Fast Threat Detection and Localization Using Super-Regenerative Transceiver in

Random Noise Radar

Yan Zhang Member, IEEE, and Shang Wang

School of Electrical and Computer Engineering The University of Oklahoma

Norman, OK 73072

Submitted to IEEE Transactions on

Aerospace and Electronics Systems

April, 2009

Corresponding author Yan Zhang (rockee@ou.edu)

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Abstract— The concept and technology of using Super-Regenerative (SRG) transceiver as a type of ultra-fast

electronics platform for threat detection and localization is introduced. Different from the traditional Coherent-

Correlation-Receiver (CCR), the received RF signal is re-transmitted to the target and built up nonlinearly in the

RF channels. The positive feedback loop associated with the presence of a target produces a target indication.

The performance of SRG in the presence of clutter and interference is analyzed and compared with CCR-based

systems. The clutter and interference are modeled as multi-loops with diversified loop gain and delays.

Moreover, the SRG may be extended to multiple channels as part of an array system, which applies simple

monopulse-type processing on transient target signatures to extract the Angle-of-Arrival (AOA) information of

the inbound threats. Simulations and detailed laboratory measurement results are presented for SRG transceiver

and monopulse processing implementations.

Index Terms— CW radar, Detection, Tracking, Antenna arrays, Microwave Receivers

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I. INTRODUCTION

iM litary aircraft or vehicles need to conduct early detection and estimation of inbound threat munitions without

compromising the platform’s electromagnetic signature management (SM). Active phased array radar sensors

used on aircraft have had the capability of multiple threat detection and tracking [1]. However, the cost and

complexity of such systems makes it difficult to be deployed on small-size aircraft, especially unmanned

vehicles. Applying noise radar technology to this challenge, on the other hand, invokes the tradeoffs among (a)

utilizing a wideband, LPI waveform for target detection and tracking, (b) ultra-fast detection and high-speed

processing, and (c) immunity to all types of clutter and interference. For early warning systems, it is desired that

minimum a-priori knowledge about the battlefield environment is required, and the radar uses the lowest

possible radiation power to achieve reasonable effective range under various weather conditions.

The time-domain coherent correlation receivers have been extensively used in noise radar and other random

signal based radars [2-6]. In general, a correlation receiver requires a variable delay line to produce the time-

delayed replica of the transmit signals. A key tradeoff of this architecture lies between the observation time and

the correlation output performance [3]. The short observation time at the correlator’s output results in a wider

main correlation peak and higher sidelobes, the long observation time, on the other hand, delays the critical

response time, which leads to disadvantages in real-time applications. Also, high-resolution delay line devices,

either based on analog or digital technologies, are difficult to implement. Solutions to avoid the use of delay

lines using spectrum information have been discussed previously [7] but no significant progress has been made.

In order to develop a microwave noise radar transceiver architecture that is fast, sensitive and low-cost, the

nonlinear feedback mechanism is gaining attention [8]. An innovative architecture of ultra-wideband noise radar

with super-regenerative (SRG) transceiver circuit is introduced [9]. Narrowband Super Regenerative Receivers

have had a long history in communication systems [10-13]. The difference between the SRG receiver and the

conventional Coherent Correlation Receiver (CCR) is the re-transmission of the receive signal to the target

during the detection stage. Thus the radar transceiver and the target return together constitute a positive

feedback loop. The presence of the target results in a closed loop and polynomial or exponential growth of

signal power in an extremely short time. As a very simple architecture, the SRG receiver does not need coherent

signal reference and fast delay lines. Moreover, the SRG architecture has potential advantages of ultra-fast

detection and, if used in an array formation, has ‘self-steering’ capability [14-21], which can act as a ‘reflector’

and steer the array beams automatically toward the target without the use of phase shifters. The challenges to

this concept, on the other hand, remain in three aspects. First, as the transceiver is nonlinear and extremely

sensitive, any environmental clutter/noise/interference may enter the loop, triggering fast power build-up until

saturation. Preliminary studies exist on the impact of multipath on retrodirective systems [22]. However, noise

and interference effects on SRG transceiver performance have not been addressed. Second, even though the

concept is attractive, there have been few practical experiments performed to validate the technology and to

characterize the actual transceiver performance. Third, the associated direction-finding and tracking

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technologies, which can extract the Angle-of-Arrival (AOA) information from the signals of such receivers, have

not been studied.

In this effort, the theory of SRG noise radar receivers is introduced and the target detection time compared to the

CCR receiver is analyzed. Both the time-domain difference equation approach and the frequency-domain

harmonic analysis approach are applied. It is seen that both the mean and variance of the loop signal increase in

polynomial fashion with respect to the time step, and the auto-correlation function of the loop signal exhibits

periodic properties. The key issue of interference immunity of SRG receiver is addressed as the first step toward

its engineering application. The concept of multiple loops with the impact from multipath and

interference/ground clutter is discussed. The loop signal behavior with different signal-to-clutter ratio (SCR)

values is analyzed. It is shown that both the relative strength and the timing of the interference source have an

impact on inter-modulation, or ‘spurious’ responses, which in turn may limit the detection speed and add

distortion to the autocorrelation functions. Several practical technologies are developed to overcome the impact

of interference/clutter, including the loop switch, which periodically turns the loop on and off to prevent

saturation (similar to the quenching switch in traditional super-regenerative receivers), and the selection of ‘ON’

time duration, which extinguishes the possible saturation from the interference response. Another technique

feeds the receive signal to a traditional CCR receiver during the loop-open and uses a fast Doppler filter to

discriminate the fast-moving target from the slow-moving clutter background.

After the fast threat detection is performed, the transient radar signatures in multiple channels are the basis for

trajectory estimation and identification. Fast estimation of the target’s Angle-of-Arrival (AOA) is equally

important to the fast detection, and it is the pre-condition of visualizing the target’s trajectory in the battlespace.

Different fast and nonlinear signal processing approaches have been used for similar scenarios [23-26]. For

wideband noise radar, however, the short reaction time demands minimum computation load in the digital

domain. In this work, lab experiments using an X-band monopulse noise radar [4] are performed to emulate the

signatures of ultra-fast moving targets. The transient ‘open loop’ signals can be sampled and processed in

different types of monopulse processors, and the processing results are related to the AOAs through simple look-

up tables. It is shown that simple monopulse beamforming is able to be combined with the SRG transceivers to

achieve fast estimation of direction. As such, a more complete conceptual design of an SRG array with both fast

detection and tracking capability can be established.

This paper is organized as follows: Section II provides time-domain analysis of the SRG and comparison with

the CCR receiver performance. In Section III, a frequency-domain perspective of the SRG loop signal is studied

and the auto-correlation properties of the loop signals are discussed. Section IV introduces an L-band ultra-

wideband SRG transceiver system implemented with commercial-off-the-shelf (COTS) components and a series

lab measurement results as validations of theoretical models. Section V discusses fast monopulse processing for

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SRG noise radar and compares the monopulse characteristic curves (MCC) resulting from emulated transient

target signatures and different monopulse processors. Conclusions are summarized in Section VI.

