3.4 : Experimental DBS TV Waveform Compression
Here we analyse experimental results of compressing sampled TV waveforms. First the conditions under which the waveforms were sampled are given. The objective here is to relate resultant ambiguity function bulk properties to what is expected from the last section. Particularly important are the range and Doppler mainlobe widths and also peak and average sidelobe levels, but also very important are the strength and location of the anticipated ambiguities over the range-Doppler plane.
3.4.1 : Sampled TV Waveforms
Five sets of coherent (16,382 complex sample) TV waveforms were captured from the reference channel of the bistatic radar receiver described in the next chapter. The waveforms were resolved into in-phase and quadrature components, low-pass filtered at 16MHz, and digitised over a 50^2 matched load at 50MHz sampling rate. Thus each waveform covered 5.12 TV lines, giving scope for five TV line ambiguities spaced at intervals of 64|xs along the r-axis. All five records were of the same TV channel taken within a 12 minute interval, with characteristics given in Table 3.1:
Name: “RTL4”
RF carrier frequency, f^. 11,391 MHz;
Polarisation: H (mag.), linear;
Video standard: PAL;
Encryption: “L’crypt”
Table 3.1. Characteristics of sampled DBS TV channel.
Calculation of the ambiguity functions of these TV waveforms was carried out over T-^- space at its outermost boundaries at intervals of 0.02ns over ±327.68)is for T and at intervals of IkHz over ±50kHz for Auto-correlation functions for the five TV waveforms along the (^=0 axis are presented in Figures 3.4-8.
Ideally, many AFs of different TV channels would have been desirable, to compare clear, scrambled and encrypted channels, and also the PAL and MAC video standards. Due to constrained workstation access time, it was only possible to compute AFs for only these five TV records from one TV channel. Also, computation of AFs for non-zero Doppler frequencies was calculated for a restricted increment of T and <^. An encrypted channel was chosen since encryption or scrambling was expected to demonstrate a greater degree of 64ps ambiguity suppression than clear channels.
cfïapter 3 (fXBS (ZV Waveforms
3.4.2 : Analysis of Results
We now compare achieved compression properties to those anticipated above in the following order:
• that mainlobe A t is inversely commensurate with B\
• that mainlobe A{ width is inversely commensurate with Tint: • that this delivers the expected compression gain;
We also inspect:
• sidelobe levels to see what typical Gtd,si and Gdo,s1 are achievable; • strengths and positions of ambiguities.
The partially deterministic, partially random nature of TV waveforms means that experimental ambiguity functions are complicated in shape, and 3D views and contour plots are difficult to interpret. Hence the approach is to first examine the auto-correlation functions (^=0 only), i.e., in the absence of frequency shifts, followed by the Doppler response functions (t=0 only). This allows mainlobe time delay and Doppler widths to be assessed. It is easier to examine the ambiguity functions if we first look at the silhouette of these along the r = 0 axis for all and then along the { = 0 axis for all T. This allows us to see the peak strengths of sidelobes and all ambiguities against T and These Figures are presented in Appendix 3. Finally, we will look at a plan view of a typical ambiguity function to see where the strongest ambiguities lie in the [z,^] plane.
3.4.2.1 : Auto-correlation and Doppler Response Functions
Referring to Figures A3.1a-e, Table 3.2 presents evaluated A t along the T-axis for the five DBS TV ambiguity functions. The average of A t is 78.2ns, significantly but not too dissimilar from the expected 100ns. Indeed, an effective bandwidth of 12.8MHz is suggested by this figure. This corresponds to a bistatic range resolution of (11.7±0.5)m giving this as a minimum radial resolution at /3=0.
Figures A3.2a-e illustrate the same TV waveform ambiguity functions along the ^-axis.
Table 3.3 presents evaluated A<^. Since each TV waveform was 5.12 lines. Tint = 327.68ps and this is expected to give A<^ = 3.05kHz. The average A<^ is in fact (2.68±0.04)kHz, significantly under, but not by a great factor. However, this corresponds to a Doppler velocity resolution of 35m s'\ again at zero bistatic angle. Obviously, a longer Tint is required for finer resolution, but the commensurate relations of A t to l/B and to 1/Tint are broadly confirmed.
CfiapteT 3 ^lyBS CZV Waveform
Finally, recalling Eq. 3.24, we can evaluate Gcomp from At and A^. The average compression gain yielded (bearing in mind here A^ is in Hz, not rad s'^) is therefore (4770±210) or (36.8±1.4)dB. This is slightly higher than that expected from a lOMHz bandwidth integrated over 327.68ps, where Gcomp should be 35.2dB, and the finer At suggests a higher bandwidth was responsible.
Waveform: 1 2 3 4 5 Average
Ar/ns 73.4 81.0 84.4 69.6 82.2 78.2±3.2
Table 3.2. Time delay mainlobe width of DBS TV waveform ambiguity functions.
Waveform: 1 2 3 4 5 Average
^ ^ l m z 2.72 2.74 2.72 2.72 2.46 2.68±0.04
Table 3.3. Doppler mainlobe width of DBS TV waveform ambiguity functions.
