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Full-Duplex WiFi Networks

Liwei Song, Yun Liao, and Lingyang Song

Abstract

The device in conventional half-duplex WiFi networks cannot perform carriersensing while in data transmission; thus it suffers from long collision duration. Tomitigate this problem, this chapter introduces full-duplex (FD) technology intoWiFi networks. A novel CSMA/CD protocol design is first presented for single-channel FD-WiFi, which facilitates continuous carrier sensing and transmissionsuspension. The network throughput performance is comprehensively analyzedby considering possible sensing errors (i.e., false alarm and miss detection) due toself-interference, and simulation results verify the performance analysis and theeffectiveness of CSMA/CD protocol. Then the protocol for multi-channel FD-WiFi is provided, where the CSMA/CD protocol for accessing a certain channelis modified by adopting a contention window adjustment rule, and a distributedchannel selection strategy is proposed based on the best-response algorithm.Simulation results indicate the performance improvement of multi-channel FD-WiFi protocol design.

Contents

WiFi Network Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Full-Duplex CSMA/CD Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5CSMA/CD Protocol Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Multi-channel Full-Duplex WiFi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Channel Access Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

L. Song • Y. Liao • L. SongSchool of Electrical Engineering and Computer Science, Peking University, Beijing, Chinae-mail: [email protected]; [email protected]; [email protected]

© Springer Nature Singapore Pte Ltd. 2017W. Zhang (ed.), Handbook of Cognitive Radio,DOI 10.1007/978-981-10-1389-8_17-1

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mailto:[email protected]



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Channel Selection Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Performance Analysis and Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

WiFi Network Basics

WiFi technologies have received a rapid proliferation over the past few decades [1].As a part of the 802 standard family, IEEE 802.11 provides an international standardfor the conventional WiFi networks. Detailed medium access control (MAC) andphysical layer (PHY) specifications for the 802.11 protocol are summarized in [2].

The fundamental access mechanism for 802.11 protocol is the distributedcoordination function (DCF), which is a random access scheme and based on carriersense multiple access with collision avoidance (CSMA/CA) [3, 4]. In DCF, usersare required to listen to the channel before access. If the channel is sensed busy,users need to wait until channel becomes idle; then they enter into a random backoffprocedure. This prevents multiple users from accessing the medium immediatelyafter completion of the preceding transmission and leading to collisions.

Specifically, in the CSMA/CA protocol, every active node which has a newpacket for transmission monitors the channel activity first. The node persists tocarrier sense until the channel is measured idle for a period of time equal to adistributed interframe space (DIFS). At this point, the node generates a randombackoff time by setting an internal timer to an integer number of slot times, whichcan be expressed as the following:

Backoff Time D Rand(CW) � Slot Time; (1)

where CW is called the contention window. The backoff time decreases in any slotas long as the channel is sensed to be idle, “freezes” when the channel is judgedbusy, and “reactivates” decrement when the channel is sensed idle again for a DIFS.The active node transmits the data packet when its backoff timer counts down tozero.

However, the collision is still possible due to concurrent transmission betweendifferent users. The exponential backoff scheme is thus adopted in the CSMA/CAprotocol to further reduce collision. At the first transmission attempt, the user’sbackoff stage is zero and CW is set equal to CWmin, called the minimum contentionwindow. After each successful transmission, the backoff stage increases and CW isdoubled, up to the maximum contention window CWmax D 2Wmax CWmin, in whichWmax is called the maximum backoff stage.

Upon packet reception, the acknowledgment (ACK) is required, i.e., the receivertransmits an ACK signal back after the interval of one short interframe space (SIFS)when transmission is finished. The SIFS is shorter than the DIFS so that the othercontending users cannot start to decrease their backoff time, which means that

Full-Duplex WiFi Networks 3

Fig. 1 Example of CSMA/CA protocol in conventional WiFi networks

the ACK has higher priority than other regular transmissions. The transmission isunsuccessful if the transmitter fails to receive the ACK signal.

Figure 1 illustrates an example of the CSMA/CA protocol. Two stations A andB share the same wireless channel for data transmission. At the end of previousdata transmission, they wait for a DIFS and randomly choose backoff time. StationA chooses 3 while station B chooses 8. Thus, after three slots, the backoff time ofstation A counts down to zero, and station A starts to transmit its data packet, duringwhich station B has its backoff time frozen. After station A finishes transmission andthe channel is sensed idle again for a DIFS, station B decrements its backoff time,and station A again chooses backoff time and contends the channel.

Although carrier sense is performed in the CSMA/CA protocol, the transmitter’ssensing result may wrongly indicate the channel condition at the receiver due todifferent network topology, which leads to two problems called hidden terminal andexposed terminal [5]. A hidden terminal lies in the transmission range of a receivingstation, but it is out of the range of the transmitting station. Therefore, the hiddenterminal is oblivious of the ongoing transmission and can initiate a new transmissionthat will cause a collision at the receiver. The occurrence of these collisions reducesthe overall performance of the network. On the other hand, an exposed terminallies in the transmission range of the transmitter but out of the transmission range ofthe receiver. Therefore, a transmission initiated by this terminal would not causea collision at the receiver. However, it remains silent due to the busy channeldetection. This effect reduces the overall throughput by stopping some stations fromtransmitting despite the fact that they would not cause a collision.

To resolve the two problems, the RTS/CTS (request to send/clear to send) schemeis adopted by IEEE 802.11 as an optional mechanism [6]. In this scheme, anactive node which wants to transmit a packet, waits until the channel is sensed idlefor a DIFS, follows the backoff procedure explained above, and then, instead ofthe packet, preliminarily transmits a special RTS frame. When the receiving nodedetects an RTS frame, it responds, after a SIFS, with a CTS frame. The transmittingnode is allowed to transmit data packet only if the CTS frame is correctly received.

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By listening to RTS/CTS frame, the neighboring nodes of transmitter and receivercan get the transmission range information; thus hidden terminal and exposedterminal problems can be resolved. The main drawback of RTS/CTS scheme is longoverhead caused by two frames.

