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Novel signal processing techniques for Doppler radar

cardiopulmonary sensing

Dennis R. Morgan



, Michael G. Zierdt

Bell Laboratories, Alcatel-Lucent, 700 Mountain Avenue 1C-260, Murray Hill, NJ 07974-0636, USA

article info

Article history:

Received 6 February 2008

Accepted 10 July 2008

Available online 22 July 2008

Keywords:

Cardiopulmonary sensing

Doppler radar

Heartbeat

Respiration

abstract

In this paper, we develop new signal processing techniques for Doppler radar

cardiopulmonary sensing. These techniques enable independent recovery of respiration

and heartbeat signals from measurements of chest-wall dynamic motion, which are

subsequently used for independent estimation of respiration and heart rate. In

particular, three novel elements are introduced: the concept of representing the

composite demodulated signal in the complex plane as a vector sum of various

components, combining dc coupling with block mean removal, and adaptive cancella-

tion of respiration harmonics. From this, algorithms are derived for arc-length

demodulation and cardio/pulmonary separation. A test signal generator is developed

to simulate actual signals. Also, an experimental setup is presented and several sets of

real data are analyzed using the new signal processing techniques.

1. Introduction

There are many potential applications for a non-

invasive technique to monitor respiration and/or heart-

beat. Doppler radar, operating at microwave frequencies

in the range of 1–10 GHz, has long been suggested as a

means to accomplish this [1–5]. More recently, RF

technology developed for mobile phones has been applied

to implement such devices [6–10], and generalized to

sensing of multiple subjects [11–13]. A particularly

comprehensive discourse on the subject including phy-

siological background can be found in [14].

Fig. 1 shows a block diagram of the basic Doppler radar

technique. A continuous-wave (CW) source feeds an

antenna through a circulator, and radiates to a desired

object in the ﬁeld that experiences motion xðtÞ. The

object reﬂects the signal back to the same antenna

(or, alternatively a separate receive antenna) which is

then captured by the circulator and sent to an I/Q

(complex) demodulator. The demodulator takes a portion

of the CW source signal, splits it into two components

with 90



relative phase shift, and mixes with the received

signal to derive in-phase and quadrature (I/Q) outputs, iðtÞ

and qðtÞ, respectively. (In early work, only one demodu-

lated channel was used, and the subject had to move into

the ‘‘sweet spot’’ so as not to be near a null when the

reference and return signals are in phase or 180



out of

phase; recent work uses the I/Q technique to avoid that

problem.) The lowpass ﬁlters (LPFs) are used to remove

interference and retain only signals that are changing

relatively slowly compared to the CW frequency. As the

scattering object moves, the phase of the return signal

varies as 2

xðtÞ=ð

=2Þ, where

¼ c=f

is the wavelength

of the CW signal, c is the velocity of light, and f

is the CW

carrier frequency. (The divisor of 2 on

is due to the two-

way propagation path to and from the scatterer.) There-

fore, as the scattering object moves radially, the phase will

rotate 360



every

=2. For example, if f

¼ 2:4 GHz, then

the wavelength is approximately

m or 12.5 cm for c ¼

3  10

m=s and the phase rotates 360



for every 6.25 cm

of motion.

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/sigpro

Signal Processing

ARTICLE IN PRESS

doi:10.1016/j.sigpro.2008.07.008



Corresponding author. Tel.: +1 908 582 3750; fax: +1908 582 7308.

E-mail addresses: drrm@alcatel-lucent.com, drrm@bell-labs.com

(D.R. Morgan).

Signal Processing 89 (2009) 45–66

Most of the studies to date have been done in the form

of laboratory experiments under ideal conditions, so there

is some concern about the prospects of developing the

technology into reliable products. Some of the potential

problems include the effects of background (BG) scatter,

motion of the subject as well as the BG, and interference

between the respiration and heartbeat signals. BG scatter

both from the ambient surroundings as well as from parts

of the subject’s body exclusive of the relevant chest-wall

area [15] adds a component to the desired signal that

must be dealt with. Gross motion of the subject, as well as

other objects in the BG will introduce undesired dynamics

into the desired signal, making the problem even more

difﬁcult. Finally, as documented in this paper for the ﬁrst

time, there is the problem of respiration harmonics falling

close to the heartbeat frequency so as to make reliable

heart-rate estimation difﬁcult. It is the intent of this paper to

study these problems and introduce novel signal processing

techniques to ameliorate these disruptive effects.

