World Applied Sciences Journal 23 (): 57-575, 23 ISSN 88-4952 IDOSI Publications, 23 DOI:.5829/idosi.wasj.23.23..89 Evolutionary Coputing Based Antenna Array Beaforing with Low Probabality of Intercept Property 2,3,3,3 Abdul Basit, I.M. Qureshi, Ihsan ul haq, A.N. Malik and Wasi khan Departent of Electronic Engineering, International Islaic University, Islaabad, Pakistan 2 Departent of Electrical Engineering, Air University, Pakistan 3 Institute of signals, systes and soft coputing (ISSS) Islaabad, Pakistan Subitted: Jun 9, 23; Accepted: Jul 2, 23; Published: Jul 25, 23 Abstract: In this work we have proposed a new approach for array antenna beaforing based on evolutionary coputing, which offers low probability of intercept. These active array antennas are highly vulnerable to intercept receivers due to their high-gain. The detection perforance of proposed approach reains unchanged as the aount of energy on the target is sae as that of the high gain bea pattern, while the intercept range of the eney receiver has been greatly reduced. In this paper, the set of coplex weights for synthesis of high gain bea pattern using spoiled set of basis patterns is derived using genetic algorith. The two ajor advantages of proposed algorith are the iproved perforance and at the sae tie the low coplexity specifically by avoiding the atrix inversions. Siulation results ensure that the bea synthesized by this technique is at par with the existing LPI beaforing techniques eploying phased arrays. Key words: Beaforing Genetic algorith Low probability of intercept antenna Pattern Search INTRODUCTION aong the above techniques are high duty cycle, wide-bandwidth wavefors which are widely exploited in Active and/or ono-static radars are very likely to be LPI applications []. Suppression of side lobes can also detected by jaers and intruders due to the aount of reduce the probability of being detected, to soe extent, energy transitted towards the target based on in the side lobe search regions. In [], a pseudo rando conventional techniques. It is very coon that intruders frequency jitter was introduced to the carrier frequency exploit, degrade and prevent radar operations and that helps to design an LPI wavefor for OFDM systes. capabilities []. This copetition between the radar and In [2], LPI perforance analysis using tie-energy intruders is tered as electronic warfare (EW) [2, 3]. anageent techniques for Digital Array Radar (DAR) The phased array antennas, which have the advantage of has been presented. uch higher gain with respect to isotropic antennas, are Alongwith the wavefor design, various other very likely to be detected and exploited by the intruders. techniques are available in literature that iprove the On the other hand, the advantage of phased array LPI perforances using different types of antennas antennas is their detection perforance which is very odifications. Antenna hopping technique as proposed high. by E.J. Baghdady has two or ore spaced antennas Various techniques have been proposed to connected with a single input or output through a switch achieve LPI while ensuring the effective detection range. [3]. Another technique eploys MIMO antennas, in Three widely used LPI techniques include i) spreading which actual transit bea is shaped in such a way that energy in tie doain using high duty cycle wavefors liits the antennas radiations in desired directions and ii) spreading energy in frequency doain using hence to achieve LPI property [4]. Siilarly in [5], LPI wide-bandwidth wavefors and iii) spreading energy in property for a network, using technique of frequency hop spatial doain using broader transit antenna beas ultiple access, is evaluated. It is assued that intruder [4-9]. Cobination of these techniques is also used to decides whether a network is operational or not, based on enhance the perforance [, 8]. The ost coon the energy received fro transitter. One of the ethods Corresponding Author: Abdul Basit, Departent of Electronic Engineering, International Islaic University, Islaabad, Pakistan. 57
