The generation of signals for radar system testing is challenging due to the complexities associated with carrier frequency generation, intricate modulation schemes and periodic (pulsed) waveforms; while the ability to accurately emulate real-world targets and conditions is essential to the thorough evaluation of radar devices and designs. Historically, radar signal generation has been accomplished with a baseband signal generator and an RF/microwave modulator. With up to 50 GS/s sampling rate at 10 bits vertical resolution, however, today’s new arbitrary waveform generators (AWG) offer the performance needed for direct generation of fully modulated RF/microwave signals. Before looking more closely at the use of AWGs for radar testing, let’s first explore some of the characteristics of radar signals.
Radar Signal Characteristics
Carrier frequencies used in radar systems cover most of the usable radio frequency spectrum, ranging from very low frequencies required for long range and over-the-horizon surveillance radar up to millimeter wave used in some high-resolution, small size military and civilian radar. Most radar systems, however, operate at frequencies less than 18 GHz (Ku-Band).
Signal types may be divided into the two main groups:
- Pulsed RF: The signal consists of periodic bursts of an RF carrier, modulated or not (simple pulse radar systems). The rate that pulses are generated is known as the pulse repetition frequency (PRF) and the period (1/PRF) is known as the pulse repetition interval (PRI).
- Continuous Wave (CW): The RF signal is continuous and range is established through time markers carried by the transmitted signal. FM modulation is a popular way to measure distance, as the instantaneous frequency received from the target depends upon its range from the transmitter.
- For pulsed RF radars, PRF may be fixed or it may vary over time for a number of reasons, which may include:
- Resolving echo (range) ambiguity. The ability to unambiguously determine the range of a target is limited by the PRI. A target located at a distance for which the round trip time of a transmitted pulse exceeds the PRI can be mistakenly positioned in range relative to the nearest transmitted pulse. This can be resolved by varying the timing of consecutive pulses, changing the position of subsequent radar returns.
- Overcoming the “Doppler Dilemma.” Radar systems use the Doppler effect to measure target velocity and/or reduce interference due to clutter. The physics behind the Doppler effect produces “blind speeds” for specific target velocities. Changing the PRF can change the location of these “blind speeds,” enabling the detection of previously invisible targets. Some radar systems switch between a high PRF to avoid blind speeds for expected target velocities and a slower one optimized to avoid range ambiguity.
- Protecting against jamming. A variable PRI, often combined with complex stagger sequences, allows easier discrimination between echoes caused by a given radar and those created by other radars operating in the same frequency band or by interference caused by intentional jamming.
For pulsed RF radar waveforms, the transmitting frequency may be fixed or variable (frequency agile). This takes the form of frequency hopping patterns. These patterns are complex, non-predictable, and typically non-repeating (or repeating over extremely long periods of time). The carrier frequency may even change for each transmitted pulse.
Since radar range is maximized as power increases while spatial resolution improves as pulses become narrower, pulse-compression techniques are widely used. The pulse compression techniques increase range resolution by transmitting longer pulses (increasing average power for a given peak power), while echo processing at the receiver results in much better spatial resolution by “compressing” the pulse through correlation or dispersion processing. There are two main pulse compression techniques:
- FM chirp. This consists of fast frequency sweeps that may be linear (LFM) or nonlinear (NLFM). NLFM has some advantages regarding bandwidth, resulting in better sensitivity and lower noise levels at the receiver.
- Phase modulation. Each pulse is composed of a series of shorter pulses where the carrier phase is controlled by some low autocorrelation binary sequence of symbols. While average power is controlled by the total duration of the sequence, spatial resolution depends on the duration of each symbol. In binary-phase coding, the carrier phase changes between 0 and 180 degrees; the Barker code is a very popular example. Polyphase pulse compression applies the same basic idea but the carrier phase takes on more than two values.
An important issue for some radar systems is carrier phase coherence. In some systems, such as those employing a high-performance coherent Moving Target Indicator (MTI) architecture, phase coherence must be preserved between consecutive pulses. Regardless of the phase characteristics of the transmitted pulse, returning echoes are a superposition of signals with a variety of relative phases. There are multiple target echoes with arbitrary delays, multiple echoes from the same target with different time of arrival due to multi-path, all kinds of clutter, and frequency shifts caused by the Doppler effect. The instantaneous amplitude and phase for a given echo is also influenced by a target’s shape and size. No matter the complexity of the transmitted signal, the reflected signal will be much more complex.
AWG Signal Generation
AWGs can generate radar signals in three ways:
- Baseband generation. The AWG generates a time-domain signal that is applied to an external RF modulator.
