Characterization of the 1350 MHz Radar Receivedat Arecibo

Steve Ellingson∗

November 25, 2002

List of Figures

1 DIF output spectra over the first 133 (of 400) acquisitions. Top/Green:max hold; Bottom/Red: linear power average. . . . . . . . . . . . . . 4

2 DIF output spectra using all 400 acquisitions and zoomed in alongthe frequency axis. Top/Green: max hold; Bottom/Red: linear poweraverage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3 Bandlimiting filter. . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Block 10. Top: Magnitude, Bottom: Phase. . . . . . . . . . . . . . . . 75 File 115. Top: Magnitude, Bottom: Phase. . . . . . . . . . . . . . . 96 Modified channel impulse responses h(τ) for Blocks 10 (top) and 115

(bottom). (Compare to Figures 4 and 5, respectively.) In each plot, theautocorrelation of the model pulse is shown as a dashed line, centeredat τ = 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

7 Max hold (top) and linear power average (bottom) of h(τ) over 400pulses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

8 Linear power average of h(τ) over 400 pulses, shown with the autocor-relation of the model pulse. . . . . . . . . . . . . . . . . . . . . . . . 13

1 Introduction

Prominent among Arecibo’s RFI problems is the 1350 MHz air traffic control radar

based at San Juan. We have examined this radar in previous reports [1, 2]. In this

report, this radar is characterized in some additional detail. Of particular interest is

the pulse modulation and multipath delay spread.

∗The Ohio State University, ElectroScience Laboratory, 1320 Kinnear Road, Columbus, OH43210, USA. Email: ellingson.1@osu.edu.

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2 Instrumentation

On Nov 3, 2002, Grant Hampson and I interfaced a custom back end (developed

under our NASA IIP project [3]) to the Arecibo Observatory in order to do some

“piggyback” mode observations with J. Cordes (Cornell), R. Bhat (Haystack), and

M. McLaughlin (Jodrell Bank) [4]. The purpose of this session was to record examples

of RFI (radars, in particular) in astronomical data (in this case, pulsars). Cordes et.al.

were observing a 100-MHz-wide swath centered at 1175 MHz using the Arecibo “L-

Wide” receiver with the Wideband Arecibo Pulsar Processor (WAPP) back end. The

WAPP accepts its input from an IF fan-out in the receiver room. This IF is 200–

464 MHz (approximately), wherein the 1175 MHz sky frequency maps to 250 MHz

(not spectrally reversed) in the IF.

To interface the IIP system, another port from this IF fan-out (specifically, the

front panel jack on Rack 4, Unit 12) was attenuated by 24 dB, upconverted using a

Mini-Circuits ZP-5 mixer with an Agilent HP8648C synthesizer as an LO, and input

to the IIP L-band downconverter just prior to it’s image rejection filter. The LO was

tuned to put the desired sky center frequency at 1420 MHz in the input to the IIP

system. Thus:

fsky = [2345 MHz]− fLO. (1)

The IIP system does a low-side downconversion to an IF center frequency of

150 MHz and samples at 200 MSPS using 10 bits. (Note: One (of two) of the IIP

system’s Mini-Circuits ZFL-500HLN amplifiers preceding the A/D was removed for

gain leveling purposes.) Because the analog IF is in the second Nyquist zone of the

A/D, the digital passband is centered at 50 MHz and is spectrally reversed. The IIP’s

”Digital IF” (DIF) FPGA module downconverts this to 0 Hz (so now the samples are

complex-valued), filters to 50 MHz bandwidth, decimates by 2, and then upconverts

to a center frequency of +25 MHz (still complex). The data emerges from the DIF

module in 16-bit “I” + 16-bit “Q” format at 100 MSPS.

The IIP system is reconfigurable in both the hardware and software sense. For

the measurements presented here, the system was configured as a coherent capture

2

system. In this mode, voltage time series samples from the DIF are collected in a FIFO

buffer of length 256K samples. When the FIFO fills (in 2.6 ms), the acquisition is

halted while the samples are transferred to a PC, which requires about 1 s. When the

transfer is complete, the FIFO is triggered and another 256K samples are collected.

The process repeats continuously.

All data collected is freely available; contact the authors for distribution informa-

tion.

3 Analysis

In this report, we examine a set of 400 acquisition blocks, representing about 1 s of

observation collected over about 13 min in real time. Figure 1 shows the summary

spectra. The radar of interest in this report is at 1350 MHz; other radar signals

are visible at 1330 MHz and 1367 MHz. The source of the 1340 MHz emission is

unknown, but it does not appear to be a radar. A close-up of the spectrum in the

region of the 1350 MHz signal of interest is shown in Figure 2.

