sensors

Article Theory and Measurement of Signal-to- Ratio in Continuous-Wave Noise

Bronisław Stec and Waldemar Susek * ID Faculty of Electronics, Military University of Technology, Gen. Urbanowicz St. No 2, 00-908 Warsaw, Poland; [email protected] * Correspondence: [email protected]; Tel.: +48-261-839-831

 Received: 14 March 2018; Accepted: 4 May 2018; Published: 6 May 2018 

Abstract: Determination of the signal power-to-noise power ratio on the input and output of reception systems is essential to the estimation of their quality and signal reception capability. This issue is especially important in the case when both signal and noise have the same characteristic as Gaussian . This article considers the problem of how a signal-to-noise ratio is changed as a result of signal processing in the correlation receiver of a noise radar in order to determine the ability to detect weak features in the presence of strong clutter-type interference. These studies concern both theoretical analysis and practical measurements of a noise radar with a digital correlation receiver for 9.2 GHz bandwidth. Firstly, signals participating individually in the correlation process are defined and the terms signal and interference are ascribed to them. Further studies show that it is possible to distinguish a signal and a noise on the input and output of a correlation receiver, respectively, when all the considered are in the form of white noise. Considering the above, a measurement system is designed in which it is possible to represent the actual conditions of noise radar operation and power measurement of a useful noise signal and interference noise signals—in particular the power of an internal leakage signal between a transmitter and a receiver of the noise radar. The proposed measurement stands and the obtained results show that it is possible to optimize with the use of the equipment and not with the complex processing of a noise signal. The radar parameters depend on its prospective application, such as short- and medium-range radar, ground-penetrating radar, and through-the-wall detection radar.

Keywords: radar receiver; correlation; radar clutter; signal-to-noise ratio; radar measurements

1. Introduction A characteristic of noise is the use of random or pseudorandom signals for probing purposes [1]. Until relatively recently, the design of noise radars was hindered by serious practical problems. Due to the absence of sufficiently fast computing platforms, the receivers of this type of radar were mainly constructed with the use of analogue solutions [2,3]. Currently, owing to the increasing availability of specialized high-performance processors and general-purpose platforms such as FPGAs (field-programmable gate arrays) and due to the availability of fast high-resolution analogue-to-digital converters, it has become possible to build noise radars equipped with digital receivers designed for various applications. The subject literature includes research on the use of noise radars in ultra-wideband SAR/ISAR (synthetic aperture radar/inverse synthetic aperture radar) systems [4], to conduct Doppler measurements [5], in anti-collision systems, in polarimetric measurements to detect objects hidden underground [6], and to detect micrometric distance changes, heartbeat, or chest movements in living organisms [3,7]. The use of signal processors with range-Doppler detection for real-time signal processing has increased the functionality of noise radars. The correlation of transmitted and received signals in the baseband can be performed simultaneously in multiple

Sensors 2018, 18, 1445; doi:10.3390/s18051445 www.mdpi.com/journal/sensors Sensors 2018, 18, 1445 2 of 11 range cells, owing to the application of different reference signal delays in the signal processor. However, compared to the computational requirements of pulse-Doppler radar, noise radar still requires considerably more computational power in order to detect an object. An additional problem is a phenomenon characteristic of continuous-wave noise radars—weak reflections from distant objects masked by strong signals coming from objects near the radar. A noise radar with a continuous wave receives both weak and strong signals simultaneously. The receiver is connected with the following phenomena: dynamic range related to target RCS (radar cross section) and dynamic range related to a distance. For instance, for a battlefield radar, the RCS of a human may be 0.5 m2, while the RCS of the ground is 1000 m2. Therefore, the dynamic range dependent on RCS changes is 33 dB. The dynamic range related to distance is based on the law that a reflected signal’s power reduces with the fourth power of distance. For example, for the shortest (10 m) to the longest (1000 m) distance ratio, the dynamic range is 80 dB. Therefore, it is necessary to ensure a very high reception path with a dynamic range equal to or exceeding 100 dB. An optimal receiver for this type of signal is a correlation receiver. A correlation receiver not only deals with the noise of the receiver’s electronic circuits and components, but also with the noise occurring as a correlation function of noise signals, which is the so-called noise floor. The RMS (root mean square) of the noise signal’s correlation function estimator is not reduced to zero with a higher distance. Therefore, it is transferred to all other distance cells. This results in the emergence of an additional (apart from the self-noise of components and circuits) interference noise source that limits the receiver sensitivity. Recently, a number of studies presenting research reducing clutter with algorithmic methods in the digital correlation processing of noise signals have been published [8–13]. This paper discusses the mutual signal power relations in an actual noise radar solution with a range-Doppler digital correlator. This research allows us to determine an achievable limit level of SNR (signal-to-noise ratio) at the output of the correlation detector depending on the SNR at its input for band-limited white noise signals without the use of algorithmic signal processing techniques to reduce the noise floor. The considerations presented in the study concern various noise signals with the same probabilistic characteristics. The signal coming from the analyzed target and the signals coming from other targets, leakage signals, and ground-reflected signals are noise signals with zero mean value and Gaussian distribution of probability density. For this reason, a classic approach to radar system parameters such as receiver sensitivity, SNR, or detection gain requires determination of the signal and the noise in a noise radar both at the input and at the output of the correlation detector. The specific nature of continuous-wave noise radars is that both the power of the noise signal received from the target and the power of the interfering signals depends on the radar transmitter signal power. One exception is the receiver self-noise. The studies which are presented in this paper focus on discovering the causes of the “noise floor” occurrence in the correlative detector output signal. The conducted measurements prove the theoretical considerations, which were sufficiently described in the work of Axelsson [14]. This paper analyzes a more complex case in which, while referring to Reference [14], an interfering signal σz consists of a signal of internal leakage, antenna leakage, and other signals received by an antenna (e.g., signals reflected from the 2 2 ground). There is also a reference signal σ ref that is not required to be equal to a received signal σ x as it is in Reference [14].

