However, the bandwidth of main lobe beam is not included in this model.
If we zoom in this PSD around the central frequency f c, in Figure 16, we could find the main lobe, i.e., the bandwidth occupied is approximately 411-389≈22 Hz, which is near to that estimated using nested sampling and is much narrower than that 32 Hz of the PSD of the original QPSK signal.
Similarly, if we zoom in this PSD around the central frequency f c, in Figure 14, we could find the main lobe, i.e., the bandwidth occupied is approximately 409-391≈18 Hz, which is much narrower than that 32 Hz of the PSD of the original QPSK signal.
The main lobe of the sinc function has a bandwidth equal to 1/((M + μ T).
Owning to the limited signal bandwidth, there might be certain width in the main lobe of the echo of scattering point after range compression and many side lobes, which would add to the difficulty in actual detection and bring unfavorable influence for imaging, such as the loss of real scattering point, production of fake scattering point, etc.
The width of the main lobe is inversely proportional to the number of subcarriers N or equivalently the bandwidth.
A TFD is considered to have the best energy concentration for a given multicomponent signal if for each signal component, it yields the smallest instantaneous bandwidth relative to component IF and the smallest side lobe magnitude relative to main lobe magnitude.
As we know, the width of the main lobe of the wavelet depends on the relative high-frequency energy and broadening the low-frequency bandwidth can effectively reduce the amplitude of wavelet side lobes (Kroode et al. 2013; Liu et al. 2013).
By changing different N1 and N2 pairs, as shown in Figure 17, it is obvious that for N1 fixed to N1 = 3, with the increase of the value of N2 from 5,7 to 13, the main lobe of the estimated PSD using nested sampling structure becomes narrower significantly, i.e., the bandwidth occupied gets smaller.
Figure 2 shows a case directional antenna gain in main lobe, side lobes, and back lobe.
