Radar Systems Analysis And Design Using MATLAB 1st Edition Bassem R. Mahafza - Solutions

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21.2 LANS and WANS are used in different circumstances. What are the different circumstances for using them? When is one more appropriate than another?
21.3 One of the regional offices of System Telecom operates in South Western France as an ‘Agence’. It sells System Telecom products and services as well as other telecommunication products such as pagers, answerphones and mobile phones. It now wishes to install a computer system for office
1.1. (a) Calculate the maximum unambiguous range for a pulsed radar with PRF of and ; (b) What are the corresponding PRIs?
1.2. For the same radar in Problem 1.1, assume a duty cycle of 30% and peak power of . Compute the average power and the amount of radiated energy during the first .200Hz 750Hz 5KW 20ms
1.3. A certain pulsed radar uses pulse width = 1us. Compute the corre- sponding range resolution.
1.4. An X-band radar uses PRF of 3KHz. Compute the unambiguous range, and the required bandwidth so that the range resolution is 30m. What is the duty cycle?
1.5. Compute the Doppler shift associated with a closing target with veloc- ity 100, 200, and 350 meters per second. In each case compute the time dilation factor. Assume that = 0.3m.
1.6. A certain L-band radar has center frequency 1.5GHZ, and PRFf, = 10KHz. What is the maximum Doppler shift that can be measured by this radar?
1.7. Starting with a modified version of Eq. (1.27), derive an expression for the Doppler shift associated with a receding target.
1.8. In reference to Fig. 1.16, compute the Doppler frequency for y = 150m/s, 0 = 30, and 0 = 15. Assume that = 0.1m.
1.9. A pulsed radar system has a range resolution of 30cm. Assuming sinu- soid pulses at 45KHz, determine the pulse width and the corresponding band- width.
1.10. (a) Develop an expression for the minimum PRF of a pulsed radar; (b) compute fr for a closing target whose velocity is 400m/s; (c) what is the unambiguous range? Assume that = 0.2m.
1.11. An L-band pulsed radar is designed to have an unambiguous range of 100Km and range resolution AR 100m. The maximum resolvable Doppler frequency corresponds to varget 350m/sec. Compute the maximum required pulse width, the PRF, and the average transmitted power if P, = 500W.
1.12. Compute the aperture size for an X-band antenna at fo = 9GHz. Assume antenna gain G = 10, 20, 30 dB.
1.13. An L-band radar (1500 MHz) uses an antenna whose gain is G = 30dB. Compute the aperture size. If the radar duty cycle isd, = 0.2 and the average power is 25KW, compute the power density at range R = 50Km.
1.14. For the radar described in Problem 1.13, assume the minimum detect- able signal is 5dBm. Compute the radar maximum range for =1.0, 10.0, 20.0m.
1.15. Consider an L-band radar with the following specifications: operating frequency fo 1500MHz, bandwidth B = 5MHz, and antenna gain G = 5000. Compute the peak power, the pulse width, and the minimum detectable signal for this radar. Assume target RCS = 10m, the single pulse SNR is 15.4dB, noise
1.16. Repeat Example 1.4 with P, 1MW, G = 40dB, and = 0.5m.
1.17. Show that the DC component is the dominant spectral line for high PRF waveforms.
1.18. Repeat Example 1.5 with L = 5dB, F = 10dB, T = 500K, T = 1.5s,d, 0.25, and R = 75Km.
1.19. Consider a low PRF C-band radar operating at fo = 5000MHz. The antenna has a circular aperture with radius 2m. The peak power is P = 1MW and the pulse width is t = 2s. The PRF isf, = 250Hz, and the effective temperature is T = 600K. Assume radar losses L = 15dB and target RCS = 10m. (a)
1.20. The atmospheric attenuation can be included in the radar equation as another loss term. Consider an X-band radar whose detection range at 20Km includes a 0.25dB/Km atmospheric loss. Calculate the corresponding detec- tion range with no atmospheric attenuation.
1.21. Let the maximum unambiguous range for a low PRF radar be Rmax (a) Calculate the SNR at (1/2)Rmax and (3/4)Rmax. (b) If a target with = 10m exists at R = (1/2)R what should the target RCS be at 'max" R = (3/4)Rmax so that the radar has the same signal strength from both tar- gets.
