Complementary Pair Radar Waveforms Figure 11 shows the two complementary base-band signals using the rectangle shaped element (dash) and the GWS shaped element with M = 4 (solid). Since the GWS representation extends over 4 bits the duration of the GWS shaped complementary signal extends over 26+3 = 29 bits. In practice the transmitter and the receiver are likely to be bandwidth limited by the hardware, which will further modify the waveforms in Figure 11 as if they passed through a low-pass filter (LPF). It is therefore expected that the waveform in the upper subplots of Figures 11 and 12 will be smoothed as shown in the bottom subplot of Figure 12. Figure 13 shows the spectrum change between the original complementary signal, with rectangle element shape, and the 4 samples/bit GWS element shape after LPF. The LPF was a simple first order Butterworth filter with cutoff frequency νn = 5 / tb. We find it important to clarify that the LPF is not an intended part of the processing. It was added to represent a likely effect of the hardware's limited bandwidth. It is also important to point out that the waveform seen in Figure 12 (bottom) is the complex envelope of the signal, which happens to be real, that coherently modulates (in both amplitude and phase) a carrier frequency. Noncoherent amplitude modulation only will exclude Doppler processing and Doppler information. The next obvious question is how the bandwidth reduction affected the autocorrelation and how well the zero range-sidelobe property was preserved. The answers are given in Figures 14 and 15. Figure 14 shows the periodic autocorrelation (linear scale) of the 26 element complementary pair when the element shape is 4 samples/element GWS, followed by LPF. Note that the only deviations from the ideal zero near-sidelobes 46 Figure 11. The two complementary base-band waveforms, each with the two sequence element shapes: rectangle (dash), GWS with 4 samples per code element (solid). Figure 12. The first complementary base-band waveforms with 4 samples/bit GWS, before (top) and after LPF (bottom). IEEE A&E SYSTEMS MAGAZINE MARCH 2017