If [alpha] > 1, the signal constellation becomes that of an HQAM. By controlling the value of [alpha], it is possible to control the bit error (BER) of the HP and LP bitstreams.
where [alpha] is the HQAM modulation parameter, [gamma] is the average signal-to-noise (SNR) per bit and [gamma] = [E.sub.b]/[N.sub.0], erfc(x) is the complementary error function which can be expressed as erfc(x) = 2/[[pi].sup.1/2] [[integral].sup.[infinity].sub.x] exp(-[t.sup.2])dt.
By solving Equation (7), select one solution of a greater than 1 as the HQAM modulation parameter.