An optimization of the FPGA/NIOS adaptive FIR filter using
linear prediction to reduce narrow band RFI for the next generation ground-based ultra-high energy cosmic-ray experiment
Zbigniew Szadkowski
a,n, E.D. Fraenkel
b, Dariusz Glas
a, Remigiusz Legumina
aaUniversity of Lodz, Department of Physics and Applied Informatics, Poland
bKernfysisch Versneller Instituut of the University of Groningen, Groningen, The Netherlands
a r t i c l e i n f o
Available online 28 June 2013 Keywords:
Linear predictor FIR
RFIfiltering
Geo-synchrotron radiation Radio detection Levinson recursion
a b s t r a c t
The electromagnetic part of an extensive air shower developing in the atmosphere provides significant information complementary to that obtained by water Cherenkov detectors which are predominantly sensitive to the muonic content of an air shower at ground. The emissions can be observed in the frequency band between 10 and 100 MHz. However, this frequency range is significantly contaminated by narrow-band RFI and other human-made distortions. The Auger Engineering Radio Array currently suppresses the RFI by multiple time-to-frequency domain conversions using an FFT procedure as well as by a set of manually chosen IIR notchfilters in the time-domain. An alternative approach developed in this paper is an adaptive FIRfilter based on linear prediction (LP). The coefficients for the linear predictor are dynamically refreshed and calculated in the virtual NIOS processor. The radio detector is an autonomous system installed on the Argentinean pampas and supplied from a solar panel. Powerful calculation capacity inside the FPGA is a factor. Power consumption versus the degree of effectiveness of the calculation inside the FPGA is a figure of merit to be minimized. Results show that the RFI contamination can be significantly suppressed by the LP FIR filter for 64 or less stages.
& 2013 Elsevier B.V. All rights reserved.
1. Introduction
Linear Prediction (LP)[1]is a method widely used in real-time audio processing such as the CELP (Code-Excited Linear Prediction) algorithm[2,3] in mobile phones. With the advent of faster signal processing techniques in FPGAs (Field Programmable Gate Arrays) it is now possible to apply similar techniques to the real-time processing of radio signals in the 10–100 MHz region[4].
The LP approach has been used to remove the RFI (Radio- Frequency Interference) lines from a signal contaminated with narrow band emitters in the detection of cosmic ray induced radio pulses[5]. Tests confirm that the LP can be an alternative to other methods involving multiple time-to-frequency domain conver- sions using an FFT (Fast Fourier Transform) procedure. The power consumption of the FPGA for these multiple conversions is an important factor because thefinal system will be powered by solar panels. The LP consumes less power and does not introduce signal distortion, which is also a problem for the fastest FFT streaming architecture.
In the LP method the covariances for 1024 ADC samples are calculated in the FPGA fast logic block. The embedded NIOSs processor solves the matrix of 32 or 64 linear equations and provides coefficients needed for the FIR filter. The calculated coefficients are next transferred from the NIOSsto the fast logic block, updating appropriate registers. They are used as the FIR coefficients in the ADC data filtering. Finally, the predicted and delayed data (expected background) is subtracted from the ADC data to clean the signal from the periodic contaminations (Fig. 1).
2. Description of the analysis
The algorithm described in Ref.[5]is implemented in the FPGA from the AlterasCyclones III family. Due to limitations in the real-time data-transfer speeds and simulation time, an equivalent calculation is done on a regular PC in order to analyze about one second of simulated data, at a sampling frequency of 180 MHz, which constitutes a trace of 2:048 10812 bit samples.
The one-second trace is simulated by generating white Gaussian background noise with an amplitude of 5 mV (57ADC- units). Subsequently an elliptic IIR (Infinite Impulse Response) band-pass filter with a passband of 25–80 MHz simulates the sensitive frequency region of the station. Instrumental noise with Contents lists available atScienceDirect
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Nuclear Instruments and Methods in Physics Research A
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http://dx.doi.org/10.1016/j.nima.2013.06.031
nCorresponding author. Tel.:+48 42 635 56 59.
E-mail addresses:zszadkow@kfd2.phys.uni.lodz.pl,zszadkow@uni.lodz.pl (Z. Szadkowski).
an amplitude of 0.25 mV (2.8ADC-units) is added after this. Finally thefloating point samples are digitized by adding a baseline of 211 ADC-units and rounding them to 12-bit unsigned integers. The simulation has been chosen such that it closely resembles the amplitudes and spectral shape of the typical setup.
Two types of environment are studied. The first is one of relatively low contamination with RFI. Three RFI lines are added to the trace by adding sines with frequencies of 40.9, 55.2, 70.7 MHz and amplitudes of 2, 3 and 4 mV respectively. The phases are chosen randomly. The second case has a higher contamination. Six RFI lines are added with frequencies of 41.2, 54.4, 73.8, 48.1, 66.5 and 71.2 MHz. The amplitudes are 6.1, 3.9, 4.4, 4.6, 4.1 and 10.0 mV respectively. In addition, the line at 41.2 MHz is amplitude modulated with a message frequency of 11.4 kHz and a modulation index of 0.5 and the line at 71.2 MHz is frequency modulated with a message frequency of 10.0 kHz and a frequency deviation of 7.5 kHz.
