Design of Computationally Efficient Sharp FIR Filter Utilizing Modified Multistage FRM Technique for Wireless Communications Systems

Modern wireless communications gadgets demand multi-standard communications facilities with least overlap between different input radio channels. A sharp digital filter of extremely narrow transition-width with lower stop band ripples offers alias-free switching among the preferred frequency bands. A computationally competent low pass filter (LPF) structure based on the multistage frequency response masking (FRM) approach is proposed for the design of sharp finite impulse response (FIR) filters which are suitable for wireless communications applications. In comparison of basic FRM with other existing multistage FRM structures, the proposed structure has a narrow transition bandwidth and higher stop band attenuation with significant reduction in terms of the number of computational steps. A design example is incorporated to demonstrate the efficiency of the proposed approach. Simulation results establish the improvement of the proposed scheme over other recently published design strategies.     

Broadband Beamforming Using TDL-Form IIR Filters

Conventional broadband beamforming structures make use of finite-impulse-response (FIR) filters in each channel. Large numbers of coefficients are required to retain the desired signal-to-interference-plus-noise-ratio (SINR) performance as the operating bandwidth increases. It has been proven that the optimal frequency-dependent array weighting of broadband beamformers could be better approximated by infinite-impulse-response (IIR) filters. However, some potential problems, such as stability monitoring and sensitivity to quantization errors, of the IIR filters make the implementation of the IIR beamformers difficult. In this paper, new broadband IIR beamformers are proposed to solve these problems. The main contributions of this paper include 1) the Frost-based and generalized sidelobe canceller (GSC)-based broadband beamformers utilizing a kind of tapped-delay-line-form (TDL-form) IIR filters are proposed; 2) the combined recursive Gauss-Newton (RGN) algorithm is designed to compute the feedforward and feedback weights in the Frost-based implementation; and 3) in the GSC-based structure, the unconstrained RGN algorithm is customized for the TDL-form IIR filters in the adaptive beamforming part. Compared with the beamformer using direct-form IIR filters, the new IIR beamformers offer much easier stability monitoring and less sensitivity to the coefficient quantization, while comparable SINR improvement over the conventional FIR beamformer is achieved     

一种可变带宽FRM滤波新结构

设计窄过渡带FIR滤波器的一种非常有效的方法是采用频率响应屏蔽技术(FRM).但是如果过渡带要求过窄,经典FRM滤波器各子滤波器的阶数会变得很高.据此,本文提出一种可变带宽镜像半带滤波FRM滤波新结构,通过增加两个镜像半带滤波器,将原型滤波器及其互补滤波器的镜像分别分成奇偶两部分,使得原型滤波器和屏蔽滤波器的设计更加灵活,并降低了滤波器的计算复杂度,达到了设计高效窄过渡带滤波器的目的.理论分析和实例均验证了该结构的有效性.     

基于Laguerre滤波器等价设计的IIR宽带波束形成

常规IIR宽带波束形成器可以获得比FIR宽带波束形成器更好的性能,但其需要多极点的自适应调整过程,存在稳定性无法保证,计算复杂度较高等问题.本文提出一种新的基于IIR滤波器的宽带波束形成算法.该算法基于高阶Laguerre宽带波束形成器,利用双线性变换和函数束方法设计相应的低阶等价IIR宽带波束形成器.仿真实验及理论分析表明,该方法无需常规IIR宽带波束形成器的多极点自适应调整过程,在保证算法稳定性的同时,减少了计算复杂度,并提高了输出信干噪比(SINR).     

Eigenspace-based adaptive array beamforming with robustcapabilities

This paper deals with adaptive array beamforming based on eigenspace-based (ESB) techniques with robust capabilities. It has been shown that ESB adaptive beamformers demonstrate the advantages of fast convergence speed and less sensitivity to steering angle error over conventional beamformers. In conjunction with a signal subspace construction method, we present an efficient technique to achieve the advantages of ESB adaptive beamforming with less computing cost and more robust capabilities over existing ESB techniques. Several computer simulation examples are provided for illustrating the effectiveness of the proposed technique     

Two-Channel FIR Filter Banks Utilizing the FRM Approach

The frequency-response masking (FRM) approach has been introduced as a means of generating narrow transition band linear-phase finite impulse response (FIR) filters with a low arithmetic complexity. This paper proposes an approach for synthesizing two-channel maximally decimated FIR filter banks utilizing the FRM technique. For this purpose, a new class of FRM filters is introduced. Filters belonging to this class are used for synthesizing nonlinear-phase analysis and synthesis filters for two types of two-channel filter banks. For the first type, there exist no phase distortion and aliasing errors, but this type suffers from a small amplitude distortion as for the well-known quadrature mirror filter (QMF) banks. Compared to conventional QMF filter banks, the proposed banks lower significantly the overall arithmetic complexity at the expense of a somewhat increased overall filter bank delay in applications demanding narrow transition bands. For the second type, there are also small aliasing errors, allowing one to reduce the arithmetic complexity even further. Efficient structures are introduced for implementing the proposed filter banks, and algorithms are described for maximizing the stopband attenuations of the analysis and synthesis filters in the minimax sense subject to the given allowable amplitude and/or aliasing errors. Examples are included illustrating the benefits provided by the proposed filter banks.     

