Near–Far Resistance to NBI

Near–Far Resistance to NBI

We first consider the situation in which there is NBI but no MAI. Let the NBI signal i be an arbitrary discrete-time wide-sense stationary process, with autocorrelation matrix R_i, which is nonnegative definite. Suppose that the spectral decomposition of R_i is given by

Equation 7.132

where l₁,...,l_N and u₁,...,u_N are the nonnegative eigenvalues and the corresponding orthogonal eigenvectors of R_i. Since

Equation 7.133

using (7.77) we obtain

Equation 7.134

When the NBI signal power is increased, the nonzero l_l's increase proportionally. Therefore, it is seen from (7.134) that the near–far resistance to NBI is nonzero if and only if R_i has at least one zero eigenvalue and the corresponding eigenvector is not orthogonal to s. On the other hand, if R_i has full rank, the near–far resistance to NBI is zero.