Computer Standards & Interfaces 34 (2012) 135–145

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Computer Standards & Interfaces

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Throughput and PER estimates harnessing link-layer measurements for indoor802.11n WLAN

Bryan Ng ⁎, Y.F. Tan, S.W. Tan, S.W. LeeFaculty of Engineering, Multimedia University, Jalan Multimedia, 63100 Cyberjaya, Selangor, Malaysia

⁎ Corresponding author. Tel.: +60 3 8312 5415; fax:E-mail addresses: bryan@mmu.edu.my, bryan.ng.mm

0920-5489/$ – see front matter © 2011 Elsevier B.V. Aldoi:10.1016/j.csi.2011.06.004

a b s t r a c t

a r t i c l e i n f o

Article history:Received 7 December 2010Received in revised form 2 June 2011Accepted 14 June 2011Available online 7 July 2011

Keywords:802.11nWLANMarkovMeasurement

The research work reported in this paper investigates if a Markov chain can model the throughput and packeterror rate (PER) performance of off-the-shelf IEEE 802.11n wireless LAN network interface cards (NICs). Wedraw together uplink -downlink information from the NIC with a Markov chain to examine the performanceof 802.11n within an indoor environment. Site measurements and point-estimates are taken and comparedwith the model predictions. Errors of less than 4% were recorded for the Markov model estimates while point-estimates recorded average errors of 9% both compared to site-measured throughput.

+60 3 8318 3029.u@gmail.com (B. Ng).

l rights reserved.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Increasing demands for multimedia services and high-speedwireless communications have led to great interest in the 802.11nvariant of the popular 802.11 WLAN standard. Going by the draftrevisions itself, the 802.11n drafts have so far seen five revisions foryear 2009 [1]. This hive of activity is expected to be further intensifiedfuelled by the maturing of the standard itself as more 802.11n-enabled NICs appear in the market.

The 802.11n standard offers ten-fold increase in physical data ratesplus increased reliability over existing 802.11a/g networks. Previousresearch has noted that the high physical data rates promised by the802.11n not necessarily translate to the throughput attained by anapplication such as a video streaming session or a voice call [2–4]. Thethroughput attained by an application fluctuates due to the changes inphysical data rate in response to signal strength (SS) variations.Fluctuating SS values, sometimes as high as 10 dBm, force switchoversbetween data rates several times within a short time-span. This isfurther complicated by the numerous data rates made available in802.11n. Under such dynamic conditions, predicting throughput onthe basis of up-to-date link layer measurements would provide betteraccuracy.

Another unexplored dimension in the literature is the effect ofSS asymmetry on throughput and PER estimation. In typical 802.11WLANs, access points (APs) have a significantly higher transmitpower compared to stations (STAs). It is common practice to set

the transmit power level in the range 20–23 dBm. This serves tomaximize AP coverage, which minimizes the number and overalldeployment cost through reducing the associated financial outlayfor AP's. Wireless STAs, though, tend to conserve power bystabilizing the transmit power thus contributing to asymmetricSS profiles between uplink and downlink. Despite many paperson physical and theoretical aspects of 802.11n link characteristics[5–7], there have been very little studies on how asymmetryinformation may be exploited for estimating throughput and error-rate.

Recognizing the aforementioned issues, this paper presents a modelharnessing link-layer measurements for estimating throughput andPER. The research reported in this paper is unique in the followingaspects:

• A hybrid approach is adopted by incorporating link-layer measure-ments into an analytical (Markov) model for improved throughputand PER prediction.

• The model takes into consideration both uplink and downlink SSchanges to ascertain transitions between different data ratesdictated by the modulation and coding scheme (MCS).

• There is a very limited set of indoor throughput and PERmeasurements on 802.11n. Reported site measurements in thispaper expand existing results on indoor 802.11n throughput andPER.

The rest of the paper is organized as follows. Section 2 describes therole of theMCSand the channelmodel in estimating the throughput andPER. Our proposed system model for capturing throughput and PERperformance is detailed in Section 3 together with the simplifying

136 B. Ng et al. / Computer Standards & Interfaces 34 (2012) 135–145

assumptions leading to their derivations. The site measurementconfiguration is explained in Section 4 followed by experimentalvalidation of the proposed Markov model in Section 5. The final sectionreviews the contributions of the paper and suggests directions forfurther improvement.

2. Indoor wireless environment and 802.11n WLAN

The MCS and the operating environment are the primary factorsthat affect the throughput and PER in 802.11n WLAN. An accuratemodel for throughput and PER must consider the MCS selection,indoor channel characteristics and the interactive nature betweenthese two factors. Wewill first examine the concept of MCS in relationto receiver sensitivity, followed with explanation on suitable channelmodels for indoor WLANs.

2.1. Modulation and coding scheme (MCS)

TheMCS determines how data is sent over the air. 802.11n APs andSTAs negotiate capabilities such as the number of spatial streams (Nss)and channel width (CW) and they must agree upon the type of radiofrequency (RF) modulation, coding rate, and guard interval (GI) to beused. The combination of all these factors determines the actualphysical data rate, ranging from a minimum 6.5 Mbps to a maxi-mum 600 Mbps (achieved by leveraging all possible high throughputoptions).

A simple integer assigned to every permutation of modulation,coding rate, GI, CW, and Nss defines the MCS number (MCS#) in the802.11n standard. It is a precise and efficient way to communicate the77 possible permutations of the factors that determine the physicaldata rate [1]. However, not all MCS#s are supported by WLAN NICmanufacturers. Some broadly supported 802.11n MCS values areselected and numbered sequentially in Table 1. Note that the MCS#entries in Table 1 do not correspond directly to the MCS# in thestandard specification [1].

