Jamming Rejection Using FFH/MFSK ML Receiver Over ... - IEEE Xplore

IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 8, NO. 7, JULY 2013

Jamming Rejection Using FFH/MFSK ML Receiver Over Fading Channels With the Presence of Timing and Frequency Offsets Ly-Minh-Duy Le, Kah Chan Teh, and Kwok Hung Li

Abstract—The composite effect of hostile multitone jamming and partial-band noise jamming on bit-error rate (BER) performance of a fast -ary frequency-shift-keying system is studied over frequency-hopped Rayleigh fading channels in the presence of timing and frequency offsets. The maximum-likelihood (ML) diversity-combining method is employed to improve BER performance of the system. Analytical BER expression of the proposed ML receiver is derived. The analytical results, validated by computer simulation, show that the proposed ML receiver can suppress the composite hostile jamming more effectively than some existing conventional diversity-combining receivers. The ML receiver is also found to be robust against inaccurate estimation of the required side information. Index Terms—Fast frequency-hopped, frequency offset, jamming rejection, maximum-likelihood receiver, multitone jamming, partial-band noise jamming, Rayleigh fading, timing offset.

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[11], the authors only derived analytical expressions for some conventional diversity-combining receivers such as the linear-combining and product-combining receivers. The impact of channel estimation errors including the amplitude and phase errors on the BER performance of a multicarrier FH coherent binary phase-shift-keying system was studied in [14] over Rayleigh fading channels. In this paper, we study the composite effects of MTJ and PBNJ on an FFH/MFSK system for a more practical scenario where both timing and frequency offsets are present. Analytical BER expressions for the ML receiver, as opposed to conventional diversity-combining receivers, are derived. These expressions are validated by simulation results. The ML receiver structure is proposed and examined. The practical issues of timing and frequency offsets are considered. In addition, the sensitivity of system performance to imperfect side information is also examined. It will be shown that the proposed ML receiver can suppress MTJ and PBNJ more effectively than the linear-combining and product-combining receivers even when frequency and timing offsets are present. This paper is organized as follows. In the next section, the system model is described. Following that, analytical BER expressions for the ML receiver are derived. Section IV provides numerical results and discussions. Finally, conclusion is given in the last section.

I. INTRODUCTION

II. SYSTEM MODEL

Multitone jamming (MTJ) and partial-band noise jamming (PBNJ) are known to be two effective strategies in degrading the performance of a frequency-hopped (FH) communication system [1]. The frequency-hopping technique is commonly used for secure communications such as military applications due to its antijamming capability, low probability of detection, resistance to the near-far problem and robustness against fading [2]–[6]. For FH communication systems, the noncoherent -ary frequencyis the MFSK shift-keying (MFSK) modulation scheme, where modulation order, is often used because of simplicity of the receiver, its insensitivity to rapid phase variation in the received signal and efficient power amplification in the transmitter [7]–[9]. Recently, the composite effect of MTJ and PBNJ has been studied in [10] for a fast FH (FFH) MFSK maximum-likelihood (ML) receiver over Rayleigh fading channels and the receiver was assumed to have perfect knowledge of the time epoch and the carrier frequency. In [11], the authors examined this composite effect on the performance of an FFH/MFSK system over Rician fading channels. In addition, the impact of frequency and timing offsets on performance of communication systems has also been investigated in [11]–[13]. In [12], the authors considered the effect of these two offsets on the performance of an MFSK communication system over additive white Gaussian noise (AWGN) channels. Joo et al. [13] reported bit-error rate (BER) performance of FFH/MFSK systems over Rayleigh fading channels in the presence of these two offsets. The BER results for an FFH/MFSK system with frequency and timing offsets were presented in [11] under the composite effect of MTJ and PBNJ in a Rician fading environment. Note that in the analysis of

