Signal Processing for Large Arrays: Convolutional Beamspace, Hybrid Analog and Digital Processing, and Distributed Algorithms

The estimation of the directions of arrival (DOAs) of incoming waves for a passive antenna array has long been an important topic in array signal processing. Meanwhile, the estimation of the MIMO channel between a transmit antenna array and a receive antenna array is a key problem in wireless communications. In many recent works on these array processing tasks, people consider millimeter waves (mmWaves) due to their potential to offer more bandwidth than the already highly occupied lower-frequency bands. However, new challenges like strong path loss at the high frequencies of mmWaves arise. To compensate for the path loss, large arrays, or massive MIMO, are used to get large beamforming gain. It is practical due to the small sizes of mmWave antennas. When large arrays are used, it is important to develop efficient estimation algorithms with low computational and hardware complexity. The main contribution of this thesis is to propose low-complexity DOA and channel estimation methods that are especially effective for large arrays. To achieve low complexity, three main aspects are explored: beamspace methods, hybrid analog and digital processing, and distributed algorithms. First, a new beamspace method, convolutional beamspace (CBS), is proposed for DOA estimation based on passive arrays. In CBS, the array output is spatially filtered, followed by uniform decimation (downsampling) to achieve dimensionality reduction. No DOA ambiguity occurs since the filter output is represented only by the passband sources. CBS enjoys the advantages of classical beamspace such as lower computational complexity, increased parallelism of subband processing, and improved resolution threshold for DOA estimation. Moreover, unlike classical beamspace methods, it allows root-MUSIC and ESPRIT to be performed directly for uniform linear arrays without additional preparation since the Vandermonde structure is preserved under the CBS transformation. The method produces more accurate DOA estimates than classical beamspace, and for correlated sources, better estimates than element-space. The idea of hybrid analog and digital processing is then incorporated into CBS, leading to hybrid CBS for DOA estimation. In hybrid processing, an analog combiner is used to reduce the number of radio frequency (RF) chains and thus hardware complexity. Also for lowering hardware cost, the analog combiner is designed as a phase shifter network with unit-modulus entries. It is shown that any general (arbitrary coefficient) CBS filter can be implemented despite the unit-modulus constraints. Moreover, a new scheme of CBS is proposed based on nonuniform decimation and difference coarray method. This allows us to identify more sources than RF chains. The retained samples correspond to the sensor locations of a virtual sparse array, dilated by an integer factor, which results in larger coarray aperture and thus better estimation performance. Besides, with the use of random or deterministic filter delays that vary with snapshots, a new method is proposed to decorrelate sources for the coarray method to work. Next, a 2-dimensional (2-D) hybrid CBS method is developed for mmWave MIMO channel estimation. Since mmWave channel estimation problems can be formulated as 2-D direction-of-departure (DOD) and DOA estimation, benefits of CBS such as low complexity are applicable here. The receiver operation is again filtering followed by decimation. A key novelty is the use of a proper counterpart of CBS at the transmitter—expansion (upsampling) followed by filtering—to reduce RF chains. The expansion and decimation can be either uniform or nonuniform. The nonuniform scheme is used with 2-D coarray method and requires fewer RF chains to achieve the same estimation performance as the uniform scheme. A method based on the introduction of filter delays is also proposed to decorrelate path gains, which is crucial to the success of coarray methods. It is shown that given fixed pilot overhead, 2-D hybrid CBS can yield more accurate channel estimates than previous methods. Finally, distributed (decentralized) algorithms for array signal processing are studied. With the potential of reducing computation and communication complexity, distributed estimation of covariance, and distributed principal component analysis have been introduced and studied in the signal processing community in recent years. Applications in array processing have been also indicated in some detail. In this thesis, distributed algorithms are further developed for several well-known methods for DOA estimation and beamforming. New distributed algorithms are proposed for DOA estimation methods like root-MUSIC, total least squares ESPRIT, and FOCUSS. Other contributions include distributed design of the Capon beamformer from data, distributed implementation of the spatial smoothing method for coherent sources, and distributed realization of CBS. The proposed algorithms are fully distributed since average consensus (AC) is used to avoid the need for a fusion center. The algorithms are based on a finite-time version of AC which converges to the exact solution in a finite number of iterations. This enables the proposed distributed algorithms to achieve the same performance as the centralized counterparts, as demonstrated by simulations.</p