To relate the MCS#, SNR and bit-error rate (BER), a BER versussignal-to-noise ratio (SNR) curve such as the one shown in Fig. 1 ismost suitable and widely understood. As an example, the contoursdelineating the MCS# and the corresponding BER–SNR range shownin Fig. 1 is based on the closed form expressions derived in [8].

The wireless NIC uses the SNR levels to select an MCS# among theavailable transmission rates. Both SNR and SS are used interchange-ably and are related by:

SNR dBð Þ = SS dBmð Þ− Nfloor dBmð Þ + Nfig dBmð Þn o

ð1Þ

where the noise floor (Nfloor) typically ranges from −93 dBm to −96dBm for the 40 MHz channel width, and Nfig (measured in dBm) is thesignal impairment due to losses in the RF signal chain. Conforming tothe behavior of the standard 802.11n NIC, the basic rate selectionmechanism outlined in Section 9.6 of the 802.11n standard [1] isassumed throughout this paper.

Table 1Modulation and coding scheme for data transmission in IEEE 802.11n (CW=40 MHZ,NSS=2).

MCS# Modulation Nss PHY rate (Mb/s) GI

0 BPSK 2 27 800ns1 QPSK 2 54 800ns2 16-QAM(3/4) 2 162.0 800ns3 64-QAM(5/6) 2 270.0 800ns

2.2. Path loss and Rician fading environment

In addition to the range of supported MCS, the throughput alsodepends on the local channel conditions. Wireless communicationchannels experience significant losses through the environmentmostly due to free space losses and fading. These losses alter the SSand SNR, which in turn elicits a change in MCS#. We start this sectionby examining two types of losses in wireless channels: path loss andsmall-scale fading. Finally, we discuss fading rates and its effect onPER.

The most widely used path loss model for 802.11n is thebreakpoint model [9]. For different scenarios described in [9],different break-point distance (dBP) were chosen to differentiatescenarios such as indoor, outdoor and path clearance. The path loss L(d)in dB is defined as,

L dð Þ =20 log10 dð Þ + 20 log10 fop

� �−144:75 if d≤dBP

20 log10 dBPð Þ + 20 log10 fop� �

−144:75 + 35 log10ddBP

� �if d> dBP

8><>:

ð2Þ

where fop is the operating frequency of 5.2 GHz (the one in which theIEEE 802.11n operates) and d is the distance separating thetransmitter and receiver. However, the path loss model cannotaccount for the shorter and steep changes in SS, and thus relies on asmall-scale model.

The Rician distribution is widely used to model small-scale SSvariation in the presence of a strong dominant line of sight (LOS) path.Rician fading models have been successfully applied in numerousindoor WLAN studies [10–12]. Denote by fp the fading envelope of asignal p, thus,

fp μ;σ2� �

=pσ2 e

−μ2 + p2

2⋅σ2

⋅ I0 k⋅pð Þ ; k =μσ2 ð3Þ

where μ is the first moment, σ2 represents the variance of the randomcomponents and I0(⋅) is the modified Bessel function of the first kind.Usually, the factor k is used to identify the Rician distribution functionfor a specific fading environment. Values of k of approximately 6 dB istypical in modeling indoor radio channel amplitude fluctuations[13,14].

Besides the SS attenuation, another aspect of fading is slow or fastvarying fades. The rate of amplitude change with respect to thesymbol duration defineswhat is called the fading rate. If we consider atypical humanmovement within indoor environment withmaximumvelocity (ν) of 1.5 m/s and fop of 5.2 GHz, the maximum Dopplerfrequency is calculated as,

f d max =fop⋅ νc

=5:2 × 109

� �× 1:5m=s

3 × 108 = 16Hz ð4Þ

while the coherence time Tc is related to fdmaxthrough,

Tc =9

16π × f d max=

916π × 16

= 11:2 × 10−3s ð5Þ

Comparing Tc with an 802.11n symbol whose duration spans 4μs[1], it is evident that Tc is much larger compared to the symbolduration. Thus, we may assume that the Rician fading is slow varyingand affects the channel for durations spanning several symbols. Theslow varying characteristics allow us to approximate PER expressionswhich would otherwise be intractable.

Fig. 1. Error probabilities for various MCS# under Rician fading conditions.

137B. Ng et al. / Computer Standards & Interfaces 34 (2012) 135–145

2.3. Related work

The empirical aspect of this paper is partly motivated by the worksof [15,16]. The authors in [15] performed experiments to evaluate linkquality at high data rates with commercial 802.11n wireless NICswhile Visoottiviseth et al. [16] studied the empirical throughput withvarious 802.11n NICs from different vendors. Their results indicatethat the high-throughput channel configurations only providemarginal increase in throughput. It was also reported that PERremained significant even at high SNR values. These problems wereattributed to hardware related issues such as failure of leveragingspatial diversity arising from poor configuration and rigidity withregards to when and how to trigger packet aggregation and blockacknowledgements. Both studies [15,16] were among the earliest topublish results on measurements of 802.11n performance, but did notconsider the use of simulation or how the results from their studiescould be of use to simulation work.

