Chirp Signals and Noisy Waveforms for Solid-State Surveillance Radars

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 www.mdpi.com/journal/aerospace Aerospace 2017, 4, 15 2 of 14 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 Aerospace 2017, 4, 15 3 of 14 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: Section2 describes the deterministic waveforms design and compares classical pulse compression waveforms with the novel ones; Section3 shows a different approach to pulse compression based on random waveforms (noisy signals) making use of CW operation; finally, Section4 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)ejφ(t) , (1) where a(t) and φ(t) denote respectively the AM and PM modulation. The stationary phase 2 principle [10,16] establishes that, at the instantaneous frequency ωt the amplitude spectrum |S(ωt)| of a given signal s(t), having the amplitude a(t), can be approximated as [10]:

a2(t) |S(ω )|2 =∼ 2π , (2) t |φ00 (t)|

0 i.e., the energy spectral density at the frequency ωt = φ (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: r 1 0 2 a(t) =∼ S φ (t) |φ00 (t)| . (3) 2π

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) Aerospace 2017, 4, 15 4 of 14

canAerospace be obtained 20172017,, 44,, 1515 as a weighted sum of the Non-Linear tangent FM term and the LFM one, hence44 ofof the 1414 name Hybrid-NLFM [21,22]: 1 2γ 2 1 2γt 2t φϕ0(t())==ππB α tg +(1−)+ (1 − α) ,, , (4)(4) (4) tg(((γγ)) T T where ∈(0,1) isis thethe relativerelative weightweight betweenbetween thethe linearlinear andand thethe tangentialtangential terms,terms, B isis thethe sweptswept where α ∈ (0, 1) is the relative weight between the linear and the tangential terms, B is the swept frequencyfrequency (nearly(nearly equalequal toto thethe signal’ssignal’s bandwidth),bandwidth), γ is is thethe Non-LinearNon-Linear tangtangent FM rate and, being frequency (nearly equal to the signal’s bandwidth), γ is the Non-Linear tangent FM rate and, being ∈−∈−h ,+,+ ,,i T denotesdenotes thethe pulse-width.pulse-width. ∈ −T +T t 2 , 2 , T denotes the pulse-width. IfIf () isis aa signalsignal withwith aa GaussianGaussian spectrum:spectrum: ||(ω)|| =exp−β 2 withwith β=1,, usingusing thethe 2 ωt If s(t) is a signal with a Gaussian spectrum: |S(ωt)| = exp −β 2 with β = 1, using the optimized values of α andand γ as as evaluatedevaluated inin [21,22][21,22] (i.e.,(i.e., thosethose valuesvalues thatthatB reachreach thethe optimumoptimum PSLRPSLR optimized values of α and γ as evaluated in [21,22] (i.e., those values that reach the optimum PSLR ⁄⁄ maximizing the transmission efficiency: = R +T/2()),, thethe energyenergy lossloss resultsresults asas lowlow asas 0.580.58 1 ⁄⁄ 2 ) maximizing the transmission efﬁciency: η = T −T/2 a (t)dt), the energy loss results as low as 0.58dB with dB respect with respect to the tocase the of case unity of amplitude. unity amplitude. Inserting Inserting Equation Equation (4) into Equation (4) into (3), Equation the amplitude (3), the amplitudemodulation modulation has been evaluated has been as evaluated shown in as Figure shown 1. inZooming Figure1 around. Zooming () around = 1,, i.e.,i.e.,a ( inint) thethe= 1 intervalinterval, i.e., in the((−0.3, interval 0.3), some (−0.3, ripples 0.3), some of the ripples relative of the amplitude relative amplitude order of order 10 of areare10 −observed.observed.3 are observed. InIn FigureFigure In Figure 2,2, thethe2, thecorresponding corresponding instantaneous instantaneous frequency frequency modulation modulation is shown. is shown.