II. TIME-DOMAIN ANALYSIS OF SRG

A. Basic architecture

As shown in Fig.1, The basic architecture of the SRG transceiver contains an initial excitation noise waveform

, which is transmitted, reflected from the target, received, and re-injected into the loop through a power

combiner. The total time delay from transmission to target echo reception is denoted as , which is the round-

trip time plus the total propagation delay of the electronics. Similarly, the total gain from transmit to receive,

including the gains in the RF channels, propagation attenuation, and target Radar Cross Section (RCS), is

defined as . A band-pass filter may be used in the feedback loop channel. The presence of multipath, clutter,

and interference can be modeled as multiple loops. Each individual loop has its own gain and delay. Therefore,

the loop signal is a combination of the signals from all feedback loops plus possible non-coherent external

interference .

As a result, each loop has its loop delay ( , ¿ , .., ¿ ) and gain ( , A ,…, A ) in Fig.1. This feedback system

is governed by the following equation:

¿0¿0 2¿2 N¿N A0A0 2A2 NAN

. (1)

B. Time-domain solution of the loop signal

We start our discussion by focusing on the simplest cases in which there are no interference (N = 0) and a single

interference source (N =1). The SRG operation can be simplified as first-order or second-order difference

equations for the special cases where only clutter is present and when both clutter and a useful signal are present:

v . (2) O (t)¡ A0vO (t ¡ ¿0) = s (t)vO (t)¡ A0vO (t ¡ ¿0) = s (t)

and

. (3)

Here, is the signal at the summation point before the BPF and is the BPF output. Considering the time-

variant loop gain and assuming the BPF does not distort the signal waveform, the general solution of

at (nn is a positive integer) of the first-order equation can be found using the theories introduced in [27]

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v (4) O (n¿0) =

"n¡1Yi=0

A0 (i¿0)

#vO (0) +

nXr=1

"n¡1Yi=r

A0 (i¿0)

#s (r¿0)vO (n¿0) =

"n¡1Yi=0

A0 (i¿0)

#vO (0) +

nXr=1

"n¡1Yi=r

A0 (i¿0)

#s (r¿0)

For the special case where the loop gain is constant, the above result can be simplified as

vO (n¿0) = An0vO (0) +

nXk=1

An¡k0 s (k¿0)vO (n¿0) = An

0vO (0) +nX

k=1

An¡k0 s (k¿0) (5)

Equations (4) and (5) show that when there is a single closed loop, the loop signal strength grows in polynomial

fashion depending on both the initial state and the excitation signal. Controlling the loop gain over time

effectively controls the loop signal behavior and avoids saturation. Next, we can extend the discussion from a

single loop to a double loop as in (3). Assuming constant loop gains, we can derive the general solutions of v at

of the second-order equation based on the similar theory used in (4):

OvO

n¿1n¿1

, (6)

with

Ckn =

n!

(n ¡ k)!k!Ck

n =n!

(n ¡ k)!k!. (7)

Equations (6) and (7) are based on n¿ because it is assumed that the desired target round trip plus electronic

delay is ¿ . Similar equations can be derived for other time steps. It is important to see from (6) and (7) that a

fairly complicated ‘inter-modulation’ between the target and clutter loops exists. As a result, both the power and

the relative timing (difference in loop delay) of the interference have significant impact on the loop signal

waveform.

1n¿1

1¿1

C. Comparison with Coherent Correlation Receiver (CCR) The SRG receiver’s performance can be compared with the traditional CCR based architecture shown in Fig.2.

The two architectures in Fig.2(a) and (b) use similar circuit elements. For the SRG, the received signal is re-

injected into the loop using a power combiner. A directional coupler (or power divider) samples the loop signal,

and a square-law detector records the power level of the loop signal. For the CCR, the output from the

correlation mixer is fed into a square-law detector. Both the SRG and the CCR sample the square law detector

outputs at the expected target range window and average them.

Assuming that excitation is a Gaussian random process with variance , for a single SRG loop, v is

a random process with time-variant variance (power), i.e.,

O (n¿0)vO (n¿0)

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¾ . (8) 20(n¿0) ¼ ¾2

s

nXk=1

jA0j2(n¡k)¾2

0(n¿0) ¼ ¾2s

nXk=1

jA0j2(n¡k)

For a double loop the simplest case is when ¿ , and the double loop returns to a single loop with loop gain

. The variance is then given by

1 = ¿0¿1 = ¿0

A1 + A0A1 + A0

. (9)

The general case of ¿ will lead to a much more complicated structure of the loop signal. A concept of how

the loop signal power grows based on different target-clutter separations can be obtained from appropriate

approximations.

1 6= ¿0¿1 6= ¿0

For example, we can consider the special case with ¿ , where "" is sufficiently small so that the first

term in (6) can be considered to be almost equal t (0)(0) (zero), and therefore ignorable, n¿1)n¿1) again

only depends n , A1A1 s(t)s(t). It can be shown tha 1)1) is still a Gaussian random process with variance

given by

1 ¡ ¿0 < "¿1 ¡ ¿0 < "

o vOvO

t v0 (n¿v0 (n¿

and

o and

v0 (v0 (

A0A0

, (10)

where is the autocorrelation of s . The ultra-wideband property of s leads to the following

approximation:

(t)s(t) (t)s(t)

R , (11) ss (¿) =

½¾2

s ; j¿ j · ¿c

0; j¿ j · ¿cRss (¿) =

½¾2

s ; j¿ j · ¿c

0; j¿ j · ¿c

where ¿ is a ‘cutoff’ correlation time for excitation signal s , and can be estimated by the inverse of the signal

bandwidth.

c¿c (t)s(t)

An obvious condition to yield non-zero terms in (11) is

r . (12) 1 = r2; m1 = m2r1 = r2; m1 = m2

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And the variance expression (10) will be simplified to

¾ . (13) 21(n¿1) ¼ ¾2

s ¢n¡1Xr=0

rXm=0

¡Cm

r Ar¡m0 Am

1

¢2¾2

1(n¿1) ¼ ¾2s ¢

n¡1Xr=0

rXm=0

¡Cm

r Ar¡m0 Am

1

¢2

Equation (13) reveals the key elements of the loop signal’s power growth. However, there are other

combinations of r which may result in j and contribute to ¾ . As a consequence, a

complicated inter-modulation response depending on the relative time delays will be introduced.

1; r2; m1; m2r1; r2; m1; m2 ¿ j < ¿cj¿ j < ¿c21 (n¿1)¾21 (n¿1)

As an example, Fig.3 shows a simulated ¾ normalized with ¾ at the 5th loop delay of a true target for

different relative delays of target and clutter/interference based on different approximations. It is clearly seen

that the strongest loop signal power occurs when ¿ , and equations (9) and (10) give the same predictions.

When ¿ , loop signal power may also show power spikes which are generally lower than the spikes for

and tend to decrease with higher SCR. Equation (13) provides a good approximation for the “base” of

the ¾¾ , which is independent of ¿¿ while it is also a conservative estimation for high SCRs.

