(Solved): 24 M-ary quadrature amplitude modulation (M-QAM) is a widely used multilevel ...

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24 M-ary quadrature amplitude modulation (M-QAM) is a widely used multilevel 28 modulation scheme. In general, a QAM signal \( \mathrm{s}(\mathrm{t}) \) can be expressed as: \[ s(t)=A_{I} \sqrt{2} \mathrm{~h}(\mathrm{t}) \cos \left(2 \pi f_{c} t\right)+A_{Q} \sqrt{2} h(t) \sin \left(2 \pi f_{c} t\right) \] where \( \mathrm{h}(\mathrm{t}) \) is a RRC pulse-shaping same as in Fig.1 with unit pulse energy and the roll-off factor equals to \( 1, A_{I} \) and \( A_{Q} \) are a set of real-valued amplitudes correspond to different modulation order, and \( f_{c} \) is the carrier frequency. Let \( \mathrm{E} \) denote the average symbol energy, and \( \mathrm{E}_{b} \) denote the average bit energy. Assume that all signals are equally likely. Answer the following questions. Fig. 5 BER vs. E/No for M-QAM a) If the data rate is \( 60 \mathrm{Mbps} \), calculate the symbol rates for the M-QAM schemes shown in Fig.5. e) Determine a set of orthonormal basis signals for the signal space with proof. 4 What is the dimensionality of the signal space? f) Assume \( A_{I}=\{-3,-1,1,3\} \) and \( A_{Q}=\{-3,-1,1,3\} \) received by the 8 digital receiver. Determine the modulation order. Plot a constellation map for the digital symbols, and calculate the average digital symbol energy \( \mathrm{E} \).