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Cooperation in Random Access Networks - Signals and Information ...

1694 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 9, OCTOBER 2012**Cooperation** **in** **R andom**

EL-SHERIF **and** LIU: COOPERATION IN RANDOM ACCESS NETWORKS: PROTOCOL DESIGN AND PERFORMANCE ANALYSIS 1695results **and** their discussions. F**in**ally, the paper is concluded**in** section VIII.II. CHANNEL AND SYSTEM MODELSA. Channel modelA Rayleigh fad**in**g channel model is considered, the signalreceived at the access po**in**t or the relay is modeled as√y ij = Gr −γij h ijx + η j (1)where i is the source **in**dex, j ∈{A, R} is the access po**in**tor the relay **in**dex, x is the transmitted signal, G is thetransmission power, assumed to be the same for all nodes,r ij denotes the distance between source node i **and** its dest**in**ationj, γ is the path loss exponent, h ij the channel fad**in**gcoefficients, modeled as zero-mean complex Gaussian r**and**omvariables with unit variance, **and** η j is an additive noise termat the dest**in**ation, modeled as zero-mean complex Gaussianr**and**om variable with variance N 0 . We assume that the channelcoefficients are constant for the duration of the transmission ofone packet. In this work, without loss of generality, we onlyconsidered the case of a symmetric network, where all the**in**ter-user channels are assumed to be statistically identical.This is possible for example when nodes are grouped **in** asmall cluster at fixed distance from the access po**in**t.Success **and** failure of packet reception is characterized byoutage events **and** outage probabilities. The outage probabilityis def**in**ed as the probability that the Signal to Noise Ratio(SNR) at the receiver is less than a given SNR threshold β.For the channel model **in** (1) the probability of outage can bewritten as,{Pijout = Pr | h ij | 2 < βN } (0r γ ij=1− exp − βN )0r γ ij.GG(2)B. Network ModelOur work **in** this paper focuses on wireless networks **in**which all nodes **and** the AP are with**in** communication rangefrom each other. In other words, we are only consider**in**g as**in**gle hop wireless network where each node is communicat**in**gonly with the AP. Based on this assumption, this s**in**glehop network does not suffer from the hidden node problems**in**ce any node can overhear all other nodes. Without loss ofgenerality, this paper also focuses on the s**in**gle relay case.Due to space limitation the case of a multi-hop network withmultiple relays is not considered **in** this paper. Extension of ourcooperation protocol design to the multiple-hop network case,how to deal with hidden nodes **and** the effect of cooperationon rout**in**g will be the subject of a future work.C. IEEE 802.11 DCF OperationThe distributed coord**in**ation function (DCF) is the fundamentalmedium access mechanism **in** the IEEE 802.11 protocol[8]. It is a r**and**om access scheme based on the CSMA/CA(Carrier Sense Multiple **Access** with Collision Avoidance)with b**in**ary slotted exponential backoff. As depicted **in** fig.1 a node with a packet to transmit **in**vokes the carrier sens**in**gmechanism to determ**in**e the busy/idle state of the channel. IfFig. 1. DCF basic access mechanism; numbers **in** figure represent node’sbackoff timer.the channel is sensed to be idle for a period of time equalto a Distributed Inter-Frame Space (DIFS), the node proceedswith packet transmission. Otherwise, it persists to monitor thechannel until it is measured idle for a DIFS. The node thendefers for a r**and**omly selected backoff **in**terval, **in**itializ**in**g itsr**and**om backoff timer, which is decremented as long as thechannel is sensed idle **and** is frozen when a transmission isdetected.The time immediately follow**in**g an idle DIFS is slotted,**and** a node is allowed to transmit at the beg**in**n**in**g of a slottime if its backoff timer reaches zero. The slot duration, σ,is set equal to the time needed for any node to detect thetransmission from any other node. It depends on the physicallayer, **and** it accounts for the propagation delay, **and** the timeneeded to detect a busy channel.The r**and**om backoff **in**terval is uniformly chosen **in** therange (0,w − 1). The value w is called the contentionw**in**dow. At the first transmission attempt, w is set equal toa m**in**imum contention w**in**dow value CW m**in** . After eachunsuccessful transmission w is doubled, up to a maximumvalue CWmax = 2 m CW m**in** , m is the maximum backoffstage. Once w reaches CWmax, it rema**in**s at this value untilit is reset to CW m**in** after a successful transmission.To signal the successful packet reception, an ACK istransmitted by the dest**in**ation. The ACK is transmitted aftera period of time called short **in**ter-frame space (SIFS). Asthe SIFS is shorter than a DIFS, no other station is able todetect the channel idle for