finally, at t = 180s, the higher power APsstop their download.

The results without and with skip-correlation areshown in Figures 15 and 16, respectively. With stan-dard Wi-Fi, one can clearly see in Figure 15 that the twoclients connected to the TP-Link AP and +3dB WARPAPs mostly starve (average throughputs of 1.3Mbps and0.24Mbps, respectively) whenever the +6dB WARP APis in operation (whose client gets average throughput of4.3 Mbps). With Skip-correlation, the starvation of boththe TP-Link AP and +3dB WARP APs are eliminatedin Figure 16, and all three clients again get about one-third the time-share (average throughputs of 24.2 Mbps,1.36 Mbps and 1.44 Mbps).

In the third experiment (Figure 12(c)), there are 4 APsand 4 smartphones, where two of the APs are TP-LinkArcher C7 and the other two APs are WARP devices.The two WARP APs act as high power APs with 3dBhigher power than the TP-Link APs. The nodes areplaced such that, when all APs run standard Wi-Fi, theWARP APs are unable to sense the TP-Link APs whilethe TP-Link APs can sense the WARP APs. Further, thetwo WARP APs cannot hear each other. At time t = 0sand t = 15s, the two TP-Link APs start their down-load to their respective clients and at time t = 30s andt = 45s, the two high-power WARP APs start their re-spective downloads. Finally, at t = 180s, the high-powerAPs stop their download.

The results without and with skip-correlation areshown in Figures 17 and 18, respectively. With standardWi-Fi, as seen in Figure 17, the two clients connectedto the low-power TP-Link APs starve (average through-puts of 1 Mbps and 1.8 Mbps) whenever the WARP APswith 3dB higher power are in operation (WARP clientsget average throughputs of 4.3 Mbps each). With skip-correlation, the starvation is eliminated in Figure 18, withall four clients getting one-half time-share each (aver-age throughputs of 39 Mbps, 43 Mbps, 2.1 Mbps and2.2 Mbps).

7.2 Green Field: Micro-benchmarksWe now look at what happens with skip-correlationunder-the-hood. For these experiments we supportfour power levels 20dBm, 23dBm, 26dBm and 29dBmand consequently use the green field preamble patterns


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shown in Figure 6 implemented on WARP nodes. We usereceived SNRs to calibrate our experiments. Our goal isto demonstrate that skip-correlation ensures carrier sens-ing symmetry for all pairs of devices.7.2.1 Establishing CthCth is determined from the false negative detectioncurves when the received power is -82dBm (Ap-pendix B). Thus, we placed two WARP nodes in line-of-sight to minimize signal variation and adjusted thetransmit power of one such that the other received at9dB SNR (-82dBm). We then collected samples from30,000 transmissions each separated by 1 second (almostover 9 hours). There was about 5dB variation in re-ceived power despite line-of-sight since there were peo-ple moving during the course of the experiment. To en-sure that the received powers were as close to -82dBmas possible we considered only those transmission thathad received SNRs in the range 9 ± 1 dB, which werelittle over 10000 in number. We then computed P (C|Xmit, −91dBm,−82dBm) for the Skip-Correlator us-ing a histogram with 100 bins over the collected data.We also computed P (C| No Xmit, −91dBm) by cor-relating against the noise samples. Using these dis-tributions we then computed the false negative curvesη−(C|−91dBm,−82dBm) and the false positive curveη+(C|−91dBm) using Eqn 15 and Eqn 16, depicted inFigure 19. The curves are “close” to the theoreticallypredicted curves in Appendix B, Figure 22. Using thepoint at η− = 0.1 in the curve, we established Cth as

shown in Figure 22; it was found to be about -15.7, veryclose to the theoretically predicted value of -15.5 in Fig-ure 22. The false positives corresponding to this thresh-old are very small. We use this value of Cth in all thefollowing experiments.

7.2.2 CS SymmetryIn this experiment, we use two WARP devices A and Bto test carrier sensing symmetry. Due to space considera-tions, three node experimental results are in Appendix D.

We conducted carrier symmetry experiments at fourdifferent non-line-of-sight location pairs L-91, L-88,L-85 and L-82. For each location pair, locations of both Aand B were changed in a way that for the location pairL-X, the devices were so placed that when one devicetransmitted at 20dBm transmit power, the other would re-ceive at X dBm. For example, for the location pair L-85,when one device transmitted at 20dBm the other receivedat -85dBm (6dB SNR). Note that since the experimentslasted a few hours, with people moving about, in real-ity there was significant variation of the received signalstrength at each location. Figure 20 shows the probabilitydistribution of received powers at B when A transmittedat 20dBm power. Thus, there was 5dB-12dB variation inreceived power across the various locations.

