Modified RHKF Filter for Improved DR/GPS Navigation against Uncertain Model Dynamics

In this paper, an error compensation technique for a dead reckoning (DR) system using a magnetic compass module is proposed. The magnetic compass‐based azimuth may include a bias that varies with location due to the surrounding magnetic sources. In this paper, the DR system is integrated with a Global Positioning System (GPS) receiver using a finite impulse response (FIR) filter to reduce errors. This filter can estimate the varying bias more effectively than the conventional Kalman filter, which has an infinite impulse response structure. Moreover, the conventional receding horizon Kalman FIR (RHKF) filter is modified for application in nonlinear systems and to compensate the drawbacks of the RHKF filter. The modified RHKF filter is a novel RHKF filter scheme for nonlinear dynamics. The inverse covariance form of the linearized Kalman filter is combined with a receding horizon FIR strategy. This filter is then combined with an extended Kalman filter to enhance the convergence characteristics of the FIR filter. Also, the receding interval is extended to reduce the computational burden. The performance of the proposed DR/GPS integrated system using the modified RHKF filter is evaluated through simulation.     

Least mean squares algorithm for fractionally spaced blind channelestimation

The authors consider the problem of blind estimation and equalisation of digital communication finite impulse response (FIR) channels using fractionally spaced samples. The system input is assumed to be a deterministic but unknown data sequence. Exploiting the periodicity of the transmitted data sequence in the frequency domain in the noise free case, it is shown that it is possible to form a linear system in terms of the unknown channel impulse response. In the presence of noise, a least mean squares (LMS) criterion is used to resolve the channel. The resulting algorithm has an appealing interpretation and can be considered as a single channel counterpart of the multi-channel cross-relation (CR) method. Finally, it is shown that the latter can be derived from the proposed algorithm     

An FIR Channel Estimation Filter with Robustness to Channel Mismatch Condition

This letter proposes a finite impulse response (FIR) channel estimation filter that has robustness against the channel mismatch due to the FIR structure. The channel impulse response is described with a complex state space model and then estimated from received data on the recent time interval. Numerical results show that the FIR channel estimation filter can provide more robust performance than conventional Kalman IIR filters when channel model parameters are not correct.     

Decision Feedback Channel and Symbol Estimation Methods for CDMA Systems in Indoor Wireless Communications

A dispersive finite impulse response (FIR) channel model is often considered for indoor wireless channels. For the FIR channel model in this paper, we consider the joint estimation of channel parameters and data symbols in indoor code division multiple access (CDMA) systems. The least squares formulation is constructed for the joint estimation incorporating the decision feedback technique. This formulation is suitable for indoor CDMA systems that usually have a small processing gain. The formulation is further modified to provide a recursive approach to estimate the channel vector.     

Performance of symbol-sampled receivers over unknown continuous-time Rayleigh channels

The performance of symbol-sampled receivers is usually evaluated via Forney's finite impulse response (FIR) model for the equivalent channel [discrete-time transversal filter (DTTF)]. This model contains a matched filter, and, thus, requires prior knowledge of the continuous-time channel-impulse response. Therefore, if the channel is continuous and unknown, it is unrealistic to use the DTTF model, which leads to an upper bound on the system performance. Using an alternative model for the equivalent discrete-time channel, where the matched filter is replaced by a receive filter matched to the symbol waveform, we propose a framework to quantitatively investigate the performance loss from a theoretical perspective. The theoretical results are corroborated using a practical system.     

