Consider transmission over a complex valued additive Gaussian noise channel with
ID: 1715702 • Letter: C
Question
Consider transmission over a complex valued additive Gaussian noise channel with total noise power N_0. Consider three two-dimensional signal constellations: QPSK. b) Hi-PSK, and c) a version of Hl-QAM depicted in Figure 1. All signal points are equiprobable in each constellation. Assume that we use a raised cosine pulse with roll-off factor .betta = 0.2 and each symbol duration is T = 10ps. Signal constellations a), b), c). The circles in a) and b) have radius R. The circles in c) have radii R, 1.5R, 2R, and 2.5R. Find minimum distance d_min for each constellation. Compute transmission data rate- for each constellation and transmission bandwidth. Express signal-to-noise ratio E_b/.N_0 in terms of R and N_0. Compute symbol error rate as a function of E_b/N_0 for each constellation, use union bound if necessary. Assuming that symbol error rate requirement is 10^-6, find minimum E_b/N_0 in dB which guarantees the prescribed error rate for each constellationExplanation / Answer
QPSK, dmin=(2R)^0.5
16PSK, dmin=[4R*sin^2(/16)]^0.5
16QAM, dmin=[R(2.5R-1.5*2^0.5)]^0.5
2) r= data rate for QPSK=4/T= 4/10 = 400000 bit/s
r = data rate for 16QPSK = 16/10 = 1.6 *10^6 bit/s
r= data rate for 16QASK=16/4= 1.6*10^6 bit/s