2. Signals in a Noise Radar Figure1 shows a simplified functional diagram of a noise radar in combination with existing signal types in real operating conditions. In a correlation receiver, the following signals exist: the desirable signal, which comes from Object 1 and is indicated in Figure1 with SR(t); and some other signals indicated with SI(t), which are interfering signals from the viewpoint of signal SR(t). The interference signals include two types of signals: a signal associated with the transmitter signal ST(t) and a signal independent of the transmitter, which is the receiver self-noise SN,R(t). These signals have the characteristics of random signals and limit the receiver sensitivity. Signals associated with the radar transmitter noise signal include: Sensors 2018, 18, 1445 3 of 11

• leakage 1—internal leakage of a signal from transmitter circuits to the receiver circuits with the Sensors 2018, 18, x FOR PEER REVIEW 3 of 11 power PLC. • leakage 2—  leakage 2—leakage of aa signalsignal betweenbetween thethe transmittingtransmitting and receiving antennas with the power PLA. PLA. • interfering signal—signal from Object 2 with the power P and signals reflected from the ground  interfering signal—signal from Object 2 with the power PR2R2 and signals reflected from the ground and other elements on its surface at different distances from the radar with the total power P a and other elements on its surface at different distances from the radar with the total power PCC a so-calledso-called clutter.clutter.

Figure 1. Functional diagram of a noise radar together with the types of the signals occurring in real Figure 1. Functional diagram of a noise radar together with the types of the signals occurring in real working conditions.conditions. LPF – Low Pass Filter.Filter

In order to simplify the analysis of the results of the noise signal correlation processing, the In order to simplify the analysis of the results of the noise signal correlation processing, the number of signals involved in the process of correlation with reference signal SREF(t) was reduced to number of signals involved in the process of correlation with reference signal SREF(t) was reduced to two: SR(t), the signal from Object 1; and SI(t), the interfering signal. The power of the interfering noise two: S (t), the signal from Object 1; and S (t), the interfering signal. The power of the interfering noise signal Rcan be defined as: I signal can be defined as:

PPPPPPPPI LC  LA  R2  C  NR ,  NT ,  NR , (1) PI = PLC + PLA + PR2 + PC + PN,R = PN,T + PN,R (1) The components of the signal SN,T(t) are sources of correlation peaks for the delay times other

than Thethe delay components time of the of the target signal in theSN ,processT(t) are of sources correlation of correlation with the reference peaks for signal. the delay However, times other they thanconstitute the delay a significant time of the interference target in the for process the signal of correlationreflected from with Object the reference 1 due to signal. the additive However, residue they constituteof the correlati a significanton function interference of these forsignals. the signal reflected from Object 1 due to the additive residue of the correlation function of these signals. 3. Noise Signal Correlation Function 3. Noise Signal Correlation Function The processing of the noise signals in a noise radar is related to the time segments of two realizationThe processings x(t) and y of(t) the of two noise stationary signals in and a noiseergodic radar stochastic is related processes to the timeX(t) and segments Y(t) [15] of. twoThe realizationsphysical meaningx(t) and of thesey(t) signals of two refers stationary to a signal and ergodicreflected stochasticfrom the target processes and a Xreference(t) and Ysignal(t)[15 or]. Thea reference physical signal meaning and of an these interference signals signal. refers toTwo a signal process reflected segments from called the targetthe noise and signals a reference of a signalspecified or aduration reference are signal considered and an interference in this paper signal.. In noise Two processradar systems, segments the called mean the values noise of signals signals of ax( specifiedt) and y(t) duration are equal are to consideredzero. In the incase this of paper. continuous In noise signals radar existing systems, in thea specified mean values time interval of signals x(t) and y(t) are equal to zero.ˆ In the case of continuous signals existing in a specified time interval (T + τ), the estimator Rxy   of their mutual correlation function (cross-correlation) can be (T + τ), the estimator Rˆ (τ) of their mutual correlation function (cross-correlation) can be represented represented by the followingxy Equation (2) [16]. by the following Equation (2) [16]. 1 T Rˆ τ x ( t ) y ( t  )d t , 0   T (2) xy    . T 0

