Enhancement of IEEE 802.15.4 MAC protocol
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Enhancement of the IEEE 802.15.4 MAC Protocolfor Scalable Data Collection in Dense Sensor Networks
USC Technical Report CENG200614
Kiran YedavalliUniversity of Southern California
Los Angeles, California
Bhaskar KrishanmachariUniversity of Southern California
Los Angeles, California
ABSTRACTWe nd that the IEEE 802.15.4 MAC protocol performspoorly for onehop data collection in dense sensor networks,showing a steep deterioration in both throughput and energyconsumption with increasing number of transmitters. Wepropose a channel feedbackbased enhancement to the protocol that is signicantly more scalable, showing a relatively
at, slowchanging total system throughput and energy consumption as the network size increases. A key feature of theenhancement is that the backoff windows are updated aftersuccessful transmissions instead of collisions. The windowupdates are based on an optimality criterion we derive frommathematical modeling of ppersistent CSMA.
1. INTRODUCTIONIEEE 802.15.4 is an important standard for lowrate lowpower wireless personal area networks that is in increasingcommercial use for a diverse range of embedded wirelesssensing and control applications. The standard providesspecications for both the physical layer and the mediumaccess control (MAC) protocol.
We characterize the performance of the IEEE 802.15.4 MACfor onehop data collection in a star topology where there aremultiple transmitters and a single receiver. Our primary focus is on settings where the number of transmitters is large.Because 802.15.4enabled devices are meant to be lowcostand operate at relatively low rates, such dense deploymentsare of interest in many sensing applications involving thesedevices.
We model the IEEE 802.15.4 as a ppersistent CSMA withchanging transmission probability p. We derive the optimal transmission probabilities to maximize the throughputand minimize energy consumption in ppersistent CSMA.We show that, particularly for large number of transmitters,the ratio of the expected idle time between successful recep
tions to the expected time between successful receptions isa constant for a given packet size when the transmissionprobabilities are optimal. Further, we nd that when thetransmission probability is lower (higher) than the optimal,the ratio is higher (lower) than this constant. This yields adistributed channel feedbackbased control mechanism thatchanges the transmission probabilities of nodes dynamically
towards the optimal. We develop an enhanced version of theIEEE 802.15.4 MAC protocol using this feedback scheme.
In our modeling and evaluation, we consider two extremesof the onehop data collection spectrum in dense sensor networks: oneshot and continuous data collection. In oneshotdata collection, each node sends only a single packet (thiscould be the response to a oneshot query) and once thatpacket is transmitted the node is no longer in contentionfor the channel. In continuous data collection, we assumethat each node is backlogged, i.e. always has a packet totransmit.
In both cases, we nd that the IEEE 802.15.4 protocol performs poorly in dense settings, showing a steep reduction in
throughput and increase in energy with network size. In contrast, the enhanced protocol that we propose is signicantlymore scalable, showing a relatively at, slowchanging totalsystem throughput and energy as the number of transmitters is increased. This is illustrated in gure 1.
The rest of this paper is organized as follows. In Section 2we present an overview of IEEE 802.15.4 and model it as a ppersistent CSMA with changing p. In Section 3 we presentthe modeling and optimization of ppersistent CSMA andcharacterize the performance of the IEEE 802.15.4 MAC inSection 4. In Section 5 we present a channel feedbackbasedmedium access control technique and adapt it to present theenhanced IEEE 802.15.4 MAC. In the same section we discuss directions of our future work. We conclude in Section 6.
2. IEEE 802.15.4In this section we present an overview of the IEEE 802.15.4MAC and model it as a ppersistent CSMA MAC with changing p.
2.1 Overview & Related WorkThe IEEE 802.15.4 standard ([6]) allows different networktopologies such as onehop star and multihop. We considerthe onehop star topology with multiple data sources and a

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Figure 1: Performance of Proposed Enhancementcompared to IEEE 802.15.4 for Continuous DataCollection
single sink. In the star topology, a global synchronizationof nodes is assumed and the time is separated by beaconstransmitted by a network coordinator. The beaconintervalconsists of a superframe and an optional energy saving timein which the nodes switch off their radio and go to sleep. Thesuperframe is divided into 16 time slots of = 320 secs duration each. The superframe consists of a contention accessperiod (CAP) and a period of guaranteed time slots (GTS).The GTS is dedicated for low latency applications. In thispaper we consider only the CAP mode (without the energysaving mode, GTS, and beacons) where medium access isthrough slotted CSMA/CA.
