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MONOPULSE ANGLE ESTIMATION

WITH CONSTRAINED ADAPTIVE BEAMFORMING

USING SIMPLE MAINLOBE MAINTENANCE TECHNIQUE

Sung-Hoon Moon, Dong-Seog Han, Hae-Sock Oh, Myeong-Je Cho

School of Electronic & Electrical Engineering, Kyungpook National University, KoreaAgency for Defense Development, Korea

ABSTRACT

A new monopulse radar system is proposed to overcome

the difficulties with conventional monopulse techniques

under jamming conditions. The proposed system uses a

simple mainlobe maintenance technique based on the es-

timated direction of the mainlobe jammer. Thereafter,

an adaptive array is used to create pattern nulls in the

incoming directions of jammers, while maintaining the

shape of the mainlobe. As a result, the proposed system

can track the target angle without any correction of the

adaptive sum and difference beam outputs.

I. INTRODUCTION

The monopulse technique, which is used to trackthe angular location of a radiation source, is widelyemployed in modern surveillance and tracking radars.However, under jamming conditions, this techniqueneeds to be combined with adaptive arrays to obtaina correct monopulse ratio. Adaptive arrays are veryeffective in improving the signal to noise plus interfer-ence ratio under jamming conditions, thereby restor-

ing a good detection performance. However, the mainbeam can be distorted when the jammer is close to thelook direction of the tracking radar. This pattern dis-tortion results in a large error in the monopulse angleestimation.

To solve this pattern distortion problem, Davies,Brennan, and Reed [1] derived three differentmonopulse formulas for the maximum likelihood esti-mation in the case of a linear array. Nickel [2] alsoderived formulas for a first-order Taylor expansion ofthe adapted monopulse characteristics, while Paine [3]developed an approach to solve the problem where the

difference beam weights are calculated via an optimiza-tion problem, which seeks target direction estimates us-ing the least mean square error. However, these meth-ods involve very complex calculations for the correctionvalue.

Yu and Murrow [4] proposed a digital beamformingsystem and processing algorithm for the angle estima-

tion, which do not require the monopulse ratio to becorrected. The system consists of an adaptive arrayand following mainlobe canceller. However, it is diffi-cult to combine an adaptive array with a suitable main-lobe maintenance technique as accurate information isrequired from the mainlobe jammer (MLJ).

Accordingly, the current paper presents a simplemainlobe maintenance technique. With a suitable side-lobe reduction, the incoming direction of the mainlobejammer is estimated using the azimuth difference, ele-vation difference, and sum patterns, then a directiona

constraint is added to the conventional beamformingin the adaptive array. As a result, the sidelobe jammers are removed from the front adaptive array, thenthe remaining mainlobe jammer is removed from thefollowing mainlobe canceller.

The remainder of the current paper is as followsThe beamforming system proposed by Yu and Mur-row is outlined in Section II. In Section III presentsthe proposed, a simple mainlobe maintenance techniquethat, which uses the estimated direction of the MLJ, isproposed. The performance of the proposed mainlobe

maintenance system is analyzed in Section IV, and someconcluding remarks are presented in Section V.

II. ADAPTIVE BEAMFORMING

FOR ANGLE ESTIMATION

A. MONOPULSE BEAMFORMING NETWORK

The monopulse technique is an angle estimationmethod that uses more than two antenna beam pat-terns where the beams are generated simultaneouslyunlike classical tracking methods, such as sequentialobing or a conical scan [5]. As a result, the per

formance of monopulse tracking is far superior to theperformance of classical methods. The problem withthe monopulse technique caused by interference can besolved by adopting adaptive beamforming. Fig. 1 is amonopulse beamforming network, where the sum anddifferent channels are used to calculate the monopulseratio. For Kantenna elements, the array input vector

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u

u

1x

2x

Kx

w

w

u

uf Re-1

Fig. 1. Monopulse beamforming network.

is given by

x = [x1, x2, , xK]T

. (1)

The input vector is combined to form the sum and dif-ference outputs as

u= wH x (2)

andu = w

Hx (3)

respectively, where w is the sum beam weight vectorand w is the difference beam weight vector. The su-perscript Hdenotes a Hermitian transpose.

The sum and difference antenna beam patterns areexpressed as

() = wH a() (4)

and() = wHa(), (5)

where a() is the array steering vector in the incidentdirection . For a uniform linear array, the array steer-ing vector can be expressed as

a() = [1, exp{j}, , exp{j(K 1)}]T, (6)

where is an inter-element phase shift given by

=2

D sin (7)

and D is the inter-element distance.

Then the sum pattern, difference pattern, andmonopulse ratio can be expressed as

() =Kk=1

exp {j(k1)} (8)

= sin(K

2 )

sin(2

)exp

j

(K 1)

2

() =

K/2k=1

j exp {j(k1)} (9)

+K

k=K/2+1

(j)exp{j(k1)}

= 2sin2 (K

4 )

sin(2

)exp

j

(K1)

2

and

f() = tanK

4

= tan

KD2

sin

(10)

respectively. The target direction of arrival (DOA) canbe estimated from the monopulse ratio in (10).

B. MONOPULSE BEAMFORMING WITH JAM

MING

The monopulse technique is severely degraded byexternal interference. Thus adaptive beamforming isessential to obtain a correct target angle from the

monopulse technique. However, adaptive beamforming distorts the beam pattern when removing the inter-ference, thereby making it difficult to track the targetusing the monopulse technique.

Yu and Murrow proposed a digital beamforming ar-chitecture that removes sidelobe jammers (SLJs) us-ing an adaptive array, while reserving the shape of themainlobe, plus the remaining MLJ is removed by thefollowing mainlobe canceller. Fig. 2 shows the digitabeamforming architecture proposed by Yu and Murrow

Assume that a planar array has N columns of ele-

ments, and each column has Melements. Fixed beam-forming is used for each column and adaptive beam-forming is only possible in the azimuth direction. After the fixed beamforming for each column the columnsum vector ue and column difference vector ue are

Column Sum & Difference

Beamforming Network

Mainlobe Canceller

Monopulse Angle Estimation

Adaptive Array with MLM

eu

eu

Au

Au

Eu

A E Eu u u

Au

u

Fig. 2. Digital beamforming architecture proposed by Yuand Murrow

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2aw

1aw

2ew

1ew

u

A

u

uE

u

u A

uE

uE

uA

A

E

E

E

u

uf

1

E

A

A

u

uf

1

A

Fig. 3. MLC for adaptive monopulse processing.

formed, as shown in Fig. 2. These vectors are thencombined with the weight vectors for the adaptive ar-ray to remove the sidelobe jammers in the array sumu, delta-azimuth uA , delta-elevation uE , and delta-delta u channels. These channels can be expressed

asu = w

Hue (11)

uA = wHue (12)

uE = wHue (13)

u = wHue , (14)

where

w = R1e

w (15)

w = R1e

w (16)

w = R1ew (17)

w = R1e

w. (18)

Re and Re are the covariance matrix of the columnsum vector ue and column difference vector ue , re-spectively, and w and w are the nominal sum anddifference beforming weights, respectively.

To prevent mainlobe distortion resulting from theadaptive beamforming, the front adaptive array needsto be combined with a suitable mainlobe maintenancetechnique, such as a structured covariance matrix using

a subspace constraint, diagonal loading, modified dom-inant mode rejection, MLJ filtering, blocking matrix,or rank-1 MLJ down-dating [4].

As a result, although no SLJs remain in the outputchannels of the adaptive array, there is still an MLJ.Thus, to remove the MLJ, a mainlobe canceller followsthe adaptive array. In the mainlobe canceller the high

mainlobe gain of the difference channel is used to re-move the MLJ in the sum channel. Applebaum, et alproposed a mainlobe canceller to remove the MLJ whilepreserving the monopulse ratio. Fig. 3. shows a blockdiagram of the mainlobe canceller. The antenna beampatterns are separable in the azimuth and elevation di-rections as

(a, e) = (a)(e) (19)

A(a, e) = (a)(e) (20)

E(a, e) = (a)(e) (21)

(a, e) = (a)(e), (22)

where (a, e), A(a, e), E(a, e), and (a, e)are the array sum, delta-azimuth, delta-elevation, anddelta-delta channel beam patterns, respectively, alongthe azimuth direction a and elevation direction eWith this property, the mainlobe canceller can removethe MLJ in one direction, while reserving the monopulseratio in the other direction.

