1. ECEN5633 Radar Theory Lecture #9 10 February 2015 Dr. George Scheets www.okstate.edu/elec-eng/scheets/ecen5633 n Read 8.4, 3.1 – 3.5 n Problems 2.38, 14.2, web1 & 2 n Reworked Quizzes due 1 week after return n Exam #1: Open book & notes u 17 February 2015 (Live) u Not later than 24 February (DL)

2. ECEN5633 Radar Theory Lecture #10 12 February 2015 Dr. George Scheets www.okstate.edu/elec-eng/scheets/ecen5633 n Read 3.6 & 3.7 n Problems 8.9, 8.10, old exam #1 n Reworked Quizzes Due u Today – Live u 1 week after return - Dl n Exam #1, 19 February 2015 u Open book & notes

3. OSI IEEE n February General Meeting n 5:30-6:30 pm, Wednesday, 18 February n ES201b n Reps from Tinker AFB will present n Dinner will be served + 3 points extra credit n All are invited

4. Signal * Wideband Noise

5. Last Time… n Radar Horizon ≈ (8*Earth Radius*height/3) 0.5 n General Receiver Configurations u Super Heterodyne F RF brought to IF for processing u Homodyne (a.k.a. Direct Conversion) F RF brought to baseband for processing u Coherent Detection F One Mixer which must be phase & freq locked Phased Locked Loops Syncs Receiver LO with received RF echoPhased Locked Loops Syncs Receiver LO with received RF echo u Quadrature Detection F Two mixers instead of one

6. Leonhard Euler n Born 1707 n Died 1783 n Swiss Mathematician & Physicist u Mostly worked in Prussia & Russia n Considered Greatest Mathematician of 18 th Century

7. Joseph Fourier n Born 1768 n Died 1830 n French Mathematician & Physicist n Researched Heat Flow 1822 published "Analytical Theory of Heat" u Postulated any function = bunch of sinusoids

8. Not Named after Oscar Myer

9. Norbert Wiener n Born 1894 n Died 1964 n American Mathematician M.I.T. Professor n Proposed filter in a 1949 paper u Minimizes the average squared error between the filter output and a "desired response".

10. Error Signal Filter Output y(n) ‘Desired’ Response d(n) Error e(n) = d(n) – y(n) - + Wiener Filter seeks to minimize. ‘Desired’ Response not always easy to find.

11. FIR Adaptive Filter x(n) x(n-1) z -1 w1w1 wNwN w2w2 Filter Output y(n)

12. Adaptive Linear Predictor z -1 FIR Adaptive Filter ‘Desired Response’ d(n) x(n) = d(n-1) y(n) + - e(n) = d(n) ^

13. z -1 FIR Adaptive Filter input d(n) d(n-1) Estimate of d(n) + - e(n) FIR Filter unable to predict future behavior. Best option, set all weights = 0. Suppose d(n) is White Noise

14. z -1 FIR Adaptive Filter input d(n) d(n-1) Estimate of d(n) + - e(n) There is some predictability between d(n-1) & d(n). FIR weights can be adjusted to reduce error power. Suppose d(n) is a Narrow Band Signal

15. Suppose x1(n) is a Narrowband Signal & x2(n) is Wideband Noise z -1 FIR Adaptive Filter input d(n) =x1(n) + x2(n) d(n-1) + - e(n) Adaptive Filter adjusts to minimize the A[e(n) 2 ] y(n)

16. Suppose x1(n) is a Narrowband Signal & x2(n) is Wideband Noise z -1 FIR Adaptive Filter input d(n) =x1(n) + x2(n) d(n-1) + - Estimate of the noise Adaptive Filter adjusts to minimize the A[e(n) 2 ] Estimate of Signal e(n)

17. Adaptive Linear Predictor z -1 FIR Adaptive Filter input d(n) =x1(n) + x2(n) d(n-1) + - Estimate of less correlated signal Adaptive (Wiener) Filter adjusts to minimize the A[e(n) 2 ] Estimate of more correlated signal e(n)

18. Commo System Multipath Suppression FIR Adaptive Filter Received Signal r(t) + - e(n) FIR Filter attempts to undo Multipath Distortion. y(n) Periodically Receive Known Sequence of Distorted Logic 1's and 0's Periodically Inject Known Sequence of Clean Logic 1's and 0's

19. Hermann Schwarz n Born 1843 n Died 1921 n German Mathematician n Modern Proof of Integral Inequality u Published in 1888 u In Vector Form || A∙B || < ||A||∙||B|| (3∟0 o )∙(4∟90 o ) = 0 < 3∙4 = 12 Equality holds iff A = kB, k a scalar constant

20. Radar Signal Representation n s(t) = p(t)∙cos(ω c t + θ(t) + φ) u Amplitude Modulation p(t) u Frequency Modulation θ(t) F For CW and fixed XMTR f c Pulse Radar, θ(t) = 0 n s(t) = p(t)∙cosθ(t)∙cos(ω c t + φ) - p(t)∙sinθ(t)∙sin(ω c t + φ) n Complex Envelope c(t) = p(t)[cosθ(t) + j∙sinθ(t)] u These terms modulate carrier frequency f c u They define (envelope) shape of S(f)

21. Marc-Antoine Parseval n Born 1755 n Died 1836 n French Mathematician n Published 5 papers in his life u #2 in 1799 stated, but did not prove F Said was self-evident Picture not Available

22. Sinc 2 Function & Noise BW f(Hz) … … Noise BW = 1/(2T p ) 1/T p 0 Tp2Tp2

23. Matched Filters n Seeks to maximize output SNR n h(t) is matched to expected signal u Direct Conversion Receiver Matched to baseband signal n Square pulse of width t p expected? u Noise BW = 1/(2t p ) Hz