In slotted CSMA/CA, a node can transmit its packet onlyafter it senses the channel free for a contention window (CW)of 2 time slots. The main purpose of the CW is to avoidcollisions between acknowledgement packets (ACKs) fromthe sink and data packets from the sources as the protocoldoes not specically provision time slots for ACKs [16]. Anode chooses a time slot uniformly at random from an initialwindow of [0, 2BE 1], where BE is the backoff exponentwith an initial value of 3. The node transmits its packet if the channel is sensed to be free in that and the next timeslots; if the channel is sensed to be busy the node backs off to a bigger window with BE = 4. On a second busy channelsensing or a collision the node backs off to a window withaMaxBE = 5 and remains constant. If a node is unableto transmit its packet within 5 backoffs the transmission isassumed to be a failure and the packet is dropped. We relaxthis condition in this paper and allow a node to retransmit
its packet until it is successful. Figure 2 shows the owchart for a node using the IEEE 802.15.4 MAC. The IEEE802.15.4 standard species a data rate of 250 kbps and amaximum MAC protocol data unit (MPDU) of 127 Bytes.Given this data rate, the transmission time for a typicalpacket of 50 Bytes is 5 time slots and for the MPDU it is 13time slots.
In [10] the the performance of the IEEE 802.15.4 MAC isevaluated in terms of throughput and energy efficiency usingns 2 simulations for a maximum of 49 nodes. In [14] the
Figure 2: Flow chart for IEEE 802.15.4 operation ata node.
performance of the standard MAC is evaluated for medicalapplications where the IEEE 802.15.4 devices interface withthe traditional MAC technologies such as Ethernet. [15]analyzes the performance in the context of medical body
area networks (BAN) where the energy efficiency of bodyimplanted sensors is the focus given that their required lifetime is in the order of 1015 years in these applications.In [12] a queuing analysis is presented for the sleep modewith possible nite buffers. In [13] the performance of thestandard MAC is evaluated in the presence of both uplinkand downlink traffic in the onehop star topology network.
2.2 Application SpaceWe consider the two extremes of the spectrum of onehopdata collection applications in dense sensor networks. Atone extreme of this spectrum is continuous data collectionand the other extreme is oneshot data collection.
Continuous Data (CD) : In this scenario the sourcescontinuously send data to the sink. We assume thatour observation time is such that all nodes always havea packet to send, i.e., their queues are backlogged.This implies that the network reaches steady stateand operates at the saturation throughput. Performance metrics of interest in this scenario are the system throughput 1 and energy consumption. Let CDand CD be the expected throughput in bps and expected energy consumption per node per successfulpacket transmission in Joules respectively.
OneShot Data (OSD) : In this scenario the sinkis interested in oneshot data queries such as Whichnodes have observed the event? or Which nodeshave recorded temperatures above 50F?, etc. The response to such oneshot queries is a single packet fromeach sensor node that contains the location of the nodeor a similar identication. Once the packet has beensuccessfully transmitted from a node it is not in contention for the channel anymore, implying that the
1 Please note that we are considering the total systemthroughput and not per node throughput. Per nodethroughput can be calculated by dividing the systemthroughput by the number of nodes.

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system does not attain steady state. The performancemetrics of interest in this scenario are the delay in obtaining packets from all sensor nodes as a performancemetric and energy consumption incurred by the sensornetwork in this operation. Let OSD and OSD be theexpected delay in seconds and the amortized expectedenergy consumption per node in Joules respectively forsuccessfully transmitting packets from all sources.
In this paper we mainly focus on dense sensor networks inwhich atleast 50 nodes contend for the channel in either scenario. We assume that the packet lengths are deterministicand constant.
2.3 ModelNow, we model the IEEE 802.15.4 MAC as a ppersistentCSMA MAC with changing p. Before we present the MACmodel, we describe the assumptions made and the energymodel used.
Assumptions : Let the number of sensor nodes in theradio range of the sink be N . All sensor nodes are synchronized to a global time which is divided into slotsof equal length and each node transmits at the beginning of a time slot. Let the packet length be L timeslots. A sensor node is informed of its packets successful transmission through acknowledgement packets (ACKs) from the sink. Failure to receive an ACKfrom the sink implies a collision. The ACK is sent bythe sink as soon as the packet reception is completed.Table 1 summarizes the notations used.
Energy Model : According to the IEEE 802.15.4 standard a node can exist in any one of the following fourstates  Shutdown, Idle, Transmit, Receive. For CD,we assume that the nodes are either in the Trasmit orthe Recieve state and are not concerned with the Shutdown or Idle states. For OSD, again each node is eitherin the Transmit or the Recieve state until its packet istransmitted, after which the node moves to the Shutdown state permanently. Let the power consumed inthe Transmit state be T and the power consumed inthe Recieve state be R . According to [1], R = 35mW and T = 31 mW for the highest transmissionpower. The power consumed in the Shutdown state isnegligible .