In [17], the authors compare empirical model predictions tomeasurements taken from indoor industrial environments. Thecomparison reveals that the wireless ranges calculated with thelink budget and extracted from the site survey measurements are ingood agreement. The wireless range predicted by the link budget isoverestimated in the presence of severe attenuation due tounaccounted factors in the path loss. Recent work reported in [18]is strongly related to our work as it combines some aspects from both802.11 receiver and Markov modeling. Using a measurement-theoretic approach, the authors in [18] develop a set of tools withlow computational complexity for estimating the quality of a radionetwork configuration. However, their contribution is targeted forrange prediction and radio network planning in a multi-hopnetwork.

Recognizing the importance of reflecting the bursty nature of realwireless channels, the authors of [19,20] use a simulation model tocapture the dynamic nature of indoor WLAN propagation. Theproposed model is accurate when compared to empirical measure-ments and the results support the conclusion that an integratedsimulation-theoretical approach is able to better reflect the realbehavior (defined by empirical assessment).

While [16–18,21] contributed to the empirical aspect of through-put in 802.11n, they did not exploit this information for further use.

Moreover, the effect of asymmetrical uplink–downlink SS profile hasalso been neglected in most of the works on 802.11n. The opportunityto make a contribution arises from leveraging measured informationand statistical modeling, and we show that this combination providesa unique solution to improving estimates for throughput and PER in802.11n systems.

3. System model: a Markov chain approach

In this section, we describe the system model and the underlyingassumptions of our model. Fig. 2 shows the transactions linking inputand output with the Markov chain as an integral part of the proposedsystem. Receiver sensitivity information (RSI) at the input determinesthe number of states and the valid SNR range in the Markov chain(denoted as transaction T01). The Markov chain is solved (denoted bytransaction T02) and its solution is expressed as a function of theuplink (denoted by UL subscript) and downlink (DL subscript)average received SS (μUL, μDL) and their respective variances (σUL

2 ,σDL2 ).

Up-to-date link-layer measurements of (μUL, μDL) and (σUL2 ,σDL

2 )derived from the channel state information (CSI) are fed to theoutput (denoted by transaction T03). The CSI is a rich source ofinformation on the profile of the propagation environment. Channelproperties such as fading, delay spread and channel correlation can beextracted from the CSI. Finally, the steady-state distribution istabulated in the form of a vector π and performance measures suchas the PER distribution (FPERa ) are extracted from the model.

AMarkov chain approach is employed due to the discrete nature oftransitions between MCS and also the assumed memoryless charac-teristics of the MCS selection. Both these properties are captured verywell by a Markov chain. The choice of this approach is validated by theconsistent and accurate predictions that will be shown when theresults are discussed. Other analytical models which may beconsidered include semi-Markov models or hybrid simulation-theoretic models [19] are beyond the scope of this paper.

3.1. Markov chain formulation

A Markov chain is described by states, S and transition probabil-ities P. For convenience, S and P are defined as matrices. Each state isdescribed by two variables ⟨k, m⟩ where k denotes the MCS# and m

Fig. 2. Schematic description of system model indicating inputs, output, transactions and their respective parameters.

138 B. Ng et al. / Computer Standards & Interfaces 34 (2012) 135–145

denotes a specific range of PER. In the interest of validating our modelwith site measurement results we devise amapping between the SNR,PER and state ⟨k, m⟩ for the NEC ATerm wireless network interface(the same NIC used for site measurement). The BER-SNR curve (suchas the one shown in Fig. 1) is divided and delineated into individual“segments” to relate the Markov chain's states to the MCS# and PERrange. The development of the model is not tied to a specific make ofany 802.11n wireless cards; hence the proposed model may be easilymodified to accommodate other wireless cards.

Each segment shall be indexed with the state variable ⟨k, m⟩ and asuperscript indicating the upper limit (U) or lower limit (L), forexample[S⟨3, 5⟩L , S⟨3, 5⟩U ] and [S⟨0, 2⟩L , S⟨0, 2⟩U ] shown in Fig. 3. Thus, eachsegment on the BER–SNR curve is uniquely identified by a state in theMarkov chain through the state variables, as shown in Table 2. Themapping shown in Table 2 is based on the manufacturer datasheetassumingNfloor=−93 dBm,Nfig=10 dBm [22]. From an application'sperspective, the PER information is more readily used thus it is bychoice that PER (rather than BER) is quantified by the Markov chainstate. However receiver characteristics are usually expressed as afunction of BER, Fig. 3 is a case in point. The conversion between PERand BER is approximated by (14).

In pictorial form, individual states are depicted as circles andconnected by directional arcs indicating transitions as shown inFig. 4. Due to the slow-varying characteristics no abrupt changes inMCS is modeled. For example, for the Markov chain shown in Fig. 4,notice that moving from state ⟨0, 4⟩ to ⟨1, 4⟩ forces a sequence oftransitions: first through state⟨0, 5⟩followed by state⟨1, 3⟩ and finallyat ⟨1, 4⟩.

3.2. One-step transition probabilities

To construct the transition matrix Pwe first look into the one-steptransition probabilities. Let Sn denote the state of the Markov chain atan arbitrary time indexed by n. The state transitions of the Markov

chain are governed by the one-step transition which describes aconditional probability that the chain transits to a given state (Sn)from the previous state (Sn-1). It is assumed that the transitionprobabilities are stationary and independent of the chain history.

Assume that the Markov chain is initially in state Sn−1= ⟨i, j⟩ andmoves toSn= ⟨k,m⟩, then the transition probability p⟨k, m⟩, ⟨i, j⟩ denotesthe probability associated with the change in state from ⟨i, j⟩ to⟨k, m⟩.As indicated in the Markov chain structure, only one-step transitionsare permitted, hence,

p k;mh i; i;jh i = Pr Sn = k;mh i jSn−1 = i; jh ið Þ= 0 if k−ij j + m−jj j > 1 ð6Þ

The remaining state transitions satisfying the condition |k− i|+|m− j|≤1 are non-null probabilities.