Although the CSMA/CA protocol has been shown effective in the WiFi networks,it suffers from the problem of long collision duration. The main reason is thatconventional WiFi networks are based on the half-duplex (HD) technology, dueto the limitation of which, unlike the CSMA/CD (collision detection) protocol inEthernet, the WiFi users cannot perform carrier sense and collision detection oncetransmitting. Thus if collision happens between some transmitting users, they cannotdetect it and still transmit left collided data packets.

The full-duplex (FD) communication technology [7], by which the users cansimultaneously transmit and receive data on the same band, has the potential toresolve the problem in conventional HD-WiFi networks. Recent years witness therevival of FD research due to the development of self-interference suppression (SIS)techniques in propagation, analog circuit, and digital domains, which significantlyreduce the self-interference to a limited level [8, 9]. Apart from the developmentof the SIS techniques in PHY layer, some FD-MAC protocols have also beenproposed recently [10–13]. In [10], a centralized FD-MAC protocol is proposedwith shared random backoff, header snooping, and virtual backoffs. In [11], theauthors design a decentralized FD-MAC protocol by adding FD acknowledgmentbits. Both protocols in [10] and [11] discuss dual-link transmissions between twoand three nodes. While [12] and [13] enable simultaneous spectrum sensing anddata transmission for wireless users, the former is for cognitive radio networks andthe latter is for ad hoc networks.

To mitigate the long collision duration problem in conventional HD-WiFinetworks, similar to [12] and [13], this chapter introduces the FD technologyinto WiFi networks to realize simultaneous carrier sensing and data transmission.In the rest of this chapter, we first present the proposed CSMA/CD protocol forsingle-channel FD-WiFi networks [14]; then we extend this FD protocol to themulti-channel WiFi scenario [15].

Full-Duplex CSMA/CD Protocol

In this section, we elaborate the CSMA/CD protocol for single-channel FD-WiFinetworks to resolve the long collision duration problem in conventional HD-WiFinetworks. By taking advantage of FD techniques, each user can sense the spectrumand determine whether other users are occupying it while transmitting its own datasimultaneously. We start with the system model, followed by the FD-WiFi protocoldescription. Performance analysis and simulation results are provided to show theprotocol’s effectiveness.


Fig. 2 The CSMA/CD protocol for the uplink traffic of FD-WiFi and two types of sensing errors(false alarm and miss detection) due to self-interference

System Model

As shown in Fig. 2, we consider a FD-WiFi network consisting of one accesspoint (AP) and N users (U1; : : : ;UN ), where the users are independently andrandomly distributed in the coverage area of the AP. Each user is equipped with twoantennas to realize FD communications. We focus on the uplink traffic, in whichdata packets are transmitted from the users to the AP, and each user is assumed toalways have a packet to transmit with the same transmission power.

The channel can serve at most one user at a time; otherwise the collision happens.Therefore, as shown in the upper part of Fig. 2, each user performs carrier sensingto detect the channel state and contends for the idle channel against each other bythe proposed protocol. When a certain user, say Un .n 2 f1; 2; : : : ; N g/, accessesthe channel, it uses one antenna for carrier sensing and the other antenna for datatransmission simultaneously. However, the residual self-interference (RSI) betweenthose two antennas leads to imperfect sensing, as shown in the lower part of Fig. 2.False alarm happens when the user mistakenly judges the channel to be occupiedby other users when it is not, while miss detection means that the user fails todetect the channel occupation of other transmitting users. Both of the sensing errorsdegrade the network performance and, thus, should be taken into considerationfor performance analysis. We now further discuss the carrier sensing in FD-WiFinetworks as follows.

6 L. Song et al.

Full-Duplex Carrier SensingSince noise is negligible compared to collision signal and self-interference, it isomitted in this chapter. Thus, a silent user has a perfect sensing, and we only needto analyze the sensing errors for transmitting users. Furthermore, the probabilityfor the case with more than two collided users is negligible compared to theprobability that only two users collide, and even when the case happens, the sensingperformance is also better due to the accumulated collision signal. Thus perfectsensing is also assumed for the case that three or more users collide, and the sensingerrors only exist in the following two cases: (1) H0, the transmitting user singlyoccupies the channel and (2) H1, the transmitting user has a collision with anotheruser.

The received signal for sensing at the transmitting user can be given by

y D

(hrst ; H0;

hrst C hcsc; H1;(2)

where st denotes the transmitting user’s signal and sc is the collided user’s signal,hc represents the collision channel, and hr denotes the equivalent RSI channelindicating the SIS degree, which depends on the adopted SIS techniques andnetwork environment. We adopt a typical path loss Rayleigh fading channel; thus,hcsc is zero-mean complex Gaussian distributed with average power P r.

dd/˛ , where

˛ is the path loss exponent,P r is the reference received signal power at the referencedistance d , and d is the distance between two users. Moreover, according to [16],hrst is also a complex Gaussian variable with zero mean and average power ˇ2P r ,where ˇ2 denotes the SIS factor.

As for the sensing strategy, energy detection is adopted, and we assume theprocess is time slotted. Thus the sensing test statistics can be given by

M D

NsXmD1

jy .m/j2; (3)

where y.m/ denotes the mth sample of received sensing signal and Ns is thesampling number in one slot.

The transmitting user compares M with the sensing threshold to decide whethera collision happens or not. Two types of sensing errors exist, i.e., false alarm andmiss detection. As shown in the lower part of Fig. 2, false alarm wastes availablechannel slots, while miss detection causes collisions. We need to balance the twotypes of sensing errors to ensure network performance.


Channel Usage

User 1

User 2

User 3

User 4

Downcounter numberSuccessful transmission Finished packet with miss detection

Unfinished packet due to false alarm

Collision

Fig. 3 The proposed CSMA/CD protocol for FD-WiFi networks, in which .wi ; Wi / denotes theresidual backoff time and the backoff stage of Ui

CSMA/CD Protocol Design

Based on the FD technology and conventional CSMA/CA concepts, we now pro-pose the CSMA/CD protocol for FD-WiFi networks. Figure 3 shows the proposedprotocol, which consists of the following several parts.

