Abstract To achieve a more reasonable cost, employment of a mono-bit quantization structure is essential in wide bandwidth millimeter-wave communications (mmW). However, in mmW channel estimation, one of the critical challenges of monobit quantization in each branch of the antenna is the loss of data amplitude. The latest researches offer several approaches to estimate the channel in mono-bit single and multiple antenna structures. Such methods not consider the recovery of channel amplitude and consequently are limited to finding direction. Moreover, they do not provide sparsity into account. Thus, two new schemes are introduced based on a non-adaptive Bayesian algorithm and adaptive sigma–delta modulation (SDM) to tackle these issues. In both methods, we exploit the sparsity of mmWC channel in the angle domain. To extract the sparsebased Laplacian density in case that the sparsity level is unknown, we propose a Bayesian algorithm which employs a hierarchical chain composed of Gaussian and exponential prior. Furthermore, in case that the sparsity level of an application is known or can be estimated, the adaptive mono-bit quantization schemes is proposed which retrieves the amplitude of the sparse channel by the aid of SDM and CS tools. Simulation results show that the adaptive mono-bit estimator outperforms the non-adaptive Bayesian approach comparing the mean square error as an index. Also, the proposed adaptive method, especially when a sufficient number of one-bit measurements are available, can asymptotically converge into optimum full-bit observations with lower computational complexity.

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