1.22. A Milli-Meter Wave (MMW) radar has the following specifications: operating frequency fo = 94GHz, PRFf, = 15KHz, pulse width = 0.05ms, peak power P, = 10W, noise figure F = 5dB, circular antenna with diameter D = 0.254m, antenna gain G = 30dB, target RCS = 1m, system losses L = 8dB, radar scan
1.23. Repeat Example 1.5 with 2 = 4, 6 = 1m, and R = 400 Km.
1.24. Using Eq. (1.80), compute (as a function of B,/B) the crossover range for the radar in Problem 1.22. Assume P, = 100W, G, = 10dB, and L, = 2dB.
1.25. Using Eq. (1.80), compute (as a function of B,/B) the crossover range for the radar in Problem 1.22. Assume P, = 200W, G, = 15dB, and L = 2dB. Assume G' = 12dB and R, = 25Km.
1.26. A certain radar is subject to interference from an SSJ jammer. Assume the following parameters: radar peak power P, = 55KW, radar antenna gain G = 30dB, radar pulse width = 2s, radar losses L = 10dB, jammer power P, = 150W, jammer antenna gain G, = 12dB, jammer bandwidth B, = 50MHz, and
1.27. A radar with antenna gain G is subject to a repeater jammer whose antenna gain is G,. The repeater illuminates the radar with three fourths of the incident power on the jammer. (a) Find an expression for the ratio between the power received by the jammer and the power received by the radar;
1.28. Using Fig. 1.30 derive an expression for R,. Assume 100% synchro- nization between the transmitter and receiver.
1.29. An X-band airborne radar transmitter and an air-to-air missile receiver act as a bistatic radar system. The transmitter guides the missile toward its tar- get by continuously illuminating the target with a CW signal. The transmitter has the following specifications: peak power P, = 4KW;
1.30. Repeat the previous problem when there is 0.1dB/Km atmospheric attenuation.
1.31. Consider an antenna with a sinx/x pattern. Let x = (Trsine)/x. where r is the antenna radius, & is the wavelength, and 8 is the off-boresight angle. Derive Eq. (1.100). Hint: Assume small x, and expand sinx/x as an infinite series.
1.32. Compute the amount of antenna pattern loss for a phased array antenna whose two-way pattern is approximated by f(y) = [exp(-21n2(y/03))1 where 3dB is the 3dB beam width. Assume circular symmetry.
1.33. A certain radar has a range gate size of 30m. Due to range gate strad- dle, the envelope of a received pulse can be approximated by a triangular spread over three range bins. A target is detected in range bin 90. You need to find the exact target position with respect to the center of the
1.34. Compute the amount of Doppler filter straddle loss for the filter defined by 1 H(f) 1+a Assume half-power frequency f3dB 500Hz and crossover frequency fc = 350Hz.
2.1. Design a cylindrical RCS calibration target such that its broadside RCS(cylinder) and end (flat plate) RCS are equal to at . The RCS for a flat plate of area is .
2.2. The following table is constructed from a radar cross-section measurement experiment. Calculate the mean and standard deviation of the radar cross section.2 55 6 67 12 73 16 90 20 98 24 110 26 117 19 126 13 133 8 139 5 144 3 150
2.4. The backscattered RCS for a corner reflector is given by This RCS is symmetric about the angle . Develop a MATLAB program to compute and plot the RCS for a corner reflector. The RCS at the is
3.1. Prove that.
3.2. Show that . Hint: You may utilize the relation.
3.3. In a multiple frequency CW radar, the transmitted waveform consists of two continuous sinewaves of frequencies and .Compute the maximum unambiguous detection range.
3.4. Consider a radar system using linear frequency modulation. Compute the range that corresponds to . Assume a beat frequency.
3.5. A certain radar using linear frequency modulation has a modulation frequency, and frequency sweep . Calculate the average beat frequency differences that correspond to range increments of and meters.
