04977010

Digital Beamforming of Multiple Simultaneous Beams for

Improved Target Search

Kai-Bor Yu

Lockheed Martin MS2

Syracuse, NY 13221-4840 USA

[email protected]

Abstract—This paper describes several digital beamforming

radar techniques for improving target detection and

determination of the angular location of a target using multiple

simultaneous received beams. These techniques improve target

search and angle estimation performance over the conventional

monopulse processing in the elimination of beam-shape loss.

I. INTRODUCTION

Conventional monopulse processing (Scheme 1) involves one

beam in transmit and multiple simultaneous beams on

receive. Typically a sum beam without any tapering is

employed in the transmit array for full power operation. A

uniform weighting will have transmit antenna pattern

narrowest beamwidth but higher sidelobes. Recently, beam-

spoiling has been applied to broaden the transmit antenna

beamwidth [1]. On receive two or more beams are formed for

target detection and angle estimation, i.e. the sum beam, the

delta-azimuth and the delta-elevation beam. The sum beam is

used for surveillance search and target detection. Once a

target is detected, the ratio of delta-azimuth beam over the

sum beam is used for azimuth angle estimation, and the ratio

of delta-elevation beam over the sum beam is used for

elevation angle estimation. This approach for angle

estimation is computationally efficient as it requires only the

computation of the monopulse ratios and a table look-up for

the angles. Received beams are typically tapered for sidelobe

control leading to wider received beamwidth. Taylor

weighting is used for the sum beam and Bayliss weighting is

used for the difference beams. A target at the peak of the

beam has the highest signal-to-noise ratio (SNR) compared to

the rest of the beam. Thus a target away from the center of

beam suffers from beam-shape loss resulting to lower SNR

and degradation in target detection and angle estimation

performance. The beam-shape loss and degradation in target

detection and angle estimation performance can be recovered

if multiple simultaneous received beams are employed. A

full digital array (i.e. an array digitized at element-level)

supports different processing architectures with different

processing performance and computational complexities.

Furthermore, these processing schemes can be combined to

balance the performance and the computational burden.

In Section 2, we discuss the processing architectures and

algorithms using multiple simultaneous received beams. First,

we review the processing architecture of the Maximum-

Likelihood Method [2, 3, 4]. This approach has been

advocated for improved radar target search and track for its

merits in the elimination of the beam-shape loss. Second, we

discuss a new processing algorithm that uses multiple sets of

monopulse beams. Third, we show how the monopulse

processing scheme and the ML processing scheme can be

combined to balance the performance and processing

requirement. In section 3, some simulations are included to

illustrate the performance of the processing schemes. Section

4 is the summary.

II. ALGORITHMS USING MULTIPLE SIMULTANEOUS RECEIVED

BEAMS

Emerging radar technology employs digital beamforming

(DBF) at the sub-array level or at the element level. The

digital degrees-of-freedom (DOFs) available provide

flexibilities and capabilities compared to analog

beamforming. These capabilities include improved dynamic

range, improved interference suppression and clutter

performance and forming of multiple simultaneous received

beams. In this paper, we consider the benefits in the

elimination of beam-shape loss and the extension of the

coverage performance using multiple simultaneous received

beams.

Radar flexibilities and capabilities increase with the level of

digitization. Element level digitization supports forming of

arbitrary number of beams and types of beams where some

approximations are required if we have only sub-array

digitization. For example, it is not possible to form Taylor

and Bayliss beams simultaneously from digital sub-array

outputs unless multiple RF sub-arrays are employed. The

elements within the sub-arrays are typically tapered for the

Taylor beam and a direct sum of the sub-array outputs will

978-1-4244-2871-7/09/$25.00 ©2009 IEEE

generate the desired Taylor sum beam. An approximation on

the Bayliss difference beam can be generated by using an

average Bayliss-on-Taylor taper for each sub-array. An

approximation is also required for forming cluster of squinted

sum beams from digital sub-arrays.

Another consideration in the algorithm development is the

processing complexity. The computational burden can be

attributed to the forming of multiple simultaneous beams and

the pulse compression and Doppler processing associated

with each beam. Also, there is substantial computational cost

associated with the angle search of the ML method. The ML

approach to angle estimation requires a two-dimensional

iterative or grid search over the entire beam.