Three novel elements are introduced in this paper

pertaining to signal processing for the Doppler radar

cardiopulmonary (CP) application. The ﬁrst is the concept

of representing the composite demodulated signal in the

complex plane as a vector sum of backscattered compo-

nents from the BG and subject. Second is the notion of

combining dc coupling with block mean removal to avoid

long transient settling times. Third is a technique for

adaptively cancelling respiration harmonics, which can

interfere with the detection of weaker heartbeat signals.

We emphasize here that the main thrust of this paper

is to introduce novel signal processing techniques for this

application from viewpoints not previously expressed in

the literature. It is not meant as a ‘‘be all, end all’’

comprehensive study that includes all of the real-world

aspects of this problem, such as performance over a

population of subjects and heart-rate variability.

The next section develops a physical model of the

signal and propagation scenario to set the stage. Then

in Section 3, we discuss the basic signal processing

techniques, including preﬁltering and analog-to-digital

conversion, extraction of the raw CP signal, and spectral

analysis. Section 4 introduces a technique for mitigating

heartbeat signal interference from the respiratory compo-

nent. Simulation techniques are developed in Section 5,

where we introduce a test signal to represent chest-wall

motion and use this to demonstrate the signal processing

techniques. Section 6 validates and extends the simulation

results using experimental data collected with a real RF

Doppler radar system using a live subject.

2. Signal model

Fig. 2(a) shows a schematic geometrical sketch of the

propagation scenario. The desired backscattered signal

comes from the chest-wall area of the subject. Undesired

interfering components will come from other backscatter-

ing areas on the subject, as well as from other BG objects

in the antenna ﬁeld of view. Using an antenna with a

narrow beam pattern (i.e., high gain) can signiﬁcantly

reduce the interference from BG objects, although there is

a trade-off here in making sure the desired subject is

entirely in the beam at all times. Also, for many

applications, it is probably not feasible to use the antenna

pattern to exclude undesired returns from subject areas

outside of the chest wall. We will subsequently designate

the two types of subject backscatter as CP and non-cardio-

pulmonary (NCP), and everything else as BG, which

includes objects, walls, ceiling, etc. that are within the

ﬁeld of view.

The return from each backscatterer within the antenna

ﬁeld of view can be visualized as a vector in the complex

plane, where its length is proportional to the reﬂection

coefﬁcient and its orientation represents the RF phase,

which as previously discussed varies with radial distance.

The various CP, NCP, and BG components discussed above

are then added in this vector space as depicted in Fig. 2(b),

where the resultant vector represents the composite

return from all scatterers. In this diagram, the BG

component is presumed stationary, but the position of

the CP and NCP subject components can lie anywhere

along the dashed circle loci. As the subject moves a small

ARTICLE IN PRESS

Source

Coupler

Circulator

Tx/Rx

Antenna

Scattering

Object

x (t)

LPF

q (t)

LPF

i (t)

90°

Demodulator

Fig. 1. Block diagram of basic Doppler radar technique.

D.R. Morgan, M.G. Zierdt / Signal Processing 89 (2009) 45–6646

amount, either voluntarily or involuntarily, the NCP

component will wander along an arc of its locus. On the

other hand, the motion of the desired CP component will

be relatively much smaller, since chest-wall movement

due to respiration is only a centimeter or so at most and

the motion due heartbeat is typically only a fraction of a

millimeter [14]. For the 2.4 GHz carrier frequency used in

this paper, the wavelength is 12.5 cm, and so 1 cm of

motion only causes 360



=ð12:5=2Þ¼57:6



along the CP

circle, thus staying within reasonable bounds. Therefore,

ARTICLE IN PRESS

Antenna

Background Object

(BG)

Subject

Chest Wall

(CP)

Exogenous

(NCP)

Background Object

(BG)

NCP

Resultant

Fig. 2. Signal model. (a) Schematic geometrical sketch of propagation scenario. (b) Phasor diagram of received backscatter.

D.R. Morgan, M.G. Zierdt / Signal Processing 89 (2009) 45–66 47

the CP component will only vary over a small arc, which

for all practical purposes can be considered as a straight

line.

Thus, for the analytical model, we assume that the

subject is near motionless and not attempting to move.

Small involuntary motions then will cause the NCP

component to wander along its circular locus, but since

there is not gross motion, the radius of the circle remains

essentially ﬁxed. On top of this, the CP component will

trace out a small arc, again with essentially constant

radius. Later in the paper, we will show some experi-

mental results when the subject is purposely moving and

comment on the difﬁculties that this presents. In that

case, the scale of the picture in Fig. 2(b) is dynamically

changing as the subject distance and aspect angle varies.