- Intermediate frequency (IF) direct carrier generation. In this case, the AWG generates a modulated signal at a relatively low carrier frequency. In some cases, this signal is applied directly to a signal-processing block in the receiver or the transmitter. In other cases, it is applied to an up-converter block to reach the final RF/microwave carrier frequency.
- RF direct carrier generation. The AWG generates a modulated carrier at the final RF/microwave frequency, requiring no additional signal-processing blocks other than filters or amplifiers.
Baseband and IF generation can be implemented with a moderate performance AWG for most signals; however, in both cases, the modulation bandwidth of the final RF/microwave signal will be limited by the characteristics of the modulator or up-converter. Direct RF signal generation, on the other hand, requires an extremely fast AWG with a sampling rate at least 2.5 times higher than the maximum RF frequency component of the signal. The latest generation of AWGs offers 10 bits of resolution at speeds up to 50 GS/s, opening the door for direct signal generation beyond Ku-Band (12 to 18 GHz).
Baseband Signal Generation
Baseband signal generation may appear relatively straightforward because modulation and up-conversion are performed externally. The modulation device may be a simple amplitude (AM) modulator for basic pulsed RF signal generation, however some baseband signals require a suppressed carrier, which is not supported by most AM modulators, as the instantaneous phase can take two values (0° and 180° or BPSK). Baseband generation of FM chirps, QPSK/QAM and UWB OFDM signals requires a two-channel AWG and an external quadrature modulator (see Figure 1) as both the instantaneous amplitude and phase of the carrier must be controlled. Sampling rate requirements depend on the modulation bandwidth which is limited by the modulator. Similarly, emulation of realistic radar echoes incorporating the effects of the target characteristics, multi-path, Doppler shifts, noise and jamming also requires quadrature modulation and a two-channel AWG.
Generating good quality wideband modulated signals using this approach is not an easy task. Frequency responses of both baseband generators and RF modulators are not flat and group delay is not constant over the bands of interest when signal bandwidths are high. Even a perfect AWG incorporating ideal digital-to-analog converters (DAC) will show a zeroth-order hold response:
H(f) = sinc(πf/Fs) = sin(πf/Fs)/( πf/Fs), Fs = Sampling Frequency (1)
This introduces linear distortion to the RF pulses, altering the shape of the transitions and modifying rise and fall times. The analog frequency response of the AWG and cabling, and the modulator’s frequency response adds to these distortions. Unwanted images resulting from the sampled nature of signals generated by AWGs can also affect signal quality, and the limited time resolution available in any AWG may result in undesired levels of pulse-to-pulse jitter.
Fortunately, AWGs can generate either undistorted or intentionally distorted signals. Predistortion mathematically applied to waveforms stored in the generator’s memory may be designed to compensate for external distortion. After careful calibration of the overall frequency response it is possible to design a compensation filter that improves flatness and group delay response. Typically, the compensation filter takes the form of a pre-emphasis filter to correct the signal generation system’s overall lowpass frequency response.
For quadrature-modulated radar signals such as FM-chirps, two baseband signals, the I and Q components, feed the external modulator. These two components are generated independently and synchronously by a two-channel AWG or by two properly synchronized single-channel AWGs. Quadrature error and imbalance cause unwanted images to appear at the RF and at symmetric frequency locations, resulting in higher noise and reduced modulation quality. While AWGs can generate a differentially corrected signal, one should be aware that generating quadrature-modulated signals with an AWG and external modulator involves a time-consuming calibration process as well as additional equipment (typically a high-end real-time oscilloscope, a wideband vector signal analyzer, and supporting software).
Direct Carrier Generation
AWGs can produce any signal from DC up to half the sampling rate (Fmax = Fs/2). With a high enough sampling rate, it is possible to directly generate a modulated RF signal. Previously, relatively low sampling rates and poor spurious-free dynamic range (SFDR) limited the capability of AWGs to generate carriers up to only a few GHz. With improved DAC performance, AWGs can now be used for direct generation of wideband signals with carriers up to 20 GHz and with almost unlimited modulation bandwidth. Direct generation offers a number of advantages over the traditional baseband/external modulator combination:
- Baseband generation and quadrature modulation are performed mathematically. As a result, there are no unwanted quadrature imbalances or errors. This approach yields higher quality and more repeatable test signals.
- No additional equipment is required, saving cost when multiple synchronous signals are required (i.e., for MIMO radar or phased array emulation).
- Direct, nearly unlimited, frequency agile radar signal emulation is possible.
- One single AWG can generate multiple dissimilar carriers or wideband noise for more realistic test scenarios.
- Calibration procedures are simplified, where only the amplitude and phase of the more stable AWG must be verified.