A Novel Diversity-Controlled Genetic Algorithm for Rapid Optimization of Bandpass FRM FIR Digital Filters Over CSD Multiplier Coefficient Space

The conventional frequency response masking (FRM) approach is one of the most well-known techniques for the design of sharp transition band finite impulse response (FIR) digital filters. The resulting FRM digital filters permit efficient hardware implementations due to an inherently large number of zero-valued multiplier coefficients. The hardware complexity of these digital filters can further be reduced by representing the remaining (non-zero) multiplier coefficient values by using their canonical signed-digit (CSD) representations. This paper presents a novel diversity-controlled (DC) genetic algorithm (GA) for the discrete optimization of bandpass FRM FIR digital filters over the CSD multiplier coefficient space. The resulting bandpass FIR digital filters are permitted to have equal or unequal lower and upper transition bandwidths. The proposed DCGA is based on an indexed look-up table of permissible CSD multiplier coefficients such that their indices form a closed set under the genetic operations of crossover and mutation. The salient advantage of DCGA over the conventional GA lies in the external control over population diversity and parent selection, giving rise to a rapid convergence to an optimal solution. The external control is achieved through the judicious choice of a pair of DCGA optimization parameters. An empirical investigation is undertaken for choosing appropriate values for these control parameters. The convergence speed advantages of the DCGA are demonstrated through its application to the design and optimization of a pair of bandpass FRM FIR digital filters with equal or arbitrary lower and upper transition bandwidths. In both cases, an increase of about an order of magnitude in the speed of convergence is achieved as compared to the conventional GAs.     

Complexity Reduction For FRM-based FIR Filters Using The Prefilter-Equalizer Technique

A new method to reduce the number of arithmetic operations in a sharp FIR filter synthesized by the frequency-response masking (FRM) technique is presented. The success of the proposed method is based on a modified FRM approach where the subfilters in the FRM approach are implemented by using recently introduced prefilter-equalizer based filters. It is shown, by means of examples, that the proposed method yields considerable savings in the numbers of multipliers and adders compared to the original single-stage FRM approach.     

基于神经网络的FRM滤波器优化设计研究

以频率响应屏蔽(FRM)技术为基础,提出了一种基于神经网络的窄过渡带FIR数字滤波器的优化设计新方法.该算法主要通过使频率响应平方误差函数最小化来获得FRM滤波器系数.文中详细介绍了基于神经网络的基本FRM滤波器和多层FRM滤波器的设计算法及设计步骤,证明了该算法的稳定性定理,给出了仿真实例,并与已有的设计方法进行了比较,设计结果表明用该方法设计的窄过渡带FIR数字滤波器性能更为优越.     

Further Study on Robust Adaptive Beamforming With Optimum Diagonal Loading

Significant effort has gone into designing robust adaptive beamforming algorithms to improve robustness against uncertainties in array manifold. These uncertainties may be caused by uncertainty in direction-of-arrival (DOA), imperfect array calibration, near-far effect, mutual coupling, and other mismatch and modeling errors. A diagonal loading technique is obligatory to fulfil the uncertainty constraint where the diagonal loading level is amended to satisfy the constrained value. The major drawback of diagonal loading techniques is that it is not clear how to get the optimum value of diagonal loading level based on the recognized level of uncertainty constraint. In this paper, an alternative realization of the robust adaptive linearly constrained minimum variance beamforming with ellipsoidal uncertainty constraint on the steering vector is developed. The diagonal loading technique is integrated into the adaptive update schemes by means of optimum variable loading technique which provides loading-on-demand mechanism rather than fixed, continuous or ad hoc loading. We additionally enrich the proposed robust adaptive beamformers by imposing a cooperative quadratic constraint on the weight vector norm to overcome noise enhancement at low SNR. Several numerical simulations with DOA mismatch, moving jamming, and mutual coupling are carried out to explore the performance of the proposed schemes and compare their performance with other traditional and robust beamformers     