Enhanced detection-guided NLMS estimation of sparse FIR-modeled signal channels

In various signal-channel-estimation problems, the channel being estimated may be well approximated by a discrete finite impulse response (FIR) model with sparsely separated active or nonzero taps. A common approach to estimating such channels involves a discrete normalized least-mean-square (NLMS) adaptive FIR filter, every tap of which is adapted at each sample interval. Such an approach suffers from slow convergence rates and poor tracking when the required FIR filter is "long." Recently, NLMS-based algorithms have been proposed that employ least-squares-based structural detection techniques to exploit possible sparse channel structure and subsequently provide improved estimation performance. However, these algorithms perform poorly when there is a large dynamic range amongst the active taps. In this paper, we propose two modifications to the previous algorithms, which essentially remove this limitation. The modifications also significantly improve the applicability of the detection technique to structurally time varying channels. Importantly, for sparse channels, the computational cost of the newly proposed detection-guided NLMS estimator is only marginally greater than that of the standard NLMS estimator. Simulations demonstrate the favourable performance of the newly proposed algorithm.     

Efficient 2-D based algorithms for WLS designs of 2-D FIR filters with arbitrary weighting functions

The impulse response coefficients of a two-dimensional (2-D) finite impulse response (FIR) filter naturally constitute a matrix. It has been shown by several researchers that, two-dimension (2-D) based algorithms that retain the natural matrix form of the 2-D filter’s coefficients are computationally much more efficient than the conventional one-dimension (1-D) based algorithms that rearrange the coefficient matrix into a vector. In this paper, two 2-D based algorithms are presented for the weighted least squares (WLS) design of quadrantally symmetric 2-D FIR filters with arbitrary weighting functions. Both algorithms are based on matrix iterative techniques with guaranteed convergence, and they solve the WLS design problems accurately and efficiently. The convergence rate, solution accuracy and design time of these proposed algorithms are demonstrated and compared with existing algorithms through two design examples.     

宽带MIMO-OFDM系统信道估计算法研究

本文提出了MIMO-OFDM系统中基于LS准则的参数化信道估计方法(LSPCE),推导出其MSE性能的下界并给出一种最优导频序列.为了降低复杂度,本文还提出了一种迭代的算法,它利用有限冲击响应信道的抽头之间的相关性从噪声中提取出信道信息并同时估计出多径时延.仿真和分析表明,相比传统的LS信道估计算法,这种基于参数化的信道估计算法可以大大提高信道估计的精度,接收端的检测性能接近理想信道估计的性能.     

Blind channel estimation via combining autocorrelation and blind phase estimation

Symbol spaced blind channel estimation methods are presented which can essentially use the results of any existing blind equalization method to provide a blind channel estimate of the channel. Blind equalizer's task is reduced to only phase equalization (or identification) as the channel autocorrelation is used to obtain the amplitude response of the channel. Hence, when coupled with simple algorithms such as the constant modulus algorithm (CMA) these methods at baud rate processing provide alternatives to blind channel estimation algorithms that use explicit higher order statistics (HOS) or second-order statistics (subspace) based fractionally-spaced/multichannel algorithms. The proposed methods use finite impulse response (FIR) filter linear receiver equalizer or matched filter receiver based infinite impulse response+FIR linear cascade equalizer configurations to obtain blind channel estimates. It is shown that the utilization of channel autocorrelation information together with blind phase identification of the CMA is very effective to obtain blind channel estimation. The idea of combining estimated channel autocorrelation with blind phase estimation can further be extended to improve the HOS based blind channel estimators in a way that the quality of estimates are improved.     

Adaptive Laguerre-lattice filters

Adaptive Laguerre-based filters provide an attractive alternative to adaptive FIR filters in the sense that they require fewer parameters to model a linear time-invariant system with a long impulse response. We present an adaptive Laguerre-lattice structure that combines the desirable features of the Laguerre structure (i.e., guaranteed stability, unique global minimum, and small number of parameters M for a prescribed level of modeling error) with the numerical robustness and low computational complexity of adaptive FIR lattice structures. The proposed configuration is based on an extension to the IIR case of the FIR lattice filter; it is a cascade of identical sections but with a single-pole all-pass filter replacing the delay element used in the conventional (FIR) lattice filter. We utilize this structure to obtain computationally efficient adaptive algorithms (O(M) computations per time instant). Our adaptive Laguerre-lattice filter is an extension of the gradient adaptive lattice (GAL) technique, and it demonstrates the same desirable properties, namely, (1) excellent steady-state behavior, (2) relatively fast initial convergence (comparable with that of an RLS algorithm for Laguerre structure), and good numerical stability. Simulation results indicate that for systems with poles close to the unit circle, where an (adaptive) FIR model of very high order would be required to meet a prescribed modeling error, an adaptive Laguerre-lattice model of relatively low order achieves the prescribed bound after just a few updates of the recursions in the adaptive algorithm     

