Low-cost Electronically Scanning Antenna with Randomly 

Selected Delay Line Lengths 

by Geoffrey Goldman 

ARL-TR-5211 June 2010 

Approved for public release; distribution unlimited. 
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Army Research Laboratory 

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ARL-TR-5211 June 2010 

Low-cost Electronically Scanning Antenna with Randomly 

Selected Delay Line Lengths 

Geoffrey Goldman 

Sensors and Electron Devices Directorate, ARL 

Approved for public release; distribution unlimited. 
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Low-cost Electronically Scanning Antenna with Randomly Selected Delay Line 

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Geoffrey Goldman 

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14. ABSTRACT 

A radar architecture that requires a single analog-to-digital converter and no active phase shifters was developed that can 

electronically search a three-dimensional (3-D) volume and provide range resolution and angular resolution proportional to the 

Rayleigh criterion for a given bandwidth and aperture size. The architecture is based on a frequency scanning antenna feed 

with delay lines whose lengths are randomly selected in combination with digital signal processing algorithms. I investigated 

the feasibility of the architecture to perform target localization in position and velocity by analyzing one-dimensional (1-D) 

antenna patterns and graphing a cost function based on an L2-norm. A single realization of the system was selected, 

simulated, and analyzed. The range and velocity resolution seen in the plots of two-dimensional (2-D) slices of the cost 

function are consistent with the position and velocity resolution derived from the Rayleigh criterion. For a low-cost solution, 

signals with Doppler shifts that exceed a given threshold should be transmitted to a central computer for more processing. 

15. SUBJECT TERMS

ESA radar scanning antenna 

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Geoffrey Goldman 

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iii 

Contents 

List of Figures iv

Acknowledgments v

1. Introduction 1

2. Radar System 2

3. 1-D Antenna Patterns 3

4. Simulation 7

5. Cost Function 11

6. Conclusions 14

7. References 16

List of Symbols, Abbreviations, and Acronyms 17

Distribution List 18 
iv 

List of Figures 

Figure 1. Block diagram of radar system with feed lines for the receive antenna whose 

length are selected randomly. ....................................................................................................2

Figure 2. Two-dimensional (2-D) geometry for a 1-D linear array for a stationary target in 

the far-field. ................................................................................................................................3

Figure 3. The 1-D receive antenna patterns for the first, second, and fifth frequency step. ...........7

Figure 4. Eigenvalues of the observation matrix created from the different antenna patterns. ......8

Figure 5. Simulated 1-D antenna pattern using matched filter and WLSQ approaches. ................8

Figure 6. The 1-D antenna patterns simulated for SNRs of 10, 20, and 25 dB. ...........................10

Figure 7. Zoomed in 1-D antenna patterns simulated for SNRs of 10, 20, and 25 dB. ................10

Figure 8. Cost function for a single target located at (5,0) m. ......................................................12

Figure 9. Cost function zoomed in for a single target located at (5,0) m. ....................................13

Figure 10. Cost function for a single target with a velocity vector of (15,15) m/s. ......................13

Figure 11. Cost function zoomed in for a single target with a velocity vector of (15,15) m/s. ....14
v 

Acknowledgments 

I would like to thank Amir Zaghloul for his helpful discussions on the antenna configuration and 

signal processing algorithms and Theo Anthony for his helpful discussions on antenna 

configurations. 
vi 

INTENTIONALLY LEFT BLANK. 
1 

1. Introduction 

Moving target indicator (MTI) radars have been used to detect and track targets since World War 

II. When searching for targets, a narrow antenna beam is typically scanned through a large 

region of interest. For most operational radar systems, the beam is scanned by rotating an 

antenna on a gimbal (1). For more recently developed systems, the beam is scanned 

electronically with a phased array antenna using switches, ferroelectrics, or other active devices. 

Phased array antennas can be expensive and consume large amounts of power. Another less 

expensive approach for scanning a radar beam is to use a frequency scanning antenna. Systems 

using frequency scanning antennas trade good angular resolution for poor range resolution (2). 

The goal of this design is to have a low-cost, low-power system with both good range and 

angular resolution. 

Numerous techniques have been developed to reduce the cost, size, and power requirements of 

electronically scanning antennas (ESA). One technique to reduce the cost is to aperiodically 

place a smaller number of antenna elements across an aperture (3). This technique has been 

shown to be feasible based on performance metrics such as peak sidelobe level (4). I am 

proposing a similar concept but different implementation for reducing the cost of the system. 

