A Multicarrier CDMA Based Low Probability of Intercept Network

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1 A Multicarrier CDMA Based Low Probability of Intercept Network Sayan Ghosal Devendra Jalihal Giridhar K. Abstract The need for covert communication in tactical battlefields has developed the ideas of low probability of intercept (LPI) networks. Spread spectrum communication is used for LPI communication. Multicarrier CDMA is a new type of spread spectrum technique that has been developed in recent years. Most of the works in MC-CDMA are focused on finding out BER performance of it when different users share the same time and spectral ranges. But, LPI performance of MC- CDMA is not explored much. In this paper we have focused on understanding the LPI property of MC-CDMA. We have found out that increasing spreading factor and application of forward error control coding improve LPI property of MC-CDMA based wireless networks to a great extent. I. INTRODUCTION Low probability of intercept (LPI) and anti-jamming (AJ) are major aims in communication in tactical battlefields. A group of soldiers having wireless nodes in a region form a wireless network. Our aim is to make their communication undetectable by any enemy interceptor present in nearby location. In frequency hopping code division multiple access (FH-CDMA) [1] the center frequency of a relatively smaller bandwidth signal is hopped pseudo randomly over a large transmission bandwidth. In military communication systems, FH-CDMA is attractive because it has good anti-jamming property [], [3]. But, concentrating transmit power over a smaller hop bandwidth increases detectability. On the other hand, spreading the bandwidth improves the low probability of intercept (LPI) property of a network. Multicarrier spread spectrum communication [4], [5], [6] has been proved to be an attractive technique in recent years. Mainly, two types of multicarrier spread spectrum schemes have been developed. First is Multicarrier CDMA (MC-CDMA), second is Multicarrier direct sequence CDMA (MC-DS-CDMA). In MC-CDMA spreading is done in frequency domain while MC-DS-CDMA does it in time domain. For slowly varying fading channels, in order to get sufficient time diversity in MC-DS-CDMA we have to use a long spreading sequence. The decision on each bit is taken only after receiving all the chips of duration T c. Thus, in MC-DS-CDMA we have to store all the information chips till the end of symbol time T s. This requirement of large memory makes the receiver structure complex. On the other hand, in MC-CDMA performance depends on the frequency diversity of the system. Here, one chip time T c is the same as the Data in Spreading Bandpass Filter Serial To Parallel RF carrier Fig. 1. ADC IFFT Transmitter OFDM block guard removal Receiver Cyclic Extension OFDM block FFT MC-CDMA transmitter and receiver DAC RF carrier combiner Data symbol time T s. At the end of each symbol time, decision on one bit is taken. Therefore, long overheads are not created. For, this reason we have proceeded with MC-CDMA for spreading. Although a quantitative analysis of anti-jamming is not discussed in this paper, we have used a combination of FH-CDMA and MC-CDMA to achieve both anti-jamming and anti-detection property respectively. In order to measure LPI quantitatively we have taken radiometers [7], [8] as standard models for interceptors. In section 1 we have given brief introduction to the combination of FH-CDMA and MC-CDMA, radiometers. In section we introduce necessary background for detectability models as developed in [9]. Using the ideas and methods that have been mentioned in section 1 and we carry out quantitative measurement of LPI of the hybrid scheme of FH-CDMA and MC-CDMA in section 3. Results show that MC-CDMA has a very good scope in the field of LPI wireless networks. A. A Hybrid of MC-CDMA and FH-CDMA A schematic diagram of MC-CDMA transmitter and receiver is shown in Fig. 1. After combining with a hopping pattern, the resulting spectrum with time for a single user is illustrated in Fig.. In Fig. and are the resulting

2 Frequency 1111 T c f d Time Z T1 (.) Wideband radiometer (.) (.) o/p OR NX k= o/p Fig.. T hop Spectrum of combination of MC-CDMA and FH-CDMA (.) Channelized radiometer bandwidths of the system after applying hopping and for MC- CDMA without hopping respectively. f d is the OFDM sub carrier separation, T c is one chip interval. T 1 is the total time over which data is transmitted. Each small time-frequency block of size f d T c carries one chip instead of one bit in OFDM and chips from the same bit are aligned along the frequency axis within the limit of hop bandwidth. M = / is the total number of hop bands and N = T 1 /T hop is the total number of hop intervals in active time T 1. Performance of single user MC-CDMA in a Rayleigh fading channel with maximum ratio combining (MRC) [1], [6] is given by equation 1. P e = [ 1 (1 µ) ] L L 1 ( ) [ ] k L 1 + k 1 (1 + µ) (1) k k= where, µ is