Optimized M-ary Orthogonal and Bi-Orthogonal Signaling using Coherent Receiver with Non-Equal Symbol Probabilities

In this letter we derive formulas to compute the optimized signal energy, bit error probabilities, and decision thresholds for M-ary orthogonal and bi-orthogonal signaling using a coherent receiver with non-equal symbol probabilities. We find that for non-equiprobable sources, the optimized systems (in which signal energies are optimized for non-equal probable symbols) have much lower error probabilities than the conventional systems (which use the constellation optimized for equal probable symbols).