Wideband data-independent beamforming for subarrays

The desire to operate large antenna arrays for e.g. RADAR applications over a wider frequency range is currently limited by the hardware, which due to weight, cost and size only permits complex multipliers behind each element. In contrast, wideband processing would have to rely on tap delay lines enabling digital filters for every element.As an intermediate step, in this thesis we consider a design where elements are grouped into subarrays, within which elements are still individually controlled by narrowband complex weights, but where each subarray output is given a tap delay line or finite impulse response digital filter for further wideband processing. Firstly, this thesis explores how a tap delay line attached to every subarray can be designed as a delay-and-sum beamformer. This filter is set to realised a fractional delay design based on a windowed sinc function. At the element level, we show that designing a narrowband beam w.r.t. a centre frequency of wideband operation is suboptimal,and suggest an optimisation technique that can yield sufficiently accurate gain over a frequency band of interest for an arbitrary look direction, which however comes at the cost of reduced aperture efficiency, as well as significantly increased sidelobes. We also suggest an adaptive method to enhance the frequency characteristic of a partial wideband array design, by utilising subarrays pointing in different directions in different frequency bands - resolved by means of a filter bank - to adaptively suppress undesired components in the beam patterns of the subarrays. Finally, the thesis proposes a novel array design approach obtained by rotational tiling of subarrays such that the overall array aperture is densely constructed from the same geometric subarray by rotation and translation only. Since the grating lobes of differently oriented subarrays do not necessarily align, an effective grating lobe attenuation w.r.t. the main beam is achieved. Based on a review of findings from geometry,a number of designs are highlight and transformed into numerical examples, and the theoretically expected grating lobe suppression is compared to uniformly spaced arrays.Supported by a number of models and simulations, the thesis thus suggests various numerical and hardware design techniques, mainly the addition of tap-delay-line per subarray and some added processing overhead, that can help to construct a large partial wideband array close in wideband performance to currently existing hardware.The desire to operate large antenna arrays for e.g. RADAR applications over a wider frequency range is currently limited by the hardware, which due to weight, cost and size only permits complex multipliers behind each element. In contrast, wideband processing would have to rely on tap delay lines enabling digital filters for every element.As an intermediate step, in this thesis we consider a design where elements are grouped into subarrays, within which elements are still individually controlled by narrowband complex weights, but where each subarray output is given a tap delay line or finite impulse response digital filter for further wideband processing. Firstly, this thesis explores how a tap delay line attached to every subarray can be designed as a delay-and-sum beamformer. This filter is set to realised a fractional delay design based on a windowed sinc function. At the element level, we show that designing a narrowband beam w.r.t. a centre frequency of wideband operation is suboptimal,and suggest an optimisation technique that can yield sufficiently accurate gain over a frequency band of interest for an arbitrary look direction, which however comes at the cost of reduced aperture efficiency, as well as significantly increased sidelobes. We also suggest an adaptive method to enhance the frequency characteristic of a partial wideband array design, by utilising subarrays pointing in different directions in different frequency bands - resolved by means of a filter bank - to adaptively suppress undesired components in the beam patterns of the subarrays. Finally, the thesis proposes a novel array design approach obtained by rotational tiling of subarrays such that the overall array aperture is densely constructed from the same geometric subarray by rotation and translation only. Since the grating lobes of differently oriented subarrays do not necessarily align, an effective grating lobe attenuation w.r.t. the main beam is achieved. Based on a review of findings from geometry,a number of designs are highlight and transformed into numerical examples, and the theoretically expected grating lobe suppression is compared to uniformly spaced arrays.Supported by a number of models and simulations, the thesis thus suggests various numerical and hardware design techniques, mainly the addition of tap-delay-line per subarray and some added processing overhead, that can help to construct a large partial wideband array close in wideband performance to currently existing hardware

Critical analysis of the eigenfilter method for the design of FIR filters and wideband beamformers

The least squares based eigenfilter method has been applied to the design of both finite impulse response (FIR) filters and wideband beamformers successfully. It involves calculating the resultant filter coefficients as the eigenvector of an appropriate Hermitian matrix, and offers lower complexity and less computation time with better numerical stability as compared to the standard least squares method. In this paper, we revisit the method and critically analyze the eigenfilter approach by revealing a serious performance issue in the passband of the designed FIR filter and the mainlobe of the wideband beamformer, which occurs due to a formulation problem. A solution is then proposed to mitigate this issue, and design examples for both FIR filters and wideband beamformers are provided to demonstrate the effectiveness of the proposed method

