In this part, we will study the optimal power and rate adaptation for continuous rate MQAM and compute the average spectral efficiency achieved through this adaptation. Then, we will compare its average spectral efficiency to the average spectral efficiency of truncated channel inversion. We assume a Rayleigh fading channel with an average SNR
γˉand the target BER is equal to P b
. *Q1. Explain the optimal rate and power adaptation policies for variable-rate variable-power MQAM through formulas in terms of the parameter K and the cut off value γ K
*Q2. Express the average spectral efficiency for the power and rate adaptation given in Q1* as an integral in terms of cutoff value γ K and the average SNR γˉ
*Q3. What is the power constraint equation that must be satisfied by the cut off value γ K ?
*Q4. Explain how γ K can be determined using the average power constraint in Q3*. *Q5. Based on your answer to Q4* write a MATLAB program to solve the equation in Q3* for given values of γˉ
and K. Hint: Express the equation in terms of exponential integral function, which is defined as expint (x)=∫ x[infinity] te −t dt, for x>0. The function expint (x) has no closed form expression,but can be calculated numerically using "expint" function of MATLAB. *Q6. Consider P b =10 −4 and γˉ=20 dB. What is the value of K ? Q7. Using your program in Q and your answer to Q6 , calculate the cutoff value γ K fo =10−4 and γˉ=20 dB *Q8. Based on your answer to Q2 * and using your program in Q4* that computes the cutoff value, write a MATLAB program to compute the average spectral efficiency for given values of average SNR and target BER. Q9. Using your program in Q8*, compute the average spectral efficiency for P b =10 −4 and γ- =20 dB
