Adaptive Complex-Coefficient 2D FIR Trapezoidal Filters for Broadband Beamforming in Cognitive Radio Systems

A novel design method is proposed for an adaptive discrete-domain beamformer for the beamforming of temporally broadband-bandpass signals in cognitive radio (CR) systems. The method is based on a complex-coefficient 2D finite impulse response (FIR) filter having a trapezoidal-shaped passband. The temporally broadband-bandpass signals are received by a 1D uniformly distributed antenna array (1D UDAA), where the outputs of the antennas are complex-quadrature sampled by the front end of the CR system. This CR system is based on a software defined radio (SDR) architecture and can be instantly reconfigured by the control system to select the appropriate frequency band and the required sampling rate. The subsequent beamforming enhances the spectral components of the desired temporally broadband-bandpass signals by arranging for the asymmetric trapezoidal-shaped passband of the 2D filter transfer function to closely enclose the region of support (ROS) of the spectrum of the desired signal, whereas the ROSs of the spectral components of the interfering signals are enclosed by the stopband. The proposed novel closed-form design method facilitates instant adaptation of the shape and orientation of the passband of the beamforming 2D FIR trapezoidal filter in order to match the time-varying frequency band and the time-varying bandwidth of the signal, as well as to track and enhance received signals with time-varying directions of arrival (DOAs). Simulated results confirm that, compared with previously reported methods, the proposed method achieves the best overall tradeoff with respect to the instantaneous adaptations of the operating frequency band, the bandwidth, and the time-varying DOAs, the distortion of the desired passband signal, and the stopband attenuation of interfering signals.     

Frequency sampling method for designing 2-D FIR real-coefficientdigital filters using Hermite interpolation

A novel frequency-sampling method for designing 2-D real-coefficient FIR filters, given the values and slope estimates of the desired frequency response at each of the node points of a rectangular grid, is presented. Based on a new class of bivariate Hermite-type polynomials suitable for interpolating at complex conjugate points, and using Kronecker products, the original 2-D filter design problem is reduced to the solution of two 1-D systems of linear equations. Additional advantages of the method are the securing of the existence and uniqueness of the solution of the design problem, computational efficiency, the use of simple and recursive 1-D algorithms; the guarantee of real accurate results; and the inherent parallelism. The method is also applied to design 2-D symmetric FIR filters and can be extended to m-D design problems     

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.     

On the Applications of the Frequency-Response Masking Technique in Array Beamforming

The frequency-response masking (FRM) technique is well known to be very efficient in the implementation of finite impulse response (FIR) filters with sharp transition bands. As sensor array beamforming is closely related to FIR filtering, the feasibility of the applications of the FRM technique in array beamforming is investigated in detail in this paper. On one hand, it is shown that there is a limitation in applying the FRM technique in passive array beamforming. On the other hand, for active array beamforming, a novel combination of the concept of effective aperture and the FRM technique does lead to the synthesis of desirable beamformers. These beamformers have effective beampatterns with sharp transition bands and low sidelobes, and can be implemented with fewer sensors than other design techniques.     

Design of two-dimensional digital filters using singular-valuedecomposition and balanced approximation method

It is shown that the singular-value decomposition (SVD) of the sampled amplitude response of a two-dimensional (2-D) digital filter possesses a special structure: every singular vector is either mirror-image symmetric or antisymmetric with respect to its midpoint. Consequently, the SVD can be applied along with 1-D finite impulse response (FIR) techniques for the design of linear-phase 2-D filters with arbitrary prescribed amplitude responses which are symmetrical with respect to the origin of the (ωΨω₂) plane. The balanced approximation method is applied to linear-phase 2-D FIR filters of the type that may be obtained by using the SVD method. The method leads to economical and computationally efficient filters, usually infinite impulse response filters, which have prescribed amplitude responses and whose phase responses are approximately linear     

宽带波束形成技术的研究

在很多情况下,要求基阵能够不失真地接收宽带信号,因此要求波束形成器的波束图具有与频率无关的特性。深入研究了利用自适应方法设计具有特定频率响应的FIR滤波器用于进行时域宽带波束形成的应用,给出了仿真结果,验证了算法的有效性。采用FPGA或DSP实现带通滤波器是一项成熟的技术,所以通过设计特定频率响应的FIR滤波器来实现宽带波束形成技术在工程上是可实现的。     