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T 1 Z Rˆ xy(τ) = x(t)y(t − τ)dt, 0 ≤ τ < T. (2) Sensors 2018, 18, x FOR PEER REVIEW T 4 of 11 0

AtAt a large time distance distance from from the the correlation correlation peak, peak, the the correlation correlation function function does does not not decrease decrease to tozero zero but but maintains maintains a residual a residual value value called called a noise a floorof the of correlation the correlation function function illustrated illustrated in Figure in Figure2, which2, whichis of special is of special importance importance to the tonoise the radar noise sensitivity radar sensitivity and range. and range.

FigureFigure 2. 2.Real Real plot plot of of the the correlation correlation function function module module square square for forD oD=o 3.2= 3.2 m, m,v =v = 0, 0,B B= = 1 1 GHz, GHz,T = 160 µs. T = 160 μs. Therefore, it is important to determine the values of the correlation function outside of the Therefore, it is important to determine the values of the correlation function outside of the correlation peak. correlation peak. 3.1. The Variance of the Random Signal Correlation Function Estimator 3.1. The Variance of the Random Signal Correlation Function Estimator It should be noted that for τ = 0, Expression (2) becomes an estimator of the RMS value of the realizationIt shouldx(t) be or ynoted(t). By that definition, for τ = 0, the Expression expected value(2) becomes of the cross-correlation an estimator of functionthe RMS estimatorvalue of the (2) isrealization determined x(t) by or Equationy(t). By definition, (3) [16]: the expected value of the cross-correlation function estimator (2) is determined by Equation (3) [16]: T T 1 Z TT1 Z  ˆ ( ) = 11[ ( ) ( − )] = ( ) = ( ) E RExyRˆτ E Ex  xt ( ty ) yt ( t  τ ) d dt t  RRxy τ dd tt  RRxy  τ .(3 (3)) xy  T T xy  xy   . 0TT000

ˆ ˆ xy Therefore,Therefore, RRxyxy(τ) is anis an unbiased unbiased estimator estimator of theof the cross-correlation cross-correlation function functionRxy R(τ)( regardlessτ) regardless of the signal duration T. Therefore, the mean squared error of estimator Rˆ (τ) is equal to its variance of the signal duration T. Therefore, the mean squared error of estimatorxy Rˆ   is equal to its according to Equation (4) below [16]: xy variance according to Equation (4) below [16]: T T 1 Z TTZ   2 ˆ22 1 2 D DRxyR(ˆτ) =  EE[x (u )y y(u u+  τ) xx( υ) y( υ +  τ)] − RRxy (τ) d d dυ udu. .(4 (4)) xy  T          xy   T0 000

ForFor further analysis, itit was assumed that two stochastic processes X(X(tt)) andand Y(Y(tt),), which are jointly andand separately separately normal normal processes, processes, would would be subjected be subjected to correlation to correlation processing. processing. Therefore, Therefore, for a normal for a randomnormal random process withprocess zero with mean zero value, mean variance value, variance (4) is expressed (4) is expressed by Equation by E (5)quation below (5) [16 below]: [16]:

 1 ∞ 2 ˆ Z           2Dd RRRRRxy  1  x  y  xy  yx    , (5) D Rˆ xy(τ) ≈ T  Rx(ψ)Ry(ψ) + Rxy(ψ + τ)Ryx(ψ − τ) dψ, (5) T  −∞ where ψ = υ − u, dψ = dυ, x(t) and y(t) are the realization of the white noise with a limited frequency whereband equalψ = υ to− Bu ,and dψ =sufficiently dυ, x(t) and longy(t )duration are the realization T. of the white noise with a limited frequency bandThe equal variance to B and of sufficientlythe estimator long of durationthe crossT-correlation. function of these realizations determined on the basis of (5) is shown in Equation (6) below [16]:

22ˆ 1  DRRRRxy  x 0 y  0   . (6) 2BT xy

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The variance of the estimator of the cross-correlation function of these realizations determined on the basis of (5) is shown in Equation (6) below [16]:

Sensors 2018, 18, x FOR PEER REVIEW 1 h i 5 of 11 D2Rˆ (τ) ≈ R (0)R (0) + R2 (τ) . (6) xy 2BT x y xy 3.2. Noise at the Correlation Detector Output 3.2. Noise at the Correlation Detector Output The analysis of signal correlation processing in the noise radar was based on the following The analysis of signal correlation processing in the noise radar was based on the following assumptions, depicted in Figure 3. assumptions, depicted in Figure3.

