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

A pre-filtering maximum likelihood approach to multiple source direction estimation.

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Bearing estimation techniques for improved performance spread spectrum receivers

The main topic of this thesis is the use of bearing estimation techniques combined with multiple antenna elements for spread spectrum receivers. The motivation behind this work is twofold: firstly, this type of receiver structure may offer the ability to locate the position of a mobile radio in an urban environment. Secondly, these algorithms permit the application of space division multiple access (SDMA) to cellular mobile radio, which can offer large system capacity increases. The structure of these receivers may naturally be divided into two parts: signal detection and spatial filtering blocks. The signal detection problem involves locating the bearings of the multipath components which arise from the transmission of the desired user’s signal. There are a number of approaches to this problem, but here the MUSIC algorithm will be adopted. This algorithm requires an initial estimate of the number of signals impinging on the receiver, a task which can be performed by model order determination techniques. A major deficiency of MUSIC is its inability to resolve the highly–correlated and coherent multipath signals which frequently occur in a spread spectrum system. One of the simplest ways to overcome this problem is to employ spatial smoothing techniques, which trade the size of the antenna array for the ability to resolve coherent signals. The minimum description length (MDL) is one method for determining the signal model order and it can easily be extended to calculating the required degree of spatial smoothing. In this thesis, an approach to analysing the probability of correct model order determination for the MDL with spatial smoothing is presented. The performance of MUSIC, combined with spatial smoothing, is also of great significance. Two smoothing algorithms, spatial smoothing and forward–backward spatial smoothing, are analysed to compare their performance. If SDMA techniques are to be deployed in cellular systems, it is important to first estimate the performance improvements available from applying antenna array spatial filters. Initially, an additive white Gaussian noise channel is used for estimating the capacity of a perfect power–controlled code division multiple access system with SDMA techniques. Results suggest that the mean interference levels are almost halved as the antenna array size doubles, permitting large capacity increases. More realistic multipath models for urban cellular radio channels are also considered. If the transmitter gives rise to a number of point source multipath components, the bearing estimation receiver is able to capture the signal energy of each multipath. However, when a multipath component has significant angular spread, bearing estimation receivers need to combine separate directional components, at an increased cost in complexity, to obtain similar results to a matched filter. Finally, a source location algorithm for urban environments is presented, based on bearing estimation of multipath components. This algorithm requires accurate knowledge of the positions of the major multipath reflectors present in the environment. With this knowledge it is possible to determine the position of a transmitting mobile unit. Simulation results suggest that the algorithm is very sensitive to angular separation of the multipath components used for the source location technique

Wavefield modeling and signal processing for sensor arrays of arbitrary geometry

Sensor arrays and related signal processing methods are key technologies in many areas of engineering including wireless communication systems, radar and sonar as well as in biomedical applications. Sensor arrays are a collection of sensors that are placed at distinct locations in order to sense physical phenomena or synthesize wavefields. Spatial processing from the multichannel output of the sensor array is a typical task. Such processing is useful in areas including wireless communications, radar, surveillance and indoor positioning. In this dissertation, fundamental theory and practical methods of wavefield modeling for radio-frequency array processing applications are developed. Also, computationally-efficient high-resolution and optimal signal processing methods for sensor arrays of arbitrary geometry are proposed. Methods for taking into account array nonidealities are introduced as well. Numerical results illustrating the performance of the proposed methods are given using real-world antenna arrays. Wavefield modeling and manifold separation for vector-fields such as completely polarized electromagnetic wavefields and polarization sensitive arrays are proposed. Wavefield modeling is used for writing the array output in terms of two independent parts, namely the sampling matrix depending on the employed array including nonidealities and the coefficient vector depending on the wavefield. The superexponentially decaying property of the sampling matrix for polarization sensitive arrays is established. Two estimators of the sampling matrix from calibration measurements are proposed and their statistical properties are established. The array processing methods developed in this dissertation concentrate on polarimetric beamforming as well as on high-resolution and optimal azimuth, elevation and polarization parameter estimation. The proposed methods take into account array nonidealities such as mutual coupling, cross-polarization effects and mounting platform reflections. Computationally-efficient solutions based on polynomial rooting techniques and fast Fourier transform are achieved without restricting the proposed methods to regular array geometries. A novel expression for the Cramér-Rao bound in array processing that is tight for real-world arrays with nonidealities in the asymptotic regime is also proposed. A relationship between spherical harmonics and 2-D Fourier basis, called equivalence matrix, is established. A novel fast spherical harmonic transform is proposed, and a one-to-one mapping between spherical harmonic and 2-D Fourier spectra is found. Improvements to the minimum number of samples on the sphere that are needed in order to avoid aliasing are also proposed

