Bit Error Rate Analysis Of Jamming For Ofdm Systems

Bit Error Rate Analysis of Jamming for OFDM Systems Jun Luo*, Jean H. Andrian*, Chi Zhou** Department of Electrical and Computer Engineering, Florida International University ** Department of Electrical and Computer Engineering, Illinois Institute of Technology Emails: {jluo001, Jean.Andrian}@fiu.edu, [email protected]

*

Abstract The Bit Error Rate (BER) analysis of various jamming techniques for Orthogonal Frequency-Division Multiplexing (OFDM) systems is given in both analytical form and software simulation results. Specifically, the BER performance of Barrage Noise Jamming (BNJ), Partial Band Jamming (PBJ) and Multitone Jamming (MTJ) in time-correlated Rayleigh fading channel with Additive White Gaussian Noise (AWGN) has been investigated. In addition, two novel jamming methods — optimal-fraction PBJ and optimal-fraction MTJ for OFDM systems are proposed with detailed theoretical analysis. Simulation results validate the analytical results. It is shown that under the AWGN channel without fading, the optimal-fraction MTJ always gives the best jamming effect among all the jamming techniques given in this paper, while in Rayleigh fading channel the optimal-fraction MTJ can achieve acceptable performance. Both analysis and simulation indicate that the proposed optimal-fraction MTJ can be used to obtain improved jamming effect under various channel conditions with low complexity for OFDM systems.

1. Introduction Orthogonal Frequency-Division Multiplexing (OFDM) is a promising technology that enables the transmission of high data rate. The basic idea of OFDM is to use a large number of parallel narrow-band sub-carriers instead of a single wideband carrier to transport information. With its capability of adapting to severe channel conditions without complex equalization, OFDM can effectively provide broadband wireless communication in hostile multipath environments. Furthermore OFDM is robust against Inter-Symbol Interference (ISI) and fading caused by multipath propagation. Since OFDM is a very important candidate for the core technique of next generation wireless communication systems, it is necessary to evaluate its performance under intentional interference over fading channel. There are some works done in this area. In [2], the performance of OFDM communication in the presence of partial-band jamming is presented. The anti-jamming property of clustered OFDM has been investigated in [3], and [4] gives a detailed study about the effect of partial band jamming on OFDM systems. Despite of all the works mentioned, a comprehensive survey about the effects of different jamming techniques for OFDM systems has not been carried out. By comparing the Bit Error Rate (BER) performance of different jamming techniques, the most effective jamming technique can be identified under various channel

conditions. This is very critical for both jamming and antijamming applications for OFDM systems. This paper evaluates the BER performance of different jamming strategies including Barrage Noise Jamming (BNJ), Partial Band Jamming (PBJ) and Multitone Jamming (MTJ) in time-correlated Rayleigh fading channel with Additive White Gaussian Noise (AWGN). In addition, two novel jamming methods — optimal-fraction PBJ and optimal-fraction MTJ for OFDM systems are proposed with detailed theoretical analysis. The theoretical and simulation results show that the most effective jamming strategy for OFDM system is the optimal-fraction MTJ since it can make jamming effect better obviously through a simple way. The paper is organized as follows. In Section 2, a brief overview of OFDM system model is presented. Section 3 details the different jamming models and their analytical BER form in OFDM systems. Simulation results and related analysis are shown in Section 4. Finally, the concluding remarks are given in Section 5.

2. OFDM system and channel model The overview of OFDM system model is illustrated in Fig.1. In this paper, we use Binary Phase Shift Keying (BPSK) and Differential Binary Phase Shift Keying (DBPSK) as our signal mapping methods. Higher order modulation techniques can be used as well, but these two are sufficient for us to analyze the essence of the problem. When applying DBPSK to OFDM systems, Frequency Domain Differential Demodulation (FDDD) is used rather than Time Domain Differential Demodulation (TDDD) since FDDD outperforms TDDD in frequency-nonselective fading channel [5]. The Cyclic Prefix is used as Guard Interval to eliminate ISI between the data blocks since samples of the channel output affected by this ISI can be discarded without any loss relative to the original information sequence [1]. The channel is modeled as a flat-fading Rayleigh channel. For every sub-carrier in OFDM systems, its bandwidth is relatively small compared with the bandwidth of the channel, so it is reasonable to make this flat-fading assumption. Based on the modified sum-of-sinusoids method of Zheng [6], we construct a time-correlated flat-fading Rayleigh model, in which the channel has a Rayleigh-distributed envelope and uniform phase, and the two are mutually independent. We assume the system is coherent, so the phase can always be estimated perfectly. Hence we neglect the phase variation of the channel. Considering the jamming and the signal are both independently attenuated by the channel, we use two independent random variables to describe the jamming channel