21(n¿1)¾21(n¿1)

¿

¿0¿0

2s¾2s

1 = ¿01 = ¿0

1 6= ¿0¿1 6= ¿0

¿0¿0

(n¿1)(n¿1)

¿1 =¿1 =

2121 1 ¡1 ¡

D. Comparison of square-law detector outputs Assuming a simple square-law detector can be used according to the property of central Chi-square distribution,

we can obtain the mean and variance of the detector output. For the single-target case,

mSRG;0 (n¿0) =2¾2

0p¼

;

¾2SRG;0 (n¿0) = 4¾4

0

·¡( 3

2)p¼

¡ 1¼

¸mSRG;0 (n¿0) =2¾2

0p¼

;

¾2SRG;0 (n¿0) = 4¾4

0

·¡( 3

2)p¼

¡ 1¼

.̧ (14)

For the target-plus- interference case,

mSRG;1 (n¿1) =2¾2

1p¼;

¾2SRG;1 (n¿1) = 4¾4

1

·¡( 3

2)p¼¡ 1

¼

¸mSRG;1 (n¿1) =2¾2

1p¼;

¾2SRG;1 (n¿1) = 4¾4

1

·¡( 3

2)p¼¡ 1

¼

.̧ (15)

Here represent the Gamma function [28]. From (14) and (15), the mean value of the square-law detector in

Fig.2 (a) is proportional to the variance, and the variance of the detector output follows the square of the

variance. Considering the variance grows in polynomial fashion with time, equations (14) and (15) indicate an

extremely fast growing, nonstationary process. For any given time index , the larger SCR will increase the

detection probability and reduce false alarms.

To compare the nonlinear SRG receiver with the commonly used coherent correlation receiver (CCR, Fig.2(b)),

assuming the sampling interval at the correlator output is ¢ , the detector output ZZ of the correlation receiver, ¿¢¿

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when the receive and reference signals are zero mean Gaussian processes with variances ¾ and ¾ , has the PDF

[29]:

21¾21

22¾22

Pm (Z) =4

¾1¾2 (1 ¡ ½2) (m ¡ 1)!

·Z

¾1¾2

¸m

Km¡1

·2Z

¾1¾2 (1 ¡ ½2)

¸I0

·2½Z

¾1¾2 (1 ¡ ½2)

¸Pm (Z) =

4

¾1¾2 (1 ¡ ½2) (m ¡ 1)!

·Z

¾1¾2

¸m

Km¡1

·2Z

¾1¾2 (1 ¡ ½2)

¸I0

·2½Z ̧ , (Z>0) (16)

¾1¾2 (1 ¡ ½2)

where ½½ is the correlation coefficient between the two random samples, is the number of samples acquired

and averaged, and II and KK are modified Bessel functions. Based on the approach introduced in [29], the

square-law detector output WW is approximately a Gaussian variable with mean and standard deviation as

mm

E [W ] = m¡1 + m½2

¢(¾1¾2)

2E [W ] = m

¡1 + m½2

¢(¾1¾2)

2 (17)

and

¾W = (¾1¾2)2 £

m (m + 2) + 2m(m2 + 4m + 2)½2 + m2 (2m + 1) ½4¤1=2

¾W = (¾1¾2)2 £

m (m + 2) + 2m(m2 + 4m + 2)½2 + m2 (2m + 1) ½4¤1=2 (18)

For CCR, the observation time is limited to the time span during which the correlation coefficient ½½ is a constant.

Compared to SRG, it is reasonable to assume that ¾ (i = 0 or 1). When the time-delay of the

transmit replica matches the true target range, ½½ , then the mean and variance of the square-law detector

output can be written as

1 = ¾s; ¾2 = Ai¾s¾1 = ¾s; ¾2 = Ai¾s

¼ 1¼ 1

mCCR;0 (n¢¿) = ¾2sA2

0n (1 + n)mCCR;0 (n¢¿) = ¾2sA2

0n (1 + n), (19)

¾2CCR;0 (n¢¿ ) = ¾4

SA40 ¢ 2n

¡2n2 + 5n + 3

¢¾2

CCR;0 (n¢¿ ) = ¾4SA4

0 ¢ 2n¡2n2 + 5n + 3

¢. (20)

For the case where both target and interference are present, the interference signal is characterized by ½ .

Assuming the link gain for the true target is A1A1, the link gain for the interference signal source is A . The mean

and variance of the square-law detector output become

¼ 0½ ¼ 0

0A0

mCCR;1 (n¢¿) = ¾2sA2

1n (1 + n) + ¾2sA2

0nmCCR;1 (n¢¿) = ¾2sA2

1n (1 + n) + ¾2sA2

0n, (21)

and

¾ . (22) 2CCR;1 (n¢¿) = ¾4

SA412n

¡2n2 + 5n + 3

¢+ ¾4

SA40(2n + n2)¾2

CCR;1 (n¢¿) = ¾4SA4

12n¡2n2 + 5n + 3

¢+ ¾4

SA40(2n + n2)

Based on (14)-(15) and (19)-(22), numeric comparisons between SRG and CCR using the same square-law

detector can be performed. A typical example assumes the target is located at a distance of 900m (6μs) and the

clutter/interference source is located at a distance of 150m (1μs). To illustrate the ultra-fast power growth of the

SRG loop signal, outputs from square-law detectors are recorded for a time duration of 10 round-trips (60 μs). It

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is assumed that the ADCs in both Fig.2(a) and Fig.2(b) have 2 MHz sampling rates. The conservative estimate

from equation (13) is used to obtain ¾ . 21(n¿1)¾21(n¿1)

The comparison results are plotted in Fig.4. For SRG, the rising speed of the mean value is about 5 dB/10 μs

when there is only clutter present. The rising speed is almost 20 dB/10 μs when SCR increases to 3 dB. For

CCR, the rising speed of correlator output is relatively faster within the first target round-trip delay, and becomes

stabilized even for high SCR (< 2 dB/ 10 μs). It is important to note that the SRG can not only provide ultra-fast

target indication compared to the CCR, but also much stronger capability to discriminate useful signals from

clutter response. This is manifested in Fig.4(a). At 60 μs, a 1.5 dB SCR increase leads to 10-20 dB stronger

detector mean output, while leading to only about a 3 dB increase in CCR’s detector mean output. It is also seen

from Fig.4(b) that at different observation times the differences among the CCR detector output levels depend

mainly on the SCR.

On the other hand, the example also illustrates the extreme sensitivity of the SRG to both the target signal and

clutter. Both mean and variance of the SRG receiver exhibit much faster growth compared to those of the CCR,

even for clutter-only cases. A strong loop signal caused by clutter/interference may be sufficient to saturate the

receiver, thus must be controlled. A much larger variance growth with time for the SRG also implies the system

requires a much larger dynamic range than the CCR in order to accommodate the large uncertainty in the

detector outputs and the ultra-fast loop responses.