Amplitude Modulation 1.2

1 0.8 0.999 0.6 a(t) a(t) 0.998 -0.3-0.3 -0.2 -0.2 -0.1 -0.1 0 0 0.1 0.1 0.2 0.2 0.3 0.3 0.4

0.2

0 -0.5-0.5 -0.4 -0.4 -0.3 -0.3 -0.2 -0.2 -0.1 -0.1 0 0 0.1 0.1 0.2 0.2 0.3 0.3 0.4 0.4 0.5 0.5 t/Tt/T

Figure 1. NormalizedNormalized amplitude amplitude weighting weighting for for HybridHybrid Non-LinearNon-Linear FrequencyFrequency ModulationModulation (HNLFM)(HNLFM) (red(red line:line: optimumoptimum weighting,weighting, blueblue line:line: sub-optimumsub-optimum weighting).weighting). f/B f/B

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

Figure 3 shows the PSLR of the matched filter output for the optimized waveform (solid line- circles). With BT decreasing,decreasing, thethe approximationapproximation duedue toto thethe principle of the stationary phase becomes worse and worse causing an increase in the PSLR. However, with BT == 6464 thethe PSLRPSLR ((−51 dB) is still Aerospace 2017, 4, 15 5 of 14

Figure3 shows the PSLR of the matched ﬁlter output for the optimized waveform (solidAerospace line-circles). 2017, 4, 15 With BT decreasing, the approximation due to the principle of the stationary5 of 14 phase becomes worse and worse causing an increase in the PSLR. However, with BT = 64 the PSLR (compatible−51 dB) is stillwith compatible many applications, with many and applications, for BT = 128 and the for PSLRBT = is 128 −75 the dB, PSLR which is −is75 suited dB, which to most is suitedapplications. to most applications. These excellentexcellent theoretical theoretical results results (circles (circles in Figure in Figure3) are only3) are possible only ifpossible the amplitude if the weightingamplitude isweighting the one shown is the one in Figure shown1 (redin Figure line) with1 (red the line instantaneous) with the instantaneous frequency of frequency Figure2. of Figure 2. PSLR (dB)

Figure 3. 3. EffectEffect of the of thecompression compression ratio ratioBT onBT the onPeak-to-Sidelobes the Peak-to-Sidelobes Ratio (PSLR), Ratio HNLFM (PSLR), (optimum HNLFM (optimumand sub-optimum) and sub-optimum) and Millet andsignals, Millet the signals, last is shown the last only is shown as a historical only as a reference. historical reference.