DIFS until the end of the ACK.If the transmitt**in**g node does not receive the ACK with**in** aspecified ACK Timeout, the packet is assumed to be lost **and**the node reschedules the packet transmission accord**in**g to thegiven backoff rules.III. RANDOM ACCESS COOPERATION PROTOCOLInherent wireless channel fad**in**g **and** transmission errorshave a significant impact on the network’s performance [9].In wireless networks, nodes are unable to detect collisionsby hear**in**g their own transmission. Therefore, there is nodifferentiation between a packet loss due to a collision, **and** apacket loss due fad**in**g. Therefore, a source node will deal witha wireless channel **in**duced packet loss **in** the same way it dealswith a collision **in**duced one. Hence, doubl**in**g its contentionw**in**dow **and** wait**in**g for a r**and**om amount of time beforereattempt**in**g transmission. As a result of **in**vok**in**g the backoffprocedure **in** a non-congested channel, the network will sufferfrom an **in**creased delay **and** lower achievable throughput [10].To combat the wireless channel impairments lead**in**g tothese problems, we propose the deployment of a cooperative

1696 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 9, OCTOBER 2012relay node **in**to the coverage area of the wireless network. Thecooperative relay node will help combat the channel fad**in**gthrough the **in**troduction of spatial diversity **in**to the network.Relay node will help source nodes forward their packets byoperat**in**g **in** an **in**cremental decode-**and**-forward mode [1]. Inthis mode, **in** case of a packet loss at the access po**in**t, therelay attempts to decode the received packet, **and** **in** case ofsuccessful detection at the relay, it forwards a regeneratedversion of the packet to the AP.The relay makes use of the AP’s ACK packet to know ifa packet is successfully received by the AP. In case the relaysuccessfully receives a packet, but the AP does not receivethat packet (ACK Timeout occurs), the relay stores it **in** itsqueue **and** sends an ACK packet over the channel to **in**formother nodes that the packet was received successfully. Uponreceiv**in**g the relay’s ACK packet, the packet owner drops itfrom its queue **and** the delivery of that packet becomes therelay’s responsibility. Because of the relay’s ACK packet, thenode with the lost packet will reset its contention w**in**dowCW m**in** .The challeng**in**g part **in** the design of our cooperationprotocol is to enable the relay to ga**in** access to the wirelesschannel without **in**creas**in**g the number of collisions, **and** hencerender**in**g its existence useless. To deal with this issue wepropose the follow**in**g relay channel access protocol:• Follow**in**g a transmission attempt from one or moresource nodes (outcome of the transmission attempt isirrelevant), the relay node attempts to transmit the packetat the head of its queue immediately after the AP’s ACK,or after the ACK Timeout.• For the relay not to be totally dependent on other nodes’transmission attempts, the relay also ma**in**ta**in**s a s**in**glestage backoff counter with contention w**in**dow size CW r• When the relay’s backoff counter reaches zero, it willattempt to transmit the packet at the head of its queuelike other network nodes.• Like other network nodes, the relay will **in**voke thebackoff procedure after each transmission attempt, theonly difference is that the relay has a s**in**gle backoff stageas opposed to m stages for other nodes.By access**in**g the channel after each transmission attempt therelay has the ability to serve the packets **in** its queue withoutcaus**in**g any collision.IV. MARKOV MODELS AND ANALYSISA number of models have been proposed to study theperformance of IEEE 802.11 DCF **in** the saturated [11], [12],unsaturated [13], [14] traffic conditions, **and** **in** the presenceof channel impairments [10]. To analyze the performance ofthe proposed cooperative protocol, we start from the discretetimeMarkov model for non-saturated sources developed **in**[14], **and** **in**corporate the channel effects **and** relay operation**in**to the model. We consider two separate Markov cha**in**s, thefirst cha**in** models source nodes while the second models therelay node.We assume that the network consists of N contend**in**gnodes **in** addition to the relay node. Each node has an **in**f**in**itequeue to store packets. Each node receives packets fromupper layer based on a Poisson arrival process with arrivalFig. 2.0,0 e 0,1 e0, 2 e0,0 0,1 0, 2i ,0m,0m ,1 m,2Source node’s Markov model.s0, W0 2e0, W 2s0s0, W01e0, W 1mW , m 2 mW , 1smrate λ s packets/sec (The super(sub)script s or r are used todifferentiate between source node **and** relay parameters), **and**fixed packet size L. The queu**in**g model used will be discussed**in** details **in** section V.A. Source NodesFig. 