III. FREQUENCY-DOMAIN AND CORRELATION CHARACTERISTICS

Another approach to analyze the SRG loop signal properties is to decompose the broadband excitations into

harmonics. The loop signal can then be considered as the combination of the responses from all frequency

elements. When the BPF matches the signal frequency band, the difference equation maybe written as

,

, (23)

where the nth signal component of v is a harmonic waveform: O (t)vO (t)

v . (24) o;n (t) = anej!ntvo;n (t) = anej!nt

In the receiver loop, each frequency element satisfies the following equation:

, (25)

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where is the harmonic signal at the summation point before the BPF, is the BPF output for the

frequency component, and and are the amplitude and frequency of the frequency component,

respectively. Again, assuming the BPF is ideal ( ), the solution for v is simply the

combination of solutions for all frequency elements based on a closed-loop transfer function, i.e.,

vo;n (t) = vs;n (t)vo;n (t) = vs;n (t) o (t)vo (t)

vo (t) =X

n

anej!nt

1 ¡ A0e¡j!n¿0 ¡ A1e¡j!n¿1vo (t) =

Xn

anej!nt

1 ¡ A0e¡j!n¿0 ¡ A1e¡j!n¿1. (26)

Strictly speaking, v is not a stationary process. However, a stable power spectrum can generally be observed

for loop signals. As such, the auto-correlation function of the output signal v can be defined as

o(t)vo(t)

o (t)vo (t)

RV (¿ ) = E fvo (t) v¤o (t ¡ ¿)gRV (¿ ) = E fvo (t) v¤o (t ¡ ¿)g. (27)

For wideband Gaussian noise, we can assume all a s are uncorrelated with each other and a uniform amount of

energy is contained across all the harmonic components. Therefore the autocorrelation function of the loop

signal becomes

nan

RV (¿) =X

n

E©a2

n

ªej!n¿

Fn (¿1; ¿0)RV (¿) =

Xn

E©a2

n

ªej!n¿

Fn (¿1; ¿0), (28)

where

Fn (¿1; ¿0) = 1 + jA0j2 + jA1j2¡2Re

¡A¤0e

j!n¿0 + A¤1ej!n¿1

¢+2Re

¡A0A

¤1e

j!n¢¿10¢Fn (¿1; ¿0) = 1 + jA0j2 + jA1j2

¡2Re¡A¤0e

j!n¿0 + A¤1ej!n¿1

¢+2Re

¡A0A

¤1e

j!n¢¿10¢ , (29)

with ¢ . When both A and A are real, the result can be simplified as ¿10 = ¿1 ¡ ¿0¢¿10 = ¿1 ¡ ¿0 0A0 1A1

Fn (¿1; ¿0) = 1 + A20 + A2

1

¡ 2A0 cos !n¿0 ¡ 2A1 cos !n¿1

+ 2A0A1 cos !n¢¿10

Fn (¿1; ¿0) = 1 + A20 + A2

1

¡ 2A0 cos !n¿0 ¡ 2A1 cos !n¿1

+ 2A0A1 cos !n¢¿10

. (30)

For two loops with equal delay (target + interference, and ¿ ), F reaches minimum value when 0 = ¿1¿0 = ¿1 nFn

! , (31) n¿1 = k¼!n¿1 = k¼

and the auto-correlation of the loop signal is simply the convolution of the auto-correlation function of the

original noise waveform with a periodic function, i.e.,

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RV (¿) = RS (¿) ¤ 1

(1¡A0 ¡A1)2

Xn

± (¿ ¡ n¿1)RV (¿) = RS (¿) ¤ 1

(1¡A0 ¡A1)2

Xn

± (¿ ¡ n¿1). (32)

Equation (32) clearly indicates the presence of discrete line spectra in the frequency-domain. The situation is

much more complicated when the target and interference loops have different time delays, especially when the

signal and interference have similar amplitudes. For this case, the local peaks of the autocorrelation function

may appear at integral multiples of , , as well as locations between them.

Fig.5 shows simulation examples of R under particular conditions. From Fig.5(a), it is seen that the SRG

loop signals exhibit clear periodicity in their auto-correlations, which will translate into discrete spectrum lines

in the frequency domain. The width of the correlation peak is similar for the SRG and CCR. From Fig.5(b), it is

seen that when the SCR is low, more correlation signal power will ‘leak’ to the sidelobes of R and

complicated inter-modulation peaks will appear.

V (¿ )RV (¿ )

V (¿ )RV (¿ )

IV. DUAL-CHANNEL, L BAND TRANSCEIVER MEASUREMENTS A dual-channel SRG transceiver prototype is designed and fabricated using commercial-off-the-shelf (COTS)

RF components. It contains two identical loops. Each loop has T/R antennas, a power amplifier, LNA, and

‘quenching control’ switches. The quenching switches (as in Fig.2 (a)) are fast GaAs switches controlling the

precise times that the feedback loops are opened and closed. The loop signals are sampled from a power divider

and correlated in an RF mixer. The two RF channels are excited by the same Gaussian noise source covering the

1-2 GHz ultra-wide frequency range. A broadband variable attenuator controls the power level of the random

noise excitation.

A. Single-loop with emulated path delay

The first experiment is designed to validate the time-domain loop signal growth speed and the impact of the

quenching switch and the actual components’ nonlinearity. The quenching switch is controlled by a 1 MHz TTL

signal with a variable duty-cycle. The loop delay is precisely emulated by a section of coaxial cable, which adds

20 ns to the 34 ns electrical component propagation delay in the loop. Another variable attenuator is used

together with a cable assembly to simulate different loop-gains. The sampled loop signals are recorded and

displayed by a high-speed digital storage oscilloscope (DSO), burst-by-burst synchronized with the quenching

switch’s ‘ON’ periods. Example waveforms in a single SRG transceiver loop are shown in Fig.7. In both

scenarios, the total loop delay is 56 ns. From Fig.7, especially the signals in the boxes, it is clear that the

unsaturated signal accumulates in the feedback loop according to equation (4) & (5), and the measured emulation

result matches the theoretical predictions. Just as theoretically-predicted, the loop signal grows at an extreme fast

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rate until near saturation when the quenching switch is OFF, and the power growth is stepped every 56 ns (total

loop delay).

An interesting phenomenon observed during both simulations and measurements is the ‘spike’ behavior at the

edges of the round-trip passes. It is believed that such spikes in the loop signal are mainly due to the circuit

bandwidth and nonlinearity, as well as the randomness of the loop excitations. Such behavior is much more

significant when the initial noise excitation power is low. When the noise excitation power is reduced by 10 dB

compared to Fig.7, the example results are given in Fig.8. Fig.8 (a) is the burst loop signal when the simulated

path attenuation is 10 dB, while Fig.8(b) is the loop signal when the path attenuation is 20 dB. The loop gain (or

attenuation) has a significant impact on the signal build-up process. As shown in Fig.8 (c), the power growth is

slowed down and repeating oscillations can be observed once the larger loop attenuation is applied. Also, just as

expected, it is observed that short quenching ON time results in slower power build-up and approach to

saturation.

