Matthew B. Hawes

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.

Location Optimization of Robust Sparse Antenna Arrays With Physical Size Constraint

The location optimization problem for robust sparse antenna array design is addressed with the aim of finding a set of antenna locations that is robust to norm-bounded steering vector errors. A constraint of the antennas physical size is also imposed to ensure the antennas can fit into the optimized locations. Narrowband and multiband design examples are provided to verify the effectiveness of the proposed design method.

Robust sparse antenna array design via compressive sensing

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 arrays response and this makes a robust array desirable. This paper presents a design method for robust sparse antenna arrays based on an extension of compressive sensing. An extra constraint is applied to the process to ensure that the change in response due to a norm-bounded steering vector error is kept below an acceptable level. Design examples are presented to validate the effectiveness of the 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.

Sparse microphone array design for wideband beamforming

The sparse wideband sensor/microphone array design problem is highly nonlinear and it is traditionally solved by genetic algorithms, simulated annealing or other similar optimization methods. This is an extremely time-consuming process and an optimum solution is not guaranteed. In this work, this problem is studied from the viewpoint of compressive sensing (CS) and a CS-based method is provided. Although there have been CS-based methods proposed for the design of narrowband arrays, its extension to the wideband case is not straightforward, as there are multiple coefficients associated with each sensor/microphone and it is not sufficient to simply minimize the l1 norm of the weight coefficients to obtain a sparse array solution. To achieve this, a modified l1 norm minimization method is derived and its effectiveness is verified by design examples.

An Improved Simulated Annealing Technique for Enhanced Mobility in Smart Cities

Vehicular traffic congestion is a significant problem that arises in many cities. This is due to the increasing number of vehicles that are driving on city roads of limited capacity. The vehicular congestion significantly impacts travel distance, travel time, fuel consumption and air pollution. Avoidance of traffic congestion and providing drivers with optimal paths are not trivial tasks. The key contribution of this work consists of the developed approach for dynamic calculation of optimal traffic routes. Two attributes (the average travel speed of the traffic and the roads’ length) are utilized by the proposed method to find the optimal paths. The average travel speed values can be obtained from the sensors deployed in smart cities and communicated to vehicles via the Internet of Vehicles and roadside communication units. The performance of the proposed algorithm is compared to three other algorithms: the simulated annealing weighted sum, the simulated annealing technique for order preference by similarity to the ideal solution and the Dijkstra algorithm. The weighted sum and technique for order preference by similarity to the ideal solution methods are used to formulate different attributes in the simulated annealing cost function. According to the Sheffield scenario, simulation results show that the improved simulated annealing technique for order preference by similarity to the ideal solution method improves the traffic performance in the presence of congestion by an overall average of 19.22% in terms of travel time, fuel consumption and CO2 emissions as compared to other algorithms; also, similar performance patterns were achieved for the Birmingham test scenario.

A quaternion-valued reweighted minimisation approach to sparse vector sensor array design

In this work, the design of sparse vector sensor arrays is studied based on quaternionic formulations, which is a further extension of the recently proposed compressive sensing (CS) based design methods. As with the traditional case, sparsity of the solution can be improved by converting the problem into a series of iteratively solved reweighted minimisations, where locations with a small absolute coefficient value are more heavily penalised compared to those with a larger absolute value. Moreover, this reweighted scheme is further modified to incorporate a size constraint into the design so that practical antennas with a non-zero size can fit into the designed locations.

Bayesian Compressive Sensing Approaches for Direction of Arrival Estimation With Mutual Coupling Effects

The problem of estimating the dynamic direction of arrival (DOA) of far-field signals impinging on a uniform linear array, with mutual coupling effects, is addressed. This paper proposes two novel approaches able to provide accurate solutions, including at the endfire regions of the array. First, a Bayesian compressive sensing Kalman filter is developed, which accounts for the predicted estimated signals rather than using the traditional sparse prior. The posterior probability density function of the received source signals and the expression for the related marginal likelihood function are derived theoretically. Next, a Gibbs sampling-based approach with indicator variables in the sparsity prior is developed. This allows sparsity to be explicitly enforced in different ways, including when an angle is too far from the previous estimate. The proposed approaches are validated and evaluated over different test scenarios and compared to the traditional relevance vector machine (RVM)-based method. An improved accuracy in terms of average root-mean-square error values is achieved (up to 73.39% for the modified RVM-based approach and 86.36% for the Gibbs sampling-based approach). The proposed approaches prove to be particularly useful for DOA estimation when the angle of arrival moves into the endfire region of the array.

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.

Design of low-complexity wideband beamformers with temporal sparsity

In this paper, a method for the design of a wideband beamformer with temporal sparsity is proposed. The main advantage of the proposed design is its low implementation complexity as the number of non-zero valued coefficients is reduced significantly. It is formulated as an l1 minimisation problem with an added frequency invariant (FI) constraint if an FI response is desired. As a result, sparsity in the tapped delay-line (TDL) coefficients associated with each sensor is introduced and at the same time the designed response still gives an acceptable performance in terms of matching a desired response.