Extending Subnoise-level Signal Recovery In Radar Applications
Authors: Christopher T. Allen, Shadab N. Mozaffar, and Torry L. Akins
Presented at ADC, 2005.
Radar sensitivity is determined by the ability to reliably detect weak signals in the presence of noise. Key noise sources in radar remote sensing systems include:
- Thermal noise
- Quantization noise
- Coherent Noise
with known techniquest for reducing thermal and quantization noise, significantly extend our ability to recover weak radar signals well below the various noise levels.
Various techniques have been developed to reduce the noise without degrading the signal thus improving radar sensitivity. These techniques exploit characteristic differences between the noise and the desired signal. We present a technique for reducing coherent noise without adversely affecting the signal. This technique, specifically stacking (coherent averages) and interpulse zero-pi (0/π) modulation, when used in conjunction
Stacking, or coherent averaging, is effective at reducing thermal noise. This technique is applicable when the radar's target or scene is oversampled so that successive radar echo signals are added together to produce an aggregate echo signal. Therefore, since the signal of interest is essentially static, averaging N samples yields a constant signal amplitude (and constant signal power). However, averaging N uncorrelated signal-plus-noise samples reduces the variance of the noise resulting in a net signal-to-noise power ratio (SNR) improvement of N. But not all noise sources have the same characteristics as thermal noise. Quantization noise, which is a by-product of employing analog-to-digital converters (ADCs), is correlated with the signal.
Dithering can be used to reduce quantization noise by ensuring that the uncorrelated thermal noise samples at the input to the ADC are above the quantization noise floor. For our system, this is achieved by using the variable gain settings of the Synthetic Aperture Radar (SAR) through which the the output thermal noise can be set 3, 6, and 10 dB above the quantization noise floor of the ADC.
Coherent noise, mainly arising from within the radar system itself, is immune to the noise suppression benefits of stacking and dithering. To reduce the coherent noise we employ interpulse 0/π phase modulation – a technique widely used to resolve rang and Doppler ambiguities.
Interpulse Zero/Pi Modulation
Rather than transmitting a train of identical pulses, we transmit a series of pulses where the odd-numbered pulses have a pi phase shift relative to the otherwise identical even-numbered pulses. Once received, the pi phase shift is removed from the echoes corresponding to the odd-numbered pulses, so that during stacking they add constructively with the even-numbered pulses.
The coherent noise, on the other hand, does not experience the alternating 0/π phase shift so that when it is received and it experiences the compensating phase shift of the odd-numbered pulses, it adds destructively with the sample of coherent noise that accompanied the even-numbered pulse. The result is a reduction or cancellation of the coherent noise while preserving the desired signal. While implementation in the analog domain would introduce amplitude and phase imperfections that will limit the cancellation of the coherent noise, nearly perfect implementation can be realized with the introduction and removal of the pi phase shift in the digital domain. This is realized by digitally generating two transmit pulses differing only in their phase and then removing the phase shift following the ADC.
The proposed concept for coherent noise reduction was tested with laboratory experiments conducted using our monostatic synthetic-aperture radar (SAR) system. We configured our SAR to operate at a center frequency of 350 MHz and a bandwidth of 40 MHz. After baseband downconversion, the signal is digitized using an Analog Devices' AD 9430 12-bit ADC clocked at a 120-MHz rate. The receiver gain is adjustable to provide a noise power at the ADC input of 3, 6, and 10 dB above the ADC noise floor of _64 dBm (defined here as the total in-band integrated noise power).
Two configurations were used to conduct the coherent noise reduction tests:
- In the first configuration (Noise Only), the receiver input was terminated with a 50-Ω load so that no radar signal was injected into the receiver front-end. The resulting digitized signal was coherently averaged up to 1 million times with and without 0/π modulation.
- In the second configuration (Weak Signal), a 0/π phase modulated radar signal was injected into the receiver with a signal power below the ADC quantization noise floor. The resulting digitized signal was coherently averaged up to 1 million times with and without 0/π modulation.
