# Optimization of NQR Pulse Parameters using Feedback Control

**ABSTRACT** A new method for increasing the probability of detecting nuclear resonance signals is demon-strated experimentally. It is well known that the detection of signals with a low signal to noise ratio (SNR) results in missed detections of false alarms. In situations where the noise is correlated or where limited data is averaging, it may not be possible to achieve a desired SNR through averaging alone. We present an alternative approach in which a feedback algorithm automatically adjusts pulse parameters so that the SNR and probability of correct detection are increased. Experimental results are presented for the detection of 14 N NQR signals.

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Page 1

Optimization of NQR Pulse Parameters using Feedback Control

J. L. Schiano, A. J. Blauch, and M. D. Ginsberga

Department of Electrical Engineering, The Pennsylvania State University,

227D Electrical Engineering West, University Park, PA 16802, USA

aUnited States Army Construction Engineering Research Laboratories,

PO Box 9005, Champaign, IL 61826, USA

Reprint requests to Prof. J. L. S.; Fax: (814) 865-7065; E-mail: schiano@steinmetz.ee.psu.edu

Z. Naturforsch. 55 a, 67–73 (2000); received August 28, 1999

Presented at the XVth International Symposium on Nuclear Quadrupole Interactions,

Leipzig, Germany, July 25 - 30, 1999.

A new method for increasing the probability of detecting nuclear resonance signals is demon-

strated experimentally. It is well known that the detection of signals with a low signal to noise ratio

(SNR) results in missed detections of false alarms. In situations where the noise is correlated or

where limited data is averaging, it may not be possible to achieve a desired SNR through averaging

alone. We present an alternative approach in which a feedback algorithm automatically adjusts

pulse parameters so that the SNR and probability of correct detection are increased. Experimental

results are presented for the detection of14N NQR signals.

Keywords:Nuclear Quadrupole Resonance; Feedback Control; Receiver Operating

Characteristics.

1. Introduction

Nuclear quadrupole resonance (NQR) provides a

noninvasive means of detecting explosives [1] and

narcotics [2] by revealing the presence of14N. Al-

though14N is essentially 100% abundant, the small

zero-field NQR splitting results in a low signal-to-

noise ratio (SNR) that leads to missed detections and

false alarms. The SNR of NQR measurements is de-

terminedbyboththestatisticalproperties ofthenoise

and the selection of pulse sequence parameters. The

standard approach to improving the SNR uses multi-

pulsesequencesthatfacilitatecoherentsignalaverag-

ing [3 - 5]. Averaging methods improve the SNR by

reducingthevarianceofthenoise,butdonotincrease

the magnitudeof the NQR signal [6]. The correlation

of the noise sources limits the minimum noise vari-

ance, andhencemaximumSNR, thatcan beachieved

through averaging [7].

In conjunction with signal averaging, we propose

another method which further improves the SNR of

NQR measurements. The NQR signal strength de-

pendsontheamplitude,frequency,durationandrepe-

0932–0784 / 00 / 0100–0067 $ 06.00 c

? Verlag der Zeitschrift f¨ ur Naturforschung, T¨ ubingen

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titionrateoftheappliedRFpulses.Inmostsituations,

these parameters are chosen before the experiment

and remain unchanged during the pulse sequence.

The selection of pulse parameters is based on the

expected response of the experiment. In applications

suchasthedetectionofexplosivesusingNQR,theop-

timal selection of RF parameters requires knowledge

that is not available in practice, such as the location

of the explosive with respect to the search coil and

the temperature of the explosive [8]. Existing NQR

detection systems sacrifice signal intensity by using

fixedpulseparameters.Wedemonstratethatfeedback

control provides a means for automatically adjusting

multiplepulse parameters so that the maximumNQR

signal strength is obtained.

In the proposed method based on feedback con-

trol, measurements of the NQR response between

RF pulses are used to optimize the pulse parame-

ters in real-time. The feedback algorithm adjusts the

pulseparameterstoproducethelargest possibleNQR

signal. We demonstrate that feedback can be used

to maximize the SNR of NQR measurements by si-

multaneously tuning both the pulse width and offset

Page 2

68J. L. Schiano et al. · Optimization of NQR Pulse Parameters using Feedback Control

t (k)

w

f(k)

∆

n=1

n=1 n=0

......

NQR signal index

Pulse parameter set index

n=0

k=0k=1

τ

Fig. 1. SORC pulse sequence

notation.