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2D 2 Eb ) N0  E 2 N J

(6)

 D 2 Eb 1 exp( ) 2 N0  E 2 N J

(7)

PBPSK (D , E ) Q(

PDBPSK (D , E )

Since there are two Rayleigh random variables with the same variance V 2 , the average BER for BPSK and DPBSK can be expressed as ff

PBPSK Fig. 1. OFDM System Model power gain GJ and the signal channel power gain Gs , which are given as (1) GS D 2 (2) GJ E 2 where  and  are independent Rayleigh random variables with variances V S2 and V J2 respectively. Because jamming and signal are under the same channel environment, V S and V J can be regarded as the same value V .

3. The effects of various jamming for OFDM systems In this section we investigate several typical jamming techniques. For every jamming type, we first give the BER form under AWGN, then consider more complicated Rayleigh fading channel.

1) BNJ under AWGN Barrage Noise Jamming (BNJ) belongs to a broadband noise jamming form. In this case, the jammer interferes with the whole bandwidth by injecting a band-limited noise to the system. Its effect is the same as that of the AWGN, so the Power Spectrum Density (PSD) of total noise becomes: (3) PSDN N 0  N J where N0 is the noise PSD of complex AWGN and NJ is the PSD of complex BNJ. Since the OFDM system performs no differently from conventional serial systems under the AWGN [9], the BER for BPSK and DPBSK is given as: 2 Eb (4) ) PBPSK Q( N0  N J  Eb 1 (5) PDBPSK exp( ) N0  N J 2 where Eb is the average energy-per-bit of OFDM signal.

2) BNJ under Rayleigh fading channel with AWGN In Rayleigh fading channel, the effective energy-per-bit becomes GSEb and the effective PSD of the BNJ becomes GJNJ. Under the assumption that the time correlation coefficient of the channel is close to 1, the time-varying property of the channel will not affect the analysis of the differential modulation. After simplifying, we get the BER

³ ³ Q( 0 0

ff

2D 2 Eb D 2  E 2 DE ˜ ˜ ) exp( )dDdE N0  E 2 N J V 4 2V 2

(8)

D 2 Eb DE D 2  E 2 ) ˜ 4 ˜ exp( )dDdE (9) 2 V 2V 2 0  E NJ 00 Certainly, the infinite upper limit of integration should be replaced by finite approximated value in practice. PDBPSK

1

³³ 2 exp(N

3) PBJ under AWGN Partial band Jamming (PBJ) is modeled as additive Gaussian noise with its power focusing on a portion of the entire bandwidth of the system. This strategy is considered more effective than BNJ since the jammer can use more power to interfere with the certain specific bandwidth. We consider the best jamming scenario: The jamming signal bandwidth falls into that of the OFDM signal completely. The portion of jamming signal bandwidth can be described by [2] Wj (10) U Wsig where W j is the bandwidth of the jamming signal and Wsig is the bandwidth of the OFDM signal. To calculate the BER, we consider two types of frequency bands: the jammed frequency bands and the unjammed frequency bands. Given the average PSD of PBJ NJ , the effective PSD of PBJ in the first type of bands becomes N J U , and there is no jamming at all in the second type of bands. Combing those two cases with (4) and (5), the BER for BPSK and DBPSK under PBJ is given as 2 Eb 2 Eb (11) PBPSK ( U ) U ˜ Q ( )  (1  U ) ˜ Q( ) N0  N J / U N0  Eb E 1 U U (12) ˜ exp( )( ) ˜ exp( b ) PDBPSK ( U ) 2 2 N0  N J / U N0 Since (11) and (12) depend on the value of U , it is necessary to find the optimal jamming fraction U * so that the jamming effect is maximized. Assuming the background AWGN is small compared to PBJ and applying the following approximation for the Q function from [8]

