Multiplicative Complementary Codes

A code with nonzero side lobes occurring only at odd powers of is generated by interlacing Golay complementary pairs. A second code with side lobes at even powers of is then generated, either via replacing by in any desired code or via using skew-symmetric codes. These two codes are transmitted using two frequencies. At the receiver, their individual matched filter outputs are multiplied, resulting in zero side lobes. This property is scale invariant and is therefore, resistant to frequency selective fading. The code length for the first code could be two times any available Golay biphase complementary code length, while the code length for the second code is arbitrary, but has to be an odd number for the skew-symmetric case. However, it is preferable to choose the lengths of the two codes such that their energies are approximately equal. A second scheme uses a Golay complementary pair generated by interlacing another pair and then transmitting them at two frequencies. At the receiver, their matched filter outputs are added to result in, either zero side lobes in the case of no frequency selective fading or reduced side lobes if fading is present. A second complementary pair is transmitted at two additional frequencies, but with replaced by. The outputs of their matched filters are also added as in the previous case. The added matched filter outputs of the two pairs are then multiplied to result in zero side lobes. This scheme, while using four frequencies, has superior performance in the presence of high noise levels.