Phase

Sensitive

Receiver

Signal

Averager

ADC

Butterworth

LPF

8th order

Signal

Averager

ADC

Butterworth

LPF

8th order

V (t)

Q

I

V (t)

f

I

V (t)

f

I

V (m)

f

I

V (m)

f

V (m)

Q

f

V (m)

Q

f

V (t)

Q

Preamp

Low Noise

Receiver

Gate

Signal across

Probe Coil

Fig. 2. Block diagram of the receiver and data acquisition system.

frequency in the strong off-resonant comb (SORC)

sequence. Within the framework of signal detection

theory, we also show that feedback can improve the

receiver operating characteristics in detection experi-

ments by increasing the probability of a correct de-

tection.

2. Dual Parameter Optimization

NQR signals are generated using the SORC se-

quence which is a periodic series of identical RF

pulses withpulse width

The frequency of the RF pulses is offset ∆ f Hz above

the transition frequency

gresses, the NQR signal observed between the RF

pulses reaches a steady-state waveform. The advan-

tageoftheSORCsequenceisthatthesignalsobtained

twand pulse separation

? [9].

?

?. As the sequence pro-

arecomparableinmagnitudetotheFIDobtainedfrom

a fully relaxed system.

InaconventionalSORCsequencethepulseparam-

eters are fixed. In this study, however,the pulse width

and offset frequency are adjusted during application

of the sequence. We use the notation shown in Fig. 1

torepresent changesinpulseparameters.The index

is usedtoreference thepulseparameterset, witheach

k

k correspondingtoadifferentsetofparametervalues.

Individual NQR signals are indexed by

corresponding to the first signal after the start of a

new set of pulse parameters.

Figure 2 shows the general block diagram of the

receiver and data acquisition system. The phase-

sensitive receiver mixes the gated signal induced in

the probe coil with the excitation frequency

where ∆ f is the applied offset frequency above res-

onance. To avoid ringing in the receiver following

n, with

n = 0

?

?+∆ f,

Page 3

J. L. Schiano et al. · Optimization of NQR Pulse Parameters using Feedback Control69

tw

Data acquisition window Ring down time

m=0m=m0

0

m=m +M-1

τ

Fig. 3. Data acquisition window between RF pulses.

the application of an RF pulse, there is a 240 µs

delay between the end of the RF pulse and when

the receiver is turned on. The in-phase

quadrature

put are passed through identical 8th-order Butter-

worth lowpass filters with a cutoff frequency of

20kHztoproduce

The signals

samplingthefilteredsignalsat100kHz.Thesampled

signals are then sent to point-by-point signal aver-

agers to form the averages¯

for

between RF pulses in shown in Figure 3.

A wide variety of signal metrics are available for

quantifyingtheamplitudeoftheSORCwaveform,in-

cluding peak-to-peak voltage, mid-signal amplitude,

signal energy, and peak spectral magnitude. For this

paper, we choose the SORC signal power as the feed-

back metric for tuning the SORC pulse parameters

[10], and for fixed pulse parameters

is given by

VI(t;

k) and

VQ(t;

k) components of the receiver out-

VI

f(t;

k)and

VQ

f(t;

k),respectively.

VI

f(m;

k) and

VQ

f(m;

k) are obtained by

VI

f(m;

k) and¯

VQ

f(m;

k)

N SORC signals. The data acquisition window

tw(k) and ∆ f(k)

P(k) =

1

M

m0+M

?1

X

m=m0

?¯

VI

f(m;

k)

?

VDC

?2

?

(1)

where

output in the absence of an NQR signal.

Methods for separately optimizing the pulse width

and offset frequency have been previously demon-

strated [10, 11]. The dual tuning algorithm presented

here is an extension of this earlier work. A gradient

ascent algorithm maximizes the performance index

VDC is the DC offset measured at the filter

J(tw(k)?∆ f(k)) =

J(k) =

P(k)(2)

by adjusting the pulse width

quency∆ f(k). The power

steady-state SORC waveform produced by fixing the

pulse parameters

fifteenhundredRFpulses,

tw(k) and offset fre-

P(k) is calculatedfrom the

tw(k) and ∆ f(k). After a period of

N consecutivesteady-state

SORC signals are acquired and coherently added to

form an average SORC signal¯

the power metric

The pulse width

are updated using the rules

VI

f(m;

k) from which

P(k) is determined.

tw(k) and offset frequency ∆ f(k)

tw(k + 1) =

tw(k) +

?

tw(k)

tw

J(k

? 1)?

k = 2?4?6?

