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Understanding the Limitations of Transmit Power Controlfor Indoor WLANs ∗
Vivek Shrivastava, Dheeraj Agrawal, Arunesh Mishra, Suman BanerjeeUniversity of Wisconsin-Madison
Madison, WI 53726{viveks,dheeraj,arunesh,suman}@cs.wisc.edu
Tamer NadeemSiemens Corporate Research
Princeton, NJ [email protected]
ABSTRACTA wide range of transmit power control (TPC) algorithmshave been proposed in recent literature to reduce interfer-ence and increase capacity in 802.11 wireless networks. How-ever, few of them have made it to practice. In many casesthis gap is attributed to lack of suitable hardware supportin wireless cards to implement these algorithms. In particu-lar, many research efforts have indicated that wireless cardvendors need to support power control mechanisms in a fine-grained manner – both in the number of possible power levelsand the time granularity at which the controls can be ap-plied. In this paper we claim that even if fine-grained powercontrol mechanisms were to be made available by wirelesscard vendors, algorithms would not be able to properly lever-age such degrees of control in typical indoor environments.We prove this claim through rigorous empirical analysis andthen build a tunable empirical model (Model-TPC) that candetermine the granularity of power control that is actuallyuseful. To illustrate the importance of our solution, we con-clude by demonstrating the impact of choice of power controlgranularity on Internet applications where wireless clientsinteract with servers on the Internet. We observe that thenumber of feasible power was found to be between 2-4 formost indoor environments. We believe that the results fromthis study can serve as the right set of assumptions to buildpractically realizable TPC algorithms in the future.
Categories and Subject DescriptorsC.4 [Computer Systems Organization]: Performance ofSystems; C.2.1 [Computer Communication Networks]:Network Architecture—Wireless Communication
∗Traces used in this paper will be available atwww.cs.wisc.edu/∼viveks/powercontrol
Permission to make digital or hard copies of all or part of this work forpersonal or classroom use is granted without fee provided that copies arenot made or distributed for profit or commercial advantage and that copiesbear this notice and the full citation on the first page. To copy otherwise, torepublish, to post on servers or to redistribute to lists, requires prior specificpermission and/or a fee.IMC’07, October 24-26, 2007, San Diego, California, USA.Copyright 2007 ACM 978-1-59593-908-1/07/0010 ...$5.00.
General TermsAlgorithms, Experimentation, Measurement, Performance
KeywordsIEEE 802.11, Transmit Power Control, RSSI Modeling, In-door WLAN, Fine-Grained, Limitations, Kullback-Leibler
1. INTRODUCTIONPower control mechanisms in wireless networks have been
used to meet two different objectives — to reduce energyconsumption in mobile devices, so as to conserve battery life,and to reduce interference in the shared medium, thereby al-lowing greater re-use and concurrency of communication. Inthis paper, our focus is to study power control as applica-ble to the interference reduction objective. As an examplein this paper, we consider the impact of power control forWLAN clients interacting with servers on the Internet. Re-cent theoretical work has shown that ideal medium accessprotocol using optimal power control can improve channelutilization by up to a factor of
√ρ, where ρ is the density
of nodes in the region (using fluid model approximations)[9]. Power control mechanisms [11, 20, 18] typically try tooptimize the floor space acquired by wireless transmissionsby limiting the transmit power of control and data packets,thereby providing opportunity for multiple flows to coexist.
A number of research efforts have studied power controlbased on the theoretical abstraction of wireless signal prop-agation in free space and consider transmit power as a con-tinuous variable (i.e., a fine grained parameter), that can beset per packet to yield optimal performance. Conventionalpower control mechanisms have exercised fine grained con-trol in the two dimensions as shown in Figure 1 : 1) Timegranularity at which power level is changed, 2) Magnitudegranularity by which the power level is changed. We ana-lyze both the dimensions of fine grained power control andprovide guidelines for power control granularity in typicalindoor environments.
Prior work [8] has pointed out that lack of vendor supportfor fine-grained power control mechanisms in the wirelesscards inhibit deployment of these mechanisms. In this paperwe ask the following questions: Is fine-grained power con-trol really useful and would lead to a better design of power-control algorithms? If not, what is the minimum granularity
Time
Magnitude
Coarse
Fine
Coarse Fine
IPMA [18]
PERF [1]
SHUSH[16] PCMA[11]
control
control
Figure 1: Two dimensions of transmit power controltaken by prior approaches. PCMA, SHUSH rely onchanging transmit power by small values ( 1dBm)and lie on the magnitude dimension. IPMA, Sub-barao et. al. rely on changing the transmit poweron a per packet basis and hence lie on the time di-mension
of power control that is useful in different wireless environ-ments, including Internet oriented wireless communication? We answer the first question in the negative. As we dis-cuss in detail in the paper, in practical indoor wireless LAN(WLAN) deployments, multipath and fading effects, cou-pled with various sources of interference in the unlicensedbands, imply that power control algorithms cannot derivesignificant benefits from very fine-grained mechanisms. Wedemonstrate this through detailed experimentation in differ-ent indoor wireless network environments. We estimate thedistributions of Received Signal Strength Indicator (RSSI)1
for various transmit power levels at the transmitter andshow that although more power at the transmitter on av-erage translates to more power at the receiver, there is sig-nificant overlap between the RSSI distributions for nearbypower levels, making them practically indistinguishable atthe receiver. This can be attributed to dominant multipathand fading effects, that lead to significant signal strengthvariations in indoor environments.
Our answer to the second question is that a power controlalgorithm can make practical use of only a few (2-3) discretenumber of power levels. The exact number and choice ofpower levels is a characteristic of the multipath and fading ofa particular wireless environment and the presence of otherinterfering sources.
Our observations are true for both ad-hoc networks andInternet oriented wireless communications (WLANs), and inthis paper we present our results from the latter setting. Inparticular, through this work we build an empirical model
1Variations in RSSI typically correspond to variations in Sig-nal to Noise Ratio (SNR) as shown by Reis et. al in theirmeasurement based study of delivery and interference mod-els for static wireless networks [7]. Moreover commoditywireless cards only report the RSSI values for each packetand hence we base our observations on the measurement forRSSI values. We further discuss this in detail in Section 3.
that allows us to characterize the specific set of power levelsthat is useful for a given environment and could be used toperform per packet power control.
Power control is also an important design considerationin cellular networks, where is it primarily used to counterfast fading. However, cellular networks primarily operate inoutdoor environment, where we show that the effect of mul-tipath is not significant enough to hinder fine grained TPC.We discuss more about relevance of our work in context ofcellular networks in Section 6.
Key contributionsThe following are the key contributions and the main obser-vations from this work:
• Measurement: We collect extensive traces from mul-tiple environments such as office building and univer-sity departments, to characterize Received Signal StrengthIndicator (RSSI) variations in different indoor settings.Through rigorous statistical analysis of the traces us-ing Allan’s Deviation (for characterizing the burst sizeof RSSI fluctuations) and Normalized Kullback-LeiblerDivergence (NKLD) (for characterizing RSSI distri-bution in real time), we observe that the number offeasible power levels that can be used in a transmitpower control mechanism is few and discrete, and onceidentified, could be used to perform power control atsmall time scales (per packet).
• Model: Through this analysis, we propose an empir-ical model to determine the set of useful power levelsin an online fashion, i.e., this model is computed andadjusted dynamically as wireless data communicationis going on. Note, that the number and choice of suchpower levels would depend on individual wireless en-vironment. In all our experimental scenarios, it wasfound to be less than 4 and often much less.
