Time-domain modified DFT modulated filter banks for multi-carrier transceiver systems

A time domain designing method is proposed for discrete Fourier transform （DFT） modulated filter banks （DFT-FBs） for application in multi-carrier transceiver systems. Instead of using the time-reversed pair limitation between the transmitting /receiving filter pair, the receiving filters in the proposed filter banks are derived from transmitting filters in accordance with the Moore-Penrose generalized inverse matrix. It can be freely obtained to design the transmitting prototype filter, which mainly affects the level of spectral containment. Furthermore, the symbol error rate （SER） performance of the proposed filter bank based trans-multiplexer with one tap equalizer is investigated in ideal channel and multi-path channel environments respectively. Simulation shows that the proposed approach can achieve significant SER reductions when square root raised cosine （RRC） prototype filter is used for comparing with the orthogonal frequency division multiplexing （OFDM） and the general DFT-FBs based applications.     

On the time‐frequency symbol density of FBMC/QAM systems

Filter bank multicarrier (FBMC) systems suffer from an inherent interference, which needs to be eliminated at the detection process. Orthogonal frequency division multiplexing/offset quadrature amplitude modulation (OFDM/OQAM) is a well‐known FBMC system, which transmits real‐valued symbols. In OFDM/OQAM, the time and frequency spacing between adjacent transmitted symbols are organized such that the inherent interference becomes pure imaginary and can be removed by a real‐taking operation. Although OFDM/OQAM provides the maximal bandwidth efficiency, it falls short in handling the spatial multiplexing techniques in multi‐input multi‐output channels. In this regard, those modified FBMC systems, which transmit complex QAM symbols (FBMC/QAM) are used to support the spatial multiplexing techniques. In this article, we present a novel matrix formulation for the FBMC/QAM transmission procedure. On the basis of this presentation, we show that the maximal achievable time‐frequency symbol density of FBMC/QAM, with the ability of perfectly removing the interference, is equal to that of the primer OFDM/OQAM.     

Reed-Solomon Codes Implementing a Coded Single-Carrier with Cyclic Prefix Scheme

This paper presents a novel Reed-Solomon codes based transmission scheme called RS-SC-CP. While RS-SC-CP is essentially a Reed-Solomon (RS) coded single carrier with cyclic prefix (SC-CP) system, a filter bank representation of the RS code is used. This filter bank representation unveils a DFT synthesis bank, just as in a traditional Orthogonal Frequency Division Multiplexing (OFDM) system (allbeit in a finite field). Therefore, RS-SC-CP is topologically equivalent with OFDM. As such, the RS-SC-CP system inherits the advantages of an SC-CP system over a traditional OFDM system like a low Peak to Average Power Ratio (PAPR). But, more importantly, it allows us to use a novel equalization technique that resembles a traditional OFDM equalizer. The equalizer of an RS-SC-CP receiver is split into two stages: the first stage encompasses a partial equalization in the complex field, which ensures that the residual channel response has integer coefficients. It is calculated using a Minimum Mean Square Error (MMSE) criterion. The residual ISI is removed by a Galois field equalizer in the second stage, posterior to the RS decoding removing the noise. Finally, the performance of the RS-SC-CP system is further evaluated by simulations showing the performance gain of the RS-SC-CP system compared to a traditional coded OFDM or single carrier with cyclic prefix (SC-CP) scheme.     

Scattering function estimation

The estimation of the scattering function of a random, zero-mean, homogeneous, time-variant, linear filter is considered. The sum of the random filter output and independent noise is the input to an estimator. The estimator structure is equivalent to a bank of linear filters followed by squared-envelope detectors; the envelope detector outputs are the input to a final linear filter. The estimator output is shown to be an unconstrained linear operation on the ambiguity function of the estimator input. Except for a bias term due to the additive noise, the mean of the estimator output is an unconstrained linear operation on the scattering function of the random filter. The integral variance of the output is found for a Gaussian channel. The mean and variance clearly indicate the tradeoff between resolution and variance reduction obtained by varying the estimator structure. For any well-behaved channel it is shown that an effectively unbiased estimate of the scattering function can be obtained if the input signal has both sufficient energy and enough time and frequency spread to resolve the random filter; the random filter is not required to be underspread. The variance of an estimate can be further reduced by increasing the time or frequency spread of the transmitted signal.     

