Recently, there is an increased interest in the study of modulo analog to digital converters (ADCs). These new systems can reconstruct a signal whose amplitude is much higher than the conventional ADC's dynamic range. Modulo ADCs are characterized by their modulo threshold and in the current literature, all existing works are limited to real-valued moduli. In this paper, we propose multi-channel modulo samplers with complex-valued moduli to sample a band-limited complex signal. Specifically, we discuss the construction of complex divisors from Gaussian integers and propose their efficient implementations. A memory-efficient, closed-form recovery algorithm is also proposed. Simulation results demonstrate that the proposed systems can provide stable reconstruction of a high dynamic range complex-valued signal at low sampling rates.

A coprime antenna array consists of two or more sparse subarrays featuring enhanced degrees of freedom (DOF) and reduced mutual coupling. This paper introduces a new class of planar coprime arrays, based on the theory of ideal lattices. In quadratic number fields, a splitting prime $p$ can be decomposed into the product of two distinct prime ideals, which give rise to the two sparse subarrays. Their virtual difference coarray enjoys a quadratic gain in DOF, thanks to the generalized Chinese remainder theorem (CRT). To enlarge the contiguous aperture of the coarray, we present hole-free symmetric CRT arrays with simple closed-form expressions. The ring of Gaussian integers and the ring of Eisenstein integers are considered as examples to demonstrate the procedure of designing coprime arrays. With Eisenstein integers, our design yields a difference coarray that is a subset of the hexagonal lattice, offering a significant gain in DOF over the rectangular lattice, given the same physical areas. Maximization of CRT arrays in the aspect of essentialness and the superior performance in the context of angle estimation will be presented in the companion paper (Part II).

We consider joint channel estimation and faulty antenna detection for massive multiple-input multiple-output (MIMO) systems operating in time-division duplexing (TDD) mode. For systems with faulty antennas, we show that the impact of faulty antennas on uplink (UL) data transmission does not vanish even with unlimited number of antennas. However, the signal detection performance can be improved with a priori knowledge on the indices of faulty antennas. This motivates us to propose the approach for simultaneous channel estimation and faulty antenna detection. By exploiting the fact that the degrees of freedom of the physical channel matrix are smaller than the number of free parameters, the channel estimation and faulty antenna detection can be formulated as an extended atomic norm denoising problem and solved efficiently via the alternating direction method of multipliers (ADMM). Furthermore, we improve the computational efficiency by proposing a fast algorithm and show that it is a good approximation of the corresponding extended atomic norm minimization method. Numerical simulations are provided to compare the performances of the proposed algorithms with several existing approaches and demonstrate the performance gains of detecting the indices of faulty antennas.

The triplet Markov field (TMF) model recently proposed is suitable for dealing with nonstationary synthetic aperture radar (SAR) image segmentation. In this letter, we propose a multiscale TMF model in wavelet domain, named as the wavelet-domain TMF (WTMF) model. In the WTMF model, a multiscale causal WTMF energy function is constructed to capture the intra- and interscale dependences in random fields (X, U). Moreover, multiscale likelihoods of the WTMF model are derived based on a wavelet hidden Markov tree to capture the statistical properties of wavelet coefficients. The proposed model can integrate the global and local information in terms of spatial configuration and image features in a more complete manner. The coarser scale information is utilized to guide the finer scale segmentation, and the coarseto-fine causal interactions are considered using a Markov chain. Experimental results prove that the proposed model can segment SAR images better than several models previously proposed.

This article proposes a simple sparse imaging scheme using a linear sparse aperiodic array and a new fast Fourier transform matched filtering (FFTMF) algorithm for a THz multistatic multiple-input and multiple-output (MIMO) imaging system. The simple linear sparse aperiodic array and multipass interferometric synthetic aperture focusing technique are used to achieve fast sampling, low system cost, and high imaging performance. Unlike a traditional generalized synthetic aperture focusing technique (GSAFT) for multistatic MIMO imaging, which is time-consuming and exhibits increased reconstruction time with increased data volume, the proposed FFTMF image reconstruction algorithm is capable of providing comparable image quality but significantly reducing the reconstruction time. For example, we show that for an image of 300 $\times$ 320 mm with a pixel size of 0.75 $\times$ 0.83 mm, the reconstruction time is reduced from about 1.50 min to 0.25 s in the 220-GHz five-pass synthetic imaging experiments. The proposed imaging algorithm uses internal zero padding, a multipass interferometric synthetic aperture focusing technique, and a wideband imaging technique to improve the imaging performance under a low-cost, sparse sampling scheme. It shows a strong antinoise ability and a high tolerance to target focusing distance. In addition, integrated with an algorithm of principal component pursuit by alternating directions method (PCPADM), sparse imaging is available to further save system cost and sampling data without a loss of image quality while the novel use of an error matrix provides an additional detection capability for imaging systems.