B. Spectrum observations for single-loop waveform The quenched loop signal is also observed by an Agilent E4448A spectrum analyzer. The overall shape of the

measured power spectrum is similar to the original 1-2 GHz excitation signal, while more details can be

revealed by zooming in around the center frequency (f0 = 1.5 GHz) with different scales. Fig.8 (a) shows the

spectrum detail with a 20 μs period, which validates the result from equation (32), as the total loop delay is about

50 ns. Fig.8 (b) further zooms in on the spectrum with a 5.238 MHz scale, which clearly indicates the impact of

the quenching switch, as the 1 MHz quenching period introduces corresponding discrete spectrum lines.

C. Multiple-loops with emulated loop delays

It is shown that some practical issues, such as channel imbalance and mutual coupling, also impact the SRG

performance. To emulate the combined effect of target echo and interference/multipath, the loop signals from the

transmitter output are split into two paths. The two paths have different propagation delays, equivalent to a

double-loop structure. Fig.10 depicts example results of the loop signal’s details when the delay difference

varies from 0 to 10 ns. As predicted by equation (10), the loop signal contains the ‘inter-modulation’ effect based

on . Fig.10 (a) shows that the loop signal has three incremental ‘pulses’ when there is no delay between the

two loops. For different , Fig.10 (b)-(d) indicate that as increases, the original ‘pulses’ start to split into

several sub-peaks. These newly generated sub-peaks are separated by exactly . The number of sub-peaks also

increases with time due to the fact that they re-enter the loop and further inter-modulate among each other. As a

consequence, the loop signal becomes much more complicated as time elapses.

13

D. Indoor target detection experiment

The cable between the transmit and receive channels are replaced with ultra-wideband, log-periodic antennas in

lab-experiments. The four antennas are arranged in a typical retro-directive formation. The two SRG channels

operate independently and the sampled loop signals are fed into a correlation receiver (broadband double-

balanced mixer plus low pass filter). The ON time of the quenching switch is tuned to an appropriate value so

that no loop signals build up when the system is located in an empty range. Fig.11 compares the correlation

output when there is no target and when a target is present. It is clear that in this wireless sensing experiment, the

bullet target gives a strong correlation peak from the loop signals of the SRG, and the target response (detection)

time is merely limited by the low-pass filter cutoff frequency of the inter-channel correlator, as well as the

quenching signal periods.

V. FAST MONOPULSE PROCESSING FOR NOISE RADAR

A. Transient Target Signature from multiple channels The previous sections conclude that the fast detection of incoming threats can be achieved through the SRG

transceiver architecture. The open-loop signals, on the other hand, can be processed by a conventional CCR

receiver for tracking functionalities. This concept leads to the architecture design as shown in Fig.12. Each loop

channel operates in ‘detection’ mode when the quenching switch is ON, and ‘tracking’ mode when the switch is

OFF.

The theories and applications of the Angle-of-Arrival (AOA) estimation using a random-noise waveform was

discussed in [4], the traditional CCR and range tracking scheme, however, does not fit the needs of ultra-fast

threat direction estimation. To fundamentally increase the estimation speed, the monopulse processor in this

work only acquires the transient correlator output from one fixed reference delay instead of scanning through

the range gates.

A detailed analysis shows that the output signals from the two front-end correlators have many frequency

components. The strongest frequency component, which carries the target Doppler information, can be expressed

as

, (33)

which is a transient AM pulse with envelope time span given by

, (34)

14

and inner ‘carrier’ frequency

(35)

as shown in Fig.13, where c is the speed of the light, v is the target speed, ωc is the center frequency of the

transmit waveform, Δω is the transmit signal bandwidth, and Δt is a time-shift associated with the starting point

of sampling.

We can see that the shape of the transient pulse is determined by the transmit frequency band and the target

velocity. In terms of system design, we may wish to choose higher transmit frequencies and narrower bands;

this will give us larger Doppler shifts and longer observation times, thus enhancing the clutter immunity. On the

other hand, this will be closer to traditional monopulse radar and may compromise the Electronic Counter-

Countermeasures (ECCM) capability.

Because of the time-of-arrival difference between the receive antennas, it can be shown that the low-pass-filtered

correlation between the sum and difference channels has a ‘monocycle’ shape, whose polarity is determined by

the sign of the AOA, and whose amplitude is proportional to the magnitude of the AOA. As a result, fast

monopulse processing can simply divide the peak value of this monocycle by the peak output of the sum-channel

square-law detector to estimate the AOA.

Simulations of AOA estimation using the fast monopulse scheme is performed with a MATLAB-based

simulation platform. We choose a very high-speed target (15 km/s) in most simulations. Although this is far

beyond the requirements of this work, it uses a shorter simulation time and manifests the principle of transient

pulses much more clearly than slower target simulation. We use a 4-5 GHz signal frequency band in the

simulations. The fixed delay τ0 is set to 2 μs. Also, stationary ground clutter at 2 μs range with different signal-

to-clutter ratio (SCR) is added.

Fig.14 shows the resultant transient pulse from one antenna channel when the signal-to-clutter ratio is 10 dB.

The pulse envelope should last about 19 μs, and the inner ‘carrier’ should oscillate at about 450 kHz. The

simulation result shows exact compliance with theoretical predictions.

B. Fast monopulse processors Fig.15 shows a monopulse processor structure for transient target signature. The received waveforms from two

antennas are correlated to the transmit replica with a fixed time delay τ0, and the transient sum (sI) and different

(dI) signals from the correlator output are recorded. The Monopulse Characteristic Curve (MCC) is calculated as

15

. (33)

As it is difficult to acquire the actual transient target signatures at this time, hardware emulation testing is

performed to validate the fast monopulse processing approach. The emulation is based on the following

principle: placing a stationary target at different directions with respect to the antenna boresight axis and

correlating the target reflection with a delayed transmit noise replica while the delay line rapidly scans over a

range of time-delays, we emulate a target reflection with 128-ns delay variation during 19.2 ms. The correlation

result is thus equivalent to the transient signature from a target having a speed of 1000 m/s. Fig.14 shows the

hardware emulation test design. We use one transmit antenna (Tx) and two receive antennas (Rx1 and Rx2) in

this test. The antennas are mounted on a precise azimuth positioner. The scanning is from -5° to +5° at 0.5°

angular intervals. Therefore, for each antenna and each I/Q component, the result is a 21×70 2D matrix. The

‘index of sample line’ is from 1 to 70 and the ‘index of AOA line’ is from 1 to 21. We first calculate the sum and

difference beams along each ‘index of sample line’ as follows:

(34)

The ‘s’ results are digitally formed sum-beams and the ‘d’ results are digitally formed difference-beams. These

two types of beams are ‘orthogonal’ to each other.

