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  1. Abstract

    We present a high‐fidelity measurement‐based nonlinear model of low‐complexity millimeter‐wave transmit and receive circuits for design and analysis of 1‐bit on‐off‐key (OOK) massive MIMO wireless communications systems. The receive model is based upon a fabricated 38 GHz energy detector, representative of state‐of‐the‐art OOK millimeter‐wave receivers. The model is validated with measurements and includes nonlinear noise modeling. Performance of a large‐scale massive MIMO system is predicted with the model, and predictions are compared against a 4‐transmit‐element, N‐receive‐element testbed. Finally, we compute the channel capacity of several OOK massive MIMO systems, exploring tradeoffs in power consumption and number of transmit and receive cells. Results indicate a 1‐bit OOK array with low power pre‐amplifiers can achieve similar capacity to a classical linear receiver with less than one tenth the power consumption. The 1‐bit array compensates for the per‐cell simplicity by increasing the total number of cells while maintaining low overall power consumption.

     
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  2. 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. 
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  3. Recent efforts to obtain high data rates in wireless systems have focused on what can be achieved in systems that have nonlinear or coarsely quantized transceiver architectures. Estimating the channel in such a system is challenging because the nonlinearities distort the channel estimation process. It is therefore of interest to determine how much training is needed to estimate the channel sufficiently well so that the channel estimate can be used during data communication. We provide a way to determine how much training is needed by deriving a lower bound on the achievable rate in a training-based scheme that can be computed and analyzed even when the number of antennas is very large. This lower bound can be tight, especially at high SNR. One conclusion is that the optimal number of training symbols may paradoxically be smaller than the number of transmitters for systems with coarselyquantized transceivers. We show how the training time can be strongly dependent on the number of receivers, and give an example where doubling the number of receivers reduces the training time by about 37 percent. 
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  4. 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. 
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  5. 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. 
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