???

?

(3)

∆ f(k + 1) = ∆ f(k) +

?∆ f

∆ f

J(k

? 1)?

k = 3?5?7?

???

?

(4)

The pulse parameters

and ∆ f(2) are initial values that are specified be-

fore the pulse sequence is started. The gradients

(k

∆ f

tw(0),

tw(1), ∆ f(0) = ∆ f(1),

tw

J

? 1) and

J(k

?1)areapproximatedas [10,11]

tw

J(k

? 1) =

G(J(k

? 1)

?

J(k

? 2))

?

G(tw(k

? 1)

?

tw(k

? 2))?

(5)

∆ f

J(k

? 1) =

G(J(k

? 1)

?

J(k

? 2))

?

G(∆ f(k

? 1)

? ∆ f(k

? 2))?

(6)

where

G(x)=

?

1

x

? 0?

? 0?

?1

x

(7)

The gradients

values of

which the parameter should be incremented in order

to increase the signal metric. The learning factors

tw

J(k) and

∆ f

J(k) can only take on

?1. The sign determines the direction in

?

in pulse parameters. When tuning pulse width, it is

useful to start with a large learning factor so that

the algorithm rapidly homes in on the optimal pulse

width[11].However,toavoidalimitcycleoscillation

with a large radius about the optimal pulse width, the

learning factor is decremented as follows

tw(k)and

?∆ fdeterminethemagnitudeofthechange

?

tw(k) =

?

?

?

20 µs

15 µs

10 µs

k = 0?2?

k = 10?12?

? 20?

???

?8?

???

?18?

k

(8)

Afixedlearningfactor

the offset frequency [10].

Because the gradients in (5) and (6) are always

non-zero, the gradient algorithm converges to a limit

cycle instead of a single point. The parameters are

?∆ f= 50Hzisusedfor tuning

Page 4

70J. L. Schiano et al. · Optimization of NQR Pulse Parameters using Feedback Control

tunedfor afixednumberofiterationswhichischosen

sufficiently large so that the algorithm converges to a

limit cycle.

3. Receiver Operating Characteristics

Binary signal detection theory [12] is a useful tool

for studying the effect of signal averaging and feed-

back on the detection of nuclear resonance signals

in noise. The binary detection system in Fig. 4 can

be used to represent a NQR detection system. In this

contextthe state

rial that produces a NQR signal, while

the absence of the material. The received signal

is a combination of the source signal

fromthechannel.Byobserving

decidewhetherthe source is in state

cision is accomplished in two stages. First, a signal

processing unit transforms the received signal

into a scalar metric

tor compares

or not a NQR signal is present

s1represents the presence of a mate-

s0represents

r(t)

s(t) and noise

r(t),thereceivermust

s0or

s1. This de-

r(t)

?(r). Second, a threshold detec-

?(r) to a threshold

? to decide whether

ˆ

s

=

?

s0

??(r)

?(r)

??

s1

?

?

??

(9)

The function

sen by the designer.

The probability of correct detection

ability of false alarm

detection system. As an illustration, Fig. 5 shows a

normal probability density function

mean

of the source. The mean is determined by the state

of the source,

?(r) and the threshold value

? are cho-

Pdand prob-

Pfare used to characterize the

N(???2) with

? and variance

?2for the two different states

? = 0 for

s =

s0and

? =

d when

s =

both states of the source. The probability of a correct

detection

sity function

probability of a false alarm

under the density function

In explosives detection a fixed threshold value is

used, and its value is chosen to limit the proba-

bility of a false alarm. Ideally, we would like

s1. The variance

?2is assumed identical for

Pd is the light gray area under the den-

N(d??2) for

?(r)

?

?. Similarly, the

Pfis the dark gray area

N(0??2) for

?(r)

?

?.

Pf

Source

s {s ,s }

0 1

Λ(r)

Noisy

Channel

Signal

Processing

Threshold

Detector

s(t)

r(t)

s^

Fig. 4. Block diagram of a binary signal detection system.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Pf

Pd

Γ

d0

Scalar metric Λ(r)

Probability density p(Λ(r))

N(0,σ2)

N(d,σ2)

Fig. 5. Probability density functions of

?(r) for

s =

s0and

s =

s1.

and

respectively.

In signal detection applications it is often assumed

thatthesignal

with a constant mean

iments this assumption can be lifted, because the ex-

perimenter can influence the magnetization signal by

varying the pulse sequence parameters. From Fig. 5,

increasing

N(d?

of correct detection

hand,with

dark gray area which determines the probability of a

false alarm.

