Patent Publication Number: US-9833200-B2

Title: Low IF architectures for noncontact vital sign detection

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of, and priority to, U.S. Provisional Application No. 62/161,359, filed May 14, 2015, which is hereby incorporated herein by reference in its entirety. 
    
    
     BACKGROUND 
     The research on vital sign detection using noncontact Doppler radar has been carried out since the 1970&#39;s. Since then, many methods have been proposed to help to improve the measurement accuracy, lower the noise level and extend the detection range. A receiver with homodyne architecture has been applied to eliminate the detection null points by using both the in-phase and quadrature-phase (I/Q) output. The RF front end also effectively depressed the phase noise from VCO with range correlation effect. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Many aspects of the present disclosure can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present disclosure. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views. 
         FIGS. 1A and 1B  are schematic diagrams of an example of a digitally assisted low IF system in accordance with various embodiments of the present disclosure. 
         FIG. 1C  is a schematic block diagram illustrating an example of processing circuitry that can be used to process the output from the digitally assisted low IF system of  FIGS. 1A and 1B  of the double sideband low IF system of  FIGS. 5A and 5B  in accordance with various embodiments of the present disclosure. 
         FIG. 2  is an image of an example of a measurement setup for testing of the digitally assisted low IF system of  FIGS. 1A and 1B  in accordance with various embodiments of the present disclosure. 
         FIGS. 3A-3B and 4A-4B  are plots illustrating comparisons of the digitally assisted low IF system of  FIGS. 1A and 1B  with other systems in accordance with various embodiments of the present disclosure. 
         FIGS. 5A and 5B  are schematic diagrams of an example of a double sideband low IF system in accordance with various embodiments of the present disclosure. 
         FIG. 6  is a flow diagram illustrating the simulation for the double sideband low IF system of  FIGS. 5A and 5B  and a direct down convert system in accordance with various embodiments of the present disclosure. 
         FIGS. 7 and 8A-8B  are plots illustrating simulation comparisons of the double sideband low IF system of  FIGS. 5A and 5B  with other systems in accordance with various embodiments of the present disclosure. 
         FIG. 9  is an image of an example of a measurement setup for testing of the double sideband low IF system of  FIGS. 5A and 5B  in accordance with various embodiments of the present disclosure. 
         FIGS. 10A-10B, 11A-11B and 12A-12C  are plots illustrating experimental comparisons of the double sideband low IF system of  FIGS. 5A and 5B  with other systems in accordance with various embodiments of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Disclosed herein are various examples related to noncontact vital sign detection using digitally assisted low intermediate frequency (IF) architectures. Reference will now be made in detail to the description of the embodiments as illustrated in the drawings, wherein like reference numbers indicate like parts throughout the several views. 
     Noncontact Doppler vital sign sensor uses the phase modulated signal backscattered by the subjects to estimate their life sign information. The homodyne architecture can simplify the radar hardware implementation in vital sign detection. However, due to the characteristics of the vital sign signal, the homodyne architecture has some disadvantages in this application scenario.
         1) Introduction of DC offset: The homodyne architecture can introduce a DC offset component in the I/Q channel outputs. This could lead to serious distortion on the vital sign signal which is typically a very low frequency signal (0.1 Hz to 1.5 Hz).   2) Susceptibility to low frequency noise: the homodyne architecture directly down converts the vital sign phase information to baseband. The down converted I/Q data will be very vulnerable to low frequency noise, in particular 1/f noise from the mixer and baseband amplifier.       

     To avoid the aforementioned disadvantages of the homodyne architecture, a heterodyne architecture has been introduced for vital sign detection. In one system, a heterodyne receiver was used for vital sign detection. The system uses a 70 MHz IF carrier and an analog/digital (A/D) converter for digital demodulation. In another system, a coherent low IF heterodyne architecture was proposed. The architecture explores the advantage of range correlation and digitally demodulates the received radar IF signal to achieve a significant improvement of signal to noise ratio (SNR). However, these systems need to know the accurate IF carrier frequency for the digital demodulation, which means the radars will need recalibration if there is an offset of the IF carrier frequency. 
     In this disclosure, a digitally assisted low IF transceiver system is presented that can provide a 15 dB signal-to-noise ratio (SNR) improvement when compared to the homodyne architecture with the same transmitting power. The low IF transceiver system samples both the IF carrier used in transmission and the received radar IF signal for digital demodulation. The architecture is more tolerant to the IF frequency offset and the phase noise from the IF carrier. 
     Principles of Digitally Assisted Low IF Transceiver 
     Referring to  FIG. 1A , shown is a schematic diagram of an example of a digitally assisted low IF transceiver system  100 , which includes a voltage controlled oscillator (VCO)  103  and an intermediate frequency oscillator (IFO)  106 . A transit mixer  109  modulates a local oscillator (LO) signal from the VCO  103  with an IF carrier from the IFO  106 . The modulated signal is transmitted toward a target  112  (e.g., a person or other vibrating object) where it is backscattered, and the received signal is down converted by a receive mixer  115 . The down converted signal and IF carrier are simultaneously sampled by an analog-to-digital converter (ADC)  118  for demodulation and further processing to determine the condition of the target  112  using processing circuitry (PC), which can include, e.g., a processor and memory. For example, the PC can be a computer, tablet, smart phone, frequency analyzer or other processing device that can determine characteristics of the target  112  from the demodulated output of the ADC  118 . 
     The low IF carrier can be defined as:
 
 S   IF ( t )= A   IF  COS(ω IF   t+φ   IF ( t )),  (1)
 
where ω IF  is the frequency of the IF carrier and φ IF (t) is the phase noise of the IF carrier. A IF  is the amplitude of the IF carrier. The low IF carrier can be used to modulate the LO signal generated from a VCO  103 . The modulated signal can be presented as:
 
