ECEN5633 Radar Theory Lecture #9 10 February 2015 Dr. George Scheets 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)

ECEN5633 Radar Theory Lecture #10 12 February 2015 Dr. George Scheets 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

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

Signal * Wideband Noise

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

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

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

Not Named after Oscar Myer

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".

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.

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

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

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

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

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)

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)

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)

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

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

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)

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

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

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