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A two-way relay channel (TWRC) in which two terminals and exchange orthogonal frequency division multiplexing (OFDM) signals with the help of an amplify-and-forward (AF) relay is considered here, and an efficient technique for allocating powers to parallel tones of OFDM is developed. A sum rate maximization problem is formulated by replacing the individual power constraints of the conventional sum rate maximization problem, which limit the power of each terminal, with the total power constraint limiting the sum of powers of all terminals. The maximization problem with the total power constraint yields a more efficient power allocation policy than the conventional problem with individual power constraints. It is shown that the closed-form solution of the maximization problem under the total power constraint can be obtained for a single-tone system ( = 1). Based on this result, a two-step suboptimal approach is proposed in which the power is optimally assigned to each tone first, and then at each tone the assigned power is distributed to the three terminals. The proposed method is shown to assign 50% of the total power to relay irrespective of the channels. It is demonstrated that the proposed method is considerably simpler to implement than the conventional dual-decomposition method (DDM), yet the performance of the former is almost identical to that of the latter.Index Terms-Amplify-and-forward, dual decomposition, orthogonal frequency-division multiplexing (OFDM), power allocation, two-way relay.

Background Wearable devices have evolved as screening tools for atrial fibrillation (AF). A photoplethysmographic (PPG) AF detection algorithm was developed and applied to a convenient smartphone-based device with good accuracy. However, patients with paroxysmal AF frequently exhibit premature atrial complexes (PACs), which result in poor unmanned AF detection, mainly because of rule-based or handcrafted machine learning techniques that are limited in terms of diagnostic accuracy and reliability. Objective This study aimed to develop deep learning (DL) classifiers using PPG data to detect AF from the sinus rhythm (SR) in the presence of PACs after successful cardioversion. Methods We examined 75 patients with AF who underwent successful elective direct-current cardioversion (DCC). Electrocardiogram and pulse oximetry data over a 15-min period were obtained before and after DCC and labeled as AF or SR. A 1-dimensional convolutional neural network (1D-CNN) and recurrent neural network (RNN) were chosen as the 2 DL architectures. The PAC indicator estimated the burden of PACs on the PPG dataset. We defined a metric called the confidence level (CL) of AF or SR diagnosis and compared the CLs of true and false diagnoses. We also compared the diagnostic performance of 1D-CNN and RNN with previously developed AF detectors (support vector machine with root-mean-square of successive difference of RR intervals and Shannon entropy, autocorrelation, and ensemble by combining 2 previous methods) using 10 5-fold cross-validation processes. Results Among the 14,298 training samples containing PPG data, 7157 samples were obtained during the post-DCC period. The PAC indicator estimated 29.79% (2132/7157) of post-DCC samples had PACs. The diagnostic accuracy of AF versus SR was 99.32% (70,925/71,410) versus 95.85% (68,602/71,570) in 1D-CNN and 98.27% (70,176/71,410) versus 96.04% (68,736/71,570) in RNN methods. The area under receiver operating characteristic curves of the 2 DL classifiers was 0.998 (95% CI 0.995-1.000) for 1D-CNN and 0.996 (95% CI 0.993-0.998) for RNN, which were significantly higher than other AF detectors ( P <.001). If we assumed that the dataset could emulate a sufficient number of patients in training, both DL classifiers improved their diagnostic performances even further especially for the samples with a high burden of PACs. The average CLs for true versus false classification were 98.56% versus 78.75% for 1D-CNN and 98.37% versus 82.57% for RNN ( P <.001 for all cases). Conclusions New DL classifiers could detect AF using PPG monitoring signals with high diagnostic accuracy even with frequent PACs and could outperform previously developed AF detectors. Although diagnostic performance decreased as the burden of PACs increased, performance improved when samples from more patients were trained. Moreover, the reliability of th...

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