A Multi-level Spreading Code to Suppress Noise Enhancement in Zero-Forcing Equalization for Direct-Sequence Spread-Spectrum Communication

Zero-forcing (ZF) equalization has been proposed to combat frequency selective fading caused by multipath propagation. The ZF equalization is effective when the matrix representing the propagation channel is well-conditioned; when ill-conditioned, however, it causes noise enhancement and, as a result, deteriorates the transmission performance. This paper proposes a new spreading code to suppress the noise enhancement. First, an arbitrary binary spreading code is represented by an N×M matrix (M is the length of a transmitting symbol and N the spreading factor). Next, the matrix is singular-value decomposed. Then, all the singular values are replaced by a positive constant, and a reverse operation to the singular-value decomposition generates a new matrix, which is amply well-conditioned. The new matrix represents a multi-level spreading code, which can suppress noise enhancement. Simulation results validated its effectiveness.