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# Problem 2: In this problem we explore the power penalty involved in going to higher level signal ...

## Question

###### Problem 2: In this problem we explore the power penalty involved in going to higher level signal ...

Problem 2: In this problem we explore the power penalty involved in going to higher level signal modulations, i.e. from QPSK to 16PSK. (a) Find the minimum distance between constellation points in 16PSK modulation as a function of signal energy Es. (b) Find aM and BM such that the symbol error probability of 16PSK in AWGN is approximately (c) Using your expression in part (b), find an approximation for the average symbol error probability of 16PSK in Rayleigh fading in terms of (d) Convert the expressions for average symbol error probability of 16PSK in Rayleigh fading to expressions for average bit error probability assuming Gray coding. (e) Find the approximate value of required to obtain a BER of 10A-3 in Rayleigh fading for QPSK and 16PSK (assuming Gray coding). What is the power penalty in going to the higher level signal constellation at this BER?

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