Efficient matched filter for the generalized chirp-like polyphase sequences

The efficient implementation of the matched filter for the generalized chirp-like (GCL) polyphase sequences is presented. These sequences can be classified as the modulatable orthogonal sequences, because they can be modulated by a string of arbitrary complex numbers of unit magnitude, retaining the ideal periodic autocorrelation function and optimum crosscorrelation function. For the applications in spread-spectrum system, where the sequence length can be significantly large, it is highly important to minimize the complexity of the corresponding matched filter. The new efficient implementation of the matched filter is based on the algebraic decomposition of GCL sequences. Some interesting special cases of the efficient pulse compressors, proposed previously for P3 and P4 codes are obtained. The subclass of GCL sequences which permits even more efficient matched filter implementation for any length N=sm² is derived. It is shown that such a subclass of the GCL sequences comprises the so-called generalized Frank sequences, which can be obtained as a special case of the GCL sequences of length N=m²