Channel Estimation for Switch-Based Millimeter-Wave Communications via Atomic Norm

Channel estimation is a challenging issue in millimeter-wave massive multiple-input-multiple-output (MIMO) communication systems due to the large number of antennas in the transceiver. Existing methods are usually based on phase shifters which may not be a simple circuit at mmWave band. In this paper, we construct a switch-based architecture for analog processors from the coarray point of view and then propose an atomic ℓ 0 -norm minimization problem. We then propose an efficient algorithm to solve this problem based on Wirtinger projection. Since the proposed method requires no angle discretization, it does not suffer from grid mismatch effect that greatly deteriorates the estimation performance of grid-based channel estimation methods. Compared to the atomic norm minimization (ANM) method, our method does not involve vectorization of the channel matrix and hence the dimensionality of the problem is much less than that of ANM. We show that our method is able to provide comparable estimation performance to ANM but with much less computational time. Extensive simulations are carried out to verify the effectiveness of our proposed method.

Gridless Multiple Measurements Method for One-Bit DOA Estimation with a Nested Cross-Dipole Array

The gridless one-bit direction of arrival (DOA) estimator is proposed to estimate electromagnetic (EM) sources on a nested cross-dipole array, and the multiple measurement vectors (MMV) mode is introduced to improve the reliability of parameter estimation. The gridless method is based on atomic norm minimization, solved by alternating direction multiplier method (ADMM). With gridless method used, sign inconsistency caused by one-bit measurements and basis mismatches by traditional grid-based algorithms can be avoided. Furthermore, the reconstructed denoising measurements with fast convergence and stable recovery accuracy are obtained by ADMM. Finally, spatial smoothing root multiple signal classification (SSRMUSIC) and dual polynomial (DP) methods are used, respectively, to estimate the DOAs on the reconstructed denoising measurements. Numerical results show that our method one-bit ADMM-SSRMUSIC has a better performance than that of one-bit SSRMUSIC used directly. At low signal to noise ratio (SNR) and low snapshot, the one-bit ADMM-DP has an excellent performance which is even better than that of unquantized MUSIC. In addition, the proposed methods are also suitable for both completely polarized (CP) signals and partially polarized (PP) signals.

DOA estimation based on sum–difference coarray with virtual array interpolation concept

The sum–difference coarray is the union of difference coarray and the sum coarray, which is capable to obtain a higher number of degrees of freedom (DOF) than the difference coarray. However, this method fails to use all information provided by the coprime array because of the existence of holes. In this paper, we introduce the virtual array interpolation into the sum–difference coarray domain. After interpolating the virtual array, we estimate the DOA by reconstructing the covariance matrix to resolve an atomic norm minimization problem in a gridless way. The proposed method is gridless and can effectively utilize the DOF of a larger virtual array. Numerical simulation results verify the effectiveness and the superior performance of the proposed algorithm.

DOA Estimation Based on Sum-Difference Coarray with Virtual Array Interpolation Concept

The sum-difference coarray is the union of difference coarray and the sum coarray, which is capable to obtain a higher number of degrees of freedom (DOF) than the difference coarray. However, this method fails to use all information provided by the coprime array because of the existence of holes. In this paper, we introduce the virtual array interpolation into the sum-difference coarray domain. After interpolating the virtual array, we estimate the DOA by reconstructing the covariance matrix to resolve an atomic norm minimization problem in a gridless way. The proposed method is gridless and can effectively utilize the DOF of a larger virtual array. Numerical simulation results verify the effectiveness and the superior performance of the proposed algorithm.