Image Cryptography using Parameterized Multiband Eigen Wavelet Filterbank

In this paper, we present an eigen filterbank based approach for image cryptography. The proposed method consists of designing a wavelet filterbank using eigenfilter based approach and use the designed filterbank for image encryption with new methodology. We have extended an eigenfilter based approach for the design of multiband two-channel filter bank. This method is based on designing multiband analysis filter, followed by the design of complementary multiband synthesis filter. The designed filterbank has various user defined parameters (key) like, number of bands in the filter spectrum, cutoff frequency of individual frequency band and the level of decomposition. Based on the selection of these parameters we can design a unique filterbank, which can be used for the image encryption. At the decryption end, the original image can be reconstructed only if user selected parameters are known. We present few design examples for the illustration purpose. We also give detail of complexity analysis of the entire cryptography system and also present the time analysis. The proposed approach provides more number of user parameters as compared to state-of-art methods, which can be used as more secure key. It is also observed that the computation time of the proposed approach is comparable

Array Signal Processing Based on Traditional and Sparse Arrays

Array signal processing is based on using an array of sensors to receive the impinging signals. The received data is either spatially filtered to focus the signals from a desired direction or it may be used for estimating a parameter of source signal like direction of arrival (DOA), polarization and source power. Spatial filtering also known as beamforming and DOA estimation are integral parts of array signal processing and this thesis is aimed at solving some key probems related to these two areas. Wideband beamforming holds numerous applications in the bandwidth hungry data traffic of present day world. Several techniques exist to design fixed wideband beamformers based on traditional arrays like uniform linear array (ULA). Among these techniques, least squares based eigenfilter method is a key technique which has been used extensively in filter and wideband beamformer design. The first contribution of this thesis comes in the form of critically analyzing the standard eigenfilter method where a serious flaw in the design formulation is highlighted which generates inconsistent design performance, and an additional constraint is added to stabilize the achieved design. Simulation results show the validity and significance of the proposed method. Traditional arrays based on ULAs have limited applications in array signal processing due to the large number of sensors required and this problem has been addressed by the application of sparse arrays. Sparse arrays have been exploited from the perspective of their difference co-array structures which provide significantly higher number of degrees of freedoms (DOFs) compared to ULAs for the same number of sensors. These DOFs (consecutive and unique lags) are utilized in the application of DOA estimation with the help of difference co-array based DOA estimators. Several types of sparse arrays include minimum redundancy array (MRA), minimum hole array (MHA), nested array, prototype coprime array, conventional coprime array, coprime array with compressed interelement spacing (CACIS), coprime array with displaced subarrays (CADiS) and super nested array. As a second contribution of this thesis, a new sparse array termed thinned coprime array (TCA) is proposed which holds all the properties of a conventional coprime array but with \ceil*{\frac{M}{2}} fewer sensors where $M$ is the number of sensors of a subarray in the conventional structure. TCA possesses improved level of sparsity and is robust against mutual coupling compared to other sparse arrays. In addition, TCA holds higher number of DOFs utilizable for DOA estimation using variety of methods. TCA also shows lower estimation error compared to super nested arrays and MRA with increasing array size. Although TCA holds numerous desirable features, the number of unique lags offered by TCA are close to the sparsest CADiS and nested array and significantly lower than MRA which limits the estimation error performance offered by TCA through (compressive sensing) CS-based methods. In this direction, the structure of TCA is studied to explore the possibility of an array which can provide significantly higher number of unique lags with improved sparsity for a given number of sensors. The result of this investigation is the third contribution of this thesis in the form of a new sparse array, displaced thinned coprime array with additional sensor (DiTCAAS), which is based on a displaced version of TCA. The displacement of the subarrays generates an increase in the unique lags but the minimum spacing between the sensors becomes an integer multiple of half wavelength. To avoid spatial aliasing, an additional sensor is added at half wavelength from one of the sensors of the displaced subarray. The proposed placement of the additional sensor generates significantly higher number of unique lags for DiTCAAS, even more than the DOFs provided by MRA. Due to its improved sparsity and higher number of unique lags, DiTCAAS generates the lowest estimation error and robustness against heavy mutual coupling compared to super nested arrays, MRA, TCA and sparse CADiS with CS-based DOA estimation