The implementation of direct carrier generation has its challenges, as well:
- For a given record length (RL) and sampling rate (Fs), the maximum time window (TW) = RL/Fs. As sampling rates for direct RF generation tend to be higher than those for baseband signal generation, the same record length translates to shorter realizable time-windows. Record length is also crucial for a realistic emulation of complex radar systems incorporating staggered pulse sequences, frequency hopping patterns or time varying echo characteristics caused by target movement or antenna vibration.
- An alternative method to extend the carrier frequency range for a particular AWG is to use an image in the second Nyquist zone, between Fs/2 and Fs. The usability of the image can be improved by filtering out the fundamental signal located in the first Nyquist zone. The quality of this signal is more limited given the much lower amplitude and the steeper roll-off in the AWG frequency response.
- Some signal generators incorporate DAC working modes to improve second Nyquist zone performance. Doublet-mode DACs (also known as Mix-Mode DACs) generate a higher amplitude image and a reduced amplitude fundamental signal while removing the first null of the zeroth-order hold response of a regular DAC. However, maximum modulation bandwidth and the capability to generate multiple carriers are still limited to less than half the sampling rate and this is only possible when the carrier frequency is located in the middle of the valid Nyquist zone (see Figure 2). In this example, the Doublet DAC mode boosts images in the second Nyquist zone and attenuates the direct signal located in the first Nyquist zone. This extends the frequency coverage of a 12 GS/s AWG but limits its carrier frequency range and modulation bandwidth compared to the regular DAC response. AWGs designed to generate signals in the first Nyquist zone do not have these limitations.
- Another way AWGs obtain higher effective sampling rates is by interleaving two DACs (see Figure 3). This is effectively a two “true-arb” model with odd and even samples stored in each channel’s memory. Since switching DAC outputs creates noise and reduces effective bits performance, an interleaved DAC architecture is used that adds the outputs from both channels with a channel-to-channel delay of half the sampling period (1/2SR). This architecture, when used in a high-speed AWG, effectively doubles the Nyquist frequency to 2×SR.
- Although direct carrier generation does not suffer any quadrature impairment due to I/Q mismatch, wideband signals may need some linear distortion to compensate for flatness and phase linearity issues, including those created by cabling and interconnections. Applying corrections based only on the amplitude response improves modulation quality, although phase response compensation is also required for optimal performance. Direct carrier generation also requires stable sampling clock jitter performance as this translates directly to phase noise in generated carriers.
Continuous signal generation with an AWG requires seamless cycling of the contents of the waveform memory through the DAC. In order to obtain useful signals, consistency of the signal around the wrap-around event must be preserved. Timing characteristics of radar signals are especially important:
- An integer number of PRIs must be stored in the waveform memory. Otherwise abnormal pulse timing (longer or shorter than required) will occur every time the waveform is cycled.
- For coherent radar emulation, the phase of the carrier must be preserved. This condition can be met if record length and sampling rate are selected in such a way that the resulting time window is an exact multiple of the carrier frequency period.
- Echo consistency requires that multi-path, filtering effects and echoes beyond the unambiguous range propagate from the end of one cycle to the next. These effects may be seen as the convolution of the transmitted signal with the target system impulse response. Applying circular convolution to consistent transmitted data will result in an echo emulation signal without any discontinuity or abnormal behavior that could confuse a radar receiver under test.
Calibration and Signal Correction
AWGs are typically flatness-corrected up to a certain frequency. Beyond that point, signal generators exhibit relatively gentle roll-off responses (see Figure 4). Moderate attenuation allows the direct generation of usable radar signals at higher frequencies. In order to improve modulation quality at those frequencies, the frequency response can be corrected or calibrated to compensate. Real-time oscilloscopes are ideal calibration tools as they show flatness and phase linearity over their full bandwidths with accurate channel-to-channel alignment. Once the correction filter response is determined in the frequency domain, it is applied to the original, uncorrected waveform through convolution. Convolution must be circular when signal looping is required.
Arbitrary waveform generators allow for the direct generation of complex radar signals at carrier frequencies up to 20 GHz. This is made possible by improved DAC performance and by the use of an interleaved DAC architecture. Some of the most complex frequency-agile or MIMO radar systems can be now be emulated using direct RF generation techniques.
Chris Loberg is a senior technical marketing manager at Tektronix responsible for oscilloscopes in the Americas region. Loberg has held various positions with Tektronix during his more than 13 years with the company, including marketing manager for Tektronix’ Optical Business Unit. His extensive background in technology marketing includes positions with Grass Valley Group and IBM. He earned his MBA in Marketing from San Jose State University.