The sum channel and difference channel outputs inthe elevation direction can be obtained as

uE =u wa1uA (23)

uE =u wa2u , (24)

where wa1and wa2are the adaptive weights to minimizethe output power of uE and uE , respectively. For alarge jammer to noise ratio, wa1and wa2are almost thesame. Then these weights are approximated as

wa=wa1=wa2. (25)

Therefore, the adapted monopulse ratio along the ele-vation direction can be derived as

fE =(a, e)(a, e)

= E(a, e) wa(a, e)

(a, e) waA(a, e)

= (e){(a) wa(a)}

(e){(a) wa(a)}

= (e)

(e). (26)

From (26), it is verified that the monopulse ratio alongthe elevation direction is maintained, while removingthe MLJ through azimuth direction beamforming. Sim-ilarly, the adapted monopulse ratio along the azimuth

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direction can be derived as

fA =(e, a)(e, a)

= A(e, a) we(e, a)

(e, a) weE(e, a)

= (a){(e) we(e)}

(a){(e) we(e)}

= (a)

(a)

, (27)

wherewe is the weight minimizing the output power ofthe sum channel and difference channel outputs, uAand uA , respectively, in the azimuth direction.

III. MONOPULSE BEAMFORMING

NETWORK WITH SIMPLE MAINLOBE

MAINTENANCE TECHNIQUE

Practically, it is very difficult to combine an adaptivearray with a suitable mainlobe maintenance techniquewhen the mainlobe jamming is incoming. Moreover,

conventional mainlobe maintenance techniques are verycomplex and not robust. For example, rank-1 MLJdown-dating subtracts the rank-1 contribution from theMLJ as R = R P1j1jH1 , (28)where R is the array covariance matrix, P1 is the powerof the MLJ, and j1 is the array response vector of theMLJ. In a modified covariance matrixR, although thereis no contribution from the MLJ, it is still very dif-ficult to estimate the power and location of the MLJsince much computation is required to analyze the co-variance matrix with conventional algorithms, such asMUSIC and ESPRIT. More importantly even a smallerror in the MLJ information can result in a seriousperformance degradation.

Accordingly, the current paper proposes a simpleand robust mainlobe maintenance technique. Fig 4.presents the architecture of the proposed monopulsebeamforming network. The column sum and differenceoutput vectors combined with the nominal sum and dif-ference vectors, respectively, are expressed as

a= wH ue (29)

anda= w

Hue , (30)

respectively. The nominal sum and difference weightvectors are windowed to reduce the sidelobe level ofeach beam pattern. Since the sidelobe level is much

Column Sum & Difference

Beamforming Network

Mainlobe Canceller

Monopulse Angle Estimation

Adaptive Array with MLM

eu

eu

Au

Au

Eu

A E Eu u u

Au

u

MLJ Azimuth

Angle Estimation

Fixed Azimuth Sum &

Difference Beamforming

MLJa

a a

Fig. 4. Proposed monopulse beamforming network.

smaller than the mainlobe gain, the effect of SLJs issignificantly much reduced in the fixed azimuth beam-forming network, as shown in Fig. 4. Thus, the azimuthangle of the MLJ can be estimated from the monopulseratio of the fixed azimuth beamforming network as

f(MLJa ) =aa

. (31)

If the power of the SLJs is much higher than that of

the MLJ, the estimated azimuth angle of the MLJ maybe slightly different from the real value. Yet this differ-ence will not severely degrade the performance of themonopulse beamforming, since the mainlobe shape ofthe beam pattern is not freely changed near the esti-mated azimuth angle of the MLJ.