Here we review the Maximum-Likelihood Beam-Space

Processing (MLBP) scheme (Scheme 2) as applied to the

digital array radar system where digital inputs can be

element-based or sub-array-based. These inputs are first

digital beamformed to generate a number of beams. The

cluster of sum beams includes a center beam surrounded by 4

squinted sum beams located on the 3dB contour or the 6 dB

contour on a 2 x 2-shape or diamond-shape configuration.

The digital beamforming can be expressed as following:

4,...0

)()()(1

)()(

=

=∑=

ΣΣ

i

trnwtrN

n

n

ii

where ,)}({,)}({,)}({ 4

0

)(

1

)(

1 =Σ=Σ= i

iN

n

iN

nn trnwtr are the digital

element or sub-array data, beamforming weights and the

corresponding beamforming outputs respectively. The

beamforming outputs are used for the maximum-likelihood

angle estimation with the following functional to be

maximized:

where rRvug ,),,( are the beam patterns, covariance matrix

of the noise data and the output beam data respectively. The

maximum can be determined using iterative search or grid

search. This method is computational intensive. It also

requires memory storage for the set of antenna beam patterns.

Once u and v are searched to sufficient accuracy, the

corresponding target magnitude can be used for target

detection. The target amplitude estimate is given by the

following:

where )ˆ,ˆ( vug is the array patterns evaluated at the ML

angle estimate ).ˆ,ˆ( vu The ML approach in fact eliminates

the beam-shape loss by pointing the beam at the desired

angular direction. However, it requires a search for all angles

at every range cell, thus it is computational very intensive.

Some modifications are required for its use in the search

radar application. A detect before angle estimate approach

can be developed similar to monopulse scheme where ML

processing is invoked only after target detection using the

center sum beam. The modified scheme using the center

beam for detection followed by MLE angle estimation

(Scheme 2A) achieves the benefits of the elimination of

beam-shape loss in angle estimation but still suffers the

beam-shape loss for the detection. Another modification can

be derived to use all the sum beams for detection, and the ML

processing can be invoked once a target is detected by one or

more beams (Scheme 2B). This approach eliminates the

beam-shape loss and the requirement to search for the target

angle for every range cell; it still requires an extensive angle

search once a target is detected.

Multiple simultaneous beams can be generated by using

multiple sets of weighting coefficients. Suppose B0 is the

transmit beam center. On receive 4 sets of monopulse beams

are generated to provide target search and angle estimation

processing. The squinted beams B1, B2, B3 and B4 are

located at a distance of a 3 dB or 6 dB beamwidth away from

B0 and can be in the configuration of 2 x 2-shaped or

diamond-shape.

The deterministic beamforming for simultaneous beams

followed by target detection and angle estimation (Scheme 3)

is given by Figure 1 and is described in the following steps:

Step 1: The sub-array or element data are combined digitally

to generate 4 sets of monopulse beams given by

4,3,2,1

)()()(

)()()(

)()()(

1

)()(

1

)()(

1

)()(

=

=

=

=

∑

∑

∑

=

∆∆

=

∆∆

=

ΣΣ

i

trnwtr

trnwtr

trnwtr

N

n

n

ii

N

n

n

ii

N

n

n

ii

EE

AA

The weighting coefficients of the squinted beams can be

constructed from those of the center beam by steering:

),(),(

),(),(

1

21

vugRvug

rRvugvu

H

H

−

−

=Γ

)ˆ,ˆ()ˆ,ˆ(

)ˆ,ˆ(ˆ

1

1

vugRvug

rRvugs

H

H

−

−

=

4,3,2,1

)(2

exp(),(

),(*.

)()()()(

)()()(

=

+=

=ΣΣ

i

yvxujvue

where

vueww

iiii

iii

λ

π

x, y are column vectors depicting the horizontal and vertical

antenna element co-ordinates, 4

1

)()( ),(=i

ii vu are the steering

directions or centers of the squinted beams, and .* refers to

point-wise multiplication of two vectors. Similarly, the delta-

azimuth and delta-elevation beams are defined as following:

4,3,2,1

),(*.

),(*.

)()()(

)()()(

=

=

=

∆∆

∆∆

i

vueww

vueww

iii

iii

EE

AA

Using these weights, the antenna patterns are given by:

4,3,2,1

),(),(

),(),(

),(),(

)()()(

)()()(

)()()(

=

−−=

−−=

−−=

∆∆

∆∆

ΣΣ

i

vvuugvug

vvuugvug

vvuugvug

iii

iii

iii

EE

AA

Step 2: Detection processing is accomplished by selecting the

maximum of the magnitudes of all the sum beams and

compared to a threshold, i.e.

max

*i beam gives the maximum detection performance. The sum

beam and the delta beam measurements are then used for the

monopulse angle estimation.

