jamming resilient cross-layer resource allocation in ...shuming/201712 ieee access anti-jamming...

Received September 26, 2017, accepted October 16, 2017, date of publication October 20, 2017,date of current version November 28, 2017.

Digital Object Identifier 10.1109/ACCESS.2017.2764914

Jamming Resilient Cross-Layer ResourceAllocation in Uplink HARQ-Based SIMOOFDMA Video Transmission SystemsSHU-MING TSENG 1, (Member, IEEE), YUNG-FANG CHEN2, (Member, IEEE),PO-HSIANG CHIU3, AND HUNG-CHANG CHI41Department of Electronic Engineering, National Taipei University of Technology, Taipei 106, Taiwan2Department of Communication Engineering, National Central University, Taoyuan 320, Taiwan3Software Engineering, EtherWAN Systems, New Taipei 231, Taiwan4Software Engineering, DELTA Networks Inc., Taipei 114, Taiwan

Corresponding author: Shu-Ming Tseng ([email protected])

This work was supported by the Ministry of Science and Technology, Taiwan, under Grant MOST 105-2221-E-027-007.

ABSTRACT The cross-layer resource assignment algorithm of orthogonal frequency division multipleaccess (OFDMA) video communication systems byWang et al. allocates the power and subcarriers accordingto both the layer 1 channel state information and the layer 5 rate distortion function. We introduce thehybrid automatic repeat request (HARQ) in layer 2 and a single-input multiple-output (SIMO) anti-jammingtechnique in layer 1, and propose an anti-jamming power/subcarrier assignment scheme crossing layers 1, 2,and 5 for HARQ-based SIMO OFDMA uplink video communication networks. We derive the new optimalcondition for anti-jamming cross-layer resource allocation analysis, and thus propose a novel resourceallocation method crossing layers 1, 2, and 5 by considering the angle between the jammer channel vectorand the sender (desired signal) channel vector. By HARQ, we can increase the target symbol error ratewithout increasing the rate of the packet error, more bits can be transmitted, and the peak signal-to-noiseratio (PSNR) (the video quality) is improved. The results of the simulations show that the PSNR increasesby 11.3 dB when we consider the angle between the jammer channel vector and the sender channel vectorin the proposed resource allocation algorithm crossing layers 1, 2, and 5. The PSNR improves further by1.82.6 dB when we add HARQ, when the average SNR = 18 dB and there are 12 users.

INDEX TERMS Anti-jamming, rate distortion function, OFDMA, subcarrier reassignment, powerallocation, hybrid automatic repeat request.

I. INTRODUCTIONMulti-user Orthogonal Frequency Division Multiplex-ing (OFDM) or Orthogonal Frequency Division MultipleAccess (OFDMA) is popular [1][7] because of its high band-width efficiency, resistance to inter-symbol interference, easyequalization, and flexible resource allocation. It is the trans-mission technology of most wireless standards [8]. However,with the limited power and bandwidth resources, increasingthe overall performance such as the data rate and video qualityis still a challenging issue. References [9][15] make use ofchannel state information (CSI) in the physical layer (layer 1)to allocate the spectrum and power. The resource allocationalgorithm in [13][15] considers the layer 1 informationsuch as the interference between the macro cell and femtocell. These works do not consider the layer 2 and layer 5

information as the proposed scheme does. The optimizationobjective function is also different. They maximize the totalcapacity (layer 1) but we minimize the total video meansquare error (MSE) distortion (layer 5).

On the other hand, [16][18] focus on the users videocontents rate distortion (RD) function information inthe application layer (layer 5) for allocating resources.A resource allocation algorithm crossing layers 1 and 5 hasbeen proposed in [19], which combines both physical layerinformation (i.e., CSI) and application layer information(i.e., RD) for assigning the power and subcarrier resources,and its video quality (average peak signal-to-noise ratio,PSNR) is better than if one considers either CSI or RD.However, it does not consider hybrid automatic repeatrequests (HARQ) in layer 2 (MAC layer). In [20], we add

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VOLUME 5, 2017

https://orcid.org/0000-0002-5017-3159

S. Tseng et al.: Jamming Resilient Cross-Layer Resource Allocation

HARQ and turbo code, and propose a resource allocationalgorithm that crosses the physical, theMAC, and the applica-tion layers. Although HARQ has been applied to cross-layerresource allocation involving layers 1 and 2 [21][23], we arenot aware of references that also include the application layer.With HARQ, we can increase the information rate to improvethe video quality. However, [20] does not consider jam-ming resiliency in the resource allocation algorithm crossinglayers 1, 2, and 5.

Protecting the secrecy of the user messages is amajor concern in communication networks [24][27]. Thereceiver, can be jammed by a stronger signal at the sameband [24][26] or it can be listened to by an eavesdrop-per [27]. The current OFDMA systems are vulnerable to avariety of signal jamming attacks [8], [28][30]. In fact, theWirelessMAN standard has developed the transmission secu-rity extension [31] for such hostile environments. However,jamming resiliency is not considered in [19].

