Another basic factor in radar’s operation is the range resolution. It determines the ability of the radar to distinguish between two targets [100]. Before formulating the range resolution, it is necessary to first introduce and determine the unambiguous range of a radar and its bandwidth.
By considering ⌧ as the two-way propagation delay time, which accounts for the time between the emission of the electromagnetic wave from the radar’s transmitter and the reflected wave coming back to the radar’s receiver, the maximum unambiguous range of a radar can be written as
Rmax =
c · ⌧
2 (2.12)
where c is the speed of light. In this equation, Rmax represents the maximum range
from which a transmitted radar signal, or pulse, can be reflected and received before the next pulse is transmitted. The range is measured by the time delay between pulse transmission and reception, ordinarily assuming that the received pulse is associated
Chapter 2. Fundamentals of FMCW MIMO Radars 25 with the most recent transmitted pulse. Therefore, targets at ranges beyond Rmax,
appear at closer ranges because of range folding. Special coding of the pulses permits discrimination between echoes from the most recent transmitted pulse and earlier ones, enabling the measurement of ranges beyond the maximum range.
Additionally, other considerations have to be made regarding the maximum unambigu- ous range, since a sampling is usually performed at the radar’s receiver side, in order to bring the signals from analogue to digital domain. This is mandatory, in order to per- form further radar digital signal processing, beam-forming and, therefore, radar image reconstruction.
Considering a sampling frequency fs, a limit on the maximum resolvable frequencies
that can be sampled, is imposed [101], which sets a maximum range of
rmax =
c0 · ∆f
2dtB (2.13)
where ∆f is half the sampling frequency, B is the operational bandwidth of the radar’s system and dt is the radar signal duration.
The bandwidth B of a radar’s signal, is one of the most important parameters to take into account when designing a radar system. This is due to the fact that the bandwidth is proportional to the range resolution performance of the radar. The larger the bandwidth, the narrower the spectrum peak and the higher performance in the range resolution can be achieve. There are two different bandwidth types that can be defined, the signal’s bandwidth, which is regulated by the pulse’s width of the signal or by its modulation, and the radar’s bandwidth. If the system requires a big resolution in range to differentiate among targets, the bandwidth needs to be large. As a matter of fact, the range resolution is proportional to the inverse of the bandwidth, and it’s defined by the relationship
∆R = c
2 · B (2.14)
where, as previously introduced, B denotes the bandwidth of the radar’s signal. The range resolution basically defines the ability of a radar system to discriminate between different targets, in the range direction. Equation2.14 can be linked to previously pre- sented concepts. For a basic pulsed radar, the bandwidth is approximately proportional to the inverse of the pulse width B = 1/⌧ , where ⌧ corresponds to a distance, as per equation 2.12, which considers that radars deal with round-trip timing measurements. Most modern radars will use a form of pulse compression in order to use longer pulses, hence with more energy, and obtain a Signal to Noise Ratio (SNR) boost while still retaining ideal range resolution. In this instance, the pulse width is no longer propor- tional to the bandwidth, since a swept frequency is used to increase the bandwidth, like in the case of FMCW radars. However, the above expression is still valid for calculating the range resolution. For CW radars, the ability to measure the range is dependent on using a swept FM modulation on the CW signal, and, again, the range resolution is still dependent on the bandwidth used for that ranging modulation.
Chapter 2. Fundamentals of FMCW MIMO Radars 26 is very small compared to the operating center’s frequency. This allows all of the com- ponents to be narrowband components which means that power amplifiers, filters, and other internal components, only have to be linear over a very small frequency range. Im- plementing wide-band or ultra-wide band signals is not trivial, but today’s technology and digital processing is making it more accessible. A wide-band design is more com- plicated, because all the radar’s internal components, including the channel in between the radar and the target, have to be linear over a much wider frequency range. The more wide band the radar is, the better the range resolution achieved, but at the same time, the harder it gets to design and implement such systems. Therefore, if a very high resolution is required, higher carrier frequencies have to be considered. For example, for an FMCW radar operating at a frequency of 16 GHz to 17 GHz, with a 1 GHz bandwidth signal, the range resolution is 15 cm. Factors which could limit the range resolution of a radar systems, are the non linearity of some of the internal components and, especially, the cutting and windowing of the radar signals in the digital processing procedures.