3.6. A CW radar uses linear frequency modulation to determine both range and range rate. The radar wavelength is , and the frequency sweep is. Let . (a) Calculate the mean Doppler shift; (b)compute and corresponding to a target at range , which is approaching the radar with radial velocity of
3.7. In Chapter 1 we developed an expression for the Doppler shift associ- ated with a CW radar (i.e.. fd = 2v/h, where the plus sign is used for clos- ing targets and the negative sign is used for receding targets). CW radars can use the system shown below to determine whether the target is
3.8. Consider a medium PRF radar on board an aircraft moving at a speed of 350 m/s with PRFs fri = 10KHz, fr2 = 15KHz, and fr3 = 20KHz; the radar operating frequency is 9.5GHz. Calculate the frequency position of a nose-on target with a speed of 300 m/s. Also calculate the closing rate of a target
3.9. Repeat Problem 3.8 when the target is 15 off the radar line of sight.
3.10. A certain radar operates at two PRFs, fri and fr2, where T = (1/f,1) = T/5 and T2 = (1/f,2) = T/6. Show that this multiple PRF scheme will give the same range ambiguity as that of a single PRF with PRI T.
3.11. Consider an X-band radar with wavelength = 3cm and bandwidth B = 10MHz. The radar uses two PRFs, f1 = 50KHz and fr = 55.55KHz. A target is detected at range bin 46 forf, and at bin 12 for fr2. Determine the actual target range.
3.12. A certain radar uses two PRFS to resolve range ambiguities. The desired unambiguous range is R = 150Km. Select a reasonable value for N. Compute the corresponding fri fra Rai, and R.2.
3.13. A certain radar uses three PRFS to resolve range ambiguities. The desired unambiguous range is R = 250 Km. Select N = 43. Compute the corresponding fri fra fr3 R1 R2 and R3
4.1. In the case of noise alone, the quadrature components of a radar return are independent Gaussian random variables with zero mean and variance .Assume that the radar processing consists of envelope detection followed by threshold decision. (a) Write an expression for the pdf of the envelope;
4.2. (a) Derive Eq. (4.13); (b) derive Eq. (4.15).
4.3. A pulsed radar has the following specifications: time of false alarm, probability of detection , operating bandwidth. (a) What is the probability of false alarm ? (b) What is the single pulse SNR? (c) Assuming non-coherent integration of 100 pulses, what is the SNR reduction so that and remain
4.4. An L-band radar has the following specifications: operating frequency, operating bandwidth , noise figure , system losses , time of false alarm , detection range , probability of detection , antenna gain, and target RCS . (a) Determine the PRF , the pulse width , the peak power , the
4.5. (a) Show how you can use the radar equation to determine the PRF , the pulse width , the peak power , the probability of false alarm , and the minimum detectable signal level . Assume the following specifications:operating frequency , operating bandwidth , noise figure , system losses , time
4.7. A radar system uses a threshold detection criterion. The probability of false alarm . (a) What must be the average SNR at the input of a linear detector so that the probability of miss is ? Assume large SNR approximation (see Problem 4.6). (b) Write an expression for the pdf at the output of
4.8. An X-band radar has the following specifications: received peak power, probability of detection , time of false alarm, pulse width , operating bandwidth , operating frequency , and detection range . Assume single pulse processing. (a) Compute the probability of false alarm . (b)Determine the
4.9. A certain radar utilizes 10 pulses for non-coherent integration. The single pulse SNR is and the probability of miss is . (a) Compute the probability of false alarm . (b) Find the threshold voltage .
4.10. Consider a scanning low PRF radar. The antenna half-power beam width is , and the antenna scan rate is per second. The pulse width is, and the PRF is . (a) Compute the radar operating bandwidth.(b) Calculate the number of returned pulses from each target illumination.(c) Compute the SNR
4.11. Using the equation calculate when and . Perform the integration numerically.
4.12. Repeat Example 4.3 with and .
4.13. Derive Eq. (4.107).
4.14. Write a MATLAB program to compute the CA-CFAR threshold value. Use similar approach to that used in the case of a fixed threshold.