My proposal is a radar system architecture based on a frequency scanning antenna with delay 

lines whose lengths are deterministic, but randomly selected, in combination with digital signal 

processing algorithms. This architecture uses temporal diversity rather than spatial diversity to 

reduce the cost and improve the performance on the system. 

Conceptually, orthogonal beam patterns at the receive antenna will be generated at each 

frequency with varying levels of energy spread spatially across the single element antenna 

pattern. Then, signal processing algorithms based on techniques such as least squares and 

maximum likelihood will be used to detect and track the targets of interest. From information 

theory, the maximum information content of a signal is obtained when the data have a uniform 

distribution and minimum information content is obtained when the data have a delta-like 

distribution (5). Traditionally, antenna patterns are delta-like functions, which are scanned 

across a field of view. More information about the targets should be obtained using a series of 

patterns that have distributions more closely resembling a uniform distribution. 

This report examines the feasibility of an architecture based upon a one-dimensional (1-D) linear 

array feed with random length lines. The major advantages of the architecture are a simple radar 

RF design, an antenna with no active elements, and a data acquisition system comprised of a 

single slow-speed analog-to-digital converter (ADC). The major disadvantages of the 

architecture are the signal processing is much more complicated, the effective signal processing 

gain associated with the antenna may be reduced relative to a similarly sized antenna, and there 

are potential ambiguities associated with target localization. 
2 

2. Radar System 

A radar architecture with a single input and single output was developed with the goal of having 

near orthogonal beams as a function of frequency in the receive antenna. The concept supports 

arbitrary waveforms and arbitrary antenna placement; however, to simplify the signal processing, 

a radar system based upon a continuous wave (CW) stepped-frequency waveform was analyzed. 

Figure 1 shows a block diagram of the radar system. The radar signal is transmitted through a 

single antenna and received with an array of antennas that are combined with feed lines of 

random length. The received signal is amplified, down converted, and then smoothed with a 

band-pass filter (BPF). Only signals from targets moving at a sufficient velocity will pass to the 

ADC. The single element antenna patterns for both transmit and receive antenna elements are 

identical. 

Figure 1. Block diagram of radar system with feed lines for the receive 

antenna whose length are selected randomly. 

Conceptually, the proposed radar system contains enough information to track moving targets in 

stationary clutter. The velocity of the targets can be determined by performing a discrete Fourier 

transform (DFT) on the time samples collected at each frequency. Conceptually, the range 

information on moving targets can be obtained by performing a DFT across the Dopplerprocessed results after motion compensation and windowing. Conceptually, the angle of the 

targets can be determined using techniques such as matched filter processing or least squares 

estimation. To estimate target parameters, stochastic optimization techniques need to be 

developed. This report studies the feasibility of estimating the target parameters by analyzing a 

cost function based upon the Euclidian norm. 
3 

3. 1-D Antenna Patterns 

Analysis of the 1-D antenna patterns provides insight into the more complicated system 

identification problem. 1-D antenna patterns were simulated and analyzed for a radar system 

similar to the block diagram shown in figure 1. For stationary targets, the BPF shown in figure 

1 was removed. The geometry associated with a 1-D array with N antenna elements for the pth 

target is shown in figure 2. 

Figure 2. Two-dimensional (2-D) geometry for a 1-D linear array for a stationary target in 

the far-field. 

For a step-frequency waveform, the returned normalized electric field from P stationary point 

scatter targets in the x-y plane is given by 

1   1 0

0 2 ( ) ( ) P N T p p

p n p

f mf j R n E m A e c

 r

      

     

   

         (1) 

where E (m) is the normalized electric field for the mth frequency (0 to M–1), p is the target 

number (1 to P), n is the antenna element number (0 to N–1), Ap is the amplitude associated with 

R0 p

N receiver 

antenna elements 

L 

θp 

pth target 

T R p

Transmit 

Antenna 
4 

the pth target, f0 is the carrier frequency, and f is the frequency step size, c is the speed of light. 

RTp is the range from the transmit antenna to the pth target and 

p p ( ) 0 cos r R n    nL  p n d  K (2) 

is the range from the pth target to the ADC for the nth antenna element. R0p is the range from the 

left most receive antenna element in the array to the pth target, L is the separation between 

antenna elements in a linear array, and θp is the angle to the pth target from the receive antenna. 