To sustain an MCS# of k and bit-error rate of m (in state Sn), it isreasoned that the uplink SS must fall between the range ½S⟨k, m⟩

L , S⟨k, m⟩U �

and the downlink SS must be at least S⟨k, m⟩L . The transition probability

reflecting this condition is expressed as a product of two distributionfunctions in the form of:

p k;mh i; i;jh i = ∫SUk;mh i

SLk;mh i

f Up μUL;σ2UL

� �dp⋅ ∫

S max

SLk;mh i

f Dp μDL;σ2DL

� �dp if k−ij j + m−jj j≤1

ð7Þ

where by fpU(μUL, σUL

2 ) and fpD(μDL, σDL

2 ) are Rician distributions definedby (2) denoting the uplink and downlink SS distribution respectivelywhile the parameter Smax denotes the maximum SS permitted by thedevice. The expression in (7) assumes that the uplink and downlink SSdistribution are independent for the product form to hold. Finally, thetransition probabilities are all expressed as a function of fourunknowns (μUL, μDL) and (σUL

2 ,σDL2 ).

With the transition probabilities collectively defined in (6) and(7), we have sufficient information to populate the matrix P. We

Fig. 3. Two distinct segments ⟨0, 3⟩ and ⟨3, 5⟩ with corresponding BER–SNR range.

139B. Ng et al. / Computer Standards & Interfaces 34 (2012) 135–145

adopt the transition probability matrix notation used in [23] anddefine P as follows:

P =

0;0h i 0;1h i ⋯ 0;3h i 1;5h i ⋯ 1;3h i ⋯ 3;2h i 3;3h i0;0h i p 0;0h i p 0;1h i 0 ⋯ 0 0 ⋯ 0 ⋯0;1h i p 0;0h i p 0;1h i ⋮ ⋯ 0 0 ⋯ 0 ⋯⋮ 0 0 ⋮ ⋯ 0 0 0 ⋯ 0 ⋯

0;3h i ⋮ ⋮ ⋮ p 0;3h i ⋮ ⋮ ⋮ ⋯ ⋮ ⋯ ⋮1;5h i 0 0 0 ⋯ p 1;5h i 0 0 ⋯ 0 ⋯⋮ 0 0 0 ⋯ ⋮ ⋮ ⋮ ⋯ 0 ⋯

1;4h i 0 0 0 ⋯ ⋮ 0 0 ⋯ 0 ⋯⋮ ⋮ ⋮ ⋮ ⋯ ⋮ ⋮ ⋮ ⋯ ⋮ ⋯ ⋮fg 0 0 0 ⋯ 0 0 0 ⋯ ⋯3;2h i ⋮ ⋮ ⋮ ⋯ ⋮ ⋮ ⋮ ⋯ ⋮ p 3;2h i ⋮3;3h i 0 0 0 ⋯ 0 0 0 ⋯ 0 ⋯ p 3;3h i

0BBBBBBBBBBBBBBBBBBB@

1CCCCCCCCCCCCCCCCCCCA

ð8Þ

The matrix P is stochastic if it is square with strictly non-negativeterms in which the elements in each row sum to 1. To understand theunderlying significance of P on the solution to the Markov model, wefirst consider the n-step transition probabilities Pi, jn . The probability ofgoing from state i to state j in n-steps is the sum over k of all possiblen-step transitions is,

Pni; j = ∑allj

Pi;k ⋅ ∏n−1

h=1Phk; j: ð9Þ

Table 2Mapping Markov chain states to receiver sensitivity.

State(k)

State(m)

SNR (dB) SS (dBm) Per range

S⟨k, m⟩L S⟨k, m⟩

U S⟨k, m⟩L S⟨k, m⟩

U High Low

0 3 4 5 −79 −78 10−1 10−3

4 5 6 −78 −77 10−3 10−4

5 6 7 −77 −76 10−4 10−5

1 3 7 9 −76 −74 10−1 10−3

4 9 11 −74 −72 10−3 10−4

5 11 13 −72 −70 10−4 10−5

2 3 13 16 −70 −67 10−1 10−3

4 16 19 −67 −64 10−3 10−4

5 19 22 −64 −61 10−4 10−5

3 3 22 23 −61 −60 10−1 10−3

4 23 24 −60 −59 10−3 10−4

5 24 25 −59 −45 10−4 10−5

For example, take n=2 and substitute into (9),

P2i;j = ∑J

k=1Pi;k⋅Pk;j = P×Pð Þi;j ð10Þ

By induction on n, it can be seen that Pn, is simply the nth power ofthe matrix P. If Pn converges to a limit as n→∝, then each row of Pn

tends to the same set of probabilities,

limn→∞

Pn = P ð11Þ

For a finite-state Markov chain with a stochastic transition matrixP, the steady-state probability vector, π is an invariant vector thatsatisfies the following relationship:

π = π⋅P ð12Þ

The invariant vector, if it exists, may be interpreted as a stationarydistribution of the Markov chain. From the theory of Markov chains,the existence of a stationary distribution as defined above is subject tothe chain possessing irreducible and aperiodic properties. The proofsfor the existence of stationary distributions for irreducible andaperiodic Markov chains have been well established [23,24] andthus invoked without giving proof.