Sensing: All users keep sensing the channel continuously regardless of its ownactivity and make decisions of the channel usage at the end of each slot with duration� , which is the required time to reliably detect the transmission of any other user.

Backoff mechanism: Once the channel is judged idle without interruption for acertain period of time as long as a distributed interframe space (DIFS) (shown asthe dotted area below each line), users check their own backoff timers and generatea random backoff time for additional deferral if their timers have counted down tozero. The additional backoff time after a DIFS is also slotted by � , i.e., the backofftime is expressed as

Backoff Time D w � � D Random .CW/ � �; (4)

where CWD 2W � CWmin is the contention window length and w D Random .CW/

is a random integer drawn from the uniform distribution over the interval Œ0;CW/,

8 L. Song et al.

where W 2 Œ0;Wmax� is the backoff stage depending on the number of unsuccessfultransmissions for a packet. The countdown starts right after the DIFS and suspendswhen the channel is detected occupied by others.

Channel access and transmission suspension: A user accesses the channel andbegins transmission when its timer reaches zero. During the transmission, if itdetects the signal from other users, it stops its transmission and switches to thebackoff procedure immediately. If the packet is finished, the user resets the backoffstage W D 0. Otherwise, it sets W D min fW C 1;Wmaxg.

Performance Analysis

In this part, we study the analytical performance of the proposed FD-WiFiCSMA/CD protocol and derive its saturation throughput. We first analyze thecarrier sensing performance and derive expressions for sensing error probabilities;then we derive the throughput performance of the CSMA/CD protocol by taking thesensing errors into consideration. Note that when only one user is transmitting, allother users can detect its transmission perfectly, which means that once a collision-free transmission begins, it either completes the packet or suspends it because offalse alarm. This process is independent with other users’ sensing and contending,and thus, contention and transmission can be considered separately.

Carrier Sensing PerformanceWe mainly derive the expressions of false alarm probability (pf ) and miss detectionprobability (pm). With Rayleigh fading channels, the sampling signal power(jy .m/j2) is Chi-square distributed. Furthermore, M is the sum of sampling signalpower in one slot; thus according to [17], M is gamma distributed, the probabilitydensity function of which can be expressed as

fM .x/ DxNs�1e

� x�

�Ns� .Ns/; (5)

where � D ˇ2P r and � D�ˇ2 C

�dd

�˛�P r for H0 and H1, respectively.

With a certain sensing threshold �, we can obtain the expressions of pf and pm

pf D Pr .M > � jH0/ D 1 � �

�Ns;

�

ˇ2P r

�; (6)

pm.d/ D Pr .M < � jH1/ D �

0B@Ns; ��

ˇ2 C�dd

�˛�P r

1CA ; (7)


where � .m; x/ D 1� .m/

R x0tm�1e�t dt is the incomplete gamma function. By

deriving the expression of � in terms of pf from (6) and substituting that into (7),the following equations are presented:

�.pf / D aˇ2P r ; (8)

pm.d/ D �

�Ns; a �

b

d˛ C c

�; (9)

where a D � �1�Ns; 1 � pf

�, b D a d

˛

ˇ2, and c D d

˛

ˇ2, in which � �1.m; x/ is the

inverse incomplete gamma function.Furthermore, users are independently and randomly distributed in AP’s coverage

area, the radius of which is denoted by R. Then we can derive the average missdetection probability:

pm D2

�R4

Z R

0

Z R

0

Z 2�

0

�

�Ns; a �

b

d˛ C c

�r0r1d�dr0dr1; (10)

where r0, r1 are the distances of transmitting user and collided user away from

the AP, � is their included angle, and d Dqr20 C r

21 � 2r0r1 cos � is the distance

between them. We can find that the expression of pm is related to the path lossexponent. Particularly, when free-space channel is considered, i.e., ˛ D 2, we canderive an approximation of pm:

pm D2

�R4

Z R

0

Z R

0

Z 2�

0

�

�Ns; a �

b

d2 C c

�r0r1d�dr0dr1

�1

R4

Z R2

0

x�

�Ns; a�

b

x C c

�dxC

Z 2R2

R2

�2R2 � x

��

�Ns; a�

b

x C c

�dx

!

�2

3�

�Ns; a �

b

R2 C c

�C1

6�

�Ns; a �

b

2R2 C c

�:

(11)According to (6), (7), (8), (9), (10), and (11), pf is negatively related to �, while

pm is positively related. Therefore, the sensing threshold should be well designed tobalance false alarm probability and miss detection probability.

Transmission ProbabilityTo obtain the network throughput, we need to calculate users’ transmission prob-ability first. We follow the assumption in [4] that each packet gets collided withthe same probability independent of the value of CWi . Let fwn;Wng denote thestate of the nth contending user. For each user, the state change can be modeled as a

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ps ps /CW0

(1– ps) /CWi

(1– ps) /CWmax

(1– ps) /CWmax1– ps

Fig. 4 Discrete-time Markov chain of the backoff window size

discrete-time Markov chain illustrated in Fig. 4. The nonzero transition probabilitiesare given as

8ˆˆ<ˆˆ:

P .wn � 1;Wnjwn;Wn/ D 1; wn 2 .0;CWi /;Wn 2 Œ0;Wmax�;

P .wn; 0j0;Wn/ Dps

CWmin; wn 2 Œ0;CWmin/ ;Wn 2 Œ0;Wmax�;

P .wn;Wn C 1j0;Wn/ D1 � ps

CWiC1

; wn 2 Œ0;CWiC1/ ;Wn 2 Œ0;Wmax/ ;

P .wn;Wmaxj0;Wmax/ D1 � ps

CWmax; wn 2 Œ0;CWmax/ ;

(12)where ps denotes the probability that the considered user successfully finishes itstransmission without awareness of collision. Note that ps does not equal to the non-collision probability due to imperfect sensing. Specifically, if two users collide, itis possible that only one user stops and the other user still transmits due to missdetection, and even when one single user is transmitting without collision, it maycease the transmission due to false alarm.