InIn practice, it it may may be be hard hard to to implement implement the the requirement requirement on on ()a(t), ,with with ripples ripples of of the the order order of of 1 1over over 1000. 1000. In In general, general, if if a aPSLR PSLR level level of of −−6060 dB dB is is required, required, a a simple simple rule rule of of thumb thumb tells us that the fidelityfidelity ofof thethewaveform, waveform, in in terms terms of of (I, (I, Q) Q) or or (Amplitude, (Amplitude, Phase) Phase) shall shall be betterbe better than than 1:1000, 1:1000, or 10 or bits, 10 nobits, matter no matter how how the waveformthe waveform is designed. is designed. It It is is widely widely known—from known—from many manypractical practical experiencesexperiences (unfortunately,(unfortunately, notnot availableavailable inin thethe openopen literature)—thatliterature)—that hardwarehardware imperfectionsimperfections increase the PSLR withwith respectrespect toto the “ideal” compressed waveform.waveform. ThisThis meansmeans thatthat ifif the required PSLR is for example −6060 dB, dB, the the intrinsic intrinsic level level of the waveform (which is ourour focus)focus) hashas toto bebe −−67 dB, the differencedifference between these figuresfigures depending,depending, ofof course,course, onon thethe stability/linearitystability/linearity of the hardware. In a recentrecent privateprivate communicationcommunication [[28]28] itit is explained that: “In“In one case, related to a NAVICO civil marine radar using GaNGaN forfor thethe solid solid state state amplifier, amplifier, and and a non-lineara non-linear FM, FM, amplitude-weighted amplitude-weighted pulse pulse with withBT = BT 150, = the150, measured the measured PSLR isPSLR−55 is dB, −55 versus dB, versus the “ideal” the “ideal”−60 dB − of60 the dB waveform”. of the waveform”. So, the effect So, the of hardware effect of ishardware significant is significant but not dramatic, but not anddramatic, can be and controlled can be withcontrolled a careful with design. a careful design. IfIf thethe amplitudeamplitude ofof thethe transmittedtransmitted signalsignal isis keptkept constantconstant (the(the powerpower amplifieramplifier workingworking inin saturation) with the the instantaneous instantaneous frequency frequency of of Figu Figurere 2,2 the, the theoretical theoretical PSLR PSLR increases increases by byabout about 25– 25–3030 dB. dB An. Animprovement improvement can can be beobtained obtained using using a asub-optimum sub-optimum waveform waveform where where the the ripples shown inin the zoom zoom of of Figure Figure 11 are are removed removed imposing imposing ()a(t =) = 1 in1 inthis this interval interval (dashed (dashed line line in Figure in Figure 1). The1). ThePSLR PSLR of this of “sub-optimum” this “sub-optimum” waveform waveform results results only 10–20 only 10–20 dB worse dB worse than the than optimized the optimized signal signalwhen when ≥ 128BT ≥ (diamonds-line128 (diamonds-line in Figure in Figure 3). Figure3). Figure 4 shows4 shows the thehalf-power half-power pulse pulse width width (τ ( τ) versus) versus the 3dB compression ratio BT. The values are compared with the ones of the LFM, i.e., τ = . 1 the compression ratio BT. The values are compared with the ones of the LFM, i.e.,τ3dB = B . For BT = 128128 (frequency(frequency swept swept of of =1 MHzB = 1 MHz andand duration duration T = 128 μs= 128),µ Figures), Figure 5a 5showsa shows the thecompressed compressed pulse, pulse, while while Figure Figure 5b reports5b reports its spectrum. its spectrum. The PSLR The PSLRreaches reaches about about−75 dB− for75 the dB foroptimum the optimum waveform waveform case and case−66 dB and for− the66 dBsub-optimum for the sub-optimum one, still compatible one, still for compatible most applications, for most applications,e.g., lower than e.g., the lower typical than two-way the typical antenna two-way sidelobes antenna in sidelobes azimuth. in The azimuth. range resolution, The range resolution,i.e., ∆ = c i.e., ∆R (=2B representing(B−3dB representing the −3 dB the bandwidth),−3 dB bandwidth), is about is 550 about m. 550 It is m. worth It is worth clarifying clarifying that thatthe −3dB thebandwidth bandwidth of a of waveform a waveform is very is very important important when when spectral spectral limitations limitations apply, apply, which which is is the the case 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. Aerospace 2017, 4, 15 6 of 14 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,, 4,, 1515 6 of 14 matched or possibly mismatched for some reason. To improveTo improve the the resolution, resolution, maintaining maintaining thethe samesame pulse pulse duration, duration, the the swept swept frequency frequency has to has be to be increased,increased,increased, with withwith the thethe only onlyonly practical practicalpractical limitation limitationlimitation being beingbeing thethe restrictedrestricted useuse use ofof of thethe the spectrum.spectrum. spectrum.

T = 100 microsec - Compressed pulse width 8 Sub-optimum HNLFM 7 Sub-optimum HNLFM 7 LFM ( = 1/B) 3dB3dB 6 5 4 3 2 1 0 32 64 96 128 160 192 224 256 BT FigureFigure 4. Effect 4. Effect of of the the compression compressionratio ratio BT onon the the compressed compressed pulse pulse width width (τ (τ). ). Figure 4. Effect of the compression ratio BT on the compressed pulse width (τ).3dB

((a))

((b))

Figure 5. HNLFMHNLFM compressedcompressed pulse:pulse: = 128 ,, = 128 μs ,, =1 MHz.. ((a)) NormalizedNormalized Figure 5. HNLFM compressed pulse: BT = 128, T = 128 µs, B = 1 MHz.(a) Normalized autocorrelation; (b)) PowerPower spectrumspectrum density.density. autocorrelation; (b) Power spectrum density. 3. Noise Radar Technology 3. Noise Radar Technology The HNLFM capability to get very low sidelobes of the compressed pulse is strictly dependent Theon the HNLFM ability of capability the signal togeneration get very and low amplific sidelobesation of chain, the compressed including the pulse RF power is strictly amplifier, dependent to on thefaithfullyfaithfully ability ofreproducereproduce the signal thethe generationamplitudeamplitude modulation andmodulation amplification ofof FigureFigure chain, 1,1, callingcalling including forfor highlyhighly the RF linearlinear power A-classA-class amplifier, to faithfully reproduce the amplitude modulation of Figure1, calling for highly linear A-class amplifiers. Aerospace 2017, 4, 15 7 of 14

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 · R = max . (5) 4 c

WRT = 2·150000 (m) = For a maximum range of 150 km, it is required that: 4 3·108 (m/s) 1 ms, 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:

THNLFM Pnoise = PHNLFM · , (6) WRTnoise 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 Figure6. The ( I, Q) samples are generated through a white Gaussian random process. The signal to be ﬁltered by the N frequency window H( f ) is {xi}i=1 where N is the number of generated samples and xi the ith complex (I, Q) sample. AerospaceAerospace2017 2017,,4 4,, 15 15 88 ofof 1414 Aerospace 2017, 4, 15 8 of 14

Figure 6. Pure noise generation block-diagram (ZMNL: Zero-Memory-Non-Linear transformation, Figure 6. Pure noise generation block-diagram (ZMNL: Zero-Memory-Non-Linear transformation, FigureFFT: Fast 6. PureFourier noise Transform, generation iFFT: block-diagram inverse-FFT). (ZMN L: Zero-Memory-Non-Linear transformation, FFT: Fast Fourier Transform,Transform, iFFT:iFFT: inverse-FFT).inverse-FFT). 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 process, the signal has to be band-limited with a proper frequency window H()( f ) whichBeing can abe white any, process,e.g., Blackman–Nuttall the signal has to [37] be orband-limited simply rectangular. with a proper In this frequency paper, we window consider the which can be any, e.g., Blackman–Nuttall [37] or simply rectangular. In this paper, we consider whichrectangular can be frequency any, e.g., windowBlackman–Nuttall to fully exploit [37] orthe simply available rectangular. bandwidth; In thisothe paper,r windows we consider can be used the the rectangular frequency window to fully exploit the available bandwidth; other windows can rectangularto gain a slight frequency improvement window into fullyPSLR exploit value. theAf teravailable the frequency bandwidth; domain othe rwindowing, windows can the be signal used betoamplitude gain used a to slight is gain saturated improvement a slight to improvementthe maximum in PSLR value. in(i.e., PSLR a unimAfter value.odular the frequency After signal the is frequencyobtained)domain windowing, value domain through windowing, the asignal Zero- theamplitudeMemory-Non-Linear signal is amplitude saturated (ZMNL) isto saturatedthe maximum transformation, to the (i.e., maximum a unim whileodular (i.e.,the phase asignal unimodular is is kept obtained) unchanged. signal value is obtained) throughSince the a valueZero-(, ) (, ) throughMemory-Non-Linearsamples acome Zero-Memory-Non-Linear from a(ZMNL) random transformation, process, (ZMNL) at each while transformation, run, thethe phase algorithm whileis kept provides the unchanged. phase different is kept Since unchanged.realizations the (I Q) Sincesampleshaving the the come ,same fromsamples average a random comeperformances fromprocess, a random in at terms each process, ofru PSLRn, the at and eachalgorithm cross-correlation run, the provides algorithm differentlevel, provides while realizations the different range realizationshavingresolution the sameonly having dependsaverage the same performanceson averagethe used performances () in terms. Figure of inPSLR 7 terms shows and of thecross-correlation PSLR spectrum and cross-correlation of the level, unimodular while level, the range whileband- () H( f ) theresolutionlimited range pure resolution only noise depends and only the dependson spectrum the used on theof a used LFM. Figure signal .7 Figure showshaving7 the showsthe spectrum same the BT spectrum. ofThe the 1 MHz ofunimodular the bandwidth unimodular band- is BT band-limitedlimitedfully exploited. pure noise pure noiseand the and spectrum the spectrum of a ofLFM a LFM signal signal having having the thesame same BT. The. The 1 MHz 1 MHz bandwidth bandwidth is isfully fully exploited. exploited. |X(f)| [dB] |X(f)| [dB]

