Waveform Design for Active Sensing Systems Chapters 1-2 Uppsala University Department of Information Technology Uppsala University Department of Information Technology Mojtaba Soltanalian May

Introduction>Applications CDMA Communications Active sensing (Radar, Sonar, etc.) Images are taken from [ visited , and [ , respectively. 2

Introduction>Applications Channel estimation Synchronization Data hiding, ultra-wideband (UWB) communications, synthesis of orthogonal matrices for source coding and complementary coding,... Images are taken from [ visited , and [ Networks.asp]-visited , respectively. 3

Introduction Periodic/Aperiodic Autocorrleation Relationship: 4

Introduction Why computational design? Metrics: 5

Introduction>Existing waveforms Chirp signal: 6

Introduction>Existing waveforms Root-of-unity codes: 7

Introduction>Existing waveforms Root-of-unity codes: are rare! Mow’s Conjecture: the only possible lengths for root-of-unity codes with M-ary alphabet are M and M. 2 8

Introduction>Existing waveforms Barker codes 9

Introduction Unimodular sequences have optimal (i.e. unity) peak-to-average ratio (PAR): 10

Sing. Ape. Seq. Des. 11

Sing. Ape. Seq. Des. 12

Sing. Ape. Seq. Des. Important step: Discussion. 13

Sing. Ape. Seq. Des. 14

Sing. Ape. Seq. Des. Cyclic minimization: 15

Sing. Ape. Seq. Des. 16

Sing. Ape. Seq. Des. 17

Sing. Ape. Seq. Des. 18

Sing. Ape. Seq. Des. 19

Sing. Ape. Seq. Des. 20

Numerical Examples 21

Numerical Examples 22

Numerical Examples Quantized CAN: 23

Discussions. 24