 S   T ( t )= A   T  cos((ω LO +ω IF ) t+φ   LO ( t )+φ IF ( t )),  (2)
 
where A T  is the amplitude of the signal, and ω w  and φ LO (t) are the frequency and phase noise of the VCO  103 , respectively. The modulated signal S T (t) is transmitted out and then backscattered from the target  112  and received by the digitally assisted low IF system  100 . The received signal can be analyzed as:
 
 S   R ( t )= A   R  cos((ω LO +ω IF )( t−t   d )+φ LO ( t−t   d )+φ IF ( t−t   d )+θ+φ V ( t )),  (3)
 
where θ is a constant due to the transmission delay and the reflection on the measurement object, φ V (t) is the phase variation related to the target&#39;s vibration, and t d  is the time delay of the round-trip transmission with t d =2d/c, where d is the distance between the radar and the target  112 , c is the speed of light in free space (c=3.0×10 8  m·s −1 ). In a vital sign application, φ V (t) is proportional to vibrations such as the subject&#39;s chest movement due to heartbeat and respiration.
 
     The received signal S R (t) can be down converted into an IF signal, which can be represented as:
 
 S   IF ′( t )= A   IF ′ cos(ω IF   t+φ   LO ( t−t   d )−φ LO ( t )+φ IF ( t−t   d )+θ′+φ V ( t )),  (4)
 
where θ′ is a constant given by θ′=θ−t d (ω LO +ω IF ). Using the range correlation relation φ LO (t−t d )≈φ LO (t), the down converted signal of Eqn. (4) can be simplified to:
 
 S   IF ′( t )= A   IF ′ cos(ω IF   t+φ   IF ( t−t   d )+θ′+φ V ( t ))  (5)
 
Since the frequency of S IF ′(t) is relatively low (e.g., about 1 kHz in the digitally assisted low IF system  100 ), it can be directly sampled via an economic A/D converter (ADC)  118 .
 
     In the digitally assisted low IF system  100 , the ADC  118  samples both S IF (t) and S IF ′(t) simultaneously and uses the sampled low IF carrier S IF (t) to demodulate the down converted signal S IF ′(t). It can be proved that after the demodulation, the I-channel signal is:
 
 I ( t )= A   I  cos((φ IF ( t−t   d )−φ IF ( t )+θ′+φ V ( t )),  (6)
 
where A I  is the amplitude. By using the range correlation φ IF (t−t d )≈φ IF (t), Eqn. (6) can be reduced to:
 
 I ( t )= A   I  cos(θ′+φ V ( t )),  (7)
 
which is the I-channel data without the IF phase noise φ IF (t). Similarly, we can have Q-channel data as
 
 Q ( t )= A   Q  sin(θ′+φ V ( t )),  (8)
 
by down converting S IF ′(t) with S IF (t−t c ), where t c  is the amount of time to introduce a 90° phase shift for S IF (t), that is t c =2π/4ω IF .
 
     One of the advantages of the digitally assisted low IF architecture of  FIG. 1A  can be seen in Eqns. (6)-(8). By demodulating the down converted IF signal S IF ′(t) with the sampled low IF carrier S IF (t), the phase noise φ IF (t) is depressed. Low IF systems that use separately generated IF carriers:
 
 I   c ( t )=cos(ω IF   ′t ), and  (9)
 
 Q   c ( t )=sin(ω IF   ′t )  (10)
 
to demodulate the IF signal will get I/Q signals of:
 
 I ′( t )=cos(Δω IF   t+φ   IF ( t−t   d )+θ′+φ V ( t )), and  (11)
 
 Q ′( t )= A   Q ′ sin(Δω IF   t+φ   IF ( t−t   d )+θ′+φ V ( t )),  (12)
 
where Δω IF =ω IF ′−ω IF ′. Thus, those systems would not be able to cancel the phase noise from the IF carrier.
 
     Another advantage of the digitally assisted low IF system  100  can be observed in Eqns. (5)-(8), where the system  100  samples the IF carrier S IF (t) for demodulation and is not affected if the IF carrier frequency ω IF  is different from its nominal value ω IF ′. For a coherent IF system however, the IF offset will cause a nonzero Δω IF  as shown in Eqns. (11) and (12). A small Δω IF  (e.g., 0.1 Hz) can introduce an interference within the vital sign frequency range and corrupt the demodulated signal, since the vital sign information φ V (t) is a low frequency signal (e.g., typically 0.1 to 1.5 Hz) with a small amplitude. 
     Referring next to  FIG. 1B , shown is a more detailed example of the digitally assisted low IF transceiver system  100  of  FIG. 1A . The IFO  106  can provide the low IF carrier S IF (t) as presented in Eqn. (1). The S IF (t) is used to modulate the LO signal S LO (t) generated from a VCO  103 :
 
 S   LO ( t )= A   LO  cos(ω LO   t+φ   LO ( t )),  (13)
 
where ω LO  is the frequency of the LO signal, φ LO (t) is the phase noise of the signal, and A LO  is the amplitude of the LO signal. The low IF carrier can be provided via a power divider  121  and the LO signal can be provided via one or more gain block  124  and power splitter  127 . Signals S LO (t) and S IF (t) are mixed via the up convert mixer  109 . The modulated signal S M (t) can be presented as:
 
                             S   M     ⁡     (   t   )       =       ⁢         S   LO     ⁡     (   t   )       *       S   IF     ⁡     (   t   )                     =       ⁢           A   IF     ⁢     A   LO       2     ⁢     {       cos   ⁡     [         (       ω   LO     +     ω   IF       )     ⁢   t     +       φ   LO     ⁡     (   t   )       +       φ   IF     ⁡     (   t   )         ]       +                           ⁢     cos   ⁡     [         (       ω   LO     -     ω   IF       )     ⁢   t     +       φ   LO     ⁡     (   t   )       -       φ   IF     ⁡     (   t   )         ]       }     .                 (   14   )               
The double sideband signal S M (t) is then filtered by a RF filter  130  where the lower frequency component (ω LO −ω IF ) is removed.
 
