Positive solutions for higher-order nonlinear fractional differential equation with integral boundary condition

In this paper, we study a kind of higher-order nonlinear fractional differential equation with integral boundary condition. The fractional differential operator here is the Caputo's fractional derivative. By means of fixed point theorems, the existence and multiplicity results of positive solutions are obtained. Furthermore, some examples given here illustrate that the results are almost sharp

Positive solutions of two-point boundary value problems of nonlinear fractional differential equation at resonance

This paper is concerned with a kind of nonlinear fractional differential boundary value problem at resonance with Caputo's fractional derivative. Our main approach is the recent Leggett-Williams norm-type theorem for coincidences due to O'Regan and Zima. The most interesting point is the acquisition of positive solutions for fractional differential boundary value problem at resonance. Moreover, an example is constructed to show that our result here is valid

Robust Transceiver Design Based on Interference Alignment for Multi-User Multi-Cell MIMO Networks with Channel Uncertainty

In this paper, we firstly exploit the inter-user interference (IUI) and inter-cell interference (ICI) as useful references to develop a robust transceiver design based on interference alignment for a downlink multi-user multi-cell multiple-input multiple-output (MIMO) interference network under channel estimation error. At transmitters, we propose a two-tier transmit beamforming strategy, we first achieve the inner beamforming direction and allocated power by minimizing the interference leakage as well as maximizing the system energy efficiency, respectively. Then, for the outer beamformer design, we develop an efficient conjugate gradient Grassmann manifold subspace tracking algorithm to minimize the distances between the subspace spanned by interference and the interference subspace in the time varying channel. At receivers, we propose a practical interference alignment based on fast and robust fast data projection method (FDPM) subspace tracking algorithm, to achieve the receive beamformer under channel uncertainty. Numerical results show that our proposed robust transceiver design achieves better performance compared with some existing methods in terms of the sum rate and the energy efficiency.Comment: 12 pages, 8 figure

A Two-student Learning Framework for Mixed Supervised Target Sound Detection

Target sound detection (TSD) aims to detect the target sound from mixture audio given the reference information. Previous work shows that a good detection performance relies on fully-annotated data. However, collecting fully-annotated data is labor-extensive. Therefore, we consider TSD with mixed supervision, which learns novel categories (target domain) using weak annotations with the help of full annotations of existing base categories (source domain). We propose a novel two-student learning framework, which contains two mutual helping student models ($\mathit{s\_student}$ and $\mathit{w\_student}$) that learn from fully- and weakly-annotated datasets, respectively. Specifically, we first propose a frame-level knowledge distillation strategy to transfer the class-agnostic knowledge from $\mathit{s\_student}$ to $\mathit{w\_student}$. After that, a pseudo supervised (PS) training is designed to transfer the knowledge from $\mathit{w\_student}$ to $\mathit{s\_student}$. Lastly, an adversarial training strategy is proposed, which aims to align the data distribution between source and target domains. To evaluate our method, we build three TSD datasets based on UrbanSound and Audioset. Experimental results show that our methods offer about 8\% improvement in event-based F score.Comment: submitted to interspeech202

Advanced NOMA Assisted Semi-Grant-Free Transmission Schemes for Randomly Distributed Users

Non-orthogonal multiple access (NOMA) assisted semi-grant-free (SGF) transmission has recently received significant research attention due to its outstanding ability of serving grant-free (GF) users with grant-based (GB) users' spectrum, {\color{blue}which can greatly improve the spectrum efficiency and effectively relieve the massive access problem of 5G and beyond networks. In this paper, we investigate the performance of SGF schemes under more practical settings.} Firstly, we study the outage performance of the best user scheduling SGF scheme (BU-SGF) by considering the impacts of Rayleigh fading, path loss, and random user locations. Then, a fair SGF scheme is proposed by applying cumulative distribution function (CDF)-based scheduling (CS-SGF), which can also make full use of multi-user diversity. Moreover, by employing the theories of order statistics and stochastic geometry, we analyze the outage performances of both BU-SGF and CS-SGF schemes. Results show that full diversity orders can be achieved only when the served users' data rate is capped, which severely limit the rate performance of SGF schemes. To further address this issue, we propose a distributed power control strategy to relax such data rate constraint, and derive closed-form expressions of the two schemes' outage performances under this strategy. Finally, simulation results validate the fairness performance of the proposed CS-SGF scheme, the effectiveness of the power control strategy, and the accuracy of the theoretical analyses.Comment: 41 pages, 8 figure

NoreSpeech: Knowledge Distillation based Conditional Diffusion Model for Noise-robust Expressive TTS

Expressive text-to-speech (TTS) can synthesize a new speaking style by imiating prosody and timbre from a reference audio, which faces the following challenges: (1) The highly dynamic prosody information in the reference audio is difficult to extract, especially, when the reference audio contains background noise. (2) The TTS systems should have good generalization for unseen speaking styles. In this paper, we present a \textbf{no}ise-\textbf{r}obust \textbf{e}xpressive TTS model (NoreSpeech), which can robustly transfer speaking style in a noisy reference utterance to synthesized speech. Specifically, our NoreSpeech includes several components: (1) a novel DiffStyle module, which leverages powerful probabilistic denoising diffusion models to learn noise-agnostic speaking style features from a teacher model by knowledge distillation; (2) a VQ-VAE block, which maps the style features into a controllable quantized latent space for improving the generalization of style transfer; and (3) a straight-forward but effective parameter-free text-style alignment module, which enables NoreSpeech to transfer style to a textual input from a length-mismatched reference utterance. Experiments demonstrate that NoreSpeech is more effective than previous expressive TTS models in noise environments. Audio samples and code are available at: \href{http://dongchaoyang.top/NoreSpeech\_demo/}{http://dongchaoyang.top/NoreSpeech\_demo/}Comment: Submitted to ICASSP202