At each location we experimented with 4 differentpower levels 20dB, 23dBm, 26dBm and 29dBm and ob-tained data for all the possible 10 unique combinationsof transmitter and receiver powers. The experiment at


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Skip-Correlation Detection ProbabilitiesA20-B20 A23-B20 A26-B20 A29-B20 A23-B23 A26-B23 A29-B23 A26-B26 A29-B26 A29-B29

F R F R F R F R F R F R F R F R F R F RL-91 1 0 6 10 45 79 89 97 7 5 46 75 89 98 48 44 89 96 88 88L-88 2 1 22 25 81 96 98 100 23 19 81 96 98 100 80 78 98 100 98 98L-85 48 45 92 90 100 100 100 100 92 85 100 100 100 100 100 100 100 100 100 100L-82 92 91 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100

Schmidl-Cox Detection ProbabilitiesA20-B20 A23-B20 A26-B20 A29-B20 A23-B23 A26-B23 A29-B23 A26-B26 A29-B26 A29-B29

F R F R F R F R F R F R F R F R F R F RL-91 0 0 0 0 3.3 0 90.5 0 0 0 90.2 0 91.2 0 5 3.3 90.5 3.3 90.5 91.2L-88 0 0 2.4 0 90.2 0 99.8 0 4.5 2.4 90.3 2.4 99.9 2.4 90.3 90.2 99.8 90.2 99.8 99.9L-85 31.9 35.7 90 35.7 100 31.9 100 35.6 90 90.4 99.9 89.9 100 90.4 100 99.9 100 100 100 100L-82 91.8 89.6 95 91.9 100 91.8 100 95 98 95 100 98 100 95 100 100 100 100 100 100

Table 3: Detection Probability Symmetry for Skip-Correlation

each location consisted of 3000 rounds. In each round,first A transmitted 4 successive transmissions at each ofthe four power levels. This was immediately followedby B transmitting 4 successive transmissions at all thefour power levels. All four possible skip-correlation pat-terns (Figure 6) for the receiver were available at eachdevice, so that we could obtain all four possible corre-lation values. We waited 1 second between each round.The hope here was that within each round the channelwould not change significantly, whereas between twoconsecutive rounds the channel would be different. Thisstrategy made sure that we tried all possible power levelcombinations in both directions over approximately thesame channel, so that 3dB increase in transmitted powerwould mean 3dB increase in the received power as wellwithin a single round. At the same time, across differ-ent rounds we could experiment across changing channelconditions, since each experiment lasted about an hourwith people moving about on the floor.

Carrier Sensing Symmetry Observations. We used thecorrelation values from the above experiments and com-puted η−(C|σ2

S , σ2N ) using Eqn 15 for all 16 power level

combinations and at all four locations (64 curves in to-tal). Note however, that since the received signal strengthwas varying in this experiment from round to round, thedistribution is computed over the entire range of variationof signal strength and not at any single received power.Figure 21 depicts a few of these curves from the L-85location. In Figure 21 the notation < TY,RZ > de-notes that that node T transmitted at power Y dBm tonode R whose transmit power was set to ZdBm. Thus,< A29, B20 > means that A transmitted at 29dBm to B

which was using a skip-correlation pattern correspond-ing to 20dBm transmit power. Similarly, < B20, A29 >represents the same link but when B transmits at 20dBmto A that uses the skip-correlation pattern correspond-ing to 29dBm. As seen from Figure 21, the η− curves< A29, B20 > < B20, A29 > almost overlap; this de-spite the variation in received signal strengths and chang-ing channel conditions at both the devices - thus indicat-ing a strict adherence to carrier sensing symmetry. Thesame is true for other power level combinations as welland demonstrates how Skip-Correlation ensure that thedetection probabilities at either ends at almost identicaldespite channel changes and signal variations.