2 represents the discrete-time Markov cha**in** used tomodel the operation of source nodes. Each node is modeledbyapairof**in**tegers(i, k). The backoff stage i, starts at 0 at thefirst attempt to transmit a packet **and** is **in**creased by 1 everytime a transmission attempt fails, up to a maximum value m.It is reset after a successful transmission. At any backoff stagei ∈ [0,m], the backoff counter, k, is **in**itially chosen uniformlybetween [0,Wiss− 1], whereWi =2 i W0 s , 0 ≤ i ≤ m, isthe range of the counter, **and** W0s is the parameter CW m**in**specified **in** the IEEE 802.11 st**and**ard. The backoff counter isdecremented by 1 **in** each idle time slot of duration σ, **and**thenode transmits when the backoff counter k =0.States (0,k) e , k ∈ [0,W0 s − 1] are **in**troduced to representthe state of the node when it has an empty queue after asuccessful transmission. Note that i =0**in** these states becauseif i>0 then a failed transmission should have occurred, so apacket must be await**in**g.The fundamental assumption **in** our model is that, at eachtransmission attempt, **and** regardless of the number of retransmissionssuffered, each packet fails with a constant **and****in**dependent probability, Pfs or P f r , for the source nodes orrelay node, respectively [11], [14].Let τ s **and** τ r be the probability that a source node or therelay transmit **in** a given slot, respectively. Now we are readyto write the Markov cha**in**’s transition probabilities, for 0 ≤i ≤ mP {(i, k)|(i, k +1)} = P i ,0 ≤ k ≤ Wi s − 2P {(i, k)|(i, k)} =(1− P i ),0 ≤ k ≤ Wi s P {(0,k)|(i, 0)} = (1 − q s)(1 − Pf s)W0s , 0 ≤ k ≤ W0 s − 1P {(0,k) e |(i, 0)} = q s(1 − Pf s)W0s , 0 ≤ k ≤ W0 s − 1(3)s0

EL-SHERIF **and** LIU: COOPERATION IN RANDOM ACCESS NETWORKS: PROTOCOL DESIGN AND PERFORMANCE ANALYSIS 1697where q s is the probability that the node’s queue is emptyupon a departure (see section V). P i is the probability that thechannel is sensed idle by the source node (i.e., all the rema**in****in**gN − 1 source nodes **and** the relay node are not attempt**in**gto transmit), **and** is given by P i =(1− τ s ) N−1 (1 − τ r ).Asource node’s transmission attempt is considered successfulif the channel is idle (i.e., no collision) **and** either the APor the relay correctly receive the transmitted packet, **in** otherwords if either the source-AP or the source-relay channel is not**in** outage. Let Pfs be the probability of a failed transmissionattempt, s**in**ce a failed transmission is the complement event ofa successful transmission (a transmission is successful if thechannel is idle **and** either the source-AP l**in**k or the sourcerelayl**in**k is not **in** outage), then Pf s =1−P i (1 − PsA outPsR out),where PsAout out**and** PsRare the outage probabilities of thesource-AP **and** source-relay l**in**ks, respectively.The first **and** second equations **in** (3) accounts for the factthat at the beg**in**n**in**g of each idle slot time the backoff counteris decremented by one, **and** that the counter rema**in**s at itscurrent state if the channel is not idle. The third **and** forthequations account for the fact that follow**in**g a successfulpacket transmission, backoff stage i is reset to 0, **and** thus thebackoff is **in**itially uniformly chosen **in** the range [0,W0 s − 1].In case of an unsuccessful transmission at backoff stagei−1, the backoff stage is **in**creased, **and** the new **in**itial backoffcounter is **in**itially chosen **in** the range [0,Wis − 1]. Oncethe backoff stage reaches the value m s , it is not **in**creased**in** subsequent packet transmissions, then we haveP {(i, k)|(i − 1, 0)} = P s f /W si ,P {(m, k)|(m, 0)} = P s f /W s m. (4)Given that the node’s queue is empty **and** the cha**in** is **in**state (0,k) e , **in** case of a packet arrival, the backoff counter isdecremented **and** the cha**in** makes a transition **in**to the (0,k−1)state if the channel is idle, **and** to state (0,k) if the channel isnot idle. In the case of an idle channel but no packets arrivesto the queue the cha**in** transits **in**to (0, (k − 1) e ). When thebackoff timer reaches zero, the node rema**in**s **in** state (0, 0 e )as long as the queue is empty. If a packet arrives, then thenode moves **in**to state (0,k), wherek is uniformly chosen **in**the range [0,W s 0 − 1]. Therefore we haveP {(0,k) e |0, (k +1) e } = P i (1 − a i ), 0 ≤ k ≤ W0 s − 2P {(0,k)|(0, (k +1) e )} = P i a i , 0 ≤ k ≤ W0 s − 2P {(0,k e )|(0,k e ))} =(1− P i )(1 − a b ), 0 ≤ k ≤ W0 s − 1P {(0,k)|(0,k e )} =(1− P i )a b , 0 ≤ k ≤ W0 s − 1P {(0, 0 e )|(0, 0 e )} =1− (P i a i +(1− P i )a b ) ,0 ≤ k ≤ W0 s − 1P {(0,k)|(0, 0 e )} = P ia i +(1− P i )a bW0s , 0 ≤ k ≤ W0 s − 1(5)where a i **and** a b are the probabilities of at least one packetarrival dur**in**g an idle or a busy slot, respectively. From thePoisson arrival assumption, these probabilities are given bya i =1− e −λsσ **and** a b =1− e −λsT b,whereσ is the idleslot duration, **and** T b the busy slot duration (for simplicitywe neglect the difference **in** durations between successful **and**Fig. 3.e0Relay node’s Markov model.12unsuccessful transmission attempts). Typically, σ =20μs, **and**T b = 2160.4μs, based on 11 Mbps channel rate **and** packetsize L = 2312 octets [8].Let π s (i, k) denote the stationary probability of be**in**g**in** state (i, k). To solve for the stationary distribution ofthis Markov cha**in** we used balance equations [15] tof**in**d expressions for all the stationary probabilities as afunction of π s (0, 0). Impos**in**g the normalization condition∑ m ∑ Wsi −1i=0 k=0π s (i, k) + ∑ W s 0 −1k=0π s (0,k) e =1, we can calculateπ s (0, 0), hence, all the steady state probabilities. Fullderivation of the closed form expressions is omitted because ofthe limited space, however a similar procedure to our analysiscan be found **in** [11].F**in**ally, s**in**ce a node will make a transmission attempt **in**a given slot time if the Markov cha**in** is **in** state π s (i, 0) fori ∈ [0,m], then, τ s , the probability that a source node makesa transmission attempt **in** a given slot time can be expressedas τ s = ∑ mi=0 π s(i, 0).B. Relay NodeA relay node operat**in**g as described **in** section III will bemodeled us**in**g the Markov cha**in** model of Fig. 3. The modelhas a s**in**gle backoff stage represented by states k ∈ [0,W r −1]. The backoff counter is uniformly chosen **in** that range, **and**the relay makes a transmission attempt when **in** state 0. Therelay node makes a transition to state e if its queue becomesempty after a successful transmission. F**in**ally, the cha**in** is **in**state t when the relay is attempt**in**g to transmit follow**in**g abusy channel.Aga**in** we have the assumption that, at each transmissionattempt, **and** regardless of the number of re-transmissionssuffered, each packet fails with a constant **and** **in**dependentprobability Pfs or P f r , for the source nodes or relay node,respectively [14], [11]. Now we are ready to write the Markovcha**in**’s transition probabilities. At the beg**in**n**in**g of each idleslot time, the backoff counter is decremented, thenWr 2Wtr1P {k|k +1} = P i , 0 ≤ k ≤ W r − 1, (6)where P i is the probability that the channel is sensed idle bythe relay node (i.e., all N source nodes are not attempt**in**g totransmit), **and** is given by P i =(1− τ s ) N .S**in**ce the relay Markov cha**in** has a s**in**gle backoff stage,follow**in**g an unsuccessful transmission attempt or a successfulattempt that leaves the relay queue non-empty, the backoffcounter is **in**itially uniformly chosen **in** the range [0,W r − 1].

1698 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 9, OCTOBER 2012ThereforeP {k|0} = (1 − q r)(1 − Pf r)W r + P frW r , 0 ≤ k ≤ W r − 1P {k|t} = (1 − q r)(1 − Pf ′r)W r + P f′rW r , 0 ≤ k ≤ W r − 1(7)where q r is the probability that a depart**in**g packet will leavethe relay queue empty, Pfr is the probability of a failed relaytransmission attempt out of state 0 (failure due to collisionor channel error), **and** Pf′r is the probability of a failed transmissionattempt out of state t (failure can be caused only bychannel errors), **and** are given by Pf r =1−(1−τ s) N (1−PRA out)**and** Pf′r = P RA outout,wherePRA is the outage probability of therelay-AP l**in**k.A successful transmission that leaves the relay queue emptyleads to a transition to state e, thenwehaveP {e|0} = q r (1 − Pf r )P {e|t} = q r (1 − P f ′r ). (8)Transitions **in**to state t occur when the relay attempts totransmit a packet immediately after any transmission attempton the channel, thusP {t|e} = Nτ s (1 − τ s ) N−1 PsA out out(1 − PsR )=aP {t|k} =1− P i , 0

EL-SHERIF **and** LIU: COOPERATION IN RANDOM ACCESS NETWORKS: PROTOCOL DESIGN AND PERFORMANCE ANALYSIS 1699The next component is the time spent **in** a backoff stage ibefore mak**in**g a transmission attempt (i.e., before the backoffcounter reaches zero). At stage i the counter is **in**itializeduniformly **in** the range k ∈ [0,Wis − 1], therefore thedistribution of the time spent **in** stage i is characterized bythe PGF, F i (z) = ∑ Wi s −1 F k (z)k=0 W.isF**in**ally, the PGF for the service time S s can be written as⎡m−1∑i∏G s (z) =(1− Pf s )z T b ⎣ (Pf s z T b) i F j (z)+(P s f z T b) mm ∏j=0i=0F j (z)j=0⎤∞∑(Pf s z T b) i Fm(z)i ⎦i=0⎡m−1∑i∏=(1− Pf s )zT b ⎣ (Pf s zT b) i F j (z)i=0j=0+ (P f szT b) m ∏ mj=0 F ]j(z)1 − Pf s , (11)zT b Fi m (z)where the term outside the brackets accounts for the busyslot **in** which the packet is successfully delivered, the firstterm **in**side the brackets accounts for the possible number offailures a packet encounters (hence, the number of backoffstages it goes through), its composed of the time spent **in** thebackoff counter decrements **and** the time spent transmitt**in**gthe packet. F**in**ally, the second term accounts for the