• Validation: Through Internet-oriented wireless ex-periments, we demonstrate the usefulness of the ourmeasurement based empirical model (Model-TPC) forimproving performance of wireless clients interactingwith servers on the Internet in our indoor WLAN de-ployment. In particular, we show that correct choiceof power levels can lead to actual throughput gains inindoor environments.
We believe that our our experiments highlight some fun-damental issues with transmit power control, that can helpin design of future wireless interfaces that are used in lap-tops, PDAs and are widely used as a major Internet accessmechanism.
The remainder of the paper is organized as follows. Sec-tion 2 motivates the infeasibility of fine grained power con-trol in indoor WLANs and discusses various transmit powermechanism proposed in literature, with their respective eval-uation in context of our practical models for transmit powercontrol. In Section 3, we analyze the RSSI distributionsunder varying indoor scenarios and propose an online mech-anism (Online-RSSI) to characterize the distribution in realtime. We use the online mechanism to derive an empiricalmodel for transmit power control (Model-TPC) describedin Section 4. Section 5 highlights the impact of using ourempirical model on end user experience through Internet ori-ented wireless experiments. We briefly discuss power control
RB−8
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RB−11
RB−12
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RB−7
T2
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LOS INDOOR
500 meters
T4
R4
500
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Figure 2: The wireless testbed, consisting of seven802.11 a/b/g nodes (transmitters marked by T1, T2and receivers marked by RB-1 - RB 12]). The dottedarrows indicate the transmitter-receiver pair T1-R2and T3-R2 for our Internet oriented experiments.
in cellular networks in section 6 and some related work in 7.Finally we conclude in section 8.
2. MOTIVATION : POWER CONTROLAPPROACHES AND LIMITATIONS
Implementation of fine grained power control mechanismshas been limited by the hardware support in current 802.11wireless cards which have only limited number of discretepower levels. As described in [8] , most of the wireless cardssupport only 4 to 5 power levels at the hardware, whichis in stark contrast to the fine grained control preferred bymost power control schemes like PCMA [11], SHUSH[18]and IPMA [20]. This being a limitation of current stateof the art hardware, can be resolved in future wireless cardsthat may support fine grained power levels. However, we ar-gue that there are fundamental constraints to power controlin indoor wireless environments, which limits the number offeasible power levels that is useful in such mechanisms. Wesubstantiate our claim through indoor WLAN and outdoorexperiments in the following section, where we show thatRSSI variations are present in both outdoor and indoor en-vironments, but are especially dominant in indoor scenarios.
2.1 Infeasibility of Fine Grained PowerControl
We present preliminary results from our detailed set ofexperiments explained in Section 3 to illustrate the funda-mental constraints of fine-grained power control.
Outdoor ScenarioThis sample experiment consists of a pair of outdoor transmitter-receiver pair (T4-R4) shown in Figure 2 operating using the802.11a standard. At R4 we capture the packets transmit-ted by T4 for different power levels available at T4’s Atherosbased wireless chipset. Since low RSSI is more likely to causea packet error, we have enabled Madwifi driver to receivepackets in error and in order to prevent the bias towards
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Figure 3: Probability Distribution of RSSI for vary-ing power levels at the transmitter is shown in thefigure. The top figure corresponds to outdoor sce-nario with 6 distinguishable power levels while bot-tom figure shows the effect of increased multipathand interference in the indoor WLAN scenario withthe number of distinct power levels reduced from 6to 3. Band:802.11g Data Packet Size:1Kbytes
high RSSI values, we include the RSSI of erroneous packetsin our calculations for RSSI distributions. Figure 3 showsthe probability density function of RSSI distribution for var-ious power levels at the transmitter. The power levels areincreased from 10mW to 60mW (max. transmit power), insteps of 10mW. For the sake of clarity, these power levelsare chosen so that there is minimal overlap between theirrespective RSSI distributions. For example at a power levelof 60 mW, the RSSI values vary from 35dBm to 45dBm,with 40 percent of the packets being received at 41dBm.The average variation in RSSI value over all power levels isapproximately 7.5 dBm.
This variation can be attributed to the multipath and fad-ing effects, due to which the packets transmitted at the samepower level, may be received with varied signal strength atthe receiver. A difference of an order of wavelength in thepaths taken by the wireless signals from the transmitter, canlead to the two signals being out of phase [16], resulting invariations in the signal strength at the receiver. Even thoughmore power at the sender translates to more power at thereceiver, the distributions of the received signal power over-laps significantly, thereby making them hardly distinguish-able. As we show next, this effect is even more pronouncedin indoor environments than in outdoor environments wherethere are only a few strong paths that impact the signal.
Indoor ScenarioWe repeat the aforementioned experiments for an indoortransmitter-receiver pair T2-R2 as shown in Figure 2. Theresulting distribution of RSSI values is shown in Figure 3.As expected the RSSI variations increase, thereby increasingthe overlap between RSSI of neighboring power levels. Thisobservation indicates that in indoor settings, the number ofpower levels having non-overlapping RSSI distributions arefurther reduced, thereby making fine-grained transmit power
control much less effective. These experiments show thatfine grained transmit power control mechanism are muchmore difficult to realize in indoor deployments.
It is evident from Figure 3 that in a collective fashion, thedistribution of all the six power levels cover a wide rangeof RSSI values (20 - 45 dBm). Also note that for any sin-gle power level, its RSSI distribution overlaps significantlywith that of neighboring power levels. The introduction offine grained power levels at the hardware will imply signifi-cant overlap between the distribution of existing power levels(0,10,14,15,17,18)dBm and the new power levels. A signifi-cant overlap between the RSSI distributions of two (succes-sive) power levels correspondingly diminishes the practicaleffect of having the respective distinct power levels – they be-come practically indistinguishable at the receiver. This canbe considered analogous to the concept of channels in 802.11band, where there are 11 channels available but only 3 chan-nels are non overlapping and hence useful. Similarly, finegrained power levels cannot be distinguished easily at thereceiver due to RSSI variations and hence may not be usefulsimultaneously.
We performed the same set of experiments at two differentlocation, at the NEC Research Labs at Princeton and at theComputer Sciences Department at University of Wisconsin-Madison. We observed that, although the exact shape of theRSSI distribution may depend on the exact indoor environ-ment and other interference effects, the general nature re-mains similar to Figure 3. In this paper, we report our mea-surements from the NEC Research Labs, which we believeare representative of a typical indoor WLAN scenario.
Next we summarize prior approaches proposed in the lit-erature that rely on fine grained power control. We showwhy such approaches might face difficulty in a practical im-plementation. We also discuss how our proposed empiricalmodel could act as an oracle to guide such algorithms tochange transmit power that are effective in practice.
2.2 Implications on Existing Power ControlApproaches
We categorize some of the prior power control methodsapplicable to WLANs into two categories : 1) fine-grainedin magnitude of transmit power and 2) fine-grained in mag-nitude of time (per-packet). Existing power control ap-proaches can be categorized in the two aforementioned cat-egories as shown in Figure 1. We explain the implicationsof our observations on both categories of protocols:
Magnitude Dimension of Fine Grained Power ControlMonks et al. proposed a power controlled multiple accesswireless MAC protocol (PCMA [11]), within the collisionavoidance framework. PCMA generalizes the transmit-or-defer ”on/off” collision avoidance models to a more flexible”variable bounded power”collision suppression model. UsingPCMA, the transmitter-receiver pairs can be more tightlypacked into the network by adjusting the power level of thetransmitter to the minimum required for a successful trans-mission, thereby allowing a greater number of simultaneoustransmissions (spectral reuse). In order to ensure successfulpacket delivery, each receiver in PCMA first calculates theextra noise that it can tolerate, such that the SNR for itsown packets is above the threshold for correct reception. Itthen advertises this noise tolerance by sending a busy toneon the auxiliary channel, and all the transmitters in the
vicinity measure the received signal strength of the tone todetermine the maximum power with which they can initi-ate their own transmissions. This mechanism requires exactcalculations of received power, which mat not be predictableunder multipath and fading effects. Moreover, the authorstreat transmit power as a continuous parameter, which maynot be feasible in indoor environments due to significantRSSI variations.