3. Basic signal processing

3.1. Preﬁltering and analog-to-digital conversion

In a practical implementation, it is necessary to digitize

the I/Q analog output signals of the complex demodulator

in Fig. 1. Since the CP component along a small arc of the

circle in Fig. 2(b) is of primary interest, it might at ﬁrst

seem best to ac couple, or highpass ﬁlter, the analog

outputs to the analog-to-digital converters (ADCs), there-

by greatly reducing the dynamic range requirements and

number of bits needed for accurate representation.

Furthermore, the cutoff frequency of the highpass ﬁlter

could be made high enough to exclude most of the

respiration signal, thereby enhancing the much smaller,

and more elusive, heartbeat signal [6–11,13,14]. However,

ac coupling has two disadvantages: long settling time and

loss of possibly useful dc and low-frequency information,

as elaborated below.

It is envisaged that CP data for a given subject under

given conditions will be acquired over a time frame on the

order of 5–30 s for most applications. If ac coupling is

employed, some time must be allotted for the ﬁlter to

settle down after the subject is in position and ready to

begin the test. The settling time of a highpass ﬁlter is

roughly the inverse of its cutoff frequency. The respiration

rate for a seated subject at rest is typically in the range

of 5–20 breaths per minute (bpm), i.e., 0.083–0.33 Hz

[14, p. 206]. Therefore, with a cutoff frequency of 0.03 Hz

(as used in some of the experiments in [6,7,11]), the

settling time will be on the order of 30 s, which is long

compared to the envisaged time frames for valid data

acquisition. Increasing the cutoff frequency can reduce

this settling time, but at the expense of losing some of the

low-frequency information, as discussed next.

It will be shown in this paper that harmonics of the

fundamental respiration frequency can seriously limit

heart-rate estimation accuracy. Means for dealing with

this interference, as discussed later in Section 4, require an

estimate of the respiration rate. Therefore, the highpass

cutoff must be set below the lowest expected respiration

frequency, thereby increasing the settling time, as dis-

cussed above. Also, it is conceivable that low-frequency

data might be useful for applications in which the actual

respiration waveform could be of diagnostic interest.

Another consideration for the preﬁltering is the anti-

aliasing LPF required. Heart rate for a seated subject at rest

is typically in the range of 45–90 beats per minute (bpm)

i.e., 0.75–1.5 Hz [14, p. 206]. Also, within a heartbeat

period, there is ﬁne detail that may be of diagnostic value,

so that frequencies of 10–100 times the highest heartbeat

frequency may be of interest. Therefore, the lowpass

cutoff frequency should be on the order of 15–150 Hz,

requiring sampling rates in the range 30–300 Hz. In our

experiments, as well as in [7,8,14], sampling rates of 25

and 50 Hz were used. With activity, such as on a treadmill,

heart rate can easily increase to 120 bpm (2 Hz). (An oft-

cited rule of thumb for maximum heart rate is 220 minus

age in years.) In such applications, somewhat higher

sampling rates may be required.

In [16, 17], a calibrated dc is added to the ac signal so that

arctangent processing can be applied for cases in which

there is large subject motion. W e do not consider such cases

in m ost of this paper , but wil l present and comme nt on

some related experimental results in the ﬁnal section.

For all of the above reasons, we believe that dc

coupling to the ADC is preferable to ac coupling. We can

still remove the dc after collection by subtracting out the

mean over the data block. In steady state, this is

equivalent to highpass ﬁltering with a very low cutoff

frequency. However, subtracting out the mean after

collection avoids the transient settling time problem.

The penalty paid for dc coupling is that the ADC then

requires more bits because of the vastly increased

dynamic range. However, considering the relatively low

sampling rates, the requirements are not onerous with

today’s technology. Indeed, commercially available 24-bit

ADCs are available at relatively modest cost and small

size. Moreover, if the BG [Fig. 2(a)] is immobile, then the

BG component in Fig. 2(b) is a dc component that can be

offset prior to the ADC in order to reduce some of the

dynamic range.

3.2. Extraction of raw CP signal

Ideally, one would like to use a dc offset to reference

the data to the center of the smaller dashed circle (CP) in

Fig. 2(b). Then the desired chest-wall displacement signal

[shown as xðt Þ in Fig. 1] could be reconstructed by merely

taking the arctangent of the complex I/Q data [16].Itis

possible and desirable to offset the dc corresponding to

the BG return in Fig. 2(a), assuming that the constituent

scattering objects are not moving. However, it is difﬁcult

to avoid the NCP component, which is necessarily induced

by voluntary or involuntary body movement. Since the

NCP component is unpredictable, we focus here on the

small CP arc, which contains the signal of interest.

If the subject is moving at a steady velocity, one can

imagine that the sum of the CP and NCP vectors in

ARTICLE IN PRESS

Note that ‘‘bpm’’ has also been previously used to designate

respiration ‘‘breaths per minute’’; however, the distinction should be

clear from the context.

