Droinet

Me

$51$

Random sequence of bits $($long sequences of equal$-$probable bits$).$

Transmitter

a$)$ Use the given signal constellation, $inR,$ with proper Gray mapping to transmit data

b$)$ Use rotation$/$translation as needed to construct minimum energy constellation for your designed transmitter based on $($a$)$

Channel

AWGN with zero mean and PSD of $\frac{N_0}{2}$

Receiver

Detection$/$Demodulation: Matched filters or correlators

Decoders: MAP, ML$,$ and Minimum Distance $($MD$)$ signal decoders

Results

Calculate the average signal constellation energy for $($a$)$ and $($b$)$ as function of $$

Draw the block diagram for the receivers above $($detection and signal decoders$)$

Draw the decision regions for $($a$)$ and $($b$)$

Reconstruct the original message, considering long sequence, with various SNRs $,$ and $15$ dB $)$ for all decoders $($MAP$,$ ML$,$ and MD$)$ assuming equal$-$probable bits first and then let $p_1=0\mathrm{.}7,p_0=0\mathrm{.}3,$ and write your observations.

Derive the exact analytical average symbol error probability $($or SER$)$ and bounds on bit error probability $($or BER$),$ plot the expression versus SNR in dB for $=1.$

Plot the Monte$-$Carlo simulation for the average symbol error probability and average bit error probability versus SNR in dB for $=1$

Compare the derived expressions of average probability of error $($in symbols and bits$)$ with the Monte$-$Carlo simulations.