where (·)∗ denotes the complex conjugate. As shown in Fig. 2, the orthogonality among spreading sequences cannot be obtained even Walsh-Hadamard sequences are used for cognitive-CDMA systems.
This is because traditional sequence design generally assumes the availability of entire spectrum band (rather than certain noncontinuous spectrum bands in a CR system as specified by the spectrum hole constraint) for every sequence.
The orthogonal property of Walsh-Hadamard sequences will be damaged if a spectrum hole constraint is imposed by spectral nulling. Hence, MAI always exists in cognitive-CDMA systems, leading to significant BER performance degradation.