Symmetric Detection Probabilities. Using the thresh-old Cth, for each transmission we made a detection de-cision and computed the detection percentages in bothdirections for each link at all power level combina-tions across all the locations. In order to compare withSchmidl-Cox, as the WARP implementation uses L =32, for the comparison to hold meaningful we chose athreshold such that when one device transmits to anotherat a received power of -82dBm (9dB SNR), the false neg-atives are at 10%. Table 3 shows all the detection proba-bilities obtained across all combinations. In Table 3, thenotation AX-BY means node A transmitting at power XdBm and node B transmitting at Y dBm. F and R indi-cate forward and reverse directions. F means A transmitsto B while R means B transmits to A. Situations wheresevere starvation occur are highlighted in gray. As seenfrom Table 3 while a power difference of greater than3dB creates severe starvation scenarios in Schmidl-Cox,Skip-Correlation preserves carrier sensing symmetry.


8 Related WorkCarrier sensing has been extensively studied [16] and hasreceived a lot of attention from the research community.Improving performance through tuning carrier sens-ing. It is well-known that carrier sensing is limited bythe fact that carrier is sensed at the sender whose chan-nel measurements may be very different from that ofthe receiver. This could result in problems such as hid-den terminal as well as missed transmission opportuni-ties termed as exposed terminals. There has been a lotof work on improving Wi-Fi performance by tuning car-rier sense threshold, along with transmit power, and/ortransmission data rate, both for wireless LANs as wellas wireless multihop networks [13, 15, 27, 28, 29, 30].However, all these papers take a network-wide viewwhere the parameters of every node can be tuned.Carrier Sense Asymmetry. Starvation in Wi-Fi net-works occurs due to variety of reasons such as flow-in-the-middle, hidden nodes, and sensing asymmetry [14].In this paper, we focus on the carrier asymmetry issuedue to transmit power differences which is known tocause starvation. To address starvation issues arising dueto carrier sense asymmetry, authors in [18, 20, 23] pro-pose solutions that jointly tune transmit power and car-rier sense threshold of nodes in the network. Authorsin [12] propose that nodes use lower transmit power anddata rate for increased overall performance in dense andunmanaged wireless settings. In contrast, we presenta solution that ensures carrier sense symmetry despitenodes choosing their transmit powers independently.Coexistence with multiple transmit powers. Authorsin [25] show that transmit power differences in whitespace networks can result in starvation of low powermobile nodes and propose a direct sequence spreadspectrum-based solution to mitigate it. The Weeble sys-tem [22] also tackles the two power asymmetry prob-lem in white space networks using a unique preamble forhigh power nodes that is different from the preamble forlow-power nodes. As we show in this paper, the use ofa unique preamble per power-level is expensive both interms of preamble length as well as computational com-plexity. Instead, we address the problem of carrier senseasymmetry efficiently through the use of a single pream-ble while supporting a range of power levels.

9 DiscussionAre power differences having a major impact in Wi-Fi performance today? Wi-Fi performance issues arecaused by numerous factors (e.g., interference, conges-tion, signal attenuation, power difference, etc.). Sincepower difference is only one among many causes forpoor Wi-Fi performance, it is not clear how often it isthe root cause of Wi-Fi performance problems. However,there are a few indications that power differences may be

a significant problem. First, transmit power differencein Wi-Fi devices are common. For example, there areseveral devices available in the market whose transmitpower ranges from 100mW (e.g. Samsung Galaxy S3 txpower is 111 mW) to 1W (e.g. Linksys EA6900 router, txpower 944 mW). Further, adapters are available for mo-bile laptops/PCs that allow 1W transmission [6]. Thus,there is both demand and supply of higher power Wi-FiAPs and devices in the market today. Second, this topichas received attention by the FCC. For example, FCC re-cently reached a settlement with TP-Link, a Wi-Fi APmanufacturer, in an investigation [5] where TP-Link wasdetermined to have enabled a software-based setting forhigher than allowed transmit power in some channels.How much power difference can be supported effi-ciently? Skip-correlation is a general technique that cansupport arbitrary power differences (the 6dB limitationis only if backward compatibility to Wi-Fi is desired).However, efficiency can suffer if the range of power dif-ference is large since the preamble needs to be appropri-ately elongated and long preambles may require largerWi-Fi slots, thereby negatively impacting efficiency [19].Given devices with transmit powers between 100 mW to1000 mW are common in the market today, we believethat support for 10dB power difference can cater to alarge number of scenarios. Based on our implementationof skip-correlator, the length of the preamble required tosupport 10x power difference with similar carrier sens-ing behavior as 100mW standard Wi-Fi is 400 samples(160+160 samples for skip correlation + 80 samples forAGC). A 400 sample preamble can fit in an existing 9µsWi-Fi slot and will thus not reduce Wi-Fi efficiency.Interactions with rate adaptation. Skip Correlation de-pends only on modifications to the PLCP Preamble. TheSIGNAL field, which follows immediately after Pream-ble, encodes the rate in its first four bits. Since thepreamble has already been received before the SIGNALfield, carrier sense is independent of the rate chosen.Thus, skip-correlation has no impact on standard Wi-Fi rate adaptation and allows any rate adaptation algo-rithms to be used. However, for systems that use ratelesscodes [21], it is not clear how best to incorporate (multi-power) carrier sensing.