     The filtered signal S T (t) of Eqn. (2) is transmitted out toward a target  112  ( FIG. 1A ). In Eqn. (2), 
               A   T     =       ⁢         A   IF     ⁢     A   LO       2           
is the amplitude of the transmitting signal of the radar. S T (t) is then backscattered from the target  112 . The backscattered signal is received by the radar, and can be processed by a low noise amplifier  133  and one or more gain block  136 . The received signal S R (t) can be presented as Eqn. (3). In a vital sign application, φ V (t) is proportional to the subject&#39;s chest movement due to heartbeat and respiration. The received signal S R (t) can be down converted into an IF signal via the down convert mixer  115  using the LO signal S LO (t) from power splitter  127 . The down converted IF signal:
 
 S   IF ′( t )=Lowpass{ S   R ( t )* S   LO ( t )},  (15)
 
as represented in Eqn. (4). According to the range correlation relation φ LO (t−t d )≈φ LO (t), Eqn. (4) can be simplified as expressed in Eqn. (5). Since the frequency of S IF ′(t) is relatively low, it can be directly sampled via an economic A/D converter  118 , which can amplify the signal.
 
     In the digitally-assisted low IF system  100 , the signals S IF (t) and S IF ′(t) are filtered by bandpass filters  139  and  142  before the A/D sampling  118 . The bandpass filtering  139  removes the dc offset in the down converted IF signal and suppresses the high frequency noise. Since the down converted IF signal S IF ′(t) is around the IF frequency ω IF , it also suffers from a lower level of 1/f noise from the baseband amplifier. The A/D converter  118  samples both the S IF (t) and S IF ′(t) simultaneously and uses the sampled S IF (t) to demodulate S IF ′(t). It can be shown that, after the demodulation, the I-channel signal is given by Eqn. (6). Using the range correlation φ IF (t−t d )≈φ IF (t), Eqn. (6) can be reduced to Eqn. (7), which is the I-channel data without the IF phase noise φ IF (t). Similarly, the Q-channel data can be reduced to Eqn. (8) by down converting S IF ′(t), with S IF (t−t c ) where t c  is the amount of time to introduce a 90° phase shift for S IF (t), that is t c =2π/4ω IF ′. 
     The advantages of sampling S IF (t) and S IF ′(t) simultaneously can be seen by analyzing (6)-(8). By using S IF (t) samples for the demodulation process, the phase noise of the signal φ IF (t−t d ) can be removed and the synchronization mechanism can be simplified. 
       FIG. 1C  shows an example of a processing system comprising processing circuitry that can be used to analyze the output from the ADC  118  of  FIGS. 1A and 1B  or  FIGS. 5A and 5B . The processing system  160  includes at least one processor circuit, for example, having a processor  163  and a memory  166 , both of which are coupled to a local interface  169 . To this end, the processing system  160  may comprise, for example, at least one computer, tablet, smart phone, frequency analyzer or like processing device. The local interface  169  may comprise, for example, a data bus with an accompanying address/control bus or other bus structure as can be appreciated. In addition, the processing system  160  include operator interface devices such as, e.g., a display device, a keyboard, and/or a mouse  1918 . In some implementations, the operator interface device may be interactive display (e.g., a touch screen) that provides various functionality for operator interaction with the processing system  160 . The digitally assisted low IF system  100  can interface with the processing system  160  to allow for acquisition of signal measurements from the ADC  118  ( FIGS. 1A and 1B ). In some implementations, the digitally assisted low IF system  100  may interface with the processing system  160  via a data acquisition board (DAQ) or other interfacing device. 
     Stored in the memory  166  are both data and several components that are executable by the processor  163 . In particular, stored in the memory  166  and executable by the processor  163  are various application modules or programs such as, e.g., a vibrational frequency module, application, or program  172  for demodulation and/or evaluation of signal measurements from the digitally assisted low IF system  100  using, e.g., an filtering and/or other applications. Also stored in the memory  166  may be a data store  175  and other data. In addition, an operating system  178  may be stored in the memory  166  and executable by the processor  163 . It is understood that there may be other applications that are stored in the memory  166  and are executable by the processor  163  as can be appreciated. Where any component discussed herein is implemented in the form of software, any one of a number of programming languages may be employed such as, for example, C, C++, C#, Objective C, Java®, JavaScript®, Perl, PHP, Visual Basic®, Python®, Ruby, Delphi®, Flash®, or other programming languages. 
     A number of software components are stored in the memory  166  and are executable by the processor  163 . In this respect, the term “executable” means a program file that is in a form that can ultimately be run by the processor  163 . Examples of executable programs may be, for example, a compiled program that can be translated into machine code in a format that can be loaded into a random access portion of the memory  166  and run by the processor  163 , source code that may be expressed in proper format such as object code that is capable of being loaded into a random access portion of the memory  166  and executed by the processor  163 , or source code that may be interpreted by another executable program to generate instructions in a random access portion of the memory  166  to be executed by the processor  163 , etc. An executable program may be stored in any portion or component of the memory  166  including, for example, random access memory (RAM), read-only memory (ROM), hard drive, solid-state drive, USB flash drive, memory card, optical disc such as compact disc (CD) or digital versatile disc (DVD), floppy disk, magnetic tape, or other memory components. 
     The memory  166  is defined herein as including both volatile and nonvolatile memory and data storage components. Volatile components are those that do not retain data values upon loss of power. Nonvolatile components are those that retain data upon a loss of power. Thus, the memory  166  may comprise, for example, random access memory (RAM), read-only memory (ROM), hard disk drives, solid-state drives, USB flash drives, memory cards accessed via a memory card reader, floppy disks accessed via an associated floppy disk drive, optical discs accessed via an optical disc drive, magnetic tapes accessed via an appropriate tape drive, and/or other memory components, or a combination of any two or more of these memory components. In addition, the RAM may comprise, for example, static random access memory (SRAM), dynamic random access memory (DRAM), or magnetic random access memory (MRAM) and other such devices. The ROM may comprise, for example, a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), or other like memory device. 
     Although the vibrational frequency module, application, or program  172  and other various systems described herein may be embodied in software or code executed by general purpose hardware as discussed above, as an alternative the same may also be embodied in dedicated hardware or a combination of software/general purpose hardware and dedicated hardware. If embodied in dedicated hardware, each can be implemented as a circuit or state machine that employs any one of or a combination of a number of technologies. These technologies may include, but are not limited to, discrete logic circuits having logic gates for implementing various logic functions upon an application of one or more data signals, application specific integrated circuits having appropriate logic gates, or other components, etc. Such technologies are generally well known by those skilled in the art and, consequently, are not described in detail herein. 
