By Topic

IEEE Quick Preview
  • Abstract

SECTION 1

INTRODUCTION

True time delay (TTD) elements are critical components in beam steering within phased-array radar systems [1]. The use of TTD elements, rather than simpler phase delays, is required to prevent the angular dispersion of transmitted broadband radar beams [1], [2]. The required range of delay variations in large antenna arrays could reach tens of nanoseconds. The realization of TTD elements using radio frequency (RF) cables tends to become bulky and lossy, and is difficult to scale toward long delay variations. Alternatively, microwave-photonic (MWP) TTD implementations provide several potential advantages [3], such as low propagation loss in optical fibers, ultrabroad transmission bandwidth of several Terahertz, immunity to electromagnetic interference, availability of high-bandwidth electrooptic modulators and detectors, and potential for light-weight, small-footprint modules. Over the last 20 years, a large number of MWP TTD realizations have been proposed and demonstrated [4], [5], [6], [7], [8], [9]. The key metrics of MWP TTD elements are the product of the processed waveform bandwidth times the range of delay variations (known as the delay-bandwidth product) and the extent of distortions that are inflicted on the processed waveform. Thus far, in spite of much effort and progress, MWP TTD setups struggle to reach delay-bandwidth products above the order of unity, and at the same time comply with the stringent distortion requirements of radars. In this paper, we report the effective, long variable delay of linear frequency modulated (LFM) radar waveforms with particularly low distortions. LFM waveforms are prevalent in many radar systems due to the relative simplicity of their generation and processing and since they can be compressed into a narrow peak with low sidelobes [10], which is referred to as the impulse response function. The impulse response of 500-MHz-wide waveforms is delayed by as long as ±50 ns, representing a delay-bandwidth product of 50. The relative delay and advancement of the impulse response are continuously variable. The ratio of the primary peak to the highest sidelobe of the processed impulse response (peak-to-sidelobe ratio, or PSLR), which quantifies the extent of noise due to a point interference, is 18 dB or higher. The ratio of energy within the primary correlation lobe to the integrated energy outside it (integrated sidelobe ratio, ISLR), which is a measure of noise due to distributed interference, is better than 20 dB. The delay principle is suited specifically to LFM signals, and it relies on their inherent ambiguity between a frequency offset and a temporal delay [11]. The obtained ISLR is 14 dB better than that of our earlier demonstration [11], which was severely restricted by multiple pronounced sidelobes in the impulse response function. The results demonstrate for the first time, to the best of our knowledge, a long MWP TTD of real-world radar waveforms with sufficient fidelity.

SECTION 2

PRINCIPLE OF OPERATION

An LFM waveform of duration Formula$T$, bandwidth Formula$B$, and central radio frequency Formula$f_{\rm RF}$ can be expressed as Formula TeX Source $$A_{\rm LFM}(t) = A_{0}\cos\left(2\pi f_{\rm RF}t + \pi{B \over T}t^{2}\right){\rm rect}\left({t \over T}\right)\eqno{\hbox{(1)}}$$ where Formula$A_{0}$ is a constant magnitude, Formula$t$ denotes time, and Formula${\rm rect}(\xi) = 1$ for Formula$\vert\xi\vert\leq 0.5$ and equals zero elsewhere. The instantaneous frequency Formula$f(t)$ of the waveform is linearly sweeping between Formula$f_{\rm RF}\pm (1/2) B$ along the waveform duration Formula$T$. The same waveform delayed by Formula$\tau$ is given by Formula TeX Source $$A_{\rm LFM}(t - \tau) = A_{0}\cos\left[-2\pi f_{\rm RF}\tau + \pi{B \over T}\tau^{2} + 2\pi\left(f_{\rm RF} - {B \over T}\tau\right)t + \pi{B \over T}t^{2}\right]{\rm rect}\left({t - \tau \over T}\right).\eqno{\hbox{(2)}}$$

The delayed waveform is approximated by the introduction of a phase offset Formula$\Delta\varphi$ and a frequency offset Formula$\Delta f$ to (1) so that [11] Formula TeX Source $$A_{\rm LFM}^{\rm offset}(t) = A_{0}\cos\left[\Delta\varphi + 2\pi \left(f_{\rm RF} + \Delta f\right)t + \pi{B \over T}t^{2}\right]{\rm rect}\left({t \over T}\right).\eqno{\hbox{(3)}}$$

Provided that Formula TeX Source $$\eqalignno{\Delta f = &\, -{B\tau \over T}&\hbox{(4)}\cr \Delta\varphi = &\, -2\pi f_{\rm RF}\tau + \pi {B\tau^{2} \over T}.&\hbox{(5)}}$$

