Signal Decomposition for

Wind Turbine Clutter Mitigation

Faruk Uysal1, Unnikrishna Pillai

1,2, Ivan Selesnick

2 and Braham Himed

3

1C&P Technologies Inc., Closter, NJ

2Dept. of ECE, NYU Polytechnic School of Engineering, Brooklyn, NY

3Wright-Patterson Air Force Base, AFRL/RYMD, Dayton, OH

Abstract — This paper addresses the problem of dynamic

clutter mitigation by focusing on the mitigation of the wind

turbine clutter from the radar data. The basis pursuit and

morphological component analysis approach are used to

decompose the radar returns into the sum of oscillatory and

transient components. The success of the morphological

component analysis rely on sparsity, thus different transform

domains needs to be identified correctly to represent each

component sparsely. The method is illustrated on a radar data

collected from a small custom built radar system to show the

success of the proposed algorithm for wind turbine clutter

mitigation.

Keywords — Signal decomposition; wind turbine clutter

mitigation; sparse signal representation;

I. INTRODUCTION

Renewable energy is currently attracting much attention and wind energy appears to be a promising source. A typical wind farm has up to several hundred wind turbines with rotating blades reaching to heights of up to a hundred feet. The enormous size and rotation of these blades present technical challenges to the effectiveness of current radar systems. Several studies have documented the adverse effect of the wind turbines and wind farms on radar returns (echoes) [1]–[3]. Methods to mitigate wind turbine clutter effects are becoming important to maintain the National Airspace System (NAS) capabilities.

Mitigation of wind turbine clutter using advanced signal processing techniques is more practical and may involve minor modification of currently installed hardware systems. Methods to separate the dynamic wind turbine clutter from terrain and topographical features (static clutter) and moving targets by using advanced signal processing techniques is the main focus of this paper. We propose an approach for decomposing the radar returns into the sum of an oscillatory component and a structured transient component. Radar returns from moving targets can be sparsely represented in the Fourier transform (FT) domain since they are assumed to be moving at constant velocity during the coherent processing interval (CPI). On the other hand, the radar echoes from the wind turbine clutter

which constitute a time-varying Doppler component are more sparsely represented using the short-time Fourier transform (STFT).

II. METHODS

A. Signal Model

Time-domain and Doppler signature of rotating objects have been well documented and numerous approaches have been proposed to define a suitable mathematical model [4]–[6]. The time-domain signature of the wind turbine clutter has been simulated using a mathematical model of rotating blades given in [5]. Although, more sophisticated modelling is required to represent real-life wind warms, the following approach will help to illustrate the time verifying Doppler present in the wind turbine clutter returns. For a set of M blades rotating with

angular velocities o with a length of L at an elevation angle

with respect to the radar line of sight, the total radar return

is given by [6]

1

( )( ) sinc ( )

M

wt k

k

okj t ts t A t e

, (1)

where o represents the transmit waveform center frequency

and

2 2

cos cosk o

L kt

M

. (2)

Expansion of (1) using Bessel functions shows that the spectrum of a single scatterer on the blades consists of

multiple spectral lines around the center frequency o with

/ 2o spacing between adjacent lines. However, due to the

various aspect angles generated at the multiple scattering centers situated along each spoke of the blades, this results in a continuous distribution for the wind turbine spectrum. As a result, returns from the wind turbines can be sparsely represented using STFT.

Moving targets can be modeled as [5]

2 2 ( ) cos /

( )tto tj f R v t c

s t e

, (3)

Contact author: Faruk Uysal , email: faruk@cptnj.com The views expressed are those of the author and do not reflect the official policy

or position of the Department of Defense or the U.S. Government. Distribution

Statement A (Approved for Public Release, Distribution Unlimited).

978-1-4799-2035-8/14/$31.00@2014 IEEE 0060

where tR is target range, is the target angle and

tv is the

target velocity. As seen from equation (3), returns from a

moving target can be sparsly represented in the Fourier

domain as a single tone.

