FFT-based Digital Receiver Architecture for Fast-scanning Application

Transcription

1 FFT-based Digital Receiver Architecture for Fast-scanning Application Dr. Bertalan Eged, László Balogh, Dávid Tóth Sagax Communication Ltd. Haller u Budapest 196 Hungary T: F: Abstract Receivers covering the VHF/UHF communications bands are the important parts of the EW/ESM systems. Currently used frequency agile signals using frequency hopping and burst transmission technique rise eminent requirements for scanning and search receivers. The fast scanning speed can be achieved with parallel signal processing based the spectrum estimation of a wide bandwidth of incoming signal. One of the technology, which is available for that purpose is a traditional FFT, but the key element of the FFT based receivers is still remain the analog to digital converter (ADC) which is used. Currently lot of high-speed, high-dynamic range ADC chips are on the market developed for the digitized mobile radio market based on Software Defined Radio (SDR) technology. In the paper we would like to introduce our currently developed digital receiver platform for fast-scanning application which is able to process up to 1MHz of instantaneous input bandwidth with down to 1 KHz resolution within 1ms processing time. Connecting it to our analog receiver front-end with highspeed synthesizers able to tune to any frequency up to 3 GHz the result is a high-speed fast scanning receiver with up to 1GHz/sec scanning speed at 1 KHz resolution. the 2-52 MHz range with an upper IF converted structure. It has got a wide-band IF output for further digital processing too. The analog IF processor contains the IF filter bank and the basic WFM/NFM/AM/CW/SSB demodulators. The microprocessor based platform controller provides a multi-drop RS-232 based serial or an TP Ethernet based TCP remote control. See figure 2. and figure 3. I. RADIO PLATFORM The radio front-end elements of a traditional analog radio is used for digital applications too. The SR-2 radio platform form Sagax Communications could be divided to an analog and a digital part. The analog part contains the down-converter, the analog IF processor and a platform controller which enables to use these parts of a platform as a conventional analog receiver (see figure 1.). Fig. 2. Signal path from RF to IF. Fig. 1. Digital and analog partition of the device. The front-end contains the optional block down-converter for frequency extension up to 3 GHz and the basic receiver covers Fig. 3. Analog IF processor and control elements.

2 Its fast switching frequency synthesizers allow 1 ch/s scanning in the frequency band or channel memory to fulfil traditional ESM requirements in the VHF/UHF communication bands. The digital parts of the platform based on the high-speed, wide-band converters based on 14 bit ADC and deep FIFO memory realized as a standard desktop PCI board with onboard FPGA resource for glue-logic and signal processing, and a master-mode PCI controller. literature in the following we deal with the signal processing attributes of the digital elements focusing on the fast scanning functionality. II. DFT BASED SPECTRUM ANALYSIS The discrete Fourier transformation (DFT) is a basic tool of spectrum analysis. The most algorithms use this method because of its good properties. The theoretical advantages are such as - direct mathematical connection with the coefficients of Fourier series, - orthogonal property as a transformation, - noise whitening. In practice after the AD converter the spectrum can be computed only at a finite frequency grid. But if assumptions of the Shannon sampling theorem are true, i.e. the maximal frequency in the signal is less than half of the sampling frequency f s then the original analog periodic signal can be reconstructed. Studying the DFT transform of a sampled signal can be divided up into two essentially different situations: coherent and non-coherent sampling. These cases are studied hereafter. The N point DFT is defined as X(k) = N 1 i= x(i)e 2π ik N (1) Fig. 4. Block diagram of the digital part. where k =,..., N 1, x(i) is the sampled signal and the inverse DFT (IDFT) is similarly x(k) = 1 N N 1 i= X(i)e 2π ik N (2) It can be seen that these are essentially the same transformation, in accordance with the duality properties of the time domain and the frequency domain. Note that for real x the series X are complex number and the following relationship is true: X(k) = X(N k) k =,..., N/2 (3) where overbar denotes the complex conjugate operation. Coherent sampling Coherent sampling means that the available sample set contains an integer numbers of periods. Mathematically Fig. 5. The PCI controller scheme. f signal f s = N number of periods N (4) The captured data could be transported to the PC based host computer memory trough a PCI bus or in real-time application external dedicated, high throughput data ports are available to connect the converter to the DSP processors directly. The platform uses a four processor DSP engine with PCI interface and external data ports. For a demodulation applications a codec chip is provided to generate the demodulated audio signal. The introduced elements are composing a cost effective and functional radio platform for EW/ESM missions. As the analog processing elements are well described in the where f signal is a component of input signal and N number of periods is integer number of cycles within the sampling window. Coherent sampling eliminates using windowing and increase the spectral resolution. In the case of this receiver this assumptions are not met therefore non-coherent sampling occurs. This case is analyzed in the next section. Let us see an example of coherent sampling. The input signal contains only one sine wave which has frequency 5 MHz and additive Gaussian noise. Let f s be 4 MHz, and the number of samples N be 124. Then the samples contains exactly 512 periods. The result of DFT after scaling can be seen in figure 6.

