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Noncoherent demodulation is an attractive choice for many wireless communication systems. It requires minimal protocol overhead for carrier synchronization, and it is robust to radio impairments commonly found in low-cost transceivers. Machine learning techniques, such as neural networks and deep learning, offer additional benefits for these systems. Practical communication systems often include nonlinearities, non-stationarity, and non-Gaussian noise, which complicate mathematical derivation of optimum demodulators. Learning approaches can optimize demodulator performance directly from simulated or measured radio data, which is often plentiful in the design and verification of today's integrated transceivers. This paper examines several candidate neural network topologies for use in noncoherent demodulation and provides a mathematical framework for their comparison. Each is based on a complex-valued feature detection layer, which may be characterized as coherent or noncoherent, followed by one or more real-valued classification layers. Backpropagation equations for the noncoherent feature layer include a synchronization term that facilitates training with noncoherent input data. The coherent layer does not synchronize training data, however a noncoherent demodulator can still be constructed by increasing the coherent layer capacity and adding a max pooling layer to marginalize the unknown signal phase. A frequency classification example highlights the differences between the topologies and confirms that optimum noncoherent demodulation can be learned in the presence of AWGN and random phase offsets. The topologies considered here are suitable for noncoherent demodulation of power-efficient modulations such as FSK and ASK, which are typical in today's short-range wireless communication systems. It is hoped that such topologies will lead to a future common architecture that can support the wide range of modulation formats in this space.

We propose a novel adaptive kernel-based regression method for complex-valued signals: the generalized complex-valued kernel least-mean-square (gCKLMS). We borrow from the new results on widely linear reproducing kernel Hilbert space (WL-RKHS) for nonlinear regression and complex-valued signals, recently proposed by the authors. This paper shows that in the adaptive version of the kernel regression for complex-valued signals we need to include another kernel term, the so-called pseudo-kernel. This new solution is endowed with better representation capabilities in complex-valued fields since it can efficiently decouple the learning of the real and the imaginary part. Also, we review previous realizations of the complex KLMS algorithm and its augmented version to prove that they can be rewritten as particular cases of the gCKLMS. Furthermore, important conclusions on the design of the kernels are drawn that help to greatly improve the convergence of the algorithms. In the experiments, we revisit the nonlinear channel equalization problem to highlight the better convergence of the gCKLMS compared to previous solutions. Also, the flexibility of the proposed generalized approach is tested in a second experiment with non-independent real and imaginary parts. The results illustrate the significant performance improvements of the gCKLMS approach when the complex-valued signals have different properties for the real and imaginary parts. [ABSTRACT FROM AUTHOR]

We propose a low-complexity, complex-valued sphere decoding (CV-SD) algorithm, which is referred to as circular sphere decoding (CSD) and is applicable to multiple-input–multiple-output (MIMO) systems with arbitrary 2-D constellations. CSD provides a new constraint test. This constraint test is carefully designed so that the elementwise dependence is removed in the metric computation for the test. As a result, the constraint test becomes simple to perform without restriction on its constellation structure. By additionally employing this simple test as a prescreening test, CSD reduces the complexity of the CV-SD search. We show that the complexity reduction is significant, while its maximum-likelihood (ML) performance is not compromised. We also provide a powerful tool to estimate the pruning capacity of any particular search tree. Using this tool, we propose the predict-and-change strategy, which leads to a further complexity reduction in CSD. Extension of the proposed methods to soft output sphere decoding (SD) is also presented. [ABSTRACT FROM PUBLISHER]