A Signal Constellation for Pilotless Communications Over Wiener Phase Noise Channels

Many satellite communication systems operating today em-ploy low cost upconverters or downconverters which create phase noise. This noise can severely limit the information rate of the system and pose a serious challenge for the detection systems. Moreover, simple solutions for phase noise tracking such as PLL either require low phase noise or otherwise require many pilot symbols which reduce the effective data rate. In the last decade we have witnessed many research papers on the design of signal constellations for channels with phase noise. In [4], the phase noise is assumed to be a memoryless Tikhonov distributed stochastic process. The authors compute the maximal information rate assuming an i.u.d input and find the optimal constellation which achieves this rate. The resulting constellations for different Tikhonov distribution