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. A fundamental problem in large scale wireless networks is the energy efficient broadcast of source messages to the whole network. The energy consumption increases as the network size grows, and the optimization of broadcast efficiency becomes more important. In this paper, we study the optimal power allocation problem for cooperative broadcast in dense large-scale networks. In the considered cooperation protocol, a single source initiates the transmission and the rest of the nodes retransmit the source message if they have decoded it reliably. Each node is allocated an-orthogonal channel and the nodes improve their receive signal-to-noise ratio (SNR), hence the energy efficiency, by maximal-ratio combining the receptions of the same packet from different transmitters. We assume that the decoding of the source message is correct as long as the receive SNR exceeds a predetermined threshold. Under the optimal cooperative broadcasting, the transmission order (i.e., the schedule) and the transmission powers of the source and the relays are designed so that every node receives the source message reliably and the total power consumption is minimized. In general, finding the best scheduling in cooperative broadcast is known to be an NP-complete problem. In this paper, we show that the optimal scheduling problem can be solved for dense networks, which we approximate as a continuum of nodes. Under the continuum model, we derive the optimal scheduling and the optimal power density. Furthermore, we propose low-complexity, distributed and power efficient broadcasting schemes and compare their power consumptions with those-of-a traditional noncooperative multihop transmission. Maximizing the output signal-to-noise ratio (SNR) of a sensor array in the presence of spatially colored noise leads to a generalized eigenvalue problem. While this approach has extensively been employed in narrowband (antenna) array beamforming, it is typically not used for broadband (microphone) array beamforming due to the uncontrolled amount of speech distortion introduced by a narrowband SNR criterion. In this paper, we show how the distortion of the desired signal can be controlled by a single-channel post-filter, resulting in a performance comparable to the generalized minimum variance distortionless response beamformer, where arbitrary transfer functions relate the source and the microphones. Results are given both for directional and diffuse noise. A novel gradient ascent adaptation algorithm is presented, and its good convergence properties are experimentally revealed by comparison with alternatives from the literature. A key feature of the proposed beamformer is that it operates blindly, i.e., it neither requires knowledge about the array geometry nor an explicit estimation of the transfer functions from source to sensors or the direction-of-arrival.