Seth et al. propose a reactive transmit power controlmechanism, called SHUSH [18], where nodes operate on theoptimum(minimum) power required for communication. Ondetecting interference, SHUSH calculates the exact power re-quired to send a RTS to the interferer and hence optimizesthe “floor space” acquired by any flow. Unlike PCMA, how-ever SHUSH transmits at a higher power only when a flowis interrupted by external interference. Again SHUSH as-sumes fine grained control on power levels and ignores RSSIvariations which can make it difficult to infer the exact inter-ference at the receiver, thereby complicating the calculationof target transmit power required to SHUSH the interferer.Our experimental observations suggest that such observa-tions are too deviant from realistic scenarios. Using our em-pirically derived power control model (Section 4), the abovemechanisms could dynamically determine an exact set offeasible power values to be used in an environment.
Time Dimension of Fine Grained Power ControlMany researchers in the past have proposed schemes whichrequire change in the power level on a per packet basis.
Akella et al. [2] discuss some power control mechanismsin their work on wireless hotspots. They propose that APsshould use the minimum transmit power required to supportthe highest transmission rate. In their scheme, the receiversends the value of observed RSSI, averaged over some smallnumber of packets, as a feedback to the transmitter. Thetransmitter on receiving the average RSSI value on the re-ceiver side, decides the optimal power level suitable for usein the current channel conditions. However they do not pro-vide exact values for power level granularity that should beused. As discussed earlier, a simple average of RSSI valuesat the receiver may not give a correct estimate of the actualSNR.
Subbarao [19] has proposed a dynamic power-consciousrouting mechanism that incorporates link layer and physicallayer properties in routing metrics. It routes the packet on apath that requires least amount of total power expended andeach node transmits with the optimum (minimum) powerto ensure reliable communication. This scheme requires perpacket power control and also needs feedback from the des-tination regarding RSSI on a per packet basis.
Similar to PCMA approach, Yeh et al. [20] proposed aninterference/power aware access control. They augment thenormal RTS/CTS mechanism of IEEE 802.11 with provi-sion for multi level RTS, where the transmit power of theRTS mechanism is set on the basis of the intended receiver.Such a dynamic per packet approach becomes difficult inthe face of significant RSSI variations and become difficultto implement on real systems.
We analyze the stationarity (coherence time) of signalstrength for various scenarios and propose a simple algo-rithm Online-RSSI, that can be used to determine the dis-tribution of signal strength for a given transmit power levelin any scenario. Once the set of feasible power levels (hav-
ing non overlapping signal strength distribution) is derived,the receiver can use this model to determine the transmitpower of the transmitter for a packet received at any givensignal strength and hence provide correct feedback to thetransmitter on a per packet basis (or similar time scales).
3. CHARACTERIZING SIGNAL STRENGTHDISTRIBUTION
Our experiments serve three main purposes: (i) to gainan understanding of the characteristics of RSSI variationsunder varying practical scenarios (in terms of user move-ments, shadowing, multipath and external interference) (ii)as a learning data-set to build our empirical model for iden-tifying the set of feasible power levels (iii) as an input tovalidate this model.
In this section, we characterize the distribution of RSSIunder varying magnitudes of multipath, shadowing and other802.11 and non 802.11 interference for a real WLAN deploy-ment shown in Figure 2. By studying the RSSI distribu-tion across different power levels and different channel condi-tions, we formulate mechanisms to dynamically predict andconstruct such distributions in real-time. Such mechanismsshall be used in the next section where we build a modelto predict the useful power-levels in a given environment.We briefly describe various components of our experimentalsetup.
3.1 RSSI measurementsThe performance of most wireless applications depends on
the packet delivery probability. The SNR is widely used inthe literature to model packet delivery probabilities: packetsare successfully received if S/(I+N) is above a certain thresh-old, and otherwise are not. Commodity wireless cards donot report the information required to compute SNR. Forinstance, our cards report only their version of RSSI, theminimum feedback allowed by the 802.11 standard. Someother cards also report an estimate of I by measuring energyin the air when no packets are being sent, but this estimatemay be inaccurate during packet delivery. It has been shownin a prior measurement based study by Reis et. al [7] thatRSSI is generally predictive of delivery probability in staticwireless networks and while wireless networks exhibit sub-stantial variability, measurements of average behavior overeven relatively short time periods tend to be stable. Thisphenomenon was also observed in our joint power and datarate adaptation experiments (described as an application ofour model in Section 5), where the power levels with sig-nificant overlap in their corresponding RSSI distribution,perform similarly in terms of rate adaptation. Since rateadaptation again depends on packet delivery rate, we caninfer that RSSI is a reasonable estimate for SNR and twopower levels with significant RSSI overlap at the receiver willperform similarly for packet delivery probabilities. Hence webase our measurements and models on RSSI values that isreadily available from the commodity wireless cards.
RSSI estimates signal energy at the receiver during packetreception, measured during PLCP headers of arriving pack-ets and reported on proprietary (and different) scales. Atheroscards, for example report RSSI as 10log10(
S+In
), where S isthe signal strength of the incoming signal, I is the interfer-ing energy in the same band, and n is a constant (−95dBm)that represents the ”noise floor” inside the radio. Atheros
��������
��������
WiFiDevice
PowerSupply
senseresistor
0.1ohm
DAQ PC
Figure 4: Figure shows the setup used to determinepower drawn by wireless cards. The DAQ samplesvoltage across the WiFi device and sends it to a PCvia USB. Performed at transmitter to validate thepower levels available at the hardware.
RSSI is thus dB relative to the noise floor. To give resultsthat are independent of card vendors, we transform RSSIvalues to received signal strength (RSS) values, that give ab-solute energy levels. That is, RSSI is defined to be S+I.Note that these RSSI measurements are performed at thereceiver and then provided as a feedback to the transmit-ter for constructing the empirical model for feasible powerlevels.
3.2 Validating Available Hardware PowerLevels
To ascertain the available power levels in 802.11 WLANcards, we measure the voltage across the wireless card of thetransmitter by the setup shown in figure 4. The setup con-stitutes of a 0.1 ohm sense resistor, R, connected in series tothe circuit of the wireless device (pcmcia card) that exposesthe voltage supplied to the device. For the pcmcia based802.11 card, we used the Sycard 140A cardbus adapter, toexpose the voltage supplied to the card. A Data AcquisitionCard (DAQ), DS1M12 Stingray Oscilloscope, samples thevoltage through R at a rate of 1 million samples per second,thereby giving us voltage measurements on a per packet ba-sis. The instantaneous power consumption, Pi can thereforebe written as Pi = Vd × VR/R where Vd is the voltage pro-vided to the WiFi device and VR is the voltage drop across Rat a given moment. These measurements are performed atthe transmitter and shows that indeed the right power levelsare implemented at the hardware circuitry of the transmit-ter’s wireless interface. On the basis of power consumed bythe wireless interface, we validated that Cisco Aironet cardsprovide 6 different power levels for 802.11g and 5 differentpower levels for 802.11a respectively.