Q ( x ) | exp( 

x2 ) /(1.64 x  0.76 x 2  4 ) 2

Eq. (11), (12) are transformed into  exp( SIR ˜ U ) PBPSK ( U ) U (1.64 2 SIR ˜ U  1.52 ˜ SIR ˜ U  4 )  U PDBPSK ( U ) exp( SIR ˜ U ) 2

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(13)

(14) (15)

where SIR represents Signal-to-Interference Ratio, which is equal to Eb / N J . The optimal jamming fraction U * can be obtained by maximizing (14) and (15) with respect to given SIR * UBPSK argmaxPˆBPSK(U)

U

for a (16)

U

* U DBPSK arg max PˆDBPSK (U )

(17)

U

(Jamming fraction constraint: 0 d U d 1 ) Let us take the partial derivative of (14) and (15) with respect to U and set them to 0 to obtain optimal jamming fractions. Here Newton-Raphson approximation is used to get numerical results. Like constrained control system, the optimal jamming fraction will saturate whenever the boundary constraints ( 0 d U d 1 ) are violated. In practice, the optimal values of jamming fraction can be generated offline based on different SIR, and then stored in hardware or software as a table. By looking up this table, the jammer can maintain optimal performance for every value of the SIR. In this paper, this special PBJ based on optimal jamming fraction table is named as optimal-fraction PBJ.

4) PBJ under Rayleigh fading channel with AWGN For the time-correlated Rayleigh fading channel, following the same steps as before, the average BER for BPSK and DPBSK becomes ff 2D2Eb DE D2  E2 2D2Eb (18) ) (1 U) ˜Q( )) ˜ exp( )dDdE (U ˜Q( P BPSK

³³

N0  E NJ / U 2

00

ff

PDBPSK

U

D Eb 2

00

0

J

2V

2

D Eb DE D  E 1 U (19) ) ˜ exp( )) ˜ exp( )dDdE 2 N0 V4 2V2

³³( 2 ˜ exp(N  E N / U) ( 2

V

N0

4

2

2

Fig. 2. Signal Space Model axis, we get AJ cos(I J )  Eb  VI1

(22)

SI1,r 2

AJ cos(I J )  Eb  VI1

(23)

where SI 1,r1 and SI1, r 2 represent the o

and VI1 is the AWGN V ’s

I1

over [0,2]. AJ and fJ are the amplitude and frequency, respectively. We assume that those q jamming tones are perfectly aligned with q sub-carriers of the OFDM system. Then the portion of jamming signal bandwidth is defined as (21) U q/M where M is the number of FFT points. After FFT in receiver block, in signal space, the jamming signal, which has fixed length AJ and random phase I J , is added to original signal o

( S1 or S 2 ) as a vector (Fig. 2), and AWGN V is another vector added to them. Projecting the compound signal onto I1

axis projection. Because the

Here we have two random variables: one is I J , which is uniformly distributed over [0,2S ] ; the other is VI1 , which satisfies the Gaussian distribution with N (0, N 0 2) . Now we A J cos( I J ) 

define Y

Eb ,

V I 1 and W X Y .

X

Then

Pr ( SI1,r1  0)

PBPSK _ MTJ

Pr (W  0)

(25)

The Probability Density Function (PDF) of cos() function is given in [7] as fZ (z)

­1 ° ®S °0 ¯

1

z  (1,1)

1  z2

(26)

The PDF of Y can be represented as

5) MTJ under AWGN

where I J is the random phase, which is uniformly distributed

axis projection of

error probabilities for S1 and S 2 are equal, only Pe s1 needs to be calculated. Hence the BER for BPSK with MTJ is given as (24) PBPSK_ MTJ Pe s1 Pr (SI1, r1  0)

(27)

1

fY ( y)

Multitone jamming (MTJ) divides its total power into q distinct, equal power, random phase tones. Every jamming tone can be modeled as (20) J (t ) AJ e j ( 2Sf J t  I J )

I1

received signals (corresponding to S1 and S 2 respectively),

2

Here we do not consider the optimization of jamming fraction, since this requires a complicated algorithm in a time-varying Rayleigh fading channel. It is not realistic to do so just for small improvement in jamming effect. Instead jamming fraction optimization table from previous section is used to obtain some improvement.