Considering the steady-state distribution of the discrete-time Markov chain, theprobability that one user stays in each state can be calculated. Let pw;W denote the


probability that one user is in the state of fw;Wg, and the probability that a certainuser begins transmission in the next slot is

p D

WmaxXWD0

p0;W D2 .2ps � 1/

.2ps � 1/ .CWmin C 1/C .1 � ps/CWmin

�1 � .2 � 2ps/

Wmax� :

(13)Then, we consider the relation between ps and p. For simplicity, we assume the

packet length L is fixed. The calculation of ps has two prerequisites:

1. The probability that the transmitting user begins collision-free transmission aftercolliding for l slots, which can be expressed as

pa .l/ D

8<ˆ:.1 � p/N�1 ; l D 0;

.N � 1/ p .1 � p/N�2 p2l�1m .1 � pm/ ; 1 � l � L � 1;

.N � 1/ p .1 � p/N�2 p2L�1m ; l D L:

(14)

2. The probability that the transmitting user successfully transmits l collision-freeslots, which can be denoted as

pb .l/ D .1 � pf /l ; 0 � l � L: (15)

Successful transmission requires at least one user transmits the entire packetwithout the awareness of collision. Thus, ps can be calculated as

ps D

LXlD0

pa.l/pb.L � l/;

D.1 � p/N�1.1 � pf /L C .N � 1/p.1 � p/N�2pm

.1 � pf /L � p2Lm

1 � pf � p2m:

(16)Combining (13) and (16), the values of p and ps can be solved numerically.

Throughput PerformanceWe use the time fraction that the channel is occupied for successful transmission asthe normalized throughput, i.e., the throughput is defined as

C DE ŒSuccessful transmission length�

E ŒConsumed time for a successful transmission�

DPsLs

Pe C Ps .Ls C DIFS/C Pc .Lc C DIFS/;

(17)

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where Ps D Np .1 � p/N�1 denotes the probability that a successful transmissionoccurs,Pe D .1 � p/

N is the probability that the channel is empty,Pc D 1�Pe�Psrepresents the collision probability, andLs; Le , andLc denote the average length ofsuccessful transmission, empty state, and collision, respectively. The average lengthof successful transmission and collision can be calculated as, respectively,

Ls D

L�1XlD1

l�1 � pf

�l�1pf C L

�1 � pf

�L�1

D1 � .1 � pf /

L�1

pfC .1 � pf /

L�1;

(18)

Lc DPc C

�N2

�p2 .1 � p/N�2

PL�1lD1 p

2lm

�1 � p2m

�l

Pc

D 1C

N

2

!p2 .1 � p/N�2

p2m�1 � p2L�2m

�Pc�1 � p2m

� :

(19)

The throughput is readily obtained by substituting (18) and (19) into (17). Wecan find that Ls is negatively related to pf , while Lc is positively proportionalto pm. Thus, the network with a larger sensing threshold can obtain a longeraverage successful transmission length; however, it also suffers from a longeraverage collision length. Therefore, the sensing threshold should be properlydesigned to achieve the maximum throughput, which can be obtained throughnumerical.

Comparison with the Basic CSMA/CA MechanismWe make a comparison between the proposed protocol for FD-WiFi with theconventional CSMA/CA for HD-WiFi in this part. For fairness, we consider thesame system with N users and omit the noise term. The analytical performanceof the CSMA/CA protocol is elaborated in [4], which are omitted here due to thespace limitation. Some main differences between the two protocols are listed asfollows.

• Collision length. In conventional CSMA/CA, the “blindness” in transmissionresults in long collision, which is typically a packet length. FD allows users todetect collision while transmitting. Thus, the average collision length Lc , as isderived in (19), is slightly more than one slot, which is sharply reduced comparedwith CSMA/CA.

• Successful transmission length. In CSMA/CA, once a collision-free transmis-sion begins, it can always be finished successfully without interruption. However,in the FD-WiFi network, the transmission may get ceased due to false alarm,especially for long packets. According to (18), if L is sufficiently large, Ls goesto 1

pf. Also, false alarm leads to unnecessary backoff and increase of contention


window, which may further degrade the performance of FD-WiFi. Thus, in FD-WiFi networks, the sensing threshold should be well designed to balance theprobabilities of two sensing errors.

Simulation Results

In this subsection, simulation results are presented to show the performance of theproposed FD-WiFi CSMA/CD protocol. We consider 20 users and AP’s radius Ris set as 10m. We set ˛ D 2 and P r D 10mW with d D 1 unit. The slotsampling number Ns is set as 100. Furthermore, the packet length is fixed to be100 slots and DIFS is 2 slots. We run for 103 transmission attempts to fully developthe WiFi network and proceed with another 106 packet transmissions to obtainthe simulated results by MATLAB. For comparison, we provide the throughputperformance of conventional HD-WiFi and bidirectional FD transmission, whichis similar to [10] and [11] and named by “dual-link FD-WiFi.” Specifically, for thedual-link simulation, once a certain user transmits data to the AP, AP also transmitsdata packets back to this user. Moreover, due to RSI, the rate of dual link at one endis less than that of single link. For simplicity, the single-link sum rate is normalizedas 1, and the dual-link sum rate is denoted as the relevant ratio.