3 Amplitude (db) Fig. 6. The result of DFT in the case of coherent sampling of a sine wave. Since the discrete frequency grid contains the exact frequency of corresponding sine signal, the result contains one Dirac delta like in the analog case. Furthermore, the correct amplitude can be measured with coherent sampling by DFT. Non-coherent sampling If one of the above mentioned conditions for coherent sampling are not met, non-coherent sampling occurs. In this case we cannot assume that the sampling frequency is the integer multiple of the fundamental frequency component of the signal. Since in practice we can not guarantee the coherent sampling, its effects has to be taken into account of the measurement. There are two important consequences of the incoherency, the first one is the leakage and the second one is picket fence. Leakage means that power of sine is distributed to other frequency point in the grid. The effect of leakage is decreasing if distant from corresponding frequency is increasing. Leakage is dependent on (random) phase of the sine. The effect of picket fence causes that amplitude of the sine can not be accurately determined. In Amplitude (db) Fig. 7. Example for non-coherent sampling. 7. figure an example of non-coherent sampling is demonstrated. Parameters of signal and DFT remain unchanged except f signal. The new value equals 7 MHz. One can see that effect of the picket fence is negligible but the effect of leakage is notable. In fast scanning receivers this causes that two signals which frequencies are enough close together and amplitudes are different may not be separated. A convenient way to increase the frequency resolution (ability of separating signals with close frequencies) is windowing. This methodology is reviewed in the next section. Windowing The windowed version of DFT is defined as X(k) = N 1 i= w(i)x(i)e 2π ik N (5) where w(i), i =,..., N 1 is the given window function that is independent of signal x. In the literature there are hundreds of window functions can be found. They have different properties and gives optimal solution for special cases. For general purpose few ones are customary used. In figure 8. the signal in figure 7. is windowed by a Hann window. Amplitude (db) Fig. 8. Example for non-coherent Hann windowed sampling. It can be seen that the effect of the leakage has been decreased but the error of amplitude has been increased. If we enlarge the band between 6 MHz and 8 MHz then it can be seen that windowing did not fully eliminate the leakage but drastically decreased. See in figure 9. In this application ability of separating two signals with close frequencies is more important than correct amplitude measurement. (Detection of communication signal has importance.) To achieve the desired level of sidelobe suppression we computed the frequency bandwidth for -6 db in some cases (table I.). In one case the function between length of the filter and the previously defined bandwidth is depicted in figure 1. There is a tricky and fast algorithm to compute DFT called Fast Fourier Transform (FFT). Computational time of FFT is proportional to N log 2 N (not a parallel realization). This is true if there exists an integer number k such that N = 2 k. Hence these values of the filter length are interesting for us. It gives some possible lengths of filters, the corresponding values of bandwidth in the case of suppression -6 db are summarized

4 1 1.8 Amplitude (db) 3 5 window values window length Fig. 9. Example for non-coherent Hann windowed sampling (magnified). bandwidth (khz) filter length Fig. 1. Bandwidth versus length of filter Chebysev(6) (f s = 1 MHz). in table 1 I. The conclusion is that using Chebysev window with nothing less than 496 samples gives us enough frequency resolution. In the time domain representation of Chebysev window can be seen in figure 11. and the frequency domain representation can be found in figure 12. III. MEASUREMENT RESULTS In this section the measurement results of the system are presented. Firstly we calibrated the system, i.e. we assigned the level pertained to the full scale. After this measurement a noise measurement was executed. Then the frequency resolution measurements were performed. Thereinafter some typical applications were executed. The results are sequentially presented in next subsections. Calibration The underlying system is measured using a sine (f = 8 MHz, dbm). The measurement result can be seen in fig 13. Since non-coherent sampling causes errors of FFT based measurement, we applied a 4-parameters sine fitting algorithm (based on Levenberg-Marquard method using approximation norm L 2 ). 1 This results are valid but it should have to note that because of the worse sidelobe rejection of Bartlett window practically it can not be used. window (db) Fig. 11. Chebisev(6) window in time domain (N =2) normalized frequency Fig. 12. Chebysev(6) window in frequency domain (N =2, f s =1Hz). Measured spectrum (dbm) Fig. 13. Level measurement with corrected amplitude (N =8192, f s =4MHz). Amplitude of the approximated sine gives us a accuracy way to the amplitude calibration. See figure 14. Note that leakage effect of non-coherent sampling does not disappeared.