Finally, dn is length of the nth delay line and K is an arbitrary constant. 

From measurements of E(m), one can estimate the angle of arrival, θp , for each target. A 

standard approach to estimating θp is to use a bank of matched filters. The matched filter output 

can be described as an inner product between the measured data and the selected matched filter 

as shown below 

  ( ), ( ) q q

A   Em m w

,

 (3) 

where ( )

q w m is the normalized electric field for a single point target at an angle of θq, range of 

zero and calculated using equation 1. It is desired to have the maximum response in equation 3 

when the data and the matched filter are at the same angles and zero when they are at 

significantly different angles. The response of the match filter calculated for the pth target 

before the summation over frequency is given by 

 0 

1

0

1

0

1

0

1

0

cos

cos

* () ()

0 2

0 *

2

p p n

M

m

N T K

p n

M

m

N

n

q

q n

nL

nL

Em m w

f mf j R R d e c

C

f mf j e c

d



 

 





  







    

  



 

                                        

 (4) 

where C is a constant and * is the complex conjugate. After some algebraic manipulation of 

equation 4, we obtain the following: 
5 

 

   

     

     

1 1 0 0

0

1

0

2

0 1

3

0 2

0

() () * 2

0 2 cos cos

0 2 2 cos cos cos

0 2 2 cos cos 2 cos

M

M Tp p m m

N

n p q

N

n p q nn p

N

n p q nn p

q

f mf Em m w C e j R R

c

f mf j e L n c

f mf j e dd L nL c

f mf j e dd L nL c

j

 

  

  

  

 

 

  

    

    

   

       

   

     

   

       

   

       



    0 1

0 2 ( 1) cos N pf mf

e dd N L c

   

   

   

     

 

 (5) 

Ideally, the terms on the left-hand side of equation 5 should add to zero or near zero for p  q. 

This would result in a beam pattern with no or small sidelobes. Now, the problem is to select 

optimal lengths for the delay lines to minimize the sidelobes calculated from equation 5. 

Obtaining this goal is a complex nonlinear problem. One approach is to use delay lines with a 

random statistical distribution, and then find solutions that minimize the expected value of a cost 

function. Using this approach, it is observed that the first term in equation 5 is independent of 

the delay line length, so its expected value cannot be set to zero by randomly varying the lengths 

of the delay line. An unbiased solution can be obtained by selecting the probability distributions 

of the delay lines so that the bias from the remaining terms in equation 5 cancels the first term. 

However, the realization of this solution is not obvious. 

Another solution is to ignore the bias created by the first term and then statistically minimize the 

contributions from the remaining terms. A simpler criterion to optimize the length of the delay 

lines is to minimize the expected value of the power in the side lobes from the matched filter 

processing. The expected value of the contributions from all the terms, except the first, will be 

zero if the probability distributions of the phase differences caused by the random delays are 

uniformly distributed from 0 to 2π for all combinations. However, this distribution is not 

realizable in hardware. If the delay lines are very long, the distributions will be approximately 

uniformly distributed due to the modulation of the phase by 2π. This occurs when the length of 

the delay lines satisfies 

d d n m  f c/ 1  (6) 

where n=0,...N–1 and m=0,...N–1 for all m and n except when m=n.. This is not a requirement, 

but should provide a best-case scenario for an approach based on statistical optimization. This 

setup results in sidelobe levels (SL) proportional to 
6 

   

 

 

 

 

1 1

0 0

1

0

0 2 cos cos

0 2 1 cos cos

0 2 1 cos cos

0 sin( cos cos )

0 sin( cos cos )

M N

m n p q

p q M

m

p q

p q

p q

f mf j SL L n e c

f mf j e L N c

SL

f mf j e L c

f mf L N

c SL C

f mf L

c

  

  

  

  

  

    













   

      

                  

      

                 

1

0

M

m





  



 

. (7) 

and a signal strength proportional to NM. This result is complicated and is difficult to visualize. 

Thus, I ran simulations to gain more insight into the problem. 

I used Monte Carlo simulations to investigate the impact of the line lengths on the 1-D antenna 

pattern using two approaches. The first approach is based on match filter processing as 

previously described. The second approach for estimating the angle of a target is based on 

minimizing the weighted squared error between a desired response and a calculated response. 