amountof time spent at the maximum backoff stage m, which isdecomposed **in**to the time spent to reach this state, the time forcounter decrements, **and** the time for packet transmission. Theservice rate can then be calculated by differentiat**in**g G s (z)**and** sett**in**g z =1, μ −1s = E[S s ]= dGs(z)dz∣ .z=1B. Relay Node Arrival RateThe time, A r , between packet arrivals to the relay queueis composed of the follow**in**g components: (i) Idle periods **in**which no node (source or relay) is transmitt**in**g. This periodshave a length σ **and** probability P i =(1− τ s ) N (1 − τ r ). (ii)Busy periods of duration T b , which occur if the relay queueis empty **and** the transmission attempt does not result **in** anarrival at the relay. This occurs with probabilityP b1 = π r (e)[1 − (1 − τs ) N−1 − (N − 1)τ s (1 − τ s ) N−2 PsA out (1− PsR out ) ] .(iii) Busy periods of duration 2T b not result**in**g **in** a relayarrival, which occur if the relay queue is not empty whena source node makes a transmission attempt. Thus has aprobabilityP b2 =[1− (1− τs ) N−1 − (N − 1)τ s (1 − τ s ) N−2 PsA out out(1−PW∑r −1π r (k).k=1sR )](iv) F**in**ally, a busy period dur**in**g which a packet enters therelay queue. This will always have a duration T b , **and** has[a probability P a = π r (e)+ ∑ ]W r −1k=1π r (k) (N − 1)τ s (1 −τ s ) N−2 PsA out out(1 − PsR ).Given the above mentioned probabilities, we can write thePGF of A r as follows,∞∑ i∑ ∑i−j[G a (z) =P a z T i!bj!k!(i − j − k)!i=1 j=1 k=0· (P i z σ ) j (P b1 z T b) k (P b2 z 2T b) i−j−k] . (12)The arrival rate can then be calculated by differentiat**in**gG a (z) **and** sett**in**g z =1, λ −1r = E[A r ]= dGa(z)dz∣ .z=1C. Relay Node Service RateSimilar to the way the source nodes service rate was calculated,we will start the calculation of the relay node service rateby def**in****in**g the different components that constitute a packet’sservice time S r . We note that, as opposed to source nodes,the relay can leave the backoff stage after any source node’stransmission attempt on the channel (Fig. 3). Therefore, thetime the packet at the head of the queue spends **in** the backoffstage can be split **in**to two components: (i) The time before thebackoff counter (**in**itialized uniformly between 0 **and** W r − 1)reaches 0, which **in** the relay case is composed only of idleslots. The PGF characteriz**in**g the distribution of that time isthen given byF 0 =W∑r −1k=0P ki zkσW r . (13)(ii) The time spent **in** the backoff stage before the Markovcha**in** reaches state t, which is composed of a s**in**gle busyperiod **and** a maximum of W r − 1 idle slots. The PGFcharacteriz**in**g the distribution of that time is then given byF t =(1− P i )z T bW∑r −2k=0P ki zkσW r . (14)F**in**ally, let the probability that a packet enters relay queuebe a = Nτ n (1 − τ n ) N−1 PsA out out(1 − PsR ), the PGF for theservice time S r can be written asG r (z) =π r (e)a(1 − P ′rf )zT b+·∞∑i=0 j=0(aP ′rf zT b+W∑r −1k=0π r (k)[(F0· (z)(1 − Pf r )z T b+ F t (z)(1 − P f ′r )z T )b⎤i∑( ) i (F0(z)Pf r )jzT b j (Ft (z)P f ′r ) zT b i−j⎦ ,(15)which accounts for the case when a packet is immediatelyserved by the relay after it enters the queue (if queue wasempty at packet arrival), the possible number of failuresa packet encounters gett**in**g transmitted from either state 0or state t, **and** f**in**ally, the periods at which the packet is)

1700 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 9, OCTOBER 2012delivered successfully. The service rate can then be calculatedby differentiat**in**g G r (z) **and** sett**in**g z =1, μ −1r = E[S r ]=∣ .z=1dG r(z)dzVI. PERFORMANCE MEASURESA. Network ThroughputLet S be the normalized network throughput, def**in**ed as thefraction of time the channel is used to successfully transmitpayload bits to the AP, which can be expressed as S = Ps·TpT s,where P s is the probability of a successful transmission to theAP (by source or relay nodes), T p is the time to transmit thepayload part of a packet, of course this is less than T b ,thetotal transmission time of a packet **in**clud**in**g the headers **and**the AP ACK packet. And T s is the expected slot duration.To calculate the probability P s , we identify the events thatresult **in** a successful packet delivery to the AP, which are:(i) If the relay queue is empty, a source node successfullytransmits a packet to the AP, or that packet fails to reachthe AP but was successfully received **and** forwarded by therelay. This event has a probability Ps1 = π r (e) [ Nτ s (1 −τ s ) N−1 ((1 − PsA out out out out)+PsA (1 − PsR )(1 − PRA )) ] . (ii) Ifthe relay queue is not empty, a source node transmissionfails to reach the AP (due to fad**in**g or collision), **and**the relay successfully transmits the packet at the head ofits queue to the AP. This occurs with probability Ps 2 =[1 − (1 − τs ) N − Nτ s (1 − τ s ) N−1 (1 − PsA out)]∑ W rk=0 π r(k).