5 TABLE I 6 DB BANDWIDTH OF SOME CUSTOMARY FILTERS (NORMALIZED FREQUENCY, I.E. f s = 1). window N = 512 N = 124 N = 248 N = 496 N = 8192 Bartlett Blackman-Haris Chebysev (6) Chebysev (7) Spectrum (dbm) Resolution We were tested the device with respecting the frequency resolution. In the first case we studied two sines (f 1 =1.6 MHz, f 2 =1.8 MHz, amplitude difference is 4 db). The used filter is Chebysev with relative sidelobe attenuation parameter of 6 db. In the figure 16. the result is depicted. It can be seen that it Fig. 14. Approximated sine in the case of level measurement (N =8192, f s =4MHz). Amplitude (dbm) 8 Noise level With the calibrated ADC the noise level measurement can be performed. The measurement was repeated 1 times and the amplitude spectra is averaged. The results can be seen in figure 15. Foreasmuch the DFT is whitening the noise we can average Noise spectrum (dbm) Fig. 15. Noise level measurement (N =496, f s =4MHz). the amplitude spectrum over frequency. Hence the estimated noise level is dbm, and the estimated noise margine is dbm/hz. As one can see the system is generating spurious, too. There are spurius which are not derived from the nonlinearity of the AD converter but these has acceptable small level, i.e. the spurius free dynamic range is more than 95 db Fig. 16. Resolution measurement (N = 8192, f s = 4MHz). is easy to separate the two signals each other (separated by 2 khz). In the second case, the input signal contained two sines (f 1 =1.7 MHz, f 2 =1.65 MHz, amplitude difference is 6 db). The measurement result can be seen in figure 17. The used filter is Chebysev with relative sidelobe attenuation parameter of 6 db. It can be concluded that in this case signals can be Amplitude (dbm) Fig. 17. Resolution measurement (N = 8192, f s = 4MHz).

6 separated but the limit is reached. It is important to notice that this resolution can be increased by more samples. determine that the frequency hoppings were performed at every 1 ms long time interval. Application Firstly, two simple application is presented. We collected 124 samples 1 times in every milliseconds. The source used ASK modulation and frequency of the modulating signal was 1 Hz. Waterfall of the result can be seen in figure 18. During this measurement we used Chebysew (6) window function Fig. 2. Waterfall of the hopping radio signal Fig. 18. Waterfall of 1 Hz ASK signal. Similarly to the previous case second application is measuring a waterfall. The difference is that in this case an FSK signal is used. The frequencies of symbol and symbol 1 were 1.7 MHz and 1.8 MHz, respectively. The waterfall can be seen in figure Fig. 21. Waterfall of the hopping radio signal (magnified) ACKNOWLEDGEMENT The authors would like to thank the National Office of Research and Technology (NKTH) for support of our Software Defined Radio related research and development work, the Department of Broadband Infocommunications and Electromagnetic Theory of Budapest University of Technology and Economics (BUTE DIE) for valuable help in performing the measurements, and the Electronic Directorate of Ministry of Defense Hungary (MoD ED) for providing the hopping radio testbed. Fig. 19. Waterfall of 1 Hz FSK signal. Finally a VHF hopping radio measurement is presented. In the IF domain the radio was hopped between 5 MHz and 15 MHz. The measurement was performed with 124 samples (f s = 4 MHz). The time difference between measurements was 1 ms. The waterfall is depicted in figure 2. The decision level was -3 dbm. In the figure 2. we can see a long measurement, and in the figure 21. the first 1 ms long time interval of same measurement is magnified. In the second figure we can REFERENCES [1] B. Eged, G. Ngyesi, Universal Software Radio Platform for Wideband, Multichannel and Phased Array Applications, in the proceedings of conference Communications 22 by Mikl ós Zr ınyi National Defense University, 22, pp , [2] L. Balogh, B. Eged, Precision Direction Finding Algorithm based on Interferometer Structure, in the proceedings of 11th MICROCOLL conference by Hungarian Academy of Sciences, 23, pp [3] L. Balogh, B. Eged, Precision Direction Finding Algorithm of Radio Signals, in the proceedings of conference Communications 23 by Mikl ós Zr ınyi National Defense University, 23, pp [4] James Tsui, Digital Techniques fo Wideband Receivers, Artech House, Boston, USA, 21.