申論題

(7) (25%) Consider a standard M-ary digital modulation scheme where the signal space diagram is spanned by two orthonormal waveforms, i.e. each symbol on the constellation has the in-phase and quadrature-phase components. Assume that the underlying channel model is additive white Gaussian noise (AWGN) with the power spectral density N₀ / 2 , and that no inter-symbol interference is happening. Further, assume that all symbols on the constellation are equally probable. Please answer the following questions.

(b) (10%) Derive the optimal symbol error probability when using the signal space diagram given in Figure I b in terms of the average symbol energy, No, and the Q-function,