     Also, any logic or application described herein, including the vibrational frequency module, application, or program  172  and/or application(s), that comprises software or code can be embodied in any non-transitory computer-readable medium for use by or in connection with an instruction execution system such as, for example, a processor  163  in a computer system or other system. In this sense, the logic may comprise, for example, statements including instructions and declarations that can be fetched from the computer-readable medium and executed by the instruction execution system. In the context of the present disclosure, a “computer-readable medium” can be any medium that can contain, store, or maintain the logic or application described herein for use by or in connection with the instruction execution system. The computer-readable medium can comprise any one of many physical media such as, for example, magnetic, optical, or semiconductor media. More specific examples of a suitable computer-readable medium would include, but are not limited to, magnetic tapes, magnetic floppy diskettes, magnetic hard drives, memory cards, solid-state drives, USB flash drives, or optical discs. Also, the computer-readable medium may be a random access memory (RAM) including, for example, static random access memory (SRAM) and dynamic random access memory (DRAM), or magnetic random access memory (MRAM). In addition, the computer-readable medium may be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), or other type of memory device. 
     Experimental Setup 
     Referring now to  FIG. 2 , shown is an example of a measurement setup for testing of various radar systems including the digitally assisted low IF system  100 . Three radar systems were implemented to compare their performance: a homodyne architecture, a coherent low IF architecture, and the digitally assisted low IF architecture of  FIG. 1 . The three systems shared the same implementation on their receiver end: a receiver implemented by an HMC318MS8G low noise amplifier (LNA), an NBB-400 gain block, and an HMC525LC4 I/Q mixer (e.g., receive mixer  115  of  FIG. 1 ). The two low IF systems use HMC219AMS8 as the up conversion mixer (e.g., transmit mixer  109  of  FIG. 1 ). An Agilent E8254A signal generator (e.g., VCO  103  of  FIG. 1 ) generated a 5.8 GHz RF carrier (or LO signal) while an Agilent 33521A function generator (e.g., IFO  106  of  FIG. 1 ) provides the 1 kHz IF carrier. All the systems used the same pair of 2×2 patch array antennas for transmitting and receiving. The down converted signals (the I/Q channel data, the IF carrier, and the IF signal) were amplified via 15× gain baseband amplifiers before sampling. The sampling frequency was 10 kHz. For post processing on a computer, baseband data estimated from all the systems was filtered with a 4th-order Butterworth digital low pass filter (20 Hz bandwidth) before comparison. 
     Experimental Results 
     Two sets of experiments were conducted for the comparison. The first group of experiments measured the vibration generated by an actuator ( FIG. 2 ). The second group included measurements on human subjects. The reason of using an actuator as the target  112  ( FIG. 1 ) was that the vibration of an actuator can be accurately controlled to have a repeatable pattern while human vital sign cannot. It was easier to perform a quantitative comparison between the systems by measuring the vibration from an actuator. 
     In the first set of experiments, the actuator was placed 1.2 m away from the radar ( FIG. 2 ). The transmitted power of the radar systems was set to −10 dBm by adding attenuators at the transmitter side, to demonstrate that the proposed system can detect small vibrations with low power transmissions. The actuator was vibrated at 1 Hz with a peak-to-peak amplitude of 1 mm to emulate human heartbeat movement. The results are shown in  FIGS. 3A and 3B .  FIG. 3A  shows examples of the time domain waveform and  FIG. 3B  shows examples of the power spectrum density of the different systems. The baseband waveforms and spectrums are normalized for the SNR comparison. 
     It can be seen from  FIG. 3A , the signal (curve  303 ) from the digitally assisted low IF system  100  ( FIG. 1 ) has a lower noise level when compared to the signal (curve  306 ) from the homodyne system. The signal (curve  306 ) from the homodyne system was seriously corrupted by high frequency noise and low frequency DC drift. The digitally assisted low IF system  100  also has a much smaller DC drift when compared to the coherent low IF system (curve  309 ). The DC drift of the coherent IF system was due to the IF carrier offset Δω w . The SNR improvement of the digitally assisted low IF system  100  can be observed from  FIG. 3B . The proposed system provides a SNR improvement of at least 15 dB when compared to the homodyne system. 
     The comparison between the homodyne system and the digitally assisted low IF system  100  on a human test target  112  ( FIG. 1 ) can be seen in  FIGS. 4A and 4B . During the test, the subject was seated at 1 m away from the radar sensors and held his/her breath for heartbeat measurements. The transmitted power of the systems was −10 dBm.  FIG. 4A  shows examples of the time domain waveform and  FIG. 4B  shows examples of the power spectrum density of the homodyne system and the digitally assisted low IF system  100 . The baseband waveforms are normalized for the comparison. It can be seen from curve  403  of  FIG. 4B  that for the digitally assisted low IF system  100 , a peak at 1.2 Hz was detected. This peak corresponds to a heart rate of 72 bpm, consistent with the 70 bpm reference. The homodyne system failed to distinguish a heartbeat peak in its power spectrum density as seen in curve  406 . 
     In this disclosure, a digitally assisted low IF system  100  for vital sign detection application had been presented. The system uses the sampled IF carrier to demodulate the down converted IF signal into the baseband signal. The system  100  simplifies the synchronization mechanism by using the same ADC  118  ( FIGS. 1A and 1B ) to sample the IF carrier and the down converted IF signal simultaneously. The architecture also eliminates the DC offset and low frequency noise problems existing in a homodyne architecture. At the same time, the digitally assisted low IF system  100  is less sensitive to the IF carrier frequency offset and IF carrier phase noise. Thus, signal degradation due to DC offset and If frequency offset can be avoided. It also improves the SNR by avoiding directly down converting the baseband signal to a DC frequency range. Experiments have been conducted with an actuator and human subjects to verify the performance of the digitally assisted low IF system  100 . 
     Principles of Double Sideband Low IF Transceiver 
     The digitally assisted low IF system  100  only uses the upper sideband of the up convert signal for transmission, which means that an RF filter  130  ( FIG. 1B ) is included at the transmitter side to suppress the lower sideband. The design can be simplified by implementing a double sideband low IF system (e.g., a radar system). By using a double sideband RF signal for transmission, the RF filter  130  at the RF front end is no longer needed. A double sideband low IF system can offer a simpler architecture and more design flexibility than the digitally assisted low IF system  100 . Instead of using a simple down convert mixer  115  ( FIGS. 1A and 1B ), an in-phase and quadrature (I/Q) mixer can be used at the receiver side to down convert the reflected RF signal into IF signals. The double sideband architecture continues to avoid DC offset distortion and lower the impact of 1/f noise. An ADC simultaneously samples the IF carrier and the IF signals from the output of the I/Q mixers for synchronization. The digital samples can then be used for digital demodulation. Compared to a direct down convert (DC) system, the double sideband low IF system can measure low frequency vibrations with a better SNR while keeping the hardware implementation simple. 
     Referring to  FIGS. 5A and 5B , shown are schematic diagrams illustrating an example of a double sideband low IF system  500 , which can be used for human vital sign measurements or for mechanical vibration measurements. The principles of the double sideband low IF system will now be discussed with respect to the diagrams of  FIG. 5A . The VCO  103  generates, e.g., a 5.8 GHz single tone RF signal:
 
