On the capacity of the partially coherent additive white gaussian noise channel

We prove that the capacity-achieving PDF for the average-power-constrained AWGN chan- nel with Tikhonov phase error is discrete in amplitude and uniform in phase (DAUP). Numerical capacity lower-bound computations show significant gains over the best previously published lower bound. Simple (but non-equiprobable) AM-PM constellations can closely approach our new lower bound on capacity.