In Fig. 5, we show the throughput of the proposed FD-WiFi protocol versus falsealarm probability, which consists of two cases with the SIS factor ˇ2 D 0:15 and

Fig. 5 Normalized throughput C versus false alarm probability pf , where the number of usersN D 20, the minimum contention window size CWmin D 23, and the maximum contentionwindow size CWmax D 28

14 L. Song et al.

ˇ2 D 0:3, respectively. Note that the normalized throughput is denoted as the timeratio that the channel is occupied for successful transmissions, as shown in (17);thus it has no dimension. Figure 5 shows that there exists an optimal value of pffor FD-WiFi to achieve the maximum throughput. Since pf is determined by �, asshown in (6), the sensing threshold should be well designed to achieve the maximumthroughput. We can also find that the optimal value of pf for the case with ˇ2 D 0:3is higher than that with ˇ2 D 0:15, which can be explained as follows. Higher SISfactor leads to worse sensing performance. Setting pf the optimal value for thecase with ˇ2 D 0:15, the collision is more frequent due to higher pm when ˇ2

increases to 0:3. Thus, to obtain the maximum throughput, pm should be decreasedby increasing pf .

In Fig. 6, by considering two cases with the packet length L D 50 and L D 200,we present the relationship between network throughput and the maximum backoffstage, with the throughput of convention HD-WiFi and dual-link FD-WiFi forcomparison. According to Fig. 6, we can find that with proper parameters, theproposed FD-WiFi protocol has a better throughput performance than HD-WiFiand dual-link FD-WiFi. For the HD-WiFi and dual-link FD-WiFi, with higherWmax, collision is less likely to happen, so the throughput increases monotonously.However, the throughput of proposed FD-WiFi protocol may drop with large Wmax,which can be found in the dashed line. The reason is that the asymptotic value of Lsis 100 with pf D 0:01, and for L > 100 slots, false alarm is quite likely to happenduring transmission, and the users are likely to enlarge their contention windows

Fig. 6 Normalized throughput C of different protocols versus the maximum backoff stage Wmax,where CWmin D 23, SIS factor ˇ2 D 0:15, and the false alarm probability in FD-WiFi CSMA/CDprotocol pf D 0:01


up to CWmax due to the unsuccessful transmissions. Thus, more time is spent in thebackoff procedure and the throughput gets smaller.

Multi-channel Full-Duplex WiFi

In this section, we extend the proposed single-channel CSMA/CD protocol to thescenario with multiple available wireless channels in the FD-WiFi networks. For themulti-channel scenario, the WiFi users need to resolve the following two problems:(1) channel selection, users choose certain channels for access according to theirchannel state information (CSI), and (2) channel access, the contending users, whichselect the same channel, need to perform a contention-based access mechanism toalleviate collisions (Fig. 7).

For the channel access problem, we propose a random access strategy basedon the CSMA/CD protocol described in section“Full-Duplex CSMA/CD Protocol.”With the existence of multiple channels, the number of contending users on a certainchannel change with time, and a fixed setting of contention parameters may lead tosevere collision or over much waiting time in some cases. Therefore, different fromthe single-channel scenario, an adjustment of contention window is added in thechannel access strategy.

As for the channel selection problem, some previous papers present their protocoldesigns for HD multi-channel systems. In [18], the authors propose a multiplespanning tree-based load-balancing routing algorithm for wireless mesh network.In [19], the authors design a multi-channel MAC protocol for ad hoc networks by

Fig. 7 Multi-channel full-duplex WiFi networks with one AP,N users andK orthogonal channels

16 L. Song et al.

channel preference negotiation between the transmitter and the receiver. In [20], theauthors derive game theoretic results for multi-channel cognitive radio networks. Inthis section, we take advantage of game theory to propose a distributed channelselection scheme for multi-channel FD-WiFi networks. Our goal is to improvenetwork performance, so user’s channel selection strategy is based on comparison ofexpected throughput on different channels, which can be evaluated from the channelaccess strategy.

The rest of this section is organized as follows. We first discuss the system modelfor multi-channel FD-WiFi networks; then the channel access strategy and channelselection strategy are presented, respectively. Comparison with CSMA/CA and HDprotocols and simulation results are provided finally.

System Model

We consider a network consisting of one AP and N FD users. There are Korthogonal channels, denoted by K D f1; 2; : : : ; Kg, each of which can serveat most one user at a time; otherwise the collision happens. The FD users, whoseset is denoted by N D f1; 2; : : : ; N g, have the same self-interference cancelationcapability and the same transmission power P . Each user n 2 N is assumed tohave the knowledge of perfect CSI of any channel k 2 K between the AP anditself, denoted by fhnkg

KkD1.

Similar to section “Full-Duplex CSMA/CD Protocol,” we mainly focus on theuplink transmissions, where data are sent by users to the AP. Moreover, the WiFinetwork is considered to be distributed, which means that the AP has no way toallocate the users or schedule their traffic. We also assume that each user is capableof detecting the occupancy of all channels and transmitting on at most one channel ata time. Let � be the minimum required time for each user to make a reliable channelsensing decision. We assume a time-slotted system in which users can transmit thedata during each slot. The users can change their channels and activity only at thebeginning of a slot.

By taking advantage of FD techniques, simultaneous carrier sensing and datatransmission become possible [21,22]. In particular, one antenna is for transmission,while the other can be used as a receiver to sense the channel information. However,when a user is transmitting, the RSI due to the imperfect self-interference cancela-tion degrades the reliability of sensing on its own current operating channel [23].Let Pf be the false alarm probability that one user falsely detects others’ presenceon the channel, and Pm denote the miss detection probability that one user fails todetect the collision while it is transmitting on the channel. Since the RSI exists onlywhen a user is transmitting, we can simply assume perfect sensing for silent users.

The transmission procedure contains the following two steps:

1. According to the expected utilities of different channels, each user n selects acertain channel cn to contend.


2. User n preforms a CSMA-/CD-based channel access strategy to avoid collision.After each successful or suspended transmission attempt, user n adjusts thecontention window and the expected utility of channel cn.

Since the expected channel utility is derived according to the specific channelaccess strategy, in the remaining section, we first present the CSMA-/CD-basedchannel access mechanism and then propose the channel selection algorithm bytaking advantage of game theory.