There are many techniques to deal with the interferencefrom jamming. Adaptive filtering is effective for narrowbandjammers with lower energy consumption [32]. The down-side of this approach is that the receiver should predict thejamming signal in order to eliminate the interference. It ismore difficult to jam spread-spectrum signals than narrowband signals [33][35]. The disadvantage of spread-spectrumis that it requires more bandwidth than adaptive filter-ing. In recent years, single-input multiple-output (SIMO)technology has been used as an anti-jamming method.Reference [24] uses two receive antennas to cancel the jam-mer and [26] further proposes to insert pilot symbols to trackthe sender and jammers channel coefficients jointly.

We propose, in this paper, a jamming resilient resourceassignment algorithm that crosses the physical, theMAC, andthe application layers for uplink OFDMA video communi-cation networks. The contributions and novelty of the paperwith respect to [19] is as follows:

1) We add HARQ in layer 2. It makes the target symbolerror rate SERt larger, = 3PN [Q

1(SERt/4)]2

(definedbelow (9)) larger too, and increases the information rateRk,m in (9). Thus the MSE in (11) decreases (video qualityimproves). Reference [19] does not consider layer 2 HARQ.

2) We propose that the resource allocation takes the angle between the sender (desired signal) channel vector and thejammer channel vector in the antenna-spatial domain intoconsideration. Reference [19] does not consider this angle inits resource allocation algorithm.

3) We first derive the new optimal condition for the anti-jamming HARQ-based power and spectrum assignment forthe case of continuous frequency (bandwidth allocation incre-ment is infinitesimal). This derivation in Appendix A is theanti-jamming and HARQ extension of the one in [19] (noanti-jamming, no HARQ).

4) The HARQ in layer 2 retransmits packets andit takes extra power (overhead). We thus propose theoverhead-adjusted information rate improvement due toHARQ. Thus it allows fair comparison between non-HARQ

and HARQ schemes. Reference [19] is a non-HARQsystem.

The remaining of this paper is organized as below. Sec. IIis the system model. The optimal derivation results forthe anti-jamming HARQ-based resource allocation crossinglayers 1, 2 and 5 for the case of continuous frequency(bandwidth allocation increment is infinitesimal) are givenin Sec. III and details and proof of Theorem I are given inAppendix A. We then propose the novel SIMO anti-jammingresource allocation algorithm crossing layers 1, 2 and 5 for thecase of discrete frequency in Sec. IV. The simulation resultsare presented in Sec. V. Sec. VI is the conclusion.

II. SYSTEM MODELA. UPLINK OFDMA SYSTEMWe show the block diagram in Fig. 1. The system model issimilar to that in [19] except for the blocks in gray. There areK users and k is the user index. The system bandwidth is W.There are M subcarriers and m is the subcarrier index.

As shown in Fig. 1, at the transmitter, an anti-jammingcross-layer resource allocation considers the angle betweenthe sender channel vector and the jammer channel vector.The resource allocation algorithm assigns the subcarriers andpower to each user. The H.264 video encoder of each usergenerates the compressed video, the channel encoder adoptsa rate 1/2 of either the convolutional code or turbo codeand divides the user video into packets. Then the bits ofthe packets are modulated adaptively and go through inversefast Fourier transform (IFFT) and become OFDM symbols.In addition, each packet is checked by the cyclic redundancycheck (CRC) at the receiver. If a packet fails CRC, it will bere-transmitted by HARQ.

B. SIMO ANTI-JAMMING MECHANISMThe single-input multiple-output (SIMO) anti-jammingmechanism is adopted from [26] for the single-antennamobile stations (MS) and the base station (BS) with tworeceive antennas. We briefly describe it. For details, the read-

ers are referred to [26]. The received signal vector[yk,my

k,m

]at

the two receive antennas (the superscript means for the 2nd

receive antenna) of the BS for the user k , the subcarrier m,can be written as:[

yk,my

k,m

]=

[Hk,mH

k,m

]xk,m +

[H jm

H j

m

]x jm,

k = 1, 2 . . .K , m = 1, 2, . . . ,M (1)

where[Hk,mH

k,m

]is the channel vector of the subcarrierm from

the user k to the BS and

[H jm

H j

m

]is the channel vector from the

jammer (denoted by superscript j) to the BS. xk,m is the datasymbol of the user k at the subcarrier m and x jm is the jammer(superscript j) symbol at the subcarrier m.

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FIGURE 1. Anti-jamming cross-layer uplink OFDMA video transmission systems.

We consider the reactive jammer, the most effective,stealthy, and energy efficient jamming strategy. Assume thepilots are numbered as p = 0, 1, 2, . . .K . The initial pilot(p = 0) is un-jammed [36], [26], so the initial sender channel

response,[Hk,m(p)H

k,m(p)

], where the pilot index p = 0 denotes

the initial pilot0, can be estimated as:

[Hk,m(0)H

k,m(0)

]=

[yk,my

k,m

]/x1k,m (2)

where x1k,m denotes the known initial pilots (the superscript1

denotes pilot, not data symbol).[Hk,m(0)H

k,m(0)

