Chirp Signals and Noisy Waveforms for Solid-State ... - MDPI

aerospace Article

Chirp Signals and Noisy Waveforms for Solid-State Surveillance Radars Gaspare Galati *, Gabriele Pavan † and Francesco De Palo † Department of Electronic Engineering, University of Rome “Tor Vergata”, via del Politecnico 1, 00133 Rome, Italy; [email protected] (G.P.); [email protected] (F.D.P.) * Correspondence: [email protected]; Tel.: +39-06-7259-7417 † These authors contributed equally to this work. Academic Editors: Yan (Rockee) Zhang and Mark E. Weber Received: 1 December 2016; Accepted: 8 March 2017; Published: 14 March 2017

Abstract: Since the advent of “pulse compression” radar, the “chirp” signal (Linear Frequency Modulation, LFM) has been one of the most widely used radar waveforms. It is well known that, by changing its modulation into a Non-Linear Frequency Modulation (NLFM), better performance in terms of Peak-to-Sidelobes Ratio (PSLR) can be achieved to mitigate the masking effect of nearby targets and to increase the useful dynamic range. Adding an appropriate amplitude modulation, as occurs in Hybrid-NLFM (HNLFM), the PSLR can reach very low values (e.g., PSLR < −60 dB), comparable to the two-way antenna sidelobes in azimuth. On the other hand, modern solid-state power amplifier technology, using low-power modules, requires them to be combined at the Radio Frequency (RF) stage in order to achieve the desired transmitted power. Noise Radar Technology (NRT) represents a valid alternative to deterministic waveforms. It makes use of pseudo-random waveforms—realizations of a noise process. The higher its time-bandwidth (or BT) product, the higher the (statistical) PSLR. With practical BT values, the achievable PSLR using pure random noise is generally not sufficient. Therefore, the generated pseudorandom waveforms can be “tailored” (TPW: Tailored Pseudorandom Waveforms) at will through suitable algorithms in order to achieve the desired sidelobe level, even only in a limited range interval, as shown in this work. Moreover, the needed high BT, i.e., the higher time duration T having fixed the bandwidth B, matches well with the low power solid-state amplifiers of Noise Radar. Focusing the interest on (civil) surveillance radar applications, such as ATC (Air Traffic Control) and marine radar, this paper proposes a general review of the two classes of waveforms, i.e., HNLFM and TPW. Keywords: radar waveforms; chirp; pulse compression; non-linear FM; low PSLR; solid-state amplifiers; Noise Radar Technology

1. Introduction For any new radar, the waveforms design is a key element, in which conflicting requirements have to be satisfied, i.e., (to mention the main ones), range resolution and accuracy (defined as the degree of conformance between the estimated or measured position and the true position), dynamic range, Multiple-Input Multiple-Output (MIMO) or polarimetric channels orthogonality, Low Probability of Intercept (LPI) [1–3], low interference to other apparatuses [4], and best exploitation of the transmitter power with a low (or unitary) crest factor. To mitigate the masking effect of nearby targets [5], the sidelobe level of the autocorrelation function of the transmitted pulse has to reach very low values comparable to the two-way antenna sidelobes in azimuth (typical of marine radars). Waveform design is of paramount interest in weather radar community, as solid-state and phased-array technology is being increasingly used also there. However, in that community the Integrated Sidelobe Level (ISL) is of interest. In this paper, mostly related to man-made targets (planes, ships) the peak sidelobe Aerospace 2017, 4, 15; doi:10.3390/aerospace4010015

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level is considered. This approach leads to specify the Peak-to-Sidelobes Ratio (PSLR) typically better than −60 dB [6,7]. One way to meet this requirement is the use of sidelobe-suppression filters in reception. However, these sidelobe-suppression filters [8,9] add Signal-to-Noise-Ratio (SNR) losses and an increase of the Doppler mismatch effect. Alternatively, the optimal design of “chirp” radar waveforms [10–12], may be considered. Since the advent of “pulse compression” radar, the “chirp” signal (Linear Frequency Modulation, LFM) has been one of the most widely used radar waveforms. It is well known that, by changing its modulation into a Non-Linear Frequency Modulation (NLFM) [13–15], better performance in terms of PSLR can be achieved. Historically, the design of chirp radar in the Western was made public in the 1960s [16] and, in the Eastern world, in the works (1950s) by Yakov Shirman [17], who received the IEEE Pioneer Award in 2009 “For the independent discovery of matched filtering, adaptive filtering, and high-resolution pulse compression for an entire generation of Russian and Ukrainian radars” [18,19]. The “chirp” theory is well established and is related to the Stationary Phase principle [10,12,20]: for a large enough number of independent samples, or product (also called Compression Ratio, or BT) between time duration T and bandwidth B, the group delay of a LFM signal is proportional to the instantaneous frequency. Moreover, the spectrum of the LFM signal after the matched filtering is quasi-rectangular, with constant amplitude and linear phase in the bandwidth B (and ideally, zero amplitude outside it). Its autocorrelation has a time duration 1/B and an unacceptable PSLR about 13.2 dB below the main peak. The sidelobes can be lowered by using an NLFM law, which can be easily designed by means of the well-known spectral windows [13,20]. However, this method, which relies on the Stationary Phase method, works well when BT is “large” (in practice for BT greater than a few thousands) but becomes less and less effective when BT decreases, as occurs in various civil applications like ATC (Air Traffic Control) radar and marine (or navigation) radar. A new design method to cope with the sidelobe problem has been presented in [21,22], leading to a kind of Hybrid NLFM (HNLFM) whose amplitude, however, is not constant during the duration T of the signal. Such a requirement creates implementation problems with the widely-used saturated (C-class) power amplifiers. This family of waveforms is enhanced and analyzed in the following. The power solid-state technology is increasingly used for radar transmitters using microwave transistor amplifiers leading, in most cases, to production/generation power issues. In fact, to achieve the typical medium-range for air or sea surveillance of civil targets, i.e., about 90 to 110 km (50 to 60 NM, Nautical Mile), a peak power of a few tens of kW has to be transmitted with a duty cycle around 10%. This power requirement is met by combining about 16 solid-state power modules at the Radio Frequency stage, typically emitting 50 to 100 W each. The pertaining implementation is not easy [23], since it should introduce low losses to minimize the attenuation of the coming through signal. It should also present good isolation between input/output ports so that each module is not influenced by the other, and finally, it should provide a well-matched circuitry to maximize the power transfer without occurring in load pulling. Apparatus size and weight can also increase if a large number of solid-state modules are needed. The high power requirement becomes more problematic if the before mentioned HNLFM signal is used because of its very precise amplitude modulation. Another method, technically unrelated to the HNLFM, is the Noise Radar Technology (NRT). It represents a valid candidate to overcome the high-power stage issue. It makes use of pseudo-random waveforms, realizations of a Gaussian noise process [24]. The higher their time-bandwidth (or BT) product, the higher their (statistical) PSLR. In fact, since the PSLR is related to how much the waveform is equal to itself, the number of independent samples (with their phases) represents the degree of freedom available to make the correlation sidelobes as low as possible. Using pure random noise, practical BT values are generally not large enough to achieve PSLR. Therefore, the generated pseudorandom waveforms should be “tailored” (TPW: Tailored Pseudorandom Waveforms) at will through suitable algorithms [25] in order to achieve the desired sidelobe level. The suppression can also be applied over a limited range interval, as will be shown throughout this paper. Since the PSLR

