Radar emission spectrum engineering Shannon D. Blunt 1 , John Jakabosky 1
1.3 LINC-optimized waveforms
In [2], one of the proposed challenge problems for spectrum engineering and waveform diversity is joint waveform/transmitter design. Instead of the usual component-wise perspective often taken in engineering, this holistic perspective presents the opportunity to exploit synergistic attributes of the waveform and transmitter akin to what is observed in nature (e.g., [50]), with the potential to realize new combinations and capabilities.
For instance, it is well known that the ability to modulate the amplitude of a radar waveform provides greater design freedom to achieve enhancements such as reduced range sidelobes (e.g., via tapering of LFM [1]) and better spectral containment (e.g., weighted series expansion of a binary-coded waveform [1]).
However, AM effects are rather difficult to maintain through a saturated PA, necessitating the means to linearize this non-linear device [24,44]. There are many different ways to achieve this goal, including outphasing, envelope track- ing, the Doherty technique, the Kahn technique, feedback linearizers, feedfor- ward linearizers and predistortion [24], along with numerous variants. As such, one can envision the transmitter architecture as being comprised of a set of parameters that, collectively with the parameterization of the waveform such as in (1.1)–(1.3), represent a rich design space from which to consider the notion of joint optimization.
As a pertinent example, linearization techniques could be used to slow down the rapid rise-/fall-time of a radar pulse which, for a spectrally well-contained waveform (e.g., most FM waveforms), is the limiting factor for spectral contain- ment of the overall emission (Figure 1.17). In principle, this task can be readily addressed by applying an amplitude taper onto the transmitted pulse. However, for a high-power radar in which the operation during the pulse rise/fall can be likened to the operation of a switch, such a task becomes more complicated.
To address this problem, consider the outphasing approach, otherwise known as linear amplification using non-linear components (LINC) [24]. Figure 1.18 illustrates the LINC architecture using a 180 hybrid coupler in which the sum (S) output terminal provides the addition of the two input signals and the difference (D) output terminal realizes the subtraction of one input signal from the other. Mathe- matically, the application of an amplitude taper onto a desired waveforms(t) can be represented as [35]
s1ðtÞ ¼sðtÞ (1.11)
s2ðtÞ ¼sðtÞexpfjfðtÞg (1.12)
where
fðtÞ ¼cos12w2ðtÞ 1
(1.13) is the phase adjustment between the two input waveforms needed to generate the real-valued amplitude taperw(t). The resulting output waveform on the sum (S) channel is thus
sSðtÞ ¼s1ðtÞ þs2ðtÞ ¼sðtÞwðtÞexpfjyðtÞg (1.14) in which
yðtÞ ¼tan1
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1w2ðtÞ p
w2ðtÞ
!
(1.15) is the residual phase response that results from combining the two waveforms in this LINC configuration. The signal produced on the difference (D) terminal can either be directed into a matched load or may be recycled to improve overall power efficiency [51].
–80–20 –70 –60 –50 –40
Normalized power (dB)
–30 –20 –10
Spectrum of waveform with
pulse envelope Spectrum of
waveform alone 0
–15 –10 –5 0
Frequency (MHz)
+5 +10 +15 +20
Figure 1.17 Notional spectral content of a 64ms pulse modulated with an LFM waveform of 1 MHz bandwidth (with and without inclusion of the pulse rise/fall)
1 SΣ (t)
S1(t)
S2(t) SΔ (t)
Σ
2 Δ
Figure 1.18 LINC transmitter implementation using a 180 hybrid coupler [35]
It is important to note that, because the weighting and associated residual phase response modify the underlying waveform sðtÞ it is necessary to optimize the resulting emissionsSðtÞto account for these effects along with any other transmitter distortion. In [35] an LFM waveform withBT¼64 has a Tukey taper applied via this LINC method such that the pulse rise/fall effectively occur during the first and last quarter of the pulse. The hardware setup is the same as for the results in Figure 1.13 from the previous section, aside from the addition of the 180 coupler and a second AWG. Per Figure 1.19 that was captured with a real-time spectrum analyzer (RSA), the taper provides about 15 dB of additional spectral containment in the out-of-band region. Of course, the Tukey taper is convenient to use because its amplitude rolls off to zero at the edges, but this taper is actually not well-suited for LFM, with the tapered waveform yielding a PSL of only16.4 dB.
It was shown in [35] that performing HiLo optimization for this hardware configuration, initialized with the tapered LFM waveform, can reduce the PSL to 42.8 dB, an improvement of 26.4 dB. Figure 1.20 depicts the associated RSA captured spectrum when HiLo optimization is performed, both with and without the Tukey taper. It is thus observed that a significant reduction in PSL can be achieved while still preserving the roughly 15 dB improvement in out-of-band suppression.
Using the associated matched filter, this particular taper resulted in an SNR loss of 3.2 dB, which clearly is not feasible for many sensing applications. Further, to realize the substantial tapering at the rise/fall edges of this 64ms pulse, where better than 30 dB suppression was achieved, picosecond level timing calibration was needed to ensure sufficient synchronization between the two AWG-generated pulsed waveforms. Without this degree of timing calibration the HiLo optimization could not converge due to drift (as determined in preliminary experimentation using lower fidelity AWGs). However, this proof of concept does demonstrate the potential for Figure 1.19 LFM spectrum with (lower trace) and without (higher trace)
Tukey taper, vertical increments are 10 dB (2014 IEEE, reprinted with permission from [35])
enhanced control over radar emissions, as a means to realize better spectral con- tainment and to start realizing the practical potential of waveform diversity.