Transient signals are simulated by adding 300 delta pulses to the trace before the band-passfiltering. These delta pulses consist of single samples with amplitudes of 0–200 mV (2276ADC-units) increasing linearly and spaced evenly within the one-second trace (Fig. 2).
3. Frequency domain analysis
The upper panels ofFigs. 3and4show spectrograms for the first 256 k samples of the traces. The lower panels show the cleaned background. It can be seen that even for strongly con- taminated input data with both an amplitude modulated and a frequency modulated peak (Fig. 4) the RFI is significantly suppressed.
Fig. 2. Schematics of the FIR (Finite Impulse Response)filter. The ADC data delayed in the 12-bit register chain are multiplied by the 18(14)-bit coefficients in the embedded DSP (Digital Signal Processing) multipliers and summed in 30-bit routine. Finally, the processed signal is subtracted from the ADC original one. The FIRfilter is implemented with the fixed-point representation.
Fig. 3. Spectrograms for artificially generated input data with only three single frequency peaks (above). The filtered signals (below) show considerable RFI suppression.
Fig. 4. Spectrograms for artificially generated input data (above) with significantly contaminated input data with both an amplitude modulated and a frequency modulated peak. The filtered signals (below) again show considerable RFI suppression.
Fig. 1. The dataflow of the FIR filter based on linear prediction.
4. Optimization of the FPGA implementation
4.1. The coefficients width
The multiplication procedure implemented in the dedicated multiplier circuitry can utilize several DSP blocks. About 9-bit data multiplied by the 9-bit coefficient uses only a single DSP block.
However, 12-bit ADC data requires at least 2 DSP blocks; 2 DSP blocks allow a multiplication by 18-bit LP coefficients. However, the use of 18 bit coefficients is too wasteful and not needed for the required accuracy. A reduction of the number of bits of the coefficients from 18 to 14 reduces the power consumption by
∼30 mW, yet differences for the cleaned signals for both config- urations appear only in 0.01% of the signal amplitudes, i.e. on the LSB (seeFig. 5). The reduction of the coefficients width to 12-bits introduces bigger differences (∼1%) with symbolic power reduc- tion (∼10 mW ). It was therefore decided to use the configuration 12 14 for all implementations.
4.2. The FIR length
The efficiency of the RFI suppression depends on the number of the FIR stages. A longerfilter removes the background with higher precision. However, this requires much more FPGA resources, increases the power consumption and decreases the refreshing time due to a larger matrix to be solved in the NIOSsprocessor.
The length of 64 stages is a reasonable compromise with even very contaminated signal (Fig. 4). Simulations show that with less contaminated input data (seeFig. 3) the RFI suppression is sufficient even for 32 stages.
5. Time domain analysis
Any filter affects the filtered data. In order to estimate the quantitative influence of the filter on the data, we calculated the distortion factor DF (Eq. (1) (for 4200 registered radio-induced events) defined as follows:
DF¼ kmax∑þ16
k¼ kmax−16
ðxreconstructedÞk−ðxADCÞk
xmax
2
ð1Þ
The analysis shows that the distortion factor weakly depends on thefilter length (Fig.6). Differences appear roughly for DF≥1, where most of the registered events contain only noise. For rather typical event (Fig. 7– DF ≤0:2827 corresponds to 65% of events) the signal shape remains almost untouched. For a relatively large distortion factor (an event with the DF from the tail of the distribution) differences between thefiltered and original shapes do not appear for a signal peak region (most important for a trigger) (Fig. 8).
6. Improvement of the signal-to-noise ratio
The efficiency of the method is analyzed by setting an ampli- tude threshold such that the trigger rate is ∼800 Hz and by comparing the pulses of the raw traces with those of the cleaned and “ideal” traces that contain no RFI at all. The value C is a measure of the performance of the LP FIRfilter. It is the slope of thefit between the signal-to-noise ratio (S=N) of the raw trace on the x-axis and the S=N of the cleaned trace on the y-axis (Fig. 9).
The value CIdeal is calculated in the same way by determining the slope between the S=N of the raw trace and the ideal trace.
1000000 number of
time-bins Histogram of differences between filtered for 12x18 and 12x14 resolutions
10000 100000
1000 10000
10 100
-5 -4 -3 -2 -1 0 1 2 3 4 5
1 10
5 3 2 1 0 1 2 3 4 5
Serie1 0 0 0 0 291 261546 299 0 0 0 0
Fig. 5. Differences infiltered signals for 12 18 and 12 14 structure of filters are only in the LSB and thus are negligible.
arbitrary units
Histogram of distortion factors for the 64 and 32-stage FIR filters 1000
100
10
1
0 0.5 1 1.5 2 2.5 3
DF
FIR-32 FIR-64
Fig. 6. The histogram of distortion factors for 64 and 32-stage FIRfilters.
1500
Input signal and filtered outputs for 64 filters.