MAC Model : In [16] the authors model the IEEE802.15.4 MAC in the contention access period (CAP)as a nonpersistent CSMA with backoff. They approximate the three original uniformrandom backoff windows to geometrically distributed backoff windowswith parameters p1 , p2 and p3 such that pi = 2BO i +1 ,(1 i 3) where BO i is the original uniformrandombackoff window size. With BO 1 = 8, BO 2 = 16 andBO 3 = 32, the respective values of p1 , p2 and p3 are
14 . 5 ,
18 . 5 and
116 . 5 .
In this paper we further simplify this model to a ppersistent CSMA in which the probability of transmission changes from p1 to p2 to p3 with each collision andremains constant after two collisions at p3 . The keydifference in our model from the nonpersistent CSMA
N Number of nodes in the network p Transmission probabilityL Length of packet in time slots Time slot length (320 secs)
R Power consumption in Receive stateT Power consumption in Transmit staten Number of nodes in an epoch
T n Delay in an epoch with n nodesE n Energy consumption in an epoch with n nodes
CD (N ) Throughput in bps in CD CD (N ) Energy consumption per node per successful
packet transmission in CD OSD (N ) Delay in secs to obtain packets from
N nodes in OSD OSD (N ) Energy consumption in Joules to obtain
packets from N nodes in OSD pT opt (n, L ) Transmission probability that minimizes
epoch delay pEopt (n, L ) Transmission probability that minimizes
epoch energy consumption
Table 1: Notation
model is that in our case the transmission probabilitychanges with a packet collision instead of a busy carrier sense. Thus in our model, a node starts out withan initial transmission probability of p1 . The nodesenses the channel at the beginning of each time slotand if the channel is found to be free for two consecutive time slots, it transmits its packet with probability p1 . If the channel is busy, the node tries to transmitthe packet with the same probability the next timeit nds two consecutive free time slots. If more thanone node transmits in the same time slot it results ina collision and if a node is involved in a collision forthe rst time it changes its transmission probability to p2 . On a second collision its transmission probability
is changed to p3 and it remains constant beyond thesecond collision.
We evaluate the accuracy of our model using simulations 2 .The results are averaged over 1000 random trials with 100different random seeds. For the CD scenario, we simulatedthe protocol for 10000 time slots for a packet length of 50Bytes (or 5 time slots).
Figure 3 plots the simulation results comparing the IEEE802.15.4 and our ppersistent CSMA model and shows thatour model is reasonably accurate. Next, we determine theoptimal performance of a generic ppersistent CSMA MACwith a similar time slot structure and characterize the performance of IEEE 802.15.4 MAC in comparison to that.
3. PPERSISTENT CSMA MACIn this section we model and analyze a generic ppersistentCSMA MAC and determine the transmission probabilitiesthat optimize its performance.2 We have written our own simulators in C forthe IEEE 802.15.4 and ppersistent CSMA MACprotocols. They are available for download athttp://ceng.usc.edu/anrg/downloads.html.

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(a) Continuous Data (b) Oneshot Data
Figure 3: IEEE 802.15.4 standard is modeled as a ppersistent CSMA with probability of transmissionreducing in three steps p1 = 14 . 5 , p2 =
18 . 5 , p3 =
116 . 5 with each new collision.
3.1 OverviewIn a slotted ppersistent CSMA ([2]), each node senses thechannel at the beginning of each time slot and if the channelis found to be free of any transmissions, it transmits itspacket with a probability p. If the channel is not free, thenode attempts to transmits its packet in the next free timeslot. If more than one node transmits in the same time slotit results in a collision.
Traditionally, system dynamics due to the ppersistent CSMAprotocol have been modeled using renewal theory (example[8], [9], [5], [4]). The key assumption that makes the useof renewal or regenerative models feasible is that the system attains stationarity and that the models capture thesystem behavior at the state. While this assumption is stilltrue for the CD scenario, it is not true for the oneshotdata scenario. Nevertheless, we observe the system at everysuccessful packet transmission like in [9] and [5], for bothscenarios and derive expressions for throughput, delay andenergy consumption.
3.2 ModelWe observe the system at every successful packet transmission. The time interval between two consecutive successfultransmissions is dened as an epoch . An epoch is made up of idle time, in which the channel is free of any transmissions,collision time, in which more than one node is transmitting
and a single successful transmission time which marks theend of the epoch, as illustrated in Figure 4.
