Page 541 - Fundamentals of Radar Signal Processing

phase. Use m = 4, , N = 1, and P = 0.01 again. It will be necessary
FA
to numerically evaluate the Marcum Q function Q . MATLAB can be
®
M
used with either the marcumq.m function available in the Signal Processing
Toolbox™ or Communications Systems Toolbox™ or the marcum.m
function available in the “MATLAB Supplements” area of the website

http://www.radarsp.com.
9. Use Albersheim’s equation to estimate the single-sample SNR χ required
1
to achieve P = 0.01 and P equal to the same value obtained in the
FA
D
previous problem. Compare to the actual SNR used in Prob. 8.
10. Repeat Prob. 9 using Shnidman’s equation in place of Albersheim’s
equation.

11. Rearrange Albersheim’s equation to derive a set of equations for P in
FA
terms of P , N, and single-pulse SNR in dB, χ .
D
1
12. Use Shnidman’s equation to estimate the single-pulse SNR χ in dB
1
required to achieve P = 10 and P = 0.9 when noncoherently integrating
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FA
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N = 10 samples. Do this for all four Swerling cases and for the
nonfluctuating case. Figure 6.14 can be used to check the results.

Problems 13 to 16 are a related group comparing the effectiveness of
coherent and noncoherent integration of measurements and showing how

to compute noncoherent integration gain.

13. Coherently integrating N samples of signal-plus-noise produces an
integration gain of N on a linear scale; that is, if the SNR of a single sample
y is χ, the SNR of is Nχ. In Probs. 13 through 16, Albersheim’s
i
equation will be used to investigate the relative efficiency of noncoherent
integration for one example case. Throughout these problems, assume P =
D
0.9 and P = 10 are required, and that a linear detector is used. Start by
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FA
assuming detection is to be based on a single sample, N = 1. Use
Albersheim’s equation to determine the SNR χ in dB needed for this
1
single sample to meet the specifications above.
14. Now consider noncoherent integration of 100 samples to achieve the same

P and P as in the previous problem. Each individual sample can then
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have a lower SNR. Use Albersheim’s equation again to determine the SNR
χ of each pulse in dB needed to achieve the required detection
nc
performance.

15. Now consider coherent integration of 100 pulses. What is the SNR χ in dB
c
required for each pulse such that the coherently integrated SNR will be
equal to the value χ found in Prob. 13?
1
16. Finally, the noncoherent integration gain is the ratio χ /χ . Find α such that
1
nc