Probability-of-error bounds for binary transmission on the slowly fading Rician channel

Chernoff bounds and tilted distribution arguments are applied to obtain error probability bounds for binary signaling on the slowly-fading Rician channel with L diversity. For the maximum likelihood receiver, the CB-optimum [optimum in the sense of minimizing the Chernoff (upper) bound on error probability] signal correlation is determined and plotted; it is found that antipodal signals should be used if
a > b^{2}(1 + b)
, where a is the signal-to-noise ratio of the specular components and
b
is that of the fading components. The CB-optimum number of diversity paths is then obtained. If
a/b > 0.2
, antipodal signaling with unlimited diversity is CB-optimum; whereas, if
a/b < 0.2
, orthogonal signaling with properly chosen diversity is very nearly CB-optimum. If restricted to orthogonal signaling, unlimited diversity is CB-optimum whenever
a/b > 1.0
. Similar results are obtained for the generally nonoptimum square-law-combining receiver. In this case, orthogonal signaling with finite diversity is always CB-optimum.