SI1,r1

SAJ 1  (

y  Eb 2 ) AJ

where y should satisfy E b  A J  y 

E b  AJ

Knowing the PDF of X, the PDF of W is f

fW ( w )

³

f X ( w  y ) f Y ( y ) dy

(28)

f E b  AJ

³

E b  AJ

1

SN 0

exp( 

(w  y) ) N0 2

1

SAJ

y  Eb 2 1 ( ) AJ

dy

Then AJ is the only unknown variable in (28), which can be obtained simply through the following equation

Eb (29) USIR Based on the result of (28), we can get PBPSK _ MTJ from (25) AJ

easily. Thus the BER for BPSK is given as

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PBPSK ( Eb , N 0 , U , SIR)

2 Eb ) N0

U ˜ PBPSK _ MTJ  (1  U )Q (

0

U ³ fW ( w)dw  (1  U )Q( f

(30)

2 Eb ) N0

If the AWGN is negligible, we can get ­U S PBPSK (Eb , U, SIR) = Pes1 = ° S ( 2  arcsin( USIR )) ®

USIR < 1

°¯0

(31) For DPBSK, let z(k-1) and z(k) be the reference and received symbol vectors respectively. The variable D is given as D Re(z(k ) z * (k 1)) Re(( AJ e

jIJ ( k )

o

 s(k )  V (k ))( AJ e

 jIJ ( k 1)

(32)

o *

 s (k 1)  V (k 1))) *

o

o

If D is less than 0, then a decision error is made. That is, the BER equals to Pr(D  0) when MTJ exists. However, the probability of D is difficult to calculate from (33), subsequently some approximations are necessary. For SIR >> SNR (Eb/N0), we can neglect some small items in (33), and get D | Eb  AJ Eb (cos(I J (k ))  cos(I J (k  1)))  Eb (VI1 (k )  VI1 (k  1))  AJ (cos(I J (k )  I J (k  1))) 2

(34) Dividing (34) by Eb yields D | Eb  AJ (cos(I J ( k ))  cos(I J (k  1)))  VI1 (k )  VI1 (k  1) 

2

Eb

(35)

(cos(I J (k )  I J (k  1)))

Compared with the case of coherent BPSK (22), there are five noise terms instead of two. Approximately, the MTJ is 2  1 / USIR times larger than that of BPSK and AWGN is 2 times larger than that of BPSK, which gives a simple way of getting differential modulation BER from coherent modulation BER Eq. (30). (36) SIR PDBPSK ( Eb , N 0 , U , SIR)

PBPSK ( Eb ,2 N 0 , U ,

(2 

1 ) USIR

ff

PBPSK

³³ (P

(D 2 Eb , N0 , U,D 2 SIR E 2 ))

BPSK

00

ff

PDBPSK

³³ (P

PBPSK ( Eb , N 0 , U ,

1 (2   0.6) USIR

DE D 2  E 2 ˜ exp( )dDdE (39) V4 2V 2

(D 2 Eb , N0 , U,D 2 SIR E 2 )

DBPSK

DE D 2  E 2 )dDdE (40) ˜ exp( 4 V 2V 2

where PBPSK (D 2 Eb , N 0 , U ,D 2 SIR E 2 ) is derived from (30), and when you calculate it, you should change all Eb and SIR to D 2 Eb , D 2 SIR E 2 correspondingly. Eq. (37) gives the value of PDBPSK (D 2 Eb , N 0 , U ,D 2 SIR E 2 ) . Here Eb and SIR should be

changed as well.