Design of linear combination of weighted medians

This paper introduces a novel nonlinear filtering structure: the linear combination of weighted medians (LCWM). The proposed filtering scheme is modeled on the structure and design procedure of the linear-phase FIR highpass (HP) filter in that the linear-phase FIR HP filter can be obtained by changing the sign of the filter coefficients of the FIR lowpass (LP) filter in the odd positions. The HP filter can be represented as the difference between two LP subfilters that have all positive coefficients. This representation of the FIR HP filter is analogous to the difference of estimates (DoE) such as the difference of medians (DoM). The DoM is essentially a nonlinear HP filter that is commonly used in edge detection. Based on this observation, we introduce a class of LCWM filters whose output is given by a linear combination of weighted medians of the input sequence. We propose a method of designing the 1-D and 2-D LCWM filters satisfying required frequency specifications. The proposed method adopts a transformation from the FIR filter to the LCWM filter. We show that the proposed LCWM filter can offer various frequency filtering characteristics including “LP,” “bandpass (BP),” and “HP” responses     

针对线性调频信号的宽带宽角相控阵发射波束形成方法

以线性调频信号为例,揭示窄带相控阵在大孔径宽扫描角情况下不能有效发射宽带高分辨信号的实质。针对线性调频信号,提出2种宽带宽角相控阵发射波束形成新方法,给出了实现示意框图。新方法采用时域数字处理,与时域采用抽头延迟线的FIR滤波器波束形成方法和频域DFT波束形成方法相比,文中方法简单、所需设备量少、易于工程实现。     

基于确知波形的宽带宽角相控阵发射波束形成方法

在大孔径宽扫描角情况下,利用窄带相控阵发射不出去宽带高分辨信号,本文经理论分析说明了这一点,并提出两种基于已知波形的宽带宽角相控阵发射波束形成方法,给出了实现示意框图,通过计算机仿真验证了其可行性.新方法采用时域数字处理,在性能上是最优的.与时域采用抽头延迟线的FIR滤波器波束形成方法和频域DFT波束形成方法相比,文中方法简单,所需设备量少,易于工程实现.     

An improved systolic architecture for 2-D digital filters

An improved systolic architecture for two-dimensional infinite-impulse response (IIR) and finite-impulse-response (FIR) digital filters is presented. Comparisons with recently published work are made. When compared with the architecture of M.A. Sid-Ahmed (1989), a substantial reduction in the number of delay elements is observed. This reduction is of the order of 10² for a 2-D IIR filter and equals N+1 for an Nth-order 2-D FIR filter. The clock period has been made independent of the order of the filter. The speed-up factor is the maximum achievable and is independent of the filter order. Comparison with the work of S. Sunder et al. (1990) shows an improvement in the latency of the systolic array, which has been reduced from 1 to 0. A reduction of N+1 delay elements has been achieved for the FIR filter. An error analysis for the architecture is made     

二维束宽恒定的二阶锥规划波束形成方法

二阶锥规划作为凸优化理论的一个分支,近些年来已应用于波束形成的研究,但在已有研究中基于均匀线阵的一维波束形成研究得较多,且较少考虑不同指向下的束宽恒定问题。因此,基于矩形平面阵,将二阶锥规划的一维束宽恒定波束形成方法扩展到二维作为主要研究目标,首先采用Dolph-Chebyshev加权方法设计出二维参考波束,再以主瓣逼近和旁瓣最小为约束,引入二阶锥规划方法设计了支持不同俯仰角和方位角指向的二维波束。经仿真分析,所提方法可实现在三维空间中的不同指向下的波束形成,且在俯仰角设定后,在不同方位指向下可实现3 dB束宽较恒定的波束,减少了指向对波束特性的影响,方便于应用。     