4.15. A certain radar has the following specifications: single pulse SNR corresponding to a reference range is . The probability of detection at this range is . Assume a Swerling I type target. Use the radar equation to compute the required pulse widths at ranges so that the probability of
4.16. Repeat Problem 4.15 for swerling IV type target.
4.18. Reproduce Fig. 4.10 for Swerling II, III, and IV type targets.
4.19. Develop a MATLAB program to calculate the cumulative probability of detection.
5.1. Derive Eq. (5.17).
5.2. Derive Eq. (5.66).
5.3. Derive Eq. (5.54).
5.4. Write a MATLAB program to perform HRR synthesis for frequency coded waveforms.
5.5. Reproduce Fig. 5.5 for . Compare your outputs. What are your conclusions?
6.1. Define and . (a) Compute the discrete correlations: , , , and . (b) A certain radar transmits the signal . Assume that the autocorrelation is equal to . Compute and sketch and .
6.2. Compute the frequency response for the filter matched to the signal(a) ; (b) , where is a positive constant.
6.3. Repeat Example 6.1 for .
6.4. Derive Eq. (6.43).
6.5. Prove the properties of the radar ambiguity function.
6.6. Starting with Eq. (6.61) derive Eq. (6.62).
6.7. A radar system uses LFM waveforms. The received signal is of the form , where is a time delay that depends on range,, and . Assume that the radar bandwidth is , and the pulse width is . (a) Give the quadrature components of the matched filter response that matched to .(b) Write an expression
6.8. (a) Write an expression for the ambiguity function of an LFM waveform, where , and the compression ratio is . (b) Give an expression for the matched filter impulse response.
6.9. Repeat Example 6.2 for , and .
6.10. (a) Write an expression for the ambiguity function of a LFM signal with bandwidth , pulse width , and wavelength. (b) Plot the zero Doppler cut of the ambiguity function. (c) Assume a target moving towards the radar with radial velocity . What is the Doppler shift associated with this target?
6.11. (a) Give an expression for the ambiguity function for a pulse train consisting of 4 pulses, where the pulse width is and the pulse repetition interval is . Assume a wavelength of . (b) Sketch the ambiguity function contour.
6.12. Hyperbolic frequency modulation (HFM) is better than LFM for high radial velocities. The HFM phase is where is an HFM coefficient and is a constant. (a) Give an expression for the instantaneous frequency of a HFM pulse of duration . (b) Show that HFM can be approximated by LFM. Express the
6.13. Consider a Sonar system with range resolution . (a) A sinusoidal pulse at frequency is transmitted. What is the pulse width, and what is the bandwidth? (b) By using an up-chirp LFM, centered at
6.14. A pulse train is given by where is a single pulse of duration and the weighting sequence is . Find and sketch the correlations ,, and .
6.15. Repeat the previous problem for .
6.16. Modify the function “train_ambg.m” to accommodate the case.
6.17. Using the MATLAB functions presented in this chapter, generate the exact plots that correspond to Figs. 6.13 and 6.14.
6.18. Using the function “lfm_ambg.m” reproduce Fig. 6.6b for a downchirp LFM pulse.
7.1. Starting with Eq. (7.17), prove Eq. (7.21).
7.2. The smallest positive primitive root of is ; for generate the corresponding Costas matrix.
7.3. Develop a MATLAB program to plot the ambiguity function associated with Costas codes. Use Eqs. (7.53) through (7.56). Your program should generate 3-D plots, contour plots, and zero delay/Doppler cuts. Verify the side lobe behaviour and the compression ratio of Costas codes.
7.4. Consider the 7-bit Barker code, designated by the sequence . (a)Compute and plot the autocorrelation of this code. (b) A radar uses binary phase coded pulses of the form , where, , and. Assume . (a) Give an expression for the autocorrelation of the signal , and for the output of the matched
7.5. (a) Perform the discrete convolution between the sequence defined in Eq. (7.59), and the transversal filter impulse response (i.e., derive Eq. (7.60). (b) Solve Eq. (7.60), and sketch the corresponding transversal filter output.
7.6. Repeat the previous problem for and . Use Barker code of length 13.
7.7. Develop a Barker code of length 35. Consider both and .
7.8. Write a computer program to calculate the discrete correlation between any two finite length sequences. Verify your code by comparing your results to the output of the MATLAB function “xcorr”.

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Radar Systems Analysis And Design Using MATLAB 1st Edition Bassem R. Mahafza - Solutions

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