Channel Access Strategy

In this part, based on the CSMA/CD protocol in section “Full-Duplex CSMA/CDProtocol,” we present a random access strategy adopted by the FD users whenthey are contending for the same channel. Here, the number of contending usersis unknown to users, and it may change with time. By using FD technology, userscan sense the channel while transmitting and stop transmission immediately when acollision is detected. Thus, collided transmissions can be significantly shorter thansuccessful transmissions, which can be observed by all contending users, who canadjust the contention window size accordingly.

Protocol DescriptionAs shown in Fig. 8, the proposed random access protocol for FD users on a singlechannel includes the following four phases:

Sensing: All users keep sensing the channel continuously regardless of its ownactivity and make decisions of the channel usage at the end of each slot.

Backoff mechanism: Once the channel is sensed idle without interruption for acertain period of time equal to DIFS, users generate a random backoff time for anadditional deferral, which can be expressed as follows:

Backoff Time D v � � D Random .w/ � �; (20)

where w is the length of contention window and v D Random .w/ is a randominteger drawn from the uniform distribution over the interval Œ0;w/. The backofftimer starts countdown immediately after the DIFS and suspends when the channelis detected occupied by others.

Channel access and transmission suspension: A user accesses the channel andbegins transmission when its backoff timer reaches zero before other transmissionsare detected. During the first slot of the transmission, if it detects the signal fromother users, a user stops its transmission and switches to the backoff procedureimmediately. Otherwise, it keeps transmitting the packet until finished.

18 L. Song et al.

Channel Usage

User 1

User 2

User 3

User 4

Downcounter numberSuccessful transmission Finished packet with miss detection

Unfinished packet due to false alarm

Collision

Fig. 8 Channel access protocol in decentralized FD networks, in which .vn;wn/ denotes theresidual backoff time and the contention window of user n

Adjustment of the contention window: When a transmission on the channel isdetected finished, all users adjust the contention window size by the followingcontention window adjustment rule and begin the contention procedure for the nextround.

Adjustment Rule of the Contention Window SizeWhen there are m users contending for a single channel, the optimum contentionwindow size can be proved to be m. However, in a fully distributed system, thenumber of users, m, is unknown, and it may change dynamically. Thus, userscannot directly use m as the contention window. In this scenario, the conventionalCSMA/CA mechanism cannot perform well, when m is smaller than the minimumcontention window size or larger than the maximum size. Note that the lengthsof collisions and successful transmissions can be different. All users are aware ofwhether the previous transmission is successful or not, as well as the average intervalbetween two transmission attempts, based on which they can estimate the numberof contending users and adjust the contention window accordingly.

When there are m users contending for a single channel with the contentionwindow size w, the access probability for a certain user can be calculated as


Algorithm 1 Contention window size adjustment ruleINPUT:

Current contention window w;Average waiting time Lw among the previous T transmissions;Whether the previous transmission is successful;

OUTPUT:New contention window w0;———————————————————————

1: if w D 1 then2: if Previous transmission is successful then3: w0 1;4: else5: w0 2;6: end if7: else8: Estimate number of users Om according to (22);9: w0 dwC ˇ . Om� w/e, where ˇ 2 .0; 1/;

10: end if

pa;w D2

wC1 [4], and the probability that none of these users accesses the channel inthe next coming slot can be expressed as the following:

pi D .1 � pa;w/m : (21)

Moreover, the waiting time between two transmission attempts has the geometricdistribution with parameter pi and mean Lw D

pi1�pi

. Thus, with the observedaverage waiting time, the number of contending users can be estimated as follows:

Om Dln�

LwLwC1

�ln .1 � pa;w/

Dln�

LwLwC1

�ln�

w�1wC1

� : (22)

Remark 1. Notice that there exists a special case in (22) when the contentionwindow w D 0. In this case, users access the channel with probability one, andaverage waiting time is 0. Collisions occur once there are more than one user onthe channel. Thus, it is only possible to tell whether there are multiple users on thechannel by observing the length of transmissions.

Remark 2. If users can sense the channel for a long time without changing thecontention window, Om can be a precise estimation of m, and the users can changetheir contention window to m to achieve the optimal throughput. However, it isinefficient and may be ineffective if the value of m varies during the longtimeestimation. Thus, we propose the adjustment rule in a dynamic learning way asshown in Algorithm 1.

In Algorithm 1, T is the number of transmissions for calculating the averagewaiting time, and ˇ is the step length in the adjustment rule. These two parameters

20 L. Song et al.

directly influence the convergence time and stability of the algorithm. Generally,when ˇ is large, the contention window size approaches the number of contendingusers more quickly, but meanwhile, the contention window size is more vulnerableto the fluctuation of the estimation of Lw, which may lead to the instability of thenetwork. On the other hand, small ˇ guarantees the stability, but the contentionwindow size may be unable to keep pace with the change of the number ofcontention users. Thus, a mediate value of ˇ requires careful design. Similaranalysis can be applied for T : shorter T introduces instability to the network, whilelonger T leads to low sensitivity to the change of number of users.

Expected ThroughputSince our goal is to improve the network throughput performance, the expectedthroughput on certain channel is considerably important for the channel selectionstrategy, which is derived as follows. For any user n attempting to transmit on thechannel, the expected throughput can be written as follows:

un DpsLs � rn

psLs C pcLc C Lw C DIFS; (23)

where ps is the probability that the user successfully accesses the channel withoutcollision, pc D 1 � ps is the collision probability, Ls is the average successfultransmission length, Lc is the average collision length, Lw is the average waitingtime for channel contention, and rn D log2.1Cjhnj

2/ is the achievable rate of usern, in which is proportional to each user’s transmit power.

The probability that the user n successfully accesses the channel k withoutcollision can be estimated as follows:

ps D

( �w�1wC1

� Om�1n is on the channel,�

w�1wC1

� Omn is not on the channel,

(24)

and the collision probability is pc D 1 � ps .Then, we consider the average successful transmission and the collision length.