FigureFigure 7.7. Spectra of Unimodular PurePure Noise,Noise, andand LFM.LFM. WithWith B=1 MHz= 1 MHz,, T= =4096 4096 μsµs.. Figure 7. Spectra of Unimodular Pure Noise, and LFM. With =1 MHz, = 4096 μs. OnceOnce compressedcompressed byby thethe matchedmatched filter,filter, thethe purepure noisenoise andand thethe LFMLFM givegive aa rangerange resolutionresolution ofof Once compressed by the matched filter, the pure noise and the LFM give a range resolution of ∆ΔR = 150 m150 m (11 μsµs) as shown in Figure8 8.. InIn thethe firstfirst 5–105–10 µμss,, thethe secondarysecondary lobeslobes ofof purepure noisenoise areare Δ = 150 m (1 μs) as shown in Figure 8. In the first 5–10 μs, the secondary lobes of pure noise are slightlyslightly fluctuatingfluctuating (the(the PSLRPSLR isis comparablecomparable toto thethe LFM).LFM). ForFor farfar lobes,lobes, thethe PSLRPSLR isis empirically relatedrelated slightly fluctuating (the PSLR is comparable to the LFM). For far lobes, the PSLR is empirically related toto thethe BTBT [[24]24] byby EquationEquation (7):(7): to the BT [24] by Equation (7): = −10 ⋅ () +[dB], (7) PSLR = −10 · log (BT) + k [dB] , (7) = −10 ⋅ 10() +[dB], (7) with of the order of 10–13 dB, which corresponds, for BT = 4096, to −23 dB (see Figure 8). The cross- withcorrelation k of of the level order order between of of 10–13 10–13 two dB, independently dB, which which corresponds, corresponds, generated for BT pure for = 4096,BT noise= to 4096,signals −23 dB to is (see− of23 theFigure dB same (see 8). level The Figure cross-as 8the). Thecorrelationautocorrelation cross-correlation level sidelobes,between level two excluding between independently two the independentlycentral generated zone. The pure generated advantage noise puresignals of noise the is ofpure signals the noisesame is oflevelsignal the as same with the levelautocorrelationrespect as to the the autocorrelation HNLFM sidelobes, signal excluding sidelobes, is two-fold: the excluding central a narrowe zone. ther centralbandwidth The advantage zone. to Theget ofthe advantage the required pure noise of range the signal pure resolution noisewith respectand a cross-correlation to the HNLFM signal level atis thetwo-fold: same valuea narrowe as itsr autocorrelationbandwidth to get sidelobes. the required range resolution and a cross-correlation level at the same value as its autocorrelation sidelobes. Aerospace 2017, 4, 15 9 of 14

Aerospacesignal with 2017, respect4, 15 to the HNLFM signal is two-fold: a narrower bandwidth to get the required range9 of 14 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]

FigureFigure 8. 8. NormalizedNormalized autocorrelations autocorrelations of of Unimodular Unimodular Pure Pure Noise and LFM: B=1 MHz= 1 MHz,, T= 4096 μs4096 µs..