In FH communication systems, the available channel bandwidth is frequency-hopped bands. The transmitted signal subdivided into hops into one of FH bands pseudo-randomly according to the output from the pseudo-noise (PN) code generator. In this paper, we assume that the signal is transmitted through a Rayleigh fading channel and the received signal is contaminated by MTJ, PBNJ and AWGN simultaneously. The hostile single-tone per-band MTJ has the total jam, which is distributed over equal-power interfering ming power tones spreading randomly over the total spread-spectrum (SS) band. For width. The power of each single jamming tone is the single-tone per-band MTJ, the number of MTJ tones is always less than or equal to the number of FH bands. An equivalent power , spectral density (PSD) of the MTJ can be defined as is the total SS bandwidth. On the other hand, the jamming where unistrategy of the PBNJ is to distribute its finite jamming power of . Thus, each hopping symbol formly over a fraction will be jammed by PBNJ with probability , while the probability that [15]. In our analysis, we model the band is not jammed is . Here is the PBNJ as AWGN of equivalent PSD the average PSD over entire spread-spectrum bandwidth [16]. When and thus its variance in the PBNJ is present, its PSD equals to , where represents the bandwidth of jammed cell is each frequency slot. The signal-to-jamming power ratio of the system , where is the bit energy and is is defined as the equivalent PSD of both MTJ and PBNJ. We also define the power ratios of PBNJ and MTJ with respect to the total jamming power as , respectively, where and denotes the total jamming power. The block diagram of an FFH/MFSK ML receiver is presented in Fig. 1. The received signal is dehopped by a frequency synthesizer controlled by a PN code generator. Following that, the dehopped signal is passed through a bandpass filter (BPF) and then detected by a bank are square-law detectors. The square-law detector outputs of . then processed by the ML method to produce the resultant outputs and are coefficients of the ML receiver structure, The terms and which will be derived in Section III. Note that , where the diversity order of FFH systems, , denotes the number of hops per symbol. After that, these resultant outputs are

Manuscript received May 15, 2012; revised November 14, 2012 and April 01, 2013; accepted May 12, 2013. Date of publication May 20, 2013; date of current version June 19, 2013. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. C.-C. Jay Kuo. The authors are with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIFS.2013.2264053

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Fig. 1. FFH/MFSK ML receiver.

combined over hops to form the decision statistics before making the final decision. In FH communication systems, imperfect time and frequency synchronization could significantly degrade BER performance. In our analysis, we consider the timing and frequency offsets for the MTJ and the desired signal. For the PBNJ, only timing offset is considered as PBNJ is the noise jammer. It is assumed that both jammers and signal experience the same timing and frequency offsets. The offsets of the and , time epoch and received carrier frequency are denoted as respectively. It is also assumed that the desired signal and the MTJ undergo independent Rayleigh fading, as shown in Fig. 1. The dehopped can signal of the th hop in the interval be expressed as [11]

and random phase of the desired signal, respectively. Similar notations and are adopted for for and , the MTJ in time intervals , , are assumed to respectively. The random variables . We also assume that the average be uniformly distributed over and the average power of power of the desired user signal remain constant from hop to hop. Note that the MTJ and are the diffused power levels of the desired signal and MTJ, respectively.

(1)

(2)

denotes the desired signal, and denote the jamming tones in the time intervals and , respectively. Note that represents the PBNJ, is the hopping duration and is the noise term due to AWGN. and (either 1 or 0) indicate whether the In (1), the terms th hop is jammed by the MTJ or not in the time intervals and , respectively. Similarly, and (either 1 or 0) are defined as the PBNJ jamming states in the time intervals and , respectively. The terms , and represent faded amplitude, baseband frequency

Note that and are its in-phase and quadrature-phase components, which are given by

where

III. PERFORMANCE ANALYSIS In order to derive the probability density function (pdf) of , we express the faded amthe square-law detector output , and as , plitudes and , , , , , and are respectively. Note that independent Gaussian random variables with zero mean and unit including the composite variance. The square-law detector output effect of MTJ, PBNJ and thermal noise is given by

and


respectively. After some mathematical manipulations, the expressions of the in-phase and quadrature-phase components can be obtained as