3.3. Solution to Markov model: stationary distribution

To solve the Markov chain, we need to identify the conditionsunder which the state probabilities vector converges to an invariantvector as found from (12). A state ⟨k,m⟩ is accessible from ⟨i, j⟩ if thereis a sequence of transitions from ⟨i, j⟩ to ⟨k, m⟩ with non-nullprobabilities. Bi-directional accessibility between two or more statesimplies that the states communicate. Moreover, a collection of statesthat communicate forms a class. Since all the states of the Markovchain in Fig. 4 communicate, the Markov chain degenerates into asingle class and henceforth termed an irreducible Markov chain.

Another basis for existence of stationary distributions is the periodof a Markov chain. A state ⟨k, m⟩ with period d⟨k, m⟩ may only returnback to itself at times that are multiples of d⟨k, m⟩. It is readily verifiedthat the chain shown in Fig. 4 has a period of one for all states. Thus

Fig. 4. Proposed Markov model for estimating throughput and PER.

140 B. Ng et al. / Computer Standards & Interfaces 34 (2012) 135–145

the Markov chain is aperiodic. The irreducible and aperiodicproperties of the finite-state Markov chain guarantee the existenceof a unique nonnegative solution to the stationary distribution.

Once the stationary distribution π is obtained from solving (12),the average throughput predicted by the model is calculated as,

Ra = ∑allk

∑allm

RPHY kð Þ⋅ 1−Oh½ �⋅π k;mh i ð13Þ

where RPHY(k) denotes the physical data rate dictated by the MCS k,while π⟨k, m⟩ is an element in the vector π denoting the stateprobability. The term [1−Oh]in (13) represents the normalizedoverhead that varies according to the different layers of the protocolstack. With the Internet Protocol (IP) header 20 bytes long and theTransmission Control Protocol/User Datagram Protocol (TCP/UDP)header 20/8 bytes long, the term [1−Oh] in (13) yields 0.71 for UDPand 0.65 for TCP.

Besides throughput, we are also interested in the PER. In general,unless a fairly accurate characterization of bit errors distributionwithin the packet is known, the relationship between PER and BER isnot straightforward. However, the CRC-32 encoding used in 802.11provides an extremely low probability of undetected errors thus therange of PER may be approximated by the binomial expansion,

PER≈1− 1−BERR½ �b ð14Þ

where b denotes the average number of bits per-frame and BERRdenotes the corresponding bounds of the BER for statem given by theBER–SNR curve. The probability the packet error rate falls between therange denoted by statem is the marginal distribution obtained via un-conditioning π on k,

FaPER mð Þ = ∑allk

π k;mh i ð15Þ

The expressions derived in (13) and (15) are approximate.However, in the next section we will show that the approximationis accurate by comparisons with site measurements.

4. Experimental setup for site measurement

To validate the proposed model, site measurements wereconducted in a site located in Cyberjaya, Malaysia. The sitemeasurements were conducted on one floor for four distinct APlocations (labeled ‘X1’ to ‘X4’ for further reference). The measurementprocedure involves a STAmounted on a trolley, moving away from theAP. At 0.5 m distance interval, packets are transmitted from the STA(source) to the AP (sink). The distance (d), average uplink SS (μUL),average downlink SS (μDL) and average throughput (Rm) are recordedfor further analysis.

4.1. Configuration

The sites exhibit typical physical properties of indoor environ-ment: buildings have concrete floors and reinforced concrete ceilings.At all offices, building walls are made brick walls and partitioned withgypsum board. The heights of all office spaces are between 4 m and5.5 m. In Fig. 5, the trajectories from AP locations marked ‘X1’ and ‘X2’

represent LOS scenario while the trajectories marked ‘X3’ and ‘X4’

represent non line of sight (NLOS) scenario.The traffic sink consists of an AP (WARPSTAR ATerm) connected

directly to a desktop computer, with receiver mounted on a bracket ata height 50 cm (hAP) from the ceiling. The transmit antenna is omni-directional, vertically polarized dipole with 2 dBi gain. Thewireless APsupports the IEEE 802.11n with output power of 14 dBm operating at5.2 GHz band with 2×2 antenna configuration.

The STA functions as the traffic source and it consists of a laptopequippedwith a wireless NIC. The NIC is of make NEC ATerm and has abuilt-in antenna with a gain of 22 dBi. The laptop height (hSTA) wasvaried between 0.5, 0.8 and 1.5 m during the site survey. Theseheights simulate a typical office user at office desk and also conferenceroom scenario. Packets are transmitted from the STA to AP while thetachometer mounted on the trolley axle records the distance.

To minimize errors such as interference arising from humanmovement and interference from other APs, the measurement datawas collected after office hours. No other NICs were active within themeasurement site except for the devices under tests.

Fig. 5. Floor layout for site survey measurement indicating AP position, measurement trajectory and major obstructions along the measurement path.