(iii) If the relay queue is not empty **and** both source nodetransmission **and** the immediately follow**in**g relay nodetransmission were successful. This occurs with probabilityPs3 = Nτ s (1 − τ s ) N−1 (1 − PsA outout)(1 − PRA ) ∑ W rk=0 π r(k).(iv) The relay succeeds **in** transmitt**in**g a packet whenits backoff counter reaches 0, which has a probabilityPs 4 = τ r (1 − τ s ) N (1 − PRA out ). F**in**ally, the probabilityP s = Ps 1 + P s 2 +2P s 3 + P s 4. The factor of 2 before P s3accounts for the fact that the associated event results **in** thesuccessful delivery of two packets to the AP.The average length of a r**and**omly chosen[slottime is given by T s = (1− τ s ) N (1 − τ r ) σ + τ r +(π r (e) 1−(1−τ s ) N −Nτ s (1 − τ s ) N−1 PsAout out(1 − PsR )]T ) b +2π r (t)T b , which accounts for the three possible slot durations.1) Idle slots of duration σ, **in** which neither the relay norany other node attempts to transmit a packet, thus hav**in**g aprobability (1 − τ s ) N (1 − τ r ). 2) Busy slots of duration T b **in**which either the relay transmits or a source node transmissionis not followed by a relay transmission. The relay transmitsif its backoff counter reaches zero, which occurs withprobability τ r . A source node transmission is not followed bya relay transmission when the relay queue is empty (whichoccurs with probability π r (e) ) **and** no arrivals to the relayoccur dur**in**g source transmission. An arrival to the relayoccurs when a source node transmission fails to reach thedest**in**ation (due to channel outage) but reaches the relay, thisevent has a probability Nτ s (1 − τ s ) N−1 PsAout out(1 − PsR ).The event of no relay arrival is then the complement of thatevent, **and** we must take care to exclude the event of nosource transmissions from that complement event. 3) Busyslots of duration 2T b , **in** which a relay transmission followsa source node transmission, hence the factor of 2, such anoccurs with probability π r (t).Based on an 11 Mbps transmission rate, **and** payload oflength L = 2312 octets, typical slot duration are σ =20μs,T p = 1681.5μs, **and**T b = 2160.4μs.B. DelayIn the proposed cooperation protocol, a packet can encountertwo queu**in**g delays; the first **in** the source node’squeue **and** the second **in** the relay’s queue. If a packetsuccessfully transmitted by a source node arrives to the AP,then this packet is not stored on the relay’s queue. Let P adenote the probability of this event. Then the total delayencountered by a packet can be modeled as{Ds , w.p. PD =a(16)D s + D r , w.p. 1 − P awhere D s **and** D r are the queu**in**g delays **in** the source **and**relay queues, respectively. We can elaborate more on (16) asfollows. For a given packet **in** the source node’s queue, if thepacket is delivered from the source to the AP directly (withoutrelay help), then the delay encountered by this packet is onlythe queu**in**g delay **in** the source nodes queue. On the otherh**and**, if the packet is delivered to the AP through the relay,then the packet will encounter the follow**in**g delays: queu**in**gdelay **in** the source nodes queue **in** addition to the queu**in**gdelay **in** the relays queue.First, we f**in**d the queu**in**g delay **in** either the source node orthe relay queue, as both are modeled as M/G/1 queues, withthe difference be**in**g **in** the average arrival **and** departure rates.For an M/G/1 queue, the mean wait**in**g time **in** queue is givenby the Pollaczek-K**in**ch**in** formula [16], E[W i ]= λiE[S2 i ]2(1−λ , i/μ i)where i ∈ (s, r), λ i is the average arrival rate, μ i the averageservice rate, **and** S i the service time. From the mean wait**in**gtime, one immediately gets the mean queu**in**g delay as D i =E[W i ]+E[S i ].The probability P a , that, for any packet, the first successfultransmission from the source node’s queue is to the AP is1−Pgiven by P a =outsA(1−PsA out )+(1−P outsR )−(1−P outsA )(1−P out).AndthesRaverage delay is thus given by D = D s +(1− P a )D r .VII. RESULTS AND DISCUSSIONSWe compare the performance of the cooperative protocol**and** the CSMA/CA protocol without cooperation. We setthe SNR threshold β =15dB **and** the path loss exponentγ = 3.7. The distance between any node **and** AP is 120m, **and** between any node **and** the relay 70 m, **and** betweenrelay **and** AP 50 m. Transmission power is 100mW , **and**noise variance N 0 =10 −11 . Source node’s **in**itial contentionw**in**dow W0s = 32 with m = 5 backoff stages, **and** relaynode’s contention w**in**dow size W0r = 32. To validate themodel, we have built a custom packet-based simulator, thatclosely follows all the IEEE 802.11 protocol details for eachsource node, **and** follows the details of our proposed protocolat the relay node. Simulation results are based on an 11 Mbpstransmission rate, **and** payload of length L = 2312 octets, slotduration σ =20μs, DIFS=128μs, **and**ACK Timeout=300μs.