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increases with the signal time duration T (assuming a fixed bandwidth B), we consider a 100% duty cycle operation for NRT with separated transmitting and receiving antennas. Then the architecture considered is a bistatic radar with co-located antennas, with low electromagnetic coupling between them. This architecture allows us to lengthen up the signal to the Waveform Repetition Time (WRT) which is the equivalent of the Pulse Repetition Time (PRT) for pulsed radar. This framework provides some advantages of the TPW approach over the pulsed HNLFM, including:

•

• •

the longer time duration allows to lower the transmitted peak power (with respect to an equivalent pulse compression radar) by about a figure of approximately 30 times, keeping unchanged the overall system requirements (e.g., maximum range, range resolution, bandwidth allocation) for the same application; the lower transmitted power calls for less solid-state modules to be combined, easing the radar transmitter architecture; a large number of quasi-orthogonal waveforms can be transmitted, alleviating mutual interference problems and paving the way for an MIMO operation [26,27].

The drawbacks of TPW include the dual antenna configuration (typical of Continuous Wave (CW) radars) as well as the burden of the real-time computation of the cross-ambiguity function. However, the matched filter approach can be successfully used. Design criteria and ensuing comparison of deterministic and pseudo-random waveforms are shown hereafter. This paper focuses the attention on two waveform classes: HNLFM and TPW, suitable to be used in (civil) surveillance radar applications, such as ATC and marine radar. Most of this paper is a review of (many) works, some unpublished, by the authors. The paper is organized as follows: Section 2 describes the deterministic waveforms design and compares classical pulse compression waveforms with the novel ones; Section 3 shows a different approach to pulse compression based on random waveforms (noisy signals) making use of CW operation; finally, Section 4 reports conclusions and future perspectives. 2. Deterministic Waveforms Design The complex envelope of a generic signal, modulated both in Amplitude and in Phase (AM-PM), is: s(t) = a(t)e jφ(t) ,

(1)

where a(t) and φ(t) denote respectively the AM and PM modulation. The stationary phase principle [10,16] establishes that, at the instantaneous frequency ωt the amplitude spectrum |S(ωt )|2 of a given signal s(t), having the amplitude a(t), can be approximated as [10]: a2 ( t ) , |S(ωt )|2 ∼ = 2π 00 |φ (t)|

(2)

i.e., the energy spectral density at the frequency ωt = φ0 (t) (in radians) is larger when the rate of change of ωt is smaller. From Equation (2) the amplitude modulation function a(t) can be evaluated as: a(t) ∼ =

r


2 1 S φ0 (t) |φ00 (t)| . 2π

(3)

However, the validity of the stationary phase approximation depends on the compression ratio BT, and it should be considered reliable only for large BT (in practice, greater than a few thousands). It is less and less effective when a low BT is required, as it happens in various radar applications. Considering the Millett waveform, i.e., a “cosine squared on a pedestal” weighting [13], the output of the Matched Filter (MF) reaches the theoretical PSLR of −42 dB only when BT is greater than about one thousand. For any lower compression ratio, a convenient frequency modulation function (in radians)

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can be obtained the Aerospace 2017, 44 of 14 Aerospace 2017, 4, 4, 15 15 as a weighted sum of the Non-Linear tangent FM term and the LFM one, hence of 14 name Hybrid-NLFM [21,22]:  2γ  2 2γt + (1 − )2t 11 ,, (4) tg + (1 − α ) (4) tg(γ(γ) T T ) where ∈ (0, 1) is the relative weight between the linear and the tangential terms, B is the swept where α ∈ (0, 1) is the relative weight between the linear and the tangential terms, B is the swept frequency (nearly equal to the signal’s bandwidth), γ is the Non-Linear tangent FM rate and, being frequency (nearly equal to the signal’s bandwidth), γ is the Non-Linear tangent FM rate and, being ∈ h− T, + T ,iT denotes the pulse-width. t ∈ − 2 , + 2 , T denotes the pulse-width. If ( ) is a signal with a Gaussian spectrum: | (ω )| = exp −βω2  with β = 1, using the If s(t) is a signal with a Gaussian spectrum: |S(ωt )|2 = exp −β B2t with β = 1, using the optimized values of α and γ as evaluated in [21,22] (i.e., those values that reach the optimum PSLR optimized values of α and γ as evaluated in [21,22]⁄⁄ (i.e., those values that reach the optimum PSLR R +T/2( ) ), the energy loss results as low as 0.58 maximizing the transmission efficiency: = maximizing the transmission efficiency: η = T1 ⁄⁄ −T/2 a2 (t)dt), the energy loss results as low as dB with to the to case unityofamplitude. InsertingInserting EquationEquation (4) into Equation the amplitude 0.58 dB respect with respect theofcase unity amplitude. (4) into (3), Equation (3), the modulationmodulation has been evaluated shown inas Figure 1. in Zooming around ( )around = 1, i.e.,a(in amplitude has beenasevaluated shown Figure 1. Zooming t) the = 1,interval i.e., in − 3 are observed. In Figure 2, the (−0.3, 0.3), some ripples of the relative amplitude order of 10 the interval (−0.3, 0.3), some ripples of the relative amplitude order of 10 are observed. In Figure 2, corresponding instantaneous frequency modulation is shown. the corresponding instantaneous frequency modulation is shown.  0 ( )=π ϕ φ (t) = πB α

Amplitude Amplitude Modulation Modulation

1.2 1.2 11 11 0.8 0.8 a(t) a(t)

0.999 0.999 0.6 0.6 0.998 0.998 0.4 0.4

-0.3 -0.3

-0.2 -0.2

-0.1 -0.1

00

0.1 0.1

0.2 0.2

0.3 0.3

-0.3 -0.3

-0.2 -0.2

-0.1 -0.1

00 t/T t/T

0.1 0.1

0.2 0.2

0.3 0.3

0.2 0.2 00 -0.5 -0.5

-0.4 -0.4

0.4 0.4

0.5 0.5

f/B

Figure Normalized amplitude amplitude weighting weighting for for Hybrid Hybrid Non-Linear Non-Linear Frequency Frequency Modulation Modulation (HNLFM) (HNLFM) Figure 1. 1. Normalized (red (red line: line: optimum optimum weighting, weighting, blue blue line: line: sub-optimum sub-optimum weighting). weighting).

