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We present a neural network decision system for determining if spectrum is occupied in a region. Given a threshold, we wish to determine if power at a given frequency exceeds the threshold, thus determining if that frequency is “occupied”. The emitting sources are unknown in number, locations, and powers. The sensors, which measure the signal power, are random in number and location. The measurements are aggregated as log-likelihood ratios into a fixed-resolution image suitable as input to a neural network. The network is trained to produce an occupancy map over a wide area, even where there are no sensors, and achieves excellent accuracy at determining occupancy. The system is robust to the number of sensors, and occupancy threshold in a variety of environments. 

One-bit transceivers with strongly nonlinear characteristics are being considered for wireless communication because of their low cost and low power consumption. Although each such transceiver can support only a low data rate, multiple such transceivers can be used to obtain an aggregate high data rate. An important part of many communication systems is the process of channel estimation, which is particularly challenging when the estimation process uses these transceivers. The standard analysis of estimation mean-square error versus training length that is available for linear transceivers does not apply with the nonlinearities inherent in one-bit transceivers. We analyze the training requirements in a large- scale system and show that the optimal number of training symbols strongly depends on the number of receivers, and the optimal number of training symbols can be significantly smaller than the number of transmitters. These results contrast sharply with classical results obtained with linear transceivers. 

We analyze the channel capacity of a system with a large number of one-bit transceivers in a classical Rayleigh environment with perfect channel information at the receiver. With M transmitters and N =alpha*M receivers, we derive an expression of the capacity per transmitter C, where C <= min(1; aalpha), as a function of alpha and signal-to-noise ratio (SNR) rho, when M -> infinity. We show that our expression is a good approximation for small M, and provide simple approximations of C for various ranges of alpha and rho. We conclude that at high SNR, C reaches its upper limit of one only if alpha > 1:24. Expressions for determining when C “saturates” as a function of alpha and rho are given. 

Classical beamforming techniques rely on highly linear transmitters and receivers to allow phase-coherent combining at the transmitter and receiver. The transmitter uses eamforming to steer signal power towards the receiver, and the receiver uses beamforming to gather and coherently combine the signals from multiple receiver antennas. When the transmitters and receivers are instead constrained for power and cost reasons to be nonlinear one-bit devices, the potential advantages and performance metrics associated with beamforming are not as well understood. We define beamforming at the transmitter as a codebook design problem to maximize the minimum distance between codewords. We define beamforming at the receiver as the maximum likelihood detector of the transmitted codeword. We show that beamforming with one-bit transceivers is a constellation design problem, and that we can come within a few dB SNR of the capacity attained by linear transceivers.