Figure 3. Illustration of signal processing in a noise radar. Figure 3. Illustration of signal processing in a noise radar. There are three input noise signals with duration T, zero mean value, and Gaussian distribution There are three input noise signals with duration T, zero mean value, and Gaussian distribution of probability density function, which occupy band B; that is, a signal received from target SR(t) with of probability2 density function, which occupy band B; that2 is, a signal received from target SR(t) with variance σR , reference signal SREF(t) with variance σREF , and interfering signal SI(t) with variance 2 2 2 variance2 σR , reference signal SREF(t) with variance σREF , and interfering signal SI(t) with variance σI . σI . As a result of the correlation processing in the noise radar receiver, these signals correlate with As a result of the correlation processing in the noise radar receiver, these signals correlate with each each other as follows: the reference signal with the signal received from the target results in the output other as follows: the reference signal with the signal received from the target results in the output signal SOUT1(∆T), which is the estimate of the cross-correlation function Rxy,I(∆T) of these signals. signal SOUT1(ΔT), which is the estimate of the cross-correlation function Rxy,I(ΔT) of these signals. The The reference signal with the interfering signal results in the output signal SOUT2(∆T), which is the reference signal with the interfering signal results in the output signal SOUT2(ΔT), which is the estimate estimate of the cross-correlation function Rxy,II(∆T) of the reference signal and the interfering signal. of the cross-correlation function Rxy,II(ΔT) of the reference signal and the interfering signal. In fact, In fact, one correlation processing is performed, which results in the determination of the estimate of one correlation processing is performed,∑ which results in the determination of the estimate of the the cross-correlation function Rxy (∆T). This estimate is identical to the sum of the estimates. cross-correlation function Rxy∑(ΔT). This estimate is identical to the sum of the estimates.

ˆ Σ  Rxyˆ (∆T) = SOUT1(∆T) + SOUT2(∆T), (7) RTSTSTxy  OUT12   OUT    , (7) wherewhere Δ∆TT = =TOT O− T−DLT, DLTO, =T O2D=O/c, 2D DO/c,O is DtheO isdistance the distance from radar from radarto an object, to an object, and TDL and is theTDL timeis the delay time ofdelay the delay of the line. delay line. ∑ BasedBased on on definition definition (5 (5),), variance variance RRxyxy∑(Δ(T∆)T can) can be be described described with with Equation Equation (8) (8) below below::

2hˆ  i  2    2    . DDD2 ˆRTSTSTΣxy  2 OUT12   2 OUT    (8) D Rxy(∆T) = D [SOUT1(∆T)] + D [SOUT2(∆T)]. (8)

 The variance of estimate RTˆ   is equal to the sum of variances of estimates SOUT1(ΔT) and ˆxyΣ The variance of estimate Rxy(∆T) is equal to the sum of variances of estimates SOUT1(∆T) and SOUT2(ΔT). The relationship between the parameters of the input and output signals of the correlation SOUT2(∆T). The relationship between the parameters of the input and output signals of the correlation detector are as follows: RR(0) = σR2 is the2 variance of the noise signal from the target equal to the power detector are as follows: RR(0) = σR is the variance of the noise signal from the target equal to 2 2 PR,IN; RI(0) = σI is the variance2 of the signal from the interference equal to the power PI; RREF(0) = σREF the power PR,IN; RI(0) = σI is the variance of the signal from the interference equal to the power is the variance of the reference signal equal to the power PREF. All powers are measured at 1 Ω resistance. On the other hand, the voltage at the correlator output for ΔT = 0 is determined by Equation (9) below:

22 SOUT1 0  α σσ R REF , (9) where α (V/W) is the coefficient of transmission of the correlation detector.

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2 PI; RREF(0) = σREF is the variance of the reference signal equal to the power PREF. All powers are measured at 1 Ω resistance. On the other hand, the voltage at the correlator output for ∆T = 0 is determined by Equation (9) below: q 2 2 SOUT1(0) = α σRσREF, (9) where α (V/W) is the coefficient of transmission of the correlation detector. By inserting Equation (6) in Equation (8), it is possible to determine the variance of the correlation function estimate, which is expressed by the following formula:

h i α2   α2   D2 Rˆ Σ (∆T) ≈ σ2 σ2 + R2 (∆T) + σ2 σ2 + R2 (∆T) . (10) xy 2BT R REF xy,I 2BT REF I xy,II The source of all signals except for receiver self-noise in a noise radar is its transmitter. These signals are therefore correlated, and are in the form of Gaussian white noise. The signal power on the correlator output, at mutual correlation of, for example, a signal reflected from the target and a reference signal for ∆T 6= 0 is smaller than this signal power by BT for ∆T = 0. This results in the fact 2 2 2 that for BT = 10, for example, component R xy,I(∆T 6= 0) is only 10% of σR σREF . A similar situation is seen in the case of the second component of Equation (10). Therefore, for a sufficiently high value 2 2 of BT, the values of factors Rxy,I (∆T) and Rxy,II (∆T) are negligible compared to the values of the 2 2 2 2 corresponding products (σR σREF ) and (σREF σI ). Considering the above, Equation (10) takes the following form: h i α2 D2 Rˆ Σ (∆T 6= 0) = P ≈ (P P + P P ). (11) xy N,OUT 2BT R,IN REF REF I Equation (11) describes the variance of the cross-correlation function estimator of the signals occurring in the noise radar. Equation (11) also allows the determination of correlator output noise power PN,OUT, or the noise floor, which is shown in Figure2. The power of the correlator output noise is equal to the variance of the correlation function estimator for ∆T, which significantly differs from zero. It is also possible to determine the PNFR (peak-to-noise floor ratio) as a ratio of the power of the ˆ Σ output signal SOUT1(∆T) for ∆T = 0, to the variance of estimator Rxy(∆T) for ∆T 6= 0.

2 2 2 |SOUT1(∆T = 0)| σRσREF PNFR = h i ≈  , (12) 2 ˆ Σ 1 σ2 σ2 + σ2 σ2 D Rxy(∆T 6= 0) 2BT R REF REF I where the numerator of Equation (12) describes the power of the correlator output signal. The denominator of (12) describes the power of the correlator output noise, or the so-called noise floor.

4. Experimental Measurements Measurements were performed on the design solution of a noise radar with a continuous wave signal. The noise radar block diagram is shown in Figure4. Basic noise radar parameters include the maximum transmitter power PT = 10 dBm, the noise signal bandwidth BRF = 150 MHz, center frequency f 0 = 9.2 GHz, and integration time T = 1 ms. In real systems, the main measurement problem is the separation of the noise signal coming from the target from other noise signals such as internal leakage, antenna leakage, and other signals received by an antenna. This includes signals reflected from the ground. These signals determine the noise power at the output of the digital correlator. Sensors 2018, 18, x FOR PEER REVIEW 6 of 11

By inserting Equation (6) in Equation (8), it is possible to determine the variance of the correlation function estimate, which is expressed by the following formula:

αα22 2ˆ    2 2  2   2 2  2  D RTRTRTxy  σ R σ REF xy,, I   σ REF σ I xy II   . (10) 22BT BT The source of all signals except for receiver self-noise in a noise radar is its transmitter. These signals are therefore correlated, and are in the form of Gaussian white noise. The signal power on the correlator output, at mutual correlation of, for example, a signal reflected from the target and a reference signal for ΔT ≠ 0 is smaller than this signal power by BT for ΔT = 0. This results in the fact that for BT = 10, for example, component R2xy,I(ΔT ≠ 0) is only 10% of σR2σREF2. A similar situation is seen in the case of the second component of Equation (10). Therefore, for a sufficiently high value of BT, the values of factors Rxy,I2(ΔT) and Rxy,II2(ΔT) are negligible compared to the values of the corresponding products (σR2σREF2) and (σREF2σI2). Considering the above, Equation (10) takes the following form:

2 2 ˆ  α D0RTPPPPPxy   N,, OUT  R IN REF  REF I  . (11) 2BT Equation (11) describes the variance of the cross-correlation function estimator of the signals occurring in the noise radar. Equation (11) also allows the determination of correlator output noise power PN,OUT, or the noise floor, which is shown in Figure 2. The power of the correlator output noise is equal to the variance of the correlation function estimator for ΔT, which significantly differs from zero. It is also possible to determine the PNFR (peak-to-noise floor ratio) as a ratio of the power of  OUT1 ˆ the output signal S (ΔT) for ΔT = 0, to the variance of estimator RTxy   for ΔT ≠ 0.

2 ST0 22 OUT1   σσR REF PNFR  , (12)  1 2 ˆ  2 2 2 2 D0RTxy   σR σ REF σ REF σ I  2BT where the numerator of Equation (12) describes the power of the correlator output signal. The denominator of (12) describes the power of the correlator output noise, or the so-called noise floor.

4. Experimental Measurements

SensorsMeasurements2018, 18, 1445 were performed on the design solution of a noise radar with a continuous wave7 of 11 signal. The noise radar block diagram is shown in Figure 4.