Step 3: The ratio of the corresponding delta-azimuth beam

over the ith sum beam is used to determine the azimuth angle

and the ratio of the corresponding delta-elevation beam over

the ith sum beam is used to determine the elevation angle

using look-up tables:

)()(

)(

)(

)(

)()(

)(

)(

)(

ˆˆ})(

)({

ˆˆ})(

)({

ii

i

i

i

E

ii

i

i

i

A

vvvtr

trrealM

uuutr

trrealM

E

A

−=⇒=

−=⇒=

Σ

∆

Σ

∆

Step 4: The directional-cosines are derived with respect to the

i-th beam. These coefficients can be transformed back to the

center beam reference:

)()(

)()(

ˆˆ

ˆˆ

ii

ii

vvv

uuu

+=

+=

Employment of multiple simultaneous beams eliminates the

beam-shape loss of conventional monopulse in target

detection and angle estimation, thus enables search

performance over larger area. This scheme eliminates the

beam-shape loss and extends the coverage performance like

the MLE approach at the expense of the computational cost

as it is required to carry the computational load of forming 12

beams and the associated pulse compression and Doppler

processing.

One of the benefits of DBF is that it supports multiple

processing schemes simultaneously. Furthermore these

schemes can be combined to balance the computational

complexity and performance. We here describe a scheme on

combining the monopulse and the MLE schemes. The

rational is that monopulse processing is computational most

efficient and performs very well when the target is within the

beam. The MLE scheme has optimal performance in the

elimination of beam-shape loss and in the extension of the

coverage at the cost of computational burden in the angle

search. Multiple sets of monopulse beams eliminate beam-

shape loss and extend coverage at the expense of

computational requirement of beamforming of 12 channels

and carrying out the associated pulse compression and

Doppler processing. Thus we combine the monopulse

processing and MLE processing by constructing a scheme

with 1 set of monopulse beams in the center and 4 additional

sum beams at the 3 dB or 6 dB away from the center beam

center as in the MLBP scheme. The 5 sum beams are used for

detection as in Scheme 2B. Once a target is detected, we

determine which sum beam generates the detection. If the

detection is attributed to the center sum beam, we know the

target is within the center beam, and monopulse processing is

used for the target detection, otherwise, the target is on the

edge or outside of the center beam, thus MLE processing

using the 5 sum beams is invoked. In this approach (Scheme

4), the beam-shape loss is eliminated and the coverage

extended and monopulse processing is utilized when the

target is within the beam. This scheme is illustrated in Figure

2.

III. SIMULATION RESULTS

In this section, we assess the beam-shape loss and the angle

estimation performance of the discussed schemes using

simulation. We consider an array with digital beamforming

at the element level with half-wavelength spacing. For each

processing scheme, the antenna gain performance and the

angle estimation are generated by stepping the target source

i

*)( )( ithresholdtr i⇒≥

Σ

over the 3 dB and 6 dB received beamwidth on a grid spacing

of 2 msine along both the u axis and the v axis. The transmit

beam is assumed to be spoiled uniformly over the entire 6 dB

beamwidth and thus the effect is included in the SNR for the

performance evaluation. The antenna gain and the angle

estimation performance are evaluated at each grid point and

are averaged over the 3 dB and 6 dB beamwidth. For the

angle estimation performance, the SNR is set to be 18 dB

when the target is at the peak of the beam. A Monte-Carlo

simulation of 100 times is used to determine the angle

performance for each grid point. The beam-shape loss and the

angle estimation performance are summarized in Table 1 and

Table 2 respectively. The values averaged over 3dB

beamwidth serve as the basic performance parameters and the

values averaged over the 6 dB beamwidth are used to

evaluate the capability in coverage performance extension.