]will be used in the

following jammer channel estimation in the p = 1 case in (5).The key point of the SIMO anti-jamming mechanism is to

project the received signal vector[yk,my

k,m

]onto the subspace

orthogonal to

[H jm

H j

m

], i.e.,

[H j

m

H jm

]. The projected signal is

the inner product of

[H j

m

H jm

]and

[yk,my

k,m

]and is given by:

yproj =

[H j

m

H jm

]T [yk,my

k,m

]= H j

myk,m Hjmy

k,m

= (H j

mHk,m HjmH

k,m)xk,m (3)

By dividing both sides of the last equal sign of (3) by H j

m,we get the signal of interest xk,m as:

xk,m =yk,m

H jmH j

my

k,m

Hk,m H jmH j

mH

k,m

(4)

The receiver updates the jammer channel ratio whenreceiving odd-numbered pilots

H jm (p)

H j

m (p)=yk,m x1k,m Hk,m(p 1)

y

k,m x1k,m H

k,m(p 1), p = 1, 3, 5, . . . ,

(5)

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Similarly, the receiver updates the sender channelswhen receiving even-numbered pilots. Specifically, whenp = 4, 8, 12 . . . , we update Hk,m (p); whenp = 2, 6, 10, . . . ,we update H

k,m (p). We can get the denominator of (4) by:

Hk,m (p)H jm (p 1)

H j

m (p 1)H

k,m (p)

= (yk,m H jm (p 1)

H j

m (p 1)y

k,m)/x1k,m, p = 2, 4, 6, (6)

C. HYBRID AUTOMATIC REPEAT REQUEST (HARQ)The maximal-ratio combining (MRC) is used in HARQ fordiversity combining. We use all of the received packets fromoriginal transmission and retransmissions. The least squaressolution for N transmissions is given by

s =h0y0 + h

1y1 + h

2y2 + . . .+ h

N1yN1

|h0|2 + |h1|2 + |h2|2 + . . .+ |hN1|2(7)

where hn denotes the channel gain of the n-th transmis-sion, n = 0, . . . ,N 1, the superscript denotes com-plex conjugate, and yn denotes the received signal of then-th transmission.

D. CHANNEL ENCODERThe rate 1/2 with encoder g(D)= [23, 35] convolutional codeis used in [19].

For improving the average PSNR, we also use the rate1/2 turbo code with g(D)= [1, 23/35]. Its memory is the sameas the convolutional code [23, 35]. We divide the user videointo packets, and each packet has 2048 bytes (16384 bits)before the encoder, similar to Wi-Fi standard [37].Therefore, the interleaver consists of a 128x128 matrixwith a block length = 16384, and is made up of aBerrou-Glavieux interleaver [38], [39].

E. NEW OVERHEAD-ADJUSTED INFORMATIONRATE IMPROVEMENT DUE TO HARQTo evaluate the advantage of HARQ, we make anew definition: the overhead-adjusted information rateimprovement (OIRI):

=

(1K

Kk=1

R

k,m

Rk,m

) 0/total (8)

where Rk,m is the information rate at SERt = 0.1 (no HARQscheme in [19]), R

k,m is the information rate at SERt = 0.3(HARQ scheme, with the same packet error rate constraintas the case of SERt = 0.1 no HARQ, as shown in Sec. V,Fig. 3). 0/total accounts for the information rate reductiondue to the HARQ overhead. total is the number of packetsof all transmissions, and 0 is the number of packets oforiginal transmission. If is larger than 1, the proposedscheme achieves a higher information rate than the previousscheme [19]. The HARQ overhead is already accounted forin the calculation of .

FIGURE 2. The angle between the sender and jammers channel vector.

FIGURE 3. Packet error rate vs. average SNR, 16 subcarriers, 12 users.

F. NEW JAMMER ANGLE DEPENDENTRATE-DISTORTION FUNCTIONThe rate distortion function is similar to that in [19] exceptthat the information rate is now a function of the anglebetween the sender (user k) and jammers channel vectorat subcarrier m in terms of sin k,m in Fig. 2. The idea ofFig. 2 is to project

Hk,m2 onto the subspace orthogonalto

[H jm

H j

m

]and get the completely unjammed vertical com-

ponentHk,m2 sin k,m, since the horizontal componentHk,m2 cos k,m is completely jammed, where k,m is the

angle between[Hk,mH

k,m

]and

[H jm

H j

m

]. The information rate is

a function of sin k,m.

Rk,m(Pk,m,Hk,m, sin k,m

)= min

{log2 [1+ Pk,m

Hk,m2 sin k,m],Rmax} (9)where = 3PN [Q

1(SERt/4)]2,Rmax is the maximummod-

ulation order, SERt is the target symbol error rate, and PN isthe noise power.

For user k and time slot s, Dsk (Bk) is the rate distortionfunction, where the encoder generated Bk bits for user k. Foreach Group of Pictures (GOP), theMSE distortion is modeled

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as [40].

Dsk (Bk) = ak +k

Bk + k(10)

where ak, k and k are content-dependent parameters, and

Bk = M

m=1u Rk,m

(Pk,m,Hk,m, sin k,m

) Ts/T0

A rate u channel code is used. The system operates in aslotted manner and the length of one time slot (one GOP)is Ts(sec). T0 is the OFDM symbol duration. If we plug theabove equation into (10), then the user ks MSE is

Dsk (B) = ak +bk

M

m=1 Rk,m(Pk,m,Hk,m, sin k,m

)+ ck

(11)

where bk =k

(uTs/T0), and ck =

k(uTs/T0)

.