When (4) and (5) are met, differences between (3) and (2) are confined to the edges of the rectangular temporal window, which is not delayed. As long as Formula$\tau\ll T$ (or, equivalently, Formula$\Delta f\ll B$), the differences between the offset waveform and the “truly delayed” one are negligible. Since Formula$T$ typically equals many microseconds, substantial delays to the impulse response are possible without excessive distortion. The impulse response function of the offset waveform is calculated as its cross-correlation with a replica of the original signal [1] Formula TeX Source $$h(\xi) = \int\limits_{- \infty}^{\infty}A_{\rm LFM}(t)A_{\rm LFM}^{\rm offset}(t + \xi)\, {\rm d}t.\eqno{\hbox{(6)}}$$

Both waveforms are often windowed in order to suppress the correlation sidelobes.

In MWP implementations, the RF LFM waveform is used to modulate an optical carrier, and is later recovered through the beating of the optical carrier and the modulation sidebands on a photodetector. The photonic realization of our proposed TTD method therefore requires that relative Formula$\Delta\varphi$ and Formula$\Delta f$ offsets are generated between carrier and sidebands. To that end, the optical carrier of frequency Formula$f_{\rm opt}$ is split in two paths. Light in one path is modulated in suppressed-carrier single sideband (SC-SSB) manner to retain only one modulation sideband which carries the LFM waveform and is subsequently offset in phase and frequency. The original, unmodulated carrier is retained in the other path, and the two are recombined prior to detection. The processing of a single optical sideband was previously employed in several MWP TTD demonstrations [2], [8], [12], [13]. The delay of single-sideband analog waveforms benefits from piece-wise treatment [2]: Since Formula$f_{\rm RF}\gg B$, it is sufficient for a MWP setup to provide an appropriate spectral phase across the window Formula$[f_{\rm opt} + f_{\rm RF} - (1/2)B, \, f_{\rm opt} + f_{\rm RF} + (1/2)B]$, and at the carrier frequency Formula$f_{\rm opt}$ itself, and the spectral phase at all other optical frequencies need not be specified. The above technique for the TTD of LFM waveforms may be regarded as a specific case of this principle, which takes advantage of the particular attributes of the waveform.

In our earlier demonstration [11], the frequency offset was implemented via an electrooptic phase modulator that was driven by a ramp waveform of magnitude Formula$2V_{\pi}$ and period Formula$1/ \Delta f$. Discontinuities and deviations from the ideal ramp shape generated high-order harmonics of the phase modulation, which resulted in multiple, periodic secondary correlation peaks. Although 500-MHz-wide LFM signals were delayed by as much as 250 ns [11], the ISLR levels were unacceptable: as low as only 7 dB for a 100-ns delay. Here, frequency offsets are directly implemented using an acousto-optic modulator (AOM) that is driven by a sine wave of frequency Formula$f_{\rm AOM}$. In an AOM, a piezoelectric transducer is used to drive an ultrasonic acoustic wave through an optical medium. Part of the power of an incident optical beam is deflected by the acoustic wave via spontaneous Brillouin scattering, and collected into an output fiber port [14]. The deflected beam is offset in frequency by Formula$f_{\rm AOM}$. The AOM is designed to operate at a nominal drive frequency of Formula$f_{{\rm AOM}, 0}$, and we consider the timing of the impulse response that is obtained using that nominal drive frequency as our zero delay reference. Relative delay or advancement of the impulse response are obtained through deviations of the driving frequency: Formula$\Delta f = f_{\rm AOM} - f_{{\rm AOM}, 0}$. Since the angle of deflection varies with the driving frequency [14], the usable range of Formula$\Delta f$ is limited to deviations of only a few Megahertz from Formula$f_{{\rm AOM}, 0}$. Nevertheless, this range of frequencies is sufficient to delay or advance the impulse response of LFM waveforms by tens of nanoseconds, as expressed in (4). As described next, the use of an AOM reduces the impulse response sidelobes and drastically improves its ISLR. In addition, the AOM requires a simpler waveform generator. The introduction of a phase bias according to (5) would require an electrooptic phase modulator in series with the AOM. Unlike the previous demonstration [11], phase modulation would only need to compensate for slow environmental drifts.