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Basic noise radar parameters include the maximum transmitter power PT = 10 dBm, the noise signal bandwidth BRF = 150 MHz, center frequency f0 = 9.2 GHz, and integration time T = 1 ms. In real systems, the main measurement problem is the separation of the noise signal coming from the target from other noise signals such as internal leakage, antenna leakage, and other signals received by an antenna. ThisFigure includes 4. The signals block diagram reflected of thefrom noise the radar ground. with These a digital signals range determine-Doppler correlator. the noise power at Figure 4. The block diagram of the noise radar with a digital range-Doppler correlator. the output of the digital correlator.

4.1. Measuring System Figure 55 shows the measuring measuring system system used used to to measure measure the the power power of the of thenoise noise radar radar signals. signals. The signalThe signal path pathwas implemented was implemented using using a coaxial a coaxial transmission transmission line with line length with length L1 to connect L1 to connect a noise a radar noise transmitterradar transmitter with a with microwave a microwave pulse pulsephase phasemodulator. modulator. The phase The phase modulator modulator was used was together used together with witha circulator a circulator to imitate to imitate a moving a moving object. object.

Figure 5. Measuring system for noise radar signals measurement. Figure 5. Measuring system for noise radar signals measurement.

The phase modulator introduced a Doppler shift corresponding to the specified radial speed of the objectThe phase into the modulator signal path. introduced The second a Doppler line L2 shift with corresponding the same length to the as specifiedL1 represents radial the speed signal of path.the object To verify into the Equation signal path. (12), The the secondpulse phase line L2 modulator with the same perform lengthed as a L1full represents reflection the of signalthe power path. suppliedTo verify to Equation it from (12),the transmitter. the pulse phase The a modulatordjustable attenuator performed T1 a ma fullde reflection it possible of theto change power the supplied value to it from the transmitter. The adjustable attenuator T1 made it possible to change the value of signal of signal SR,IN(t), which reached the receiver signal input through a power combiner. Reference signal S (t), which reached the receiver signal input through a power combiner. Reference signal S (t) SREFR,IN(t) was transmitted to the receiver reference input through a power divider. Part of the signalREF wasfrom transmitted the noise transmitter to the receiver was transferred reference input to the through combiner a powerthrough divider. the power Part divider of the signaland adjustable from the attenuator T2, and then, to the receiver signal input. This signal represents the sum of the following signals: internal leakage, leakage between antennas, and ground-reflected signals specified in Equation (1). At the receiver input, there was a known value of noise signal PR,IN coming from the target and the value of interference power PI. The lengths of the transmission lines connecting the to the correlation receiver in the reception and reference paths were negligible in relation to the length of the lines L1 and L2. The power of the receiver self-noise included in the power of interference noise according to Equation (1) was calculated on the basis receiver noise ratio measurement.

4.2. Measurement Results

Figure 6 shows three pairs of characteristics: PR,OUT and PN,OUT of the correlation receiver output for ΔT = 0 as a function of input signal power PR,IN. These characteristics were plotted for three different values of interfering signal power PI. The change in the value of power PR,IN was

Sensors 2018, 18, 1445 8 of 11 noise transmitter was transferred to the combiner through the power divider and adjustable attenuator Sensors 2018, 18, x FOR PEER REVIEW 8 of 11 T2, and then, to the receiver signal input. This signal represents the sum of the following signals: internalimplemented leakage, using leakage an between adjustab antennas,le attenuator and T1. ground-reflected The plot of the signals measured specified characteristics in Equation PR (1).,OUT = Atf the(PR,IN receiver) was consistent input, there with was the a equation known value below of: noise signal PR,IN coming from the target and the value of interference power PI. The lengths of the transmission lines connecting the noise generator to P2 k kσ 4 2 P P , the correlation receiver in the receptionR, and OUT reference T 1 T 3 paths T were R , IN negligible REF in relation to the length( of13) the lines L1 and L2. The power of the receiver self-noise included in the power of interference noise where kT1 and kT3 are coefficients of the transmittance of the noise generator signal power for the according to Equation (1) was calculated on the basis receiver noise ratio measurement. receiving channel and the reference channel, respectively, and σ2T is the variance of the noise 4.2.generator Measurement signal. Results Three characteristics PR,OUT were plotted for different values of power PI starting at points (A), (B),Figure and (C),6 shows marked three in pairs Figure of characteristics:6, and partially PoverlapR,OUT andpedP withN,OUT eachof the other. correlation These points receiver correspond output forto∆ Tthe= 0unit as a value function of the of input SNR signalat the powercorrelatorPR,IN output. These for characteristics PI1 = PLC+PN,R were, PI2 = plotted PI1+1nW for, and three P differentI3 = PI1 + 0.1 valuesμW. ofFigure interfering 6 also signalincludes power PN,OPUTI .measured The change under in the the value same of conditions, power PR,IN whichwas implemented partially overlap usingped anas adjustable well. This attenuator is similar T1. to The the plot signal of the characteristics. measured characteristics In this case,PR, OUT output= f ( P noiseR,IN) was power consistent PN,OUT is withdemonstrated the equation by below: a broken curve described by the following Equation (14): 2 4 2 PR,OUT = α kT1kT3σT = α PR,IN PREF, (13) k kσ4 k σ 2 k σ 2 σ 2  22TTTTTTTNR1 3 3 2 ,  PPPPR, IN REF REF I where kT1 and kT3 arePN, OUT coefficients of the transmittance of the noise generator signal. power for(14) BTBT2 the receiving channel and the reference channel,RF respectively, and σ T is theRF variance of the noise generator signal.

