Design of Linear Phase FIR Filters in Subexpression Space Using Mixed Integer Linear Programming

In this paper, a novel optimization technique is proposed to optimize filter coefficients of linear phase finite-impulse response (FIR) filter to share common subexpressions within and among coefficients. Existing approaches of common subexpression elimination optimize digital filters in two stages: first, an FIR filter is designed in a discrete space such as finite wordlength space or signed power-of-two (SPT) space to meet a given specification; in the second stage, an optimization algorithm is applied on the discrete coefficients to find and eliminate the common subexpressions. Such a two-stage optimization technique suffers from the problem that the search space in the second stage is limited by the finite wordlength or SPT coefficients obtained in the first stage optimization. The new proposed algorithm overcomes this problem by optimizing the filter coefficients directly in subexpression space for a given specification. Numerical examples of benchmark filters show that the required number of adders obtained using the proposed algorithm is much less than those obtained using two-stage optimization approaches.     

Design of discrete coefficient FIR filters by a fast entropy-directed deterministic annealing algorithm

We present an entropy-directed deterministic annealing optimization algorithm and show its applicability to the problem of designing digital filters with discrete coefficients, each implemented as a sum of signed power-of-two terms and additional general hardware constraints. The algorithm is based on analogies from statistical mechanics and is related to the well-known mean field annealing algorithm. It utilizes estimates of conditional entropy to prune the problem during the optimization, thereby reducing the computational time by 30 to 50%. In conjunction with a scheme to compute the value of the objective function as a sequence of updates, this approach leads to a very fast algorithm. As an application example demonstrating the potential of the new method, we consider the design of digital filters with discrete coefficients consisting of a minimum number of signed power-of-two terms.     

FIR Variable Digital Filter With Signed Power-of-Two Coefficients

Variable digital filters (VDFs) are useful for various signal processing and communication applications where the frequency characteristics, such as fractional delays and cutoff frequencies, can be varied online. In this paper, we investigate the design of VDFs with discrete coefficients as a means of achieving low complexity and efficient hardware implementation. The filter coefficients are expressed as the sum of signed power-of-two terms with a restriction on the total number of power-of-two for the filter coefficients. An efficient design procedure is proposed that includes an improved method for handling the quantization of the VDF coefficients for both the min-max and the least-square criteria leading to an optimum quantized solution. For the least-square criterion, a reduced search region around the optimum quantized solution is further constructed and the branch and bound method in conjunction with an efficient branch cutting scheme is presented to search for an optimum solution in this reduced region.     

Design of High-Order Extrapolated Impulse Response FIR Filters with Signed Powers-of-Two Coefficients

Expensive multiplication operations can be replaced by simpler additions and hardwired shifters so as to reduce power consumption and area size, if the coefficients of a digital filter are signed power-of-two (SPT). As a consequence, FIR digital filters with SPT coefficients have been widely studied in the last three decades. However, most approaches for the design of FIR filters with SPT coefficients focus on filters with length less than 100. These approaches are not suitable for the design of high-order filters because they require excessive computation time. In this paper, an approach for the design of high-order filters with SPT coefficients is proposed. It is a two-step approach. Firstly, the design of an extrapolated impulse response (EIR) filter is formulated as a standard second-order cone programming (SOCP) problem with an additional coefficient sensitivity constraint for optimizing its finite word-length effect. Secondly, the obtained continuous coefficients are quantized into SPT coefficients by recasting the filter-design problem into a weighted least squares (WLS) sequential quadratic programming relaxation (SQPR) problem. To further reduce implementation complexity, a graph-based common subexpression elimination (CSE) algorithm is utilized to extract common subexpressions between SPT coefficients. Simulation results show that the proposed method can effectively and efficiently design high-order SPT filters, including Hilbert transformers and half-band filters with SPT coefficients. Experiment results indicate that 0.81N∼0.29N adders are required for 18-bit N-order FIR filters (N=335∼3261) to meet the given magnitude response specifications.     

CORDIC-Based Unified Architectures for Computation of DCT/IDCT/DST/IDST

In this paper, CORDIC (coordinate rotation digital computer)-based Cooley-Tukey fast Fourier transform (FFT)-like algorithms for power-of-two point discrete cosine transform/discrete sine transform/inverse discrete cosine transform/inverse discrete sine transform are proposed and their corresponding unified architectures are developed by fully reusing the unique two basic processing elements. The proposed algorithms have some distinguished advantages, such as FFT-like regular data flow, unique post-scaling factor, and arithmetic-sequence rotation angles. The developed unified architectures can compute four different transforms by simple routing the data flow according to the specific transform without feeding different transform coefficients or different transform kernels. The unfolding technique is used to overcome the problem of difficult to realize pipeline that occur in iterative CORDIC algorithms. Compared to existing unified architectures, the proposed architectures have a superior performance in terms of hardware complexity, control complexity, throughput, scalability, modularity, and pipelinability.     