SECTION 3

EXPERIMENTAL SETUP AND RESULTS

Fig. 1 shows the experimental setup for the variable delay of the impulse response of LFM waveforms with suppressed sidelobes. The output of a continuous wave (CW) laser diode is split in two paths. Light in the upper path is amplified and then modulated by an electrooptic amplitude modulator, driven by an LFM waveform Formula$(T = 5 \ \mu\hbox{s}, B = 500 \ \hbox{MHz})$ from the output of an arbitrary waveform generator (AWG). The LFM's central frequency is up-converted to Formula$f_{\rm RF} = 7.5 \ \hbox{GHz}$ using an RF mixer. The modulated optical waveform is brought into SC-SSB format using a narrow fiber Bragg grating (FBG), which reflects only a single optical sideband back into the fiber path and removes the optical carrier and the complementary sideband. The remaining sideband is frequency-offset by an AOM, that is driven by a sine wave of magnitude Formula$V$ and frequency Formula$f_{\rm AOM}$. The nominal drive frequency of the AOM used in the experiment is 40 MHz. The processed sideband is combined with the original optical carrier, which is retained in the lower path (see Fig. 1). A modified electrical LFM waveform is reconstructed through the beating of the carrier and sideband on a broadband detector. The detected waveform is down-converted to an intermediate central frequency of 1 GHz and sampled by a real-time oscilloscope of 6 GHz bandwidth. The impulse response of the waveform is calculated by cross-correlating the sampled signal against a reference waveform, which was acquired at the AWG output. Both waveforms were filtered by an optimized Hanning window for sidelobe suppression.

Figure 1
Fig. 1. Experimental setup for the variable delay of the impulse response of linear frequency modulated waveforms. CW: continuous wave. EDFA: erbium-doped fiber amplifier. PC: polarization controller. IF: intermediate frequency (Formula$\sim$1 GHz). RF: radio frequency (Formula$\sim$7.5 GHz). LO: radio-frequency local oscillator (6.5 GHz).

Fig. 2 shows the experimental impulse response functions, which had been obtained for five values of Formula$f_{\rm AOM}$ in the range of 35–45 MHz. A relative delay of the impulse response by as much as ±50 ns is evident, in agreement with (4). The delay was restricted by the reduced efficiency of the AOM at drive frequencies that are far detuned from its predesigned value of 40 MHz. For all values of Formula$\Delta f$, the full-width at half-maximum (FWHM) of the impulse response main lobe, signifying resolution, was 2 ns. The PSLR of all impulse response measurements was higher than 18 dB, and the ISLR was better than 20 dB. Our earlier work, which employed ramp phase modulation, had reached longer delay variations of 0–250 ns with equal resolution and PSLR [11]. However, the ISLR for delay variations larger than 20 ns were unacceptably low, between 7–9 dB [11]. The application of an AOM eliminated the multiple periodic correlation sidelobes that hindered the performance of the earlier setup. The remaining sidelobes stem from a residual incident beam that is not shifted, as well as from anti-Stokes and higher order scattering in the AOM. The drive voltage Formula$V$ was adjusted to minimize the sidelobes. The range of frequency offset values Formula$\Delta f$ may be increased, in principle, with the construction of double-pass AOM in which the angle of beam deflection remains fixed. Note that the bias phase Formula$\Delta\varphi$ was not controlled in the experiment. Bias phase adjustments would be mandatory in beam steering experiments involving multiple elements to avoid spatial distortion [2].

Figure 2
Fig. 2. Measured, normalized impulse responses of 500-MHz-wide, 5- Formula$\mu\hbox{s}$-long LFM waveforms. The frequency offsets Formula$f_{\rm AOM}$ (in MHz) are 35 (blue), 38 (red), 40 (green), 42 (black), and 45 (magenta). A magnified view of the primary correlation peaks is shown in the inset.
SECTION 4

CONCLUSION

The variable delay and advancement of the impulse response of LFM waveforms by ±50 ns was demonstrated experimentally. The delay-bandwidth product of the experimental demonstration is 50. For the first time, such long MWP TTDs of real-world radar waveforms are achieved with the high fidelity that is required in system applications. The method is suitable for providing the delays required in large phased-array antennas. The technique is applicable to the processing of LFM waveforms with arbitrary bandwidths and central RFs. Ongoing work is dedicated to the extension of the technique to the processing of additional waveforms, such as nonlinear frequency modulated (NLFM) radar signals.

Footnotes

Corresponding author: A. Zadok (e-mail: Avinoam.Zadok@biu.ac.il).

References

No Data Available

Authors

No Photo Available

Yonatan Stern

No Bio Available
No Photo Available

Ofir Klinger

No Bio Available
No Photo Available

Thomas Schneider

No Bio Available
No Photo Available

Kambiz Jamshidi

No Bio Available
No Photo Available

Avi Peer

No Bio Available
No Photo Available

Avi Zadok

No Bio Available

Cited By

No Data Available

Keywords

Corrections

None

Multimedia

No Data Available
This paper appears in:
No Data Available
Issue Date:
No Data Available
On page(s):
No Data Available
ISSN:
None
INSPEC Accession Number:
None
Digital Object Identifier:
None
Date of Current Version:
No Data Available
Date of Original Publication:
No Data Available

Text Size