The authors consider the worst-case transceiver design problem under spectrum bounded channel uncertainty matrices. Their design aims to minimise the trace and the determinant of the estimate error covariance matrix, respectively. The authors relax the formulated problem into an optimisation problem with bilinear matrix inequality constraints (i.e. BMI problem), from which a local optimal solution is obtained by applying semi-definite programming. Furthermore, the authors consider norm bounded source symbols and extend their approach to design the worst-case transceiver with respect to both channel uncertainties and norm bounded source symbols.