4. Simulation results and analysis In this section, the BER performance of different jamming techniques for OFDM system is evaluated by the means of software simulation. Based on the 802.11a standard [10], the main parameters used in the simulation are summarized as Table 1. In this table, to simplify the problem, we use 64 as the number of sub-carriers instead of 52 in the 802.11a standard. Hence the occupied bandwidth is changed from 16.6 MHz to 20 MHz correspondingly. Fig. 3 shows the comparison between simulation results and theoretical results of all non-optimal jamming types (BNJ, the fixed-fraction PBJ and the fixed-fraction MTJ) in the paper. In the simulation, every test is repeated 200-1000 times to eliminate the fluctuations caused by intrinsic random nature of the OFDM communication system. It is shown that the simulation results of all non-optimal jamming types are in

)

Table 1: Main parameters used in simulation

This equation is valid only for SIR >> SNR. From simulation, we found that when SIR is close to SNR, the simulation values of BER will deviate from theoretical values to some smaller values. In order to compensate this deviation, Eq. (36) was modified empirically to (37) SIR PDBPSK ( Eb , N 0 , U , SIR)

Similar as before, the average BER for BPSK and DPBSK for MTJ under Rayleigh fading channel with AWGN is

00

(33)

Re(( AJ e jIJ (k )  Eb  V (k ))( AJ e jIJ (k 1)  Eb  V * (k 1)))

AJ

Solving it with different SIR will generate MTJ jamming fraction optimization table of BPSK. For DBPSK, the optimal jamming fraction can be obtained from simulation results. The optimization tables of BPSK and DBPSK will be used by optimal-fraction multitone jammer to achieve optimal performance.

6) MTJ under Rayleigh fading channel with AWGN

where s(k ) and s (k  1) are transmitted constellations at time k and k-1. D is used by differential detector to decide which symbol was transmitted. Due to symmetry, we can assume a given phase difference zero to compute the error probability [1], so s(k ) and s (k  1) can be specified as Eb . Hence D Re(z(k ) z* (k 1))

which shows good results in the simulation. In MTJ, optimal jamming fraction should also be considered, so that we get the optimal-fraction MTJ. Again, assuming the background AWGN is negligible, from (31) following the same process as PBJ, we can get U* 1 S  0.5˜ SIR * (  arcsin( UBPSK ˜ SIR))  BPSK 0 (38) * * S 2 S UBPSK˜ SIR(1 UBPSK ˜ SIR )

)

Signal bit rate

20 MHz

Modulation scheme

BPSK/DBPSK

Number of sub-carriers

64

Cyclic prefix

0.8 us

FFT length

64

Channel model OFDM symbol period Jamming bandwidth

Rayleigh fading channel with AWGN

Doppler frequency Signal bandwidth

40 Hz 20 MHz

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3.2 us Depend on different jamming techniques

agreement with the analytical prediction perfectly under AWGN. On the contrary, in Rayleigh fading channel, there are some small deviations between simulation results and theoretical values. They are caused by precision errors of numerical integration (for all non-optimal jamming types) and equation approximation (only for DBPSK of MTJ). All these deviations are less than 10%, therefore they are acceptable. To verify the optimization process about PBJ and MTJ, optimal jamming fraction data is listed as Table 2, in which SNR is fixed to 20db and SIR is varied from -2db to 10db under AWGN. We show both analytical predictions and simulated values for PBJ and MTJ except MTJ for DBPSK, to which only simulated values are shown since precise theoretical equation is hard to obtain. Since 64-FFT is used in the proposed OFDM system, every U * has been rounded to the closest integer multiple of 1/64. In Table 2, the bold part is the analytical prediction and its right side is the corresponding simulated results. The biggest error between them is less than 5%, which validates the correctness of the analytical model. Fig. 4 shows the comparison between the optimal-fraction jamming and the fixed-fraction jamming of PBJ and MTJ. It is revealed that under AWGN only, the optimal-fraction jamming always gives the best jamming effect. On the contrary, this can not be promised in Rayleigh fading channel. In fact, in Fig. 4 (c), (d), (g) and (h), it is found that the best jamming effect can be achieved by just setting jamming fraction to 0.9 simply. Thus in deep fading channel, the jamming power should be distributed to the whole bandwidth to gain the best jamming effect. On the other hand, from Fig. 4, it is found that the optimal-fraction jamming also performs quite well even in Rayleigh fading channel. Therefore the optimal-fraction jamming can obtain optimal performance under AWGN (best case channel model) and relatively good performance under Rayleigh fading channel (worst case channel model). In general, the optimal-fraction jamming gives us a simple way to obtain good jamming effect under various channel conditions. Finally, optimal-fraction MTJ, optimal-fraction PBJ and Table 2: Optimal jamming fraction (SNR = 20dB) SIR (dB)