G. PROBLEM FORMULATION OF UPLINKRESOURCE ALLOCATIONWe want to minimize the sum of the users MSE distortion.That is

minPk,mK

k=1

bkM

m=1Rk,m(Pk,m,Hk,m, sin k,m

)+ck

(12)

Each uplink user, over all subcarriers, has a power con-straint P, and each subcarrier cant be shared bymore than oneuser. Therefore the optimization problem has two constraints:C1:

Mm=1 Pk,m = P k

C2: If Pk,m 6= 0 then Pk,m = 0 k 6= k

For the optimization problem formulated in (12), becausethe C2 constraint is not convex, the optimization is NP-hard.We thus propose a suboptimal iterative scheme. Before wedescribe the proposed algorithm in detail in Sec. IV, we statethe optimal condition for the continuous frequency channelresponse setting, where the bandwidth increment is infinites-imal, as opposed to where the bandwidth increment is a sub-carriers bandwidth in the OFDMA system. This optimizationcondition gives the insights and motivates the proposed algo-rithm in Sec. IV.

III. OPTIMAL CONDITION DERIVATION RESULTFOR ANTI-JAMMING CROSS-LAYER RESOURCEALLOCATION ANALYSIS FOR CONTINUOUSFREQUENCY CHANNEL RESPONSEDifferently from [19], we consider the layer 2 HARQoverhead-adjusted information rate improvement (in termsof ) and the SIMO anti-jamming (in terms of sin k) in thederivation of the optimal metric.

We consider the continuous frequency channel and onlytwo users, that is, K = 2. Assume Bi is the frequency bandallocated for user i,Hk (f ) is the channel coefficient for user kat frequency f . To get the closed form of the optimal conditionand make its derivation tractable (the derivation of Theorem Iin Appendix A does not consider the maximum modulation

order constraint), we ignore the modulation order constraintin the following optimization problem. A similar approxi-mation is also made in [19]. The optimization problem thusbecomes

minP=

2k=1

bkBk

log2[1+ Pk (f ) |Hk (f )|2 sin k ]df + ck

(13)

After the bandwidth allocation, the power allocation isaccording to the water-filling. Given Btot , we can viewthe optimal bandwidth allocation as bandwidth partitionBtot = Bopt1 B

opt2 , where B

opt1 and B

opt2 is the optimal

bandwidth set for two users in a sense of minimum distortion.We define the following notations and variables.Definition 1:

a) |.| denotes the bandwidth in Hz. For example,Bopt1 is

the optimal bandwidth allocated for user 1.b) We define r1 =

Bopt1

log2(1 + P1(f ) |H1(f )|2

sin 1)df and r2 = Bopt2

log2(1 + P2(f ) |H2(f )|2

sin 2)df as the optimal information rate (bits/sec) fortwo users, respectively.

c) We define W1 = P1 (f ) + 1|H1(f )|2sin1

and W2 =

P2 (f )+ 1|H2(f )|2sin2

as the optimal water-filling levelfor two users.

d) We define Bopt2 as an infinitely small frequencyband for user 2,

H 1 2 and H 2 2 as the channel gainsin frequency band for users 1 and 2, respectively, andthey are constants because is infinitely small.

e) Similar to Pi (f ), the difference between the water-filling level and the noise level, we define i =(Wi 1

H i 2

)+as the non-negative distance between

the water-filling level for user i and the noise level,where [x]+ = x if x > 0, and [x]+ = 0 if x 0,For any frequency band of Bopt2 , W2

1H 2 2 > 0.

Theorem 1:For a continuous bandwidth Btot , the optimal band alloca-

tion Bopt1 and Bopt2 minimize the total distortion, and it should

satisfy (14), as shown at the top of the next page, for anyfrequency band .

Proof: The proof is given in Appendix A.

Si =bi

(ri+ci)2(15) ln

(1+ i

H i )

Bopti

|Hi(f )|2 sin iBopti (1+ Pi(f ) |Hi(f )|2 sin i)i df (16)

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b1(r1+c1)

2

ln (1+ 1 H 1 ) Bopt1

|H1(f )|2 sin 1Bopt1 (1+P1(f )|H1(f )|2 sin 1)1df

b2(r2+c2)

2

ln (1+ 2 H 2 ) Bopt2

|H2(f )|2 sin 2Bopt2 (1+P2(f )|H2(f )|2 sin 2)2df 1 (14)

The numerator or denominator of (14) is the productof (15) and (16). (15) is the absolute value of the RD function(Di = ai +

biri+ci

) slope in the application layer and actslike a weighting, and (16) is the physical layer informationincluding sin i for the jamming effect. Therefore, (15) givesus the insight that we should consider the user with the steep-est RD curve slope for gaining subcarriers. From (16), as thebandwidth of approaches infinitely small, (16) is regardedas the marginal rate change of reassigning a frequency bandfrom one user to the other and consists of two parts, wherethe first part is the direct physical layer rate change due tolosing or gaining ,

ln(1+ i

H i 2) (17)and the second part,

Bopti

|Hi(f )|2 sin iBopti (1+ Pi(f ) |Hi(f )|2 sin i)i df (18)is the corresponding physical layer rate change caused by thewater-filling level change and jamming effect sin i.We summarize the insights observed from the analysis: (15) gives us the insight that we should consider theuser with the steepest slope of the RD curve (largestweighting) for gaining subcarriers.

