Pseudo-random binary sequence design for finite impulse response identification

The design of pseudo-random binary sequence (PRBS) signals for finite impulse response identification is investigated. We derive a relationship between the PRBS design parameters and the maximum eigenvalue of the parameter error covariance matrix, which yields some useful insights and design guidelines. From the perspective of minimizing the "worst-direction" error represented by the maximum eigenvalue, PRBSs are not the best test signals in the case that disturbances are colored noises. We show that by linearly combining several shifted versions of a PRBS according to the noise model, one can improve the estimation result.