SVM自适应波束成形算法

在天线阵列过载,以及强干扰与期望用户信号夹角过近的情况下,传统的线性阵列信号处理算法,如MMSE(minimum mean-squareerror)、NLMS(Normalized Least Mean Squares)等表现并不理想。SVM(SupportVectorMachine)是机器学习领域的最新成果,有较强的泛化能力,收敛快以及低复杂度等优点。本文提出了在上行波束成形中使用SVM算法,提高空域滤波的分辨率,与其他相关算法相比较,系统性能有了明显的改进。     

Frequency-Response Masking Filters Based on Serial Masking Schemes

In this paper, computationally efficient filter structures based on the frequency-response masking (FRM) technique are proposed for the synthesis of arbitrary bandwidth sharp finite impulse response (FIR) filters. A serial masking scheme is introduced in the new structures to perform the masking task in two stages, which reduces the complexity of the masking filters. Compared to the original FRM and interpolated FIR-FRM (IFIR-FRM) structures, the proposed structures achieve additional savings in terms of numbers of arithmetic operations.     

A unified approach to multistage frequency-response masking filter design using the WLS technique

This paper presents a unified approach to the optimal design of sharp linear-phase finite-impulse-response (FIR) digital filters synthesized using the multistage frequency-response masking (FRM) technique. In this approach, the design of a k-stage FRM filter is achieved in a recursive manner. The minimax design problem arising at each step of the synthesis process is converted into a corresponding weighted least-squares (WLS) problem. The WLS problem is highly nonlinear with respect to the coefficients of the filter. Consequently, it is decomposed into several linear least-squares (LS) problems, each of which can be solved analytically. It is then solved iteratively by using an alternating variable approach. Numerical design examples are included to demonstrate the effectiveness of the method.     

Broadband beamforming using Laguerre filters

Space-time processing is a well-substantiated method for designing broadband beamformers. In the conventional Frost space-time beamformer, tapped delay line (TDL) filters are used in each branch of the array to create a wideband response for interference suppression. In this article a new space-time beamforming method is introduced in which Laguerre filters replace the traditional TDL filters in the Frost beamformer. The Laguerre filters are fundamentally IIR filters but with only one pole in their structure. Unlike other IIR-based space-time beamforming methods, the proposed method does not need an adaptive procedure for the pole adjustment and is inherently stable. Simulation results show superior performance of the proposed method compared to the Frost beamformer and comparable results against other IIR-based beamformers with much less computational complexity and guaranteed stability.     

Applications of RF aperture-array spatially-bandpass 2-D IIR filters in sub-Nyquist spectrum sensing,wideband doppler radar and radio astronomy beamforming

The application of two-dimensional (2-D) infinite impulse response (IIR) spatially-bandpass (SBP) filters as a digital beamformer for a wide spectrum of practical applications spanning wireless cognitive radio communications, doppler radar, and radio astronomy instrumentation is discussed. The paper starts with an introduction of the recently proposed 2-D SBP filter. The first application is a spectrum sensing scheme for dynamic spectrum access based cognitive radios. A 2-D IIR SBP filter is used in conjunction with a sub-Nyquist wideband signal reconstruction technique to achieve aperture-array directional spectrum sensing using sub-Nyquist sparse sampling based on the recently reported Eldar algorithm. The second application is related to wideband pulse and continuous-wave frequency modulated Doppler radar sensing. The SBP filter is integrated with a wideband radar back-end connected to an electronically-steerable aperture antenna. A a low-complexity directional localization algorithm is presented, which estimates the range and angle of a target scatterer with a signal to interference ratio improvement of 10 dB. We also present applications of 2-D IIR SBP in the fields of classification and remote sensing of unmanned aerial vehicles. Finally, a digital aperture-array wideband beamforming model using the 2-D IIR SBP filters is presented for radio telescope systems based on dense aperture arrays and time-domain beamforming. A well-known example is the study of pulsar astrophysics using a highly-directional aperture antenna system. The 2-D IIR SBP beamformer is simulated as the digital backend of the time-domain beamforming system with array signals synthesized using measured time-domain signatures from the Crab pulsar obtained from the GAVRT. The SBP filter shows a gain of 12.3 dB with an order of magnitude lower circuit complexity compared to traditional phased-array digital beamformers. To obtain comparable levels of SINR improvement, the wideband phased-array beamformers require 48-point FFTs per antenna. Assuming the optimum three real-multiplications per complex multiplication for the Gauss algorithm, it is discovered that the proposed 2-D IIR SBP beamformers are more than 97 % lower in digital multiplier complexity compared to traditional FIR phased-array FFT-beamformers.     