Case A: Noise Only
In the first case (Fig. 1) the receiver gain was set to cause the thermal noise to be 3 dB greater than the ADC noise floor. Only frequencies between 10 and 50 MHz are shown as this is the intermediate frequency range of interest in our SAR system.
The top plot shows the spectrum when no coherent averaging is performed.
The middle plotplot shows the spectrum after one million averages with no 0/π phase modulation. The noise, being incoherent, is largely suppressed while coherent signal components can be clearly seen. The noise floor level is suppressed by less than 60 dB (N = 106) indicating that some component of the broadband noise is coherent.
The bottom plot shows the advantage of 0/π phase modulation where the strong coherent terms are significantly reduced and the largest frequency spur at 40 MHz is reduced by almost 40 dB.
|Fig. 1. Measured power spectra of noise digitized at a 120 MHz rate. Top plot is no averaging, Middle and bottom plots are spectra after one million averages without and with 0/π phase modulation.
Overall, the total noise power between 10 and 50 MHz after 1 million average is about -106 dBm, a reduction of about 25 dB compared to the previous case that did not employ 0/π phase modulation.
Using the total noise power as the figure of merit (Fig. 2), the benefits of coherent averages from 1 to one million and with three receiver gains set at 3, 6, and 10 dB above the ADC noise floor were investigated. In all cases, coherent averages produce the expected reduction in noise floor up to about 100 averages. For the non-0/π case, the power from the coherent spurious components begin to dominate beyond 100 averages and the incremental benefit from additional coherent averaging starts to decrease up to 10,000 averages. Going beyond 10,000 averages results in no discernable improvement.
|Fig. 2. Measured total ADC noice (in the 10-50 MHz band) as a function of the number of coherent averages.
For the cases involving 0/π phase modulation, the benefit from additional averaging continues to agree with the theoretical predictions (dashed lines) up to about 10,000 averages, beyond which the incremental benefits continue up to about 100,000 averages. For all three initial input noise levels (3, 6, and 10 dB above the ADC noise floor) the final ADC noise floor after one million averages is the same, about -106.5 dBm. Further averaging produces no significant benefits. Overall, the application of 0/π phase modulation provides about 25 dB of additional ADC noise floor suppression by reducing the spurious noise power.
Case B- Weak Signal
In the second experimental setup (Fig. 3), a coherent time-gated 30-MHz sinusoid with a 10-ms duration and a signal power of _88 dBm was injected into the receiver front end. At this power level, the signal-to-noise ratio at the ADC input is less than _28 dB. As before the signal and noise are digitized at a 120-MHz rate and coherently averaged with and without 0/π modulation.
|Fig. 3. Measured power spectra of a 30-MHz signal in noise digitized at a 120-MHz rate. Top and bottom plots are spectra after one milllion averages without and with 0/π phase modulation.
The spectrum obtained after one million coherent averages with no 0/π modulation is shown in the top plot of Fig. 3. In addition to the 30-MHz signal, coherent spurs at 10, 20, 40, and 50 MHz are also well above the noise floor power with 20-MHz being the dominant spur at -91 dBm. Hence, the signal to spurious free dynamic range (SFDR) for the no 0/π case turns out to be 3 dB after 1 million coherent integrations.
The bottom plot in Fig. 3 shows the results of processing a similar data with 0/π phase modulation. After one million averages, the 30-MHz signal remains at its full strength whereas the spurious signals are significantly reduced. The previously dominant 20-MHz spur remains above the noise floor, however its power level is now _114 dBm. The SFDR is 26 dB, a 23 dB improvement over the no 0/π case.
The application of 0/π interpulse phase modulation has been experimentally demonstrated to increase the ability of coherent averaging to reduce coherent spurious components both in the receiver and the ADC. The transmitted signal is similarly phase modulated so as to be unaffected while coherent noise terms are reduced appreciably, up to 20 to 23 dB beyond what is possible without phase modulation.