3.3.3.3. Range Range Sidelobe Sidelobe Suppression Suppression Algorithms Algorithms ManyMany approaches approaches have have been been used used in in the the past past ye yearsars to to cope cope with with the the range range sidelobe sidelobe problem, problem, startingstarting 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 algorithmsalgorithms able able to to generate generate signals signals with with suitable suitable autocorrelation autocorrelation characteristics characteristics without without the the need need of sidelobeof sidelobe suppression suppression in inreception. reception. The The main main differ differenceence between between these these two two approaches approaches is is that, that, using using thethe generation generation algorithms, algorithms, significant significant complexity complexity is is demanded demanded to to the the generation generation side side in in terms terms of of computationalcomputational burdenburden to to achieve achieve a “useful”a “useful” waveform. waveform. In any In case, any thiscase, issue this can issue be trivially can be overcometrivially overcomeby offline generatingby offline generating a large enough a large set enough of noisy set waveforms of noisy waveforms ready to be ready transmitted, to be transmitted, and stored and in a storedmass memory in a mass [31 memory]. [31]. Generally,Generally, a a noise generation al algorithmgorithm starts starts from from a a random process realization (e.g., (e.g., the the unimodular,unimodular, band-limitedband-limited one, one, see see Figure Figure6) and6) and runs runs in order in order to minimize to minimize a certain a objectivecertain objective function functionwith defined with constraints.defined constraints. In this case, In this the case, objective the objective function function is the PSLR is the and PSLR the and constraints the constraints are the arelimited the limited bandwidth bandwidth and the and unity the amplitude unity amplitude needed needed to fully to exploit fully exploit the solid-state the solid-state amplifier. amplifier. Often, Often,due to due convergence to convergence considerations, considerations, the Integrated-Side-Lobe the Integrated-Side-Lobe (ISL) is(ISL) minimized is minimized instead instead of the of PSLR the PSLRbecause because the former the former is an integratedis an integrated value value over allover the all sidelobe the sidelobe region region while while the latter the latter is only is only a local a localvalue value that canthat rapidly can rapidly change change point point by point. by point. AA well-known well-known sidelobe sidelobe suppressi suppressionon algorithm algorithm family family is is the the Cyclic Cyclic Algorithm Algorithm New New (CAN) (CAN) [25] [25] thatthat provides provides several several interesting interesting ways ways to to approach approach the the suppression suppression problem. problem. To To suit suit the the algorithm algorithm to particularto particular needs, needs, the the authors authors of ofthis this paper paper ha haveve developed developed a anew new algorithm algorithm to to generate generate noisy noisy waveformswaveforms having aa limitedlimited bandwidthbandwidth and and an an unimodular unimodular amplitude, amplitude, with with the the possibility possibility to tuneto tune the thesuppressed suppressed zone zone length length depending depending on theon the particular particular application. application. In theIn the following, following, some some results results are areshown shown and and discussed, discussed, highlighting highlighting advantages advantages and and drawbacks. drawbacks. InIn some some applications, applications, the the matched matched filter filter output output is is performed performed by by a a periodic periodic correlation correlation between between thethe radar radar return return and and the the reference, reference, which which can can signif significantlyicantly differ differ from from the the aperiodic aperiodic case. case. The The periodic periodic approachapproach can can be be considered considered in in the the case case of ofFFT FFT impl implementation,ementation, with with it being it being a spectrum a spectrum product, product, i.e., ai.e., circular a circular correlation. correlation. In this In paper, this paper, only only the aperiodic the aperiodic correlation correlation is discussed. is discussed. CANCAN algorithms [[25]25] havehave been been developed developed both both for for aperiodic aperiodic and and periodic periodic cases; cases; in general, in general, there thereare no are large nobasic large differences basic differences between between them. The them. main The idea main is to minimizeidea is to themi differencenimize the between difference the betweenobtained the and obtained the desired and autocorrelationthe desired autocorrelation functions through functions a process through that a proces runs cyclicallys that runs until 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 Aerospace 2017, 4, 15 10 of 14 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. EspeciallyAerospace in2017 MIMO, 4, 15 radar configuration, a number of M orthogonal waveforms10 are of 14 required to discriminate, after the matched filter, the mth 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 alsosidelobes provides as well a “MIMO”as the mainlobe version width for(i.e., the the needed algorithms bandwidth) in which or others. the quantity to be minimized is the differenceEspecially between in MIMO the obtainedradar configuration, and the a desired number of covariance M orthogonal matrix waveforms [25], are until required a stop to criterion 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 mainlobereached. of the signal generated by using the CAN algorithm is very narrow. In fact, these algorithms preferThe main a deep drawback sidelobe of the CAN suppression algorithms is at their the inability expense to manage of having the bandwidth a full-Nyquist increase, occupied bandwidth,i.e., which the mainlobe unfortunately of the signal is notgenerated suitable by usin forg applications the CAN algorithm in which is very spectrum narrow. In regulations fact, these must be 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,be met. the Only SCAN one hasCAN been algorithm applied (Stopband to generate CAN (SCAN) noise [25]) unimodular is able to manage signals the with spectrumBT = 4096 and B = 1 MHzconstraint.. The related In this study, aperiodic the SCAN autocorrelation has been applied is to showngenerate innoise Figure unimodular9a. Keeping signals withBT BTunchanged, = the SCAN4096 algorithm and B = improves1 MHz. The the related PSLR aperiodic by about autocorr 20 dBelation with is respectshown in toFigure the unimodular9a. Keeping BT noise from 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-shapedin Figure within 10, is well-shaped the required within 1 MHz the required bandwidth. 1 MHz bandwidth.

Figure 9. CompressedFigure 9. Compressed pulse pulse comparison comparison between between Unimodular Noise: Noise: (a) Stopband (a) Stopband Cyclic Algorithm Cyclic Algorithm New (SCAN); (b) Band Limited Algorithm for Sidelobes Attenuation (BLASA) Single Input, Single New (SCAN);Output (b (SISO):) Band B = Limited 1 MHz, T Algorithm= 4096 μs. for Sidelobes Attenuation (BLASA) Single Input, Single 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 drawbackSidelobes Attenuation) of the SCAN algorithm algorithm whose is result that is the shown sidelobes in Figure close 9b. It to comes the mainlobe from the same are CAN still quite high. To overcomeidea the andissue, provides the very authors low sidelobes have developedeven in the area the close BLASA to the mainlobe. (Band Limited It is called Algorithm “SISO” (Single for Sidelobes Attenuation)Input, algorithm Single Output) whose because result a single is shownwaveform in isFigure generated9b. at Iteach comes run. The from BLASA the SISO same spectrum CAN idea and provides veryis shown low in sidelobes Figure 10 and even it isin still the well area shaped close within to the the mainlobe.allowed 1 MHz It isbandwidth, called “SISO” providing (Single a 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. Aerospace 2017, 4, 15 11 of 14