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and

(11)

(3)

Following that, by substituting (8) and (9) into (7), the ML receiver output can be obtained as

and

(12) (4) and represent inderespectively. In (3) and (4), pendent zero-mean Gaussian random variables with variance , where is the variance of and are the normalized AWGN. Note that timing and frequency offsets [12]. The derived in-phase and quadrature-phase components in (3) and (4) are Gaussian random variables with zero mean and a common variance given by

and

where . The corresponding pdf expressions of

can be derived as

(13) After some algebraic manipulations, the characteristic function (CF) of can be shown to be (14)

(5) According to [17, p. 41–42], the distribution of square-law detector output is central chi-squared with two degrees of freedom. The can be expressed as corresponding conditional pdf expression of

Following that, the CF of the final decision statistics is given by (15) and are the PBNJ and MTJ jamming distribution patwhere terns, respectively, given by

(6) The resultant output of the ML receiver can be expressed as [18] (7) where represents the signal hop and From (6), we have

denotes the nonsignal hop.

(8) and

(9) where

and

.. .

.. .

..

.

.. .

.. .

.. .

..

.

.. .

The proposed ML receiver structure derived in (12) is simple, but it requires side information on the noise variance, PBNJ variance, power level of the MTJ, as well as timing and frequency offsets. The Gaussian noise variance can be estimated from a “noise-only” channel for noise power measurement [19], and the PBNJ variance and power level of the MTJ can be extracted from an energy detector [20], [21]. The timing offset can be estimated by using the ML epoch-estimation scheme proposed in [22], which is based on the multiple-hop combining of single-hop autocorrelation (SHAC) power sums. On the other hand, the frequency offset can be obtained from a nondata-aided carrier frequency offset estimator [23]. Following that, the average BER is given by (16)

(10)

where is the conditional probability of symbol error, conditioned . To obtain , we average the conditional probability of on

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symbol error and , that is

over all the possible combinations of

(17) where represents the probability of both MTJ and PBNJ jamming pattern, given by [11]

Fig. 2. Analytical and simulated worst-case BER results of the ML receiver , , SNR dB, and . with

(18) Note that denotes the conditional symbol error probability, conditioned on the jamming pattern described by matrices and , which can be obtained by

(19) where the pdf of the final decision statistic forming the inverse Fourier transform

can be obtained by per-

(20)

IV. NUMERICAL RESULTS AND DISCUSSIONS In this section, we present the worst-case BER results of the proposed ML receiver under the composite effect of MTJ and PBNJ with the presence of timing and frequency offsets. For a fair comparison, the total spread-spectrum bandwidth is fixed and the total number of for BFSK modulation case without FH bands is set to be . To obtain the worst-case BER value, we numeridiversity cally search through the number of MTJ tones and PBNJ fraction which gives the maximum BER. For subsequent numerical results,

BER values are plotted against SJR. We also compare BER performance of the ML receiver with that of two conventional diversity-combining receivers, namely, the linear-combining and product-combining receivers. In Fig. 2, both analytical and simulated BER results of the proposed ML receiver over Rayleigh fading channels are provided when both the timing and frequency offsets are present. The power ratios of the MTJ and , respectively. The close and PBNJ are set to be match in both results validates the analytical BER expressions derived in Section III. This figure also shows sensitivity of BER performance to the combined effect of timing and frequency offsets when the desired signal is jammed by both MTJ and PBNJ. It can be observed that this combined effect significantly degrades the system performance, i.e., up to one order of magnitude. In this figure, we also include simulated BER results of the linear-combining receiver with to show the effectiveness of the proposed ML receiver in suppressing the composite hostile jamming effect. Comparing BER curves of the and that of the linear-combining reML receiver with , we can observe that the former with ceiver (LCR) with is even better than the timing and frequency offsets of latter without these two offsets for moderate-to-high jamming power , which are of practical interest. When regions the combined effect of timing and frequency offsets becomes more se, or ), performance of the ML vere ( receiver is still slightly better than that of the LCR for strong jamming condition. Fig. 3 shows the benefits of using diversity for the FFH/MFSK ML receiver with the presence of composite jamming effect when timing and frequency offsets are present and absent . When the diversity level is increased, FFH systems can more effectively counteract the jamming and fading effects. However, at the same time, system performance degrades due to the noncoherent diversity-combining loss [17]. Therefore, there exists an optimum diversity order for the proposed ML receiver. When , this optimum diversity order is observed to be . Fig. 4 demonstrates whether performance of the proposed ML receiver is sensitive to either the timing or frequency offset. In general, increasing the timing or frequency offset degrades the system performance. This is because these two offsets cause the loss of orthogonality. In addition, the second source of degradation in system performance