141B. Ng et al. / Computer Standards & Interfaces 34 (2012) 135–145

4.2. Data collection

The laptop and the desktop computers are installed with the iPerfsoftware package and Wireshark for the analysis of the 802.11nframes. The iPerf is configured to log data at the transport layer (usingUDP). At each test point (0.5 m apart), the transmitter generates1×106 packets to determine the throughput and PER performance.The packet size is set to 1472 bytes to avoid fragmentation at the IP-layer. The logged data are further processed for throughput and PER

Table 3Comparison of analytical prediction and measurement data for point X1(LOS).

d (m) μUL±95%CI/μDL±95%CI-(dBm) Rm (Mbps) Ra (

0.5 48.0±0.5/46.0±0.5 188.6 1871.0 48.0±0.3/47.0±0.4 189.1 1872.0 48.5±0.4/46.0±0.5 188.7 1863.0 49.5±0.4/45.5±0.5 188.8 1867.0 52.5±0.5/47.0±0.4 188.3 1868.0 52.0±0.6/48.0±0.5 188.1 1869.0 53.0±0.4/48.0±0.4 187.9 18610 52.5±0.4/48.5±0.4 187.5 18515 57.7±0.3/53.5±0.3 150.2 14730 63.0±0.5/59.5±0.4 112.4 10935 69.0±0.5/61.0±0.5 98.55 95.940 70.0±0.6/64.5±0.5 37.85 36.445 72.5±0.4/68.5±0.5 37.34 36.4

information as follows. In each test run that is executed, performancemeasures regarding averages are calculated on the basis of 1×106

packets. The test run is repeated 20 times and reported withconfidence intervals of 95% (denoted by 95%CI) around the averages.

4.2.1. ThroughputThe throughput reading from iPerf is directly recorded and

averaged over all samples. The symbol Rm denotes the measuredthroughput in the results. Measured values of Rm are compared

Mbps) Rpt (Mbps) % error DJS(⋅) PER

.2 191.7 0.71 0.53 ≈0

.7 191.7 0.76 0.51 ≈0

.8 191.7 1.00 0.81 ≈0

.5 191.7 1.22 0.96 ≈0

.2 191.7 1.13 1.13 3.6

.8 191.7 0.95 0.98 3.5

.5 191.7 1.05 1.07 3.6

.1 191.7 1.51 1.05 3.4

.2 191.7 1.98 1.18 4.0

.7 115.0 2.43 0.97 7.2115.0 2.67 0.92 6.9115.0 3.58 0.95 7.038.3 2.49 1.09 7.2

Table 4Comparison of analytical prediction and measurement data for point X2(LOS).

d (m) μUL±95%CI/μDL±95%CI-(dBm) Rm (Mbps) Ra (Mbps) Rpt (Mbps) % error DJS(⋅) PER

0.5 54.5±0.4/54.0±0.5 187.2 184.71 191.7 1.33 0.38 ≈01.0 54.5±0.5/53.5±0.5 186.9 184.09 191.7 1.50 0.55 ≈02.0 55.0±0.6/54.0±0.5 187.5 182.65 191.7 2.59 0.53 0.43.0 55.0±0.5/54.5±0.5 180.4 178.21 191.7 1.21 0.41 2.57.0 57.5±0.5/53.0±0.5 147.8 145.42 191.7 1.61 0.77 4.28.0 58.3±0.3/54.0±0.5 123.9 122.43 115.0 1.19 0.93 4.39.0 61.5±0.5/55.0±0.6 122.1 120.70 115.0 1.51 0.95 4.310 61.0±0.2/55.0±0.5 122.7 119.87 115.0 2.31 1.04 4.115 64.0±0.5/59.0±0.5 100.3 97.50 115.0 2.79 1.15 4.330 69.5±0.3/62.5±0.5 36.9 35.46 115.0 3.93 1.09 6.935 72.0±0.5/67.0±0.4 35.8 35.15 38.3 1.82 1.18 6.240 75.5±0.3/70.0±0.5 18.5 18.26 38.3 1.29 1.01 7.345 78.5±0.5/74.5±0.6 17.2 16.54 19.2 3.78 1.17 7.4

Table 5Comparison of analytical prediction and measurement data for point X3(NLOS) — single wall obstruction.

d (m) μUL±95%CI/μDL±95%CI-(dBm) Rm (Mbps) Ra (Mbps) Rpt (Mbps) % error DJS(⋅) PER

0.5 59.5±0.5/57.0±0.7 145.4 141.4 191.7 2.74 0.67 ≈01.0 59.0±0.6/57.5±0.6 147.9 145.3 191.7 1.27 0.58 1.12.0 59.8±0.5/57.0±0.6 144.6 142.9 191.7 1.12 0.71 0.43.0 59.0±0.5/56.4±0.5 118.0 115.5 115.0 2.05 0.89 1.07.0 61.0±0.6/58.0±1.1 98.7 99.0 115.0 0.65 0.93 4.48.0 64.0±0.6/58.0±0.8 100.4 99.3 115.0 2.02 1.05 4.79.0 64.5±0.5/58.0±0.7 99.1 96.8 115.0 2.27 1.13 4.610 65.0±0.5/58.5±0.9 99.0 95.5 115.0 3.51 1.05 4.715 69.0±0.5/62.5±0.8 36.8 35.9 115.0 2.22 1.16 5.730 73.5±0.7/68.0±0.7 30.8 30.5 38.3 0.68 1.31 7.135 75.8±0.7/69.5±0.9 18.6 17.1 38.3 2.50 1.29 7.240 78.5±0.7/71.0±1.0 18.7 18.2 19.2 2.62 1.35 7.045 81.5±0.7/71.0±0.9 18.5 18.4 19.2 0.43 1.45 7.1

142 B. Ng et al. / Computer Standards & Interfaces 34 (2012) 135–145

against the predicted analytical throughput Ra. For comparison, wedefine a point-estimate for throughput Rpt, determined solely on thebasis of average uplink SS (μUL) with minimum computationaloverhead. The purpose of introducing Rpt is to compare the gain inaccuracy by introducing the Markov model's post-processing. Thispoint-estimate is defined as Rpt=RPHY (μUL)⋅ [1−Oh] whereby RPHY(μUL) is determined via looking up the physical data rate entrymatching the argument μUL in the receiver sensitivity informationwhile [1−Oh] is the normalized overhead defined in (13).