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 unimodularAerospace pure 2017 noise., 4, 15 11 of 14 As inAerospace the CAN 2017, family,4, 15 even for the BLASA SISO, a “MIMO” version exists which is11 ableof 14 to jointly Being a “SISO” algorithm, BLASA does not lower the cross-correlation level between two generate a number M of waveforms at each run, i.e., M signals belonging to the same set. The BLASA independentlyBeing a “SISO” generated algorithm, waveforms. BLASA Hence, does their not crolowerss-correlation the cross-correlation is at the same level level between as the initial two MIMO hasindependentlyunimodular been developed pure generated noise. to managewaveforms. the Hence, suppression their cross-correlation of both auto is at andthe same cross-correlation level as the initial functions, still keepingunimodular theAs bandwidthin the pure CAN noise. family, limited. even for the BLASA SISO, a “MIMO” version exists which is able to jointly As in the CAN family, even for the BLASA SISO, a “MIMO” version exists which is able to jointly Due togenerate the limited a number number M of waveforms of samples at each that run, BLASA i.e., M signals MIMO belonging can manipulate, to the same set. the The joint BLASA suppression generateMIMO has a number been developed M of waveforms to manage at each the suppressionrun, i.e., M signals of both belonging auto and tocross-correlation the same set. The functions, BLASA region in cross and auto correlations cannot be as long as the whole length of the pulse. The length of MIMOstill keeping has been the bandwidthdeveloped tolimited. manage the suppression of both auto and cross-correlation functions, the suppressedstill keepingDue zone to thethe depends limited bandwidth number on limited. the of number samples thatM ofBLASA the waveformsMIMO can manipulate, in the generated the joint suppression set: the lower M, the longerregion theDue suppressed in tocross the andlimited auto length. number correlations Moreover, of samples cannot that the be BL as suppressedASA long MIMOas the wholecan zone manipulate, length length of dependsthe pulse.joint suppression The on length the amplitude region in cross and auto correlations cannot be as long as the whole length of the pulse. The length constraint:of itthe increases suppressed if zone amplitude depends on modulation the number M is of allowedthe waveforms while in the it decreasesgenerated set: if the the lower unimodular ofM ,the the suppressed longer the zone suppressed depends onlength. the number Moreover, M of the the suppressedwaveforms inzone the generatedlength depends set: the on lower the constraint is applied. Hereafter, only the unimodular case will be considered. Mamplitude, the longer constraint: the suppressed it increases length. if amplitude Moreover, modulation the suppressed is allowed zone whilelength it dependsdecreases on if the Figureamplitudeunimodular 11 shows constraint: constraint the BLASA itis applied.increases MIMO Hereafter, if compressedamplitude only modulationthe pulse unimodular with is allowed Mcase= will 2 andwhile be considered. the it decreases unimodular if the amplitude constraint.unimodular It isFigure generated 11 constraint shows for the isBT BLASAapplied.= 256 MIMO Hereafter, which compressed isonly the the maximum pulse unimodular with M value case= 2 and will atthe be which unimodular considered. the currentamplitude algorithm Figure 11 shows the BLASA MIMO compressed pulse with M = 2 and the unimodular amplitude version canconstraint. work. The It is occupiedgenerated for bandwidth BT = 256 which is always is the maximumB = 1 MHz value but, at which as it the happens current withalgorithm the HNLFM, constraint.version can It work. is generated The occupied for BT bandwidth = 256 which is isalways the maximum B = 1 MHz value but, asat itwhich happens the currentwith the algorithm HNLFM, the −3 dB bandwidth is a quarter of the total occupied bandwidth. versionthe −3 dB can bandwidth work. The is occupied a quarter bandwidth of the total is occupied always B bandwidth. = 1 MHz but, as it happens with the HNLFM, 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 = B Figure 10. Figure4096Spectrum μ s,10. M Spectrum = 2. comparison comparison among among Unimodular Unimodular Noise, Noise, SCAN SCAN and BLASA and SISO: BLASA B = 1SISO: MHz, T = = 1 MHz, T = 4096 µs,4096M μ=s, 2.M = 2.

