Formation of Ambiguity Functions with Frequency-Separated Golay Coded Pulses

Returns from radar transmitters are filtered to concentrate target power and improve signal-to-noise ratio (SNR) prior to detection. An ideal "thumbtack" filter response in delay and Doppler is impossible to achieve. In practice target power is distributed over the delay-Doppler plane either in a broad mainlobe or in sidelobes with inherent limitations given by Moyal\´s identity. Many authors have considered the use of pairs or sets of complementary codes as the basis of radar waveforms. The set of filter outputs when combined reduces output to a thumbtack shape, at least on part of the delay-Doppler domain. This paper shows firstly that a pair of complementary codes cannot be multiplexed in frequency because of a phase difference which depends on the unknown range to any targets, thereby preventing the individual filter outputs from being combined coherently. It is shown that the phase term can be removed by multiplexing the second code twice, at offsets equally spaced above and below carrier, enabling the recovery of the sum of squared ambiguity functions. A proposed modification to the Golay pair results in codes whose squared ambiguities cancel upon addition. This enables complementary behaviour to be achieved by codes which are separated in frequency at the expense of introducing cross-terms when multiple closely separated returns are present. The modified Golay codes are shown to successfully reveal low power returns which are hidden in sidelobes when other waveforms are used.