ECEN5633 Radar Theory Lecture #24 9 April 2015 Dr. George Scheets n Read 5.1 & 5.2 n Problems 4.3, 4.4, 5.1 n Reworked exams due 16 April (Live) u Around 23 April (DL)

Coherent Detection (PLL) n Single Echo Will operate along X(τ,0) u Matched Filter output envelope u Zero doppler n Multiple Echoes in ≈ same range bin u Strong will operate along X(τ,0) u Weak will operate in X(τ,ν) u If equal strength, both may operate in X(τ,ν) n Noncoherent Detection u All echoes operate in X(τ,ν)

Rectangular Pulse Ambiguity Function source: skolnik, Introduction to Radar Systems

Nulls at 1/tp Hz n Doppler Blind Speeds n Moving Target Indicator u Delay Line Canceler u Has Blind Speeds at n(PRF), n a + integer n Ambiguity Function Blind Speeds u h(t) = 1; 0 < t < tp? u Doppler Frequency of 1/tp Hz? u 1 complete Sinusoid Cycle in tp seconds u Area under h(t)p(t) = Matched Filter Output = 0

M = 5 Pulse Integration n One way to do this is with a filter matched to 5 pulses. n What will the Ambiguity time axis look like? u X(τ,0) = Autocorrelationof complex envelope g(t) t g(t) & h(t) source: Levanon, Radar Principles

M = 5 Pulse Integration n One way to do this is with a filter matched to 5 pulses. n What will the Ambiguity frequency axis look like? X(0,ν) = F.T. of signal's magnitude t g(t) & h(t) source: Levanon, Radar Principles

Frequency Domain Processing Doppler shift is 0 Hz here. Dashed Line Sinc Function: Set by Pulse Shape Inside smaller Sinc Function: Set by Pulse train Length Distance between small Sinc Functions: Set by PRF PRF Source: Communication and Radar Systems. Nicolaos Tzannes Main lobe is 1/(2Window) Hz wide 1/t p

"3D" View, 5 Pulse Ambiguity source: Levanon, Radar Principles

Top Down View, 5 Pulse Ambiguity source: Levanon, Radar Principles Plenty of opportunities to track wrong peak.

5 Pulse Ambiguity Function n Of Academic Interest u Integration typically not done this way n Matched Filter usually set for single pulse u Integrate by adding M outputs together u Make decision based on sum n But… u Center pulse can be made arbitrarily narrow

Along the time axis source: Levanon, Radar Principles n Pulse width t p can be made real small n Slowing PRF will move triangles apart

Along the Frequency Axis PRF Source: Communication and Radar Systems. Nicolaos Tzannes Main lobe is 1/(2Window) Hz wide 1/t p n Number of pulses can be made large u Window (function of M, t p & 1/PRF) gets larger u Small sinc functions become spikier n Slowing PRF not good here

M Pulse Ambiguity Function n Shows center pulse can be made arbitrarily narrow n Ambiguity Function volume must go elsewhere u Goes into other spikes n Is there another technique that can yield good time and doppler accuracy? u I.E. a narrow spike centered at X(0,0) ?

Baseband Linear Up-Chirp Signal n f s = 100 sps n t p = 1 second n Start at 0 Hz n End at 6 Hz n RCVR LO set to run at f low.

Autocorrelation of Up-Chirp Right Hand Side n Right Hand Side n Pulse lasted 100 samples n Autocorrelation hits zero around 7 samples n Matched filter output & Ambiguity Function should look similar

Chirped Pulse n f s = 100 sps n t p = 1 second n Start at 0 Hz n End at 6 Hz n Equal Energy Unchirped Pulse Output.