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.

(d) (5%) Since the minimun distance of a constellation dominates the performance of a modulation scheme, one would desire a signal diagram with the same minimum distance constraint that has smaller average symbol energy. Please design a 7-ary signal diagram on the I/Q-constellation with  = 2 and its average symbol energy no larger than 3.43. red