Hybrid DS/FFH Spread-Spectrum: A Robust, Secure. Transmission Technique for Communication in Harsh. Environments. Mohammed M. Olama1, Xiao Ma2, ...
The 2011 Military Communications Conference - Track 5 - Communications and Network Systems
Hybrid DS/FFH Spread-Spectrum: A Robust, Secure Transmission Technique for Communication in Harsh Environments Mohammed M. Olama1, Xiao Ma2, Teja P. Kuruganti1, Stephen F. Smith1, and Seddik M. Djouadi2 1
2
Computational Sciences and Engineering Division Oak Ridge National Laboratory Oak Ridge, TN 37831
Abstract—Spread-spectrum modulation techniques have been adopted for many current and future military communication systems to accommodate high data rates with high link integrity, even in the presence of significant multipath effects and interfering signals. A more recent synergistic combination is a direct-sequence spread-spectrum (DSSS) signaling with the use of integrally coordinated frequency hopping (FH) and/or timehopping (TH) modulation, generically dubbed hybrid spreadspectrum (HSS). A highly useful form of this transmission scheme for many types of command, control, and sensing applications is the specific code-related combination of standard DSSS modulation with "fast" frequency hopping (FFH), wherein multiple frequency hops occur within a single data-bit time. In this paper, detailed error-probability analyses are performed for a hybrid DS/FFH system over standard Gaussian and fading-type channels, progressively including the effects from wide-band, partial-band, and follow-on jamming, multi-user interference and/or varying degrees of Rayleigh and Rician fading. In addition, a simulation-based study of the DS/FFH performance is performed and compared to several forms of existing standard DSSS and FHSS wireless networks. The parameter space of HSS is also explored to further demonstrate the adaptability of the waveform for varied harsh RF signal environments. Keywords- Hybrid spread spectrum; direct sequence; frequency hopping; wide-band jamming; multi-user interference; Rayleigh/Rician fading; Monte Carlo simulation
I.
INTRODUCTION
Reliable, secure, affordable communications is an essential component in any distributed sensing or informationdistribution system. In recent years there has been a great interest in using spread spectrum techniques for military communications in addition to their use in commercial applications. Present-day commercial off-the-shelf hardware, while beginning to be available for the two lower-frequency ISM bands (915 MHz, 2.45 GHz), in either direct-sequence or frequency-hopping formats, is neither compact nor inexpensive. Spread-spectrum systems offer the flexibility of immediate (domestic) license-free operation in four distinct frequency bands and can be deployed in several other (military) bands to accommodate high data rates with high link integrity (i.e., low error rates), even in the presence of significant multipath effects and interfering signals. New opportunities
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Electrical Eng. and Computer Science Department University of Tennessee Knoxville, TN 37916
like wireless local area networks, operational communication networks, and digital cellular radios have created the need for research on how spread-spectrum systems can be optimized for the most efficient use in these environments [1-3]. A further requirement is for high wireless signal security, especially in military applications; HSS is uniquely suited for such needs. A more recent synergistic combination is a direct-sequence spread-spectrum (DSSS) signaling with the use of integrally coordinated frequency-hopping (FH) and/or time-hopping (TH) modulation, generically dubbed hybrid spread-spectrum (HSS) [4]. A highly useful form of this transmission scheme for many types of command, control, and sensing applications is the specific code-related combination of standard DSSS modulation with "fast" frequency hopping (FFH), denoted hybrid DS/FFH, wherein multiple frequency hops occur within a single data-bit time. Specifically, the most significant benefit to FFH is that each bit is represented by chip transmissions at multiple frequencies. If one or more chips are corrupted by multipath or interference in the RF link, statistically a majority should still be correct. Indeed, with suitable error detection, if even one chip is correct, the original data bit can still be recovered correctly. Standard or "slow" frequency hopping (SFH), in contrast, transmits at least one (and usually several data bits in each hopping interval). A thorough analysis of hybrid systems, emphasizing the effect of FFH, is not well investigated in the literature since fast frequency hopping rates were limited by the technology of frequency synthesizers. The work in this paper extends the one in [5, 6] from a DS system to a hybrid DS/FFH system in addition to taking jamming impacts into consideration. In [7], the performance of a SFH system is considered. In [8, 9], the performance of a DS/SFH system over an AWGN channel and multi-user interference is considered. The performance of an FFH system over fading channels is examined in [10], and extended in [11] to include the effects of partial-band noise jamming. Although [12, 13] computed the error probability of DS/SFH under jamming tones in both AWGN and Rician fading channels, only a single user was considered. In this paper, detailed error-probability analyses are performed for a hybrid DS/FFH system over standard Gaussian and fading-type channels, progressively including the effects
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from wide-band, partial-band, and follow-on jamming, multiuser interference and/or varying degrees of Rician fading. In addition, a simulation-based study of the DS/FFH performance is performed and compared to several forms of existing standard DSSS and FHSS wireless networks. The parameter space of HSS is also explored to further demonstrate the adaptability of the waveform for varied harsh RF signal environments. II.
