Frequency Hopping Zero Sidelobe Code Set with Desirable Frequency Selective Fading and Multipath Interference Properties

This paper proposes a method of generating a zero-sidelobe code set from a given code/code set via interleaving each code with zeroes and multiplication of their matched filter outputs, resulting in complete cancellation of the side lobes while reinforcing the main lobe. The new code set is generated via up sampling each code, in the underlying desired code set, by a number belonging to a set of relatively prime numbers. Each code is transmitted at a different frequency. With careful selection of the relatively prime numbers, the codes can be interlaced in the time domain resulting in a frequency hopping mechanism. Frequency selective fading will only change the magnitude of the reinforced main lobe, but the cancellation of the side lobes is not affected. This removes a fundamental weakness in Golay complementary sets due to the undesirable effect of inexact cancellation of the side lobes of Golay complementary sets, due to frequency selective fading, resulting in the reemergence of nonzero side lobes. In addition to that, the underlying code set of the proposed scheme can be chosen totally freely without any predetermined conditions, unlike the Golay complementary sets which have to satisfy the complementary property. The proposed code set is also shown to be resistant to the effects of multipath.