10 ConclusionWe propose a novel carrier sensing solution, skip-correlation, to address the starvation of low-power de-vices given the increasing proliferation of high power de-vices in unlicensed spectrum.

11 AcknowledgmentsWe would like to thank our shepherd, Heather Zheng,and the anonymous reviewers of NSDI’17 for their com-ments towards improving the paper.


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Appendix

A Proof of P1 and P2 Section 5.3Proof of P1. The second piece of SRecvPk

starts at γ PN

Pk

and SXmitPiends at sample number γ PN

Pi. When Pi ≥ Pk,

PN

Pk≥ PN

Pi, thus SXmitPi

∩ SRecvPkcomprises only the first

piece of SRecvPki.e., S[1, γ].

Proof of P2. Any preamble piece is always completelycontained between the ends of SXmitPj

and SXmitPj+1. Thus,

when i < k there are k−i preamble pieces starting at theend of SXmitPk

until the end of SXmitPi. The total number

of samples N(i, k) in SXmitPi∩ SRecvPk

is given by,

N(i, k) = γ+

j=k−i∑j=1

λk,i = γ+Pkγ

(1

Pi− 1

Pk

)=PkPiγ.

(8)

B Sensing Through Preamble CorrelationIn this section we describe the preamble correlation pro-cess and provide the necessary background.The Problem of Preamble Detection. Let S(n) be thepreamble of length L samples that is transmitted. The re-ceived signal Srecv(n) when no preamble is transmittedand when a preamble is transmitted given by,

Srecv(n) =N(n) no Xmit

R(n) +N(n) Xmit (9a)R(n) = S(n)∗H. (9b)

In Eqns 9a,9b, N(n) is the receiver noise, H is the chan-nel response that captures how the channel transformsthe transmitted signal into R(n) due to effects such asmulti-path fading and ∗ is the convolution operation. Thegoal of detection techniques is to reliably distinguish be-tween the no transmission and transmission scenarios inEqn 9a based on Srecv(n). While there exist several de-tection schemes, we now describe the two most popularschemes – the matched filter and Schmidl-Cox [24].Matched Filter. In this scheme the receiver computesthe normalized cross-correlation of the preamble with thereceived signal as,

C =

∣∣∣∣∣i=L∑i=1

Snormrecv (i)Snorm(i)

∣∣∣∣∣2

(10)

In Eqn 10 Snorm and Snormrecv are scaled versions of S

and Srecv respectively such that its total energy is 1. IfC > Cth, the channel is deemed busy and otherwise not.

Schmidl and Cox Detection. Here S(n) comprises twoidentical halves i.e., S(i) = S(i + L

2 ). As the transmis-sion passes through the channel, each of its halves areeffected by the channel in exactly the same way. Conse-quently R(i) = R(i + L

2 ). The receiver correlates twoconsecutive L

2 length windows from the received signalas,

C =

∣∣∣∣∣∣∣i=L

2∑i=1

Srecv(i)Srecv(i+L

2)

∣∣∣∣∣∣∣2

(11)

A high correlation (C > Cth) indicates that a preamblewas transmitted and the channel is deemed busy.Why Matched Filter is Typically Not Used for CS inPractice. The matched filter technique has two signifi-cant drawbacks. First, due to frequency selective fadingin the channel, R(n) is often very different from S(n)in Eqn 9b. Consequently, correlating R(n) with S(n)typically yields a low correlation. Schmidl-Cox does notsuffer from this problem since, both halves are affectedby the channel identically and thus results in a high cor-relation. Second, as discussed in Section 6, the circuitcomplexity of implementing a matched filter can be twoorders of magnitude greater than that of Schmidl-Cox.Thus, in the rest of this section we confine our discus-sion to Schmidl-Cox detection.Probability Distributions of C in Schmidl-Cox. Sup-pose that the noise floor is σ2

N (variance of noise), thedistribution of C when no preamble is transmitted isgiven by,

P (C|no Xmit, σ2N ) = P

∣∣∣∣∣∣∣i=L

2∑i=1

N(i)N(i+L

2)

∣∣∣∣∣∣∣2 (12)

Invoking the central limit theorem, the sum ofN(i)N(i + L

2 ) is a zero mean Gaussian with varianceL2 σ

4N . Thus, P (C|no Xmit, σ2

N )is a χ21 distribution with

mean L2 σ

4N .