3.3 WLAN Trace CollectionIn order to understand the behavior of RSSI under vary-
ing interference and multipath effects, we conduct detailedexperiments to collect RSSI traces in an office building un-der varied indoor settings. In all our experiments, we use afixed data rate of 1Mbps and fixed packet size of 1KB, sothat the time intervals are directly translated into number ofpackets (modulo 802.11 DCF), which is the X axis for mostof our plots. This facilitates easier packet based analysis ofRSSI traces and their implications to power control mecha-nisms, which generally base their decisions on a per packetbasis. For our experiments, 1 sec of receiver time window≈ 1000 packets of 1KB each (unless otherwise specified).We repeated the same experiments with other wireless cardsand found the results were consistent with the ones reported
here. We discuss the exact set up for each of these scenarios.
Line of Sight - light interference(LOS-light)These experiments represent a scenario where the transmitter-receiver pair are in direct line-of-sight and have minimal tozero external interference. Figure 2 shows the placement oftransmitter-receiver pair T2 and R2 respectively for LOS-light experiment. The experiment used 2 IBM Thinkpadlaptops running Linux kernel 2.6. Each of the laptops housedan Atheros chipset based 802.11a/g Linksys wireless cardand used Madwifi drivers. We used Netperf 2.2 to generateUDP flows between the two laptops and collected MAC-leveltraces for the packets received at the receiver using the pcapstandard library. We vary the power of the transmitter tounderstand their corresponding effects on RSSI.
Non Line of Sight - light interference(NLOS-light)The experiment comprises of a single transmitter T1 and 5receivers (RB-1, RB-8, RB-10, RB-11 and RB-12) as shownin Figure 2 placed at various locations in the building andused netperf and pcap library to generate flows and col-lect traces respectively. None of the receivers were in directline-of-sight of T1 and this setup too had minimal to zeroexternal interference.
Line of Sight - heavy interference(LOS-heavy)We investigate the effect of controlled interference on RSSI.We use our experimental testbed shown in figure 2 for line ofsight experiments to evaluate the effect of heavy interference(like bulk data transfers) on RSSI variations. Nodes RB-12, RB-11 and RB-2 act as separate APs and perform bulkdata transfers with their respective clients (3 IBM laptops).Nodes T2 and R2 form a transmitter-receiver pair.
Non Line of Sight - heavy interference(NLOS-heavy)We use our experimental testbed shown in figure 2 for non-line of sight experiments to evaluate the effect of heavy inter-ference (like bulk data transfers) on RSSI variations. NodesRB-12, RB-11 and RB-2 act as separate APs and performbulk data transfers with their respective clients (3 IBM lap-tops). Nodes T1 and RB-8 form a transmitter-receiver pair.
3.4 Analyzing WLAN TracesFigure 5 shows the smoothed moving average of RSSI
per packet for the four categories of traces described inprevious section. Although we collect many traces fromeach category (namely LOS-light, NLOS-light,LOS-Heavyand NLOS-heavy), we present only one representative tracefrom each category. The representative trace is chosen suchthat it manifests the basic characteristic of traces from thatparticular category. All these traces are collected at 1Mbpsof data rate with packet size of 1000 bytes.
As clear from Figure 5, the variations in RSSI is minimumfor LOS-light trace and is maximum for the NLOS-heavytrace. This behavior is expected because the factors con-tributing to RSSI variations increase in both number andmagnitude from the topmost plot to the bottom. Figure6 show the probability distribution of RSSI values at thereceiver for the four scenarios. Clearly, the distribution ofRSSI becomes flatter (larger variation) with the increase ininterference and multipath effects, with the distribution ofLOS-light and NLOS-light resembling a Gaussian distribu-tion. Next we analyze these trace in detail to understand
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Figure 5: Exponentially weighted moving average ofRSSI over time for four traces collected under var-ious practical scenarios, with varying degree of ex-ternal interference, multipath, shadowing and fadingeffects. The packets are sorted in order of receivedtime. The traces from topmost plot to the bottombelong to LOS-light, NLOS-light, NLOS-heavy andLOS-heavy. The high variation of RSSI for NLOS-heavy can be observed.
temporal variations in RSSI and propose an algorithm todynamically characterize the distribution of RSSI in any en-vironment.
StationarityFigure 5 shows the variation of RSSI on a per packet ba-sis, but it would also be useful to observe the amount offluctuation over a set of packets (or a burst). Such an anal-ysis would reveal any characteristic burst intervals whereRSSI values vary largely over different bursts but deviateminimally within a burst. Also note that since our experi-ments are conducted with the traffic sent at uniform ratespacket intervals directly correspond to time intervals (mod-ulo 802.11 DCF effects). One way to summarize changesat different time scale is to plot the Allan deviation [3] ateach packet interval. Allan deviation is the square rootof the two sample variance formed by the average of thesquared differences between successive values of a regularlymeasured quantity taken from sampling periods of the mea-surement interval. Allan deviation differs from standard de-viation in that it uses differences between successive sam-ples, rather than the difference between each sample andlong term mean. In this case, the samples are the fractionof packets delivered in successive intervals of a particularlength. The Allan deviation is appropriate for data setswhere data has persistent fluctuations away from the mean.The formula for the Allan deviation for N measurements ofTi and sampling period τ0 is:
σy(τ0) =
s PN−1i=1 (Ti+1 − Ti)2
2(N − 1)(1)
The sampling period is varied by averaging n adjacent valuesof Ti so that τ = nτ0. Now the Allan deviation for different
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Figure 6: Probability distribution of RSSI for thefour traces shown in Figure 5. The spread in RSSIdistribution is noticeable in all the traces, with theNLOS-heavy trace having the maximum deviation.In the NLOS-heavy scenario, the RSSI values showpersistent fluctuations about two different RSSI val-ues (bimodal distribution).
values of n can be given by:
σy(τ) =
s PN−2n+1i=1 [ 1
n(Pi+2n−1
j=i+n Tj −Pi+n−1
j=i Tj)]2
2(N − 2n + 1)(2)
The Allan deviation inherently provides a measure of thebehavior of the variability of a quantity as it is averagedover different measurement time periods, which allows it todirectly quantify and distinguish between different types ofRSSI variations. The Allan deviation will be high for inter-val lengths near the characteristic burst length. At smallerintervals, adjacent recent samples will change slowly, andthe Allan deviation will be low. At longer intervals, eachsample will tend towards the long term average, and theAllan deviation will again be small.
