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Design Article

# Simulation, test of stepped frequency radar systems

## 10/17/2012 11:06 AM EDT

In any radar receiver, the received echo signals contain the target return and background clutter. Detection of the target in an environment with background clutter requires high range and cross-range resolution in the radar system. The traditional way to accomplish this goal involves use of short duration pulse waveforms and wideband-FM pulses. However, this approach requires a complex system architecture and results in higher implementation cost due to its wideband receiver usage. Another way to achieve high range resolution, without increasing system complexity, is to employ Stepped Frequency Radar (SFR), a scheme well known for its use in non-destructive testing and ground searching applications.

With SFR, the echoes of stepped frequency pulses are synthesized in the frequency domain to obtain wider signal bandwidth. Using frequency hopping, both high resolution and a high signal-to-clutter ratio can be received. Because of its high resolution and low cost it is today widely used in both the commercial and aerospace/defense (A/D) industry. However, it is very difficult to get an analytical solution for SFR receiver performance in the presence of background clutter caused by reflections from ground, structures, vegetation, and so on. As a result, simulation becomes more important. Using it to accurately design, verify and test SFR systems under real-world environments has become absolutely essential.

Understanding SFR

To better understand why SFR is so advantageous, first consider the pulse radar waveform shown in Figure 1 (left-most image).

Figure 1: On the left is a pulse radar waveform. The right-most image depicts a SFR waveform.
Assuming the pulse width is τ and the bandwidth of the signal is ƒ0= 1/ τ, the range resolution, Rs, can be calculated as
(1)

where c is the velocity of the light.

As an example, assuming the pulse width τ = 0.25 µs and the pulse repetition interval T = 10 µs, the range resolution would be 37.5 m. For a resolution of less than 1 meter, from (1) the pulse duration would have to be shortened to say, T = 3.9 ns. The resulting range resolution would then be 0.58 m and instead of handling a 4-MHz bandwidth the new system bandwidth would be 250 ns/3.9 ns = 64 wider than the original system bandwidth.

To achieve a high resolution at the 0.58 m without reducing the pulse duration, SFR could be employed. As shown in Figure 1, SFR transmits sequences of N pulses at a fixed pulse-repetition frequency, but not at a fixed radar frequency. Unlike the pulse signal, each pulse in the sequence of a stepped frequency waveform has the same pulse width and time duration, but different carrier frequency. That frequency is given by fi = fo+N*dF, where dF is the amount of frequency increased, indicating that frequency hopping and time division are used.

Assuming the N-step stepped frequency is used, the pulse width and pulse repetition interval are still τ = 0.25 µs and T = 10 µs where N = 64, as from the previous example, and dF = 4 MHz, the resulting range resolution bandwidth would be Rs = c/{2*(ƒo+(N-1)*dF)} = 0.58 m. As is clearly evident from this result, SFR has a high range resolution (less than one meter). Moreover, it was achieved without having to shorten the resolution, making it preferable to pulse radar in this scenario.