Robust Adaptive Beamformers Based on Worst-Case Optimization and Constraints on Magnitude Response

In this paper, novel robust adaptive beamformers are proposed with constraints on array magnitude response. With the transformation from the array output power and the magnitude response to linear functions of the autocorrelation sequence of the array weight, the optimization of an adaptive beamformer, which is often described as a quadratic optimization problem in conventional beamforming methods, is then reformulated as a linear programming (LP) problem. Unlike conventional robust beamformers, the proposed method is able to flexibly control the robust response region with specified beamwidth and response ripple. In practice, an array has many imperfections besides steering direction error. In order to make the adaptive beamformer robust against all kinds of imperfections, worst-case optimization is exploited to reconstruct the robust beamformer. By minimizing array output power with the existence of the worst-case array imperfections, the robust beamforming can be expressed as a second-order cone programming (SOCP) problem. The resultant beamformer possesses superior robustness against arbitrary array imperfections. With the proposed methods, a large robust response region and a high signal-to-interference-plus-noise ratio (SINR) enhancement can be achieved readily. Simple implementation, flexible performance control, as well as significant SINR enhancement, support the practicability of the proposed methods.     

A weighted least squares approach to the design of FIR filters synthesized using the modified frequency response masking structure

This paper presents an application of the weighted least squares (WLS) method to the design of sharp linear phase finite-impulse response (FIR) digital filters synthesized using a modified frequency-response masking (FRM) structure. In our approach, the original minimax design problem is converted into a WLS problem. The WLS problem is highly nonlinear with respect to the coefficients of the filter. However, it can be decomposed into four linear least squares (LS) problems, each of which can be solved analytically. The design problem is then solved iteratively by using an alternating variable approach. The effectiveness of the method is demonstrated through solving a low-pass linear phase sharp FIR digital filter example.     

On the synthesis of very sharp decimators and interpolators using the frequency-response masking technique

Decimation and interpolation are very common multirate signal processing operations. Conventional decimation or interpolation technique using polyphase filters has the advantage that for a given transition-band sharpness, the filter's computational complexity decreases with increasing interpolation or decimation factor. Nevertheless, if the transition band of the decimation or interpolation filter is very sharp, the complexity of the filter may still be very high. The complexity of a very sharp filter may be reduced using the frequency-response masking (FRM) technique. However, as shown in this paper, for a given transition-band sharpness, the computational complexity of the classical FRM method does not reduce as rapidly as the increase in decimation or interpolation factor. In this paper, we present a novel variant of the FRM technique for interpolation or decimation application. In this new variant, the computational complexity reduces as rapidly as the interpolation or decimation factor increases. The reduction in computational complexity increases with decreasing transition width. Over an order of magnitude reduction in computational complexity is achieved when compared with conventional polyphase approach in a particular example presented in this paper.     

Modified constant modulus algorithm for digital signal processingadaptive antennas with microwave analog beamforming

This paper proposes a novel algorithm, called modified constant modulus algorithm (M-CMA), which is able to give adaptability to microwave beamforming phased array antennas. Since microwave analog beamformers basically require much fewer RF devices than digital beamformers, microwave analog beamformers based on M-CMA, that is, adaptive microwave beamformers, can be cheaply fabricated. Therefore, they are very suitable for mobile communication systems where both miniaturization and low cost are required for the mobile terminals. M-CMA obtains a gradient vector by a combination of analytical calculation and perturbation of the microwave beamforming control voltage. Though M-CMA is implemented with a digital signal processor, M-CMA controls the microwave analog beamformer by utilizing the gradient vector. The microwave analog beamformer based on M-CMA is analyzed to have the following characteristics: (1) the beamformer can point its main beam to the desired direction in additive white Gaussian noise (AWGN) channels; (2) although the beamformer may possibly fail in ill solutions in cochannel interference (CCI) channels, M-CMA can converge to the optimum solution when the desired direction is roughly a priori known     

PSO Assisted DD-ESB Beamforming with Robust Capabilities

This paper deals with adaptive array beamforming based on the decision-directed eigenspace-based (DD-ESB) technique with robust capabilities. It has been shown that DD-ESB adaptive beamformer demonstrates the advantages of better output signal-to-interference plus noise ratio performance and less sensitivity to pointing error over conventional ESB beamformers without any specific training bits. In conjugation with particle swam optimization assisted scheme to obtain more correct desired user’s transmitted bits from the output of the ESB, the more correct steering vector of the desired user can be reconstructed for DD-ESB adaptive beamforming in the presence of larger pointing error and relatively low interference-to-noise ratio. Computer simulations are provided to illustrate the effectiveness of the proposed approach.