expressed as γb µ = () L + γ b γ b is the average SNR per bit γ b = Ēb N where Ēb is the average bit energy and N is the noise power spectral density. L is the achievable frequency diversity; L = W f c where f c is the coherence bandwidth of the channel. B. Interceptor Models: The Radiometers For this paper, radiometers have been used as interceptor models. A radiometer looks over a range of frequency (or a set of bands of frequencies) over a particular time (called the integration time) for finding out presence of signal. If the received energy within the concerned bandwidth exceeds certain threshold, radiometers detect that there is signal. There are two types of radiometers, Wideband radiometers and Channelized radiometers [7], [8], [1]. Probability of detection (P D ) and the probability of false alarm (P F ) are two performance metrics for radiometers. If we fix the false alarm probability P F in the radiometer design, then from the total energy that is received in the radiometer, we can calculate the probability of detection P D. A simple block diagram of both kinds of radiometers are shown in Fig. 3. A wideband radiometer looks for energy all Fig. 3. Wideband and Channelized radiometers over the frequency and time interval T 1. On the other hand, a channelized radiometer consists of M filters each of which looks for energy in a bandwidth of and time interval T hop. Based on the information gathered from N number of hop intervals, channelized radiometer detects signal. We assume perfect alignment of frequency and time intervals for both radiometers. II. DETECTABILITY MODELS FOR LPI NETWORK For a quantitative measurement of LPI, two types of network intercept models have been developed by Mills and Prescott [9], [1]. First is the dispersed network intercept model and second is the stand-off network intercept model In dispersed network intercept model, friendly nodes that form the wireless network are assumed to be geographically dispersed. The enemy interceptor can come within the region of friendly nodes. On the other hand, in a stand-off model all the friendly nodes are assumed to be gathered in a smaller region and interceptor is far away. A. Performance metric for Dispersed network intercept model If we know the probability of false alarm P F and how much energy is received in a time-frequency window of size T 1, we can calculate the probability of detection P D in wideband radiometers [9]. Similarly, the knowledge of energies obtained in each hop time T hop over each hop bandwidth allows us to find out P D for a fixed value of P F in a channelized radiometer [9]. For a specific value of diversity gain L and bit error rate (BER) in the communication link we can find out the necessary SNR per bit E b /N for MC-CDMA system from equation 1. This SNR level at the intended receiver and communication range R C controls the power level at the transmitter. For the same BER in the communication link (say, BER=1 4 ) if SNR requirement is different in different communication schemes then the transmitter has to transmit different power levels. Depending on the level of transmitted power, detectability of a network changes. We have followed the same evaluation procedure carried out in [9], [1] to find LPI parameters in a dispersed network intercept model. To

3 measure LPI in this model, we have placed a number of nodes in a region all of which are transmitting power for the same time duration of T 1 using different orthogonal hop patterns with hop time T hop and hop bandwidth. For a specific communication scheme used, we have found out P D for both kind of radiometers at all points in the region. If P D is above certain threshold value (say,.95) then the interceptor is able to detect presence of signal at that point in the region. The total area over which radiometers are able to detect signal is called the intercept area. Amount of this area gives a measurement of LPI of the communication scheme used. Smaller the area better is the LPI property of the network. Fig. 4 illustrates the concept of intercept area. B. Performance metric for Stand-off network intercept model In a stand-off network intercept model it is assumed that the interceptor is far away from the network. So, from the point of view of interceptor, the whole network looks like a single node transmitting sum of all the powers transmitted by individual transmitter nodes. If individual transmitters use omni directional antennas then power radiated is identical in all directions. For this model, we can measure the distance over which radiometers can detect communication activity. This distance is called intercept range and it gives us a measurement of LPI. A good LPI communication scheme implies shorter intercept range. Using the procedures carried out in [9], [1] we get equations 3 and 4 [ ] E UT (R I ) WR = α 1 1 R b G I b N G C α(r C ) (3) T1 [Q 1 (P F ) Q 1 (P D )] Here, U is the total number of active users in the network. So, out of M number of hop bandwidths only