World Appl. Sci. J., 23 (): 57-575, 23 proposed in recent past to achieve LPI is presented in [], in which case the high-gain scanned patterns are spoiled to get series of low-gain spoiled basis patterns. The spoiled patterns are fored by applying a selected phase shift to each array eleent. These spoiled bea patterns are coherently cobined using coplex weights to generate the overall effect of high gain pattern in desired direction. Since the total energy on the target is sae hence the detection perforance of antenna reains unchanged. These spoiled bea patterns ensure significant reduced peak power in any direction and hence the radar probability of being detected is reduced []. In this paper, genetic algorith (GA) is being proposed to copute the coplex weights for synthesizing the high-gain bea using a series of low-gain spoiled patterns. The fitness evaluation function for this algorith is ean square error which is used to evaluate the error between the desired bea and the synthesized one using set of coplex weights. The proposed algorith is tested for siulated environent containing Additive White Gaussian Noise (AWGN). The proficiency and effectiveness of these schees are tested on the basis of Monte Carlo siulations. The rest of the paper is organized as follows: In section-ii proble is forulated, section-iii discusses the proposed ethodology, section-iv is for the siulation results and section V concludes and gives future work direction. Proble Forulation: Consider a unifor linear array (ULA) having inter-eleent distance d shown in Figure. Fig. : N-eleent Phased Array Antenna. represent n the phase shift values for spoiling bea the search region by applying a linear progressive phase shift across the array. Fundaental phase scan shift is defined as = 2 /N. Defining = +, =,,2,...,( N ), the reaining set of N- scanned pattern throughout the search region we get: N n= jn ( ) h( ) = e ; =,2,...,( N ) To ensure the LPI property, these high gain scanned pattern are spoiled in a way that their peak power in any particular direction reduces significantly. In [], quadratic phase variance technique has been introduced to find a set of phase values ( n) to defocus the ain bea and siultaneously to reduce its gain. The corresponding phase shift values fro the set n are applied to each eleent of array antenna respectively as shown in Fig. This set of spoiled bea patterns is defined as set of basis patterns. (2) The output of ULA is given as: j j2 j( N ) h( ) = + e + e +... + e N = n= h( ) e Equation (a) can be written as: jn ( ) (a) (b) These N basis patterns l( expressed as: N j j j j2 j jn ( ) l( ) = + e e + e e +... + e e 2 N j j j j2 j jn ( ) l( ) = + e e + e e +... + e e j 2 N j j j2 j jn ( ) l( ) = + e e + e e +... + e e ); =,2,..,(N-) are N 2 N N N (3) where = kd sin( ) kd sin( ) and k = 2 /. The pattern defined in () has a high-gain ain lobe in the direction of spatial angle easured fro the broadside of the array and is the entire surveillance region vector i.e. [- /2 /2]. This high gain bea pattern can be scanned throughout These N steered versions of the fundaental bea patterns are linearly independent []. The basic objective is to construct the high gain bea pattern with the linear cobination of set of these spoiled beas l( is closest to h( h ˆ( ) ), such that ) in the ean square error sense. 57
World Appl. Sci. J., 23 (): 57-575, 23 This can be done as follows: w, w, w, N hˆ( ) l( ) w, w, w, N hˆ( ) l ( ) = hˆ ( ( ) l,,, N ) N wn wn w N N (4) The proble is how to copute the set of coplex weights using genetic algorith (GA). The set of spoiled beas l( ) is represented in vector for as I N.We want to generate the high gain beas h( ) using the linear cobination of these spoiled beas. The vector for of h ˆ( ) and coplex weights atrix are denoted by hˆ N and WN N respectively. The equation (4) can be expressed as: ĥ=wl MATERIALS AND METHODS The contest between radars systes and electronic devices that are used to degrade, exploit or effect the radar operations is always there. Active radars have the advantage of high detection rate of target based on the energy transission. On the contrary, active radars are very likely to be visible to intruders. Therefore, in this respect active radars need to be hidden fro intruders in soe sense without affecting the detection perforance. LPI techniques are used to hide the active radars fro intruders. In [], an LPI technique is used to spoil the phased array antenna bea patterns using the set of phase