Design of optimal digital lattice filter structures based on genetic algorithm

In this paper, a new class of lattice-based digital filter structures is derived. The optimum structure problem is formulated in terms of minimizing the signal power ratio with respect to the two sets of free parameters in the proposed structures. An efficient genetic algorithm is proposed to solve the optimum structure problem with the constraint on the structure parameters to be represented in signed power-of-two format. Two design examples are given, in which the optimized structures show excellent finite wordlength properties such as very low parameter sensitivity and very uniform signal powers across signal nodes and outperform the classical lattice structures.     

FIR filter design over discrete coefficients and least square error

The difference routing digital filter (DRDF) consists of an FIR filter followed by a first-order integrator. This structure with power-of-two coefficients has been studied as a means of achieving low complexity, high sampling rate filters which can be implemented efficiently in hardware. The optimisation of the coefficients has previously been based on a time-domain least-squares error criterion. A new design method is proposed that includes a frequency-domain least-squares criterion with arbitrary frequency weighting and an improved method for handling quantisation of the filter coefficients. Simulation studies show that the new approach yields an improvement of up to 7 dB over existing methods and that oversampling can be used to improve performance     

Noise reduction in recursive digital filters using high-order errorfeedback

The problem of solving the optimal (minimum-noise) error feedback coefficients for recursive digital filters is addressed in the general high-order case. It is shown that when minimum noise variance at the filter output is required, the optimization problem leads to set of familiar Wiener-Hopf or Yule-Walker equations, demonstrating that the optimal error feedback can be interpreted as a special case of Wiener filtering. As an alternative to the optimal solution, the formulas for suboptimal error feedback with symmetric or antisymmetric coefficients are derived. In addition, the design of error feedback using power-of-two coefficients is discussed. The efficiency of high order error feedback is examined by test implementations of the set of standard filters. It is concluded that error feedback is a very powerful and versatile method for cutting down the quantization noise in any classical infinite impulse response (IIR) filter implemented as a cascade of second-order direct form sections. The high-order schemes are attractive for use with high-order direct form sections     

认知无线电中非高斯噪声下数字调制信号识别方法简

针对认知无线电系统中传统数字调制识别方法在非高斯Alpha稳定分布噪声下识别性能差、计算复杂度高的问题,提出了一种基于分数低阶循环谱相关系数的数字调制识别新方法。该方法提取分数低阶循环谱截面和频率谱截面以及其投影面的5个相关系数作为识别特征参数,并采用判决树分类器,实现了非高斯噪声下数字调制信号识别。仿真结果表明,在非高斯Alpha稳定分布噪声下,该识别方法不仅具有较高的识别率和良好的稳健性并且计算复杂度更低,更适合于认知无线电系统。     

Analysis and implementation of variable step size adaptivealgorithms

Stochastic gradient adaptive filtering algorithms using variable step sizes are investigated. The variable-step-size algorithm improves the convergence rate while sacrificing little in steady-state error. Expressions describing the convergence of the mean and mean-squared values of the coefficients are developed and used to calculate the mean-square-error evolution. The initial convergence rate and the steady-state error are also investigated. The performance of the algorithm is studied when a power-of-two quantizer algorithm is used, and finite-word-length effects are considered. The analytical results are verified with simulations encompassing variable applications. Two CMOS implementations of the variable-step-size, power-of-two quantizer algorithm are presented to demonstrate that the performance gains are attainable with only a modest increase in circuit complexity     

Design and Complexity Optimization of a New Digital IF for Software Radio Receivers With Prescribed Output Accuracy

This paper studies the design, signal round-off noise, and complexity optimization of a new digital intermediate frequency (IF) architecture for a software radio receiver (SRR). The IF under study consists of digital filters with fixed coefficients, except for a limited number of multipliers required in the Farrow-based sampling rate converter (SRC). The fixed-coefficient filters can be implemented efficiently using sum-of-power-of-two (SOPOT) coefficients and the multiplier-block technique, which gives minimum adder realization. Apart from the multipliers required in the SRC, the digital IF can be implemented without any multiplications. While most multiplier- less filter design and realization methods address only the coefficient round-off problem by minimizing the number of SOPOT terms used, the proposed design methodology aims to minimize more realistic hardware complexity measure, such as adder cells and registers, of the digital IF subject to a given spectral and accuracy specifications. The motivation is that the complexity is closely related to the target output accuracy, which is specified statistically by its total output noise power generated by rounding the intermediate data. Two novel algorithms for optimizing the internal wordlengths of linear time-invariant systems are proposed. The first one relaxes the solution to real valued and formulates the design problem as a constrained optimization. A closed-form solution can be determined by the Lagrange multiplier method. The second one is based on a discrete optimization method called the Marginal Analysis method, and it yields the desired wordlengths in integer values. Both approaches are found to be effective and suitable to large scale systems. A design example and the field programmable gate array (FPGA) realization of a multi-standard receiver are given to demonstrate the proposed method     

An Improved Lattice Filter Structure with Minimum Roundoff Noise Gain

In this paper, a new filter structure is derived by combining the lattice structure and error feedback technique, which contains a free parameter used for structure optimization. The roundoff noise of the proposed structure is analyzed, and the corresponding mathematical expression is deduced. The problem of how to optimize the free parameter is investigated in terms of minimizing the roundoff noise gain. When the free parameter is expressed as an integer power-of-two, for an Nth-order digital filter, the proposed structure requires \(5N+1\) multipliers, which yields the same implementation complexity as the normalized lattice structure. A numerical example is given to show the finite wordlength performance of the proposed structure.     