(16) is the marginal rate variation of reassigning a fre-quency band from one user to the other.

The optimal cross-layer 1, 2, 5 resource allocationwouldallocate a frequency band to the user and has a largestproduct of (15) (layer 5) and (16) (layer 1).

The MAC layer effect disappears in (14) due to can-cellation in the derivation in Appendix A.

The jamming effect sin i affects only the physical layerpart, (16), and does not affect the weighting (applicationlayer part), (15).

In the above analysis, the bandwidth increment wasinfinitely small, while in the OFDMA bandwidth allocation,the increment is a single subcarriers bandwidth which expe-riences block fading. Therefore, the layer 1 metric of (16)would be invalid. We therefore propose an iterative subcar-rier assignment scheme in the next section. Inspired by theoptimal condition in (14), the layer 5 metric is the RD curveslope. The optimal allocation would assign band to the userwho maximizes (14). The user with a steep slope has priority(larger weighting) to gain subcarriers.

IV. THE PROPOSED SIMO ANTI-JAMMING CROSS-LAYERRESOURCE ALLOCATION ALGORITHMThe proposed algorithm extends [19], and the differences arethat we have multiple antennas at the BS and we consider theangle between the spatial channel vectors of the sender signaland the jammer signal sin k,m.Step: 1 (Initialization):First of all, we assign each subcarrier to the user with the

best channel response. The difference from [19] is that weassign each subcarrier to the user whose

Hk,m2 sin k,m,instead of

Hk,m2, is the maximum.Step: 2 (Water Filling and Slope Calculation):Each user uses the power water filling allocation [41] to

solve the sumMSE distortion minimization problem. But thedifference between the power water filling in [19] and that inthe proposed method is sin k,m. We define A

(i)k is the set of

subcarriers assigned to user k at the i-th iteration. The powerof user k that uses water filling allocation can be written as

Pk,m =

[1k

1

Hk,m2 sin k,m

]+, m A(i)k (19)

where k is found numerically to satisfy the total powerconstraint

mA(i)k

Pk,m P. Let rk be the optimal information

rate (in bits/symbol); user k gets to use the water filling and itis summed from user ks assigned subcarriers, and is given by

rk =mA(i)k

log2[1+ Pk,m

Hk,m2 sin k,m] (20)The slope of the RD function of the k-th user can be calculatedby

Sk =d bkrk+ckdrk

rk=rk

= bk(

rk + ck)2 (21)

where bk and ck are constants that depend on the videocontent in the application layer. Let k = argmin {Sk} bethe user with the steepest RD function slope, which is theuser who stands to benefit (lower MSE distortion) the mostfrom receiving an increment of rate, that is, an additionalsubcarrier.Step: 3 (Subcarrier Reassignment):We consider each subcarrier m which is not currently

assigned to the user k. Define (i)m as the user who isassigned subcarrier m at the i-th iteration. Define 1k,m 0as the absolute value of the MSE performance change of

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user k by gaining or losing subcarrier m. We calculate theMSE performance change 1

(i)m,m of user (i)m from losing

subcarrier m, and the MSE performance change 1k,m ofthe userk from gaining subcarrier m. Differently from [19],the MSE in (10) is a function of sin k,m by the informationrate Rk,m

(Pk,m,Hk,m, sin k,m

), instead of Rk,m

(Pk,m,Hk,m

)in [19].

If (1k,m 1(i)m ,m ) > 0, we reassign subcarrier m to

user k at iteration i + 1, (i+1)m = k, and return to Step (2)to update k.

If (1k,m 1(i)m ,m) < 0, reassigning any subcarrier to

user k will not enhance the overall performance. Afterward,we return to Step (2) to update k until there is no subcarrierthat can be assigned.

The important meaning of doing cross layer 1, 2,and 5 power and subcarrier assignment is as follows. Step (1)considers layer 1 CSI and each subcarrier is assigned tothe user with maximum

Hk,m2 sin k,m. In Step (2), theinformation rate is increased because the HARQ in layer 2makes SERt larger and = 3PN [Q

1(SERt/4)]2

(definedbelow (9)) larger too. In Step 3, we compare the MSE vari-ation (layer 5 information) before and after the subcarrierreassignment. For example, user 1 wins a subcarrier fromuser 2. The user 1 MSE decreases by 15 and user 2s MSEincreases by 10. The total MSE decreases by 5, so we makethe subcarrier exchange.

The complexity of the proposed algorithm is computed asfollows. Step (1) has the complexityO(KM). In each iteration,the user with the steepest RD curve slope checks all Msubcarriers for possible subcarrier reassignments. We denoteL as the number of iterations between Steps (2) and (3).The complexity of the proposed iterative SIMO anti-jammingcross-layer resource allocation algorithm is O(KM+LM).

