Complexity reduction for non-coherent iteratively detected differentially encoded quaternary phase shift keying based on trellis decomposition

In this letter, we investigate complexity reduction for non-coherent iterative detection of differentially encoded quadrature phase shift keying applied to digital audio broadcast receivers. We use 2D blocks in an orthogonal frequency division multiplexing scheme and trellis decomposition to calculate, iteratively, the a posteriori probabilities of the information symbols. Furthermore, the trellis decomposition method allows us to estimate the unknown channel phase efficiently. This phase is related to sub-trellises of which we can determine the a posteriori probabilities. In our first approach, we investigate a method that is based on finding, at the start of each new iteration, the dominant sub-trellis first and then do the forward- backward processing for demodulation only in this dominant sub-trellis. This method reduces the number of multiplications by a factor of 3, the normalizations by a factor 8 and, after five iterations, introducing ≈ 0.05 dB loss in performance on the COST-207 TU-6 channel. Our second approach involves choosing the dominant sub-trellis only once, before starting with the iterations. This results in reducing the number of multiplications and normalizations by a factor of 8 and introduces ≈ 0.5 dB loss in performance.