The performance of a dection system is charac-

terized usinga receiver operatingcharateristic (ROC)

curvewhichisatwo-dimensionalplotoftheprobabil-

ities

to a fixed threshold

the ROC curve. In Sect. 4 we show how feedback

effects the ROC curve.

Pd to be as close as possible to 0 and 1,

s1(t)isfixed,resultinginasignalmetric

d. In nuclear resonance exper-

d shifts the probability density function

?2) to the right, thereby raising the probability

Pdfor a fixed

?. On the other

? fixed, increasing

d has no effect on the

Pdand

Pf. Each point on the curve corresponds

?. By varying

? we move along

4. Experimental Results

The experiments were performed using a 50 g

sample of sodium nitrite at room temperature near

the

dominated by a single spin-lattice relaxation time

?

? = 3?6 MHz transition. The

?

?transition is

T1?which was measured using the method of pro-

gressive saturation. The spin-spin relaxation time

was measured using a two-pulse spin-echo decay.

These time constants are estimated as 0.3 s and 6 ms,

T2

Page 5

J. L. Schiano et al. · Optimization of NQR Pulse Parameters using Feedback Control71

0

100

200

−2

−1

0

1

2

0

0.1

0.2

0.3

0.4

0.5

0.6

Pulse Width (µs)

Offset Frequency (kHz)

Performance Index

Fig. 6. Performance index as

a function of pulse width and

offset frequency.

respectively. The

termined from the spin-echo decay, and is approxi-

mately 1 ms.

A custom-made 1 kW pulsed spectrometer was

used in the experiments [13]. This system can ac-

quire data, perform calculations, and update pulse

parameters in real-time. The quality factor of the

probe coil is approximately 150. The amplitude of

the applied RF pulses is fixed so that the mag-

netic field amplitude at the coil center is approx-

imately 5 Gauss. The corresponding output power

of the transmitter is approximately 25 Watts. In

all experiments, the pulse separation was fixed

at 1 ms.

ThepoweroftheSORCwaveformisusedasamet-

ric,orperformanceindex,indeterminingtheoptimal-

ity of pulse parameters. The dependence of the per-

formance index on pulse width and offset frequency

is shown in Figure 6. With the pulse width held con-

stant, the steady-state SORC signal was recorded for

offset frequencies ranging from –2.5 kHz to 2.5 kHz

in 50 Hz steps. This experiment was repeated for

pulse widths ranging from 10 µs to 200 µs in 10 µs

steps. For each pulse width and offset frequency, two

thousandsteady-stateSORCsignalswerefilteredand

averaged. The performance index for a given pair of

pulse parameters represents the power of the aver-

age waveform. Consistent with the results reported

by Marino [9, 14], the SORC signal intensity can

vary widely as a function of pulse parameters.

T

?

2line-shape parameter was de-

The ability of the dual tuning algorithm to maxi-

mize the signal metric

this experiment

prove the SNR. The initial pulse width and offset fre-

quencies are chosen as

∆ f(0) = ∆ f(1) = 0 Hz, and ∆ f(2) = 50 Hz re-

spectively. The actual offset frequency was unknown

due to temperature variations of the sample. With no

sample present, the performance index remains un-

changed, and provides a graphical representation of

the noise floor. With a sample present, the dual tun-

ing algorithm increased the performance index well

above the noise floor.

TheeffectoffeedbackontheROCcurvewasdeter-

mined by performing a series of two hundred experi-

ments, half with the sample present and half with the

sample absent. Foreach experiment,the performance

index is compared against the threshold

whetheror notasampleispresent. Let

sent the number of experiments where the sample is

present(absent)andthesignalmetricislargerthan

The probabilities of correct detection and false alarm

are then calculated as

curve is generated using one hundred values of

ranging from 0 to 1 in 0.01 steps.

The ROC curves in Fig. 8 show the effect of feed-

back on the detection of an NQR signal. The solid

curve is obtainedwitha fixedset of pulse parameters.

The dashed and dotted ROC curves are obtained af-

ter the control algorithm tunes the pulse parameters

P(k) is shown in Figure 7. In

N = 36 signals were averaged to im-

tw(0) = 20 µs,

tw(1) = 40 µs,

? to decide

Nc(Nf) repre-

?.

Nc

?100 and

Nf

?100. The ROC

?