Figure 2. Instantaneous normalized frequency for HNLFM. Figure 2. Instantaneous normalized frequency for HNLFM.

Figure 3 shows the PSLR of the matched filter output for the optimized waveform (solid linecircles). With BT decreasing, the approximation due to the principle of the stationary phase becomes worse and worse causing an increase in the PSLR. However, with BT = 64 the PSLR (−51 dB) is still

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PSLR (dB)

Figure 3 shows the PSLR of the matched filter output for the optimized waveform Aerospace 2017, 4, 15 5 of 14 (solid line-circles). With BT decreasing, the approximation due to the principle of the stationary phase becomes worse and worse causing an increase in the PSLR. However, with BT = 64 the PSLR withcompatible many applications, and for BT = 128 thefor PSLR −75the dB,PSLR which is75 suited to most (compatible −51 dB) is still with many applications, and BT =is128 is − dB, which is applications. suited to most applications. These excellent excellenttheoretical theoretical results (circles in Figure 3) are only possible if the amplitude These results (circles in Figure 3) are only possible if the amplitude weighting weighting is the one shown in Figure 1 (red line) with the instantaneous frequency is the one shown in Figure 1 (red line) with the instantaneous frequency of Figure 2.of Figure 2.

Figure 3. 3.Effect Effect of the compression the Peak-to-Sidelobes RatioHNLFM (PSLR),(optimum HNLFM of the compression ratio ratio BT onBT the on Peak-to-Sidelobes Ratio (PSLR), (optimum and sub-optimum) Millet the lastonly is shown only as a reference. historical reference. and sub-optimum) and Milletand signals, thesignals, last is shown as a historical

In practice, practice, it In it may may be be hard hardto toimplement implementthe therequirement requirementon on a((t),),with withripples ripplesofofthe theorder orderofof1 over 1000. In general, if a PSLR level of −60 dB is required, a simple rule of thumb tells us that the the 1 over 1000. In general, if a PSLR level of −60 dB is required, a simple rule of thumb tells us that fidelity of the waveform, in terms of (I, Q) or (Amplitude, Phase) shall be better than 1:1000, or 10 fidelity of the waveform, in terms of (I, Q) or (Amplitude, Phase) shall be better than 1:1000, or 10 bits, bits,matter no matter the waveform is designed. widelyknown—from known—frommany manypractical practical experiences experiences no howhow the waveform is designed. It It is is widely (unfortunately, not available in the open literature)—that hardware imperfections increase the PSLR PSLR (unfortunately, not available in the open literature)—that hardware imperfections increase the with respect respect to to the the “ideal” “ideal” compressed compressed waveform. waveform. This This means means that that if if the the required required PSLR PSLR is is for for example example with −60 dB, the intrinsic level of the waveform (which is our focus) has to be −67 dB, the difference −60 dB, the intrinsic level of the waveform (which is our focus) has to be −67 dB, the difference between these these figures figures depending, depending, of of course, course, on on the thestability/linearity stability/linearity of the hardware. hardware. In recent between of the In aa recent private communication communication [28] [28] it it is is explained explained that: that: “In “In one civil marine marine radar radar private one case, case, related related to to aa NAVICO NAVICO civil using GaN for the solid state amplifier, and a non-linear FM, amplitude-weighted pulse with = using GaN for the solid state amplifier, and a non-linear FM, amplitude-weighted pulse with BT =BT 150, 150, the measured PSLR is −55 dB, versus the “ideal” −60 dB of the waveform”. So, the effect of the measured PSLR is −55 dB, versus the “ideal” −60 dB of the waveform”. So, the effect of hardware hardware is significant but notand dramatic, can be with controlled with a careful design. is significant but not dramatic, can beand controlled a careful design. If the amplitude of the transmitted signal is kept constant (the power amplifier amplifier working working in in If the amplitude of the transmitted signal is kept constant (the power saturation) with 2, 2, thethe theoretical PSLR increases by about 25– saturation) with the theinstantaneous instantaneousfrequency frequencyofofFigure Figure theoretical PSLR increases by about 30 dB. An improvement can be obtained using a sub-optimum waveform where the ripples shown 25–30 dB. An improvement can be obtained using a sub-optimum waveform where the ripples shown in the imposing 1 in this interval (dashed lineline in Figure 1). The in the zoom zoomof ofFigure Figure1 1are areremoved removed imposing(a()t= 1 in this interval (dashed in Figure 1). ) = PSLR of this “sub-optimum” waveform results only 10–20 dB worse than the optimized signal when The PSLR of this “sub-optimum” waveform results only 10–20 dB worse than the optimized signal ≥ 128 in Figure 3). Figure 4 shows the half-power pulse width (τ (τ) versus the when BT ≥(diamonds-line 128 (diamonds-line in Figure 3). Figure 4 shows the half-power pulse width ) versus 3dB

compression ratio BT. BT. TheThe values are are compared with the the ones of the LFM, i.e.,i.e., τ τ3dB = =. B1 . the compression ratio values compared with ones of the LFM, For BT = = 128 128 (frequency (frequency swept swept of of B ==1 MHz 1 MHz and duration T = 128 µs), Figure 5a shows and duration = 128 μs), Figure 5a shows the the compressed pulse, while Figure 5b reports its spectrum. The PSLR 75 the dB compressed pulse, while Figure 5b reports its spectrum. The PSLR reachesreaches about about −75 dB−for for the optimum waveform andfor−the 66 dB for the sub-optimum one, still for compatible for most optimum waveform case andcase −66 dB sub-optimum one, still compatible most applications, applications, e.g.,the lower thantwo-way the typical two-way antennainsidelobes azimuth. The range resolution, e.g., lower than typical antenna sidelobes azimuth.inThe range resolution, i.e., ∆ = i.e., ∆R(= 2B c representing (B−3dB representing thebandwidth), −3 dB bandwidth), about m.worth It is worth clarifying the −3 dB is aboutis 550 m.550 It is clarifying that that the −3dB the bandwidth of a waveform is very important when spectral limitations apply, which is the case bandwidth of a waveform is very important when spectral limitations apply, which is the case of of most civil radar. Of course, bandwidth values only give a rough indication of the range resolution, whose correct numerical value is of course the −3 dB width of the output of the reception filter, either matched or possibly mismatched for some reason.