Toward Wide-Band High-Resolution Analog-to-Digital Converters Using Hybrid Filter Bank Architecture

The paper presents the problem of design and simulation of a high-speed wide-band high-resolution analog-to-digital (ADC) converter working in a bandpass scenario. Such converters play a crucial role in software-defined radio and in cognitive radio technology. One way to circumvent the limits of today’s ADC technologies is to split the analog input signal into multiple components and then sample them with ADCs in parallel. The two main split approaches, time interleaved and frequency splitting, can be modeled using a filter bank paradigm, where each of these two architectures requires a specific analysis for its design. In this research, the frequency splitting approach was implemented with the use of a hybrid filter bank ADC, which requires an output digital filter bank perfectly matched to the input analog filter bank. To achieve this end, an analog transfer function, together with an assumption of strictly band-limited input signal, has been used to design the digital filter bank so far. In contrast, the author proposes dropping the band-limit assumption and shows that the out-of-band input signal has to be taken into account when designing a hybrid filter bank.     

矩阵整流器输入与输出滤波器特性的研究

矩阵整流器是一种真正的降压型四象限AC-DC变换器,可以用在各种三相电压供电的直流电源领域。鉴于矩阵整流器采用波形高频合成原理实现输入电压-输出电压的变换和输出电流-输入电流的变换,并非纯硅变换器,输入LC滤波器与输出LC滤波器的设计至关重要,并决定着整流器系统的功能、性能和可靠性。在理论分析矩阵整流器与电流源PWM整流器具有共同变换本质的基础上,采用电路DQ转换方法,建立输入LC滤波器-矩阵整流器-输出LC滤波器系统的DC等效电路,重点分析了DC特性高低对滤波器参数设计要求,进而给出设计原则和参数选择公式,并进行实验验证。     

Nonuniform filter bank design with noises

This work solves the signal reconstruction problem involving nonuniform filter bank systems with rational decimation factors and noise. Three main nonuniform filter bank systems, i.e., filter-block decimator (FBD) structure, upsampler-filter-downsampler (UFD) structure, and tree structure, are included in this study. According to different operating conditions, two different signal reconstruction problems for nonuniform filter bank systems with noise under the unknown but identifiable input signal model and the unknown input signal model are discussed, respectively. At the first stage, a unified block state space model for different nonuniform filter bank systems with noise is developed. Then, by incorporating the identified input signal model with this unified state space model and appropriate choice of the augmented state vector, the signal reconstruction problem is reduced to an equivalent state estimation problem for resulting augmented systems if the input signal is identifiable. If the input signal is lacking in modeling, the signal reconstruction is discussed from the minimax estimation point of view. Two state estimation techniques involving robust Kalman filtering and H_∞ filtering are employed, respectively, to treat the signal reconstruction problem of nonuniform filter bank systems according to different a priori knowledge of the input signal. Finally, several numerical examples are presented to illustrate the proposed algorithms and exhibit the performances     

Optimization of filter banks using cyclostationary spectralanalysis

This paper proposes a design method of optimal biorthogonal FIR filter banks that minimize the time-averaged mean squared error (TAMSE) when the high-frequency subband signal is dropped. To study filter banks from a statistical point of view, cyclostationary spectral analysis is used since the output of the filter bank for a wide-sense stationary input is cyclostationary. First, the cyclic spectral density of the output signal is derived, and an expression for the TAMSE is presented. Then, optimal filter banks are given by minimizing the TAMSE with respect to the coefficients of the filters under the biorthogonality condition. By imposing the additional constraints on the coefficients, the optimal biorthogonal linear phase filter bank can be obtained     

On Bounds of Shift Variance in Two-Channel Multirate Filter Banks

Critically sampled multirate FIR filter banks exhibit periodically shift variant behavior caused by nonideal antialiasing filtering in the decimation stage. We assess their shift variance quantitatively by analysing changes in the output signal when the filter bank operator and shift operator are interchanged. We express these changes by a so-called commutator. We then derive a sharp upper bound for shift variance via the operator norm of the commutator, which is independent of the input signal. Its core is an eigensystem analysis carried out within a frequency domain formulation of the commutator, leading to a matrix norm which depends on frequency. This bound can be regarded as a worst case instance holding for all input signals. For two channel FIR filter banks with perfect reconstruction (PR), we show that the bound is predominantly determined by the structure of the filter bank rather than by the type of filters used. Moreover, the framework allows to identify the signals for which the upper bound is almost reached as so-called near maximizers of the frequency-dependent matrix norm. For unitary PR filter banks, these near maximizers are shown to be narrow-band signals. To complement this worst-case bound, we derive an additional bound on shift variance for input signals with given amplitude spectra, where we use wide-band model spectra instead of narrow-band signals. Like the operator norm, this additional bound is based on the above frequency-dependent matrix norm. We provide results for various critically sampled two-channel filter banks, such as quadrature mirror filters, PR conjugated quadrature filters, wavelets, and biorthogonal filters banks.     