It is important to note that, for CD, the number of nodesremain constant in all epochs. However, for OSD the number of nodes decreases by one with each passing epoch. LetT n be the epoch delay the time interval between two consecutive successful packet transmissions in seconds andE n be the energy consumption the total energy consumedby all contending nodes in Joules, for the epoch with ncontending nodes. Then
Figure 4: An epoch illustrating the time intervalbetween consecutive successful transmissions.
CD (N ) =1
E [T N ] (80L) bps (1)
CD (N ) =E [E N ]
N Joules (2)
OSD (N ) =N
n =1
E [T n ] seconds (3)
OSD (N ) = 1N
N
n =1
E [E n ] Joules (4)
where 80 L in Equation 1 is the packet length in bits. Clearly,the above metrics are optimized when E [T n ] and E [E n ] areminimized. First we determine expressions for E [T n ] andE [E n ].
Proposition 1. For a constant packet length L, the ex

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pected epoch delay for n contending nodes is given by
E [T n ] =L (L 1)(1 p)n
np(1 p)n 1 (5)
Proof. As illustrated in Figure 4 the delay in an epochis due to idle time, collision time and successful transmissiontime. Therefore, the expected delay in epoch n , is given by
E [T n ] = E [T Idle,n ] + E [T Collision,n ] + E [T Success ] (6)
where E [T Idle,n ] is the expected number of idle time slots,E [T Collision,n ] is the expected number of collision time slotsand E [T Success ] is the expected number of time slots of successful transmission. Since the packet length L is a constantE [T Success ] is equal to L and independent of n .
If E [N coll,n ] is the expected number of collisions in an epochwith n nodes, then
E [T Idle,n ] = ( E [N coll,n ] + 1) E [T IdlePeriod,n ] (7)E [T Collision,n ] = E [N coll,n ] E [T CollisionPeriod,n ] (8)
where E [T IdlePeriod,n ] is the expected number of idle timeslots between two consecutive packet transmissions (collision or successful) and E [T CollisionPeriod,n ] is the expectednumber of collision time slots at each collision. Owing to theconstant probability of transmission p within an epoch, theIdlePeriod s between any two consecutive packet transmissions are i.i.d random variables with the same mean value.Also, since the decision to transmit in a time slot after a freechannel sense is independent of the number of previous freechannel senses, the number of collisions is independent of the
length of IdlePeriod s. This holds true for CollisionPeriod salso, thus justifying the above two equations.
E [N coll,n ] and E [T IdlePeriod,n ] are given by [5]:
E [N coll,n ] =1 (1 p)nnp(1 p)n 1
1 (9)
E [T IdlePeriod,n ] =(1 p)n
1 (1 p)n (10)
We use the above two equations to derive the expected delay in the epoch n . Since the packet length is constant
E [T CollisionPeriod,n ] = L. Therefore,
E [T Idle,n ] =1 p
np (11)
E [T Collision,n ] =L(1 (1 p)n np (1 p)n 1 )
np (1 p)n 1(12)
Substituting the above equations in Equation 6, we get Equation 5.
Proposition 2. For a constant packet length of L, theexpected epoch energy consumption for n contending nodesis given by
E [E n ] = R L (L 1)(1 p)n 1
p(1 p)n 2+ T
L(1 p)n 1(13)
Proof.Similar to Equation 6, the energy consumptionin the epoch n is equal to the sum of the energy consumption
in idle time, the energy consumption in collision time andthe energy consumption in a successful transmission.
E [E n ] = E [E Idle,n ] + E [E Collision,n ] + E [E Success ] (14)
Using equations from Proposition 1, E [E Idle,n ] can be calculated as
E [E Idle,n ] = ( E [N coll,n ] + 1)
n R
E [T IdlePeriod,n ](15)
= n R 1 p
np= R
1 p p
(16)
Surprisingly, for a constant p, the idle time energy consumption is independent of the number of contending nodes in anepoch, and depends only on p. Similarly, the collision timeenergy consumption is given by
E [E Collision,n ] = E [N coll,n ] E [E CollisionPeriod,n ] (17)
The expected energy consumption in a CollisionPeriod ,
E [E CollisionPeriod,n ], is equal to the sum of the expectedenergy consumption by nodes involved in packet transmissions and the expected energy consumption by nodes in idlestate during the CollisionPeriod . Therefore,
E [E CollisionPeroid,n ] = LT n
i =2
iP {Trans. = iCollision }+ LR
n
i =2
(n i)P {Trans. = iCollision }(18)
where P
{Trans. = i
Collision
}is the probability that i
(2) nodes transmit their packets given that a collision hasoccurred, and it is given by
P {Trans. = iCollision }= P {Trans. = iTrans. 2}=
ni p
i (1 p)n i1 (1 p)n np(1 p)n 1
(19)
Substituting the above equation in Equation 18, we get

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E [E CollisionPeriod,n ] =L(T R ) np(1 (1 p)n 1 )
1 (1 p)n np(1 p)n 1+ nL R (20)
Substituting the above equation in Equation 17, we get
E [E Collision,n ] =L(T R ) (1 (1 p)n 1 )
(1 p)n 1+ LR (1 (1 p)
n np(1 p)n 1 ) p(1 p)n 1
(21)
And nally, the expected energy consumption during a successful transmission is give by
E [E Success ] = T L + R L (n 1) (22)
Substituting the above equations in Equation 14 we getEquation 13.