4.2.2. Packet error rate (PER)For the purpose of evaluating PER, we construct a distribution over

a set of empirical histograms. The first step is to measure the ratio ofthe number of failed packets to the total number of packetstransmitted in a sampling interval. The ratio is defined as Yh foreach sample indexed by an integer h. The resulting sequence of Yh is

Table 6Comparison of analytical prediction and measurement data for point X4(NLOS) — single wa

d (m) μUL±95%CI/μDL±95%CI-(dBm) Rm (Mbps) Ra (

0.5 62.0±0.5/61.0±0.8 110.6 1081.0 62.5±0.5/60.5±0.7 112.5 1102.0 62.5±0.6/61.0±0.8 108.0 1053.0 62.5±0.5/62.0±0.9 109.5 1057.0 64.5±0.6/62.0±1.0 99.3 1038.0 65.0±0.8/62.5±0.9 101.1 979.0 65.0±0.6/62.5±0.8 98.7 9610 65.0±0.9/62.5±0.9 99.6 9715 68.5±0.7/64.0±1.0 45.5 4430 74.0±0.6/69.5±0.8 20.4 1935 77.0±0.9/70.5±1.0 18.6 1840 80.0±0.8/72.5±1.0 18.4 1745 84.0±0.8/74.5±1.1 18.8 18

summarized in a histogram of frequencies of occurrence. Thehistogram is converted to a probability distribution by the function:

FmPER mð Þ = n mð ÞN

ð16Þ

where n(m) counts the number of samples whose ratio Yh falls betweenthe error range indicated by state m (see Table 2) while N is the totalnumber of data points. Sampling intervals are set to 1×104 transmittedpackets, thusN=100. Besides PER distribution, the average PER (denotedby PER) is another important measure and it is calculated as follows:

PER =Nsent−Nrcv

Nsentð17Þ

whereNsent is thenumberofpackets sentby the sourceandNrcv is the totalpackets correctly received at the sink during the test session.

ll obstruction.

Mbps) Rpt (Mbps) % error DJS(⋅) PER

.2 115.0 2.12 0.51 ≈0

.9 115.0 1.34 0.57 0

.8 115.0 1.97 0.56 1.5

.1 115.0 3.96 0.53 1.3

.1 115.0 3.84 0.62 3.9

.7 115.0 3.13 0.65 4.5

.0 115.0 2.71 0.59 4.5

.7 115.0 1.86 0.71 4.4

.4 115.0 2.25 1.24 6.3

.9 38.3 2.41 1.40 6.6

.1 19.2 2.37 1.37 7.5

.7 19.2 3.53 1.28 7.3

.5 19.2 1.17 1.47 6.8

a

b

Fig. 6. Stationary probability distribution π, for point X1 and X3 at 10 m.

143B. Ng et al. / Computer Standards & Interfaces 34 (2012) 135–145

5. Validation

The process of validation compares the analytical predictions to themeasured results. Accuracy of throughputpredictions is indicatedby thepercentage error between Rm and Ra. On the other hand, the similaritybetween two probability distributions is indicated by the Jensen-Shannon divergence [25]. The use of Jensen-Shannon divergence isappropriate in this context due to: (a) the Jensen-Shannon divergencemeasure is well defined across the domain of interest (FmPER ; FaPER ),therefore eliminating ambiguous interpretation; (b) the use of Jensen-Shannon divergence has been documented in reliable statistical studies[26,27]. The Jensen-Shannon divergence denoted by DJS(FPERm |FPERa )returns a measure between [0,∝) indicating the difference betweenthe empirical distributions FPER

m and the analytical distribution FPERa .

Define H Fð Þ = ∑all i

−p Fið Þ⋅ log p Fið Þð Þ to be the entropy function for a

distribution function F (Fi is the datum in F), and then the Jensen-Shannon divergence is expressed as follows,

DJS FmPER jFaPER� �

= HFmPER + FaPER

2

� �−H FmPER

� �+ H FaPER

� �2

: ð18Þ

The measure DJS(⋅) in (18) is zero if FPERa and FPERm are identical. The

larger the value of DJS(⋅), the more divergent FPERa is relative to FPERm .

Since both FPERa and FPER

m are discrete distributions, the entropyfunctions H(⋅) for every term in (18) are well defined.

The results from site measurements and numerical evaluation areuniformly presented in the form of tables. The first column shows thedistance d from the AP, the second column shows the averagemeasuredSS for uplink and downlinkmeasured over 50 readings. The third, fourthand fifth columns give the measured throughput (Rm), the analyticallyestimated throughput (Ra) and the point-estimate for throughput (Rpt).Column six shows the percentage error between Ra and Rm and the finaltwo columns relate to the accuracy of PER predictions.

The first set of results given in Tables 3 and 4 compares theanalytical predictions from the Markov model with site measurementdata. The results shown in both Tables 3 and 4 represent typical LOSconditions in office environment. Firstly, channel asymmetry is clearlyvisible and the average uplink/downlink SS is decreasing withdistance. However, measurement results show poor correlationbetween distance and SS. We also notice that Rpt inaccuratelyestimates the throughput compared to Rm when the average SS isbetween the boundaries of two adjacent MCS#. When μUL or μDL fallsaround the levels of −61, −70 and −76 dBm (RSI in Table 2), thepoint estimates diverge significantly from the measured throughputwhile the Markov model predictions track the measured throughputclosely as seen when d=15 m, 35 m, 40 m in Table 3 and d=9m,30 m, 40 m Table 4.