The weighted squared error in integral form is given by 

   

/ 2

/ 2

2

( ) sHv d d





          (8) 

where 

      1

0

cos

N

n

v e jk nL d n   



   , (9) 

0 2( ) f m f k

c

    , (10) 

and Bd (θ) is the desired antenna pattern, θ is the azimuth angle, s is a vector of beam forming 

coefficients, () is the single element pattern for a radiator, and v()is a M x 1 array manifold 

vector that is a function of frequency step number rather than antenna element number (6). The 

error is minimized by breaking the integral in equation 8 into a summation over I intervals, and 

then approximating each interval as a single digital sample. Now, the solution to minimizing the 

weighted squared error is given by 

  1

T T s WH H H W



 ,

 (11) 

where 

Hv v v    11 1     ...     , (12) 

and W is a diagonal matrix with elements given by (i) (7). 
7 

4. Simulation 

I performed simulations to investigate the 1-D antenna patterns of stationary targets and the cost 

function of moving targets. I selected the parameters for the simulation based on the competing 

goals of having a low-cost system and near orthogonal antenna patterns. Simulations were 

performed with a carrier frequency of 10 GHz, a bandwidth of 1 GHz, 64 frequency steps, 64 

antenna elements with λ/2 antenna element spacing and Gaussian beam patterns centered at 

broadside with one-way 3-dB beamwidths of 120°, and delay lines lengths that were randomly 

selected with a uniform distribution between 0 and 20 λ. Figure 3 shows the antenna patterns for 

the first frequency at 10 GHz, the second frequency which is incremented by 15.6 MHz, and the 

fifth frequency, which is incremented by 4 × 15.6 MHz. 

Figure 3. The 1-D receive antenna patterns for the first, second, and fifth frequency step. 

The orthogonality of the antenna patterns can be analyzed by performing a single value 

decomposition (SVD) on the observation matrix calculated in equation 12. Figure 4 show the 

eigenvalues associated with the simulation parameters. The results indicate that eigenvalues are 

near zero around the 30th eigenvalue. Clearly, the antenna patterns are not orthogonal. The rank 

of the matrix can be improved by using more elements, longer delay lines, and more bandwidth, 

but it is never full ranked for a realizable system. 
8 

Figure 4. Eigenvalues of the observation matrix created from the different antenna patterns. 

One-dimensional antenna patterns were simulated using algorithms based on matched filter 

processing and weighted least squares (WSLQ). The matrices required for the WLSQ fit were 

generated by sampling the array manifold vector in angle every π/512 radians and the matrix 

inverse was computed in MATLAB using the pseudo inverse function. The results are shown in 

figure 5. The red curve shows the results for a WSLQ fit to the desired antenna pattern shown by 

the blue curve, and the black curve is generated using conventional or a matched filter approach. 

As expected, the sidelobes are high. 

Figure 5. Simulated 1-D antenna pattern using matched filter and WLSQ approaches. 
9 

The sidelobes levels in the antenna patterns can be reduced using adaptive digital signal 

processing techniques that do not distort the desired signal response while minimizing the signals 

from another direction. Mathematically, these conditions are described using 

 0 0 H

w V   (13) 

 

  1

H

d

d

w V

V



  (14) 

where θd is the desired angle, 0 is the desired null angle, and is the Euclidian norm. The 

corresponding filter coefficients can be calculated by projecting the unconstrained solution or the 

matched filter solution on to the subspace constrained by equation 13 [6 – van trees]. The 

corresponding projection matrix is given by 

      0

1

0 0 0 [ ] 0 H H

P V V   V  V 



 (15) 

and the resulting coefficients are given by 

  j j M wH V d I P    . (16) 

These equations will reduce the sidelobe level at a desired angle. To reduce all the significant 

sidelobes, the null angle can be scanned while keeping the desired angle fixed, and then finding 

the minimum response as shown below: 

  min , 1...   H Y V jJ     w j . (17) 

where wj are the coefficients calculated for the jth null angle and v() is a M x 1 array manifold 

vector for a given angle that is a function of frequency step number (8). This procedure requires 

that only one signal be present. For applications where the targets are sparse and the signals can 

be separated in Doppler, this may be a reasonable assumption. If there is more than one target, 

then the additional targets need to be located, and then nulled, before the new target is detected. 

This process requires an additional degree of freedom for each additional target and slightly 

degrades the performance of the algorithm. The results from figure 5 were reprocessed using 

equation 17. 

