Multi-Layer Bilinear Generalized Approximate Message Passing

In this paper, we extend the bilinear generalized approximate message passing (BiG-AMP) approach, originally proposed for high-dimensional regression, to multi-layer case handling of cascaded problem such as matrix-factorization arising in relay communication among others. Assuming statistically independent matrix entries with known priors, new algorithm called ML-BiGAMP could general sum-product loopy belief propagation (LBP) limit enjoying a substantial reduction computational complexity. We demonstrate that, large system limit, asymptotic MSE performance be fully characterized via set simple one-dimensional equations termed state evolution (SE). establish that predicted by ML-BiGAMP' SE matches perfectly exact MMSE replica method, which is well-known Bayes-optimal but infeasible practice. This consistency indicates may still retain same estimator applications, although ML-BiGAMP's burden far lower. As an illustrative example ML-BiGAMP, provide detector design estimate channel fading and data symbols jointly high precision two-hop amplify-and-forward systems.