where the nonnegative real parameter k is the Rician channel coefficient for the k th user; k ( , t ) is a zero-mean complex Gaussian random process that represents the equivalent lowpass time varying impulse response for the fading channel [6]. The covariance function for the fading process in a WSSUS channel is [15, 16] k ( , ; t , s)
SYSTEM MODEL
Assume there are K users in the whole system. For the k th user, the transmitted signal is represented by:
sk t 2Pbk t ak t cos 2 f c f hk t t
(1)
[16], where the covariance function k (0, t s) is defined as
|t | 1 T , | t | Tc k (0, t ) otherwise 0,
carrier frequency, { f hk (t )} denotes the hopping frequency of the k th user, the data signal bk (t ) is a sequence of statistically independent, unit amplitude, positive and negative rectangular pulses of duration Tb , and ak (t ) is the code waveform for the
a
n
k n
pTc (t nTc ),
where {ank } is the discrete periodic signature sequence assigned to the k th user and p (t ) is a rectangular pulse that starts at t 0 and ends at t . Consider M frequency hopping channels with L (assume L is odd) hops per bit. Let T Tb / L denote the duration of each hop and Tc Tb / NL denote the chip duration for PN sequence, where N is the period of the PN sequence and it is assumed to be odd. Denote the bandwidth of DS by WDS . Also assume there is a wideband jamming with bandwidth WJ . The jamming band corrupts W hopping channels fully and another one channel partially (let WJp be the part of the channel affected by the jamming). The fading channel considered here is modeled as a general wide-sense-stationary uncorrelated scattering (WSSUS) channel [5]. Following [6, 14, 15], the received signal can be written as
Similar to [17], the time delays and data symbols for the k th user are modeled as mutually independent random variables which are uniformly distributed on [0, T ] and {1, 1}, respectively. We also assume i 0 when considering the output of the k th ( k i ) correlation receiver.
III.
For each user k , the other K 1 users are considered as interference. Three different situations may occur in one hop:
k 1
1)
j users out of K 1 jump into the same hopping channel of user k and no jamming corrupts the channel.
2)
j users out of K 1 jump into the same hopping channel of user k and jamming fully corrupts the channel.
3)
j users out of K 1 jump into the same hopping channel of user k and jamming partially corrupts the channel.
(2) where J (t ) and n(t ) represent the jamming term and AWGN term, which have two-sided spectral densities N J / 2 and N0 / 2, respectively; and
(3)
ERROR PROBABILITY ANALYSIS
In this section, we first investigate the error probability for one hop, and then we employ majority voting to compute the overall error probability for one bit.