Algorithms for a Sparse Reconfigurable Adaptive Filter and a Photonic Switch Architecture

A nonblocking photonic switch can be used to implement a tapped delay line with a large number of adaptive weights and a wide range of time delays. An advantage of using optical tapped delay lines for adaptive filtering is that the operating frequency can be quite high, in the 10?100 GHz range. We present a sparse reconfigurable adaptive filter (SRAF) based on a photonic switch with an input/output connection architecture that can be represented by a matrix of adaptive weights. This unique parallel structure can be reconfigured in an adaptive manner to implement a sparse filter impulse response for use in many applications. We consider an adaptive algorithm for this filter that chooses the input and output delays using a cross-correlation-based approach and connects these delays by weights that are adapted using a gradient algorithm. An alternative adaptive algorithm is also considered that is based on a system identification formulation where the weights are first adapted, and then the appropriate delay combinations are chosen. A search algorithm for implementing the connection constraint required by the SRAF is also discussed whereby each input is connected to only one output at any moment. Computer simulation examples are presented to illustrate the behavior of the filter for a system identification model.      

Modeling of time-interleaved ADCs with nonlinear hybrid filter banks

In this paper, we model time-interleaved analog-to-digital converters (TIADCs) with nonlinear hybrid filter banks (NHFBs), which greatly unifies and simplifies the analysis of TIADCs. The input/output relation of such a nonlinear hybrid filter bank can be used to describe combined offset, gain, aperture delay, input behavior, and nonlinearity mismatches and is therefore an extendable starting point for profound analyses of TIADC behaviors. We show the connection of offset and gain mismatches to nonlinearity mismatches and reveal the two error sources of timing mismatches.     

Optimal signal reconstruction in noisy filter bank systems:multirate Kalman synthesis filtering approach

A multirate Kalman synthesis filter is proposed in this paper to replace the conventional synthesis filters in a noisy filter bank system to achieve optimal reconstruction of the input signal. Based on an equivalent block representation of subband signals, a state-space model is introduced for an M-band filter bank system with subband noises. The composite effect of the input signal, analysis filter bank, decimators, and interpolators is represented by a multirate state-space model. The input signal is embedded in the state vector, and the corrupting noises in subband paths are generally considered as additive noises. Hence, the signal reconstruction problem in the M-band filter bank systems with subband noises becomes a state estimation procedure in the resultant multirate state-space model. The multirate Kalman filtering algorithm is then derived according to the multirate state-space model to achieve optimal signal reconstruction in noisy filter bank systems. Based on the optimal state estimation theory, the proposed multirate Kalman synthesis filter provides the minimum-variance reconstruction of the input signal. Two numerical examples are also included. The simulation results indicate that the performance improvement of signal reconstruction in noisy filter bank systems is remarkable     

Time-Interleaved Analog-to-Digital-Converter Compensation Using Multichannel Filters

Published methods that employ a filter bank for compensating the timing and bandwidth mismatches of an $M$ -channel time-interleaved analog-to-digital converter (TIADC) were developed based on the fact that each sub-ADC channel is a downsampled version of the analog input. The output of each sub-ADC is filtered in such a way that, when all the filter outputs are summed, the aliasing components are minimized. If each channel of the filter bank has $N$ coefficients, the optimization of the coefficients requires computing the inverse of an $MN times MN$ matrix if the weighted least squares (WLS) technique is used as the optimization tool. In this paper, we present a multichannel filtering approach for TIADC mismatch compensation. We apply the generalized sampling theorem to directly estimate the ideal output of each sub-ADC using the outputs of all the sub-ADCs. If the WLS technique is used as the optimization tool, the dimension of the matrix to be inversed is $N times N$. For the same number of coefficients (and also the same spurious component performance given sufficient arithmetic precision), our technique is computationally less complex and more robust than the filter-bank approach. If mixed integer linear programming is used as the optimization tool to produce filters with coefficient values that are integer powers of two, our technique produces a saving in computing resources by a factor of approximately $(10^{0.2N(M - 1)})/(M-1)$ in the TIADC filter design.      