 RF ( t )= A   RF  sin(ω RF   t+φ   RF ( t )),  (16)
 
where ω RF  is the frequency of the RF signal, A RF  is the amplitude of the RF signal, and φ RF (t) is the phase noise of the VCO. RF(t) can be modulated by the IF carrier generated by the IFO  106 :
 
IF( t )= A   IF  sin(ω IF   t+φ   IF ( t )),  (17)
 
via the up convert mixer  109 . In Eqn. (17), φ IF (t) is the phase noise of the IF carrier, ω IF  is the frequency of the IF carrier, and A IF  is the amplitude. The modulated signal can be presented as:
 
                             RF   M     ⁡     (   t   )       =       ⁢       RF   ⁡     (   t   )       *     IF   ⁡     (   t   )                     =       ⁢       A   M     ⁢     sin   ⁡     (         ω   IF     ⁢   t     +       φ   IF     ⁡     (   t   )         )       ⁢     sin   ⁡     (         ω   RF     ⁢   t     +       φ   RF     ⁡     (   t   )         )                     =       ⁢     -         A   M     2     [       cos   ⁡     (         (       ω   RF     +     ω   IF       )     ⁢   t     +       φ   RF     ⁡     (   t   )       +       φ   IF     ⁡     (   t   )         )       -                           ⁢     cos   ⁡     (         (       ω   RF     -     ω   IF       )     ⁢   t     +       φ   RF     ⁡     (   t   )       -       φ   IF     ⁡     (   t   )         )       ]     ,                 (   18   )               
where A M =A IF *A RF .
 
     The modulated signal RF M (t) is a double sideband signal that is transmitted out via the TX antenna. The transmitted signal is backscattered from the subject (or object for mechanical vibration measurements), where the backscattered signal RF M ′(t) can be represented as:
 
 RF   M ′( t )= A   M ′ sin(ω IF ( t−t   d )+φ IF ( t−t   d ))*sin(ω RF ( t−t   d )+φ RF ( t−t   d )+θ RF ),  (19)
 
where θ RF  is the phase change due to the reflection on the surface of the subject, t d  is the round-trip time delay of the RF signal, and A M ′ is the amplitude. It can be shown that:
 
                       t   d     =       2   ⁢     (       d   0     +     Δ   ⁢           ⁢     d   ⁡     (   t   )           )       c       ,           (   20   )               
where c is the light speed in free space, d 0  is the average distance between the subject and the double sideband low IF system  500 , and Δd(t) is the displacement due to the physiology activities of the subject (or movements of the object for mechanical vibration measurements). It can be shown that RF M ′(t) can also be presented as:
 
                         RF   M   ′     ⁡     (   t   )       =       -       A   M   ′     2       ⁢     {       cos   ⁡     (         ω   RF   +     ⁡     (     t   -     t   d       )       +     θ   1       )       -     cos   ⁡     (         ω   RF   -     ⁡     (     t   -     t   d       )       +     θ   2       )         }         ,           (   21   )               where ω RF   + =ω RF +ω IF ,ω RF   − =ω RF −ω IF ,θ 1 =φ RF ( t−t   d )+φ IF ( t−t   d )+θ RF , and θ 2 =φ RF ( t−t   d )−φ IF ( t−t   d )+θ RF .
 