B. Problem Formulation

Radar returns from moving targets can be sparsely represented in the Fourier Transform domain since they can be assumed to be moving at constant velocity during the coherent processing interval. On the other hand, the radar echoes from the wind turbine clutter represent the transient part, and their short intermittent rotary-based motion can be sparsely represented using Short-Time Fourier Transform. Our focus in this paper is to exploit the rotary aspect and separate out the wind turbine clutter using sparsity based signal processing methods.

For a given observed signal s containing N samples, the

superposition of two signals – wind turbine clutter wcs and

moving target ts is,

wc t s s s . (4)

Morphological component analysis (MCA) provides an

approach to recover the components wcs and

ts individually.

MCA relies on each of wcs and

ts having a sparse

representation in some suitable domains; otherwise, MCA is not applicable. The forward short-time Fourier transform linear operators and the Fourier transform linear operators

(Discrete Fourier Transform matrix) are denoted by 1F and

2F

respectively. Both the Fourier transform and the STFT satisfy the perfect reconstruction and energy preservation properties respectively. Thus, we have

* *

1 1 1 1

1 * *

2 2 2 2 2 2

,

, .

F F I F F I

F F F F F F I (5)

Here, *F denotes the complex conjugate transpose of .F

Assuming that wcs and

ts can be sparsely represented in the

bases (or frames) 1F and

2 ,F respectively, we have

*

1 1wcs F a and *

2 2at s F , where 1a and

2a are assumed to

be sparse, but unknown. As a result, they can be estimated by

minimizing the non-linear cost function,

1 2

1 21 1,

* *

1 1 2 2

arg min (1 )

subject to: + .

a a

a a

s F a F a

(6)

Here, the L1-norm is used to induce sparsity as small values

have more significant representation in L1-norm compared to

the L2-norm. Estimating 1a and

2a from (6), the desired

components ˆwcs and ˆ

ts are given as *

1 1ˆ

wc s F a and

2

*

2ˆ

t s F a .

C. Solution

The solution to the L1-norm minimization problem cannot

be solved in closed form; instead an iterative numerical

algorithm is necessary [8] – [15]. Several algorithms have

been proposed to solve this type of optimization problem. The

Split Augmented Lagrangian Shrinkage Algorithm (SALSA)

is one of the recently developed algorithms for convex

optimization problems which provides fast and effective

solutions for the Basis Pursuit and Morphological Component

Analysis problems [14].

The objective function (6) can be minimized iteratively

using SALSA [10] – [11], [14]. Equation (6) can be written

by introducing auxiliary variables, 1u and

2u as,

1 2

1 21 1,

* *

1 1 2 2

1 1

2 2

arg min (1 )

subject to: +

0

0.

u u

u u

F a F a s

u a

u a

(7)

Then, we can use the Augmented Lagrangian method

(ALM) which is also known as the method of multipliers

(MM), as follows:

1 2 1 2

2

1 1 1

1 2

*

1 1 21, , ,

1 2 2

2

*

1

2 2 2 2 211 2

1 2 2

arg min || ||

,|| ||

,su

initialize : 0, ,

repeat

+

until co

ch that :

nvergence.

u u a a

d d

u u a d

u uu u a d

a as F a F a

(8)

We may alternate between the 1a and

1u minimization to

obtain the algorithm,

1

2

1 2

1 2

2

1 1 1 1 11 2

2

2 2 2 2 21 2

2 2

1 1 1 2 2 22 21 ,

* *21 1 2 2

1 1 1 1

2 2 2 2

initialize : 0, ,

repeat

arg min

arg min (1 )

arg min

such that: +

u

u

a a

d d

u u u a d

u u u a d

u a d u a da

as F a F a

d d u a

d d u a

until convergence.

(9)

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Here, and are user-specified scalar parameters for

SALSA, and selected empirically.

