ECEN5633 Radar Theory
Lecture #9
10 February 2015
Dr. George Scheets
www.okstate.edu/elec-eng/scheets/ecen5633
Read 8.4, 3.1 – 3.5
 Problems 2.38, 14.2, web1 & 2
 Reworked Quizzes due 1 week after return
 Exam #1: Open book & notes

 17
February 2015 (Live)
 Not later than 24 February (DL)
ECEN5633 Radar Theory
Lecture #10
12 February 2015
Dr. George Scheets
www.okstate.edu/elec-eng/scheets/ecen5633
 Read 3.6 & 3.7
 Problems 8.9, 8.10, old exam #1
 Reworked Quizzes Due
– Live
 1 week after return - Dl
 Today

Exam #1, 19 February 2015
 Open
book & notes
OSI IEEE
February General Meeting
 5:30-6:30 pm, Wednesday, 18 February
 ES201b
 Reps from Tinker AFB will
present
 Dinner will be served + 3 points extra credit
 All are invited

Signal * Wideband Noise
Last Time…


Radar Horizon
≈ (8*Earth Radius*height/3) 0.5
General Receiver Configurations
 Super Heterodyne
 RF brought to IF for processing
 Homodyne (a.k.a. Direct Conversion)
 RF brought to baseband for processing
 Coherent Detection
 One Mixer which must be phase & freq locked
• Phased Locked Loops
Syncs Receiver LO with received RF echo
 Quadrature
Detection
 Two mixers instead of one
Leonhard Euler
Born 1707
 Died 1783
 Swiss Mathematician
& Physicist

 Mostly
worked in Prussia
& Russia

Considered Greatest Mathematician
of 18th Century
Joseph Fourier
Born 1768
 Died 1830
 French Mathematician
& Physicist
 Researched Heat Flow
1822 published "Analytical Theory of Heat"

 Postulated
any function = bunch of sinusoids
Not Named after Oscar Myer
Norbert Wiener
Born 1894
 Died 1964
 American Mathematician
M.I.T. Professor
 Proposed filter in a 1949 paper

 Minimizes
the average squared error between
the filter output and a "desired response".
Error Signal
Filter Output y(n)
Error e(n) = d(n) – y(n)
+
‘Desired’ Response d(n)
Wiener Filter seeks to minimize <e(n)2>.
‘Desired’ Response not always easy to find.
FIR Adaptive Filter
x(n)
z-1
w1
x(n-1)
w2
z-1
z-1
wN
Filter Output y(n)
Adaptive Linear Predictor
‘Desired Response’ d(n)
+
e(n)
-
z-1
x(n)
= d(n-1)
FIR
Adaptive
Filter
^
y(n) = d(n)
Suppose d(n) is White Noise
+
input d(n)
e(n)
-
z-1
d(n-1)
FIR
Adaptive
Filter
Estimate
of d(n)
FIR Filter unable to predict future behavior.
Best option, set all weights = 0.
Suppose d(n) is a Narrow Band Signal
+
input d(n)
e(n)
-
z-1
d(n-1)
FIR
Adaptive
Filter
Estimate
of d(n)
There is some predictability between d(n-1) & d(n).
FIR weights can be adjusted to reduce error power.
Suppose x1(n) is a Narrowband Signal
& x2(n) is Wideband Noise
input d(n) =x1(n) + x2(n)
+
e(n)
-
z-1
d(n-1)
FIR
Adaptive
Filter
y(n)
Adaptive Filter adjusts to minimize the A[e(n)2]
Suppose x1(n) is a Narrowband Signal
& x2(n) is Wideband Noise Estimate
input d(n) =x1(n) + x2(n)
of
the noise
+
-
z-1
d(n-1)
FIR
Adaptive
Filter
e(n)
Estimate
of Signal
Adaptive Filter adjusts to minimize the A[e(n)2]
Adaptive Linear Predictor
input d(n) =x1(n) + x2(n)
Estimate
of less
correlated
signal
+
-
z-1
d(n-1)
FIR
Adaptive
Filter
Estimate of
more
correlated
signal
e(n)
Adaptive (Wiener) Filter adjusts to minimize the A[e(n)2]
Commo System Multipath Suppression
Periodically Inject
Known Sequence of
Clean Logic 1's and 0's
+
e(n)
-
Received Signal r(t)
FIR
Adaptive
Filter
Periodically Receive
Known Sequence of
Distorted Logic 1's and 0's
y(n)
FIR Filter attempts to undo Multipath Distortion.
Hermann Schwarz
Born 1843
 Died 1921
 German Mathematician
 Modern Proof of Integral Inequality

 Published
in 1888
 In Vector Form || A∙B || < ||A||∙||B||
(3∟0o)∙(4∟90o) = 0 < 3∙4 = 12
Equality holds iff A = kB, k a scalar constant
Radar Signal Representation

s(t) = p(t)∙cos(ωct + θ(t) + φ)
 Amplitude
Modulation p(t)
 Frequency Modulation θ(t)
 For
CW and fixed XMTR fc Pulse Radar, θ(t) = 0
s(t) = p(t)∙cosθ(t)∙cos(ωct + φ) p(t)∙sinθ(t)∙sin(ωct + φ)
 Complex Envelope c(t)
= p(t)[cosθ(t) + j∙sinθ(t)]

 These
terms modulate carrier frequency fc
 They define (envelope) shape of S(f)
Marc-Antoine Parseval
Born 1755
 Died 1836
 French Mathematician
 Published 5 papers in his life

 #2
in 1799 stated, but did not prove
 Said
was self-evident
Picture
not
Available
Sinc2 Function & Noise BW
Tp2
Noise BW = 1/(2Tp)
1/Tp
… …
0
f(Hz)
Matched Filters
Seeks to maximize output SNR
 h(t) is matched to expected signal

 Direct
Conversion Receiver
Matched to baseband signal

Square pulse of width tp expected?
 Noise
BW = 1/(2tp) Hz