3.3 OptimalityLet pT opt (n, L ) and pEopt (n, L ) respectively be the transmission probabilities at which E [T n ] and E [E n ] are minimized.
Proposition 3. For n > 1, the transmission probability that minimizes the expected epoch delay E [T n ] is given by
pT opt (n, L ) =1n
, L = 1 (23)
pT opt (n, L )
n 2 + 2 n(n 1)(L 1) n
n(n 1)( L 1), L > 1(24)
Proof. The value of p that minimizes E [T n ] is obtainedby equating its rst derivative with respect to p to zero.
dE [T n ]dp
= 0 (25)
For L = 1,
E [T n ] =
np(1 p)n 1(26)
Taking the derivative and equating it to zero results in p =1n . Similarly, for L > 1, equating the derivative of E [T n ]from Equation 5 to zero yields the following equation.
(1 p)n = L
L 1 (1 np) (27)
For np < 1, (1 p)n can be approximated to 1 np n ( n 1)2 p2 . Using this approximation and further simplication, Equation 27 reduces to Equation 24 as an unique root
to a quadratic equation. It can be veried that d2 E [T n ]
dp 2 > 0for p = pT opt (n, L ), thus minimizing E [T n ].
Proposition 4. For n > 1 and = T R the transmission probability that minimizes the expected epoch energy consumption E [E n ] is given by
pE
opt (n, L ) n 2 + 2 n(n
1)(L
1) + 4 L(n
1)(
1)
n
n(n 1)( L 1) + 2 L(n 1)( 1) (28)Proof. Similar to the previous Proposition equating dE [E n ]dp
to zero yields
(1 p)n = L
L 1 (1 np p2 (n 1)( 1)) (29)
The same approximation as in the previous proposition andfurther simplication of the above equation results in Equation 28. It can be veried, as in the previous Proposition,
that the second derivative of E [E n ] with respect to p is positive for p = pEopt (n, L ), thus minimizing E [E n ].
Numerical calculations show that the approximations arevery close to the actual values. For n = 1, the optimumtransmission probability is equal 1, i.e., when there is a single sensor node left, delay and energy are minimized whenit transmits its packet with probability 1. Figure 5 plots pT opt (n, L ) and pEopt (n, L ) as a function of the number of contending nodes from n = 100 to n = 2 for different values of . As the gure shows, for optimal performance the probability of transmission should increase with decreasing number of nodes in an epoch in order to avoid excessive idletime slots. We can also see that the transmission probabil
ities are higher for lower values of . This is because if thenode spends more energy in the Receive state than in theTransmit state, energy is saved if it transmits more than itreceives.
Figure 5: The optimal probability of transmission.
Corollary 1. If T = R , then pT opt (n, L ) = pEopt (n, L ),i.e., the delay and energy consumption are jointly optimized with a single probability of transmission for T = R .

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Proof. For = 1 Equations 24 and 28 are equal, whichproves the corollary.
3.4 Optimality CriteriaNow, we discuss some interesting optimality criteria for theepoch delay and energy consumption.
Proposition 5. Let (L) =( L
1) 2
L 2L 1 . If L > 1and n is large such that n 1n 1 then for optimal transmission probability the average epoch delay is a constant equal to (L).
p = pT opt (n, L )E [T n ] (L) (30)Proof. For optimal transmission probability, sub
stituting Equation 27 into Equation 5 we get
E [T n ] =(L 1)(1 pT opt (n, L ))
1 np T opt (n, L )(31)
For n large such that n 1n 1, from Equation 24 pT opt (n, L )
0 (32)
np T opt (n, L ) 2L 1 1
L 1(33)
Substituting the above equations into Equation 31 provesthe proposition.