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most civil radar. Of course, bandwidth values only give a rough indication of the range resolution, whose correct numerical value is of course the −3 dB width of the output of the reception filter, either Aerospace 2017, 2017, 4, 4, 15 15 of 14 14 Aerospace 66 of matched or possibly mismatched for some reason. To improve the the resolution, maintaining pulseduration, duration, swept frequency has To improve improve the resolution, maintainingthe the same same pulse pulse duration, thethe swept frequency has to to beto be To resolution, maintaining the same the swept frequency has be increased, with the only practical limitation being the restricted use of the spectrum. increased, with the only practical limitation being the restricted use of the spectrum. increased, with the only practical limitation being restricted use of the spectrum. T= = 100 100 microsec microsec -- Compressed Compressed pulse pulse width width T

88 77

Sub-optimum HNLFM HNLFM Sub-optimum LFM (( = 1/B) LFM 3dB = 1/B) 3dB

66 55 44 33 22 11 00 32 32

64 64

96 96

128 128

BT BT

160 160

192 192

224 224

256 256

Figure 4. Effect of of thethe compression BT on onthe thecompressed compressed pulse width Figure 4. Effect Effect of the compressionratio ratio BT on the compressed pulse width (τ (τ).).3dB ). Figure 4. compression ratio pulse width (τ

(a) (a)

(b) (b) Figure 5. 5. HNLFM HNLFM compressed compressed pulse: pulse: Figure

= 128 128 ,, =

= 128 μs 128 μs ,, =

= 1 MHz 1 MHz .. (a) (a) Normalized Normalized =

Figure 5. HNLFM(b) compressed pulse: BT = 128, T = 128 µs, B = 1 MHz. (a) Normalized autocorrelation; Power spectrum spectrum density. autocorrelation; (b) Power density. autocorrelation; (b) Power spectrum density.

3. Noise Noise Radar Radar Technology Technology 3.

3. Noise Radar Technology The HNLFM HNLFM capability capability to to get get very very low low sidelobes sidelobes of of the the compressed compressed pulse pulse is is strictly strictly dependent dependent The on the the ability of ofcapability the signal signal to generation and amplification chain, including the thepulse RF power power amplifier, to The HNLFM get veryand lowamplification sidelobes ofchain, the compressed is strictly dependent on ability the generation including RF amplifier, to faithfully reproduce thegeneration amplitude modulation modulation of Figure Figure 1, calling calling for highly highly linear A-class faithfully reproduce the amplitude of 1, for A-class on the ability of the signal and amplification chain, including the RFlinear power amplifier, to faithfully reproduce the amplitude modulation of Figure 1, calling for highly linear A-class amplifiers.

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Moreover, the available bandwidth is not fully exploited because of the particular frequency law of Equation (4), which is the main law responsible for the low sidelobe level. Noise Radar Technology (NRT) [29–35] may be a valid alternative to overcome the high-power amplitude modulation issue. NRT makes use of pseudo-random waveforms that are realizations of a Gaussian band-limited random process [24]. These “pure noise” realizations, once generated and stored, are not strictly random anymore as they act as deterministic signals with known PSLR, range resolution and ambiguity function. The number of different possible realizations to be used is theoretically unlimited (modern pseudorandom numbers generator can reach a period of 21492 [36], as implemented in Matlab generator—practically infinity), so that each radar can operate with its own radar signal, possibly different from the others. Being noisy, the waveforms themselves possess a low enough degree of mutual cross-correlation to pave the way for distributed MIMO operation with a low level of mutual interferences [27] even operating at the same, or nearby, carrier frequency. For a pure noise waveform, the PLSR value does not strongly depend on the amplitude modulation [24] but, rather, on the Time Bandwidth product BT. The bandwidth being limited by the application context (e.g., about 50 MHz, and 200 MHz as a maximum, for marine radar), BT may be increased at will by selecting a continuous wave (CW) architecture instead of the pulsed one, keeping unchanged the compression processing (computation of the correlation or the ambiguity function) at the receiver side. The power can be significantly lowered with respect to an equal-performance pulse radar architecture. 3.1. Power Budget Let us consider a typical maximum range of 150 km (80 NM) with a range resolution of 150 m. A comparison between pulsed HNLFM and CW noise radar can be done while keeping the transmitted energy constant. For this purpose, let us consider the saturated HNLFM since the power loss with respect to the optimal amplitude modulation is only 0.58 dB. In a CW architecture, the maximum delay due to range is generally set as one-fourth of the Waveform Repetition Time (WRT), which corresponds to the signal time duration if we neglect the data processing time between consecutive sweeps: WRT 2 · Rmax = . 4 c

(5) 2·150000 (m)

For a maximum range of 150 km, it is required that: WRT = 3·108 (m/s) = 1 ms, 4 i.e., WRT = 4000 µs, i.e., 4096 µs in order to work with power-of-two values. Knowing the time duration of the noise signal (WRTnoise ) together with the HNLFM pulse width (THNLFM ), the relationship between the needed peak powers can be evaluated as: Pnoise = PHNLFM ·

THNLFM , WRTnoise

(6)

where Pnoise and PHNLFM are respectively the peak power of CW noise and pulsed radar. With WRTnoise = 4096 µs and THNLFM = 128 µs, it results: Pnoise = 0.03125 · PHNLFM . The equality holds also for the optimal amplitude modulated HNLFM if the 0.58 dB power loss is considered. Equation (6) states that the required power for a CW noise radar is about 15 dB lower than the peak power required for a pulsed radar, keeping unchanged the maximum range. Lowering the transmitted power means less solid-state modules and a straightforward RF power production/generation design. The generation of M independent pure noise band-limited signals is shown in Figure 6. The (I, Q) samples are generated through a white Gaussian random process. The signal to be filtered by the frequency window H ( f ) is { xi }iN=1 where N is the number of generated samples and xi the ith complex ( I, Q) sample.

