pairwise error probability and union bound of space time code i have a question that might seem silly. 
For a given space time code, say a constellation of 16 unitary matrices. When using the union bound to derive an upper bound on the average error probability (using the equation in the image below)



is it logical to have the Bit Error Rate result higher than 1 for a given SNR? even if what i am deriving is an upper bound ?

Thank you
The union bound can indeed result in a BER higher than 1. As you say, it is just an upper bound, and it becomes tighter as the SNR increases. For low SNR, the union bound can be quite loose.