U are busy at a time. R b is the data rate. T 1 is the time over which transmitters transmit data. is total transmission bandwidth. E b /N is SNR per bit required at the receiver. G I and G C are antenna gains in interceptor receiver and intended receiver respectively. α(r C ) is the path loss at a distance R C. If a wideband radiometer goes beyond the range (R I ) WR its probability of detection goes below P D. [ ] E T (R I ) CR = α 1 hop R b G I b N G C α(r C ) (4) Thop [Q 1 (p F ) Q 1 (p D )] In equation 4, T hop and are hop interval and hop bandwidth respectively. p F is the probability of detection for a time-frequency window of size T hop in a channelized radiometer. p F is the probability of false alarm in T hop and bandwidth. If a channelized radiometer goes beyond the distance (R I ) CR, its probability of detection goes below P D. III. CALCULATION OF LPI FOR MC-CDMA A. Dispersed network intercept model Fig. 4 shows a typical situation of a dispersed network intercept model using parameters given in table I. We have assumed standard vehicular A channel model [11] with maximum mobility v = 3 km/hr. Using parameters from table I, Parameter Value Parameter Value T 1.1 sec f d 1 KHz T c 1 =.1 msec f d N c 51 N cf d = 5.1 MHz T hop 1T c U 6 τ rms.44 µsec v(max.speed) 3 km/hr carrier freq. f GHz f c 1 =.8 MHz τ rms f Doppler Hz MHz M = 3 Y x 4 meters TABLE I PARAMETERS USED FOR DISPERSED NETWORK INTERCEPT MODEL X x 4 meters Fig. 4. Intercept area for dispersed network intercept model, BR= 1 kbps, BER= 1 4, T hop = 1T c, = 5.1 MHz, = MHz, M = 3. (a) No coding. Nc = 51. (b) With 1/ rate 8db coding gain. Nc = 56. L = / f c = [5.1/.8] =. For BER of 1 4 E b /N is found to be 19.3 db from equation 1. We take path loss model α as in equation 5, [11] WR CR α(f, R) db = Alog 1 (R) + B + 1 log 1 (f) (5) A = 4( h b ) B = 8 18 log 1 ( h b ) h b is the node height from average rooftop level in meters (for simulation say 3 meters). For all the communication links, we take link range R C = 1 km. So, transmitters radiate power in order to maintain required SNR per bit at intended receiver at a maximum distance of 1 km. Fig. 4 shows P D =.95 contours for wideband and channelized radiometers. Inside these contours P D >.95. So, area enclosed by P D =.95 contours give us the intercept area. Repeating our simulation for different spreading factors but maintaining the same total system bandwidth = MHz we have got the results in table II. From table II we observe that as we move from

4 N c in MHz M WR intercept CR intercept TABLE II INTERCEPT AREAS FOR DIFFERENT SPREADING FACTORS N c N c in MHz M WR intercept CR intercept TABLE III CODING GAIN 4DB, CODE RATE 1/ lower spreading factor (N c ) to higher spreading factor, area of intercept reduces considerably. Detectability performance depends on transmitted power. As forward error correction coding (FEC) allows us to transmit bits at lower bit energy E b for the same bit error rate (BER), its application is necessary to reduce transmitted power. In this work we have maintained a standard WiMax like sub carrier separation and symbol time structure for multicarrier data transmission. WiMax employs turbo codes as FEC. To show the effect of error correction coding on LPI we have simply assumed hypothetical FEC schemes with rate 1/ which gives us coding gains of 4db, 6db and 8 db respectively for slowly varying Rayleigh fading channel together with MC- CDMA. For 1/ rate codes, coded bit rate is twice than information bit rate. So, for the same spreading factor N c, required hop bandwidth to transmit same information bit rate doubles after applying FEC. As an example, for N c = 56, f d = 1 KHz and bit rate 1 kbps in uncoded MC-CDMA is.56 MHz. For FEC coded MC-CDMA, for the same value of N c, becomes 5.1 MHz. If the chips obtained after spreading a coded bit are interleaved in frequency domain with chips obtained from another coded bit within a hop bandwidth of, then each coded bit achieves full frequency diversity N c in MHz M WR intercept CR intercept TABLE IV CODING GAIN 6DB, CODE RATE 1/ N c in MHz M WR intercept CR intercept TABLE V CODING GAIN 8DB, CODE RATE 1/ Parameter value Parameter value T 1.1 sec R b 1 kbps G C db(omni) G I 1 db R C 1 km MHz P F 1 4 P D.95 T c 1 4 sec T hop 1T c ( ) nocoding N cf d ( ) 1/ratecode N cf d TABLE VI TABLE OF PARAMETERS FOR STAND-OFF MODEL of L = / f c. Then, SNR per bit for uncoded MC-CDMA E b /N with spreading factor N c occupying hop bandwidth and SNR per bit for FEC coded MC-CDMA for spreading factor N c / and hop bandwidth are related by equation 6 (in db scale) [ ] [ ] Eb Eb = G code (6) N coded N uncoded G code is the coding gain in db. Using equation 6 for modified SNR per bit, we have repeated our simulations for different spreading factors for these coding gains and results have been shown in tables III-V. Starting from uncoded MC-CDMA system with spreading factor N c = 18 which gives us intercept area of sq.km for wideband radiometer, we have reached