1) Conventional monopulse processing

A conventional monopulse processor is used first to calculate the monopulse ratio along 70 ‘index of sample

lines’ and for each angular interval, i.e.,

, (35)

which performs further low-pass filtering on both the numerator and denominator terms. The LPF ‘smoothing’

is expected to give better results for the Monopulse Characteristic Curve (MCC) albeit at the cost of additional

processing time. The extracted monopulse response from traditional monopulse processing (equation (35))

results along sample lines 34, 36 and 38 are shown in Fig.17. We observe that within the -1º to 2º range, the

extracted monopulse response can be viewed as approximately linear with respect to the AOA.

The angular ambiguity associated with the MCC can be resolved by several methods, namely, using multiple

antennas or using sum-channel information, or comparing the signal strengths of two receive antenna channels.

16

A key approach is based on a look-up table. Note that the shapes of the monopulse characteristic wave as well as

the look-up table are dependent on the AOA and target type, but not dependent on the target range.

2) Fast monopulse processing For fast monopulse processing, we calculate the correlation between the sum and difference signals, applying

digital low-pass filtering (LPF) on them before computing their ratios. For example,

. (36)

Fig.18 shows the 3D map of the monopulse processing result using equation (33). It can be seen that the low-

pass filtering has ‘pushed’ the MCC curve to the edge of the figure. The MCC still shows a strong response at

about zero AOA. Ideally, the monopulse characteristic curves should be periodic, but because of

reflection/interference or multipath, the actual curves may be distorted for large angles off-boresight. Again,

these range-independent curves serve as the basis of a look-up table for angle estimation. The results

demonstrate that fast monopulse processing is able to accurately extract target AOA from transient target

signatures of receive array channels. We also observe that, through additional filtering, the linear response region

of the MCC can be improved.

Now consider the fast monopulse processing given by (36), which takes the peak values of the cross and auto

correlations at each AOA and across the range index, reducing the MCC to 2D curves. The processing results

based on either the real or imaginary parts of sum-difference channels and the same data are given in Fig.19. It

is clear that fast monopulse processing on transient target signatures results in strong nonlinear behavior of the

MCC. However, the target response is still very significant near boresight, which serves as a reliable indication

of the target direction.

VI. CONCLUSION

The potentials of using SRG transceiver architectures for ultra-wideband, ultra-fast target detection and AOA

estimation are explored. Time-domain modeling based on solutions of difference equations can be used to

characterize the fast growth of the loop signals and comparison with Coherent Correlation Receiver (CCR)

architectures. The ultra-fast power growth, random nature of radar signals, and the nonlinear properties of the

system require the implementation of appropriately designed quenching signals. Hardware emulation

experiments at L band and X band have validated the theoretical predictions of SRG signal behaviors and the

feasibility of fast AOA estimation based on monopulse processing and transient target signatures.

17

ACKNOWLEDGMENTS

The authors would like to give thanks for the support and guidance of Dr. Ram Narayanan at Pennsylvania State

University and Dr. Dwight Woolard, US Army Research Office, as well as Dr. Chieh-Ping Lai’s experimental

support during the 2006 prototyping effort. The authors also greatly appreciate the laboratory facility support of

the Radar Innovations Laboratory, University of Oklahoma and Pennsylvania State University.

18

REFERENCES [1] G. W. Stimson, Introduction to Airborne Radar, 2nd edition, Mendham, NJ: SciTech Publishing, Inc., 1998. [2] R. M. Narayanan, and X. Xu, “Principles and applications of coherent random noise radar technology,” in SPIE

Conference on Noise in Devices and Circuits, Santa Fe, NM, 2003, pp. 503-514. [3] Y. Zhang, and R. M. Narayanan, “Design Considerations for a Real-Time Random Noise Tracking Radar,” IEEE

Trans. on AES, vol. 40, no. 2, pp. 434-445, 2004. [4] Y. Zhang, and R. M. Narayanan, “Monopulse Radar Based on Spatiotemporal Correlation of Stochastic Signals,”

IEEE Trans. on AES, vol. 42, no. 1, pp. 160-173, 2006. [5] J. R. Forrest, and D. J. Price, “Digital Correlation for Noise Radar Systems,” Electronics Letters, vol. 14, no. 8, pp.

581-582, Aug, 1978. [6] G. Johnson, D. Ohlms, and M. Hampton, “Broadband correlation processing,” in Proceedings of ICASSP'83, 1983,

pp. 583-586. [7] G. L. Guosui, H. G. Hong, and W. Su, “Development of random signal radars,” IEEE Trans. on AES, vol. 35, no. 3,

pp. 770-777, July, 1999. [8] V. I. Kalinin, and V. V. Chapurskii, “Ultrawideband Noise Radar Based on Antenna Arrays with Signal

Recirculation ” Journal of Communication Technologies and Electronics, vol. 52, no. 10, pp. 1266-1277, 2008. [9] Y. Zhang, and R. M. Narayanan, “Ultra-fast Threat Detection and Tracking Using Random-noise Retrodirective

Array and Monopulse,” in 25th Army Science Conference, Orlando, FL, 2006. [10] U. L. Rohde, and A. K. Poddar, “Super-Regenerative Receiver (SRR),” in IEEE Conference on Electron Devices

and Solid State Circuits, 2007. [11] F. X. Moncunill-Geniz, P. Pala-Schonwalder, and O. Mas-Casals, “A Generic Approach to the Theory of

Superregenerative Reception ” IEEE Trans. on Circuits and Systems - I: Regular Papers, vol. 52, no. 1, pp. 54-70, Jan, 2005.

[12] D. M. W. Leenaerts, “Chaotic behavior in super regenerative detectors,” IEEE Trans. on Circuits and Systems - I, vol. 43, no. 3, pp. 169-176, 1996.

[13] M. Anis, R. Tielert, and N. Wehn, “Fully integrated self-quenched super-regenerative UWB impulse detector,” in ISWPC 2008, 2008, pp. 773-775.

[14] E. R. Brown, Retrodirective Noise-Correlating Radar in X-band: MDA/DARPA research project final report, 2005. [15] E. R. Brown, R. F. Sinclair, and E. B. Brown, “Retrodirective Radar for Small Projectile Detection,” in

IEEE/MTT-S International Microwave Symposium, 2007, pp. 777-780. [16] C. C. Cutler, R. Kompfner, and L. C. Tillstson, “A Self-steering Array Repeater,” Bell System Technology Journal,

vol. 42, pp. 2013-2032, 1963. [17] V. F. Fusco, and S. L. Karode, “Self-phasing Antenna Array Techniques for Mobile Communications

Applications,” Electronics and Communication Engineering Journal, vol. 11, pp. 279-286, Dec., 1999. [18] E. Muehldorf, “Self-steered retrodirective arrays with amplification,” IEEE Trans. on Antennas and Propagation,

vol. 17, no. 1, pp. 42-49, 1969. [19] C. Pon, “Retrodirective array using the heterodyne technique ” IEEE Trans. on Antennas and Propagation, vol. 12,

no. 2, pp. 176-180, March, 1964. [20] E. Putzer, and R. Ghose, “Redirective and retrodirective antenna arrays ” IEEE Trans. on Antennas and

