In this letter, the problem of estimating an unknown deterministic parameter is studied, where each sensor acquires a noisy version of the signal and the data at fusion center are unlabeled. Two scenarios are studied, one is that each sensor uses analog communication to transmit its observations with different channel coefficients. Another is that each sensor uses a different threshold to quantize the noisy signal with a transition matrix describing the channel. Sufficient conditions are provided under which maximum likelihood (ML) estimators can be found in polynomial time, and numerical simulations are conducted to evaluate performances of ML estimators.
In this study, the problem of recovering structured sparse signals with a priori distribution whose structure patterns are unknown is studied from one-bit adaptive (AD) quantised measurements. A generalised approximate message passing (GAMP) algorithm is utilised, and an expectation maximisation (EM) method is embedded in the algorithm to iteratively estimate the unknown a priori distribution. In addition, the nearest neighbour sparsity pattern learning (NNSPL) method is adopted to further improve the recovery performance of the structured sparse signals. Numerical results demonstrate the effectiveness of GAMP-EM-AD-NNSPL method with both simulated and real data.
In this letter, we propose a two-stage approach to estimate the carrier frequency offset (CFO) and channel with one-bit analog-to-digital converters (ADCs). Firstly, a simple metric which is only a function of the CFO is proposed, and the CFO is estimated via solving the one-dimensional optimization problem.Secondly, the generalized approximate message passing (GAMP) algorithm combined with expectation maximization (EM) method is utilized to estimate the channel. In order to provide a benchmark of our proposed algorithm in terms of the CFO estimation, the corresponding Cramér-Rao bound (CRB) is derived. Furthermore, numerical results demonstrate the effectiveness of the proposed approach when applied to the general Gaussian channel and mmWave channel. keywords: CFO, channel estimation, millimeter wave system, one-bit quantization I. INTRODUCTIONTo provide a high-speed data rate in celluar systems, the mmWave multiple input multiple output (MIMO) system has been proposed as the key technology of the fifth generation (5G) cellular system [1,2]. Because of the larger bandwidths that accompany mmWave, the cost and power consumption are huge due to high precision (e.g., 10-12 bits) analog-to-digital converters (ADCs) [3]. As a result, a low precision (e.g., 1-4 bits) ADC is employed to relieve this ADC bottleneck [4,5]. However, as low precision quantization is severely nonlinear, traditional algorithms designed for high precision systemscan not be applied directly because of significant performance degradation. As a consequence, new signal processing algorithms dealing with channel estimation and transmit precoding have been proposed, which work well in systems with low precision ADCs [6][7][8][9]. For the channel estimation in mmWave systems, it can be regarded as one-bit compressed sensing (CS) problems [10][11][12][13][14], as the mmWave MIMO channel is approximately sparse in angle domain [15]. Therefore, many CS-based algorithms have been proposed to estimate the mmWave MIMO channel. In [16,17], a modified expectation maximization (EM) algorithm
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