TABLE 1. Parameters of the simulation.

V. SIMULATION RESULTSWe consider an uplink 16-subcarrier OFDMA video commu-nication system. The bandwidth of each subcarrier is 50 kHz.We assume MQAM, with M = 4, 8, 16, 32, 64, 128 or 256.The parameters are given in TABLE 1, and the same asin [19]. The jammers power and path loss model is assumedto be the same as the sender (desired signal).

In a time slot, a Group of Pictures (GOP) is transmitted.,The simulation result is the average of 500 times for each user.

We consider four schemes. All schemes have the SIMO anti-jamming mechanism in subsection IIB.

Scheme A (proposed, turbo code, anti-jamming resourceallocation, HARQ): SERt = 0.3. HARQ is used.The rate 1/2 turbo code is used. The number ofretransmissions is 3.

Scheme B (proposed, convolutional code, anti-jammingresource allocation, HARQ): SERt = 0.3. HARQ is used.The rate 1/2 convolution code is used. The number of retrans-missions is 3.

Scheme C (proposed, convolutional code, anti-jammingresource allocation, no HARQ): SERt = 0.1. The rate1/2 convolution code is used.

Scheme D (existing work [19]): convolutional code,original resource allocation without considering sin k,m,no HARQ, SERt = 0.1.

By HARQ,- we suppose that the SERt = 0.1 can beincreased to SERt = 0.3 without increasing the packet errorrate. This is checked in Fig. 3; Schemes A and B (SERt = 0.3,HARQ) have lower packet error probabilities than Scheme C(SERt = 0.1, no HARQ).

The average PSNR is defined as 10 log10255255MSE ,

the same as [19].

FIGURE 4. Average PSNR (video quality) vs. number of retransmissions,12 users, 16 subcarriers, average SNR = 18dB.

The average PSNR value without retransmission redun-dancy consideration is shown in Fig. 4. Scheme A andScheme B outperform Scheme C because the HARQ usesMRC to combine the original packet and retransmissionpackets in the receiver. Scheme B outperforms Scheme Cby 2.24.5 dB, and Scheme A outperforms Scheme Cby 2.64.8 dB. However, the HARQ introduces the redun-dancy and the redundancy should be computed and deductedfrom the PSNR gain.

The HARQ in layer 2 retransmits packets and it takesextra power (overhead). To quantize the overhead due toHARQ and allow fair comparison for non-HARQ and HARQschemes (the average overhead-adjusted PSNR is definedlater in (23)), the average accumulated redundancy due to

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retransmission is shown in Fig. 5. We define the averageaccumulated redundancy as

= 10 log10 (total/0), (22)

where total/0 is defined in Section II-E.In each time of retransmission, the turbo code retrans-

mits fewer packets than the convolution coded scheme. Thedifference between total of Scheme A (turbo code) andScheme B (convolutional code) increases as the number ofretransmissions increases. For example, Scheme A retrans-mits 100 and 80 packets at the first two retransmissions.Scheme B retransmits 180 and 120 packets at the first tworetransmissions. The total difference is 180 100 = 80 atthe first retransmission, and (180+120)(100+80) = 120 atthe second retransmission. Because total is the total numberof original and retransmitted packets (accumulated), the gapbetween Scheme A and Scheme B in Fig. 5 increases with thenumber of retransmissions.

FIGURE 5. Average accumulated redundancy vs. number ofretransmissions, SERt = 0.3, 12 users, 16 subcarriers, average SNR =18dB.

Based on the average accumulated redundancy in (22)and Fig. 5, the average overhead-adjusted PSNR for mea-suring video quality for non-HARQ and HARQ schemes isdefined as

g = PSNR (dB) (dB) (23)

In Fig. 6, we note that Scheme A is better than Scheme Bby more than 1dB due to the advantage of the turbo codeover the convolutional code. We also note that the numberof retransmissions (3) is a good tradeoff for the delay andoverhead-adjusted PSNR.

In Fig. 7, we compare four schemes for different num-bers of users and see the significant PSNR gap betweenthe proposed schemes (Schemes A, B, C) and the exist-ing work (Scheme D) due to considering the angle sin k,mbetween the desired signal and jammer channel vectorin the proposed anti-jamming cross-layer resource alloca-tion algorithm. Scheme C outperforms Scheme D by more

FIGURE 6. Average overhead-adjusted PSNR vs. number ofretransmissions, 12 users, 16 subcarriers, average SNR = 18dB.

FIGURE 7. Average overhead-adjusted PSNR vs. number of users,16 subcarriers, average SNR = 18dB.

FIGURE 8. Average overhead-adjusted PSNR vs. average SNR, 12 users,16 subcarriers.

than 11.3 dB in PSNR. The PSNR improves further whenwe add HARQ. For example, Schemes A and B outperformScheme C by 1.82.6 dB, when the average SNR = 18 dBand 12 users.

We also consider the average overhead-adjusted PSNR forvarious average SNRs in Fig. 8. The PSNR of Scheme A is

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larger than that of Scheme B by 4.3 dB in the lower averageSNR because turbo code is good at lower SNR. In the higheraverage SNR, we can see that the performance of Scheme Ais similar to that of Scheme B. The proposed Schemes A, B,and C outperform Scheme C by a large margin because weconsider the angle between the jammer channel vector andthe sender channel vector in the proposed cross-layer resourceallocation.