Propagation vol. 17, no. 3, pp. 276-279, 1969. [21] E. Sharp, and M. Diab, “Van Atta Reflector Array,” IRE Transactions on Antenna and Propagation, vol. 8, no. 4,

pp. 436-438, July, 1960. [22] C. Loadman, and Z. Chen, “A study of retrodirective array performance in the presence of multipath,” in

Proceedings of Second Annual Conference on Communication Networks and Services Research, 2004, pp. 56-60. [23] T. K. Bhattacharya, G. Jones, and D. DiFilippo, “Time frequency based detection scheme for missile approach

warning system (MAWS),” in Proceedings of IEEE Radar Conference, 1997, pp. 539-543. [24] C. E. Baum, “Signature-based target identification and pattern recognition,” IEEE Antennas and Propagation

Magazine, vol. 36, no. 3, pp. 44-51, June, 1994. [25] A. Hommes, H. Essen, P. Knott et al., “Investigations on signatures of projectiles for sniper detection applications,”

in 2008 IEEE Radar Conference, 2008, pp. 1-6. [26] R. B. Sinitsyn, and A. J. Beletsky, “Fast Signal Processing Algorithms for Noise Radars,” in EuRAD 2006, 2006,

pp. 245-248. [27] S. Elaydi, A Introduction to Difference Equations (3rd edition), New York, NY: Springer, 2005. [28] A. D. Polyanin, and A. V. Manzhirov, Handbook of Mathematics for Engineers and Scientists Boca Raton, FL:

Chapman & Hall/CRC; 1st edtion, 2007. [29] K. Milne, “Theoretical Performance of a Complex Cross-Correlator with Gaussian Signals,” IEE Proceedings - F,

vol. 140, no. 1, pp. 81-88, Feb, 1993.

19

LIST OF FIGURES Fig. 1. The generic schematic of the SRG transceiver operation using multiple loops. ......................................... 21  Fig. 2. The different single-channel transceiver architectures for noise radar, using similar circuit elements, (a) The SRG architecture, (b) The CCR architecture. ................................................................................................. 21  Fig. 3. Simulated ¾ for different . = 3 μs, A0 , . is Gaussian random noise covering 1 to 2 GHz bandwidth, and . The solid lines are results based on equation (10), the dotted lines are based on (9), and the dashed lines are based on (13). .............................................................................. 22 

21(n¿1)¾21(n¿1) SCR = A1=A0SCR = A1=A0

n = 5n = 5¿0¿0 = 1A0 = 1 ¾s = 1¾s = 1 s(t)s(t)

Fig. 4. A comparison between the square-law detector output growth of SRG and CCR, for different

== 11 , ¾21(n¿1SCRs. , ¿0 1 ¹s¿0 1 ¹s ¿ = 6 ¹s¿ = 6 ¹s )¾21(n¿1) estimation is based on (13). Totally 10 round-trip observations are

recorded. (a) mean-value of detector output from SRG, (b) mean-value of detector output from CCR, (c) variance of detector output from SRG, (d) variance of detector output from CCR. .............................................. 24  Fig. 5. Example RV for target + interference, assuming A0 = 0.01, A1 = 0.001 – 0.1. (¿ )RV (¿ ) = 5 ns, = 10 ns. (a) comparing auto-correlation of the open-loop signal (in CCR) and closed-loop signal (in SRG), and (b) comparing auto-correlation of the loop signals with various SCR. ....................................................................... 25  Fig. 6. Picture of a double-loop SRG transceiver prototype .................................................................................. 26  Fig. 7. Loop signal measurement using a coax cable to emulate path delays. The noise-source’s output power is -26 dBm/Hz. The total loop delay is 56 ns, (a) theoretically predicted time-domain loop waveform with A0 =1, (b) Measured waveform, path attenuation = 10 dB. .............................................................................................. 27  Fig. 8. Same as Fig.7 except the noise-source output power is reduced by 10 dB, (a) theoretically predicted time-domain loop waveform with A0 =1, (b) Measured waveform, path attenuation = 10 dB, (c) Path attenuation = 20 dB. ......................................................................................................................................................................... 28  Fig. 9. Measurement of loop signal using spectrum analyzer. (a) when the span scale is 100 MHz, (b) when the span scale is 5.238 MHz. ....................................................................................................................................... 29  Fig. 10. Measurement of the double-loop signal using a digital storage oscilloscope (DSO). The first loop has a delay of ns, while the other loop has a delay longer than the first loop by . (a) = 0; (b) = 2 ns; (a) = 5 ns; (d) = 10 ns; For convenience of comparison, we concentrate on the first three pulses of the burse signal before it gets saturated. ...................................................................................................................... 30  Fig. 11. The in-door experiment with an M-16 bullet with shell (3-meter from an SRG transceiver) as target. (a) Correlation between the two RF channels, when the target is removed, (b) Correlation between the two RF channels when target is present.............................................................................................................................. 31  Fig. 12. The conceptual hardware architecture for combined SRG ...................................................................... 32  Fig. 13. A generic structure of the transient signal output from fixed-delay CCR. .............................................. 33  Fig. 14. Simulated transient correlation pulse from one antenna channel for ........................................................ 33  Fig. 15. Processor structure for fast random-noise monopulse ............................................................................. 34  Fig. 16. Hardware emulation setup design. ........................................................................................................... 34  Fig. 17. Extracted MCC for conventional monopulse processing using equation (35).......................................... 35 

20

Fig. 18. 3D map of monopulse processing result using equation (33). ................................................................. 35  Fig. 19. Extracted mean MCC for fast monopulse processing using equation (36). ............................................. 36 

+

( )ts0A0τ

BPF( )tOv

1τ 1A

Nτ NA

( )tsi

( )tSv

Fig. 1. The generic schematic of the SRG transceiver operation using multiple loops.

+ BPF

ADC

TX

RX

( )2•( ) 2

1

1 m

Ok

v km =

⎡ ⎤⎣ ⎦∑

Ov

(a)

BPF

ADC

TX

RX

( )2•( ) 2

1

1 m

Ok

v km =

⎡ ⎤⎣ ⎦∑

×

Ov

(b)

Fig. 2. The different single-channel transceiver architectures for noise radar, using similar circuit elements, (a)

The SRG architecture, (b) The CCR architecture.

21

-3 -2 -1 0 1 2 315

20

25

30

35

40

45 σ 12(nτ 1)

τ1 - τ0 (μs)

dB SCR = 2 dB

SCR = 0 dB

SCR = 4 dB

Fig. 3. Simulated ¾ for different SC . ¿0¿0 = 3 μs, A0 , . s is Gaussian random noise covering 1 to 2 GHz bandwidth, and n . The solid lines are results based on equation (10), the dotted lines are based on (9), and the dashed lines are based on (13).