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Figure 6. Pure noise generation block-diagram (ZMNL: Zero-Memory-Non-Linear transformation, Figure 6. noise generation block-diagram (ZMNL: Zero-Memory-Non-Linear transformation, 6. Pure noise generation block-diagram FFT: Fast Fourier Transform, iFFT: inverse-FFT).(ZMNL: Zero-Memory-Non-Linear FFT: Fast Fourier Transform, iFFT: inverse-FFT). Fourier Transform, iFFT: inverse-FFT).

|X(f)| [dB] |X(f)| [dB]

3.2. Unimodular Pure Noise 3.2. Unimodular Pure Noise Being a white process, the signal has to be band-limited with a proper frequency window ( ) Being a white frequency window window H f )) the signal has to[37] be or band-limited with aa proper frequency which can be any, process, e.g., Blackman–Nuttall simply rectangular. In this paper, we consider ((the which can be be any, any, e.g., e.g.,Blackman–Nuttall Blackman–Nuttall[37] [37]ororsimply simply rectangular. In this paper, we consider rectangular. In this paper, we the rectangular frequency window to fully exploit the available bandwidth; other windowsconsider can be used the rectangular frequency window to fully exploit the available bandwidth; other windows can rectangular frequency window to fully available bandwidth; otherwindowing, windows can besignal used to gain a slight improvement in PSLRexploit value. the After the frequency domain the be used to gain a slight improvement in PSLR value. After the frequency domain windowing, to gain a slight improvement in PSLR value. After the frequency domain windowing, the signal amplitude is saturated to the maximum (i.e., a unimodular signal is obtained) value through a Zerothe signal is amplitude istosaturated to the maximum asignal unimodular signal is obtained) amplitude saturated(ZMNL) the maximum (i.e., a unimodular obtained) value through a value Zero( , ) Memory-Non-Linear transformation, while (i.e., the phase isiskept unchanged. Since the ( , ) through a Zero-Memory-Non-Linear (ZMNL) transformation, while the phase is kept unchanged. Memory-Non-Linear (ZMNL) transformation, while the phase is kept unchanged. Since the samples come from a random process, at each run, the algorithm provides different realizations Since thethe Q)from samples come from a random process, at and each run, the algorithm provides different ( I,same samples come a random process, each run, the algorithm provides different realizations having average performances inatterms of PSLR cross-correlation level, while the range realizations having the same average performances in terms of PSLR and cross-correlation level, while having the same average performances in terms of PSLR and cross-correlation level, while the range resolution only depends on the used ( ). Figure 7 shows the spectrum of the unimodular bandthe rangepure resolution onlythe depends on the Hsignal shows theBT. spectrum of thebandwidth unimodular ( f ).7Figure resolution only depends onspectrum the used ). Figure shows of the unimodular bandlimited noise and of (aused LFM having7the thespectrum same The 1 MHz is band-limited pure noise and the spectrum of a LFM signal having the same BT. The 1 MHz bandwidth limited pure noise and the spectrum of a LFM signal having the same BT. The 1 MHz bandwidth is fully exploited. is fully exploited. fully exploited.

Figure MHz, T = µs. Figure 7. 7. Spectra Spectra of of Unimodular Unimodular Pure Pure Noise, Noise, and and LFM. LFM. With With B ==11 MHz, = 4096 4096 μs. Figure 7. Spectra of Unimodular Pure Noise, and LFM. With = 1 MHz, = 4096 μs.

Once compressed compressed by by the the matched matched filter, filter, the the pure pure noise noise and and the the LFM LFM give give aa range range resolution resolution of of Once compressed by the matched filter, the pure noiseμs, and LFM give a range resolution of Δ = 150 m (1 μs) thethe secondary lobes of pure pure noise are are ∆R =Once 150 m (1 µs) as shown in Figure 8. In the first 5–10 µs, the secondary lobes of noise Δslightly = 150 m (1 μs) as shown Figure 8. In to thethe first 5–10For μs,far the secondary lobes of pure noise are fluctuating (the PSLRin comparable LFM). lobes, the PSLR PSLR is empirically empirically related slightly fluctuating (the PSLR isiscomparable to the LFM). For far lobes, the is related slightly fluctuating (the PSLR is comparable to the LFM). For far lobes, the PSLR is empirically related to the the BT BT [24] [24] by by Equation Equation (7): (7): to to the BT [24] by Equation (7): ( ) + [dB] , (7) = −10 ⋅ PSLR = −10 ·⋅ log10 ((BT )) + dB] ,, (7) (7) = −10 + k [[dB] with of the order of 10–13 dB, which corresponds, for BT = 4096, to −23 dB (see Figure 8). The crosswith of the order ofof10–13 dB, which corresponds, for BT −23 dB Figure 8).level The crosswith k of the order 10–13 dB, which corresponds, for= 4096, BT = to4096, tois(see −of23the dBsame (see Figure 8). correlation level between two independently generated pure noise signals as the correlation level between two independently generated pure noise signals is of the same level as the The cross-correlation level between two independently generated pure noise signals is of the same autocorrelation sidelobes, excluding the central zone. The advantage of the pure noise signal with autocorrelation sidelobes, excluding the central zone. The advantage the pure noise with level as to thethe autocorrelation sidelobes, excluding the central zone. advantage ofrange thesignal pure noise respect HNLFM signal is two-fold: a narrower bandwidth to The getof the required resolution respect to the HNLFM signal is the two-fold: a narrower bandwidth to get the required range resolution and a cross-correlation level at same value as its autocorrelation sidelobes. and a cross-correlation level at the same value as its autocorrelation sidelobes.

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9 of 14 to the HNLFM signal is two-fold: a narrower bandwidth to get the required range resolution and a cross-correlation level at the same value as its autocorrelation sidelobes. The main reason suggesting the use of noisy signals, beyond the MIMO application, is their The main reason suggesting the use of noisy signals, beyond the MIMO application, is their capability to be tailored at will to reach better PSLR values, e.g., −60 dB as discussed above. capability to be tailored at will to reach better PSLR values, e.g., −60 dB as discussed above.

Normalized Output [dB]

Aerospace 2017,respect 4, 15 signal with

Figure8.8.Normalized Normalizedautocorrelations autocorrelationsof ofUnimodular Unimodular Pure Pure Noise Noise and and LFM: LFM: B = MHz, T = 4096 µs. Figure = 11 MHz, = 4096 μs.

