Massive MIMO Channel Models: A Survey

The exponential traffic growth of wireless communication networks gives rise to both the insufficient network capacity and excessive carbon emissions. Massive multiple-input multiple-output (MIMO) can improve the spectrum efficiency (SE) together with the energy efficiency (EE) and has been regarded as a promising technique for the next generation wireless communication networks. Channel model reflects the propagation characteristics of signals in radio environments and is very essential for evaluating the performances of wireless communication systems. The purpose of this paper is to investigate the state of the art in channel models of massive MIMO. First, the antenna array configurations are presented and classified, which directly affect the channel models and system performance. Then, measurement results are given in order to reflect the main properties of massive MIMO channels. Based on these properties, the channel models of massive MIMO are studied with different antenna array configurations, which can be used for both theoretical analysis and practical evaluation

Sparse Array Design for Wideband Beamforming with Reduced Complexity in Tapped Delay-lines

Sparse wideband array design for sensor location optimization is highly nonlinear and it is traditionally solved by genetic algorithms (GAs) or other similar optimization methods. This is an extremely time-consuming process and an optimum solution is not always guaranteed. In this work, this problem is studied from the viewpoint of compressive sensing (CS). Although there have been CS-based methods proposed for the design of sparse narrowband arrays, its extension to the wideband case is not straightforward, as there are multiple coefficients associated with each sensor and they have to be simultaneously minimized in order to discard the corresponding sensor locations. At first, sensor location optimization for both general wideband beamforming and frequency invariant beamforming is considered. Then, sparsity in the tapped delay-line (TDL) coefficients associated with each sensor is considered in order to reduce the implementation complexity of each TDL. Finally, design of robust wideband arrays against norm-bounded steering vector errors is addressed. Design examples are provided to verify the effectiveness of the proposed methods, with comparisons drawn with a GA-based design method

Design of Fixed Beamformers Based on Vector-Sensor Arrays

Vector-sensor arrays such as those composed of crossed dipole pairs are used as they can account for a signal’s polarisation in addition to the usual direction of arrival information, hence allowing expanded capacity of the system. The problem of designing fixed beamformers based on such an array, with a quaternionic signal model, is considered in this paper. Firstly, we consider the problem of designing the weight coefficients for a fixed set of vector-sensor locations. This can be achieved by minimising the sidelobe levels while keeping a unitary response for the main lobe. The second problem is then how to find a sparse set of sensor locations which can be efficiently used to implement a fixed beamformer. We propose solving this problem by converting the traditional norm minimisation associated with compressive sensing into a modified norm minimisation which simultaneously minimises all four parts of the quaternionic weight coefficients. Further improvements can be made in terms of sparsity by converting the problem into a series of iteratively solved reweighted minimisations, as well as being able to enforce a minimum spacing between active sensor locations. Design examples are provided to verify the effectiveness of the proposed design methods

Compressive Sensing Based Design of Sparse Tripole Arrays

This paper considers the problem of designing sparse linear tripole arrays. In such arrays at each antenna location there are three orthogonal dipoles, allowing full measurement of both the horizontal and vertical components of the received waveform. We formulate this problem from the viewpoint of Compressive Sensing (CS). However, unlike for isotropic array elements (single antenna), we now have three complex valued weight coefficients associated with each potential location (due to the three dipoles), which have to be simultaneously minimised. If this is not done, we may only set the weight coefficients of individual dipoles to be zero valued, rather than complete tripoles, meaning some dipoles may remain at each location. Therefore, the contributions of this paper are to formulate the design of sparse tripole arrays as an optimisation problem, and then we obtain a solution based on the minimisation of a modified l1 norm or a series of iteratively solved reweighted minimisations, which ensure a truly sparse solution. Design examples are provided to verify the effectiveness of the proposed methods and show that a good approximation of a reference pattern can be achieved using fewer tripoles than a Uniform Linear Array (ULA) of equivalent length

Compressive Sensing Based Approach to the Design of Linear Robust Sparse Antenna Arrays with Physical Size Constraint

In sparse arrays, the randomness of antenna locations avoids the introduction of grating lobes, while allowing adjacent antenna spacings to be greater than half a wavelength. This means a larger array size can be implemented using a relatively small number of antennas. However, careful consideration has to be given to antenna locations to ensure that an acceptable performance level is achieved. Model perturbations can also cause steering vector errors, which in turn cause discrepancies in the array's response, making robust arrays desirable. This study presents various compressive sensing-based methods that can solve this problem, while also imposing the antenna size as a constraint on the minimum adjacent antenna separations. Narrowband and multiband design examples are presented to verify the effectiveness of the proposed design methods, with comparisons being drawn with a previously proposed genetic algorithm-based approach