an intercept area of only 4.18 sq.km for coded MC-CDMA with coding gain 8 db and spreading factor 51. As found out in earlier works with LPI networks [9], we have seen that for all our simulation scenarios wideband radiometer still covers larger intercept area than channelized radiometer. B. Stand-off network intercept model We have used the same parameters and channel models for stand-off intercept model. The set of parameters are given in the table VI. Then, from equation 3 and 4 we can calculate intercept range. For, spreading factors 56, 51 and 14, we have plotted intercept range vs number of active users in Fig. 5. From Fig. 5 we have observed that, if number of active users increases, intercept range increases for both the radiometers but increasing rate is faster in wideband radiometer. We have also observed that for a fixed number of users, as we apply higher spreading factor in MC-CDMA scheme, intercept range reduces. For higher spreading gain, transmission of a single bit over higher sub bandwidth achieves higher frequency diversity (L) in our system. So, for the same BER (1 4 ), required SNR per bit (E b /N ) goes down. Thus, we have to transmit less power for transmitting same number of bits in a timefrequency window of size T 1. This reduction of total power reduces the intercept range for wideband radiometer. Apart from this reduction in total power, there is another reason for decrease in the range for channelized radiometers. For higher spreading factor hop bandwidth increases, which implies that even for the same energy detection, the sub filters in channelized radiometer have to look over longer range in frequency. So, probability of detection reduces. As a result, higher value of N c implies better LPI property with respect to both the radiometers.

5 Intercept range (km) Intercept range (km) =.56 MHz =5.1 MHz =1.4 MHz Fig. 5. U (Number of active users) wideband radiometer channelized radiometer Intercept range vs U for uncoded MC-CDMA =.56 MHz =5.1 MHz =1.4MHz U (Number of active users) wideband radiometer channelized radiometer factor of MC-CDMA systems contributes to huge performance improvement in terms of LPI property. Application of high gain FEC is important as it reduces detectability of network. It has also been observed that in most situations wideband radiometers pose greater threat to LPI networks than channelized radiometers. But for small number of active users, channelized radiometers can outperform wideband radiometers in a standoff intercept situation. REFERENCES [1] Proakis, J. G., Digital Communications, Fourth edition, McGraw-Hill. 1 [] Glenn, A. B., Low probability of intercept. IEEE Communications Magazine, Number 1, Page 6-33, [3] Ziemer, R. E. and Peterson, R.L., Introduction To Digital Communication. Prentice Hall. 1. [4] Hara, S and Prasad, R., Overview of Multicarrier CDMA, IEEE Communication magazine, vol 35, no. 11, Dec [5] McCormick, A. C., Al-Susa, E. A., Multicarrier CDMA for future generation mobile communication, Electronics & Communication Engineering Journal, April. [6] Hanzo, L., Munster, M., Choi, B. J., keller, T., OFDM and MC-CDMA for Broadband Multi-user Communications, WLANs and Broadcasting. John Wiley & Sons, 3. [7] Dillard, R. A., Detectability of spread spectrum signals. IEEE Transactions on Aerospace and Electronic Systems. July, [8] Dillard, R.A., Detectability of spread spectrum signals. Norwood, MA: Artech House [9] Mills, R. F., and Prescott, G.E., Detectability models for multiple access low probability of intercept networks. IEEE Transactions on Aerospace and Electronic Systems,36, ,. [1] Mills, R.F., and Prescott, G.E. Waveform design and analysis of frequency hopping LPI networks. MILCOM 95. [11] C8.-3/7. Channel Models for IEEE 8. MBWA System Simulations, IEEE 8., July Fig. 6. Intercept range vs U for 1/ rate 4db gain FEC coded MC-CDMA It is observed from Fig. 5 that for most of the values of U, wideband radiometer range is longer than channelized radiometer. But, for small values of U channelized radiometer can perform better. Comparing Fig. 5 and Fig. 6 we have seen that compared to uncoded MC-CDMA, 1/ rate 4db gain FEC coded MC-CDMA (occupying the same hop bandwidth, total system bandwidth at bit rate 1 kbps and BER of 1 4 ) can perform better in terms of LPI. This improvement of LPI performance is provided by the additional coding gain of FEC. This coding gain reduces SNR per bit E b /N and thus it reduces overall transmitted power. Reduction of total transmitted power reduces intercept range. IV. CONCLUSION In this paper we have brought together works done in the fields of low probability of intercept networks and MC- CDMA to show that MC-CDMA is a promising candidate for LPI communication system designs. It can be built by adding spreading blocks on top of OFDM based systems and makes communication hard to detect. Quantitative analysis of the LPI property of MC-CDMA shows that higher spreading

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