VI. CONCLUSIONThe proposed anti-jamming resource allocation crossing lay-ers 1, 2, and 5 for HARQ-based SIMO OFDMA videotransmission systems considers the angle between the senderchannel vector and the jammer channel vector in the antenna-spatial domain. Then we derive the new optimal condition forthe anti-jamming cross-layer resource allocation.

The simulation results show that the PSNR increasesby 11.3 dB when we consider the angle between the jammerchannel vector and the sender channel vector in the pro-posed cross-layer resource allocation. The PSNR improvesfurther by 1.8 dB (Scheme B, convolutional code), 2.6 dB(Scheme A, turbo code) when we add HARQ, when theaverage SNR = 18 dB and 12 users.

APPENDIX APROOF OF THEOREM IDifferently from [19], the derivation here considers theHARQ effect in layer 2 (in terms of ) and SIMO anti-jamming (in terms of sini ). In [20], anti-jamming capabilitiesare not considered, so it does not derive new results.

Assume Bopt1 and Bopt2 are the optimal allocation, and

assume Bopt1 and Bopt2 are the new allocation. If an

allocation is optimal, any reallocation will have a larger or thesame total distortions, and then

b1r1 + c1

+b2

r2 + c2

b1(r1 +1r1)+ c1

+b2

(r2 1r2)+ c2(A.1)

where 1r1 and 1r2 and the information rate change due tothe exchange of frequency band . There are two scenarios:Scenario 1: 1 > 0 or W1 >

1H 1 2

User 1 has a physical layer information rate increase due tothe extra frequency band . That is1r1 > 0 and1r2 > 0, andwe apply a reduction of fractions to a common denominatorto (A.1)

b1(r1 + c1)2 +1r1 (r1 + c1)

1r1

b2

(r2 + c2)2 1r2 (r2 + c2)1r2 (A.2)

When | | 0, 1riri+ci 0, we can ignore1ri (ri + ci). Thenwe get

b1(r1 + c1)2

1r1 b2

(r2 + c2)21r2 (A.3)

Here we can see that bi(ri+ci)2

is the application layer term,acting like weighting, and 1ri is the physical layer term.Next, we want to find lim

| |0

1r11r2

for the new band alloca-

tion; the first user gets Bopt1 and the second user getsBopt1 . P1, is the total power that the first user is goingto assign over frequency band . Because 0, we collectP1, uniformly from B

opt1 and redistribute it uniformly over

frequency band . W1 = P1 (f ) + 1|H1(f )|2 sin 1

is the water-filling level (signal level plus noise level) of the first userbefore reassignment, and W

1 is the water-filling level afterreassignment.

W1 P1,Bopt1 =

1

H 1 2 +

P1,| |= W

1 (A.4)

whereH 1 2 = H1 (f0 + | |2 )2 denotes the channel gain

over the frequency band , and f0denotes the left limit offrequency band .

We reorganize (A.4) for solving P1, and get

P1, =

(W1

1

H 1 2

)Bopt1 | || | +

Bopt1

= 1

Bopt1 | || | +

Bopt1 = | |1 if | | 0

1 = P1,/ | | (A.5)

Before band reallocation, the old rate for user 1 is:

Bopt1

log2(1+ P1(f ) |H1(f )|2 sin 1

)df ; after getting

band , the new rate is as follows, according to the powerredistribution in (A.4)

Bopt1

log2

1+ P1(f ) P1,Bopt1

|H1(f )|2 sin 1 df

+ | | log2

(1+

P1,| |

H 1 2) (A.6)

Then the rate difference (new-old) is

1r1

=

Bopt1

log2

1+

(P1(f )

P1,Bopt1 )|H1(f )|2 sin 1(

1+ P1(f ) |H1(f )|2 sin 1)

df + | | log2

(1+

P1,| |

H 1 2)

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lim| |0

1r11r2= lim| |0

Bopt1

log2

(1 P1, |H1(f )|

2 sin 1Bopt1 (1+P1(f )|H1(f )|2 sin 1))df + | | log2

(1+ P1,

| |

H 1 2)

| | log2(1+ P2,

| |

H 2 2) Bopt2

log2

(1+ P2, |H2(f )|

2 sin 2Bopt2 (1+P2(f )|H2(f )|2 sin 2))df

= lim| |0

Bopt1

ln

(1

1 | ||H1(f )|2 sin 1Bopt1 (1+P1(f )|H1(f )|2 sin 1)

)df + | | ln

(1+ 1

H 1 2)

| | ln(1+ 2

H 2 2) Bopt2

ln

(1+


)df

(A.10)

b1(r1+c1)2

ln (1+ 1 H 1 2) Bopt1


b2(r2+c2)2

ln (1+ 2 H 2 2) Bopt2

|H2(f )|2 sin 2Bopt2 (1+P2(f )|H2(f )|2 sin 2)2df 1 (A.12)

b1(r1+c1)2

ln (1+ 1 H 1 2) Bopt1


b2(r2+c2)2

ln (1+ 2 H 2 2) Bopt2

|H2(f )|2 sin 2Bopt2 (1+P2(f )|H2(f )|2 sin 2)2df= 0 < 1 (A.13)