To study the time domain characteristics of the 1350 MHz radar, it is desirable

to suppress the other signals. To do this, the 1350 MHz sky frequency is shifted to

a center frequency of zero and a tight bandlimiting filter is applied by convolution in

the time domain. The magnitude response of this filter is shown in Figure 3. It is a

119-coefficient FIR filter obtained from the Kaiser window with β = 0.4, designed to

have a bandpass which is flat to within a few tenths of a dB inside ±2.5 MHz and in

full cutoff (> 50 dB attenuation) beyond ±5 MHz.

After each sample block is filtered as described above, the pulse modulation can

be explored. Figure 4 shows Block 10, which contains one of the strongest pulses in

the data set. The nearly-constant magnitude and phase over the pulse period indicate

that this radar is of the “pulsed CW” variety, in which the pulses are formed by gating

a sinusoid using a rectangular window. The pulse width is 5.8 µs between half-power

(−3 dB) points and 6.5 µs between −20 dB points.

Many of the pulses in the dataset exhibit significant multipath. Figure 5 shows

what is perhaps the most spectacular example, Block 115. Delayed copies of the

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1325 1330 1335 1340 1345 1350 1355 1360 1365 1370 13750

5

10

15

20

25

30

35

freq (MHz)

PS

D (

dB)

per

381

Hz

Figure 1: DIF output spectra over the first 133 (of 400) acquisitions. Top/Green:max hold; Bottom/Red: linear power average.

4

1348 1348.5 1349 1349.5 1350 1350.5 1351 1351.5 13520

5

10

15

20

25

30

35

freq (MHz)

PS

D (

dB)

per

381

Hz

Figure 2: DIF output spectra using all 400 acquisitions and zoomed in along thefrequency axis. Top/Green: max hold; Bottom/Red: linear power average.

5

0 5 10 15 20 25 30 35 40 45−160

−140

−120

−100

−80

−60

−40

−20

0

20

Frequency (MHz)

Mag

nitu

de (

dB)

Figure 3: Bandlimiting filter.

6

450 460 470 480 490 500 510 520 530 540 5500

2000

4000

6000

8000

10000

12000

time (microseconds)

mag

nitu

de (

linea

r vo

ltage

uni

ts)

455 460 465 470 47590

100

110

120

130

140

150

time (microseconds)

phas

e (d

eg)

Figure 4: Block 10. Top: Magnitude, Bottom: Phase.

7

original pulse are clearly visible more than 50 µs after the main pulse. In fact, the

main pulse itself seems to contain overlapping multipath components.

In the development of RFI mitigation techniques, such as pulse blanking, it is very

useful to know the multipath response independent of the signal which is actually

transmitted. For example, if s(t) is the transmitted pulse and x(t) is the received

signal, then the multipath can be described in terms of the channel impulse response

h(t) where

x(t) = h(t) ∗ s(t) + n(t) (2)

where “∗” denotes convolution and n(t) is the uncorrelated noise associated with

the measurement. Because s(t) is both band-limited and contains spectral nulls, the

deconvolution of s(t) and h(t) is ill-conditioned and it is not practical to solve directly

for h(t). However, we can obtain a modified channel impulse response h(t) using the

following procedure: In the frequency domain, we have:

X(ν) = H(ν)S(ν) + N(ν) (3)

where the upper case quantities denote the Fourier transforms of the associated lower

case quantities. Multiplying both sides by S∗(ν) (where the superscript “∗” denotes

conjugation):

S∗(ν)X(ν) = ‖S(ν)‖2H(ν) + S∗(ν)N(ν) (4)

Note that if the signal-to-noise ratio (SNR) is large, the first (signal) term on the

right-hand side dominates over the second (noise) term. Neglecting the noise term

and transforming back into the time domain we have

s∗(t) ∗ x(t) ∼ F−1{‖S(ν)‖2} ∗ h(t) (5)

Recall that s(t) is a rectangular pulse, and therefore S(ν) is a sinc function. Therefore,

F−1{‖S(ν)‖2} is a triangular pulse function, and Equation 5 is the desired channel

impulse response h(t) but “smeared” in the time domain due to the convolution with

a triangular pulse function. We shall call this modified version of the impulse response

h(t). h(t) is a more useful estimate of the impulse response than Equation 2 because

8

2030 2040 2050 2060 2070 2080 2090 2100 2110 2120 21300

2000

4000

6000

8000

10000

12000

time (microseconds)

mag

nitu

de (

linea

r vo

ltage

uni

ts)

2030 2040 2050 2060 2070 2080 2090 2100 2110 2120 2130

−150

−100

−50

0

50

100

150

time (microseconds)

phas

e (d

eg)

Figure 5: File 115. Top: Magnitude, Bottom: Phase.