Fig. 3. BER performance of the ML receiver with with different diversity orders and

, SNR

dB,

.

Fig. 4. Worst-case BER results of the ML receiver with dB, and . SNR

,

,

due to timing offset is that the imperfect timing synchronization leads to the signal attenuation in the detector matched to the incoming frequency [12]. It can also be observed that when the normalized offset ( and ) is less than 0.3, the effect of timing offset on the BER performance is more severe than that of frequency offset. However, the opposite observation is true when the normalized offset is greater than 0.3. In Fig. 5, we compare BER performance of the ML receiver with that of the linear-combining and product-combining receivers under , 0.5 and 1). Both the timing and different jamming conditions ( . It should be frequency offsets are present for the case of noted that BER results of the two conventional diversity-combining receivers are obtained via simulation. When the jamming power is high, it can be seen that the BER curve under the composite jamming effect lies between the BER curves under one type of jamming only. Moreis obviously over, BER performance of the ML receiver with . Thus, it can be concluded that the probetter than that with posed ML receiver is more effective in mitigating MTJ than PBNJ. This is because each MTJ tone is basically a sinusoidal waveform and it is

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Fig. 5. Worst-case performance comparisons among various receivers with , , SNR dB, with different jamming conditions.

Fig. 6. Worst-case BER results of the ML receiver with dB, , and . SNR

,

,

easier for the proposed ML receiver to estimate and mitigate the MTJ as compared to that of the PBNJ which is Gaussian noise in nature. As expected, we can observe from Fig. 5 that the proposed ML receiver always outperforms the conventional receivers for all jamming conditions. The improvement in system performance achieved by using this ML scheme can be as large as two orders of magnitude when the desired signal is jammed by MTJ only. Hence, it is interesting to examine . the BER performance of the ML receiver with In Fig. 6, we investigate the combined effect of timing and frequency offsets on BER performance of the proposed ML receiver when the desired signal is contaminated by MTJ only. The system parameters are , , , , . We can obset to be serve that the BER curves are almost flat throughout the range of SJR levels for all offset values. It can be concluded that the ML receiver can almost completely remove the MTJ regardless of whether offsets are present or not. Lastly, we study the sensitivity of system performance to imperfect side information in Fig. 7. Numerical results with imperfect side information are obtained via simulation. From Fig. 7, it confirms

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Fig. 7. Worst-case BER results of the ML receiver with , , dB, , , and with imperfect side information on SNR parameters , .

that performance of the proposed ML receiver is robust against inaccuracy in estimation of the required side information. V. CONCLUSION The composite effect of hostile MTJ and PBNJ, as well as timing and frequency offsets on the performance of an FFH/MFSK system employing ML diversity-combining method has been studied over Rayleigh fading channels. Based on the characteristic function approach, analytical BER expressions for the ML receiver have been derived. Analytical results have been validated by simulation results. Although the ML receiver requires side information, it has been shown that its BER performance is not sensitive to inaccuracy in estimation of the required side information. Our analysis shows that the proposed ML receiver is more effective in suppressing MTJ than PBNJ. Moreover, the ML receiver has been found to give significant advantages over other existing diversity-combining receivers in mitigating the composite effect of MTJ and PBNJ.

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