Distortion factor = 0.2827
1000 Output
0 500
-500
-16 -12 -8 -4 0 4 8 12 16
1500 -1000
sample index -1500
Input
ADC-unit
Fig. 7. An example of relatively low distortion factor. Differences between shapes of input andfiltered signals are almost negligible.
1500
Input signal and filtered outputs for 64 FIR filters Distortion factor = 1.558
1000
Input Output
0 500
-500
-1616 -1212 -88 -4 0 4 8 12 16
-1000
4 8 12 16
sample index -1500
ADC-unit
Fig. 8. An example of an event with a large distortion factor. This event corresponds to a relatively high contaminated signal. However, thefilter suppresses the periodic contribution remaining weekly affected a peak region important for a trigger.
The efficiency F is calculated from these values as F¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C2−1 C2Ideal−1 vu
ut ð2Þ
If the amplitude of the pulses remains unchanged by thefilter then F may be interpreted as the percentage of the removed amplitude of the RFI.
The value of F is determined for the two RFI environments (see Figs. 3and 4) and for FIRfilters with 32, 48 and 64 coefficients (Table 1). We conclude that only little improvement is gained by increasing the number of coefficients from 32 to 64 for the situation with few RFI lines. The case of more RFI lines shows that some performance is gained by the increase.
7. Power consumption
Power consumption is a significant factor for a system driven from solar panels. Thefilter based on the FFT conver- sion consumes∼2 W for two polarizations (two channels)[6].
Simulations and measurements (Table 2) performed for the EP3C120F780C7 FPGA show that thefilter based on the linear
predictor is much more efficient. The RFI suppression of even very contaminated signal for a length of 64 stages is strong enough, a longer filter is not necessary. For a weaker con- taminated environment even the shorter filter (32 stages) sufficiently suppresses RFI lines. The FFT approach requires
∼1 W per channel (for EP3C80F780C6), while the LP filter needs approximately twice less for 64 stages or even three times less for 32 stages. A reduction of the bus width from 18 bits to 14 bits for the LP coefficients practically does not introduce any error (Fig. 5) and neither does it reduce the power consumption (∼25 mW) significantly. Differences between power consumptions for EP3C80F780C6 (used cur- rently in realfilters) and EP3C120F780C7 (used in the devel- opment kit) are on the level of a few percent.
8. Conclusions
The algorithm originally presented in[5]has been significantly optimized. Simulations performed for very contaminated signals Fig. 9. Analysis in the time domain for data with few peaks (two graphs at the top) and with a significant contamination (two graphs at the bottom). Signal-to-noise ratio is similar for 64 (left) and 32 (right) stages for data with few peaks. For significantly contaminated data, a 64-stage FIR filter is beneficial.
Table 1
The efficiency of the filtering for various FIR filter lengths and for different structures of thefiltered signal. The efficiency of filtering of signals with few narrow peaks is close to the ideal case.
Stages F, few (%) F, more (%)
32 73.371.7 58.371.6
48 78.171.8 67.871.7
64 77.471.8 69.671.7
Table 2
Power consumptions for EP3C120F780C7 with 180 MHz sampling, for significantly contaminated signal (column“more”and for few peaks in the frequency domain (column“Few”). Measured power consumption (column “Pwr mea”) is ∼15% less than simulated in the Quartus II package (column“Pwr sim”).
Length More Pwr sim mW
Pwr mea mW
Few Pwr sim mW
Pwr mea mW
64 12 18 587 499 12 18 595 509
64 12 14 558 475 12 14 573 487
48 12 18 492 416 12 14 447 401
32 12 18 328 280 12 14 333 285
showed that the suppression efficiency is sufficient for 64 or even 32 stages of the FIRfilter. For such lengths the power consumption of the LPfilter is less than for the FFT approach by a factor of 2–3.
Thefilter will be tested soon in real conditions in the Argentinean pampas.
Acknowledgments
This work is being developed for the next generation of cosmic rays detector supported by the ASPERA-2 consortium and was funded by the Polish National Centre for Research and Develop- ment under NCBiR Grant No. ERA/NET/ASPERA/02/11.
References
[1]J. Makhoul, Linear prediction: a tutorial review, Proceedings of the IEEE 63 (April (4)) (1975) 561–580.
[2]M.R. Schroeder, B.S. Atal, Speech Communication 4 (1–3) (1985) 155.
[3]I.M. Trancoso, J.S. Marques, C.M. Ribeiro, Speech Communication 9 (5–6) (1990) 389.
[4]P. Abreu, et al., [Pierre Auger Collaboration], The Pierre Auger Observatory V:
Enhancements, in: Proceedings of the 32nd ICRC, Beijing, August 2011 arXiv:1107.
4807v1.
[5]Z. Szadkowski, E.D. Fraenkel, A. M. van den Berg, FPGA/NIOS implementation of an adaptivefir filter using linear prediction to reduce narrow-band rfi for radio detection of cosmic rays, in: IEEE Real Time Conference, Berkeley (CA), 2012.
[6]A. Schmidt, H. Gemmeke, A. Haungs, K-H. Kampert, C. Rühle, Z. Szadkowski, IEEE Transactions on Nuclear Science 58 (August (4)) (2011) 1621.