Corollary 2. For optimal transmission probability and for large number of nodes such that n 1n 1 thethroughput of ppersistent CSMA MAC protocol is a constant independent of n and depends only the length of the packet.
OptimalThrougput L 2L 1
(L 1)2packets / timeslot
(34)
Proof. Throughput is calculated as the inverse of the epoch delay. Equation 34 is a direct result fromProposition 5.
Proposition 6. Let R (L) = L 2L 1( L 1)( 2L 1 1)
. If L > 1 and n is large such that n 1n 1, then for optimal transmission probability the ratio of average idletime in an epoch to the average epoch delay is a constant equal to R (L). Also, if the transmission probability is greater than optimal then the ratio is lower than R (L) and vice versa.
p = pT opt (n, L )
E [T Idle,n ]
E [T n ] R (L) (35)
p pT opt (n, L )E [T Idle,n ]
E [T n ]R (L) (36)
Proof. Using Equations 9, 5 and 27 for optimal p,
E [T Idle,n ]E [T n ]
= 1L 1
1np T opt (n, L ) 1 (37)
For n 1n 1, using Equation 24
np T opt (n, L ) 2L 1 1
L 1(38)
Substituting the above equation into the previous equation the rst part of the proposition is proved.Similarly, for p pT opt (n, L )
np2L
1
1
L 1 (39)
E [T Idle,n ]E [T n ]
R (L) (40)
Hence the proposition is proved.
Figure 6 illustrates Proposition 6 for L = 5. The approximation of the ratio to R (L) is primarily due theapproximation in Equation 24. As the gure shows, forlow values of n the ratio deviates away from R (L).
Figure 6: Ratio of expected idle time to expectedepoch delay.
Figure 7 plots the expected delay and energy consumption for an epoch with n = 50 nodes as a functionof the transmission probability p for different valuesof the packet length L. The gure can be explainedthrough the following question:
In ppersistent CSMA, if the length of thepacket is increased from L to L + l ( l > 0),should the value of transmission probability p be increased or decreased to maintain thedelay and energy consumption constant?
Figure 7 shows us that the answer to the above question is that it depends on the value of p. If p < pT opt (n, L ), then for the same delay, p should be increased and if p > p T opt (n, L ) then p should be decreased. The same answer holds true for energy if pT opt (n, L ) is replaced by pEopt (n, L ). The gure alsoshows that the optimal transmission probability values pT opt (n, L ) and pEopt (n, L ) decrease with increasingL.
Figure 8 plots ratios of consecutive epoch delays andenergy consumptions as functions of n . In this gure,if the ratio is greater than 1 it implies that the delay

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Figure 7: Expected delay and energy consumptionin an epoch with n nodes as a function of transmission probability, p, for different values of packetlength L.
or energy value increases with decreasing n and viceversa . Greater the difference from 1 higher the rate of increase or decrease. The following observations canbe made from the gure:
For p = pT opt (n, L ), E [T n ] is almost constant overall n . For p > p T opt (n, L ), E [T n ] shoots up forhigher values of n due to higher number of collisions. For p < p T opt (n, L ), E [T n ] shoots up forlower values of n due to higher number of idletime slots.
For p = pEopt (n, L ), E [E n ] increases monotonicallywith increasing n . For p > p Eopt (n, L ), E [E n ]
shoots up for higher values of n due to highernumber of collisions. For p < p Eopt (n, L ), E [E n ] ishigher than the optimal energy consumption values for lower values of n due to higher number of idle time slots.
Figure 8: Ratio of expected delays and energy consumptions for consecutive epochs.
For CD the implication of this criterion is that the delaybetween two successful packet transmissions is independentof the number of nodes in the network as long as the nodesare transmitting at optimal transmission probabilities. ForOSD, the implication is the following proposition.
Proposition 7. For OSD, if n is large such that n 1n 1, then the transmission probability is optimal if and only if the epoch of delay of two consecutive epochs are equal.
p = pT opt (n, L ) E [T n 1 ] = E [T n ] (41)
Proof. (i) To prove that
p = pT opt (n, L )E [T n ] = E [T n 1 ] (42)
From Equation 27 p is optimal when
(1 p)n = L
L 1 (1 np) (43)
For optimal value of p,
E [T n ]E [T n 1 ]
=(1 pT opt (n, L ))(1 (n 1) pT opt (n 1, L ))
(1 pT opt (n 1, L ))(1 np T opt (n, L )) 1 for
n 1n 1 (44)
We have used Equation 24 in the above simplication.