9

it has clearly defined peaks, whereas Equation 2 is smeared by convolution with a

rectangular pulse function, which leaves no identifiable peaks.

To facilitate an analysis of the channel impulse response, the following procedure

is used:

1. X(ν) is obtained from the measured data x(t) using the FFT.

2. S(ν) is obtained from a model consisting of a single rectangular pulse 5.8 µs

long.

3. h(t), our estimate of the modified channel impulse response described above, is

obtained by taking the inverse FFT of S∗(ν)X(ν).

4. The peak of h(t) is found, and the time at which it occurs is defined as τ = 0.

The “excess delay” τ refers to the time relative to the arrival of this peak,

facilitating comparisons between different pulses.

The results for Blocks 10 and 115 are shown in Figure 6. As a check of the method,

Figure 6 also shows the autocorrelation of the model pulse; that is, h(τ) computed for

the case in which S(ν) is used in lieu of X(ν). Note that the agreement between the

autocorrelation of the model pulse and main peak of the modified impulse response

is excellent, which confirms that the simple rectangular pulse is a reasonable model

for the actual pulse.

The two cases shown in Figure 6 display the two extremes of behavior observed

in the dataset. In Block 10, a single impulse is seen, with no temporally-resolvable

multipath visible greater than 40 dB below the main peak. In Block 115, we see at

least 6 temporally-resolved components distributed over ∼ 175 µs, varying in strength

between −17 dB and −29 dB below the main peak.

Naturally, this raises the question of the statistics of h(τ) over many pulses. To

address this question, h(τ) was computed for each of the 400 pulses in the dataset.

The linear power average and max hold over the results were computed and are shown

in Figure 7. The “max hold” measurement is computed as follows: For each value of

τ , one uses the maximum value of h(τ) observed from the available pulses. Note that

10

−50 0 50 100 150 200 250 300

−80

−70

−60

−50

−40

−30

excess delay (microseconds)

pow

er (

dB)

(arb

itrar

y re

fere

nce)

−50 0 50 100 150 200 250 300

−80

−70

−60

−50

−40

−30

excess delay (microseconds)

pow

er (

dB)

(arb

itrar

y re

fere

nce)

Figure 6: Modified channel impulse responses h(τ) for Blocks 10 (top) and 115 (bot-tom). (Compare to Figures 4 and 5, respectively.) In each plot, the autocorrelationof the model pulse is shown as a dashed line, centered at τ = 0.

11

−50 0 50 100 150 200 250 300

−80

−70

−60

−50

−40

−30

excess delay (microseconds)

Pow

er (

dB)

(arb

itrar

y re

fere

nce)

Figure 7: Max hold (top) and linear power average (bottom) of h(τ) over 400 pulses.

the average curve reveals an exponential decay characteristic that can be traced to

about 100 µs, where it is about −36 dB relative to the main peak and merges into

the noise. Note also that individual multipaths are detected as long as 200 µs after

the main pulse, and one multipath precursor is detected about 10 µs before the main

pulse.

Figure 8 shows a close-up of the linear power average result, with the autocor-

relation of the model pulse shown for comparison. Note that the main peak is very

similar to the model pulse to about −20 dB, at which point the spread of delayed

(τ > 0) multipath becomes visible.

Acknowledgments

Thanks to J. Cordes, R. Bhat, and M. McLaughlin for permitting us to “piggyback”

on their observations; and to P. Perillat and L. Wray for advice and technical support

in obtaining the data.

12

−20 −15 −10 −5 0 5 10 15 20−80

−75

−70

−65

−60

−55

−50

−45

−40

−35

−30

excess delay (microseconds)

Pow

er (

dB)

(arb

itrar

y re

fere

nce)

Figure 8: Linear power average of h(τ) over 400 pulses, shown with the autocorrelationof the model pulse.

13

References

[1] S.W. Ellingson, “Characterization of Some L-Band Signals Visi-

ble at Arecibo,” Sep 27, 2002. Available at http://esl.eng.ohio-

state.edu/∼swe/ska1/docserv.html.

[2] S. Ellingson and G. Hampson, “RFI and Asynchronous Pulse Blank-

ing at Arecibo,” Nov 12, 2002. Available at http://esl.eng.ohio-

state.edu/∼swe/ska1/docserv.html.

[3] G. Hampson and S. Ellingson, “Modular Digital Back Ends for Microwave Ra-

diometry”, Nov 1, 2002. http://esl.eng.ohio-state.edu/∼swe/ska1/naic0211.pdf.

[4] S. Ellingson, “RFI Monitoring Experiment @ Arecibo,” Nov 3, 2002.

http://esl.eng.ohio-state.edu/∼swe/ska1/ap021103.txt.

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