Soft detection method reduces complexity using maximum entropy priors
Orbital Detection: On Maximum-Entropy Priors
Information Theory
Summary
Detecting transmitted symbols in communication systems is usually slow because it involves checking many possible values. The authors show that by grouping symbols based on their amplitudes and using a special kind of probability distribution that is uncertain about phase but exact about amplitude, the detection can be made much faster. This method preserves key statistical properties, leading to simpler calculations that still keep accuracy high. Experiments show this faster method performs close to the best known detectors but with far less effort.
What this means in practice
- •For wireless communication engineers: Speed up symbol detection in modulated signals by reducing complexity while maintaining accuracy using amplitude-based priors.
- •For radar signal processors: Improve real-time target identification from noisy phase-amplitude measurements by applying maximum-entropy phase distributions.
Authors
Kuranage Roche Rayan Ranasinghe, Takumi Takahashi, Giuseppe Thadeu Freitas de Abreu
Abstract
Soft-input detection over a discrete constellation \(\mathcal{M}\) of cardinality \(M\) requires computing a posterior whose mean and mode are respectively given by the minimum mean square error (MMSE) and maximum a posteriori (MAP) estimates, both of which incur a computational cost of order \(\mathcal{O}(M)\) per symbol. We show that this cost is reduced to \(\mathcal{O}(L)\), where \(L \le M\) is the number of distinct amplitudes (rings), once the discrete prior is replaced by its maximum-entropy counterpart subject to the same radial marginal. This orbital prior, which is a mixture of uniform circular shells, is obtained by maximizing a mixed discrete-continuous entropy. We prove in this paper that such a distribution is the only distribution on \(\mathbb{C}\) that preserves the amplitude statistics of \(\mathcal{M}\) exactly while remaining maximally noncommittal in phase. Under the additive white Gaussian noise (AWGN) channel, the orbital prior induces a closed-form posterior that factors into a softmax over the \(L\) rings and a von Mises phase distribution whose concentration is supplied entirely by the observation, yielding closed-form orbital MMSE and MAP detectors of the discrete symbol at \(\mathcal{O}(L)\) cost. The resulting hierarchical rule selects the ring by posterior mass and the phase by conditional mode. We compare the pairwise ring boundary with that of the joint posterior-density and quantify the leading-order outward shift at high signal-to-noise ratio (SNR). Numerical results using standard constellations confirm that the orbital detectors maintain similar symbol error rate (SER) performance to optimal detectors, at a fraction of the complexity.