K
(5)
(n ) N , n is a positive integer less than N , 0 1 and (Tc )1T [6].
y(t ) Re{rk (t k ) exp{2 ( f c f hk (t ))(t k )}} J (t ) n(t )
rk (t ) k k ( , t ) 2 Pbk (t )ak (t )d 2 Pbk (t )ak (t )
(4)
In this paper, we focus on one class of WSSUS channels known as time-selective fading channels [15] and its covariance function as given by k ( , t s) k (0, t s) ( )
where P is the common transmitted signal power, f c is the
k th user in DSSS and is given as ak (t )
1 E{ k ( , t ) k* ( , t )} k ( , t s) ( ) 2
The error probability Pk of one hop for user k can be computed as:
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where l 1 for l n and n ; i (l ) Ri (l 1) Ri (l ), and l (a) N (l al ), i ,k (l ) i (l ) Rk (l ),
K 1
Pk Pk ( j users ) j 0
N 1
K 1
{Pk ( j users, no jam)
(6)
j 0
Pk ( j users, partial jam)} which is equivalent to K 1
Pk {P( j users, no jam) P k ( | j users, no jam) j 0
P( j users, full jam corrupts) P k ( | j users, full jam) P( j users, partial jam) P k ( | j users, partial jam)}
(7) From the problem formulation, we can obtain:
K 1 1 1 P( j users, no jam) 1 j M M j
K 1 j
K 1 1 1 P( j users, full jam) 1 j M M j
l 1 N
N 1
R (l ) R (l 1).
l 1 N
i
k
Ri (l ) is the usual
aperiodic autocorrelation function for the PN sequence.
Pk ( j users, full jam)
j
mi , k 2 Ri (l ) Rk (l )
M W 1 M
K 1 j
K 1 1 1 P( j users, partial jam) 1 j M M
Ri (l ) Ru 1
1
( N 1) 2 ln(
4N
), l 0. Plugging them back
into I kj and assuming k as a constant for simplicity, thus
I kj I j
1 M
The error probabilities for each case of jamming over Rician fading channels are discussed next. A. Case 1: No Jamming When there is no jamming, the error probability for BPSK modulation is given by [18]
2 2 1 2 1 ( 1) N 2 N 3N 2
2 2 j 2 2 5 2 4 3 13 2 N Ru NRu N N N (n 1) Ru 3 6 3 3 N4 17 13 4 (n 1) Ru2 n(n 1) Ru2 Ru2 ( N n)(1 2 2 ) 6 6 3 2 2 1 4 j (2 N 4 Ru ( N 1)) 2 Ru2 ( 2 ) 2 3 6N 3 (11)
(8)
1 P k ( | j users, no jam) Q NSR / 2 I k j
2
we get an upper bound on I kj as:
W M
K 1 j
In this paper, we employ a maximum-length sequence (MLS) as the signature sequence. However, there is no closedform expression for MLS aperiodic autocorrelation function, which means we cannot compute (10) explicitly for a general MLS of length N unless we exactly know the specific sequence code used. Actually, two different MLS codes with the same length will have different aperiodic autocorrelation functions. Therefore we consider in this work an upper bound on MLS’s aperiodic autocorrelation function derived in [19] to compute an upper bound on the error probability of the HSS system. From [19], we have and Ri (0) N
B. Case 2: Full Jamming (9)
When jamming fully corrupts the user k ’s channel, the error probability for BPSK is given as:
where I kj is the interference to signal ratio introduced by the other users hopping in user k ’s channel; NSR N0 / 2PT is the noise to signal ratio. Following the statements in [6, 17], I kj is computed as [6]:
I kj
2 k2 1 2 1 ( 1) N 2 N 3N 2 2 i 1, i k N j 1
2 l
2
2 i 4
R (l ) R (l ) (1/ 2) l
i
k
l
[ i , k (l ) k ,i (l )]l (2 / 3)
j 1
1 mi , k 3 6 N i 1, i k
(12)
where JSR N J / 2PT is the jamming to signal ratio.