We assume a fixed packet length L for all users. Taking the false alarm probabilityinto account, the average successful transmission length can be written as follows:

Ls D�1 � Pf

�LC Pf : (25)

Similarly, the average collision length is given by considering the miss detectionprobability:

Lc D .1 � Pm/C PmL: (26)

It can be seen from Algorithm 1 and (24) that all users can adjust the contentionwindow size to the same value and estimate the expected throughput on the channelin a fully distributed manner.


Channel Selection Strategy

In this part, we tackle with the channel selection problem and formulate it as adistributed multi-channel random access game, in which each user uses the localinformation and observation of all channels to determine its channel selectionstrategy. Since our goal is to improve the network throughput, the expectedthroughput on each channel is adopted as the utility.

More specifically, in the multi-channel FD-WiFi network, each user needs tochoose one channel to contend. After selecting the channel, the user performsaccess or backoff using the strategy described in section “Channel Access Strategy.”According to our assumption, all users can monitor the occupancy of all channels.Thus, a user can estimate its expected throughput on each channel by using themethod in section“Expected Throughput,” and we can assume that when a userswitches to a new channel, it can automatically adopt the same contention windowsize as the ongoing users on the same channel.

By extending (24) to multi-channel scenario, we can derive the utility for anyuser n attempting to transmit on channel kn as the following:

un .kn;k�n/ Dps;knLs � rnkn

ps;knLs C pc;knLc C Lw;kn C DIFS; (27)

where kn 2 Sn is the strategy of user n, k�n D .k1; k2; : : : ; kn�1; knC1; : : : ; kN /

is the strategy vector of all users except user n, ps;kn is the probability that usern successfully accesses channel kn, pc;kn is the collision probability, Lw;kn is theaverage waiting time for channel contention on channel k, and rnk D log2.1 Cjhnkj

2/ is the achievable rate of user n on channel k.In this distributed network, each user tries to maximize its own expected

throughput by adjusting its channel selection strategy, which can be formally writtenas follows:

k�n D arg maxkn2Sn

un .kn;k�n/ ; 8n 2 N : (28)

Note that the expected throughput of any user n on any channel k is largelydependent on the choices of other users. Thus, we formulate the channel selectionprocess as a game defined as follows.

Definition 1. A channel selection game G is defined as G WD< N ; .Sn/n2N ;

.un/n2N >, where N D f1; 2; : : : ; N g is the set of users, Sn WD

fkn D 1; 2; : : : ; Kg is the set of all possible choices of user n, and un .kn;k�n/is the utility function of user n when all users choose k�n.

We are interested in the Nash equilibrium of the channel selection game, whichprovides the strategy stability of each user’s selection strategy.

22 L. Song et al.

Definition 2 (Nash Equilibrium). A strategy profile k� is a pure strategy Nashequilibrium if and only if no user can improve its utility by deviating unilaterally,i.e.,

un�k�n ;k

��n

�� un

�kn;k

��n

�; 8n 2 N ; kn 2 Sn: (29)

Theorem 1. The channel selection game G has at least one pure strategy Nashequilibrium.

Proof. The utility function un .kn;k�n/ defined in (27) is quasiconcave continuousin k. The feasible set is also compact and convex. Consequently, according to [24],there exists at least a pure Nash equilibrium. Similar proof for Aloha game can bealso found in [25].

To achieve the Nash equilibrium, we present a best-response-based channelselection mechanism. In this algorithm, each user chooses the channel with thelargest expected throughput to contend on and then performs random channel accessstrategy in section “Channel Access Strategy.” Meanwhile, each user monitors thestates of all channels continuously and adjusts the contention window size accordingto the channels’ occupancy. Once the user fails to contend for a channel or finishesa transmission, it estimates the expected throughput of all channels and chooses thechannel with the largest expected throughput to update its selection strategy. Thischannel selection mechanism is formally described in Algorithm 2.

Performance Analysis and Comparison

In this subsection, we provide theoretical comparison of the proposed FD protocolwith CSMA/CA and HD protocols.

Comparison with CSMA/CA ProtocolsWe make a comparison between the proposed FD-WiFi channel access protocolon a single channel with the conventional CSMA/CA mechanism in this part. Forfairness, we consider the single-channel network with m users and omit the noiseterm.

In CSMA/CA, there exists the minimum contention window length CWmin

and the maximum backoff stage wmax. After each failed transmission attempt, thetransmitted user doubles its contention window until to the maximum contentionwindow length CWmax D 2

wmax CWmin. After each successful transmission, the userresets the contention window as CWmin. According to the analysis in [4], the averageaccess probability can be written as follows:

p D2 .2ps � 1/

.2ps � 1/ .CWmin C 1/C .1 � ps/CWmin .1 � .2 � 2ps/wmax/

; (30)


Algorithm 2 Channel selection mechanismStep 1: Initialization1: 8n 2 N , estimate the value of hnk , for all k D 1; 2; : : : ; K;2: Initialize contention window wk D 1, 8k 2 K ;3: Initialize backoff time vnk D 0, 8n 2 N ; k 2 K ;4: Set cn D arg max

kfjhnk j

2g;

Step 2: Channel selection and random access1: while in each time slot do2: for k D 1 W K do3: if Channel is currently occupied then4: Transmitting users keep transmitting and detecting whether their current transmis-

sions collide with other transmissions. If collision is detected, stop transmission;5: else6: All users on channel k keep downcounting vnk , a user n accesses channel k when vnk

reaches 0;7: end if8: end for9: All users sense and judge the occupancy of all channels during the whole slot;

10: for all channel k whose occupancy has just changed do11: All users that fail to contend for channel k or users that just finish a transmission collect

Lw;k0 (k0 D 1; 2; : : : ; K), and update the utilities unk0 of all channels according to (27).We denote the set of these users as Ntochange;

12: 8n 2 Ntochange, update channel selection strategy as cn D arg maxkfunkg;

13: Update contention window wk according to Algorithm 1;14: end for15: if there exists a set of channels Ki whose waiting time exceeds the contention window

then16: Judge all the channels k 2 Ki as unoccupied by any users, and set contention windows

wk D 1;17: end if18: end while

where ps is the successful transmission probability, given by

ps D 1 � .1 � p/m�1 : (31)

It can be verified that the access probability is less than 2mC1

, which is the asymptoticvalue of access probability under the proposed contention adjustment rule.