The estimated azimuth angle of the MLJ can be ap-plied to maintain the mainlobe of the beam patterns ofthe adaptive array. The multiple constrained minimumvariance (MCMV) beamforming criteria are given by

minw wH

Rw subject to wH

Ac = cT

, (32)

where c = [c1, c2]T is the constraint vector, in which

c1 is the desired gain for the tracking axis, c2 is theadditional constraint value depending on the estimatedangle of the MLJ, and Ac is the constraint matrix ex-pressed as

Ac =

a(s) a(MLJ)

, (33)

where, a(s) and a(MLJ) are the array response vec-tors for the target and MLJ, respectively. Then theoptimum weight vector is given by

wopt= R1Acc

AHc R1Ac

. (34)

The operations of the following mainlobe cancellerand target angle estimation are the same with those ofthe monopulse beamforming architecture presented inSection II.

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80 60 40 20 0 20 40 60 8070

60

50

40

30

20

10

0

10

Azimuth [deg]

Gain[dB]

Row sumRow diff.DOAs

Fig. 5. The fixed azimuth sum and difference beam patterns.

IV. SIMULATION RESULTS

The performance of the proposed monopulse beam-forming network was is analyzed using a planar arraywith 15 columns of elements, where each column has15 elements. The target is incoming from an azimuthand elevation angle of (0, 0) with an SNR of 10 dB.Through the mainlobe the MLJ is incoming from an

azimuth and elevation angle of (3, 2) with a JNRof 20 dB. A sidelobe jammer is also incoming from anazimuth and elevation angle of (25, 35) with a JNRof 40 dB. A Chebyshev window is applied to reduce thesidelobe level of the beam patterns and maintain thepeak sidelobe level at 20 dB below the look directiongain.

Fig. 5 shows the fixed azimuth sum and differencebeam patterns used to estimate the azimuth directionfor the MLJ, while Fig. 6 confirms that the azimuthangle of the MLJ is estimated with only a small error

when using the simple fixed azimuth monopulse beam-forming.

Figs. 7 and 8 show the estimated target directionas regards the azimuth and elevation direction, respec-tively. The estimated azimuth and elevation directionis (0.27, 0.45). There is only a small bias in the esti-mated target direction despite the MLJ and SLJ.

V. CONCLUSIONS

A monopulse beamforming architecture with a sim-ple and robust mainlobe maintenance technique is pro-

posed. The proposed mainlobe maintenance techniquedoes not require a complex analysis of a covariance ma-trix, such as MUSIC and ESPRIT. Furthermore, theproposed method can estimate the azimuth angle of theMLJ more quickly than any other conventional DOA es-timation method used to maintain the mainlobe of anadaptive array.

6 4 2 0 2 4 65

4

3

2

1

0

1

2

3

4

5

Azimuth [deg]

Monopulseratio

Monopulse ratioOutput sum/diff. ratioDOA of MLJ

Fig. 6. MLJ azimuth angle estimation.

6 4 2 0 2 4 65

4

3

2

1

0

1

2

3

4

5

Azimuth [deg]

Monopulseratio

Monopulse ratioOutput sum/diff. ratioTarget DOA

Fig. 7. Target azimuth angle estimation.

6 4 2 0 2 4 65

4

3

2

1

0

1

2

3

4

5

Elevation [deg]

Monopulseratio

Monopulse ratioOutput sum/diff. ratioTarget DOA

Fig. 8. Target elevation angle estimation.

REFERENCES

[1] R. C. Davies, et al, Angle estimation with adaptive arraysin external noise field, IEEE Trans. Aerosp. Electron. Syst.vol. AES-12, no. 2, pp. 179-186, Mar. 1976.

[2] U. Nickel, Monopule estimation with adaptive arrays, IEEProc. Radar, Sonar Navig., vol. 140, no. 5, pp. 303-308, Oct

1993.[3] A. S. Paine, Minimum variance monopulse technique for a

adaptive phased array radar,IEE Proc. Radar, Sonar Navig.vol. 145, no. 6, pp. 374-380, Dec. 1998.

[4] K. B. Yu and D. J. Murrow, Adaptive digital beamformingfor angle estimation in jamming, IEEE Trans. Aerosp. Electron. Syst., vol. 37, no. 2, pp. 508-523, Apr. 2001.

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