Periodic On–Off Keying Codes for Laser Radar Incoherent Pulse Compression

Pulsed laser systems for long range target detection process multiple pulses to increase signal-to-noise ratio SNR from that of a single pulse. Unipolar
on
–
off
keying (OOK) periodic pulse modulation codes are appropriate for an incoherent system. Mismatched filters for cross-correlation with codes are solutions to exactly determined linear equations, so all zero sidelobes are realized for any nonsingular set of equations and codes that are not all zeros. Therefore, maximum SNR is proposed as the criterion for code-filter pair adoption at a given code length. The fast solution of the mismatched filtering circulant equations allows all codes for a set of balancing values [differences of numbers of
on
(ones) and
off
(zeros)] to be tested for odd code lengths up through 33. M-sequences and Legendre codes of prime lengths one less than a multiple of four and an excess of one more
on
than
off
lead to optimal SNR code-filter pairs. These Legendre codes are suggested for longer codes since they are easily constructed. Code-filter pairs that optimize SNR for a given code length and balancing values of ±1, ±3, ±5, and ±7 are reported. For a balancing value of –1, a new set of codes with corresponding two-value filters is found.