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In wireless sensor networks, various applications involve learning one or multiple functions of the measurements observed by sensors, rather than the measurements themselves. This paper focuses on the class of type-threshold functions, e.g., the maximum and the indicator functions. A simple network model capturing both the broadcast and superposition properties of wireless channels is considered: the collocated Gaussian network. A general multiround coding scheme exploiting superposition and interaction (through broadcast) is developed. Through careful scheduling of concurrent transmissions to reduce redundancy, it is shown that given any independent measurement distribution, all type-threshold functions can be computed reliably with a nonvanishing rate in the collocated Gaussian network, even if the number of sensors tends to infinity. [ABSTRACT FROM AUTHOR]

The capacity scaling laws of two overlaid networks are investigated, which are located in the same area sharing the same wireless resources with different priorities. The primary network can be regarded as an existing communication system operated in a licensed band and, therefore, is assumed to operate in an order-optimal fashion to achieve its standalone capacity scaling law. The secondary cognitive network must keep its interference to the primary network below a certain threshold while at the same time maximizing its own throughput scaling law based on cognition information. The existing scaling results for cognitive networks inherently assume multihop communication, which is a restricted coding model. By contrast, in this paper, a general coding model is considered without any specific physical layer coding assumptions. The capacity scaling exponents for both networks are analyzed when the numbers of primary nodes n , primary base stations l , which support the communication between primary nodes, and secondary nodes m increase with the relations , \beta >1 , and l=n^\gamma , 0\leq \gamma \leq 1 . For the extended network model, the capacity scaling exponents are completely characterized as \max \2-\alpha /2,1/2,\gamma \ and \max \2-\alpha /2,1/2\ for the primary and secondary networks respectively, where \alpha >2 denotes the path-loss exponent. That is, the capacity scaling laws for the primary and secondary networks are represented, respectively, by n^{\max \{2-\alpha /2,1/2,\gamma \}\pm \epsilon } and m^{\max \{2-\alpha /2,1/2\}\pm \epsilon }$ for \epsilon >0$ arbitrarily small. For the dense network model, when the primary network achieves its standalone capacity scaling exponent of 1, the secondary network is shown to achieve a scaling exponent of 1-{1}/({2\beta }) , which improves the previous scaling exponent of 1/2 achieved by multihop. For both models, it turns out that the conventional multihop approach is in general quite suboptimal. [ABSTRACT FROM AUTHOR]

We study a layered K-user M-hop Gaussian relay network consisting of Km nodes in the m^th layer, where M\geq 2 and K=K1=KM+1. We observe that the time-varying nature of wireless channels or fading can be exploited to mitigate the interuser interference. The proposed amplify-and-forward relaying scheme exploits such channel variations and works for a wide class of channel distributions including Rayleigh fading. We show a general achievable degrees of freedom (DoF) region for this class of Gaussian relay networks. Specifically, the set of all (d1,\ldots , dK) such that di\leq 1 for all i and \sum i=1^{K} di\leq K\Sigma is achievable, where di is the DoF of the i^th source-destination pair and K\Sigma is the maximum integer such that K\Sigma \leq \mathop min\limits m\{Km\} and M/K\Sigma is an integer. We show that surprisingly the achievable DoF region coincides with the cut-set outer bound if M/ \mathop min\limits m\{Km\} is an integer; thus, interference-free communication is possible in terms of DoF. We further characterize an achievable DoF region assuming multi-antenna nodes and general message set, which again coincides with the cut-set outer bound for a certain class of networks. [ABSTRACT FROM PUBLISHER]