3.3. Range Range Sidelobe Sidelobe Suppression Suppression Algorithms Algorithms 3.3. Many approaches approaches have have been been used used in in the the past past years years to to cope cope with with the the range range sidelobe sidelobe problem, problem, Many starting from from the the time time (or (or frequency) frequency) weighting weighting of of the the received received signal signal [10,11], [10,11], to to the the modern modern starting algorithms able ableto togenerate generatesignals signalswith withsuitable suitableautocorrelation autocorrelation characteristics without need algorithms characteristics without thethe need of of sidelobe suppression reception. The main differencebetween betweenthese thesetwo twoapproaches approachesisisthat, that, using using sidelobe suppression in in reception. The main difference the generation generation algorithms, algorithms, significant significant complexity complexity isis demanded demanded to to the the generation generation side side in in terms terms of of the computational burden a “useful” waveform. In any issue be trivially computational burdentotoachieve achieve a “useful” waveform. Incase, any this case, thiscan issue can beovercome trivially by offline generating a large enough setenough of noisyset waveforms ready to beready transmitted, and storedand in a overcome by offline generating a large of noisy waveforms to be transmitted, mass memory [31]. stored in a mass memory [31]. Generally, aa noise noise generation generation algorithm algorithm starts starts from from aa random random process process realization realization (e.g., (e.g., the the Generally, unimodular, band-limited Figure 6) and runsruns in order to minimize a certain function unimodular, band-limitedone, one,see see Figure 6) and in order to minimize a objective certain objective with defined In this case, thecase, objective functionfunction is the PSLR theand constraints are the function with constraints. defined constraints. In this the objective is theand PSLR the constraints are the limited bandwidth theamplitude unity amplitude fully exploit the solid-state amplifier. limited bandwidth and theand unity neededneeded to fullytoexploit the solid-state amplifier. Often, Often, to convergence considerations, the Integrated-Side-Lobe is minimized instead the due todue convergence considerations, the Integrated-Side-Lobe (ISL) is(ISL) minimized instead of theof PSLR PSLR because the former is an integrated over the sidelobe region the latter is only a because the former is an integrated valuevalue over all theallsidelobe region whilewhile the latter is only a local local thatrapidly can rapidly change by point. valuevalue that can change pointpoint by point. A A well-known well-known sidelobe sidelobe suppression suppression algorithm algorithm family family is is the the Cyclic Cyclic Algorithm Algorithm New New (CAN) (CAN) [25] [25] that suppression problem. ToTo suit thethe algorithm to that provides providesseveral severalinteresting interestingways waystotoapproach approachthe the suppression problem. suit algorithm particular needs, thethe authors of of this paper to particular needs, authors this paperhave havedeveloped developeda anew newalgorithm algorithmto to generate generate noisy noisy waveforms having aa limited limitedbandwidth bandwidthand andananunimodular unimodular amplitude, with possibility to tune waveforms having amplitude, with thethe possibility to tune the the suppressed zone length depending on the particular application. In the following, some results suppressed zone length depending on the particular application. In the following, some results are are shown discussed, highlighting advantages drawbacks. shown andand discussed, highlighting advantages andand drawbacks. In In some some applications, applications, the the matched matched filter filter output output is is performed performed by by aa periodic periodic correlation correlation between between the the radar radar return return and and the the reference, reference, which which can can significantly significantly differ differ from from the the aperiodic aperiodic case. case. The The periodic periodic approach case of of FFT implementation, with it being a spectrum product, i.e., approachcan canbe beconsidered consideredininthe the case FFT implementation, with it being a spectrum product, ai.e., circular correlation. In this onlyonly the aperiodic correlation is discussed. a circular correlation. In paper, this paper, the aperiodic correlation is discussed. CAN algorithms [25] [25]have havebeen beendeveloped developed both aperiodic periodic cases; in general, CAN algorithms both forfor aperiodic andand periodic cases; in general, there there nobasic largedifferences basic differences them. idea is tothe minimize thebetween difference are noare large betweenbetween them. The mainThe ideamain is to minimize difference the between and autocorrelation the desired autocorrelation functions through a process that runsuntil cyclically obtainedthe andobtained the desired functions through a process that runs cyclically a stop until a stop criterion is satisfied, e.g., the difference between two consecutive steps is less than a given threshold. The constraints to be satisfied within this minimization lead to different algorithms

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criterion is satisfied, e.g., the difference between two consecutive steps is less than a given threshold. The constraints to be satisfied within this minimization lead to different algorithms belonging to the CAN family. These constraints can be the unit amplitude, the number of suppressed sidelobes as well as the mainlobe width (i.e., the needed bandwidth) or others. Aerospacein 2017, 4, 15 of 14 Especially MIMO radar configuration, a number of M orthogonal waveforms 10 are required to th discriminate, after the matched filter, the m signal among the others. For this purpose, the CAN belonging to the CAN family. These constraints can be the unit amplitude, the number of suppressed family also provides a “MIMO” version algorithms in which the quantity to be minimized sidelobes as well as the mainlobe widthfor (i.e.,the the needed bandwidth) or others. Especially in MIMO radar configuration, number of M orthogonal waveforms required to criterion is the difference between the obtained and theadesired covariance matrix [25],are until a stop is reached.discriminate, after the matched filter, the mth signal among the others. For this purpose, the CAN family also provides a “MIMO” version for the algorithms in which the quantity to be minimized is The main drawback of the CAN algorithms is their inability to manage the bandwidth increase, the difference between the obtained and the desired covariance matrix [25], until a stop criterion is i.e., the mainlobe reached. of the signal generated by using the CAN algorithm is very narrow. In fact, these The main drawback of the CAN algorithms is to manage the bandwidth increase, occupied algorithms prefer a deep sidelobe suppression attheir theinability expense of having a full-Nyquist i.e.,which the mainlobe of the signal generated by using the CAN algorithm is very narrow. Inregulations fact, these must be bandwidth, unfortunately is not suitable for applications in which spectrum algorithms prefer a deep sidelobe suppression at the expense of having a full-Nyquist occupied met. Only one CAN algorithm (Stopband CAN (SCAN) [25]) is able to manage the spectrum constraint. bandwidth, which unfortunately is not suitable for applications in which spectrum regulations must In this study, theOnly SCAN applied to generate noise[25]) unimodular signalsthe with BT = 4096 and be met. one has CANbeen algorithm (Stopband CAN (SCAN) is able to manage spectrum constraint. In this study, the SCAN has been appliedistoshown generate in noise unimodular signals with BTunchanged, = B = 1 MHz. The related aperiodic autocorrelation Figure 9a. Keeping BT and B = improves 1 MHz. Thethe related aperiodic autocorrelation is respect shown into Figure 9a. Keeping BTnoise from the SCAN4096 algorithm PSLR by about 20 dB with the unimodular unchanged, the SCAN algorithm improves the PSLR by about 20 dB with respect to the unimodular which the algorithm starts. The mainlobe is kept wide since the SCAN spectrum, shown in Figure 10, noise from which the algorithm starts. The mainlobe is kept wide since the SCAN spectrum, shown is well-shaped within the required 1 MHz bandwidth. in Figure 10, is well-shaped within the required 1 MHz bandwidth.