=

Bopt1

log2

1 P1, |H1(f )|2 sin 1Bopt1 (1+ P1(f ) |H1(f )|2 sin 1)

df + | | log2

(1+

P1,| |

H 1 2) (A.7)

Similarly, for user 2, we get

P2, =

(W2

1

H 2 2

)Bopt2 | || | +

Bopt2

= 2

Bopt2 | || | +

Bopt2 = | |2 if | | 0 (A.8)

2 = P2,/ | |

1r2 =

| | log2

(1+ P2,

| |

H 2 2)Bopt2

log2

(1+ P2, |H2(f )|

2 sin 2Bopt2 (1+P2(f )|H2(f )|2 sin 2))(A.9)

We use LHopitals rule and get (A,10), as shown at the top

this page. Note that, by calculus

lim| |0

dd

ln

1 1 | | |H1(f )|2 sin 1Bopt1 (1+ P1(f ) |H1(f )|2 sin 1)

= lim| |0

1 |H1(f )|

2 sin 1Bopt1 (1+P1(f )|H1(f )|2 sin 1)1


= 1 |H1(f )|

2 sin 1Bopt1 (1+ P1(f ) |H1(f )|2 sin 1)We then get

lim| |0

1r11r2

=

ln(1+ 1

H 1 2) Bopt1

|H1(f )|2 sin 1Bopt1 (1+P1(f )|H1(f )|2 sin 1)1dfln(1+ 2

H 2 2) Bopt2

|H2(f )|2 sin 2Bopt2 (1+P2(f )|H2(f )|2 sin 2)2df(A.11)

We combine (A.3) and (A.11), and the optimal band andpower allocation algorithm should satisfy (A,12), as shownat the top this page.

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bi(ri+ci)2

ln (1+ i H i 2) Bopti

|Hi(f )|2 sin iBopti (1+Pi(f )|Hi(f )|2 sin i)i df

bj(rj+cj)2

ln(1+ j

H j 2) Boptj

|Hj(f )|2 sin jBoptj (1+Pj(f )|Hj(f )|2 sin j)j df

1 (A.14)

Scenario 2: 1 = 0 or W1 1

H 1 2

In this case, no power is allocated because W1 1H 1 2

and because of the water-filling principle in (17). In this case,1r1 = 0, 1r2 = 0. If we plug 1 = 0 into the numeratorof (A.12), as shown at the top of the previous page, we have(A.13), as shown at the top of the previous page.

Combining both scenarios, the optimal solution shouldsatisfy (A.12). This completes the proof of Theorem I,equation (14).

For a number of users>2, we deduce that, , the followingshould be satisfied for any user i 6= j, (A.14) as shown at thetop of this page.

The above derivation is different from that in [19] becausewe consider HARQ and the angle between the spatial channelvectors of the sender signal (user j) and the jammer signalsin j defined in Fig. 2. Therefore the derivation in [19] isa special case of ours when the jammer angle is 90 degrees(sini = 1).

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SHU-MING TSENG (M99) received the B.S.degree from National Tsing Hua University, Tai-wan, and the M.S. and Ph.D. degrees from PurdueUniversity, IN, USA, in 1994, 1995, and 1999,respectively, all in electrical engineering. From1999 to 2001, he was with the Department of Elec-trical Engineering, Chang Gung University, Tai-wan. Since 2001, he has been with the Departmentof Electronic Engineering, National Taipei Univer-sity of Technology, Taipei, Taiwan, where he has

been a Professor since 2007. He has authored 39 SCI journal papers, includ-ing 11 in the IEEE. His research interests include MU-MIMO, OFDMA,cross-layer optimization for video transmission, jamming resiliency, NOMAfor 5G, and network performance evaluation. He has been serving as anEditor of theKSII Transactions on Internet and Information Systems, indexedin SCI, since 2013.

YUNG-FANG CHEN (M98) received the B.S.degree in computer science and information engi-neering from National Taiwan University, Taipei,Taiwan, in 1990, the M.S. degree in electricalengineering from the University ofMaryland, Col-lege Park, in 1994, and the Ph.D. degree in elec-trical engineering from Purdue University, WestLafayette, IN, in 1998. From 1998 to 2000, he waswith Lucent Technologies, Whippany, NJ, wherehe was with the CDMA Radio Technology Perfor-

mance Group. Since 2000, he has been with the Faculty of the Department ofCommunication Engineering, National Central University, Taoyuan, Taiwan,where he is currently a Professor and the Chairman. His research interestsinclude resource management and signal processing algorithm designs forwireless communication systems.

PO-HSIANG CHIU received the M.S. degreein electronic engineering from the NationalTaipei University of Technology, Taipei, Taiwan,in 2017. He is currently with EtherWAN Systems,New Taipei, Taiwan.

HUNG-CHANG CHI received the M.S. degree inelectronic engineering from the National TaipeiUniversity of Technology, Taipei, Taiwan, in 2016.He is currently with DELTANetworks Inc., Taipei.

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