Let the received preamble energy per sample (signalpower) be E(R(i)R(i)) = σ2

S (E denotes expectation).Further, typical preambles also have E(R(i)) = 0. SinceR(i) = R(i+ L

2 ), the distribution of C when a preambleis transmitted is given by,

(13)P (C|Xmit, σ2N , σS

2) =

P

∣∣∣∣∣∣i=L

2∑i=1

σ2S + 2R(i)N(i) + N(i)N(i+

L

2)

∣∣∣∣∣∣2

Invoking central limit theorem, the sum of R(i)N(i) isa zero mean Gaussian with variance L

2 σ2Nσ

2S . Thus, the

distribution of P (C| Xmit, σ2N , σS

2) is a non-central χ21

distribution with mean at L2

4 σ4S + Lσ2

Nσ2S + L

2 σ4N .

Thus, the probability distribution of computed corre-lations in the presence and absence of a preamble are χ2

1

distributions with means given by Eqns 14a, 14b respec-tively as,


µ(C) =

{LE

2N/2 no preamble(14a)

(LES)2/4 + (LES)EN + LE

2N/4 preamble (14b)

While we have only shown the above property forSchimdl-Cox, it holds for other correlation based tech-niques as well.

log10

(C)

-17.5 -17 -16.5 -16 -15.5 -15

Pro

ba

bil

ity

10-6

10-5

10-4

10-3

10-2

10-1

100

η-

η+

Cth

η-=10%

Figure 22: How threshold Cth is selected in Schmidl-Cox

Selection of Cth. There can be two kinds of errors inpreamble detection. False negatives occur when a pream-ble is transmitted but not detected while false positivesoccur when a preamble was not transmitted but erro-neously detected. The false negative rate is given by,

η−(C|σ2

N , σ2S

)=

∫ C

c=0P (c|Xmit, σ2

N , σ2S)dc (15)

and the false positive rate is given by,

η+(C|σ2

N

)= 1−

∫ C

c=0P (c|no Xmit, σ2

N )dc (16)

The selection of Cth is based on the Wi-Fi specificationof 10% false negative rate (90% detection rate) when theaverage received power is -82dBm [9]. As an example,Figure 22 depicts the curves for η− and η+ for a noisefloor of -91dBm and L=8 samples (0.4µs). Cth is cho-sen for η− = 10% (90% detection rate). Note that cor-responding to this value of Cth, the false positive proba-bility is well below 10−6.Effect of False Positives. A high false positive rate (η+)leads a device to erroneously conclude that there is anongoing transmission, resulting in an unnecessary back-off and loss of throughput. For a false detection rate ofη=10−2, once every 100 samples (5µs), a preamble willbe falsely detected. Since 5µs < 9µs (WiFi slot width)this means that the WiFi device will end up falsely de-tecting a preamble in almost every slot and will not beable to transmit any packets. Usually a false detectionrate of η− < 10−3 is needed for reasonable performance.At 10−3, once every 1000 samples or 6 Wi-Fi slots, apreamble is falsely detected. However, upon detectingan STS, the device then uses the Long Training Sequence(LTS) (Figure5) to tune its receiver parameters. If no LTSis detected then the receiver deems the channel free. Theprobability of falsely detecting a preamble in the LTS as

log10

(C)

-14 -13 -12 -11

Pro

ba

bil

ity

10-3

10-2

10-1

100

η-

ηc

η+

Figure 23: Performance of Orthogonal Preambles for 4power levels and L = 128.

well is now very low (< 10−6). This means that the de-vice will typically lose on average one WiFi slot for ev-ery packet transmission. Given that typical WiFi packettransmissions last several 100s of µs to few milliseconds,this results in a throughput drop of <2%.Approximating Detection Probability for Low FalseRate Scenario. When the false positive rate is very low,the typical operating regime of receivers, (LES)2/4 >>(LES)EN +LE2

N/4 and thus the mean reduces approx-imately to (LES)2/4. Consequently, the detection prob-ability is dependent on the product (LES).