21(n¿1)¾21(n¿1) R = A1=A0SCR = A1=A0

= 5n = 5= 1A0 = 1 ¾s = 1¾s = 1 (t)s(t)

22

0 10 20 30 40 50 600

10

20

30

40

50

60

70

80

90 Mean Value - SRG

Time (μs)

dB

Clutter Only SCR = -3 dB SCR = -1.5 dB SCR = 0 dB SCR = 1.5 dB SCR = 3 dB

(a)

0 10 20 30 40 50 60 700

5

10

15

20

25

30 Mean Value - CCR

Time (μs)

dB

Clutter Only SCR = -3 dB SCR = -1.5 dB SCR = 0 dB SCR = 1.5 dB SCR = 3 dB

(b)

23

0 10 20 30 40 50 60-50

0

50

100

150

200

250

300

350

400 Variance - SRG

Time (μs)

dB

Clutter Only SCR = -3 dB SCR = -1.5 dB SCR = 0 dB SCR = 1.5 dB SCR = 3 dB

(c)

0 10 20 30 40 50 60 705

10

15

20

25

30

35

40 Variance - CCR

Time (μs)

dB

Clutter Only SCR = -3 dB SCR = -1.5 dB SCR = 0 dB SCR = 1.5 dB SCR = 3 dB

(d) Fig. 4. A comparison between the square-law detector output growth of SRG and CCR, for different SCRs.

, ¿1 , ¾¿0 = 1 ¹s¿0 = 1 ¹s = 6 ¹s¿1 = 6 ¹s 21(n¿1)¾21(n¿1) estimation is based on (13). Totally 10 round-trip observations are recorded. (a)

mean-value of detector output from SRG, (b) mean-value of detector output from CCR, (c) variance of detector output from SRG, (d) variance of detector output from CCR.

24

-30 -20 -10 0 10 20 30-1

-0.5

0

0.5

1

τ (ns)

Rv

SRG (closed-loop) signal CCR (open-loop) signal

(a)

-30 -20 -10 0 10 20 30-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

τ (ns)

Rv

SCR = 10 dB SCR = 3 dB SCR = -10 dB

(b) Fig. 5. Example RV for target + interference, assuming A0 = 0.01, A1 = 0.001 – 0.1. (¿ )RV (¿ ) = 5 ns, = 10 ns. (a) comparing auto-correlation of the open-loop signal (in CCR) and closed-loop signal (in SRG), and (b) comparing auto-correlation of the loop signals with various SCR.

25

Fig. 6. Picture of a double-loop SRG transceiver prototype

26

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (μ s)

Volta

ge (V

olts

)

The burst loop signalThe quenching pulse

(a)

(b) Fig. 7. Loop signal measurement using a coax cable to emulate path delays. The noise-source’s output power is -26 dBm/Hz. The total loop delay is 56 ns, (a) theoretically predicted time-domain loop waveform with A0 =1, (b) Measured waveform, path attenuation = 10 dB.

27

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Time (μ s)

Vol

tage

(Vol

ts)

The burst loop signalThe quenching pulse

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

-0.5

0

0.5

1

Time (μ s)

Vol

tage

(Vol

ts)

The quenching pulseThe burst loop signal

0 0.2 0.4 0.6 0.8 1

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Time (μ s)

Vol

tage

(Vol

ts)

The burst loop signalThe quenching pulse

Fig. 8. Same as Fig.7 except the noise-source output power is reduced by 10 dB, (a) theoretically predicted time-domain loop waveform with A0 =1, (b) Measured waveform, path attenuation = 10 dB, (c) Path attenuation = 20 dB.

28

-50 -40 -30 -20 -10 0 10 20 30 40 50-74

-72

-70

-68

-66

-64

-62

-60

-58

-56

f-f0 (MHz)

Pow

er (d

Bm

)

(a)

-3 -2 -1 0 1 2 3-85

-80

-75

-70

-65

-60

f-f0 (MHz)

Pow

er (d

Bm)

(b)

Fig. 9. Measurement of loop signal using spectrum analyzer. (a) when the span scale is 100 MHz, (b) when the

span scale is 5.238 MHz.

29

0.5 0.52 0.54 0.56 0.58 0.6 0.62 0.64-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Time (μ s)

Vol

tage

(Vol

ts)

Δτ = 0 ns

0.5 0.52 0.54 0.56 0.58 0.6 0.62 0.64-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Time (μ s)

Vol

tage

(Vol

ts)

Δτ = 2 ns

Δτ

(a) (b)

0.5 0.52 0.54 0.56 0.58 0.6 0.62 0.64 0.66-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Time (μ s)

Vol

tage

(Vol

ts)

Δτ = 5 ns

Δτ

0.5 0.52 0.54 0.56 0.58 0.6 0.62 0.64 0.66 0.68-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Time (μ s)

Volta

ge (V

olts

)

Δτ = 10 ns

Δτ

(c) (d)

Fig. 10. Measurement of the double-loop signal using a digital storage oscilloscope (DSO). The first loop has a delay of ns, while the other loop has a delay longer than the first loop by . (a) = 0; (b) = 2 ns; (a) = 5 ns; (d) = 10 ns; For convenience of comparison, we concentrate on the first three pulses of the burse signal before it gets saturated.

30

(a)

(b)

Fig. 11. The in-door experiment with an M-16 bullet with shell (3-meter from an SRG transceiver) as target. (a) Correlation between the two RF channels, when the target is removed, (b) Correlation between the two RF channels when target is present.

31

Noise source

FixedDelayline

mixer

Power combiner

Power splitter

Power Amplifier(SS)

LNA

SP2Tswitch

180° hybrid

Subarray

T1

T2

R2

R1

1I 1Q 2I 2Q

correlator

DigitalControl

0τ

Fig. 12. The conceptual hardware architecture for combined SRG

and CCR for fast detection and direction-finding.

32

t

Starting point of Correlation receiver Sampling (detection)

∆t

tωc

2vj ce~−

Δωvc~ΔT⋅

( ) 0τtc

2vτtτ =−′=

( ) τtτ ′=

Fig. 13. A generic structure of the transient signal output from fixed-delay CCR.

0 5 10 15 20 25

-50

0

50

100

150

Time (μs)

Cor

rela

tion

outp

ut fr

om o

ne re

ceiv

e ch

anne

l

Fig. 14. Simulated transient correlation pulse from one antenna channel for

signal-to-clutter ratio (SCR) = 10 dB.

33

+

-

( )2•

÷( )0τts −

Fig. 15. Processor structure for fast random-noise monopulse

TxRx1

Rx2

Fast scan variable delayline

Noise source

5 m

I1 Q1 I2 Q2

DAQ

anechoic chamber

Fig. 16. Hardware emulation setup design.

34

-5 0 5-6

-4

-2

0

2

4

6

AOA (°)

Mon

opul

se p

roce

ssor

out

put

Range#34 Range#36 Range#38

Fig. 17. Extracted MCC for conventional monopulse processing using equation (35).

Fig. 18. 3D map of monopulse processing result using equation (33).

35

-5 0 5-5

-4

-3

-2

-1

0

1

2

3

AOA (°)

| r

| (dB

)

Using sI, dI

Using sq, dq

Fig. 19. Extracted mean MCC for fast monopulse processing using equation (36).

36