The solution to the minimization problem for iu (where

1,2i ) in equation (9) can be expressed explicitly and

compactly using soft-thresholding.

The minimizer iu of

2

1 2i i u u y is given by

soft ( , / 2)i u y . Here, soft( , )Ty is the soft-threshold rule

with threshold T [10] – [13], which is defined as

soft( , ) max 0, 1 /T T y y y y , .T

The minimization problem for ia in equation (9) is a

constrained least squares problem. The solution can be

expressed explicitly in matrix form [10] – [13]. After some

simplifications, the algorithm (9) can be implemented as,

1 2

1 1 1 1

2 2 2 2

1 1* *1

1 2

2 22

1 1 1

2 2 2

initialize : 0, ,

repeat

1soft ,

12

1

2

until convergence.

d d

u a d d

u a d d

d uFs F F

d uF

a d u

a d u

(10)

III. APPLICATION OF THE ALGORITHM

To complement our theoretical effort, we have set up an

experimental facility using a custom made 2.4 GHz, S-band

frequency-modulated continuous wave (FMCW) Doppler

radar with 10 mW of power similar to that described in [15]

(shown in Fig.1b). We have remodeled the blades of a fan and

adjusted its distance to our radar to simulate a large surface

area resembling a basic wind turbine in Fig.1a

The radar unit was powered by a 5 volt battery supply and

was connected via an audio card to a computer running

MATLAB. The computer then sampled the output of the

Doppler radar using a sound card at 96 kilo-samples per

second. A 15 KHz anti-aliasing low-pass filter was installed

between the radar and the computer. Single and multi-blade

situations have been illustrated in the experimental setup by

using a basic wind turbine model. The spectrogram of the

captured data for a 3-blade wind turbine model is shown in

Fig 2 (Note that, different look angle and/or angular velocity

results with different clutter signature).

In order to evaluate the proposed algorithm a flying

metal object was employed as a moving target in the presence

of the rotating blades. Fig.3 shows the collected radar data in

the STFT domain which includes target and rotating blades

echoes together. In Fig.3, a moving target signature is buried

under the wind turbine clutter, and hence traditional filtering

techniques (such as: frequency filtering, thresholding) are

insufficient to separate the target. Fig.4 and Fig.5 show the

results of the proposed method in (10) when applied to the

real-time data captured for a 3-blade fan with an accelerating

Fig. 1. Pictures of experimental facility; Wind turbine model (a) and

custom build radar (b)

Fig. 2. Spectogram (STFT) of collected echoes from wind turbine model

(a)

(b)

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Fig. 3. Spectogram (STFT) of collected echoes

Fig. 4. Spectogram of ˆwcs wind turbine clutter (after process)

Fig. 5. Spectogram of ˆts target (after process)

metal object. Optimization parameters selected as 0.05

and 0.3 . For 1F we used the DFT; for transform

2F , we

used the STFT with a frame length of 16 samples and 50%

overlapping. Notice that the blade flashes representing the

wind turbine clutter have been separated out in Fig.4, and the

moving target signature is well separated in Fig.5. In other

words, the algorithm in (10) is able to represent the data in

Fig. 3 as the sum of those in Fig.4 and Fig.5. The simulated

scenario may be considered as the take-off of a plane where

the radar signal is disturbed by a wind turbine clutter. The

algorithm is able to separate the accelerating object and the

wind turbine clutter successfully.

IV. CONCLUSION

This paper considers the problem of separating out moving

targets buried in wind turbine generated clutter using sparsity-

based methods. Two transform domains—the Fourier domain

and the Short-Term Fourier domain are identified, where each

data set is sparse. The dual-basis algorithm is shown to

successfully separate out the moving target in wind-turbine

like clutter. A custom built micro-radar and micro-turbine

were used to study and validate the proposed method. The

results of our experiments show that sparsity based approaches

are extremely promising to suppress wind-turbine clutter. We

plan to further investigate the effectiveness of our algorithm

on other real data sets.

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