Design of two-dimensional rectangular array beamformers withpartial adaptivity

This paper considers the problem of designing a two-dimensional (2-D) rectangular array beamformer with partial adaptivity. Using the eigenstructure of the signal data received by a 2-D rectangular array beamformer, we first show that the optimal weight matrix when using full adaptivity can be obtained from a set of singular vectors. Then the design problem of using partial adaptivity is formulated. As a result, the optimal solution for the partially adaptive weight matrix can be found by solving two basic problems, namely determining the proper dimension of the partially adaptive weight matrix and the set of the singular vectors. We develop the detection formulas for the information theoretic criteria AIC and MDL to find the proper dimension. Next, an efficient method is presented so that the optimal solution for the set of the singular vectors can be found analytically. We also investigate the required computational complexity. It is shown that 2-D partially adaptive beamforming using the proposed technique requires less computational complexity than 2-D fully adaptive beamforming using conventional techniques. Moreover, computer simulations demonstrate that the proposed 2-D partially adaptive technique provides satisfactory array performance when compared with conventional fully adaptive techniques     

Two-dimensional FIR compaction filter design

The design of signal-adapted multirate filter banks has been an area of research interest. The authors present the design of a 2-D finite impulse response (FIR) compaction filter followed by a 2-D FIR filter bank that packs the maximum energy of the input process into a few subbands. The energy compaction property of the 2-D compaction filter is extremely good for higher filter orders and converges to the ideal optimal solution as the order tends to infinity. The design procedure is very straightforward and involves a 2-D spectral factorisation     

Realization of 2-D linear-phase FIR filters by using thesingular-value decomposition

The singular-value decomposition (SVD) technique is investigated for the realization of a general two-dimensional (2-D) linear-phase FIR filter with an arbitrary magnitude response. A parallel realization structure consisting of a number of one-dimensional (1-D) FIR subfilters is obtained by applying the SVD to the impulse response of a 2-D filter. It is shown that by using the symmetry property of the 2-D impulse response and by developing an appropriate unitary transformation, an SVD yielding linear-phase constituent 1-D filters can always be obtained so that the efficient structures of the 1-D linear-phase filters can be exploited for 2-D realization. It is shown that when the 2-D filter to be realized has some specified symmetry in its magnitude response, the proposed SVD realization would yield a magnitude characteristic with the same symmetry. An analysis is carried out to obtain tight upper bounds for the errors in the impulse response as well as in the frequency response of the realized filter. It is shown that the number of parallel sections can be reduced significantly without introducing large errors, even in the case of 2-D filters with nonsymmetric magnitude response     

Low power and high-speed implementation of fir filters for software defined radio receivers

The most computationally intensive part of the wideband receiver of a software defined radio (SDR) is the intermediate frequency (IF) processing block. Digital filtering is the main task in IF processing. The computational complexity of finite impulse response (FIR) filters used in the IF processing block is dominated by the number of adders (subtracters) employed in the multipliers. This paper presents a method to implement FIR filters for SDR receivers using minimum number of adders. We use an arithmetic scheme, known as pseudo floating-point (PFP) representation to encode the filter coefficients. By employing a span reduction technique, we show that the filter coefficients can be coded using considerably fewer bits than conventional 24-bit and 16-bit fixed-point filters. Simulation results show that the magnitude responses of the filters coded in PFP meet the attenuation requirements of wireless communication standard specifications. The proposed method offers average reductions of 40% in the number of adders and 80% in the number of full adders needed for the coefficient multipliers over conventional FIR filter implementation methods     

Design of 2-D FIR narrow transition band filters by double transformations using GA approach

In this investigation, subfilters are cascaded in the design of a 2-D narrow transition band FIR digital filter with double transformations, a transformation from wide transition band subfilter into 1-D narrow transition band filter and a McClellan transformation from 1-D filter into 2-D filter. The traditional method for designing a 2-D FIR digital filter with a narrow transition band yields very high orders. The difficulty of the design and implementation will increase with orders exponentially. Numerous identical low-order subfilters are cascaded together to simplify the design of a high-order 2-D filter compared to traditional design method. A powerful genetic algorithm (GA) is presented to determine the best coefficients of the McClellan transformation. It can be used to design any contours of arbitrary shape for mapping 1-D to 2-D FIR filters very effectively. A generalized McClellan transformation is presented, and can be used to design 2-D complex FIR filters. Various numerical design examples are presented to demonstrate the usefulness and effectiveness of the presented approach.

