This paper presents two polynomial-complexity techniques for assigning Gray-like binary labels to arbitrary Grassmannian constellations. In the first technique, the constellation of interest, , is matched directly to an auxiliary constellation that can be readily Gray labelled. The optimal matching in this technique can be obtained efficiently, but its application is limited to cases in which an auxiliary constellation with a geometric structure that resembles that of can be identified. In the second technique no auxiliary constellation is required and the labels are generated by matching the distance spectrum of with that of a hypothetical constellation that is assumed to be perfectly Gray labelled. Optimal matching in this case is computationally prohibitive. Instead, an efficient suboptimal matching algorithm is proposed. When compared with several existing schemes, the proposed labellings provide better performance in both uncoded and BICM-based non-coherent MIMO systems with iterative demapping and decoding (IDD). Furthermore, with the proposed labels, the Grassmannian-based BICM-IDD scheme performs better than a training-based counterpart that employs the Golden code and optimal demapping. Index Terms-Non-coherent MIMO communication, Grassmannian constellations, Gray labelling, combinatorial assignment problem, quadratic assignment problem.
This paper presents a technique for assigning binary labels to the points in an arbitrary Grassmannian constellation in a manner that approximates the Gray labelling. The idea behind this technique is to match the Grassmannian constellation of interest to the points in an auxiliary constellation that can be readily Gray labelled. In order to demonstrate the efficacy of the proposed technique, the labelled constellations are utilized in a BICM-encoded non-coherent MIMO communication system with iterative detection and decoding. Numerical simulations indicate that this labelling technique results in a non-coherent communication system that provides better bit error rate performance than systems that utilize the same constellation but employ labels that are generated either randomly or via a quasi-set-partitioning technique.
A bit-interleaved coded modulation (BICM) scheme with iterative demapping and decoding (ID) is developed for non-coherent communication over a multiple-input multipleoutput (MIMO) channel. The scheme exploits the underlying Grassmannian geometry of the signalling scheme that achieves the ergodic capacity of the non-coherent model at high signal-tonoise ratios. In particular, this geometry gives rise to an efficient list-based demapping algorithm that substantially reduces the computational complexity of the receiver. By allowing the decoder to augment the demapping list, the performance degradation of this efficient algorithm can be rendered insignificant. We compare the performance of the proposed scheme with that of a training-based BICM-ID scheme and show, via simulation, that the proposed scheme can provide significantly better performance at high data rates.
A bit-interleaved coded modulation (BICM) scheme with iterative (soft) demapping and decoding (IDD) is developed for non-coherent communication over a multipleinput multiple-output (MIMO) channel. The scheme exploits the underlying Grassmannian geometry of the signalling scheme that approaches the ergodic capacity of the noncoherent model at high signal-to-noise ratios. This geometry guides the construction of the MIMO constellation and gives rise to a computationally-efficient list-based demapping algorithm. The incorporation of a scheme that enables the decoder to augment the demapping list virtually eliminates the mild performance degradation of the efficient demapper. Simulation results demonstrate that at high data rates the proposed scheme can provide significantly better performance than several training-based BICM-IDD schemes.
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