(ii) To prove that
E [T n ] = E [T n 1 ] p = pT opt (n, L ) (45)
Using equation 5, E [T n ] = E [T n
1 ] implies
L (L 1)(1 p)nnp(1 p)n 1
= L (L 1)(1 p)n 1
(n 1) p(1 p)n 2(46)
Algebraic manipulations reduce the above equation to
(1 p)n = L
L 1 (1 np) (47)
which is the same as equation 27, which implies p = pT opt (n, L ).
Hence proved.
4. CHARACTERIZATION OFIEEE 802.15.4Having determined the performance of optimal ppersistentCSMA, we characterize the performance of IEEE 802.15.4MAC in this section.
Figure 9 plots the average transmission probabilities for theIEEE 802.15.4 MAC (obtained using the ppersistent CSMAmodel) in comparison to the transmission probabilities foroptimal ppersistent CSMA for both CD and OSD. The

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transmission probabilities shown for IEEE 802.15.4 are obtained using the default values specied in the standardincluding the two required sensing slots, which is not required for the generic ppersistent CSMA MAC. For OSD,the transmission probability for IEEE 802.15.4 quickly stabilizes at 116 . 5 = 0 .0606 and for CD, close to that value. Thisbehavior is in contrast to the trend shown by optimal probabilities. This implies that the backoff mechanism of IEEE802.15.4 protocol can be modied for optimal performanceas follows:
The change of backoff window sizes should happen atsuccessful transmissions instead of at collisions or busychannel senses. Further, for OSD, successful packettransmissions are a better indicator for future congestion than collisions or busy channel senses.
For CD, the average transmission probability for IEEE802.15.4 MAC remains almost constant irrespective of the number of contending nodes, while for optimal ppersistent CSMA it reduces with N . For optimal performance the window sizes should be reective of thenumber of contending nodes.
For OSD, the backoff window size should actuallydecrease with every successful transmission as the optimal transmission probability increases.
Figure 9: Comparison of transmission probabilitiesfor IEEE 802.15.4 and optimal ppersistent CSMAfor CD and OSD.
In the next section, we present a channel feedback enhancedIEEE 802.15.4 MAC that incorporates the above features.
5. ENHANCED IEEE 802.15.4The key idea in enhancing the performance of the IEEE802.15.4 is to use the optimality criteria for ppersistentCSMA derived in Section 3. In particular, we consider thecriterion described in Proposition 6 which requires measurement of the idle time as well as the delay between two consecutive successful transmissions. These measurements canbe construed as feedback from the channel. Before we describe how this feedback can be used, we review the relatedwork in channel feedbackbased medium access control techniques.
5.1 Related WorkThe idea of using feedback from the channel to control thetransmission probabilities of contending nodes has been usedfor a long time. Rivest in [17] has proposed a ternary feedback model in which each node has to monitor three channel conditions  absence of transmissions, successful transmissions and, collisions. Rivest has shown that estimatingthe true value for the number of nodes n and setting thetransmission probability to 1n maximizes the throughput inslottedAloha type protocols (in which the packet length isequal to a single time slot). If the packet length is of multiple time slots, this results does not hold true as we haveshown in Proposition 3 in Section 3. In [4] a control mechanism has been presented that uses the energy consumedby a tagged node in the network in the above three channel conditions between two successful packet transmissions.This mechanism is not applicable in the case of OSD because each node has a single successful packet transmission.Similar strategies based on the estimation of the three channel conditions have been proposed ([11], [3], [7]) all of whichare more suitable for steady state conditions (like in CD) inwhich the number of contending nodes remain constant.
A good control mechanism should depend on the networkand traffic conditions as well as the application requirements. Our objective is to present a feedback control mechanism that is suitable for both CD and OSD scenarios. Onemajor challenge presented in OSD is to estimate the truesystem state using channel conditions in the face of constantly changing state of the system (decreasing number of contending nodes). Nevertheless, the analysis presented inSection 3 presents us with unique opportunities to efficientlycontrol the transmission probabilities in real time.
5.2 Our ApproachOur approach for channel feedbackbased control of transmission probabilities is mainly based on Proposition 6. According to the proposition, if the transmission probabilityis optimal then the ratio of idle time to the delay betweentwo consecutive successful packet transmissions is R (L). If the transmission probability if higher than the optimal valuethen the ratio is lower than R (L) and vice versa .
First we describe how this optimality criterion can be usedfor an enhanced ppersistent CSMA and then adapt it todesign an enhanced IEEE 802.15.4 MAC protocol.