Comparing Ra and Rpt with Rm column-wise, it is observed that theMarkov model predictions for throughput closely track the sitemeasurement data while the point-estimates are at times quite far off.For PER prediction, themagnitude ofDJS(⋅) varies between0.5 and 1.2. Itis observed from the “% error” column that the Markov modelunderestimates the throughput performance possibly due to the coarsemodel approximation while the point-estimates predict significantlyhigher throughput compared to actual measurements. The average PERPER� �

for both X1 and X2 varies between 0 and 7.5%, this is well withinthe 10% error limits set by the standard specification indicating that thewireless NIC under test is functioning within normal limits. When thesource is very close to the sink, the PER values are very small (in theorder of 10−6) and it is replaced with “≈0”.

For NLOS conditions the performance measures are tabulated inTables 5 and 6. From the Rm columns, it is clear that the throughputhas significantly dropped compared to what was observed for the LOSscenario. Again, the Markov model consistently tracks the measuredthroughput and offers better accuracy over point-estimates. The

inaccuracies of point-estimates are mainly attributed to the failureto account for the distributive tendencies of the MCS# selection, thussignificantly reducing its prediction accuracy. The trends in theanalytical predictions are consistent with the site measurement resultswith prediction errors hovering around 4%, which is comparable to theerrors observed for LOS scenario.

The PER distribution accuracy for NLOS scenario is almost identicalto the LOS scenario judging by the Jensen-Shannon divergenceparameter. The magnitude for DJS(⋅) generally increases with d butit is range bound between 0.5 and 1.5. In addition to the coarse modelapproximation, another reason for possible prediction errors in NLOSscenario is that the SNR distribution deviates from Rician assumption.

In the NLOS scenario, correlated direct paths between transmit andreceive devices are obstructed leading to a reduction in SNR at thereceiver. Consequently, the receiver selects a lower MCS# to increasethe bit protection. The lower MCS# provides lower throughput butcircumvents excessive bit errors therefore there is no significantchange in PER even with the throughput halved. The statedistribution, π for LOS in Fig. 6(a) and NLOS in Fig. 6 (b) shows thatthe NLOS distribution is spread over i=2 and i=3 while the statedistribution for the LOS scenario is concentrated on states ⟨2, 0⟩ and⟨2, 1⟩. The Markov model analysis suggests that the throughput seenby an application is a confluence of multiple physical rates weightedby the distribution π. The overall analysis show that the percentageerror in throughput is below 4% and PER predictions has a distancemargin of DJS(⋅)b1.5 while average PER is below 7.3%.

Fig. 7. Throughput and PER information visualized through software designed for use with Markov model.

144 B. Ng et al. / Computer Standards & Interfaces 34 (2012) 135–145

In relation to previous works characterizing 802.11a/b and802.11e, the error margin of less than five percent is within acceptablerange of those achieved by other modeling studies [17,18]. Thoughmodeling details may be further refined, it requires that the wirelesschannel information and perhaps some hardware details within thereceiver be knownwith a level of detail that is generally impractical atthe link-layer.

Finally, the results are better-appreciated using data visualizationtechniques such as throughput contour maps. Fig. 7 shows a screencapture of a simple program developed in Visual Basic with thecomputation engine based on the proposedMarkovmodel. Firstly, thereceiver sensitivity information is selected from a list of knowndevices from the top left pane (or entered based on manufacturerdatasheet), which is somewhat similar to the entries in Table 2. Uponclicking the “Evaluate” button, it initiates the process of measuring theSS. The software interfaces with the low-level drivers (libPcap) toextract the parameters σUL

2 , σDL2 and μUL, μDL from the CSI headers.

Subsequently, it tabulates the expected throughput and linearlyinterpolates the throughput and PER between evaluation points. Theresulting contours are overlaid on amap selected by the user. A salientfeature of the system model is that it makes use of readily availableinformation (measured SS) and the model readily accommodates off-the-shelf 802.11n devices through changes in the driver [28,29].

6. Conclusion

In this paper a model for throughput and PER is proposed forindoor IEEE 802.11n wireless LAN. It was investigated if thethroughput and PER according to the proposed Markov modelmatches the throughput and PER from site survey measurements.Good statistical agreement is demonstrated between the analyticalmodel predictions and the measured data. Smaller percentage errors

are recorded for less volatile changes in MCS. However, due to thesimplifications made so that mathematical tractability can beachieved, finer details such as adaptive MCS algorithms and powercontrol mechanisms cannot be accommodated in the Markov model.Removing some assumptions made in the modeling process orperhaps considering more complex uplink–downlink interactionwould make for interesting future research.

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Bryan Ng obtained his BEng, PhD all in the field ofengineering and applied mathematics. He was previouslyaffiliated with the Nokia wireless lab at MultimediaUniversity, Malaysia. He is currently a postdoctoral fellowworking on Traffic matrix analysis.

Tan Yi Fei obtained her BSc, MSc and PhD in the field ofmathematical sciences at the University of Malaya. Herresearch areas cover queuing theory and stochasticprocesses.

Tan SuWei obtained his PhD at the University of Kent, UK.His research interests include application layer multicastand traffic engineering. He is currently a senior lecturer atMultimedia University, Cyberjaya, Malaysia.

Lee Sze-Wei obtained his PhD in UMIST, UK. His research

interests cover the area of wireless networks and digitalsignal processing (DSP). He is currently a professor atTunku Abdul Rahman University, Malaysia.