angles to spread the high-gain bea pattern in the entire search region. Once the spoiled bea patterns are achieved, the linear cobination of the is used to synthesize the high gain pattern in the desired direction. The coplex weights used for linearly cobining the spoiled beas are derived taking the inverse of a atrix []. Evolutionary coputing techniques have been extensively utilized to solve the probles of array signal processing. GA is a proising candidate of evolutionary coputing techniques which is used to find the set of coplex weights. A trailered GA hybridized with Pattern Search (PS) is used to derive the coplex weights in the presence of AWGN noise. The steps used in ipleentation of proposed algorith are suarized below: Algorith : Genetic Algorith (5) Step : Generate appropriate nuber of rando units (chroosoes) in which each unit contain unknown paraeters (genes). This set of chroosoes is generated between the upper and lower liit suitable for the unknown coplex weights. Step 2: Calculate the fitness of each chroosoe using the fitness function. The fitness function is given as: M i= D = (/ M) h ( i) y ( i), =,,2,...,( N ) th where h denotes eleent of the vector h; M= length (h ) and y N = W j, l j j= ( ) This procedure is repeated for all the rows of the weight atrix. These chroosoes are sorted regarding their fitness values. Step 3: Crossover operation will produce offspring fro the selected set of parents. Step 4: Generation of new population. Step 5: Mutation (optional) When there is no iproveent in fitness in generation or proble converges fast, utation operation is perfored. Step 6: Stopping criteria. Stopping criterion is prepared, keeping in ind the best possible value a fitness function can achieve. The algorith terinates when that fitness value stopping criteria or the given nuber of cycles is reached. Else go to step 3. GA Hybridized with PS: To iprove the results for AWGN scenario, the hybridization of GA with Pattern Search (PS) is very useful. GA hybridized with PS outperfors GA alone. RESULTS AND DISCUSSION A linear array with 32 eleents is considered (N=32) for evaluation of proposed technique. The inter-eleent distance is the sae for the whole array ( ). 2 d = 2 572
World Appl. Sci. J., 23 (): 57-575, 23 Table : Settings of the Algoriths GA PS Paraeters Settings Paraeters Settings Population Size 2 Mesh initial size. Chroosoe Size 64 Mesh Maxiu size Inf Creation function Unifor Initial penalty Selection function Stochastic Unifor Penalty factor Reproduction crossover frac..6 Bind tolerance e-3 Mutation function Adaptive heuristic Mesh Tolerance e-6 Crossover function Heuristic Max iterations 64 Migration direction Both Max Func. Evaluation 28k Hybrid function None Tie liit Inf No of generations X tolerance e-6 Function tolerance e- Function Tolerance e-6 Nonlinear constraint tolerance e- Nonlinear constraint tolerance e-6 Mean square Error (MSE) between desired and estiated bea patterns is used as fitness function. Siulations are done using the optitool of MATLAB R22b. Both cases (i.e. no noise and presence of noise) are taken into account and siulation results show the perforance of GA and GA hybridized with PS. Table gives details about paraeter setting for GA and PS algoriths. The gain coparison between high gain bea pattern and spoiled bea pattern is shown in Fig 2. The fundaental ULA bea pattern has high-gain while the processed spoiled bea is defocused and has low-gain. The defocused and spoiled bea pattern is achieved by adding defined phase shift values (i.e. set of n shown in Fig.) to each eleent of ULA. It can be seen that high gain bea pattern has 5dB gain. On the other hand, the spoiled bea pattern has gain of.7db that is significantly lower than that of the fundaental pattern. Other high-gain patterns as well as spoiled low gain basis patterns throughout the search region can be fored by putting on linear phase progression to these fundaental patterns. Fig. 3 shows the first five spoiled patterns fro the set of basis patterns. These patterns have very low-gain and thus ensure the LPI property. Once the spoiled basis patterns are known, the linear cobination of these basis pattern can synthesize high-gain pattern in any desired direction. The perforance of GA in the presence, as well as, in the absence of AWGN is discussed below. Fig. : Coparison between High gain bea pattern and fundaental spoiled bea pattern for a 32-eleent linear phased array, steered at deg CASE : No Noise It is assued that no AWGN noise disturbs the process of spoiling high gain bea patterns. To insure the LPI property, high gain bea patterns are synthesized in Fig. 2: First five spoiled bea patterns, 5 BASIS PATTERNS 573