Low-Rank Channel Estimation for Millimeter Wave and Terahertz Hybrid MIMO Systems

Massive multiple-input multiple-output (MIMO) is one of the fundamental technologies for 5G and beyond. The increased number of antenna elements at both the transmitter and the receiver translates into a large-dimension channel matrix. In addition, the power requirements for the massive MIMO systems are high, especially when fully digital transceivers are deployed. To address this challenge, hybrid analog-digital transceivers are considered a viable alternative. However, for hybrid systems, the number of observations during each channel use is reduced. The high dimensions of the channel matrix and the reduced number of observations make the channel estimation task challenging. Thus, channel estimation may require increased training overhead and higher computational complexity. The need for high data rates is increasing rapidly, forcing a shift of wireless communication towards higher frequency bands such as millimeter Wave (mmWave) and terahertz (THz). The wireless channel at these bands is comprised of only a few dominant paths. This makes the channel sparse in the angular domain and the resulting channel matrix has a low rank. This thesis aims to provide channel estimation solutions benefiting from the low rankness and sparse nature of the channel. The motivation behind this thesis is to offer a desirable trade-off between training overhead and computational complexity while providing a desirable estimate of the channel

Rational invariant subspace approximations with applications

Includes bibliographical references.Subspace methods such as MUSIC, Minimum Norm, and ESPRIT have gained considerable attention due to their superior performance in sinusoidal and direction-of-arrival (DOA) estimation, but they are also known to be of high computational cost. In this paper, new fast algorithms for approximating signal and noise subspaces and that do not require exact eigendecomposition are presented. These algorithms approximate the required subspace using rational and power-like methods applied to the direct data or the sample covariance matrix. Several ESPRIT- as well as MUSIC-type methods are developed based on these approximations. A substantial computational saving can be gained comparing with those associated with the eigendecomposition-based methods. These methods are demonstrated to have performance comparable to that of MUSIC yet will require fewer computation to obtain the signal subspace matrix

Millimeter-Wave Radar Beamforming with Spatial Path Index Modulation Communications

To efficiently utilize the wireless spectrum and save hardware costs, the fifth generation and beyond (B5G) wireless networks envisage integrated sensing and communications (ISAC) paradigms to jointly access the spectrum. In B5G systems, the expensive hardware is usually avoided by employing hybrid beamformers that employ fewer radio-frequency chains but at the cost of the multiplexing gain. Recently, it has been proposed to overcome this shortcoming of millimeter wave (mmWave) hybrid beamformers through spatial path index modulation (SPIM), which modulates the spatial paths between the base station and users and improves spectral efficiency. In this paper, we propose an SPIM-ISAC approach for hybrid beamforming to simultaneously generate beams toward both radar targets and communications users. We introduce a low complexity approach for the design of hybrid beamformers, which include radar-only and communications-only beamformers. Numerical experiments demonstrate that our SPIM-ISAC approach exhibits a significant performance improvement over the conventional mmWave-ISAC design in terms of spectral efficiency and the generated beampattern.Comment: 6pages4figures, Submitted to IEE

The Road to Next-Generation Multiple Access: A 50-Year Tutorial Review

The evolution of wireless communications has been significantly influenced by remarkable advancements in multiple access (MA) technologies over the past five decades, shaping the landscape of modern connectivity. Within this context, a comprehensive tutorial review is presented, focusing on representative MA techniques developed over the past 50 years. The following areas are explored: i) The foundational principles and information-theoretic capacity limits of power-domain non-orthogonal multiple access (NOMA) are characterized, along with its extension to multiple-input multiple-output (MIMO)-NOMA. ii) Several MA transmission schemes exploiting the spatial domain are investigated, encompassing both conventional space-division multiple access (SDMA)/MIMO-NOMA systems and near-field MA systems utilizing spherical-wave propagation models. iii) The application of NOMA to integrated sensing and communications (ISAC) systems is studied. This includes an introduction to typical NOMA-based downlink/uplink ISAC frameworks, followed by an evaluation of their performance limits using a mutual information (MI)-based analytical framework. iv) Major issues and research opportunities associated with the integration of MA with other emerging technologies are identified to facilitate MA in next-generation networks, i.e., next-generation multiple access (NGMA). Throughout the paper, promising directions are highlighted to inspire future research endeavors in the realm of MA and NGMA.Comment: 43 pages, 38 figures; Submitted to Proceedings of the IEE