On the Feasibility of Linear Interference Alignment for MIMO Interference Broadcast Channels with Constant Coefficients

In this paper, we analyze the feasibility of linear interference alignment (IA) for multi-input-multi-output (MIMO) interference broadcast channel (MIMO-IBC) with constant coefficients. We pose and prove the necessary conditions of linear IA feasibility for general MIMO-IBC. Except for the proper condition, we find another necessary condition to ensure a kind of irreducible interference to be eliminated. We then prove the necessary and sufficient conditions for a special class of MIMO-IBC, where the numbers of antennas are divisible by the number of data streams per user. Since finding an invertible Jacobian matrix is crucial for the sufficiency proof, we first analyze the impact of sparse structure and repeated structure of the Jacobian matrix. Considering that for the MIMO-IBC the sub-matrices of the Jacobian matrix corresponding to the transmit and receive matrices have different repeated structure, we find an invertible Jacobian matrix by constructing the two sub-matrices separately. We show that for the MIMO-IBC where each user has one desired data stream, a proper system is feasible. For symmetric MIMO-IBC, we provide proper but infeasible region of antenna configurations by analyzing the difference between the necessary conditions and the sufficient conditions of linear IA feasibility.Comment: 14 pages, 3 figures, accepted by IEEE Trans. on Signal Processin

On the Degrees of Freedom of Asymmetric MIMO Interference Broadcast Channels

In this paper, we study the degrees of freedom (DoF) of the asymmetric multi-input-multi-output interference broadcast channel (MIMO-IBC). By introducing a notion of connection pattern chain, we generalize the genie chain proposed in [11] to derive and prove the necessary condition of IA feasibility for asymmetric MIMO-IBC, which is denoted as irreducible condition. It is necessary for both linear interference alignment (IA) and asymptotic IA feasibility in MIMO-IBC with arbitrary configurations. In a special class of asymmetric two-cell MIMOIBC, the irreducible condition is proved to be the sufficient and necessary condition for asymptotic IA feasibility, while the combination of proper condition and irreducible condition is proved to the sufficient and necessary condition for linear IA feasibility. From these conditions, we derive the information theoretic maximal DoF per user and the maximal DoF per user achieved by linear IA, and these DoFs are also the DoF per user upper-bounds of asymmetric G-cell MIMO-IBC with asymptotic IA and linear IA, respectively.Comment: 6 pages, 3 figures, submitted to ICC 201

Acoustics of Sequential Spaces

“Sequential spaces” are spatial systems comprising multiple spaces in sequence connected by openings, common in public spaces with crowd transit (e.g., museums, shopping malls, and transportation hubs). Related to sound diffraction and insulation, this thesis aims to achieve a minor breakthrough in architectural acoustics through establishing disciplines, not focusing on a single or performance space, but targeting large-scale buildings with a listener in motion. The necessity of applying good practice in asymmetric dynamic auditory perception between approaching and receding sound sources, and inconsistent sound attenuation with distance for separating partitions of same construction is demonstrated by subjective and objective outcomes through real and virtual acoustics. The first stage observes dynamic auditory perception of noise as a stationary primary sound source in a museum. The asymmetry of the loudness and listener envelopment between approaching and receding sources occurs with broadband noise. Perceptual priority increases with a rising level. The second stage confirms sound attenuation with distance in accordance with the needs of users (connected room volume, individual room volume, source position, and room absorption) in practice. As connected room volume increases, average sound pressure level is remained for rooms originally connected, while reverberation time generally decreases. The level difference between source and first receiving room is magnified to 1.5 times the sequential one. The third stage explores sound attenuation with distance when parameters of contextual (opening dimension and position, number of rooms), acoustic (absorption coefficient and distribution) and source (directional radiation from the opening and an additional source) factors are efficient in predictions based on finite element method. The final stage examines dynamic auditory perception of voice and music with or without background noise through a validated reproduction of virtual environment. Three perceptual distinctions emerge between approaching or receding sound sources and are defined as approach, plummet, and convergence effect

A Study of American Individualism: Taking Friends as an Exampl

Friends are a famous American situation comedy since 1990s. It tells the story of six “common” youths living in New York of the United States including their emotion, career, joys and pains. Based on the study of Friends case, this article analyses the importance of American individualism to American culture, and tells us the reasons why individualism became the core of American culture. It also discusses the concrete embodiment of individualism value in American daily life from the life, career and feelings. This paper understands the importance of American individualism in American culture through current situations of American individualism. It helps us to understand deeply the impact and important significance on American culture which is caused by the American individualism. And helps us to better understand and look at the essence of American society and culture, understand the difference between USA and China. It also contributes a lot to promote cultural exchanges and common progresses between China and America and common progress.