  Convexity/concavity properties of symbol error rates (SER) of the maximum
likelihood detector operating in the AWGN channel (non-fading and fading) are
studied. Generic conditions are identified under which the SER is a
convex/concave function of the SNR. Universal bounds for the SER 1st and 2nd
derivatives are obtained, which hold for arbitrary constellations and are tight
for some of them. Applications of the results are discussed, which include
optimum power allocation in spatial multiplexing systems, optimum power/time
sharing to decrease or increase (jamming problem) error rate, and implication
for fading channels.