U *

U *

U *

U *

U *

U *

U *

PBJ BPSK (A1)

PBJ BPSK (S2)

PBJ DBPSK (A)

PBJ DBPSK (S)

MTJ BPSK (A)

MTJ BPSK (S)

MTJ DBPSK (S)

-2 62/64 62/64 1 1 1 1 1 -1 57/64 1 48/64 63/64 57/64 1 51/64 0 46/64 61/64 41/64 55/64 45/64 1 40/64 1 35/64 52/64 32/64 43/64 36/64 51/64 32/64 2 31/64 41/64 24/64 32/64 29/64 40/64 25/64 3 26/64 32/64 20/64 27/64 23/64 32/64 20/64 4 21/64 25/64 15/64 21/64 18/64 25/64 16/64 5 15/64 21/64 12/64 16/64 14/64 20/64 13/64 6 11/64 17/64 11/64 12/64 11/64 16/64 10/64 7 9/64 14/64 8/64 10/64 9/64 13/64 9/64 8 7/64 10/64 7/64 8/64 7/64 10/64 6/64 9 6/64 8/64 5/64 6/64 6/64 8/64 5/64 10 4/64 7/64 4/64 5/64 5/64 6/64 4/64 * (A1): Analytical * (S2): Simulated * This table is generated under AWGN channel without Rayleigh fading

BNJ are compared in Fig. 5. Under AWGN, the optimal MTJ clearly outperforms the other two for BPSK and DBPSK. When the channel condition degenerates to the worst case channel model — Rayleigh fading channel, BNJ performs best since BNJ is the special case of PBJ, whose jamming fraction equals to 1. From observation it is noticed that even BNJ is best in Rayleigh fading channel, its advantage over optimalfraction MTJ is not so obvious. So it is reasonable to believe that the optimal-fraction MTJ can be used to obtain improved jamming effect under different channel conditions with low complexity.

5. Conclusion The BER performance of different jamming strategies for OFDM system is investigated. Both analytical form and simulation values are given. In addition, two new jamming methods — optimal-fraction PBJ and optimal-fraction MTJ are proposed in this paper. Through analysis and simulation, it is shown that under the best channel condition (AWGN only), the optimal-fraction MTJ clearly outperforms other jamming types in the paper, and as the channel condition gets worse into deep fading, the optimal-fraction MTJ still shows competitive performance. The results of the experiment and the analysis of those results show that the optimal-fraction MTJ is a very effective jamming technique for OFDM system in various channel conditions.

REFERENCES [1] A. Goldsmith, Wireless Communications, Cambridge University Press, 2005. [2] R. F. Ormondroyd and E. Al-Susa, “Impact of multipath fading and partial-band interference on the performance of a COFDM/CDMA modulation scheme for robust wireless communications,” IEEE MILCOM, vol. 2, pp. 673-678, 1998. [3] H. Zhang and Y. Li, “Anti-jamming property of clustered OFDM for dispersive channels,” IEEE MILCOM, vol. 1, pp. 336-340, Oct. 2003. [4] J. Park, D. Kim, C. Kang and D. Hong, “Effect of partial band jamming on OFDM-based WLAN in 802.11g,” ICASSP 2003, vol. 4, pp. 560-563, Hongkong, China, 6-10 April 2003. [5] S. Lijun, T. Youxi and L. Shaoqian, “BER Performance of Frequency Domain Differential Demodulation OFDM in Flat Fading Channel,” GLOBECOM, vol. 1, pp. 1-5, 2003. [6] Y. R. Zheng and C. Xiao, “Improved models for the generation of multiple uncorrelated Rayleigh fading waveforms,” IEEE Communications Letters, vol. 6, no. 6, pp. 256-258, 2002. [7] A. Papoulis, Probability, Random Variables and Stochastic Processes, 3rd Edition, McGraw-Hill, New York, Feb. 1991 [8] N. Kingsbury, “Approximation Formulae for the Gaussian Error Integral, Q(x),” Connexions, June 7, 2005. [9] L. Hanzo, M. Münster, B. J. Choi, T. Keller, OFDM and MCCDMA for Broadband Multi-User Communications, WLANs and Broadcasting, Wiley-IEEE Press, September 2003. [10] IEEE 802.11a, “Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications: High-speed Physical Layer in the 5GHz Band,” supplement to IEEE 802.11 Standard, Sept. 1999.