Figure 9. Compressed pulse comparison between Unimodular Noise: (a) Stopband Cyclic Algorithm Figure 9. Compressed pulse comparison between Unimodular Noise: (a) Stopband Cyclic Algorithm New (SCAN); (b) Band Limited Algorithm for Sidelobes Attenuation (BLASA) Single Input, Single New (SCAN); (b) Band Limited Algorithm for Sidelobes Attenuation (BLASA) Single Input, Single Output (SISO): B = 1 MHz, T = 4096 μs. Output (SISO): B = 1 MHz, T = 4096 µs.

The drawback of the SCAN algorithm is that the sidelobes close to the mainlobe are still quite high. To overcome the issue, the authors have developed the BLASA (Band Limited Algorithm for The drawback of the SCAN algorithm thatisthe sidelobes close the mainlobe are CAN still quite high. Sidelobes Attenuation) algorithm whoseisresult shown in Figure 9b. Ittocomes from the same To overcome the authors have developed theclose BLASA (Band Limited Algorithm for Sidelobes ideathe andissue, provides very low sidelobes even in the area to the mainlobe. It is called “SISO” (Single Input, Single Output) because a single waveform generated at each run. The BLASA spectrum Attenuation) algorithm whose result is shown inisFigure 9b. It comes from theSISO same CAN idea and is shown in Figure 10 and it is still well shaped within the allowed 1 MHz bandwidth, providing a provides very low sidelobes even in the area close to the mainlobe. It is called “SISO” (Single Input, range resolution of 150 m.

Single Output) because a single waveform is generated at each run. The BLASA SISO spectrum is shown in Figure 10 and it is still well shaped within the allowed 1 MHz bandwidth, providing a range resolution of 150 m.

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Being a “SISO” algorithm, BLASA does not lower the cross-correlation level between two independently generated waveforms. Hence, their cross-correlation is at the same level as the initial unimodular pure2017, noise. Aerospace 4, 15 11 of 14 2017, 4, 15 of 14 As in Aerospace the CAN family, even for the BLASA SISO, a “MIMO” version exists which is11able to jointly Being a “SISO” algorithm, BLASA does not lower the cross-correlation level between two generate a independently number M of waveforms at each run, i.e., M signals belonging to the same set. The Being a “SISO” algorithm, BLASA doestheir not cross-correlation lower the cross-correlation level two BLASA generated waveforms. Hence, is at the same levelbetween as the initial generated waveforms. Hence, their cross-correlation is at and the same level as the initialfunctions, MIMO hasindependently been developed to manage the suppression of both auto cross-correlation unimodular pure noise. unimodular pure noise. Asbandwidth in the CAN family, even for the BLASA SISO, a “MIMO” version exists which is able to jointly still keeping the limited. As inathe CAN M family, even for the BLASA SISO, a “MIMO” version exists able toBLASA jointly generate number of waveforms at each run, i.e., M signals belonging to thewhich same is set. The Due to the limited number of samples that BLASA MIMO can manipulate, the joint suppression generate a number M of waveforms at each run, i.e., M signals the same set. The BLASA MIMO has been developed to manage the suppression of bothbelonging auto and to cross-correlation functions, region in cross and auto correlations cannot be as long as the whole length of the pulse. The MIMO has been developed to manage the suppression of both auto and cross-correlation functions, length of still keeping the bandwidth limited. still keeping the bandwidth limited. the suppressed zone depends on the M of the waveforms in the generated set: the lower M, Due to the limited number ofnumber samples that BLASA MIMO can manipulate, the joint suppression Due to the limited number of samples that BLASA MIMO can manipulate, the joint suppression in cross and auto correlations cannotthe be as long as the whole of depends the pulse. The the longer region the suppressed length. Moreover, suppressed zonelength length on length the amplitude region in cross andzone autodepends correlations cannot be as long as waveforms the whole length of the pulse. The length ofittheincreases suppressed on the number Mis ofallowed the in the generated set:if the lower constraint:of if amplitude modulation while it decreases the unimodular depends on the number M ofthe the suppressed waveforms in the generated set: theon lower M,the thesuppressed longer thezone suppressed length. Moreover, zone length depends the constraint M, is applied. Hereafter, only the unimodular case will be considered. the longer the suppressed length. Moreover, the suppressed zone while lengthit depends amplitude constraint: it increases if amplitude modulation is allowed decreasesonif the the constraint: it increases ifcompressed amplitude is allowed while it decreases if theamplitude Figureamplitude 11 shows the BLASA MIMO with M 2 and the unimodular unimodular constraint is applied. Hereafter, only modulation thepulse unimodular case=will be considered. constraint isBT applied. Hereafter, only themaximum unimodular case will bewhich considered. 11 showsfor the BLASA MIMO compressed pulse with Mvalue = 2 and the unimodular amplitudealgorithm constraint.unimodular It isFigure generated = 256 which is the at the current Figure 11 shows the BLASA MIMO compressed pulse with M = 2 and the unimodular amplitude constraint. It is generated for BT = 256 which is the maximum value at which the current algorithm version canconstraint. work. Theis occupied bandwidth is always B = 1 MHz but, as it the happens algorithm with the HNLFM, generated for BTbandwidth = 256 which the maximum at it which version canItwork. The occupied is is always B = 1 MHzvalue but, as happens current with the HNLFM, the −3 dB version bandwidth is a quarter of the total occupied bandwidth. can work. Theisoccupied always Bbandwidth. = 1 MHz but, as it happens with the HNLFM, the −3 dB bandwidth a quarterbandwidth of the totalisoccupied the −3 dB bandwidth is a quarter of the total occupied bandwidth.

Figure 10. Spectrum comparison among Unimodular Noise, SCAN and BLASA SISO: B = 1 MHz, T =

Figure 10. Figure Spectrum comparison among Noise, SCAN and SISO: BLASA 10.MSpectrum comparison amongUnimodular Unimodular Noise, SCAN and BLASA B = 1SISO: MHz, TB= = 1 MHz, 4096 μs, = 2. 4096 M = 2. T = 4096 µs, Mμs, = 2.

