Abstract-We propose and investigate a compressive architecture for estimation and tracking of sparse spatial channels in millimeter (mm) wave picocellular networks. The base stations are equipped with antenna arrays with a large number of elements (which can fit within compact form factors because of the small carrier wavelength) and employ radio frequency (RF) beamforming, so that standard least squares adaptation techniques (which require access to individual antenna elements) are not applicable. We focus on the downlink, and show that "compressive beacons," transmitted using pseudorandom phase settings at the base station array, and compressively processed using pseudorandom phase settings at the mobile array, provide information sufficient for accurate estimation of the two-dimensional (2D) spatial frequencies associated with the directions of departure of the dominant rays from the base station, and the associated complex gains. This compressive approach is compatible with coarse phase-only control, and is based on a near-optimal sequential algorithm for frequency estimation which can exploit the geometric continuity of the channel across successive beaconing intervals to reduce the overhead to less than 1% even for very large (32 × 32) arrays. Compressive beaconing is essentially omnidirectional, and hence does not enjoy the SNR and spatial reuse benefits of beamforming obtained during data transmission. We therefore discuss system level design considerations for ensuring that the beacon SNR is sufficient for accurate channel estimation, and that inter-cell beacon interference is controlled by an appropriate reuse scheme.

Mobile network traffic is set to explode in our near future, driven by the growth of bandwidth-hungry media applications. Current capacity solutions, including buying spectrum, WiFi offloading, and LTE picocells, are unlikely to supply the orders-of-magnitude bandwidth increase we need. In this paper, we explore a dramatically different alternative in the form of 60GHz mmwave picocells with highly directional links. While industry is investigating other mmwave bands (e.g. 28GHz to avoid oxygen absorption), we prefer the unlicensed 60GHz band with highly directional, short-range links (∼100m). 60GHz links truly reap the spatial reuse benefits of small cells while delivering high per-user data rates and leveraging efforts on indoor 60GHz PHY technology and standards. Using extensive measurements on off-the-shelf 60GHz radios and systemlevel simulations, we explore the feasibility of 60GHz picocells by characterizing range, attenuation due to reflections, sensitivity to movement and blockage, and interference in typical urban environments. Our results dispel some common myths, and show that there are no fundamental physical barriers to high-capacity 60GHz outdoor picocells. We conclude by identifying open challenges and associated research opportunities.

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Deep neural networks represent the state of the art in machine learning in a growing number of fields, including vision, speech and natural language processing. However, recent work raises important questions about the robustness of such architectures, by showing that it is possible to induce classification errors through tiny, almost imperceptible, perturbations. Vulnerability to such "adversarial attacks", or "adversarial examples", has been conjectured to be due to the excessive linearity of deep networks. In this paper, we study this phenomenon in the setting of a linear classifier, and show that it is possible to exploit sparsity in natural data to combat ∞-bounded adversarial perturbations. Specifically, we demonstrate the efficacy of a sparsifying front end via an ensemble averaged analysis, and experimental results for the MNIST handwritten digit database. To the best of our knowledge, this is the first work to show that sparsity provides a theoretically rigorous framework for defense against adversarial attacks.