World Appl. Sci. J., 23 (): 57-575, 23 CASE 2: Presence of AWGN Fig. 3: Synthesis of High Gain Bea by GA steered at,-45 and +45 deg respectively. AWGN noise is added to the basis spoiled patterns. It is desired to synthesize a high gain bea pattern in the desired direction with sae peak power. To test the perforance in this scenario AWGN is added to the spoiled bea patterns ensuring signal to noise ratio (SNR) of db. Fig. 5 shows the perforance coparison between GA and hybridized GA with PS algorith to synthesize the high gain bea pattern steered at. SNR is db. The hybridized GA with PS algorith gives better perforance than GA. The pattern synthesized by hybridized GA with PS has considerably low side lobes as copared to the GA synthesized bea pattern. CONCLUSION In this paper the high gain bea patterns are synthesized by weighted cobination of low gain, spoiled pattern. This high gain synthesized bea pattern guarantees the LPI property. The coplex weights are calculated using GA algorith. The perforance of GA is tested for no noise as well as the AWGN noise scenarios. The Hybridization of GA algorith with PS algorith works better in the presence of AWGN noise. This coes at the cost of enlarged eory and data processing swiftness. In future, other evolutionary coputing and swaring techniques can be used for this LPI beaforing application. REFERENCES Fig. 4: Coparison between the synthesized bea by GA and Hybridized GA with PS in presence of AWGN Noise desired direction using linear cobination of these spoiled bea patterns. The coplex weights, for cobining the spoiled bea patterns, are coputed using GA algorith and thus avoiding the inverse of a atrix as used in []. Fig. 4 shows the Genetic Algorith (GA) based synthesized high-gain bea patterns steered at, 45 and -45. It is vibrant fro fig.4 that high gain patterns have the sae gain (5dB) in the desired direction as of conventional array antennas as well as the bea fored in [].. Lawrence, D.E., 2. Low probability of intercept antenna array beaforing, IEEE Transactions on Antennas and Propagation, pp: 2858-2865. 2. Schleher, D.C., 986. Introduction to Electronic Warfare. Boston, MA:Artech House, 3. Skolnik, M., 99. Radar Handbook, 2nd Ed. New York: McGraw-Hill, 4. Schrick, G. and R. Wiley, 99. Interception of LPI radar signals, In Proc. IEEE Int. Radar Conf., pp: 8-. 5. Fuller, K.L., 99. To see and not be seen, Proc. Inst. Elect. Eng. Radar and Signal Processing, F, 37: -. 6. Pace, P.E., 24. Detecting and Classifying Low Probability of Intercept Radar. Norwood, MA: Artech House, 574
World Appl. Sci. J., 23 (): 57-575, 23 7. Schleher, D.C., 26. LPI radar: Fact or fiction, IEEE 2. Qing-long, B., Y. Jian, Z. Yue and C. Zeng-ping, 29. Aerosp. Electron. Syst. Mag., 2: 3-6. LPI perforance of Digital Array Radars, IET 8. Carlson, E.J., 988. Low probability of intercept (LPI) international Radar conference, pp: -4. techniques and ipleentations for radar systes, 3. Baghdady, E.J., 99. Directional signal odulation Proc. IEEE National Radar Conf., pp: 56-6. by eans of switched spaced antennas, IEEE Trans. 9. Wu, P., 25. On sensitivity analysis of low Coun., 38(4): 399-43, 99. probability of intercept (LPI) capability, Proc. IEEE 4. Hai Deng, 2. Wavefor design for MIMO radar Military Counications Conf., 5: 2889-2895. with low probability of intercept (LPI) property,. Shiran, Y., S. Leshchenko and V.M. Orlenko, 23. IEEE International Syposiu on Antennas and Advantages and probles of wideband radar, Propagation (APSURSI), pp: 35-38. Proc. Int. Radar Conf., pp: 5-2. 5. Mills, R.F. and G.E. Prescott, 995. Wavefor. Bouanen, M., F. Gagnon, G. Kaddou, D. Couillard Design and Analysis of Frequency Hopping LPI and C. Thibeault, 22. An LPI Design for Secure Networks, IEEE Military Counications OFDM Systes, Military Counications Conference, 2: 778-782. Conference, pp: -6. 575