C Performance of Orthogonal PreamblesIn this section we consider the practical viability of theorthogonal preamble scheme proposed in Section 3 thatuses a bank of matched filters. For this experiment wegenerated 4 different PN sequences of length 128 cor-responding to each of the four power levels. In orderto generate a PN sequence, we first generated a randomvector comprising 128 complex numbers, each of whichhad a random phase between 0 to 360 degrees but hadunit magnitude. Then we took an Inverse Fourier Trans-form of this random vector to create the PN sequence.This method ensured that equal energy was transmittedat various parts to frequency band to make it robust tofrequency selective deep fades. A device transmitted thissequence and a receiver received these samples. We thenfound the normalized cross-correlation with each of the4 PN sequences. The sequence that gave the maximumcorrelation was chosen and the power level was identifiedas corresponding to this sequence. This meant that therewould be errors due to erroneously concluding an incor-rect power level in addition to false positives. The largerthe number power levels the worse is the performanceand longer the length of preamble that is required. Fig-ure 23 shows the false detection rates due to noise η+,false preamble detections where the power level was in-correctly inferred ηc and the false negative rates η− as afunction of correlation values when the received poweris -82dBm for L = 128. As seen from Figure 23 eventhough at L = 128 η− is very small, the incorrect iden-


Figure 24: The setup for 3-node experiment

Setting-ILinks A-B B-A A-C C-A B-C C-A

Schmidl-Cox 100 0 97.8 12.9 24.2 99.8Skip 100 100 99.9 100 100 99.9

Setting-IISchmidl-Cox 100 0 97.7 6.9 24.1 33.7

Skip 100 100 97.4 99.6 39.7 41.7

Setting-IIISchmidl-Cox 24.2 33.6 0 0 6.9 0

Skip 39.8 41.6 0.2 6.5 20.8 3.5

Table 4: Detection Probabilities for various links in3 node experiment [%]

tification of power levels (ηc) becomes the dominatingcause for errors. Table 5 shows the various values of ηcand η+ for different values of L. While η+ is acceptablylow at L = 128, ηc is very high at 14%. This experimentshows why orthogonal preamble approach is not only ex-tremely computationally inefficient (Section 6) but alsoperforms poorly.

L 8 16 32 64 128ηc 69.8 58.12 54.5 36.08 14.22η+ 11.08 9.05 6.14 1.53 < 0.1

Table 5: False positive rates [%] for various lengths oforthogonal preambles

D CS Symmetry - Three Node Experi-ments

In this experiment we placed three WARP boards A, Band C at three different fixed locations and change theirtransmit powers to create three different scenarios - Set-ting I, Setting II and Setting III depicted in Figure 24.The transmit powers of the devices and their average re-ceived powers over the course of the experiment are alsodepicted in Figure 24. Similar to our experiment withtwo nodes, in each setting we run 5000 rounds where alldevices transmit once each in a single round. We waitabout 1 second between each round. The total durationof this experiment was about 5 hours and there was about

5-8dB variation in received signal strength during thecourse of the experiment. We use both Schmidl-Cox aswell as Skip-Correlation to evaluate the detection proba-bilities, which are provided in Table 4. X-Y indicates Atransmitting to Y.Setting-I: This setting is similar in the example illus-trated in Figure 12(b) where A can be sensed by bothB and C while the reverse is not true. Also, B can senseC but not the other way round. As seen from Table 4,Schmidl-Cox experiences carrier sensing asymmetry inall three pairs as expected, however in Skip-Correlationthis the detection probabilities are symmetric in eitherlink directions.Setting-II: In this setting we reduce C’s power to 20dBmto remove the asymmetry between B and C. Thus, bothB and C can sense A but not each other. As in Setting-I, A cannot sense both B and C. As seen from Ta-ble 4, Schmidl-Cox experiences shows carrier sensingasymmetry between A,B and A,C pairs while Skip-Correlation exhibits carrier sensing symmetry betweenall pairs.Setting-III: In this setting we reduce the power of A to20dBm to remove all link asymmetries. As seen fromTable 4, both Schmidl-Cox and Skip-Correlation do notshow any carrier sensing asymmetry as expected.

These results demonstrate that Skip-Correlation pre-serves carrier sensing symmetry under various scenarios.


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