     From Eqn. (21), it can be seen that the backscattered signal RF M ′ is a double sideband signal with two frequency components: ω RF   +  and {dot over (ω)} RF   − . The signal RF M ′(t) is received by the RX antenna of the double sideband low IF system  500  and down converted by the I/Q mixer  503 . The I/Q mixer  503  down converts RF M ′(t) using the signal RF(t) from the VCO  103  as the LO signal. The down converted I′ channel signal can be represented as: 
                             I   ′     ⁡     (   t   )       =       ⁢     Low   ⁢           ⁢   Pass   ⁢           ⁢   filtering   ⁢           ⁢     {         RF   M   ′     ⁡     (   t   )       *     RF   ⁡     (   t   )         }                   =       ⁢           A   M   ′     ⁢     A   RF       4     ⁢     {       sin   ⁡     (         ω   IF     ⁢   t     -       ω   RF   +     ⁢     t   d       +     θ   1     -       φ   RF     ⁡     (   t   )         )       +                           ⁢     sin   ⁡     (         ω   IF     ⁢   t     +       ω   RF   -     ⁢     t   d       -     θ   2     +       φ   RF     ⁡     (   t   )         )       }     .                 (   22   )               
For short distance measurements (e.g., d 0 &lt;10 m), the phase noise φ RF (t) of the VCO  103  can be treated as a low frequency signal, i.e. φ RF (t)≈φ RF (t−t d ), which allows Eqn. (22) to be further simplified to:
 
                       I   ′     ⁡     (   t   )       =           A   M   ′     ⁢     A   RF       2     ⁢     cos   ⁡     (         ω   RF     ⁢     t   d       -     θ   RF       )       *       sin   ⁡     (         ω   IF     ⁢   t     -       ω   IF     ⁢     t   d       +       φ   IF     ⁡     (     t   -     t   d       )         )       .               (   23   )               
The frequency of the IF carrier, f IF , in the experiments is around 1 kHz, which means that for short distance measurements the following:
 
                         ω   IF     ⁢     t   d       =         4   ⁢           ⁢   π   ⁢           ⁢   d       λ   IF       ∼     10     -   4           ,           (   24   )               
is a negligible term (λ IF  is the wavelength of the IF carrier) and
 
     
       
         
           
             
               
                 
                   
                     
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     The ADC  118  samples the IF carrier IF(t) from the power divider  121  and the down converted I′(t) from the I/Q mixer  503 , and uses the IF(t) to digitally down convert signal I′(t) into the baseband/channel signal: 
                           I   ⁡     (   t   )       =       ⁢     Low   ⁢           ⁢   Pass   ⁢           ⁢   Filtering   ⁢           ⁢     {         I   ′     ⁡     (   t   )       *     IF   ⁡     (   t   )         }                   =       ⁢           A   M   ′     ⁢     A   RF     ⁢     A   IF       4     ⁢     cos   ⁡     (         ω   RF     ⁢     t   d       -     θ   RF       )       ⁢   cos   ⁢           ⁢     ω   IF     ⁢       t   d     .                     (   26   )               
Using the short distance approximation of Eqn. (24), the baseband I channel signal can be approximated as:
 
                     I   ⁡     (   t   )       ≈           A   M   ′     ⁢     A   RF     ⁢     A   IF       4     ⁢       cos   ⁡     (         ω   RF     ⁢     t   d       -     θ   RF       )       .               (   27   )               
Similarly, the ADC  118  can sample the down converted Q′(t) signal from the I/Q mixer  503  and digitally down convert it into the baseband Q channel signal:
 
                     Q   ⁡     (   t   )       ≈           A   M   ′     ⁢     A   RF     ⁢     A   IF       2     ⁢       sin   ⁡     (         ω   RF     ⁢     t   d       -     θ   RF       )       .               (   28   )               
By demodulating the baseband I/Q signals from Eqns. (27) and (28), the phase information can be retrieved as:
 
                     ψ   =           ω   RF     ⁢     t   d       -     θ   RF       =         4   ⁢           ⁢     π   ⁡     (       d   0     +     Δ   ⁢           ⁢     d   ⁡     (   t   )           )           λ   RF       -     θ   RF           ,           (   29   )               
where λ RF  is the wavelength of the RF carrier. The physiology activities of the subject or the displacement of objects Δd(t) can then be measured by processing Eqn. (29).
 
     Comparison Between a Direct Down Convert System and a Double Sideband Low IF System. 
     Non-ideal characteristics of I/Q demodulators like LO leakage can introduce DC offset in the output of the mixers, degrading the low frequency I/Q signals. Another factor that can cause the degradation of signals is the 1/f noise from the mixer and the baseband amplifier. The power level of the 1/f noise is inversely proportional to the frequency, which means signals at low frequency are more vulnerable to 1/f noise. 
     For a DC radar system, the demodulated I/Q signals can be represented as: 
                         I     D   ⁢           ⁢   C       ⁡     (   t   )       =       A     D   ⁢           ⁢   C       ⁢     cos   ⁡     (         4   ⁢           ⁢     π   ⁡     (       d   0     +     Δ   ⁢           ⁢     d   ⁡     (   t   )           )           λ   RF       -     θ   RF       )           ,   and           (   30   )                     Q     D   ⁢           ⁢   C       ⁡     (   t   )       =       A     D   ⁢           ⁢   C       ⁢     sin   ⁡     (         4   ⁢           ⁢     π   ⁡     (       d   0     +     Δ   ⁢           ⁢     d   ⁡     (   t   )           )           λ   RF       -     θ   RF       )           ,           (   31   )               
From these equations, it can be seen that Δd(t) is a low frequency signal corresponding to the low frequency vibrations and vital sign activities. Thus, I DC (t) and Q DC (t) are signals around the DC frequency range. So for a DC radar system, the demodulated I/Q signals suffers strong 1/f noise and is distorted by the DC offset.
 