Figure 11. Autocorrelation of BLASA Multiple-Input Multiple-Output (MIMO): B = 1 MHz, T = 256 Figure 11.Figureμs, AutocorrelationM = 11. 2. Autocorrelation of ofBLASA BLASA Multiple-Input Multiple-Input Multiple-Output Multiple-Output (MIMO): B = (MIMO): 1 MHz, T =B 256= 1 MHz, 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 Aerospace 2017, 4, 15 12 of 14

−3 dB bandwidthAerospace 2017 (see, 4, 15 Figure 12), the mainlobe is four times wider than the expected12 150 of 14 m, which corresponds toThe a 1limited MHz length bandwidth. of the suppressed zone represents a valid tool to mitigate the clutter effect, Nevertheless,especially in this the proximity behaviour of the is mainlobe, deterministic i.e., the target’s and can closest be range overcome cells. Because by properly of the narrow choosing the signals’ occupied−3 dB bandwidth bandwidth. (see Figure The 12), big the advantage mainlobe is offour the times BLASA wider MIMOthan the pseudorandomexpected 150 m, which 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. Insignals’ fact, occupied if the transmitted bandwidth. The waveform big advantage changes of the each BLASA WRT MIMO within pseudorandom the dwell signals time, with the averaged compressedrespect pulse to presentsthe deterministic a sidelobe HNLFM level is the reduced possibility by to the coherently quantity average [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 level reduced by the quantity [24]: ∆SL = 10 · log10(L) , (8) Δ = 10 ⋅ log() , (8) where ∆SLwhereis the ΔSL lowering is the lowering in the in sidelobethe sidelobe level level withwith respect respect to tothe thenot-averaged not-averaged case and case L is the and L is the number ofnumber coherently of coherently integrated integrated returns. returns. |X(f)| [dB]

Figure 12.FigureSpectrum 12. Spectrum ofBLASA of BLASA MIMO: MIMO: BB == 1 MHz, 1 MHz, T = 256T = μ 256s, M µ= s,2. M = 2.

Summing up all the considered waveforms, Table 1 shows their comparison. Each algorithm is Summingchecked up to all verify the whether considered it allows waveforms, a MIMO vers Tableion, 1the shows level of their the comparison.sidelobes, the frequency Each algorithm is checkedoccupancy to verify and whether its capability it allows to be coherently a MIMO integrated. version, the level of the sidelobes, the frequency occupancy and its capabilityTable to1. Comparison be coherently of algorithms integrated. (BTOT denotes the swept frequency).

MIMO Amplitude Algorithm Sidelobe Level and Suppression Interval Table 1. ComparisonVersion of algorithms (BTOT denotes the swept frequency).Modulation Pseudo trapezoidal HNLFM No −67 dB at BT = 4096 400% AM Pure UnimodularMIMO BTOT Amplitude Algorithm No Sidelobe Level−23 dB and at BT Suppression = 4096 Interval 100% Unimodular Noise Version B−3 dB Modulation SCAN No −45 dB at BT = 4096 (within 15%) 100% Unimodular Pseudo HNLFMBLASA SISO No No −−6750 dB dB at atBT BT= 4096= 4096 100% 400% Unimodular −30 dB at BT = 256 (within 12%) if trapezoidal AM BLASA MIMO Yes 400% Unimodular unimodular amplitude with M = 2 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 SCANcross-correlation No level equal to− the45 dBauto-correlation at BT = 4096 (withinlevel. The 15%) frequency occupancy 100% gives Unimodular the information of how much the mainlobe is enlarged by the algorithm. − BLASA SISOThe SCAN Nosidelobe level refers to the50 zone dB atwithinBT = 15% 4096 of the whole length, 100%as shown in Figure Unimodular 9, while the −30 dB of BLASA −MIMO30 dB is at relatedBT = 256to the (within suppressed 12%) area if which is about 12% of the BLASA MIMO Yes 400% Unimodular whole length when two signals unimodular(M = 2) are jointly amplitude generated with withM a= unimodular 2 amplitude.

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 Figure9, 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. Aerospace 2017, 4, 15 13 of 14

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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