Figure 6. The plot of signal power transmittance for various interfering signals for BRF = 150 MHz, Figure 6. The plot of signal power transmittance for various interfering signals for BRF = 150 MHz, T = 1 ms, f0 = 9.2 GHz. SNROUT: output signal-to-noise ratio. T = 1 ms, f 0 = 9.2 GHz. SNROUT: output signal-to-noise ratio.

If signal power PR,IN is much less than the interfering signal power PI, then (14) takes the form below: Three characteristics PR,OUT were plotted for different values of power PI starting at points (A), (B), 2 and (C), marked in Figure6, and partially overlapped with each other. These points correspond to the PPP . (15) N, OUTBT REF I unit value of the SNR at the correlator output for PI1 = PRFLC+PN,R, PI2 = PI1+1nW, and PI3 = PI1 + 0.1 µW. Figure6 also includes PN,OUT measured under the same conditions, which partially overlapped as well. As it follows from Equation (15), PN,OUT does not depend on the power of the input signal coming This is similar to the signal characteristics. In this case, output noise power P is demonstrated by from the target. In Figure 6, this situation is represented by a flat part in Nthe,OUT characteristics with the a broken curve described by the following Equation (14): level depending only on the value of the interfering signal power PI. PR,IN ≫ PI (15) is simplified to   the form below: 4 2 2 2 kT1kT3σ + kT3σ kT2σ + σ 2 T T T N,R 2 PR,IN PREF + PREF PI PN,OUT = α 2 = α . (14) BRFT  BRFT PPPN,, OUT R IN REF . (16) BTRF The output noise power is proportional to the input signal power and is inversely proportional to the BRFT. For PR,IN = const, the difference in the signal power levels and noise power levels at the correlator output, expressed in dB, is equal to value 10log(BRFT).

Sensors 2018, 18, 1445 9 of 11

If signal power PR,IN is much less than the interfering signal power PI, then (14) takes the form below:

2 ∼ α PN,OUT = PREF PI. (15) BRFT

As it follows from Equation (15), PN,OUT does not depend on the power of the input signal coming from the target. In Figure6, this situation is represented by a flat part in the characteristics with the level depending only on the value of the interfering signal power PI. PR,IN  PI (15) is simplified to the form below: 2 ∼ α PN,OUT = PR,IN PREF. (16) BRFT TheSensors output 2018, noise18, x FOR power PEER isREVIEW proportional to the input signal power and is inversely proportional9 of to 11 the B T. For P = const, the difference in the signal power levels and noise power levels at the RFThe applicationR,IN of the proposed measurement system presented in Figure 5 enabled the correlator output, expressed in dB, is equal to value 10log(B T). separation of the useful signal from the interference signalsRF , even though all of the signals were in The application of the proposed measurement system presented in Figure5 enabled the separation the form of white noise and occurred together. Based on the results presented in Figure 6, it is possible of the useful signal from the interference signals, even though all of the signals were in the form of to determine the value of internal leakage signal power for a given noise radar structure. This signal, white noise and occurred together. Based on the results presented in Figure6, it is possible to determine along with the antenna leakage signal and signals reflected from other objects (e.g., ground), the value of internal leakage signal power for a given noise radar structure. This signal, along with the influences the level of noise on the correlative detector output. While measuring the total power of antenna leakage signal and signals reflected from other objects (e.g., ground), influences the level of noise on the correlator output, it is not possible to determine the measurement corresponding to the noise on the correlative detector output. While measuring the total power of noise on the correlator power of the input signal, which is similar in the case of output SNR. On the correlator output, the output, it is not possible to determine the measurement corresponding to the power of the input signal, signal-to-noise ratio may adopt the same value for different levels of input signal power (e.g., points which is similar in the case of output SNR. On the correlator output, the signal-to-noise ratio may A and B in Figure 6). adopt the same value for different levels of input signal power (e.g., points A and B in Figure6). Figure 7 shows the impact of the reference channel signal power PREF on PR,OUT and PN,OUT at the Figure7 shows the impact of the reference channel signal power P on P and P at correlation receiver output as a function of the input signal power. REF R,OUT N,OUT the correlation receiver output as a function of the input signal power.