Figure 11. Autocorrelation of BLASA Multiple-Input Multiple-Output (MIMO): B = 1 MHz, T = 256 BLASA Multiple-Input Multiple-Output (MIMO): B =(MIMO): 1 MHz, T =B256= 1 MHz, μs, Autocorrelation M =11. 2. Autocorrelation Figure 11.Figure ofofBLASA Multiple-Input Multiple-Output μs, M = 2. T = 256 µs, M = 2.

The limited length of the suppressed zone represents a valid tool to mitigate the clutter effect, especially in the proximity of the mainlobe, i.e., the target’s closest range cells. Because of the narrow

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Aerospace 2017, 4, 15 of 14 −3 dB bandwidth (see Figure 12), the mainlobe is four times wider than the expected12150 m, which corresponds toThe a 1limited MHz length bandwidth. of the suppressed zone represents a valid tool to mitigate the clutter effect, especially inthis the proximity of the i.e., the target’s closest cells. Because of the narrow Nevertheless, behaviour is mainlobe, deterministic and can be range overcome by properly choosing the −3 dB bandwidth (see Figure mainlobe isof four wider MIMO than the pseudorandom expected 150 m, which signals’ occupied bandwidth. The12), bigthe advantage thetimes BLASA signals with corresponds to a 1 MHz bandwidth. respect to the deterministic HNLFM is the possibility to coherently average the range sidelobes in Nevertheless, this behaviour is deterministic and can be overcome by properly choosing the azimuth. In fact, occupied if the transmitted waveform changes WRT within the dwellsignals time,with the averaged signals’ bandwidth. The big advantage of theeach BLASA MIMO pseudorandom respect to presents the deterministic HNLFM is the possibility coherently average compressed pulse a sidelobe level reduced bytothe quantity [24]: the range sidelobes in

azimuth. In fact, if the transmitted waveform changes each WRT within the dwell time, the averaged compressed pulse presents a sidelobe∆SL level = reduced by the [24]: 10 · log ( Lquantity ), Δ

10

= 10 ⋅ log ( ) ,

(8)

(8)

|X(f)| [dB]

where ∆SLwhere is the lowering in the level respect not-averaged and L is the ΔSL is the lowering in sidelobe the sidelobe level with with respect to to the the not-averaged case andcase L is the number ofnumber coherently integrated returns. of coherently integrated returns.

Figure 12. Spectrum of BLASAMIMO: MIMO: BB==1 MHz, T = 256 M µs, = 2. M = 2. Figure 12. Spectrum of BLASA 1 MHz, T =μs, 256

Summing up all the considered waveforms, Table 1 shows their comparison. Each algorithm is checked verify it allows a MIMO version, level oftheir the sidelobes, the frequency Summing uptoall the whether considered waveforms, Table the 1 shows comparison. Each algorithm occupancy and its capability to be coherently integrated. is checked to verify whether it allows a MIMO version, the level of the sidelobes, the frequency occupancy and its capability be coherently integrated. Tableto 1. Comparison of algorithms (BTOT denotes the swept frequency). Algorithm

MIMO

Amplitude

Sidelobe Level and Suppression Interval Table 1. Comparison of algorithms (BTOT denotes the swept frequency). Version Modulation

HNLFM

No

−67 dB at BT = 4096

400%

MIMO Pure Unimodular Algorithm and Interval No Sidelobe Level −23 dB at BTSuppression = 4096 100% Noise Version SCAN

HNLFM BLASA SISO No BLASA MIMO

No No Yes

−45 dB at BT = 4096 (within 15%) BT = 4096 −−50 67dB dBat at BT = 4096 −30 dB at BT = 256 (within 12%) if unimodular amplitude with M = 2

100% 100% 400%

Pseudo trapezoidal AM

Amplitude BTOT Unimodular B−3 dB Modulation Unimodular

Unimodular Pseudo 400% trapezoidal AM Unimodular

Pure Unimodular No −23 dB at BT = 4096 100% Unimodular Noise The column “MIMO version” refers to the capability of jointly generated M waveforms with a cross-correlationNo level equal to−the auto-correlation level. The frequency occupancy the SCAN 45 dB at BT = 4096 (within 15%) 100% givesUnimodular information of how much the mainlobe is enlarged by the algorithm.

BLASA SISOThe SCAN No −50zone dB at BT =15% 4096 Unimodular sidelobe level refers to the within of the whole length, 100% as shown in Figure 9, while the −30 dB of BLASA − MIMO to the suppressed 30 dBisatrelated BT = 256 (within 12%) area if which is about 12% of the BLASA MIMO Yes two signals (M = 2) are jointly generated with a unimodular amplitude. 400% Unimodular whole length when unimodular amplitude with M = 2

The column “MIMO version” refers to the capability of jointly generated M waveforms with a cross-correlation level equal to the auto-correlation level. The frequency occupancy gives the information of how much the mainlobe is enlarged by the algorithm. The SCAN sidelobe level refers to the zone within 15% of the whole length, as shown in Figure 9, while the −30 dB of BLASA MIMO is related to the suppressed area which is about 12% of the whole length when two signals (M = 2) are jointly generated with a unimodular amplitude.

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4. Conclusions The design of the transmitted signal is an increasingly important element in the development of modern radars. The availability of stable and accurate waveform generators and of real-time, high dynamic range digital correlators makes it possible to use, as radar signals, arbitrary waveforms with a number of degrees of freedom, i.e., independent samples, of the order of a thousand and even more, permitting pulse compression with a processing gain of the same order of magnitude. In this paper, two classes of novel waveforms for pulse-compression (and continuous-wave) radars have been discussed and evaluated: (i) a (deterministic) type of frequency modulated pulse with a “trapezoidal-like” amplitude modulation and; (ii) a subset of noisy waveforms in the Noise Radar Technology context. Both are designed in order to make the range sidelobes as low as possible, which are the main issue in the matched filter approach, both for pulsed and continuous-wave radars. A set of representative results has been shown in terms of sidelobe level, width of the main lobe and spectral occupancy. The selection of the particular waveform depends, of course, on the application. Author Contributions: Gaspare Galati proposed the basic ideas, gave the theoretical support and completed/checked the paper. Gabriele Pavan contributed to the HNLFM analysis and gave the Matlab software support together with Francesco De Palo who also contributed to the Noise Radar and signals generation. Conflicts of Interest: The authors declare no conflict of interest.

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