One-dimensional antenna patterns were simulated for signal-to-noise ratios (SNRs) of 10, 20, 

and 25 dB, as shown in figures 6 and 7. The SNRs were calculated for a single antenna element. 

The array of null angles went from –/2 to /2 in /256 increments, with the region at the desired 

angle ± /128 excluded. The antenna patterns were calculated at angles going from –/2 to /2 

in /256 increments, but were offset by /512. 
10 

Figure 6. The 1-D antenna patterns simulated for SNRs of 10, 20, and 25 dB. 

Figure 7. Zoomed in 1-D antenna patterns simulated for SNRs of 10, 20, and 25 dB. 

The results indicate that the maximum peak sidelobe level is ~15 dB below the signal of interest 

for an SNR of 10 dB. The performance improves with an increasing SNR. The Rayleigh 

criterion for angular resolution for a linear array at broadside is given by 

  0 / 2

c

Lf B

  

   

  

 (18). 

For the parameters selected, this corresponds to an angular resolution of ~0.03 radians or 1.7°. 

This angular resolution was almost achieved in the plots shown in figure 7. 

The simulation results indicate that reasonable 1-D patterns can be generated for stationary 

targets. The sidelobe levels in the 1-D patterns improve as the number of elements and the 

fractional bandwidth is increased. The performance also improved as the number of frequencies 
11 

is increased, but levels off as it approaches the number of antenna elements. For the parameters 

selected, reasonable sidelobe levels required a relatively high SNR. 

5. Cost Function 

A radar system based upon this architecture needs to detect, and then estimate the location and 

velocity of targets in its field of view. The relationship between the parameters required for 

tracking and the target returns is complex and cannot be estimated using conventional radar 

signal processing algorithm. The estimation problem can be formulated as a nonlinear 

optimization problem of a cost function. The cost function can be minimized using a variety of 

techniques depending upon the application. Genetic algorithms, simulated annealing, or particle 

swarm algorithms can be used to minimize cost functions with multiple local minimums (9). 

These techniques can be combined with traditional approaches such as gradient descent, 

Newton’s method, or the Nelder-Mead method once the global minimum is located (10). 

One possible cost function to minimize the Euclidian or L2-norm is 

ppp ppp p

1

min(A ,x ,v , ) D(m,k)- ( D(m,k,A ,x ,v , ) ˆ P

p

p

  

           (19) 

where Ap is the amplitude of the pth scattering center, xp

 is the position of the pth scattering 

center, vp

 is the velocity of the pth scattering center, p is the phase of the ith scattering center, 

P is the total number of target scattering centers, D(m,k) is the DFT of n data values measured at 

the m

th frequency step, k is the Doppler bin number, and p pp p D(m,k,A ,x ,v , ) ˆ    is the predicted 

value of D(m,k). This is a complicated optimization problem, but for some applications, the 

number of targets in each Doppler bin should be zero or one, and for many applications there is 

only one or a few scattering centers per target. This should simplify the problem considerably. 

Two-dimensional slices of the cost function described in equation 19 were generated for a target 

with an initial position of (5, 0) m and a velocity of (15, 15) m/s in the x-y plane, with no phase 

offset, acceleration, or noise using the same radar parameters as previously described for the 1-D 

antenna simulation. Two-dimensional slices of the cost functions are plotted in figures 8 through 

11 as a function of position and velocity, while the other parameters are fixed at their correct 

values. The plot increments are at 0.8 of the theoretical range and velocity resolution derived 

from the Rayleigh criterion. 

The theoretical angular resolution for a stationary target given by the Rayleigh criterion is by 

  0 cos( ) / 2

c

L fB





 

   

  

 (20) 
12 

where α=atan(0/5)=1. The figures are plotted at increments given by 

0.8

2

c

x

B

        (21) 

y r   0.8   (22) 

0.8  4 V T

   (23) 

where c is the speed of light, B is the bandwidth of the transmitted signal, r is the range (5 m), 

and T is the time for each step-frequency waveform. 

Figure 8. Cost function for a single target located at (5,0) m. 
13 

Figure 9. Cost function zoomed in for a single target located at (5,0) m. 

Figure 10. Cost function for a single target with a velocity vector of (15,15) m/s. 
14 

Figure 11. Cost function zoomed in for a single target with a velocity vector of (15,15) m/s. 