Figure 7 shows the Allan deviation of RSSI over largescale packet intervals (thousands of packets). We can ob-serve that although there are no prominent peaks for theRSSI bursts for any scenario, but Allan Deviation becomesquite stable (between 0.2 and 0.5) for LOS-light, NLOS-lightand LOS-heavy scenarios. The NLOS-heavy has relativelyhigher deviation and shows significant fluctuations in therange of (1.6-1.8). In Figure 8, we show the zoomed ver-sion for Allan deviation for intervals less than 100 packets.This figure shows the short term characteristic of RSSI vari-ations. As clear from the figure, Allan deviation for LOS-light, NLOS-light and LOS-heavy is maximum at 1 packet,then decreases sharply because averaging over longer inter-vals rapidly smoothes out fluctuations. This means that theRSSI variations for the aforementioned three categories areindependent for intervals less than 100 packets. On the otherhand, NLOS-heavy shows sharp increase in Allan Deviationfrom 0.6 to 1.4. This indicates that in NLOS-heavy trace,the RSSI averaged over small sample sizes (τ in Equation2), change quickly leading to a sharp increase in Allan De-viation at such small scales. On further analysis, we foundthat deviation for NLOS-heavy reaches 1.7 for about 400-
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Figure 7: Allan deviation for the four representativetraces shown in figure 5. The y axis shows the Allandeviation (σ(τ)), while the value of n (sampling pe-riod in Equation 2) is varied on the x axis. It showsthat there are no clear peaks for the RSSI burstsfor any scenario, however it is clear that Allan De-viation becomes quite stable (between 0.2 and 0.5)for LOS-light, NLOS-light and LOS-heavy scenar-ios. The NLOS-heavy has relatively higher devia-tion and shows significant fluctuations but remainsin the range of (1.6-1.8).
500 packets and as shown in Figure 7, fluctuates around thatvalue for larger packet intervals as well. We agree that thereis no clear decrease in the Allan deviation for any scenario,so we approximate the value of burst size at the point whenthe deviation becomes quite stable (or the rate of increase indeviation becomes very low). Hence we choose ≈ 400 pack-ets for NLOS-heavy and on the order of thousand packetsfor LOS-heavy, LOS-light and NLOS-light.
We report these burst size for various LOS and NLOS sce-narios in Table 1. The burst size information is used by ouralgorithm Online-RSSI (explained in Section 3.5), that sam-ples the packets in multiples of these burst sizes for deter-mining the signal strength distribution for a given transmitpower level. As RSSI varies significantly across bursts, theonline mechanism needs to consider at least an incrementof burst size in its sampling process to determine if the on-line distribution being computed has stabilized. This allowsus to quickly converge on an accurate RSSI distribution asexplained in Section 3.5.Summary: RSSI variations are bursty for intervals of theorder of ≈ 1000 packets for LOS-light, NLOS-light and LOS-heavy scenarios. But for NLOS-heavy traces, the Allan de-viation increases even in the small interval of 100 packets,depicting bursts even in short packet intervals. This can beexplained because the interference coupled with multipatheffects make the wireless channel highly variable and leads tobursts even in very short time intervals. This behavior wasobserved in all our NLOS-heavy traces (for various receivers)and indicates high variability in wireless environment. Allandeviation provides an estimate of burst length of a trace andcould be interpreted as an effect of temporal variations inwireless channel. So if Allan deviation shows that a trace
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Figure 8: Zoomed version of Allan deviation forshort interval of time (≈ 100 packets). Allandeviation decreases sharply for LOS-light, NLOS-light and LOS-heavy traces, indicating independentpacket losses. But Allan deviation for NLOS-heavyincreases, indicating very small bursts and highlyvariable wireless channel. This is a strong indica-tion that fine grained power control becomes evenmore difficult when multipath effects are coupledwith 802.11 interference.
has very small burst periods (as in the case of NLOS-heavy),it can be used as an indication that per-packet power con-trol will be highly unpredictable. Finally we observe that allthe scenarios show substantial non-stationarity in RSSI vari-ations, which will further impede fine grained mechanismsfor power control.
EntropyThrough the empirical analysis presented in Section 2.1, weobserved that due to multipath, fading and other propaga-tion effects, the RSSI values at the receiver show significantvariation (also corroborated by Figure 6). Depending onthe exact environment, RSSI distributions for close trans-mit power levels can have substantial overlap, making thempractically indistinguishable at the receiver. For a powercontrol scheme to be effective, it needs to determine the setof useful power levels i.e. power levels with minimum over-lap. In order to estimate the number of power levels in anysetting, we need to estimate the corresponding RSSI distri-bution for various power levels. Ideally, we can sample theRSSI values for a very long period of time (≈ 10mins) to ob-tain the true behavior of the RSSI distribution. But, as weshow next, sampling very large number of packets may notbe necessary (or practical, due to computation and storagelimitation on the clients) in most settings. This observationleads us to the following question: What is the minimumnumber of packets we should sample to get a “good”approximation of RSSI distribution ?
We first describe an offline mechanism to determine thenumber of samples that are required to generate a distribu-tion close to the one computed over large number of packets,as shown in Figure 6. On the basis of insights obtained fromthe offline analysis, we then present a simple online mecha-
nism to dynamically determine the number of packets suffi-cient to characterize RSSI distribution in any environment.
Let us define the actual probability distribution functionfor RSSI (over large packets ≈ 100, 000) as p(x). The ap-proximate distribution obtained by our mechanism is de-noted by q(x). We now describe the statistical measure thatwe use to quantify the performance of the model.
Let p(x) and q(x) be two probability distribution func-tions defined over a common set χ. We describe a commonlyused statistical measure Kullback-Leibler Divergence (KLD)that quantifies the ’distance’ or the relative entropy betweentwo probability distributions. This comprises a general mea-sure and allows us to compare the statistics of all the ordersfor the two distributions. The Kullback-Leibler Divergence(KLD) [6] is defined as
D(p(x)||q(x)) =Xx∈χ
p(x)
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The KLD is zero when the two distributions are identicaland increases as the distance between two distributions in-crease. The KLD is a measure used in information theory tocalculate the ’distance’ between two distributions p(x) andq(x). The definition of the KLD carries a bias for randomvariables with higher entropy. Hence to evaluate the rela-tive distance accurately for our purposes, it is important toweigh in the entropy of the original distribution which canbe large. The entropy H(p(x)) of the random variable xwith distribution p(x) is the average length of the shortestdescription of the random variable given by:
H(p(x)) =Xx∈χ
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Hence we use the normalized Kullback-Leibler divergenceNKLD [13] defined below as a measure of distance betweentwo distributions
NKLD(p(x)||q(x)) =D(p(x)||q(x))
H(p(x))(5)
However the above metric is asymmetric and we makeit symmetric by taking an average of NKLD(p(x)||q(x)) andNKLD(q(x)||p(x)). The symmetric average distance betweentwo distributions is given by
NKLD(p(x), q(x)) =1
2
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Ideally we could have characterized the distance betweentwo probability distributions by calculating the area of theirintersection on some data set X. However this will requirecalculating their points of intersections and some numericalintegration techniques, which may be cumbersome depend-ing on the exact shape of the distribution. Hence we useNKLD as it compares the statistics of all orders for two dis-tributions and is very simple to compute in real time. Fur-ther NKLD works efficiently for our experimental scenarios.
We consider the long term probability distribution as p(x)and those derived from our offline mechanism as q(x). Letn be the length of the packet sequence that is used for com-puting the distribution q(x). The value of n is varied and wemeasure the corresponding NKLD for each q(x) (with p(x)as the reference long term distribution).
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Figure 9: Normalized Kullback-Leibler Divergence(NKLD) for the four representative traces. Clearlyfor NLOS-heavy trace, NKLD decreases sharplywith the increase in number of packets, reachinga value of 1 for a sample size of the order of 5000packets. For LOS-light however, this value is around30,000 packets.
