The asymptotic error probability for transmission of orthogonal signals over the generalized incoherent channel

The probability of error for the transmission of one of
M
-orthogonal, equally likely, equal-energy signals over the white Gaussian noise channel is known. For large values of
T
it is shown that this result is asymptotically equivalent to the error probability for the same signal set transmitted over a different channel, termed here the generalized incoherent channel of order
v
. For
v = 2
this channel is identical to the phase incoherent channel. This problem, for larger values of
v
, also arises in a number of other applications, some of which are given.