n
l 0
1 P k ( | j users, full jam) Q NSR / 2 JSR / 2 I k j
(10)
i (l ) k (l )l (3 / 4) 3
3 l
C. Case 3: Partial Jamming When jamming partially corrupts the user k ’s channel, the error probability includes two portions: one is the part of the channel corrupted, and the other is the uncorrupted part. Let q WJp / WDS denote the fraction of the channel jammed. Then the error probability for the BPSK case is given as:
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q P k ( | j users, partial jam, corrupted portion)
(13)
(1 q) P ( | j users, partial jam, uncorrupted portion) k
where P k ( | j users, partial jam, corrupted portion) 1 Q NSR / 2 JSR / 2 I k j
(14)
and P k ( | j users, partial jam, uncorrupted portion) 1 Q NSR / 2 I k j
(15)
Based on the arguments above, the error probability per hop, Pk , is obtained. Without loss of generality, we assume the Rician channel coefficients for all users are equal, i.e. k , then, for simplicity, Pk can be represented as P . To calculate the error probability PE for one bit, we employ the majority voting decision scheme given as:
PE
L d Ld ( P ) (1 P ) d L 1 d L
2
(16)
Due to the monotonicity of Q() , using (11) provides an upper bound on Pk and thus an upper bound on PE . IV.
NUMERICAL RESULTS
In the previous section, we investigated a probabilistic approach to compute the bit error rate (BER) of a hybrid DS/FFH system over time-selective fading channels. In this section, we present numerical results to evaluate the performance of a hybrid DS/FFH system and compare it with the other spread-spectrum systems. First, we demonstrate the performance over Rician time-selective channels as investigated in Section III. Then we demonstrate the performance over frequency-selective channels using a systemlevel simulation model approach.
example are: total number of users is K = 100; number of hops per bit is L = 5; number of frequency hopping channels is M = 30; period of PN sequence in DSSS is N = 127; jamming-tonoise ratio (JNR) is 13 dB; number of channels fully jammed is 5; Rician channel coefficient 0.1 (represents the channel fading part); channel covariance function scaling factor 10.8 ; and the portion of the channel partially corrupted is 0.4. The parameter space of HSS system is explored to demonstrate its effectiveness under different conditions and scenarios. In the following analysis, we successively vary one parameter in the reference system model while fixing the other parameters. Figure 1 shows the effect of different number of continuously transmitting users (multi-user interference) on the performance of a hybrid DS/FFH system. Figure 2 demonstrates the DS/FFH performance for different jamming to noise ratios (JNRs), and Figure 3 demonstrates the performance for varying number of fully jammed channels. It can be noticed from Figures 2 and 3 that under high SNRs the performance gap reduces for different JNRs and different numbers of fully jammed channels. Figure 4 demonstrates the DS/FFH performance for different numbers of hops per bit. Notice that the performance of the DS/FFH system is superior to that of the DS/SFH system (represented by the 1 hop/bit case). Also notice the high improvement in performance at high SNRs when increasing the number of hops per bit. This reveals the effectiveness of the employed majority logic voting (hard decision) scheme at high SNRs. Figure 5 demonstrates the DS/FFH performance for different numbers of available hopping channels. Increasing the number of hopping channels reduces the likelihood of hits from other users using the same spreading PN code, and therefore enhances the performance. Figures 6 and 7 demonstrate the DS/FFH performance over varying degrees of Rician fading in the channels. Figure 6 illustrates how the performance deteriorates with increasing the fading component in the Rician channel represented by the parameter . Figure 7 shows that the channel covariance function scaling factor, , can improve the overall performance when it is smaller.
A. Time-Selective Channels In this section, the performance of a hybrid DS/FFH system is evaluated over Rician time-selective fading channels, progressively including the effects from wide-band and partialband jamming, multi-user interference and varying degrees of Rician fading. The performance measure is the upper bound of BER described in (16) by employing (11). The parameters of the reference system model considered in this numerical
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-1
10
80 users 100 users 120 users 140 users
-2
10
Error Probability
P k ( | j users, partial jam)
-3
10
-4
10
-5
10
5
10
15
20
SNR(dB)
Figure 1. Performance of a hybrid DS/FFH system. Effect of different number of users (multi-user interference).