EL-SHERIF **and** LIU: COOPERATION IN RANDOM ACCESS NETWORKS: PROTOCOL DESIGN AND PERFORMANCE ANALYSIS 1701Aggregate arrival rate350340330320310300290CSMA/CACoop.1−λ r/μ r10.99950.9990.99850.9982800 10 20 30 40 50Number of nodes "N"0.99750 5 10 15 20 25Number of nodes "N"Fig. 4. Maximum achievable aggregate arrival rate vs number network nodes.Queu**in**g delay (Sec.)1.81.61.41.210.80.60.40.2CSMA/CACSMA/CA Sim.Coop.Coop. Sim.00 5 10 15 20 25Number of nodes "N"Fig. 5. Queu**in**g delay vs. number of nodes for λ s =15.Fig. 6. Probability that relay queue is empty vs. number of nodes for λ s =15.Collision Probability0.060.050.040.030.020.01CSMA/CACSMA/CA Sim.Coop.Coop. Sim.00 5 10 15 20 25Number of nodes "N"Fig. 7. Collision probability vs. number of nodes for λ s =15.Fig. 4 depicts the maximum aggregate arrival rate (sumof the arrival rates of all network nodes) supported by thenetwork while ma**in**ta**in****in**g queues stability versus the numberof network nodes. We can observe that, for a given numberof nodes, the proposed cooperative protocols resulted **in** a7% average **in**crease **in** the maximum supported aggregatearrival rate. This **in**crease is due to the fact that the relaynode provides a more reliable path to the AP lead**in**g to ahigher packet delivery rate. Therefore, source nodes are able toempty their queues at a faster rate, thus, free**in**g the channel forrelay access, **and** for additional nodes that the network mightaccommodate. As the number of nodes **in**crease the supportedarrival rates start to decrease s**in**ce the network starts to getcongested **and** the queues’ stability can no longer be supportedwithout a decrease **in** arrival rates.Fig. 5 shows the delay performance of our cooperativeprotocol compared to the non-cooperative CSMA/CA protocol.It is clear that our protocol outperforms CSMA/CA **in**terms of queu**in**g delay. This is ma**in**ly because most of therelay’s transmission attempts are made just after source nodes’transmissions, **and** not by wait**in**g for the backoff counter toreach 0. Therefore, the relay is guaranteed a high degree ofuncontested channel access. Moreover, as the network load**in**creases, the average number of source nodes’ transmissionattempts **in**crease, which offers the relay more channel accessopportunities to service its queue that now has a higher arrivalrate. To prove this, the quantity (1 − λ r /μ r ), which fromqueu**in**g theory is the probability that the relay queue is empty,is plotted **in** Fig. 6. It can be seen that there is less than 1%variation **in** the probability over the range of supported numberof nodes.Fig. 7 compares between the collision probability ofCSMA/CA **and** our cooperative protocol. Another merit ofour cooperation protocol **and** its channel access mechanism isthat, the **in**troduction of the relay node **in** the network does notresult **in** an **in**creased collision probability as it is the case withany r**and**om access protocol. We further notice a decrease **in**the collision probability, which is because of the second pathto the AP the relay offers to the network nodes. This secondpath helps the different nodes empty their queues at a fasterrate, hence, nodes do not have to access the channel as oftenas **in** the case without cooperation, which reduces the collisionprobability. F**in**ally, Fig. 8 demonstrates the effect of cooper-