Optimization design of mth-band FIR filters with application to image processing

Cone programming (CP) is a class of convex optimization technique, in which a linear objective function is minimized over the intersection of a set of affine constraints. Such constraints could be linear or convex, equalities or inequalities. Owing to its powerful optimization capability as well as flexibility in accommodating various constraints, the cone programming finds wide applications in digital filter design. In this thesis, fundamentals of linear-phase M th-band FIR filters are first introduced, which include the time-domain interpolation condition and the desired frequency specifications. The restriction of the interpolation matrix M for linear-phase two-dimensional (2-D) M th-band filters is also discussed by considering both the interpolation condition and the symmetry of the impulse response of the 2-D filter. Based on the analysis of the M th-band properties, a semidefinite programming (SOP) optimization approach is developed to design linear-phase 1-0 and 2-D M th-band filters. The 2-D SOP optimization design problem is modeled based on both the mini-max and the least-square error criteria. In contrast to the 1-D based design, the 2-D direct SDP design can offer an optimal equiripple result. A second-order cone programming (SOCP) optimization approach is then presented as an alternative for the design of M th-band filters. The performances as well as the design complexity of these two design approaches are justified through numerical design examples. Simulation results show that the performance of the SOCP approach is better than that of the SDP approach for 1-D M th-band filter design due to its reduced computational complexity for the worst-case, whereas the SDP approach is more appropriate for the 2-D M th-band filter design than the SOCP approach because of its efficient and simple optimization structure. Moreover, the designed M th-band filters are proved useful in image interpolation according to both the visual quality and the peak signal-to-noise ratio (PSNR) for the images with different levels of details

Low power digital filtering using adaptive approximate processing

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1997.Includes bibliographical references (p. 167-173).by Jeffrey Thomas Ludwig.Ph.D

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

Digital Filter Design Using Improved Artificial Bee Colony Algorithms

Digital filters are often used in digital signal processing applications. The design objective of a digital filter is to find the optimal set of filter coefficients, which satisfies the desired specifications of magnitude and group delay responses. Evolutionary algorithms are population-based meta-heuristic algorithms inspired by the biological behaviors of species. Compared to gradient-based optimization algorithms such as steepest descent and Newton’s like methods, these bio-inspired algorithms have the advantages of not getting stuck at local optima and being independent of the starting point in the solution space. The limitations of evolutionary algorithms include the presence of control parameters, problem specific tuning procedure, premature convergence and slower convergence rate. The artificial bee colony (ABC) algorithm is a swarm-based search meta-heuristic algorithm inspired by the foraging behaviors of honey bee colonies, with the benefit of a relatively fewer control parameters. In its original form, the ABC algorithm has certain limitations such as low convergence rate, and insufficient balance between exploration and exploitation in the search equations. In this dissertation, an ABC-AMR algorithm is proposed by incorporating an adaptive modification rate (AMR) into the original ABC algorithm to increase convergence rate by adjusting the balance between exploration and exploitation in the search equations through an adaptive determination of the number of parameters to be updated in every iteration. A constrained ABC-AMR algorithm is also developed for solving constrained optimization problems.There are many real-world problems requiring simultaneous optimizations of more than one conflicting objectives. Multiobjective (MO) optimization produces a set of feasible solutions called the Pareto front instead of a single optimum solution. For multiobjective optimization, if a decision maker’s preferences can be incorporated during the optimization process, the search process can be confined to the region of interest instead of searching the entire region. In this dissertation, two algorithms are developed for such incorporation. The first one is a reference-point-based MOABC algorithm in which a decision maker’s preferences are included in the optimization process as the reference point. The second one is a physical-programming-based MOABC algorithm in which physical programming is used for setting the region of interest of a decision maker. In this dissertation, the four developed algorithms are applied to solve digital filter design problems. The ABC-AMR algorithm is used to design Types 3 and 4 linear phase FIR differentiators, and the results are compared to those obtained by the original ABC algorithm, three improved ABC algorithms, and the Parks-McClellan algorithm. The constrained ABC-AMR algorithm is applied to the design of sparse Type 1 linear phase FIR filters of filter orders 60, 70 and 80, and the results are compared to three state-of-the-art design methods. The reference-point-based multiobjective ABC algorithm is used to design of asymmetric lowpass, highpass, bandpass and bandstop FIR filters, and the results are compared to those obtained by the preference-based multiobjective differential evolution algorithm. The physical-programming-based multiobjective ABC algorithm is used to design IIR lowpass, highpass and bandpass filters, and the results are compared to three state-of-the-art design methods. Based on the obtained design results, the four design algorithms are shown to be competitive as compared to the state-of-the-art design methods