# FMCW radar beat resolution with target spectral width, non-linearity and receiver resolution

The question is about resolution of FMCW radars whcich send triangular frequency waveform, receive it's echo then mix it with sent signal, extract beat frequency. The beat frequency is proportional to range and can be to speed. Then the range is extracted from FFT of signal. OK, what's the question?

Question:

In Article "Receiver Frequency Resolution for Range Resolution in Homodyne FMCW Radar, 1993" have told :

Beat frequency resolution is limited by the convolution of the target spectral width with the receiver frequency resolution

1.Exactly what is target spectral width, and why this convolving to receiver?

It also tells for sawtooth infrequency domain waveform:

beat frequency signal is a train of pulses of length Tm-td repeating every Tm.

Note: Tm is sweeps time duration.

2.Why removing nonlinearity will cause: $$\Delta f_t=\Delta f_r$$

3.Why non-linearity will cause spectral width to widen? I know hoe it effects $$f_b$$(because we then have multiple values of $$\Delta f_t$$, described in "Understanding millimeter wave FMCW radar" article), but don't how it effect on $$\Delta f_t$$?

What I've don: 1)I've read the book "Design of CW multi-frequency radar" but the related section is really ambiguous. 2)I know there is new book called "Design of FMCW radar" but I don't have access to that. 3)Also the mentioned article does not referenced this concept.

I only know why the receiver resolution is 1/Ts, it's because signal duration in time is inverse to spectrum width, one of the Fourier transform property.