We consider the multihop broadcasting problem for @math nodes placed uniformly at random in a disk and investigate the number of hops required to transmit a signal from the central node to all other nodes under three communication models: Unit-Disk-Graph (UDG), Signal-to-Noise-Ratio (SNR), and the wave superposition model of multiple input single output (MISO). In the MISO model, informed nodes cooperate to produce a stronger superposed signal. We do not consider the problem of transmitting a full message nor do we consider interference. In each round, the informed senders try to deliver to other nodes the required signal strength such that the received signal can be distinguished from the noise. We assume sufficiently high node density @math . In the unit-disk graph model, broadcasting needs @math rounds. In the other models, we use an Expanding Disk Broadcasting Algorithm, where in a round only triggered nodes within a certain distance from the initiator node contribute to the broadcasting operation. This algorithm achieves a broadcast in only @math rounds in the SNR-model. Adapted to the MISO model, it broadcasts within @math rounds. All bounds are asymptotically tight and hold with high probability, i.e. @math .
Launched by the seminal paper of @cite_35 , the SNR (Signal to Noise Ratio) model has gained a lot of interest. Here, signals can be received if the energy of the sending nodes is a constant factor larger than the sum of noise energy and interference. This model leads to a smooth receiver area with near convexity properties @cite_31 .
@cite_35 @cite_31
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Many speech processing algorithms and applications rely on the explicit knowledge of signal-to-noise ratio (SNR) in their design and implementation. Estimating the SNR of a signal can enhance the performance of such technologies. We propose a novel method for estimating the long-term SNR of speech signals based on features, from which we can approximately detect regions of speech presence in a noisy signal. By measuring the energy in these regions, we create sets of energy ratios, from which we train regression models for different types of noise. If the type of noise that corrupts a signal is known, we use the corresponding regression model to estimate the SNR. When the noise is unknown, we use a deep neural network to find the “closest” regression model to estimate the SNR. Evaluations were done based on the TIMIT speech corpus, using noises from the NOISEX-92 noise database. Furthermore, we performed cross-corpora experiments by training on TIMIT and NOISEX-92 and testing on the Wall Street Journal speech corpus and DEMAND noise database. Our results show that our system provides accurate SNR estimations across different noise types, corpora, and that it outperforms other SNR estimation methods. In this paper, we consider two different models of partial channel state information at the base station transmitter (CSIT) for multiple antenna broadcast channels: 1) the shape feedback model where the normalized channel vector of each user is available at the base station and 2) the limited feedback model where each user quantizes its channel vector according to a rotated codebook that is optimal in the sense of mean squared error and feeds back the codeword index. This paper is focused on characterizing the sum rate performance of both zero-forcing dirty paper coding (ZFDPC) systems and channel inversion (CI) systems under the given two partial CSIT models. Intuitively speaking, a system with shape feedback loses the sum rate gain of adaptive power allocation. However, shape feedback still provides enough channel knowledge for ZFDPC and CI to approach their own optimal throughput in the high signal-to-noise ratio (SNR) regime. As for limited feedback, we derive sum rate bounds for both signaling schemes and link their throughput performance to some basic properties of the quantization codebook. Interestingly, we find that limited feedback employing a fixed codebook leads to a sum rate ceiling for both schemes for asymptotically high SNR.