Fast Array Multichannel 2D-RLS Based OFDM Channel Estimator

In this paper a Fast Array Multichannel Two-Dimensional Recursive Least Square (FAM 2D-RLS) adaptive filter is proposed for estimating an OFDM channel in frequency domain. This filter makes use of the shift structure of the input data vector. Thus the computational cost of the classical RLS filter which is O(M ²) is reduced to O(M) for each iteration where M is the order of the filter. In order to ensure numerical stability in finite precision, we make use of array-based methods for implementing FAM 2D-RLS. The adaptive filters illustrated in the standard literature consist of a weight vector and desired data as a scalar. But in our scenario of OFDM channel estimation the weight is a matrix while the desired data are a vector. Hence the algorithm for the matrix form of FAM-2D RLS and its steady state equations are derived. Numerical stability, steady state and convergence performance are verified using MATLAB simulations.     

An Efficient Scheme to Achieve Differential Unitary Space‐Time Modulation on MIMO‐OFDM Systems

Differential unitary space‐time modulation (DUSTM) has emerged as a promising technique to obtain spatial diversity without intractable channel estimation. This paper presents a study of the application of DUSTM on multiple‐input multiple‐output orthogonal frequency division multiplexing (MIMO‐OFDM) systems with frequency‐selective fading channels. From the view of a correlation analysis between subcarriers of OFDM, we obtain the maximum achievable diversity of DUSTM on MIMO‐OFDM systems. Moreover, an efficient implementation strategy based on subcarrier reconstruction is proposed, which transmits all the signals of one signal matrix in one OFDM transmission and performs differential processing between two adjacent OFDM blocks. The proposed method is capable of obtaining both spatial and multipath diversity while reducing the effect of time variation of channels to a minimum. The performance improvement is confirmed by simulation results.     

Non-Wiener solutions for the LMS algorithm-a time domain approach

A time domain analysis of the LMS algorithm is presented for a sinusoidal deterministic reference input. For the sinusoidal reference input only, the N-dimensional time-varying linear matrix recursion for the weight vector is solved using a 2-D orthogonal subspace decomposition. Using this weight vector solution, it is shown that there exists a linear time-invariant relationship between the desired input and the filter output     

Modeling, analysis, and optimum design of quantized M-band filterbanks

This paper provides a rigorous modeling and analysis of quantization effects in M-band subband codecs, followed by optimal filter bank design and compensation. The codec is represented by a polyphase decomposition of the analysis/synthesis filter banks and an embedded nonlinear gain-plus-additive noise model for the pdf-optimized scalar quantizers. We construct an equivalent time-invariant but nonlinear structure operating at the slow clock rate that allows us to compute the exact expression for the mean square quantization error in the reconstructed output. This error is shown to consist of two components: a distortion component and a dominant random noise component uncorrelated with the input signal. We determine the optimal paraunitary and biorthogonal FIR filter coefficients, compensators, and integer bit allocation to minimize this MSE subject to the constraints of filter length, average bit rate, and perfect reconstruction (PR) in the absence of quantizers. The biorthogonal filter bank results in a smaller MSE but the filter coefficients are very sensitive to signal statistics and to average bit constraints. By comparison, the paraunitary structure is much more robust. We also show that the null-compensated design that eliminates the distortion component is more robust than the optimally-compensated case that minimizes the total MSE, but only at nominal conditions. Both modeling and optimal design are validated by simulation in the two-channel case     

双环耦合结构及其在多路耦合器中的应用

腔体宽带超高频(UHF)多路耦合器因其结构原因导致滤波器端口至其合路点的等效电长度过长,造成通带性能下降。为解决这一问题,提出了一种应用于腔体可调带通滤波器的双环输入/输出耦合结构。对这种结构进行了理论分析以及仿真和实验验证。结果表明:利用这种结构能够在不显著降低可调滤波器通带特性的同时实现对其阻带反射特性的独立调节,可以有效减小可调滤波器端口的等效电长度。设计了采用双环耦合结构的同轴腔可调滤波器,并且利用四个双环滤波器制作了四路的UHF多路耦合器,实验结果显示了这种耦合结构的有效性。