Figure 7. The plot of the signals power transmittance for various reference signals for BRF = 150 MHz, Figure 7. The plot of the signals power transmittance for various reference signals for BRF = 150 MHz, T = 1 ms, f0 = 9.2 GHz. T = 1 ms, f 0 = 9.2 GHz. Correspondingly, all the characteristics presented the same shape as those in Figure 6. The value of Correspondingly, all the characteristics presented the same shape as those in Figure6. The value the reference channel power PREF decided only the increase in the output power of the signals. of the reference channel power P decided only the increase in the output power of the signals. However, SNROUT for specified PREFR,IN remained unchanged. However,OneSNR of theOUT basicfor specifiedcharacteristicsPR,IN remainedof a correlation unchanged. receiver that describes the SNR as a function of inputOne signal of the power basic is characteristics shown in Figure of a 8. correlation receiver that describes the SNR as a function of input signal power is shown in Figure8.

Figure 8. The plot of the SNR at the correlator output for PREF = −18 dBm, BRF = 150 MHz, T = 1 ms, f0 = 9.2 GHz.

Sensors 2018, 18, x FOR PEER REVIEW 9 of 11

The application of the proposed measurement system presented in Figure 5 enabled the separation of the useful signal from the interference signals, even though all of the signals were in the form of white noise and occurred together. Based on the results presented in Figure 6, it is possible to determine the value of internal leakage signal power for a given noise radar structure. This signal, along with the antenna leakage signal and signals reflected from other objects (e.g., ground), influences the level of noise on the correlative detector output. While measuring the total power of noise on the correlator output, it is not possible to determine the measurement corresponding to the power of the input signal, which is similar in the case of output SNR. On the correlator output, the signal-to-noise ratio may adopt the same value for different levels of input signal power (e.g., points A and B in Figure 6). Figure 7 shows the impact of the reference channel signal power PREF on PR,OUT and PN,OUT at the correlation receiver output as a function of the input signal power.

Figure 7. The plot of the signals power transmittance for various reference signals for BRF = 150 MHz, T = 1 ms, f0 = 9.2 GHz.

Correspondingly, all the characteristics presented the same shape as those in Figure 6. The value of the reference channel power PREF decided only the increase in the output power of the signals. However, SNROUT for specified PR,IN remained unchanged. One of the basic characteristics of a correlation receiver that describes the SNR as a function of inputSensors signal2018, 18 ,power 1445 is shown in Figure 8. 10 of 11

Figure 8. The plot of the SNR at the correlator output for PREF = −18 dBm, BRF = 150 MHz, T = 1 ms, Figure 8. The plot of the SNR at the correlator output for PREF = −18 dBm, BRF = 150 MHz, T = 1 ms, f0 = 9.2 GHz. f 0 = 9.2 GHz.

The characteristic was plotted for the interference power equal to PI, which corresponds to the sum of internal leakage power PLC and receiver self-noise power PN,R. According to Equation (12), SNROUT ratio as a function of SNRIN is expressed in Equation (17) below:

B T = RF SNROUT −1 . (17) 1 + SNRIN

It can be observed that Equation (17) takes the following form for SNRIN << 1: ∼ SNROUT = BRFT · SNRIN. (18)

SNROUT is directly proportional to the value of the SNR at the input with a factor of proportionality equal to BRFT. On the other hand, for SNRIN  1, (17) takes the form below: ∼ SNROUT = BRFT. (19)

Then, the SNR at the output does not depend on the input signal power and tends to be equal to a constant value of BRFT. The above analytical conclusions are consistent with the measurement results shown in Figure8.

5. Conclusions The proposed measurement system allows us to determine the relation between output SNR and input signal power, and therefore to optimize the noise radar parameters depending on the desired application. This system allows for the separation of random signals with the same probabilistic characteristics into signals that can be termed signal and noise at the input and output of the correlation detector. The measurements of the signal power and the noise power at the correlation receiver output fully support the theoretical relations expressed by Equation (12). It is important to note that by using the experimental measurements shown in Figure6, it is possible to determine the values of the noise radar. This includes basic parameters such as transmitter power, operating band, integration time, maximum range, reference signal power, and permissible values of internal leakage and antenna leakage. Sensors 2018, 18, 1445 11 of 11

Recently, an intensive research study was conducted to reduce the noise floor level (i.e., to reduce the interfering signal power PI defined by Equation (1)). This reduction can be achieved through a hardware solution by minimizing powers PLC and PLA, as well as through signal processing.

Author Contributions: B.S. conceived of the experiments. W.S. designed the experiments. B.S. and W.S. performed the experiments. B.S. analyzed the data. W.S. wrote the paper. Funding: This research received no external funding Conflicts of Interest: The authors declare no conflict of interest.

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