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Optimal noncoherent trellis decoding

Chachlakis Dimitrios

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Year 2016
Type of Item Diploma Work
Bibliographic Citation Dimitrios Chachlakis, "Optimal noncoherent trellis decoding ", Diploma Work, School of Electrical and Computer Engineering, Technical University of Crete, Chania, Greece, 2016
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In this diploma thesis, we study the problem of optimal noncoherent trellis decoding, that is, the maximization of |s(x)^H y| over x, where y is a complex vector, x is a discrete symbol sequence, and s(x) is a vector that is produced by x through a trellis structure. Two example cases of noncoherent trellis decoding are noncoherent detection of a minimum-shift keying (MSK) modulated sequence and noncoherent decoding of convolutionally encoded data. Specifically, MSK is a modulation scheme that limits problems associated with nonlinear distortion and is used in a variety of applications, like signal transmission from satellites and broadcasting. Although the optimal coherent MSK receiver simplifies to constant-complexity symbol-bysymbol detection, optimal noncoherent reception of MSK takes the form of sequence detection (due to channel-induced memory) which has exponential (in the sequence length) complexity when implemented through an exhaustive search among all possible sequences. Convolutional codes are used extensively to achieve reliable data transfer in numerous applications, such as digital video, radio, and satellite communications. They are modeled by a trellis structure and optimal noncoherent reception of convolutionally encoded data also takes the form of sequence detection. In this work, we present an algorithm that performs generalized-likelihood-ratio-test (GLRT) optimal noncoherent sequence detection of MSK signals in flat fading with log-linear (in the sequence length) complexity. Moreover, for Rayleigh fading channels, the proposed algorithm is equivalent to the maximum-likelihood (ML) noncoherent sequence detector. We then discuss how the proposed algorithm can be generalized for use on noncoherent convolutional decoding. To simplify the presentation, we consider a particular convolutional code and modify the proposed algorithm to perform optimal noncoherent trellis decoding with empirically low complexity. Simulation studies indicate that the optimal noncoherent MSK detector attains coherent-detection performance when the sequence length is on the order of 100, offering a 5–6 dB gain over the typical single-symbol detector. Similar results are obtained for the generalized algorithm on convolutional decoding.

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