Radar Performance of Ultra Wideband Waveforms

1. Introduction

In the early days of radar, range resolution was made by transmitting a short burst of electromagnetic energy and receiving the reflected signals. This evolved into modulating a sinusoidal carrier into transmitting pulses at a given repetition interval. To get higher resolution in the radars the transmitted pulses got shorter and thereby the transmitted spectrum larger. As will be shown later the Signal-to-Noise Ratio (SNR) is related to the transmitted energy in the radar signal. The energy is given by the transmitted peak power in the pulse and the pulse length. Transmitting shorter pulses to get higher range resolution also means that less energy is being transmitted and reduced SNR for a given transmitter power. The radar engineers came up with radar waveforms that was longer in time and thereby had high energy and at the same time gave high range resolution. This is done by spreading the frequency bandwidth as a function of time in the pulse. This can be done either by changing the frequency or by changing the phase.

If the bandwidth is getting large compared to the center frequency of the radar, the signal is said to have an Ultra Wide Bandwidth (UWB), see (Astanin & Kostylev, 1997) and (Taylor, 2001). The definition made by FFC for an UWB signal is that the transmitted spectrum occupies a bandwidth of more than 500 MHz or greater than 25% of the transmitted signal center frequency. UWBsignals have been used successfully in radar systems for many years. Ground Penetrating Radar (GPR) can penetrate the surface of the ground and image geological structures. Absorption of the radar waves in the ground is very frequency dependent and increases with increasing frequency. Lower frequencies penetrate the ground better than higher frequency. To transmit a low frequency signal and still get high enough range resolution calls for a UWB radar signal. The interest in using UWB signals in radar has increased considerably after FFC allocated part of the spectrum below 10 GHz for unlicensed use. Newer applications are through the wall radar for detecting people behind walls or buried in debris. Also use of UWB radar in medical sensing is seeing an increased interest the later years.

UWB radar signal may span a frequency bandwidth from several hundred of MHz to several GHz. This signal bandwidth must be captured by the radar receiver and digitized in some way. To capture and digitize a bandwidth that is several GHz wide and with sufficient resolution is possible but very costly energy and money wise. This has been solved in the impulse waveform only taking one receive sample for each transmitted pulse. In the Step-Frequency (SF) waveform the frequencies are transmitted one by one after each other. A general rule for UWB radars is that all of the different waveform techniques have different methods to reduce the sampling requirement. The optimal would be to collect the entire reflected signal in time and frequency at once and any technique that is only collecting part of the received signal is clearly not optimal.

This chapter will discuss how different UWB waveforms perform under a common constraint given that the transmitted signal has a maximum allowable Power Spectral Density (PSD). The spectral limitations for Ground Penetration Radars (GPR) is given in Section 2 together with a definition on System Dynamic Range (SDR). In Section 3 a short presentation on the mostly used UWB-radar waveforms are given together with an expression for the SDR. An example calculation for the different waveforms are done in Section 4 and a discussion on how radar performance can be measured in Section 5.

2. Radar performance

There are different radar performance measures for a given radar system. In this chapter only the SDR and related parameters will be discussed. Another important characteristic of a radar waveform is how the radar system behave if the radar target is moving relative to the radar. This can be studied by calculating the ambiguity function for the radar system. In a narrow band radar the velocity of the radar target gives a shift in frequency of the received waveform compared to the transmitted one. For a UWB-waveform the received waveform will be a scaled version of the transmitted signal. This is an important quality measure for a radar system but will not be discussed in this chapter.

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