# Towards mmWave Altimetry for UAS: Exploring the Potential of 77 GHz Automotive Radars
## 5 Operational Requirements and Radar Specifications
### Maximum and Minimum Measurable Altitude  
The determination of the minimum altitude is tied to the resolution of the range bin and the application of a high-pass filter to mitigate coupling effects from the Tx chain. This is an inherent challenge as the Tx and Rx chains operate simultaneously in FMCW radars. Owing to a wavelength, \(\lambda\), of 3.9 mm at the 77 GHz operating frequency, even with an antenna separation of 10\(\lambda\), the high-pass filter can be conveniently programmed to filter out the coupling effects. Although the concept of the range bin is related to the signal-processing domain, it is important to discuss it in the context of the minimum measurable altitude. A range bin is the smallest measurable unit by a radar. It may be interchangeably used with the range resolution as per the discussion in Section 5.2. It is governed by the ADC sampling rate, \(F_{s}\), chirp slope, \(S\), and size of the FFT, \(N_{FFT}\)[28; 46]. The mathematical expression is as follows:  
\[\Delta R(F_{s},N_{FFT},S)=\frac{cF_{s}}{2 SN_{FFT}}. \tag{44}\]  
Nevertheless, this raises the question about the necessity of having two distinct expressions for the range resolution, (20) and (44). Each equation holds its validity within its context. Achieving the range resolution as defined by Equation (20) requires adjusting the parameters in Equation (44) accordingly. It explicitly signifies that a higher-order FFT is bound to enhance the separation of the frequency components in a time-domain signal, resulting in a finer range resolution. In essence, Equation (20) delineates the range resolution based on the chirp BW of the waveform provided that the signal-processing chain, accordingly, offers the required FFT size. Accordingly, \(\Delta R\) can be expressed in terms of (20) and (44) as  
\[Alt_{acc}\geq Max\bigg{(}\frac{cF_{s}}{2 SN_{FFT}},\frac{c}{2B}\bigg{)}. \tag{45}\]  
The readings, starting from the DC range bin to the \(m\)th range bin, with \(m\Delta R\) corresponding to the Tx and Rx antenna separation, are to be removed from the altitude measurement. This necessitates a lower bound for the minimum measurable altitude. For a separation between the Tx and Rx antenna, \(\Delta x\), the value of the range bin indices to be removed can be given as  
\[m=Roundup\bigg{(}\frac{\Delta x}{\Delta R}\bigg{)}. \tag{46}\]  
where \(Roundup\) is rounding off the decimal value to the next nearest integer. The minimum measurable altitude, \(Alt_{min}\), can then be given as a lower bound:  
\[Alt_{min}\geq m\Delta R. \tag{47}\]  
For mmWave frequencies, \(R_{min}\) is much smaller than the requirements specified in the reference MOPS. However, for small-sized drones flying at low altitudes, the requirement may be stringent. The radiation patterns of an antenna are impervious to the distance from the source only in the far-field region. Therefore, any interference from a nearby radiating source in the near field and Frensel region is likely to cause destructive or constructive inference and affect the far-field radiation pattern [64]. This commands the Tx and Rx antennae to be separated at least by a distance, \(\Delta y\), dictated by the following expression  
\[\Delta y\geq\frac{2L^{2}}{\lambda}. \tag{48}\]  
where \(L\) is the largest dimension of the antenna and \(\lambda\) is the wavelength. This separation requirement is significantly higher for the 4.2-4.4 GHz band, owing to the large wavelength. Subsequently, filtering the coupling signature from the Tx antenna requires a high-pass filter with a greater cut-off frequency followed by a higher value of the minimum measurable altitude. Nonetheless, this is another inherent benefit of mmWave FMCW radars coupledwith a simultaneous transmit and receive operation--very low altitudes can be reported accurately unlike the Pulse Doppler counterpart. The far-field region of a microstrip patch antenna designed for 77 GHz allows the Tx and Rx antennae to be placed in close proximity, enabling a relaxed lower bound on the altitude measurement.