Comparison with Half-Duplex ProtocolsCompared with the HD protocols, the most significant difference is that userscan sense the channels while transmitting, i.e., users are no longer “blind” intransmission. Once a collision is detected, users can stop transmission immediately.This feature can significantly reduce the average length of collision. Additionally,contending users can obtain additional information of whether the previous trans-mission is successful by simply detecting the length of the transmission.

24 L. Song et al.

• Collision length. In HD protocols, the “blindness” in transmission results inlong collision, which is typically a packet length. FD allows users to detectcollision while transmitting. As derived in (26), the average collision lengthLc D 1CPm .L � 1/, as is derived in (26), is slightly more than one slot, whichis substantially reduced from a packet length L.

• Successful transmission length. In HD protocols, once a collision-free transmis-sion begins, it can always be finished successfully without interruption. However,in the proposed FD protocol, the transmission may be ceased due to false alarm.According to (25), it can be seen that Ls D L � .L � 1/Pf is reduced becauseof false alarm. Furthermore, false alarm may lead to unnecessary increase ofcontention window and decrease of expected throughput of the channel, whichmay further degrade the performance of the proposed protocol.

Simulation Results

In this part, simulation results are presented to evaluate the performance of theproposed protocol for multi-channel FD-WiFi network. We consider K D 4

channels with up to N D 15 users. The packet length L is fixed on 50 slots, andDIFS time is 2 slots. The number of transmissions taken into account for contentionwindow adjustment is T D 10. The channel sensing error probabilities, i.e., Pm andPf , are set as 0.01.

In Fig. 9, we first verify the effectiveness of the proposed FD protocol. Weconsider the channel selection process of ten users. It can be seen from Fig. 9 that

0 5 10 15 20 25 30 35 40 45 50

1

2

3

4

t/slot

User number: N = 10Channel number: K = 4

Fig. 9 Channel selection process under the proposed mechanism


0 2 4 6 8 10 12 14 150

5

10

15

20

25

30

35

Number of Users

Tota

l Thr

pugh

put

proposed FD protocol − 4 channels

greedy CSMA − 4 channels

proposed FD protocol − 1 channel

greedy CSMA − 1 channel

Fig. 10 Channel selection process under the proposed mechanism

the channel selection mechanism converges to the Nash equilibrium quickly, and allusers do not change their strategies afterward.

In Fig. 10, we consider the total throughput of the multichannel network, which isthe throughput of all theN users on allK channels. We present comparison betweenthe proposed FD protocol and a greedy CSMA-based FD protocol in which eachuser accesses the channel with maximum achievable rate and performs contentionbased on CSMA mechanism with minimum contention window CWmin D 1

and maximum backoff stage wmax D 4. Note that we do not adopt the originalwindow size CWmin D 8 and wmax D 5 in CSMA in the simulation since thenumber of users is small, and the adoption of large contention window size leadsto worse performance. Firstly, it is shown in the dash-dotted and dotted lines inFig. 10 that the proposed protocol can achieve higher throughput in single-channelcase, especially when the number of users is large. This is because the contentionwindow adjustment rule guarantees a more proper window size for all users tomaximize their access and successful transmission probability. Also, Fig. 10 showsin the solid and dashed lines that the proposed protocol can achieve higher totalthroughput than that of the greedy CSMA, especially when the number of usersis close to the number of channels. This is because in the proposed protocol,users can automatically avoid to choose crowded channels to increase their accessand successful transmission probability. Additionally, it can be seen that whenN � K (N � 4 in Fig. 10), the throughput increases almost proportionally with thenumber of users, and the slope is close to EŒlog2

�1C jhj2

��. This indicates that

26 L. Song et al.

all users intend to occupy a channel exclusively without sharing with other users.However, when the number of users increases, the greedy mechanism may graduallyapproach the proposed protocol. This is because when many users contending forlimited channels, it is likely that all channels are crowded at a similar level, andthe users do not have the much motivation to deviate from the channel with thelargest rate. This makes the channel selection profile almost the same as the greedymechanism.

Summary

This chapter has first discussed the CSMA/CA protocol in conventional HD-WiFinetworks and pointed out its long collision duration problem due to the failureof carrier sensing during transmission. To mitigate this problem, the CSMA/CDprotocol has been proposed for single-channel WiFi networks by taking advantageof the FD technology. Compared with CSMA/CA protocol, the new CSMA/CDprotocol has two adaptations: (1) continuous carrier sensing by enabling simul-taneous sensing and transmission and (2) transmission suspension procedure, bywhich users stop transmitting immediately once detecting a collision. To obtain acomprehensive network performance analysis, this chapter has calculated two typesof sensing error probabilities due to residual self-interference, namely, false alarmand miss detection. The normalized throughput has also been derived as the averagechannel utilization for successful data transmission. Both performance analysis andsimulation results have shown that the full-duplex CSMA/CD protocol improvesWiFi throughput performance.

Then this chapter has extended the CSMA/CD protocol to the multi-channel FD-WiFi network and divided this scenario into two parts: (1) channel selection, eachuser selects which channel for access, and (2) channel access, all contending users,which select same channel, perform a contention-based channel access scheme. Forthe channel access problem, a random access strategy has been proposed based onthe described CSMA/CD protocol for single-channel scenario, except not adoptingthe exponential backoff scheme. Instead, by learning from historical waiting time,the proposed channel access strategy provides an adjustment rule of contentionwindow size to accommodate the number change of contending users. For thechannel selection problem, a distributed selection protocol has also been providedbased on the best-response algorithm, by which the WiFi user always selects thechannel with the highest expected throughput. Simulation results have also beenprovided to verify the effectiveness of multi-channel FD-WiFi protocol.

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http://arxiv.org/pdf/1107.0607.pdf

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