-1
-1
10
10
JNR=10dB JNR=13dB JNR=14.7dB JNR=16dB
50 hopping channels 40 hopping channels 30 hopping channels 20 hopping channels
-2
10
-2
Error Probability
Error Probability
10
-3
10
-3
10
-4
10
-5
10
-4
10
5
10
15
20
5
10
-1
-1
10
10 2 channels 4 channels 6 channels 8 channels
fully fully fully fully
=0.1 =0.3 =0.5 =0.7
jammed jammed jammed jammed
-2
-2
10
10 Error Probability
Error Probability
20
Figure 5. Performance of a hybrid DS/FFH system. Effect of different number of available hopping channels.
Figure 2. Performance of a hybrid DS/FFH system. Effect of different jamming-to-noise ratios (JNRs).
-3
10
-3
10
-4
10
15 SNR(dB)
SNR(dB)
5
10
15
-4
10
20
SNR(dB)
5
10
15
20
SNR(dB)
Figure 6. Performance of a hybrid DS/FFH system. Effect of different Rician fading channel parameters.
Figure 3. Performance of a hybrid DS/FFH system. Effect of different number of fully jammed channels.
-1
-1
10
10
=10.8 =21.6 =32.4 =43.2
-2
10
-2
Error Probability
Error Probability
10
-3
10
-3
10 7 hops/bit 5 hops/bit 3 hops/bit 1 hop/bit
-4
10
-4
-5
10
5
10
15
10
20
5
10
15
20
SNR(dB)
SNR(dB)
Figure 7. Performance of a hybrid DS/FFH system. Effect of different Rician fading channel parameters.
Figure 4. Performance of a hybrid DS/FFH system. Effect of different number of hops per bit.
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B. Frequency-Selective Channels Performance analyses for the different spread-spectrum systems (DS, SFH, FFH, DS/SFH, and DS/FFH) over frequency-selective fading channels are presented in this section. Our analysis technique is based on a system-level simulation model approach with an equal-bandwidth constraint. The performance is represented by the BER and computed using Monte Carlo simulations. Due to page limitations, we present in this paper only a single scenario that demonstrates performance results for a two-path Rayleigh fading communication environment and 5 users. The first path has zero delay and a Rayleigh-distributed gain with parameter 0.7, and the second path has a propagation delay of 0.3 s and a Rayleigh-distributed gain with parameter 0.4. A maximallength code is used as the PN spreading code and coherent detection is assumed. We also assume an equal-bandwidth constraint for all spread-spectrum systems. The DS system is simulated for a spreading factor (SF) of 16, SFH with 16 hopping frequencies and 4 bits/hop, FFH with 16 hopping frequencies and 4 hops/bit, and hybrid DS/SFH and hybrid DS/FFH are simulated with 4 hopping frequencies with a 16-chip PN sequence. It can be observed in Figure 8 that the hybrid DS/FFH system outperforms the other spread-spectrum systems. The hybrid DS/FFH system is preferred over the other systems because of its unique advantages like the better spreading properties gained by frequency hopping and better multipath rejection via the direct-sequence modulation.
Numerical results exploring the parameter space of the HSS system have also been presented to demonstrate its effectiveness under different conditions and scenarios. The detailed security aspects of HSS signals will be analyzed in a future paper. ACKNOWLEDGMENT Oak Ridge National Laboratory is managed by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the U.S. Department of Energy. REFERENCES [1]
[2] [3]
[4] [5]
[6]
[7]
0
10
[8] -1
10
[9] -2
10
[10] -3
BER
10
[11]
-4
10
-5
10
2-Path Rayleigh BPSK DS SFH FFH Hybrid DS-SFH Hybrid DS-FFH
-6
10
-7
10
0
1
2
3
4
[12]
[13] 5 SNR
6
7
8
9
10
[14] [15]
Figure 8. Performance of a two-path Rayleigh hybrid DS/FFH system. Performance comparison.
V.
[16]
CONCLUSION
[17]
In this paper, the performance of a hybrid DS/FFH system over Rician and Rayleigh fading channels was considered. We derived the average BER for a hybrid DS/FFH system that includes the effects from wide-band and partial-band jamming, multi-user interference and/or varying degrees of Rician fading.
[18] [19]
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