As a generalized coprime array structure, the coprime array with displaced subarrays (CADiS) allows a large minimum inter-element spacing by introducing a specific displacement between two sparse subarrays. While this structure can effectively reduce mutual coupling, the holes in its difference co-array greatly decrease the achievable number of uniform degrees of freedom (DOFs). In this paper, we first provide a complete characterization for the hole locations in the difference co-array generated by a tailored CADiS (tCADiS) as the union of four subsets of locations related via simple symmetry properties. We then introduce two representation approaches for the hole locations, revealing that the latter can be generated from the differences between sensor locations in the subarray of tCADiS and a small uniform linear array, referred to as a padded subarray. Subsequently, we propose novel padded coprime arrays (PCAs) by incorporating the padded subarray into tCADiS to enlarge the consecutive segments in the difference co-array. This not only contributes to increase the number of available uniform DOFs, but also helps mitigating the mutual coupling by limiting the number of sensor pairs with small separations. Finally, numerical simulation results are provided to demonstrate the superiority of PCAs over existing sparse array configurations in terms of DOF, mutual coupling and DOA estimation accuracy.

Generally, massive multiple-input multiple-output (MIMO) system incorporates hundreds of antennas at the base station for various attractive merits, whereas severe mutual coupling arises in the dense structure. In this paper, we introduce the sparse array configuration, coprime array, into the massive MIMO system to alleviate mutual coupling, increase the degrees of freedom (DOFs) and enhance the spatial resolution. Specifically, we propose the extended coprime array structures through two systematical schemes. One scheme is to slide one subarray of the typical augmented coprime array to decompose the interleaved subarrays and the resulting sliding extended coprime array (SECA) produces weaker mutual coupling than the traditional dense uniform linear array, especially the newly proposed super nested array and augmented nested array. Meanwhile, SECA can produce an augmented co-array with more antennas than the physical array and resultantly increase the available DOFs as well as the array aperture. The other scheme is to relocate a proper number of antennas in the generalized coprime array composed of two subarrays with a displacement, namely CADiS, and the resulting relocating extended coprime array (RECA) can further alleviate mutual coupling and enhance the consecutive co-array. Furthermore, we provide the closed-form expressions of the co-array, sliding factor, the minimum number of relocating sensors and their corresponding positions.

In this letter, we investigate the issue of sparse array design for direction of arrival (DOA) estimation of non-circular (NC) signals, and propose the transformed nested array (TNA) which reduces overlapping virtual sensors between the difference and the sum co-array generated by the conventional nested array (NA) and can thus obtain a sum-difference co-array with higher degrees of freedom (DOFs). From the co-array redundancy perspective, we construct the TNA via two operations. The first is to exchange positions of the two subarrays of NA in order to redistribute its sum co-array to separate overlapping virtual sensors. The second is to split the dense subarray into two parts and relocate one of them aiming to further decrease redundant virtual sensors and enlarge the virtual array aperture as well. Theoretical results and numerical simulations are provided to assess the superiority of the proposed configuration.

In the past decade, sparse arrays have aroused considerable attention for the ability to provide larger array aperture, more degrees of freedom (DOFs) and better estimation performance compared with the uniform linear array (ULA). In this paper, the problem of sparse array design is investigated for direction of arrival (DOA) estimation of non-circular (NC) signals, where both the difference co-array (DCA) and sum co-array (SCA) of physical array configuration can be utilized. Specifically, we first introduce a sliding array strategy which moves the array along the axis as a whole in order to reduce the co-array redundancy and enhance the consecutive DOFs of the sum-difference co-array (SDCA). Subsequently, we focus on the SCA of the conventional nested array (NA) and propose an approach which increases the DOFs of the SCA by relocating proper sensors. Furthermore, based on the above strategy and approach, we derive an extended sliding nested array (ESNA) with few redundant virtual sensors and an enhanced SCA, which can offer increased consecutive DOFs, enlarged virtual array aperture (VAA) and can thus bring high angle estimation accuracy of NC signals. Finally, analytic solutions and simulation results are given to validate the superiority of the proposed ESNA in terms of DOFs and estimation performance.

With the rapid development of low-Earth-orbit (LEO) satellite communications, multi-beam precoding has emerged as a key technology for improving spectrum efficiency. However, the long propagation delay and large Doppler frequency offset pose significant challenges to existing precoding techniques. To address this issue, this paper investigates downlink precoding design for multi-beam LEO satellite communications. First, the downlink channel and signal models are established. Then, we reveal that traditional zero-forcing (ZF), regularized zero-forcing (RZF), and minimum mean square error (MMSE) precoding schemes all require the satellite transmitter to acquire the instantaneous channel state information (iCSI) of all users, which is challenging to obtain in satellite communication systems. Subsequently, we propose a downlink precoding design based on statistical channel state information (sCSI) and derive closed-form solutions for statistical-ZF, statistical-RZF, and statistical-MMSE precoding. Furthermore, we propose that sCSI can be computed using the positions of the satellite and users, which reduces the system overhead and complexity of sCSI acquisition. Monte Carlo simulations under the 3GPP non-terrestrial network (NTN) channel model are employed to verify the performance of the proposed method. The simulation results show that the proposed method achieves sum-rate performance comparable to that of iCSI-based schemes and the optimal transmission performance based on sum-rate maximization. In addition, the proposed method significantly reduces the computational complexity of the satellite payload and the system feedback overhead.

In this paper, we derive the discrete Fourier transform (DFT) method for direction of arrival (DOA) estimation by generating the massive virtual difference co-array with the nested array. By contrast with the spatial smoothing (SS) subspace-based methods for nested array, which halve the array aperture, the proposed method can take full advantage of the total array aperture. Since the conventional DFT method is a non-parametric method and is limited by Rayleigh threshold, we perform the phase rotation operation to obtain the fine DOA estimates. Owing to the full utilization of the array aperture and phase rotation operation, the proposed method can achieve better performance than SS subspace-based methods for far-field sources especially with massive virtual difference co-arrays which possess a large number of virtual sensors. Besides, as the fast Fourier transform (FFT) is attractive in practical implementation, the proposed method lowers the computational cost, as compared with the subspace-based methods. Numerical simulation results validate the superiority of the proposed method in both estimation performance and complexity.