8/12/2019 ECE/EAS 4870 (Spring 2014) Homework 7

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EAS487: Radar Remote Sensing Spring 2014

HOMEWORK 7: Coding

Reference: Lectures 34-37 Due: 2014 April 25

Problem 1. We discussed in class that, due toits slow rotation rate, Venus is an underspread tar-get (or nearly so) at the Arecibo S-band radar fre-quency of 2.38 GHz. This is not true for Mars, which

rotates with a period of 1.03 Earth days. If we ig-nore echoes from portions of Mars sufficiently distantfrom the subradar point, however, we can make theplanet effectively underspread. This means that onlya narrow strip of the surface near the equator can bemapped, however.

a) Verify that Mars is overspread at 2.38 GHz.The radius of mars is about 3400 km. IsMars also overspread for the 430 MHz radar atArecibo?

b) Find the size of the region of Mars that can

be mapped without frequency aliasing.

c) Suppose that we use a long cyclic code witha repetition period (effective IPP) ofn = 2p 1bauds, where the baud length is 4 s. What pe-riod (what integer value ofp) should you chooseto give the appropriate IPP? Ignore the rotationof Earth for this problem, even though it is notreally negligible.

Problem 2. A receiver is matched to a single5-baud binary Barker code (+ + + +).

a) What will be the output of the filter if theinput consists of contiguous (touching) Barkercodes, each of length 5, assuming no Dopplershift?

b) Repeat (a) for the case when the two codesare separated by exactly one baud length andthe second is inverted in sign, i.e., the sequenceis (++ ++0+). The receiver decoder(filter) remains the same as for (a). You shouldnotice that some of the range sidelobes vanishfor the second case. This sort of code providestwo samples of echos from a given target sepa-rated by a very short time interval. This kindof information could be useful in probing over-spread targets.

Problem 3. Complementary codes are pairs ofbinary phase codes which work together to produceno range sidelobes. The idea is to transmit the firstpulse in the pair, wait for an IPP, and then transmitthe second pulse. Matched filter decoding is per-formed separately for the two pulses, and then the

results are added together prior to detection (squar-ing of the voltages). So long as the echoes are slowlyfading and remain phase coherent for an entire IPP,the range sidelobes of the two pulses in the pair can-cel identically.

a) The shortest complementary code pair is(1, 1) followed by (1,1). Verify that this is in-deed a complementary phase code pair.

Longer complementary codes can be assembledfrom the basic code in part (a). To form the firstcode in the pair, concatenate together both of theprevious codes (i.e. get (1, 1, 1,1)). To form thesecond code in the pair, take the first one you justcalculated and reverse the signs of the bauds in thesecond half of the code (i.e. get (1, 1,1, 1)). Repeatas necessary.

b) Find the complementary code with 8-baudpulses and verify that it produces no range side-lobes.

Problem 4. Barker codes can be combined toproduce much longer codes. The idea is to modulatethe sub-pulses of a Barker coded pulse with anotherBarker code. For example, ifB4 = (+++) andB5= (+ + + +), then B54 = (+ + + +,+ + +

+,

+

,+ + +

+), where the commas arentbreaks but are just intended to help illustrate whatsgoing on. Note that the 20-bit code that results isnot itself a Barker code.

a) Write down the sequence for B43.

b) Calculate the matched filter output for thiscode.

c) What are the sidelobe level and compressionratio?

CORNELL UNIVERSITY c DAVE HYSELL (08/04/15)

HW 71