For these simulated parameters, the target is clearly localized in velocity and downrange with 

resolution equal to the Rayleigh criteria, but the minimum associated with the cross-range 

position of the target has a relatively low separation between competing local minimums. The 

localization of the cross-range position will be more sensitive to noise, but the global minimum 

is centered around the correct value and is slightly wider than the value predicted by the 

Rayleigh criteria. This result is expected, since the stationary 1-D antenna patterns also had 

large sidelobes. The sidelobes of the cost function plots can be improved by changing the radar 

and waveform parameters. Increases in the percent bandwidth of the waveform, the length of the 

time delays, and the number of elements will reduce the sidelobes in the plots of the cost 

functions. Also, performance improvements can be achieved by extended this concept from a 

single array with one ADC to multiple subarrays with a dedicated ADC for each subarray. These 

results indicate that it is possible to estimate the position and velocity of a point scatter target 

from 2-D slices of the proposed cost function with resolution close to the Rayleigh criterion. 

6. Conclusions 

A simple radar architecture with a single input and single output was developed that supports 

three-dimensional (3-D) electronically scanning of moving targets with high spatial resolution. 

The architecture is based on a frequency scanning antenna with random length feed lines. In this 

study, I investigated the feasibility of the architecture to perform target localization in position 

and velocity by analyzing 1-D antenna patterns and a cost function based upon an L2-norm. A 
15 

single realization of the system was selected, simulated, and analyzed. The results indicate that 

the concept is feasible, but requires a high SNR and complex signal processing. 

For the selected parameters, the 1-D antenna patterns generated using matched filter and 

weighted least squares processing had high sidelobe levels. To improve the results, the sidelobes 

were nulled over all angles except the desired angular region. A final antenna pattern was 

formed by taking the minimum value of each antenna pattern at every angle. This resulted in 

antenna patterns with a resolution predicted by classical array theory, but it required increased 

signal processing and was susceptible to interference by other targets. Two-dimensional patterns 

can be generated using the same techniques. 

Target localization will require nonlinear optimization of a cost function. Two-dimensional 

slices of a cost function based upon an L2 norm indicated that global minimum exists for 

localizing simple targets. However, the y-position estimate had a relatively small separation 

between other competing local minimums. The range and velocity resolution seen in the plots of 

the cost function were consistent with the range and velocity resolution calculated from the 

Rayleigh criterion. 

For the system to be practical, the solution to the localization algorithm should be calculated 

from the radar platform. Doppler detections that exceed a given threshold could be wirelessly 

transmitted to a central computer for more processing. This process would reduce the cost, size, 

and power requirements of the radar front end. The power, size, and cost of the central computer 

system would be larger than traditional radar systems, but it could serve multiple roles and be 

located in a secure location with adequate resources. 
16 

7. References 

1. Skolnik, M. I. Introduction to Radar Systems; McGraw-Hill: New York, 1981. 

2. Ishimaru, A.; Tuan, H. S. Theory of Frequency Scanning Antennas. IRE Trans. Antennas 

Propag. Mar. 1962, 10. 

3. Bernhard, J. T.; et al. Wideband random Phased Arrays: Theory and Design. Wideband and 

Multi-band Antennas and Arrays, 2005, IEE 2005. 

4. Lo, Y. T. A mathematical theory of antenna arrays with randomly spaced elements. IEEE 

Trans. on Antennas and Prot. Mar 1964, 12, 257–268. 

5. Shannon, C. E. A Mathematical Theory of Communication. Bell System Technical Journal

July, October, 1948, 27, 379–423, 623–656. 

6. Van Trees, H. L. Optimal Antenna Design Part IV; Wiley Interscience: New York, 2002. 

7. Kay, S. M. Fundamentals of Statistical Signal Processing: Estimation Theory; Prentice-Hall, 

1993. 

9. Avriel, Mordecai. Nonlinear Programming: Analysis and Methods; Dover Publishing, 2003. 

10. Nelder, J. A.; Mead, R. Computer Journal 1965, 7, 308–313. 
17 

List of Symbols, Abbreviations, and Acronyms 

1-D one-dimensional 

2-D two-dimensional 

3-D three-dimensional 

ADC analog-to-digital converter 

BPF band-pass filter 

CW continuous wave 

DFT discrete Fourier transform 

ESA electronically scanning antenna 

MTI moving target indicator 

SL sidelobe level 

SNR signal-to-noise ratios 

SVD single value decomposition 

WSLQ weighted least squares 
18 

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