Algorithm for complementary-derived orthogonal sequences applied to measurements in noisy channels

Complementary sequences are currently being applied to multiple fields of engineering not only when an active signal must be coded to obtain large noise immunity (proportional to the sequences length) but also when multiuser or multisensory operations need to be conducted (because of their orthogonality properties). The orthogonality between complementary sequences is only defined for sequences with the same length. This constraint limits complementary sequences implementation in cases in which all the sequences feature the same length. This paper describes the way in which orthogonal sequences of different length can be generated starting from given complementary sequences. A possible application to a noisy channel is also analysed. In the said application, a pair of complementary sequences of short length is used to code the desired information, while simultaneously an orthogonal complementary pair of larger length is used to measure the channel attenuation.