A frequency-agile single-chip QAM modulator with beamformingdiversity

Architecture and circuit design techniques for VLSI implementation of a single-chip quadrature amplitude modulation (QAM) modulator with frequency agility and antenna beamforming characteristics are presented. In order to achieve reliable wireless communication modem function, the single chip all-digital QAM modulator implements various features, including high data rates with bandwidth efficiency, flexibility, meeting a wide variety of user throughput requirements with variable and width and data rates in a multi-user system, and robustness, incorporating diversity and redundancy techniques to guarantee robust communication for various operating environments. The modulator components consist of several digital processing building blocks, including various finite-impulse-response (FIR) filters, an innovative variable interpolation filter, a four-channel frequency translator with quadrature mixer for antenna beamforming diversity, a quadrature direct digital frequency synthesizer (QDDFS), a numerically controlled oscillator (NCO), a QAM formatter, a pseudorandom noise (PN) generator, an x/sinx filter, and a microcontroller interface. An optimized architecture and chip implementation for the variable modulator is derived and evaluated which will support symbol rates from 6 kBaud to 8.75 MBaud continuously and digitally flexible IF frequencies up to 70 MHz with four-channel antenna beamforming function     

接收端配备滤波器的分布式波束形成技术

基于频率选择性信道中由一个发射节点、一个目标节点和多个中继节点构成的中继网络,该文提出一种新型的分布式波束形成技术。该技术除了在中继节点上采用滤波而后转发的中继数据中转策略之外,在接收节点也配备一个有限长响应(Finite Impulse Response, FIR)滤波器,共同均衡发射节点与中继节点以及中继节点与接收节点之间的频率选择性信道。该文中,此两种滤波器将得到联合优化以提高接收节点的服务质量,并同时满足中继节点的发射功率限制。仿真结果表明,相较于放大而后转发以及滤波而后转发但无接收滤波器的波束形成器而言,所提波束形成技术极大地提高了频率选择性信道中中继网络的性能。     

A fast matrix iterative technique for the WLS design of 2-D quadrantally symmetic FIR filters

High computational complexity is a major problem encountered in the optimal design of two-dimensional (2-D) finite impulse response (FIR) filters. In this paper, we present an iterative matrix solution with very low complexity to the weighted least square (WLS) design of 2-D quadrantally symmetric FIR filters with two-valued weighting functions. Firstly, a necessary and sufficient condition for the WLS design of 2-D quadrantally symmetric filters with general nonnegative weighting functions is obtained. Then, based on this optimality condition, a novel iterative algorithm is derived for the WLS design problem with a two-valued weighting function. Because the filter parameters are arranged in their natural 2-D form and the transition band is not sampled, the computation amount of the proposed algorithm is reduced significantly, especially for high-order filters. The exponential convergence of the algorithm is established, and its computational complexity is estimated. Design examples demonstrating the convergence rate and solution accuracy of the algorithm, as well as the relation between the iteration number of the algorithm and the size and transition-band width of the filter are given.     

Performance analysis of instantaneous frequency-based interferenceexcision techniques in spread spectrum communications

Jammers characterized by their instantaneous frequencies can be effectively mitigated in direct sequence spread spectrum communications by using open-loop adaptive excision filters. The primary requirement for these filters is that they must possess a notch in tune with the jammer instantaneous frequency (IF) to annihilate the interference power at every time sample. The interference time-varying frequency can be obtained using existing IF estimators, including quadratic time-frequency distribution methods. Without focusing on any specific estimator, we develop expressions for the receiver performance using a general class of multiple-zero FIR excision filters and show the dependence of the bit error rate (BER) on the filter order and its group delay. The effect of inaccuracies in the jammer instantaneous frequency information on the receiver performance is considered and evaluated as a function of the filter notch bandwidth. The latter is defined by the filter zero multiplicity, which is shown to be an important factor in the analysis of the correlator signal-to-noise ratio (SNR)