5.2.1 Enhanced pPersistent CSMA MAC Each contending node can start by choosing a transmissionprobability uniformly at random in a small interval of say
(0, 0.05). Each node in the network measures the currentepochs idle time and delay and uses these measurements todetermine the transmission probability for the next epoch.If the ratio of idle time to the delay is lower than R (L) thenit means that the transmission probability would have beengreater than the optimal value. Therefore the transmissionprobability of the next epoch should be lower than the current epochs to bring the delay closer to optimal. Similarly,if the ratio if higher than R (L) the next epochs transmission probability should be increased for optimal delay. Thus,the transmission probability update rule is given by

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pnext = pcurrent
R (L)(48)
where = T Idle,currentT current . In this update rule the increase ordecrease in the transmission probability is directly proportional to the value of the ratio .
5.2.2 Enhanced IEEE 802.15.4The IEEE 802.15.4 MAC protocol uses different windowsizes to control the transmission of packets. In order to usethe above optimality criterion the transmission probabilityupdate rule should be converted into a window size updaterule. For this we make use of the approximation we used inSection 2 to model the IEEE 802.15.4 MAC as a ppersistentCSMA MAC with changing p. In this, if a uniformrandombackoff window has a size of W time slots then it can beclosely modeled as a geometricrandom choice of time slotwith parameter p as long as p = 2W +1 . Thus a transmission probability can be converted into window size by usingthe inverse relationship, i.e., W = 2 pp . Based on this andthe transmission probability update rule given above, the
window update rule for the Enhanced IEEE 802.15.4 MACis:
W next =(W current + 1) R (L)
(49)
A key aspect of this update rule is that, all nodes in thenetwork should updated their windows at every successfulpacket transmission. Figure 10 shows the ow chart for theEnhanced IEEE 802.15.4 MAC operation at a node.
Figure 10: Flow chart for Enhanced IEEE 802.15.4
operation at a node.It should be noted that all aspects of the original IEEE802.15.4 MAC have been preserved except for when the window is changed and how it is changed.
5.2.3 EvaluationFigure 11 shows the performance gains for the EnhancedIEEE 802.15.4 MAC in comparison to the original. Thegure also shows the performance of the optimal ppersistentCSMA and enhanced ppersistent CSMA. It should be noted
that the performance of the enhanced IEEE 802.15.4 MACmatches that of the enhanced ppersistent CSMA MAC forCW = 0, i.e., if the nodes do not sense the channel fortwo consecutive free slots but transmit their packet oncetheir chosen time slot occurs. Thus, for the enhancement weuse, the performance of the enhanced ppersistent CSMA isan upperbound on the performance of the enhanced IEEE802.15.4 MAC.
An important observation from the gure is that the systemthroughput reduces drastically with increasing number of contending nodes for the original IEEE 802.15.4 MAC. Butfor the enhanced version, the system throughput is almostconstant with the number of nodes. Implying that it is muchmore scalable than the original. This holds for energy also.These signicant gains in performance are observed for bothCD and OSD scenarios.
5.2.4 DiscussionIn actual implementation the measurement of idle time andthe delay between two consecutive successful packet transmissions can be achieved easily at each node by observingACKs from the sink. If all nodes in the network are in theradio range of each other then all nodes see the same idletime between two consecutive successful packet transmissions. If on the other hand, all nodes are in the radio rangeof the sink but not in the radio range of each other theneach node sees an idle time that is based on the numberof nodes in its neighborhood. Thus, the above update ruletries to optimize the transmission probability for the number of nodes in the neighborhood of each node and not forthe entire network. However, the sink can measure the idletime for the entire network and piggy back this value in theACKs to the sensor nodes. The sensor nodes measure theepoch delay as the interval between the ACKs. Thus, in thiscase, the channel feedback is via the sink.
The performance difference in terms of degradation or improvement, if any, between the local feedback and globalfeedback based mechanisms needs to be investigated. Thiswill be one of the directions for our future work.
An important aspect of the Enhanced IEEE 802.15.4 MACprotocol is that all nodes should change their window sizesand choose a new time slot (or start a new counter) at everysuccessful packet transmission. Otherwise, only a few nodesoptimize their window sizes and this could lead to unfairnessin the CD scenario.
Another important aspect to consider is the effect of channelerrors. The current standard MAC assumes channel errorsbased packet losses to be collisions and backsoff accord
ingly, thus misconstruing channel errors as congestion. Butthe enhanced MAC protocol does not change any protocolparameters due to channel errors based packet losses, as successful packet transmissions are taken as the only indicatorsof channel congestion. Nevertheless, a thorough investigation of the effect of channel errors will be an important partof our future work.
In this paper we have focused on dense sensor networks. Thefollowing table shows the throughput performance comparison of the original and enhanced IEEE 802.15.4 MAC pro

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