ESE 471 The Union Bound for Symbol Error

I use the union bound to derive an expression for the probability of symbol error for an arbitrary M-ary modulation. I start with a pairwise error event, E_{j|i}, the error of receiving a measurement on the wrong side of the dividing subspace between symbol i and symbol j, given symbol i was sent. Then I sum over all j and average over all i to get the overall union bound expression.
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