Orthogonal M-ary spread spectrum system under carrier frequency offset

Orthogonal M-ary spread spectrum (M-ary/SS) systems under carrier frequency offset (CFO) are investigated. It is known that CFO destroys orthogonal relations between a transmitted sequence and those not transmitted. The purposes of this paper are first to analyze the performance of M-ary/SS system under CFO, then to derive some conditions on robust orthogonal spreading code sets against CFO, and finally to evaluate the performance of the systems with several orthogonal spreading code sets under CFO. It is shown that CFO introduces spurious signals in filters not matched to the transmitted sequences, and these spurious signals are made from the offset frequency components of the signal after the despreading process, and some conditions on robust orthogonal spreading code sets are derived. Three orthogonal spreading code sets, Walsh functions, the rows of m-sequence type Hadamard matrices and optimal signal sets are investigated and the performance of the systems with these spreading code sets are evaluated. The results of evaluation show that the rows of m-sequence type Hadamard matrices are good orthogonal spreading code sets in communication channels with CFO