D.R. Morgan, M.G. Zierdt / Signal Processing 89 (2009) 45–6648

Fig. 2(b) will rotate about the center of the larger dashed

circle, i.e., the head of the presumably static BG vector. As

the subject moves in this manner, the CP and NCP

components will maintain a rough alignment because

the chest wall nominally moves with the rest of the body.

However, there will be some angular motion of one with

respect to the other because of relative local motion and,

of course, the actual desired CP motion of the chest wall.

As will be shown later in the experimental work, we have

not yet found a reliable way to extract the CP signal in this

case. Thus, for the remainder of the theoretical discussion

we will assume that the subject is nominally stationary at

rest.

If the subject is at rest, the CP component can be

extracted by ﬁrst removing the mean over the data block,

as discussed above, and then combining the I/Q compo-

nents in such a way as to render the best estimate of

chest-wall motion. As previously mentioned, the relatively

small motion of the chest wall means that the CP arc can

for all practical purposes be considered as a straight line.

Therefore the I/Q components of the CP signal are

essentially linearly related. Typically, the I/Q signals will

be unequal in magnitude, depending on the orientation of

this line in the complex plane [see Fig. 2(b)]. For example,

if the resultant phase is oriented mostly toward the right

(real), then the Q component of the CP signal will be larger

than the I component; conversely, the I component will be

larger than the Q signal if the resultant phase points

mostly upward (imaginary).

In recent work, various means have been used to

extract the CP signal from the I/Q signals for further

processing, including selection of the largest [9,10], and

principal component analysis [14, p. 273]. Here, we will

use linear regression to establish the best mean-square ﬁt

of a straight line to the CP arc. This is roughly equivalent to

the principal component approach, however, it is some-

what simpler to implement.

Denote the sampled I/Q signals after A/D conversion as

iðnÞ and qðnÞ, n ¼ 1; 2 ; ...; N, where N is the block length of

the collected data. Subtracting out the mean value over

the data block then yields the zero-mean data

iðnÞ¼iðnÞ

n¼1

iðnÞ (1a)

qðnÞ¼qðnÞ

n¼1

qðnÞ (1b)

Now let us assume a nominal linear relationship between

the I/Q components so that we can write

qðnÞ¼a

iðnÞþvðnÞ (2)

where a is the slope and vðnÞ represents additive noise or

interference. Fig. 3 shows a sketch of what a typical data

set (x’s) might look like relative to the CP arc (solid) and its

straight-line tangent (dashed). Linear regression deter-

mines the best estimate of the slope in the sense of

minimizing the mean-square residual, and is given by

a ¼

n¼1

iðnÞ

qðnÞ

n¼1

ðnÞ

(3)

With this slope estimate, the distance along the arc can be

calculated as

sðnÞ¼

iðnÞþ

qðnÞ

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

þ 1

(4)

Thus, we see that sðnÞ¼

iðnÞ for the limiting case when

a ¼ 0, and likewise sðnÞ¼

qðnÞ when

a ¼1. For inter-

mediate values,

a acts as a weighting factor to optimally

combine

iðnÞ and

qðnÞ.

Note that although arc length is an appropriate

measure of chest-wall motion, its scale is not inherently

calibrated since the amplitude of the I/Q signals depends

on transmitted power, chest-wall reﬂection coefﬁcient,

antenna and receiver gain, etc. Therefore, if an absolute

chest-wall displacement measurement is desired, it is

necessary to calibrate the system under the speciﬁed

conditions. (Note that such calibration, which is range and

aspect angle dependent, is only necessary for physiologi-

cal studies, and is not required for simple rate monitor-

ing.) This can be most conveniently accomplished by

having the subject rock back and fourth at a slow rate

(e.g., period of 1–5 s) over at least a half wavelength

(e.g., 6.25 cm at 2.4 GHz), so that the I/Q signals trace out a

full circle in the complex plane [cf. Fig. 2(b)]. Then, we

know that the voltage corresponding to the diameter of

the circle thus traced out corresponds to an absolute arc

length of ð

=2Þ=

(1.99 cm at 2.4 GHz). This calibration

thus enables absolute measurements of chest-wall dis-

placement in the direction of the antenna. An example of

this will be given later in the experimental section.

3.3. Spectral analysis

Conventional spectrum analy sis is useful for estimating

heart and respiration rates from the extract ed CP signal.

In this domain, the fundamental frequency along with

ARTICLE IN PRESS

q (n)

i (n)

s (n)

Fig. 3. Sketch of zero-mean I/Q data along the CP arc.

D.R. Morgan, M.G. Zierdt / Signal Processing 89 (2009) 45–66 49

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