     In the double sideband low IF system  500 , the problems of the DC system can be avoided by down converting the RF signal into the IF frequency range (in the experiments, ω IF =2π*10 3  rad·s −1 ). From Eqn. (25), the I/Q mixer  503  down converts the signals to a frequency around ω w , which is far away from DC. Thus the low frequency DC offset generated by the I/Q mixer  503  can be easily filtered from signals I′(t) and Q′(t) using bandpass filters  139 . The ADC  118  can be used to sample the filtered IF signals I′(t) and Q′(t) for digital demodulation. Signals I′(t) and Q′(t) also have a lower 1/f noise level since the frequency of the signals is far above the DC frequency. 
     Comparison Between a Double Sideband Low IF System and a Digitally Assisted Low IF Radar System. 
     A digitally assisted low IF system  100  ( FIGS. 1A and 1B ) can also help to avoid DC offset and lower the 1/f noise. However, the system  100  uses an RF filter  130  ( FIG. 1B ) at the transmitter end to generate a single sideband RF signal for transmission. A digitally assisted low IF radar transmits the modulated signal of Eqn. (2) for vibration measurements or vital sign detection. As it is shown in Eqns. (16)-(18), the output of the up convert mixer  109  is a double sideband RF signal which contains two frequency components: components around frequency ω RF ±ω IF . To generate the single sideband signal in Eqn. (2), an RF filter  130  is used at the transmitter end to suppress the lower sideband (the component with a frequency around ω RF −ω IF . The filter  130  can increase the complexity of the radar hardware, since a highly selective RF filter should be used for the lower sideband suppression at the lower sideband frequency, while a high speed ADC  118  should be used for the IF signal sampling at the higher sideband frequency. 
     For the double sideband low IF system  500 , the RF filter  130  is no longer needed since the system  500  transmits a double sideband RF signal for detection. The receiver end can retrieve the vibration information by using an I/Q mixer  503  to down convert the RF signal into signals I′(t) and Q′(t). This helps to simplify the design. In addition, the choice of the IF frequency can be more flexible without concerning the implementation of an RF filter in the double sideband low IF system  500 . 
     Simulation Results. 
     A simulation is set up in Matlab environment to verify the advantages of the double sideband low IF radar system. The simulation is to compare the SNR of the signals from a double sideband low IF system  500  and a DC system with the presence of 1/f noise. 
     Referring to  FIG. 6 , shown is a flow diagram illustrating the Matlab 1/f noise simulation for the double sideband low IF system  500  and the direct down convert system. In the simulation, both systems were simulated to measure a 0.2 Hz triangle wave vibration. To simulate the measurement condition in which two radar systems use the same transmitting power and the same receiver chain, the signals from the output of I/Q mixers of the two systems were normalized to the same power level (18.2 dBm). The 1/f noise was added to the signals to simulate the noise in the mixer and the baseband circuits of the radar systems.  FIG. 7  shows the power spectrum density of the added noise. It can be seen that the power density of the noise is inversely proportional to the frequency. Eventually, the noisy signals from the two systems were demodulated using an arctangent demodulation method and filtered by the same bandpass filter (0.1 Hz˜30 Hz passband) for the SNR comparison. 
     Referring to  FIGS. 8A and 8B , shown are the time domain waveforms and the power spectrum density, respectively, of the noise simulation results for the direct down convert system and the double sideband low IF system  500 , with the power density spectrums normalized to the power of the triangle signals to compare the SNR. The demodulated waveforms of the simulation are shown in  FIG. 8A . It can be seen that the waveform from the double sideband low IF system  500  has a better SNR. This can be further verified from  FIG. 8B , where the power spectrum density of the two waveforms are compared. It can be observed that the noise level in the double sideband low IF system  500  is at least 10 dB lower than that of the DC system. This may be attributed to the double sideband low IF system  500  down converting the RF signal to the f IF  frequency range (1 kHz for the simulation), while the DC system down converts the RF signal directly to the frequency around DC. The power level of the 1/f noise is much lower at f IF  as compared to the frequency around DC (see  FIG. 7 ). 
     Experimental Setup 
       FIG. 5B  shows an example of the hardware implementation of the double sideband low IF radar system  500  used for the experiments. When the up convert mixer  109  (e.g., HMC  219 ) is connected to the circuit and the RF switch  506  is off, the system  500  works as a double sideband low IF system. During the experiments, a 1 kHz sinusoidal IF carrier from an Agilent 33220A function generator (acting as an IFO  106 ) was mixed with the 5.8 GHz RF carrier via the up convert mixer  109 . The mixer  109  generated a double sideband radar signal for transmission. When the up convert mixer  109  was disconnected away from the rest of the circuits and the RF switch  506  was turn on, the system worked as a direct down convert radar system. In this case, the single tone RF carrier (5.8 GHz) was transmitted out directly via the RF switch  506 . The two radar systems share the same circuits at their RF receiver ends. The loss of the attenuator  509  was adjusted so that under the two configurations, the transmitting power of the system is the same. This setup was consistent with the simulation conditions discussed above. 
     The baseband bandpass filters  139 / 142  for the two configurations were different: for the double sideband low IF configuration, the passband was 980 Hz to 1020 Hz; and for the direct down convert configuration, the passband was 0.1 Hz to 40 Hz. So the bandwidth of the filters  139 / 142  under the two configurations was the same (40 Hz). The bandpass filtered signals (down converted I/Q signals and the IF carrier) were amplified via a baseband amplifier with the same gain (20×) across the two passbands. The signals are then sampled by an ADC  118  (e.g., NI USB-6210). The sampling frequency was 40 kHz for each channel. During post processing by the processing system  160  ( FIG. 10 ), digital demodulation was used to demodulate the I/Q data samples. The demodulated baseband data from the two systems were filtered with a 4th order Butterworth low pass filter (20 Hz bandwidth) before the comparison. 
       FIG. 9  shows the experiment setup for the measurements. The radar system used a pair of 2×2 patch array antennas for transmitting and receiving. An actuator was affixed 1 m away from the antenna array. The actuator was programmed to thrust a 30 mm×50 mm copper plane to generate the vibration movements for the experiments. 
     Experimental Results 