Figure 9 shows the NKLD curve obtained for the repre-sentative traces from the four categories discussed before.NKLD is a decreasing function of n, although the exactshape of the curve varies as per the environment. We assumewithout the loss of generality, the tolerable error or relativedistance between actual distribution and distribution ob-tained by sampling n packets be 10%. Figure 9 can be usedto calculate the length of packet sequence required to achievethe error bound under varying scenarios. While LOS-lightand NLOS-light require about 20,000 packets each, LOS-heavy and NLOS-heavy scenarios require less than 10,000packets as shown in Table 1.Summary: The number of packets required to determine aclose approximation for RSSI distribution is especially highfor the LOS-light scenario while for a NLOS-heavy scenariothe number is relatively lower. The accuracy of an RSSI dis-tribution varies directly with the number of bursts captured.Since, the NLOS-trace trace seen has short burst sizes wecan obtain large number of bursts using a smaller trace toaccurately model the RSSI distribution while the trace re-quired for LOS-light scenario is larger owing to longer burstsizes. This analysis shows that sampling very large numberof packets (≈ 100000) to obtain RSSI distribution is not re-quired in majority of traces, with the notable exception ofLOS-light scenario.
3.5 Algorithm Online-RSSIBased on the above analysis, we describe an online algo-
rithm to compute the RSSI distribution in an online fashionby predicting the number of packets needed in order to ac-curately characterize the distribution in any environment.As shown in Figure 9, initially NKLD (or error) decreasesrapidly with the increase in n, but stabilizes after a thresholdT, slowly tending to zero. It implies, that beyond a certainlength of packet sequence, the decrease in NKLD(or error)is minimal and hence there is not much gain in sampling
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Figure 10: Comparison between distributions ob-tained from n packets (as determined by the onlinealgorithm) and the true distributions obtained fromlong term traces. The two distributions are remark-ably similar thereby indicating the efficacy of ouronline mechanism
Online-RSSI(burst size,tolerance)
initialize n to 1sample(n) = Sample Random Sequence(n)q(x) = Compute RSSI Distribution(sample(n))don’ = n + k * burst sizesample(n’) = sample(n) + Sample Random Sequence(k *burst size)q’(x) = Compute RSSI Distribution(sample(n’))if Compute NKLD(q′(x)||q(x)) ≤ tolerancereturn q(x)update n = n’, q(x) = q’(x) and continue
Figure 11: Algorithm to find length sequence n forwhich the RSSI distribution stabilizes
longer packet sequences. The online algorithm is shown inFigure 11. The enabling observation for the above algo-rithm is that after the NKLD curve stabilizes, increasingthe length of packet sequence does not change the distri-bution substantially. So we compute the RSSI distributionfor n and n + burst size for varying values of n and returnthe value for which both the distributions have relative dis-tance less than the tolerance level. We use burst size asan increment, as RSSI varies significantly across bursts andwe need to consider at least a gap of more than burst sizeto conclude that the RSSI distribution has stabilized. Forour experiments we find that typically an increment of oneburst size is sufficient to yield correct results using the on-line mechanism. Table 1 shows the values of n obtained forthe four representative traces shown in figure 5. The value ofn obtained using an online mechanism is close to the valueobtained using offline analysis of the traces. In order toevaluate the efficacy of our online mechanism (to determinen) we compare the distribution obtained using a packet se-quence of length n with the distribution obtained using large
traces (≈ 100, 000). Figure 10 shows that the distributionobtained using n as determined by the online mechanismclosely approximates the true distribution for all the traces.
Trace Burst Size Offline Online# of pkts # of pkts NKLD # of pkts NKLD
LOS-light ≈ 1000 30,000 0.5 22,000 0.8NLOS-light ≈ 2500 20,000 0.5 20,000 0.8LOS-heavy ≈ 3000 16,000 0.5 9000 0.8NLOS-heavy≈ 400 3000 0.5 5000 0.05
Table 1: Minimum packet length sequence for cap-turing the distribution of RSSI, as calculated by of-fline and online mechanisms. Corresponding NKLDdistance with the long term ”true” distribution isalso given. NKLD of 0.5 is chosen as the thresh-old for determining the packet length sequence inthe offline mechanism. Burst sizes corresponding tofirst noticeable peak in Allan deviation is shown.
Validating Efficiency of Online-RSSI : We validate theefficiency of Online-RSSI by using the traces collected in ourindoor WLAN deployment as described in Section 3.1. Us-ing those traces, we first build an accurate estimate of thesignal strength distribution for each scenario for differentpower levels. These distributions are computed over largetraces (comprising of ≈ 100, 000 packets) and act as a base-line against which we compare the distribution generated byOnline-RSSI. Figure 10 shows the accuracy of Online-RSSIfor a given power level in different scenarios. The results fordifferent power levels are similar in nature to the ones pre-sented here. The base line distributions for different scenar-ios are shown in dotted lines and the real time distributiongenerated by Online-RSSI is shown in solid lines. As shownin the figure, Online-RSSI is able to accurately estimate sig-nal strength distribution and the errors (NKLD distance be-tween baseline and estimated) are found to be within 5%for LOS-light, NLOS-light and NLOS-light, while for NLOSheavy it was found to be with 20 %. This indicates that thealgorithm has reasonable accuracy in estimating the RSSIdistribution in an online fashion for different scenarios.
4. EMPIRICAL MODEL FOR POWERCONTROL
As discussed in Section 2.1, RSSI values of neighboringpower levels tend to overlap significantly in indoor scenar-ios, with some indoor settings more prone to multipath ef-fects (like cubicles) than others (like large conference halls).Similarly the interference and other factors that determinethe extent of RSSI variations will be different for differentindoor environments. Hence, it is possible that some in-door environments may allow more power levels to be dis-tinguishable (where RSSI variations are low) as compared toothers (where RSSI variation is high). Based on our onlinemechanism to dynamically determine the number of packetsrequired to characterize RSSI distribution in any environ-ment, we present an empirical model for transmit powercontrol, Model-TPC, that outputs the set of feasible (non-overlapping distribution) power levels for a given indoor set-ting.
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Figure 12: Probability distribution function forRSSI values received at varying power levels at thetransmitter. The plots represent the distributions atreceiver RB-10, RB-11, RB-12 and RB-8, in orderfrom top to bottom. The exact positions of these re-ceivers with respect to the transmitter can be seenin figure 2. The amount of overlap varies with thelocation and only 2-3 power levels are distinguish-able at most of the receivers.
Figure 13: Steps involved in construction of Model-TPC. The receiver estimates the RSSI distributionusing our Online-RSSI and computes set of feasiblepower levels as applicable to itself. This informationis then sent to the transmitter to be used in powercontrol
4.1 Model-TPCConstruction of our model proceeds through the following
important steps, also shown in Figure 13. Assume we areoperating in the context of a wireless node X.
1. Estimating RSSI distribution: The RSSI distribu-tion for any given power level is estimated using theOnline-RSSI algorithm described in Section 11. Notethat the RSSI distribution is captured at the receiverand communicated back to the sender as a feedback,as shown in Figure 13. Many proposed approaches(such as [2]) already incorporate protocol-level con-structs to implement such functionality. Ongoing datacommunication between the participating nodes canbe leveraged to gather this information. This processis repeated for different power levels available in thehardware. Note that for our experiments, this proce-dure is repeated for different hardware available powerlevels (6 for Cisco Aironet). In future, if the wirelesshardware supports a large number of power levels, the
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Figure 14: Cumulative distribution of throughputachieved by the wireless clients with/without theempirical model for adaptation at location T1. Theaverage throughput for the adaptation process isalso shown in the figure
cost for this step can be limited through a combina-tion of sampling and simple approximation techniquesto determine the RSSI distribution of power levels. Weleave such extensions as directions for future work.
