The zeros of random polynomials: further results and applications

We consider the density of the zeros of random polynomials with nonzero mean correlated Gaussian coefficients. We show that for most communication problems the original result by Hammersley (1956) can be expressed in a simpler form. In order to illustrate the usefulness of the presented theory, two applications are considered. First, the zeros of frequency-selective Ricean fading channels are investigated. Second, the zeros of the transfer function corresponding to channel impulse response estimates obtained by a least-squares approach are calculated. For both applications implications for equalizer design are discussed.