Low Complexity Max-log LLR Computation for Nonuniform PAM Constellations

In this letter, we derive a low-complexity method for demodulating nonuniform PAM signals. With uniform Gray-coded M-PAM constellations, the reflective symmetry can be exploited to demodulate the signals with low complexity. However with nonuniform constellations, this symmetry is lost and more complicated computations are required. We derive an analytic expression for the max-log LLR functions and show that they are piecewise linear functions. Based on this, we devise a demodulation algorithm that has complexity O (log(2) M) as opposed to O(M) for the exhaustive search. We also present an approximation with reduced complexity and only modest performance degradation.