2. Deciding the feasible power levels: At comple-tion of Step 1, the wireless node X would have builtan empirically tuned model for the different power lev-els, much like Figure 12. At this point, if the NKLD ofdistributions of any two power levels is greater then athreshold NKLDthresh, then the two power levels areconsidered to be distinct and can be used simultane-ously. In theory, dynamic programming can be used todetermine the largest set of feasible power levels sat-isfying above condition. For simplicity, we scan frommaximum power level to lowest power level, picking allthe power levels that satisfy the NKLDthresh criteria.
Figure 12 shows the distribution of RSSI for various re-ceivers in our indoor WLAN deployment (Figure 2), whenT1 is used as a transmitter and power level is varied atthe granularity of 10mW. The power levels are not shownin the graph for the sake of clarity. The top most plot isfor receiver RB-10, followed by RB-11, RB-12 and RB-8 inthat particular order. We use the steps outlined above todetermine the feasible power levels for the aforementionedreceivers. The distributions corresponding to these feasiblepower levels are marked in black in Figure 12. As can beseen, the selected power levels overlap minimally (NKLD ≥4). We also computed the error (captured by the NKLDfunction) between the accurate distributions and the distri-butions estimated by Online-RSSI. For each of these powerlevels, we found the error to be within 10 % of the desiredmaximum error. Clearly the amount of overlap (and hencethe number of distinguishable power levels) depends on thelocation of the receiver, with RB-10 observing less overlap ascompared to RB-11, which practically observes only a singlepower level. These results clearly indicate that the set offeasible power levels is highly correlated with the location ofthe receiver and motivates the case for location-based power
control, where the transmitter uses a different set of powerlevels for each client depending on client’s location.
4.2 SummaryFor a given a wireless environment, our proposed model
and its associated algorithms were able to accurately deter-mine a good and useful set of power levels. The set of usefulpower levels as computed by Model-TPC are valid till trafficcharacteristics (other interference source) and wireless envi-ronments (physical obstacles etc) remain similar. Using ourOnline-RSSI algorithm, we already sample sufficient packetsto reflect small scale changes in the wireless environmentsin our model. However the set of power levels must be re-computed against large scale changes in the wireless wire-less environment like transmitter mobility, introduction ofa new physical obstacle or a new interference source. Weare investigating various triggering mechanisms to refreshthe Model-TPC, although a simple strategy to refresh themodel every 10 minutes seems to work fine for our indoorexperiments.
5. EXPERIMENTAL EVALUATION OFMODEL-TPC
To validate our model, we pick an existing algorithm [15]that uses transmit power control for improving client through-put and spatial re-use. The algorithm proposed increasestransmit power in steps and measures signal quality to as-certain the optimal power setting for a given client.
At a high level, the algorithm operates as follows. It startswith the lowest power level and performs normal data rateadaptation using Onoe [1](a standard data rate adaptationmechanism). Once the data rate stabilizes around a value,the power level is increased and the rate adaptation processis continued. This process is repeated until the transmitterreach the maximum rate available or reaches the highestpower level.
To demonstrate the benefits of our proposed model, wecreate a set of useful power levels through Model-TPC andrestrict the above algorithm to use only this set of powerlevels in its adaptations. We then compare the adaptationperformance of the algorithm under two different scenarios– (i) which uses all possible power levels as available fromthe wireless interface, and does not use our model-TPC, and(ii) which uses the power levels provided by Model-TPC.
There are two benefits of Model-TPC: First, it allows forsignificantly faster convergence for the transmitters to thebest suited power level in their operating environments. Sec-ond, by eliminating the need to explore many redundantpower levels with corresponding poor throughput perfor-mance, the transmitters achieve higher throughput over theentire adaptation duration. This is particularly importantfor clients that are mobile in nature and hence, need to adapttheir transmission parameters, including power levels, quitefrequently. We illustrate these gains through our referenceimplementation of the algorithm in [15], both with andwithout Model-TPC.
5.1 SetupFor the experiment described, the setup is identical to
NLOS scenario, with the transmitter using an Atheros cardhaving five power levels as validated by our power level val-idation setup in Figure 4. The mobile client continuously
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Figure 15: Joint power and data rate adaptation mechanism with/without the empirical model. Con-vergence is much faster with the empirical model.
transmits data from itself to a departmental server locatedat the position of receiver R2, shown in Figure 2. The clientroams from locations T1 to T2 to T3, which are annotated inthe Figure 2 of our indoor WLAN deployment. Initially theclient is at T1, which has 3 feasible power levels of 10mW,20mW and 40mW, as per Model-TPC. After 12 seconds, theclient goes to location T2, which is very close (LOS) to theserver R2 and hence the client is decreases its power leveland is able to use the lowest power level of 10mW to achievea data rate of 54Mbps. After 2 seconds, the client againmoves to location T3, which has four feasible power levelsas per our empirical model. We show the data rate andpower adaptation process at T1 and T3 (The adaptation atT2 is obvious, with the client simply reducing power levelsas it is very close to the server).
5.2 ResultsWe present the cumulative distribution function of the
instantaneous throughput (measured every 100 ms) of thetwo variants of the transmit power control algorithm in Fig-ure 14. The figure shows that using Model-TPC to restrictpower levels lead to higher instantaneous throughput for asignificant part of the experiment as shown in Figure 16. Weexplain this difference by examining the adaptation mecha-nisms in the two cases in Figure 15.
Figure 15(a) shows the adaptation behavior when all fivepower levels are used by the algorithm. We can see thatover time, the algorithm attempts to identify signal qual-ity at each different data rate and power level, spending asignificant amount of time testing parameter values whichare redundant for a give environment, thus impacting per-formance. In contrast, Figure 15(b) shows that adaptationwith our Model-TPC. Clearly adaptation is much faster with
our model, with more pronounced gains at T1 (as differencebetween hardware and feasible power levels is more) thanT3.
Note that here we only show the throughput gains arisingfrom quicker convergence from a small power level to theright (greater) power level for locations T1 and T3. Model-TPC also provides much better convergence when adaptingfrom a high power level to lower (right) power level as forT2, by skipping all the redundant high power levels in be-tween. A faster convergence reduces the energy consumedin scanning high power levels and leads to energy savings,which is an important consideration for mobile clients. Dueto lack of space, we do not present our energy results in thissection.
5.3 SummaryOur gains of in the above Internet-oriented wireless exper-
iments stem from faster adaptation achievable when usingthe Model-TPC as an input to power control. Note thatin our experiments, we compared benefits when only fivepower levels are available from the wireless interface. Theperformance gains of Model-TPC will only be greater if thewireless interface makes more power levels available to thesystem software, that will clearly increase the number ofredundant channels that transmitter will scan in a typicalpower control algorithm, while our model will facilitate muchfaster convergence and performance.
6. DISCUSSIONWhile our work in this paper is targeted towards indoor
WLANs, we discuss the relevance of our work in context ofcellular networks, where power control is again an impor-
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Figure 16: Goodput of the end wireless clients in joint power and data rate adaptation mechanismwith/without the empirical model.
tant design parameter. Power control in cellular networksis used for reducing co-channel interference, managing voicequality, dealing with fast fading and near-far problem [10,17]. However cellular networks primarily operate in outdoorenvironments, where the effects of multipath are mush lesspronounced as shown in Figure 3. Moreover, cellular net-works do not perform rate adaptation in the inner loop (realtime or per packet basis) of power control, whereas data rateadaptation is an integral component of 802.11 based WLANsystems. Thus the SNR threshold for cellular networks isvaried slowly in the outer loop of power control, whereas inWLANs, data rate adaptation is performed on very smalltime scales, thereby making RSSI variations even more crit-ical for system performance.