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0

0

10

10

-1

-2

BER

BER

10

10

-1

10

-3

10

-4

10

-2

-2

0

2

4 SIR

6

8

10

10

-2

0

(a) BNJ under AWGN

2

4 SIR

6

8

10

(b) BNJ under Rayleigh fading channel

0

0

10

10

-1

BER

BER

10

-1

10

-2

10

-2

-3

10

\

-2

0

2

4 SIR

6

8

10

10

-2

(c) PBJ under AWGN ( is fixed to 0.5)

0

2

4 SIR

6

8

10

(d) PBJ under Rayleigh fading channel ( is fixed to 0.5)

0

0

10

10

-1

-2

BER

BER

10

10

-1

10

-3

10

-4

10

-2

-2

0

2

4 SIR

6

8

10

10

(e) MTJ under AWGN ( is fixed to 0.5)

: :

Fig.3:

Analytical BER of BPSK Analytical BER of DBPSK

-2

0

2

4 SIR

6

8

(f) MTJ under Rayleigh fading channel ( is fixed to 0.5)

Simulated BER of BPSK : Simulated BER of DBPSK :

Comparison between simulation results and theoretical values of all non-optimal jamming types (SNR is fixed to 10dB)

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10

0

0

10

10

-1

10

-1

-2

BER

BER

10

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-2

10 -3

10

-4

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-2

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2

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6

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-2

(a) PBJ under AWGN (BPSK) 0

4 SIR

6

8

10

8

10

0

10

-1

BER

BER

2

(b) PBJ under AWGN (DBPSK)

10

10

-2

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0

-2

-1

10

-2

0

2

4 SIR

6

8

10

10

(c) PBJ under Rayleigh fading channel (BPSK)

-2

0

2

4 SIR

6

4 SIR

6

(d) PBJ under Rayleigh fading channel (DBPSK)

0

0

10

10

-1

10

-1

-2

BER

BER

10

10

-2

10 -3

10

-4

10

-2

-3

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2

4 SIR

6

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-2

(e) MTJ under AWGN (BPSK)

10

0

-1

BER

BER

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-2

-2

2

(f) MTJ under AWGN (DBPSK)

0

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8

10

10

(g) MTJ under Rayleigh fading channel (BPSK)

0

2

4 SIR

6

8

10

(h) MTJ under Rayleigh fading channel (DBPSK) : Optimal  : =0.9

Fig.4:

-2

=0.1 : =0.5 :

Comparison between optimal-fraction jamming and fixed-fraction jamming of PBJ and MTJ (SNR is fixed to 10dB)

Authorized licensed use limited to: INDIAN INSTITUTE OF TECHNOLOGY MADRAS. Downloaded on May 28, 2009 at 21:22 from IEEE Xplore. Restrictions apply.

0

0

10

10

-1

10

-1

-2

BER

BER

10

10

-3

10

x

: Optimal-fraction MTJ under AWGN : Optimal-fraction PBJ under AWGN : BNJ under AWGN

-2

10

x

: Optimal-fraction MTJ under Rayleigh fading

: Optimal-fraction MTJ under Rayleigh fading

*

: Optimal-fraction PBJ under Rayleigh fading

*

: BNJ under Rayleigh fading

-4

10

-2

: Optimal-fraction MTJ under AWGN : Optimal-fraction PBJ under AWGN : BNJ under AWGN

: Optimal-fraction PBJ under Rayleigh fading : BNJ under Rayleigh fading

-3

0

2

4 SIR

(a) Comparison for BPSK

6

8

10

10

-2

0

2

4 SIR

6

(b) Comparison for DBPSK

Fig.5: Comparison of optimal-fraction MTJ, optimal-fraction PBJ and BNJ (SNR is fixed to 10dB)

Authorized licensed use limited to: INDIAN INSTITUTE OF TECHNOLOGY MADRAS. Downloaded on May 28, 2009 at 21:22 from IEEE Xplore. Restrictions apply.

8

10