BER performance for M-ary signalling

Examples
Example 3.2
Questions
Question 3.5

We would expect intuitively that as we increase the number of symbol states, the ability of the receiver to distinguish between symbols in the presence of noise will decrease, unless we significantly increase the energy in each symbol. Based on exactly the same type of analysis used for the binary case, it can be shown (see Proakis (1989)) that

the symbol error probability for M-ary bipolar baseband signalling is given by:

 Ps  M-aryBipolar =
 [(M-1)/Merfc([3/(M2-1)]·Es average/N0)1/2 

where M is the number of symbols used.


This result is plotted here as a function of the average energy per bit Eb rather than the average energy per symbol Es where Eb = Es/k (k is the number of bits per symbol).