7. RELATED WORKWe discussed prior work on power control mechanisms in
Section 2. In this section, we present other previous workthat deals with signal strength measurement and character-ization for wireless networks.
• Measurement based modeling : Some recent ef-forts have been made to use empirical observationsto improve wireless protocols. Reis et al.[7] proposea measurement based model for delivery and inter-ference in static wireless networks. Their work takesRSSI values of wireless packets as an input to predictthe delivery rate and interference in the system. Di-vert [4] attempts to reduce packet loss rates in WLANsystems by rapidly switching between APs to toleratebursty losses. ExOR [5] leverages spatial loss indepen-dence to reduce packet transmissions in multi-hop net-works by using opportunistic packet reception. These
efforts indicate that there is much room to improvewireless protocols by adapting them to realistic condi-tions. Our work provides one such tool.
• RF-based location determination : RF-based lo-cation determination mechanisms [21, 14] use signalstrength values for fingerprinting different locations ina WLAN. Kaemarungsi et al. [12] study the prop-erties of indoor received signal strength for locationfingerprinting. They propose an analytical model forindoor positioning system by modeling the RSSI vari-ations as a Gaussian distribution. While such workin location determination had to examine RSSI (andhence, power) variations between a transmitter and areceiver, the focus of such RF-based localization tech-nique did not require a careful exploration of variouspower level choices, and their implications on powercontrol mechanisms.
• Feasibility Analysis : Abdesslem et al [8] describethe hardware and software limitations, like limited powerlevels in the wireless chipsets and lack of suitable de-vice drivers, that hinder the implementation of trans-mit power control mechanisms. While their work isan important step towards determining feasibility ofpower control mechanisms (due to hardware/softwarelimitations), they do not explore the more fundamen-tal issues with fine grained power control that arisedue to the inherent nature of wireless medium.
8. CONCLUSIONS AND FUTURE WORKMultipath, fading, shadowing and external interference
from wireless devices, make the implantation of power con-
trol mechanism challenging in practical settings. The focusof this paper has been in understanding what the right setof power control mechanisms are useful to design efficientpower control algorithms. More specifically, we show thatfine-grained power control cannot be effectively used by suchalgorithms in a systematic manner. In fact, our work sug-gests that a few 3-5 discrete power level choices is sufficientto implement any robust power control mechanism in typ-ical indoor WLAN environments. Through our work, wealso build an empirical model that guides these appropri-ate number and choices of power values that is adequate.Our model can be used as a plug-in to previously proposedpower control mechanisms, to make them implementable inreal settings. We believe our work provides an importantframework that can be used by researchers to develop ro-bust and practical power control mechanisms.
We have used NKLD as a statistical tool to measure thedistance between two RSSI distributions. Although it workswell for our environments and is easy to compute in a realtime fashion, there are other statistical tools like momentbased estimators, that capture the spread of the two dis-tributions better and may be more effective in distinguish-ing between two probability distributions. Comparing theperformance of NKLD with moment based estimators is anavenue of future work for us.
We are also investigating various triggering mechanisms torefresh Model-TPC. Currently we refresh it periodically ev-ery 10 minutes, which not be optimal for every scenario. Therefresh period is tightly coupled with large scale variationsin the wireless environments, like addition of an interferingsource or a new obstacle and we are performing more exper-iments to detect such changes that can trigger the updateof Model-TPC.
Although our main objective is to evaluate the feasibil-ity of using fine grained power control in indoor environ-ments, the model developed in this section can be read-ily used by access points (APs) to profile various locationsin the environment and perform location-based power con-trol. Through collaborative measurements made by differentclients over time, the APs can create a location-dependentmodel for power control which can be downloaded to clientsduring association. Also the network as a whole could aggre-gate such models to create a single model which is networkdependent but location independent that trades-off complex-ity and accuracy for simplicity of use. We are currently look-ing such location-specific power control approaches that canbe implemented using a centralized controller that managesthe wireless APs in enterprise WLANs. The flexibility inestimating and building the empirical model allows for itsapplicability to a wide range of power control algorithms andmight find interest outside the scope of 802.11 networks.
Acknowledgment:. We would like to thank all the review-ers for their comments. Special thanks to our shepherd Dr.Darryl Veitch, whose guidance bought this paper togetherinto its final form. Vivek Shrivastava, Arunesh Mishra, andSuman Banerjee were supported in part by NSF awardsCNS-0639434, CNS-0627589, CNS-0627102, and CNS-0520152.
9. REFERENCES[1] ONOE rate control.
http://madwifi.org/browser/trubk/ath rate/onoe.
[2] P. Steenkiste A. Akella, G. Judd and S. Seshan. Selfmanagement in chaotic wireless deployments. In ACMMobiCom 2005.
[3] D.W. Allan. Time and frequency (time domain)characterization, estimation and prediction ofprecision clocks and oscillators. In IEEE TransactionsNov. ’87.
[4] Hari Balakrishnan Allen Miu, Godfrey Tan and JohnApostolopoulos. Divert: Fine-grained path selectionfor wireless lans. In ACM Mobisys ’04.
[5] Sanjit Biswas and Robert Morris. ExOR:opportunistic multi-hop routing for wireless networks.In SIGCOMM 2005.
[6] T.M. Cover and J.A. Thomas. Elements ofInformation Theory, 1991.
[7] Charles Reis et al. Measurement-based models ofdelivery and interference in static wireless networks. InSIGCOMM ’06.
[8] Fehmi Ben Abdesslem et al. On the feasibility ofpower control in current IEEE 802.11 devices. InPERCOMW 2006.
[9] P. Gupta and P. Kumar. Capacity of wirelessnetworks. In IEEE Transactions on InformationTheory.
[10] Prashanth Hande, Sundeep Rangan, and MungChiang. Distributed uplink power control for optimalSIR assignment in cellular data networks. InINFOCOM, 2006.
[11] V. Bharghavan J. Monks and W. Hwu. A powercontrolled multiple access protocol for wireless packetnetworks. In INFOCOM ’01.
[12] Kamol Kaemarungsi and Prashant Krishnamurthy.Modeling of Indoor Positioning Systems Based onLocation Fingerprinting. In IEEE INFOCOM ’04.
[13] S. Kullback. Information theory and statistics, 1959.
[14] J. Lansford and P. Bahl. The Design andImplementation of Home-RF: A Radio-FrequencyWireless Networking Standard for the ConnectedHome. In IEEE ’00: 1662-1676.
[15] K. Leung and L. Wang. Controlling QoS by IntegratedPower Control and Link Adaptation in BroadbandWireless Networks.
[16] Allen K. Miu, Hari Balakrishnan, and Can E. Koksal.Improving Loss Resilience with Multi-Radio Diversityin Wireless Networks. In MOBICOM ’05.
[17] Zvi Rosberg. Asymptotically optimal transmissionpower and rate control for CDMA channels withmultiple user classes. In INFOCOM, 2005.
[18] Anmol Sheth and Richard Han. SHUSH : ReactiveTransmit Power Control for Wireless MAC Protocols.In WICON ’05.
[19] M. Subbarao. Dynamic power-conscious routing formanets: An initial approach. In IEEE VehicularTechnology Conference ’99.
[20] Chi-Hsiang Yeh. IPMA: An interference/power-awaremac scheme for heterogeneous wireless networks.ISCC, 2003.
[21] M. Youssef and A. Agrawala. The Horus WLANLocation Determination System. In Mobisys ’05.