     Three groups of experiments were set up to evaluate the performance of the double sideband low IF system  500 . First, measurements were conducted to compare the performance of the proposed low IF system  500  and a direct down convert radar system. Then, experiments were conducted to demonstrate the capacity of measuring mechanical vibration using the low IF radar system  500 . Finally, experiments for measuring human vital signs using the double sideband low IF system  500  were conducted. 
     The Comparison Between the Double Sideband Low IF System and the Direct Down Convert Radar System. 
     The comparison between the double sideband low IF system  500  and the direct down convert system can be seen in  FIGS. 10A and 10B .  FIG. 10A  shows the measured baseband waveforms and  FIG. 10B  shows the power spectrum density of the baseband waveforms, with the waveforms normalized to 1 mm. Both systems were used to measure the mechanical vibration generated by an actuator. The actuator generated a periodic triangle wave vibration. The frequency of the vibration was 1 Hz and the peak-to-peak amplitude of the vibration was 3 mm. The distance between the radar and the actuator was fixed at 1 m for the experiment. 
     In  FIG. 10A , the waveforms are offset from zero for the convenience of comparison. It can be seen from  FIG. 10A  that the measurement result from the double sideband low IF system  500  has a better SNR as compared to the waveform from the direct down convert system. This can be further verified in  FIG. 10B , where the power spectrum density of the two waveforms are compared. In higher frequency range (&gt;1 Hz), the noise level of the low IF system  500  is at least 10 dB lower than that of the direct down convert system. This result is consistent with the simulation results. From  FIG. 10B , it can also be observed that the waveform of the direct down convert system has a higher power level near the DC frequency, corresponding to the distortion due to the DC offset from the mixer. The double sideband low IF system  500 , since it down converts the RF signal to the IF frequency range, is insensitive to the DC offset and low frequency noise. 
     The Measurement of Mechanical Vibrations Using the Double Sideband Low IF Radar System. 
     Experiments were conducted to evaluate the performance of the double sideband low IF system  500  for vibration measurements. For the measurements, the actuator was set up 1 m away from the low IF radar system  500 . The actuator generated a periodic triangle wave vibration. Multiple measurements were conducted under different vibration frequencies and amplitudes. The measurement data was processed with a 20-second window. 
       FIG. 11A  shows an example of the measurement of a mechanical vibration using the double sideband low IF system  500 . For this measurement, the peak-to-peak amplitude of the vibration was 0.5 mm, and the frequency was 1 Hz. It can be seen from  FIG. 11A  that the radar provides an accurate measurement result. The radar waveform is a triangle periodic signal with the expected amplitude and vibration frequency. The quantitative results of the measurements are shown in the table of  FIG. 11B . Under different vibration conditions, the double sideband low IF system  500  can provide accurate estimations of both the frequency and the amplitude of the vibrations. 
     The Measurement of Human Vital Sign Using the Double Sideband Low IF Radar System. 
     Experiments were conducted to demonstrate the capacity of measuring human vital sign using the double sideband low IF system  500 . During the measurements, the subjects sat about 1 m away from the vital sign radar. A contact sensor (e.g., a model  1010  piezoelectric pulse transducer) was attached to subjects&#39; fingers to provide the reference heart rate. The waveform of the vital sign measurement data is shown in  FIG. 12A . It can be seen that during the experiment, the subject breathed with a rate around 10 breath-per-minute. The displacement of the front chest was about 5 mm. 
     To further process the radar signal, a digital bandpass filter (0.7 Hz-1.5 Hz passband) was used to separate the heartbeat waveform from the noise and the respiration signal. The filtered radar heartbeat waveform and the reference heartbeat waveforms are shown in  FIG. 12B . It can be seen that the filtered heartbeat waveform is consistent with the reference waveform from the contact sensor. The filtered heartbeat waveform was then transformed into frequency spectrum by FFT. The FFT was conducted with a 10-second measurement window. The heart rate was then estimated using the frequency spectrum. A 5-second incremental step size was used for the heart rate update. The estimated heart rate is shown in  FIG. 12C . It can be seen that the double sideband low IF system  500  can provide an accurate heart rate estimation when compared to the reference heart rate. The average error of the measurement is 2.4 beat-per-minute (bpm). 
     In this disclosure, a double sideband low IF system was presented. The system was designed for noncontact mechanical vibration and vital sign measurement. The proposed radar architecture down converts RF signals to the IF frequency range, which helps to avoid the DC offset and lower the noise level. The system  500  uses a double sideband signal for transmission to allow the RF filter in the digitally assisted low IF system  100  to be removed from the transmitter side. By sampling the I/Q signals and the IF carrier simultaneously with an ADC, the architecture simplifies the synchronization mechanism. Simulations and experiments were conducted to evaluate the performance of the double sideband low IF system  500 . Results showed that the system  500  can provide accurate measurements on low frequency mechanical vibrations and human vital sign. 
     It should be emphasized that the above-described embodiments of the present disclosure are merely possible examples of implementations set forth for a clear understanding of the principles of the disclosure. Many variations and modifications may be made to the above-described embodiment(s) without departing substantially from the spirit and principles of the disclosure. All such modifications and variations are intended to be included herein within the scope of this disclosure and protected by the following claims. 
     It should be noted that ratios, concentrations, amounts, and other numerical data may be expressed herein in a range format. It is to be understood that such a range format is used for convenience and brevity, and thus, should be interpreted in a flexible manner to include not only the numerical values explicitly recited as the limits of the range, but also to include all the individual numerical values or sub-ranges encompassed within that range as if each numerical value and sub-range is explicitly recited. To illustrate, a concentration range of “about 0.1% to about 5%” should be interpreted to include not only the explicitly recited concentration of about 0.1 wt % to about 5 wt %, but also include individual concentrations (e.g., 1%, 2%, 3%, and 4%) and the sub-ranges (e.g., 0.5%, 1.1%, 2.2%, 3.3%, and 4.4%) within the indicated range. The term “about” can include traditional rounding according to significant figures of numerical values. In addition, the phrase “about ‘x’ to ‘y’” includes “about ‘x’ to about ‘y’”.