1702 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 30, NO. 9, OCTOBER 2012Service rate "μ s"350300250200150CSMA/CACoop.1000 5 10 15 20 25Arrival rate "λ " sFig. 8. Source node’s service rate vs. arrival rate for N =15.ation on how fast nodes’ queues get empty by compar**in**g thesource node’s service rates under both cooperative **and** noncooperativeprotocols. An average **in**crease of 28% is observed**in** the service rate, which **in**terprets the reduction achieved **in**the collision probability.VIII. CONCLUSIONSIn this paper, we have proposed a novel cooperative protocolfor IEEE 802.11 based wireless r**and**om access networks.Through cooperation, the proposed protocol mitigates thedetrimental effects of wireless channel errors on the performanceof CSMA/CA r**and**om access protocol. **Cooperation** isachieved by deploy**in**g a relay node that will help differentnetwork nodes to forward their packets to the AP. By virtue ofthe relay’s channel access mechanism, the **in**crease **in** collisionprobability associated with the addition of more nodes to thenetwork is mitigated.The protocol’s performance is thoroughly **in**vestigated **and**compared to the non-cooperative CSMA/CA protocol. Performancecharacterization is achieved through the developmentof a Markov model coupled with queu**in**g analysis of thenetwork operation. The developed Markov model accuratelydescribed the network dynamics **in** the presence of relay, **and**captured the **in**teractions between different network nodes.Results revealed a significant improvement **in** terms of themaximum achievable arrival nodes’s rates, delay, **and** thenumber of nodes supported by the network.REFERENCES[1] J. N. Laneman, D. N. C. Tse, **and** G. W. Wornell, “Cooperative diversity**in** wireless networks: efficient protocols **and** outage behavior,” IEEETrans. Inf. Theory, vol. 50, pp. 3062–3080, Dec. 2004.[2] W. Su, A. K. Sadek, **and** K.J.R. Liu, “Cooperative communications**in** wireless networks: Performance analysis **and** optimum power allocation,”Wireless Personal Communications, vol. 44, no. 2, pp. 181–217,Jan. 2008.[3] K.J.R.Liu,A.K.Sadek,W.Su,**and**A.Kwas**in**ski, CooperativeCommunications **and** Network**in**g, Cambridge University Press, 2008.[4] A. K. Sadek, K. J. R. Liu, **and** A. Epheremides, “Cognitive multipleaccess via cooperation: Protocol design **and** performance analysis,”IEEE Trans. Inf. Theory, vol. 53, no. 10, pp. 3677–3696, Oct. 2007.[5] A. A. El-Sherif, A. Kwas**in**ski, A. K. Sadek, **and** K. J. R. Liu,“Content-aware multiple access protocol for cooperative packet speechcommunications,” IEEE Trans. Wireless Commun., vol. 8, no. 2, pp.995–1005, Feb. 2009.[6] R. L**in** **and** A. P. Petropulu, “A new wireless medium access protocolbased on cooperation,” IEEE Trans. Signal Process., vol. 52, no. 12,pp. 4675–4684, Dec. 2005.[7] M. K. Tsatsanis, R. Zhang, , **and** S. Banerjee, “Network-assisteddiversity for r**and**om access wireless networks,” IEEE Trans. SignalProcess., vol. 48, pp. 702–711, March 2000.[8] IEEE Computer Society LAN MAN St**and**ards Committee, WirelessLAN medium access control (MAC) **and** physical layer (PHY) specifications,IEEE St**and**ard 802.11-1999, New York, NY: IEEE, 1999.[9] P. Chatzimisios, A.C. Boucouvalas, **and** V. Vitsas, “Performance analysisof ieee 802.11 dcf **in** presence of transmission errors,” **in** Proc. Intl.Conf. on Comm. (ICC), June 2004, pp. 3854–3858.[10] Y. Zheng, K. Lu, D. Wu, **and** Y. Fang, “Performance analysis of ieee802.11 dcf **in** imperfect channels,” IEEE Trans. Veh. Technol., vol. 55,no. 5, pp. 1648–1656, Sep. 2006.[11] G. Bianchi, “Performance analysis of the ieee 802.11 distributedcoord**in**ation function,” IEEE J. Sel. Areas Comm., vol. 18, no. 3, pp.535–547, Mar. 2000.[12] Y. Xiao, “Saturation performance metrics of the 802.11 mac,” **in** Proc.IEEE Veh. Technol. Conf., Oct. 2003, vol. 3, pp. 1453–1457.[13] K. Duffy, D. Malone, **and** D. J. Leith, “Modell**in**g of 802.11 distributedcoord**in**ation function **in** non-saturated condition,” IEEE Commun. Lett.,vol. 9, no. 8, pp. 715–718, Aug. 2005.[14] D. Malone, K. Duffy, **and** D. Leith, “Modell**in**g the 802.11 distributedcoord**in**ation function **in** nonsaturated heterogeneous conditions,”IEEE/ACM Trans. Netw., vol. 15, no. 1, pp. 159–172, Feb. 2007.[15] G. R. Grimmett **and** D. R. Stirzaker, Probability **and** **R andom** Processes,Oxford University Press, 2001.[16] Ronald W. Wolff, Stochastic Model