The performance of the monopulse processing is used as the

benchmark for comparison. The beam-shape loss for

monopulse processing is 1.1 dB and 2.6 dB over the 3dB

beamwidth and 6 dB beamwidth respectively. The RMSE for

angle estimation is 2.87 msine and 4.03 msine for the 3dB

beamwidth and 6 dB beamwidth respectively. The results

show that the beam-shape loss can be recovered by ML

processing or by employment of multiple simultaneous

received beams. The beam-shape loss using 4 sets of

monopulse beams (Scheme 3) is 0.7 dB over both the 3 dB

and the 6 dB beamwidth, and the beam-shape loss using 5

sum beams (Scheme 2B) is 0.4 dB over both the 3 dB and 6

dB beamwidth. For angle estimation, Scheme 3 with multiple

sets of monopulse beams has the best performance results

where Scheme 4 approaches the performance of the

monopulse scheme within the 3 dB beamwidth and the

performance of MLE scheme within the 6 dB beamwidth.

IV. SUMMARY

Conventional monopulse processing suffers beam-shape loss

in target detection and angle estimation. MLBP eliminates

beam-shape loss at the expense of computational cost. The

computational burden is on the implementation of the 2-

dimensional angle search. DBF of multiple sets of

monopulse beams eliminates beam-shape loss and extends

detection and angle estimation coverage at the expense of

computational cost. The computational burden is due to the

digital beamforming of 12 beams and the associated pulse

compression and Doppler processing. DBF provides

flexibility in the processing schemes and these schemes can

be combined to improve the performance and computational

complexity. A scheme is developed where monopulse

processing is employed if target is in the center beam and a 5

beam MLE is employed if the target is on the edge of the

center beam or in the outer beams. In this manner,

computational complexity is controlled, beam-shape loss is

eliminated and the coverage performance is extended.

REFERENCES

[1] C. Kerce, G. Brown and M. Mitchell,” Phase-Only Transmit Beam Broadening for Improved Radar Search,” Proceedings of 2007 IEEE Radar Conference. April 17-20, 2007, pp. 451-456.

[2] R. M. Davies and R.L. Fante, “ A Maximum-Likelihood Beamspace Processor for Improved Search and Track,” IEEE Transactions of Antennas and Propagation, vol.49, no. 7, July 2001, pp. 1043-1053.

[3] Y. Liu, C.G. Wong and W. Kennedy, “Computationally Efficient Angle Estimation Using Maximum Likelihood in a Digital Beam-Forming Radar,” Proceedings of 2007 IEEEl Radar Conference, April 17-20, 2007, pp. 337-342.

[4] E. Baranoski and J. Ward, “ Source localization using adaptive subspace beamformer outpus,” Proc. 1997 IEEE Conf. Acoustics, Speech and Signal Processing (ICASSP97), vol. 5, pp.3773-3776.

Figure 1 Multiple sets of monopulse beams (Scheme 3)

Figure 2 Switching monopulse and MLE processing

(Scheme 4)

Ti≥Σ )max( )(

)0(

A∆

DB

F

•

•

•

• )0(

E∆

4

0

)( }{=

Σ i

i Target Detection

MLE using 5

Beam

Center Beam

Monopulse Processing

i=0

Yes

No

Ti≥Σ )max( )(

4

1

)( }{=

∆ i

i

A

})(Re{ˆ)(

)(1)(

i

i

Ei fvΣ

∆=

−

DBF

•

•

•

•

4

1

)( }{=

∆ i

i

E

})(Re{ˆ)(

)(1)(

i

i

Ai fuΣ

∆=

−

4

1

)( }{=

Σ i

i Target Detection

Angle

Estimation

)ˆ,ˆ( )()( ii vu

i-th Beam

Scheme Beam-Shape Loss

averaged over 3 dB

beamwidth

Beam-Shape Loss

averaged over 6 dB

beamwidth

Monopulse

Processing

(Scheme 1)

1.1 dB 2.6 dB

MLBP

(Scheme 2)

0 dB 0 dB

MLBP with center

beam for detection

(Scheme 2A)

1.1 dB 2.6 dB

MLBP with all beams

for detection

(Scheme 2B)

0.4 dB 0.4 dB

Multiple sets of

monopulse beams

(Scheme 3)

0.7 dB 0.7 dB

Combined Monopulse

& MLE

(Scheme 4)

0.4 dB 0.4 dB

Table 1 Summary of beam-shape loss performance

Scheme Total angle

RMSE

averaged over

3 dB

beamwidth

Total angle

RMSE

averaged over

6 dB

beamwidth

Monopulse

Processing

(Scheme 1)

2.87 msine 4.03 msine

MLBP

(Scheme 2)


Multiple sets of

monopulse beams

(Scheme 3)


Combined

Monopulse & MLE

(Scheme 4)


Table 2 Summary of RMSE angle estimation performance

04977010

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