Channel equalization via channel identification: algorithms andsimulation results for rapidly fading HF channels

The problem of channel equalization via channel identification (CEQCID) that has previously been considered by a handful of researchers is explored further. An efficient algorithm for mapping the channel parameters to the equalizers coefficients is proposed. The proposed scheme is compared with a lattice least squares (LS) based receivers. For the particular application of the high frequency (HF) radio channels, we find that the CEQCID has lower computational complexity. In terms of the tracking performance, also, the CEQCID has been found to be superior to the LS based receivers. We emphasize on the implementation of a fractionally tap-spaced decision feedback equalizer (DFE) and compare that with the T-spaced DFE. We show that the former is a better choice for the multipath HF channels     

Promising Technique of Parameterization For Reconfigurable Radio,the Common Operators Technique: Fundamentals and Examples

In the field of Software Radio (SWR), parameterization studies have become a very important topic. This is mainly because parameterization will probably decrease the size of the software to be downloaded, and also because it will limit the reconfiguration time. In this paper, parameterization is considered as a digital radio design methodology. Two different techniques, namely common functions and common operators are considered. In this paper, the second view is developed and illustrated by two examples: the well known Fast Fourier Transform (FFT) and the proposed Reconfigurable Linear Feedback Shift Register (R-LFSR), derived from the classical Linear Feedback Shift Register (LFSR) structure.     

New low roundoff noise realizations of second-order digital filtersections

New structures for second-order filter sections are proposed that yield lower output roundoff noise than many well known structures and are free of zero-input limit cycle oscillations. These new low-roundoff structures are based on these suggested by Bomar (1989) and are obtained by putting the constraint that some of the state-space coefficients be sum-of-two power-of-two terms. Numerical results are included to illustrate the performance of the proposed structures for narrow-band filters and to compare them with other structures     

Synthèse des filtres numériques non récursifs à phase linéaire et coefficients de longueur finie

This paper presents some different methods for the design of finite impulse response linear phase digital filters with finite wordlength coefficients. An approximation problem with discrete variables is stated for which we search a solution in a Chebyshev sense. The optimal algorithm proposed associates the Remez algorithm and a branch and bound technique (BaB). The use of this kind of algorithm may sometimes lead to relatively important computer time, so two local search algorithms are also considered. The application of these algorithms with or without constraints is illustrated by examples.     

Correction to: SPMI: Single Phase Multiple Initiator Protocol for Coverage in Wireless Sensor Networks

One of the complex problems nowadays in communication systems is the lack of frequency spectrum. To solve this problem, cognitive radio is considered the best candidate that can opportunistically exploit the spectrum. The periodogram based spectrum sensing technique can be used to detect the spectrum in cognitive radio. It is a useful technique since does not need to prior information about the primary signal. In this paper, a new periodogram is presented using the Discrete Cosine Transform (DCT). Results are analyzed and compared with the current raw periodogram. It is observed that the DCT periodogram outperforms the raw technique in terms of probabilities of false alarm and detection, variance, and complexity. In addition, the lowest power of DCT coefficients can be removed without compromising the sensing performance. The proposed system shows high probability of detection with low probability of false alarm even in the case of low Signal-to-Noise Ratio (SNR).     

现阶段文成县山区农村广播电视覆盖的探讨

对文成县山区的广播电视发展和覆盖情况作了介绍，并对“盲村”所采取的电视覆盖方式作了分析，认为采用无线传输进行电视节目覆盖将是主要实现方式。数字无线传输具有其独特的优势和发展空间，通过对几种数字地面传输体制的分析，最后提出适合文成县实际的数字电视地面传播网技术体制和实施方案。     

Combined FRM and GDFT filter bank designs for improved nonuniform DSA channelisation

Multistandard channelisation for base stations is a big application of generalised discrete Fourier transform modulated filter banks (GDFT‐FBs) in digital communications. For technologies such as software‐defined radio and cognitive radio, nonuniform channelisers must be used if frequency bands are shared by different standards. However, GDFT‐FB‐based nonuniform channelisers can suffer from high filter orders when applied to wideband input signals. In this paper, various combinations of GDFT‐FB with the frequency response masking technique are proposed and evaluated for both uniform and nonuniform channelisation applications. Results show that the proposed techniques achieve savings in both the number of filter coefficients and the number of operations per input sample. Copyright © 2015 John Wiley & Sons, Ltd.     

Genetic approach to design of multiplierless FIR filters

The design of multiplierless FIR filters using genetic algorithms is presented. The proposed algorithm uses simple operators (reproduction, crossover, and mutation) to search through the discrete coefficient space of predefined power-of-two coefficients. This approach has proved to be highly effective and outperformed existing multiplierless FIR design techniques.<>