3.4.2.2 : Ambiguity Function Silhouettes
Figures A3.3a-e illustrate DBS TV waveform ambiguity functions viewed as a silhouette along the ^=0 axis. This allows overall sidelobe peaks and ambiguities over the T-<^-plane to be visibly seen. The first point to note is that AF sidelobe power is almost entirely below -15dB, except at the immediate locality of first or second TV line ambiguities at T
= ±64ps or ±128ps, which means DBS TV waveforms integrated over a sufficiently long integration time give Gtd,si and Gdo,s1 that are suitable for radar purposes in the light of a clutter constraint - even an urban one. Table 3.4 summarises the peak sidelobe power, which must be greater than Gtd.si, that occurs within each 64ps TV line interval, while Table 3.5 summarises the peak ambiguity power at each 64ps interval. Both show a progressive roll-off in power with increasing T.
Waveform: 1 2 3 4 5 Average (0 to l)x64ps -18.5 -18.6 -12.6 -20.2 -20.3 -18.0±1.6 (1 to 2)x64ps -19.2 -20.8 -19.4 -20.7 -22.2 -20.5±0.6 (2 to 3)x64ps -19.9 -22.1 -19.9 -22.4 -21.9 -21.2±0.6 (3 to 4)x64ps -23.5 -23.7 -21.9 -24.5 -23.5 -23.4±0.2 (4 to 5)x64fis -27.0 -26.0 -23.8 -33.4 -28.5 -27.7±1.8
Table 3.4. Peak sidelobe power against T within 64ps line repetition intervals over all
Waveform: 1 2 3 4 5 Average 64.0ps -13.4 -15.7 -13.2 -16.9 -15.3 -14.9±0.8 128.0ps -13.5 -18.1 -16.5 -17.4 -22.3 -17.6±1.6 192.0ps -19.5 -20.5 -19.4 -17.3 -23.1 -20.0±1.1 256.0ps -23.0 -26.1 -24.0 -20.3 -27.0 -24.1±1.3 320.0ps -38.0 -39.0 -38.2 -28.0 -38.4 -36.3±2.3
Table 3.5. Peak ambiguity power against t at 64ps line repetition intervals over all
CHapter3 ‘lyBS ^ Waveform
Figures A3.4a-e illustrate the same AF silhouettes as above, but now viewing the silhouette along the T=0 axis. Again, peaks of sidelobes generally remain below -15dB, but the TV line ambiguities (due to line frequency at l/64ps = 15.625kHz) are stronger than -15dB in more localities compared to Figures A3.3a-e. Table 3.6 summarises peak ambiguity power at each 15.625kHz interval, while Table 3.7 summarises peak sidelobe power within these intervals. This means that clutter suppression would be weak at these differential Doppler frequencies. The position of these ambiguities in the T-<^-plane is therefore of importance, since this is where stationary clutter or a large RCS target can create false targets. However, we shall return to this in the next section.
W aveform: 1 2 3 4 5 Average
(0 to l)x l/6 4 |is -15.1 -15.3 -17.3 -14.6 -14.2 -15.3±0.6
(1 to 2 )x l/6 4 |is -14.0 -12.3 -16.4 -16.6 -21.0 -16.1±1.6
(2 to 3)xl/64p s -20.2 -19.3 -16.8 -18.2 -19.6 -18.8±0.7
(3 to 4)xl/64|as -16.7 -19.3 -13.1 -20.8 -20.9 -18.2±1.6
fab le 3.6. Peak sidelobe power against ^ within 15.625kHz line frequency intervals over 1
Waveform: 1 2 3 4 5 Average
15.625kHz -14.8 -18.9 -11.5 -12.3 -16.6 -14.8±1.5
31.125kHz -12.6 -16.7 -15.3 -16.0 -17.6 -15.6±1.0
46.875kHz -15.6 -16.3 -18.0 -17.2 -16.2 -16.7±0.5
62.500kHz -14.8 -11.5 -19.0 -19.9 -18.9 -16.8±1.8
Table 3.7. Peak ambiguity power against ^ at 15.625kHz line frequency intervals over all T.
For reasons of limited computing power, these silhouette AFs were computed at restricted intervals of T (320ns rather than 20ns) and range of ^ (up to 62.5kHz, instead of 25MHz).
One can gain an idea of the loss of information by comparing, for example. Figure A3.3a to Figure A 3.la. However, one may also see that the general features are not affected.
The second point to note is the overall structure of the AFs, which may be decomposed into three parts. Firstly, the mean sidelobe power (disregarding ambiguity peaks) steadily rolls off with T. Secondly, at each 64ps interval, an increment in power occurs of
approximately the same amount above the mean sidelobe power. Thirdly, at T=0, the power reaches OdB within V2AT that has been found above. It may be seen in Figure A3.la that the mainlobe widens suddenly once below -15dB, about the power of the next ambiguity. Each feature appears as a pedestal of approximately Gaussian profile with increasingly narrow width. The explanation is that from the central limit theorem, in the long term the PDF of a pixel signal will be Gaussian. This convolutes with the TV modulation standards’ scanning pattern so that the narrowest pedestal is pixel auto correlation, the second is pixel-to-line cross-correlation, and the third is pixel-to-screen cross-correlation.