用滤波器组构成的传送多路复用器结构实现MMSE盲信道均衡

冗余滤波器组构成的传送多路复用器可以用来对FIR信道进行估计和均衡.本文提出一种在FIR滤波器组框架结构下,首先利用信号的相关矩阵对信道进行估计,然后在此基础上用MMSE准则下设计的FIR均衡器对数据进行均衡的盲算法.该均衡算法的性能要明显好于基于ZF准则的方法,并且在消除ISI的同时可以抑制噪声的影响,从而使系统的输出信噪比达到最优,而增加的复杂度很有限.文中最后在两种典型信道下对所提出的盲信道均衡算法进行了仿真,结果验证了上述性能.     

A direct approach to H2 optimal deconvolution ofperiodic digital channels

This paper studies the H₂ optimal deconvolution problem for periodic finite impulse response (FIR) and infinite impulse response (IIR) channels. It shows that the H₂ norm of a periodic filter can be directly quantified in terms of periodic system matrices and linear matrix inequalities (LMIs) without resorting to the commonly used lifting technique. The optimal signal reconstruction problem is then formulated as an optimization problem subject to a set of matrix inequality constraints. Under this framework, the optimization of both the FIR and IIR periodic deconvolution filters can be made convex, solved using the interior point method, and computed by using the Matlab LMI Toolbox. The robust deconvolution problem for periodic FIR and IIR channels with polytopic uncertainties are further formulated and solved, also by convex optimization and the LMIs. Compared with the lifting approach to the design of periodic filters, the proposed approach is simpler yet more powerful in dealing with multiobjective deconvolution problems and channel uncertainties, especially for IIR deconvolution filter design. The obtained solutions are applied to the design of an optimal filterbank yielding satisfactory performance     

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     

The expectation-maximization Viterbi algorithm for blind adaptive channel equalization

A blind maximum-likelihood equalization algorithm is described and its convergence behavior is analyzed. Since the algorithm employs the Viterbi algorithm (VA) to execute the expectation step of the expectation-maximization (EM) iteration, we call it the expectation-maximization Viterbi algorithm (EMVA). An EMVA-based blind channel-acquisition technique which achieves a high global convergence probability is developed. The performance of the method is evaluated via numerical simulations under static and fading channel conditions.     

Multichannel MLSE equalizer with parametric FIR channelidentification

We propose a parametric finite impulse response (FIR) channel identification algorithm, apply the algorithm to a multichannel maximum likelihood sequential estimation (MLSE) equalizer using multiple antennas, and investigate the improvement in the overall bit error rate (BER) performance. By exploring the structure of the specular multipath channels, we are able to reduce the number of channel parameters to provide a better channel estimate for the MLSE equalizer. The analytic BER lower bounds of the proposed algorithm as well as those of several other conventional MLSE algorithms in the specular multipath Rayleigh-fading channels are derived. In the derivation, we consider the channel mismatch caused by the additive Gaussian noise and the finite-length channel approximation error. A handy-to-use simplified BER lower bound is also derived. Simulation results that illustrate the BER performance of the proposed algorithm in the global system for mobile communications (GSM) system are presented and compared to the analytic lower bounds     

Signal Processing by Generalized Receiver in?DS-CDMA Wireless Communication Systems with?Frequency-Selective Channels

The generalized receiver (GR) based on a generalized approach to signal processing (GASP) in noise is investigated in a direct-sequence code-division multiple access (DS-CDMA) wireless communication system with frequency-selective channels. We consider four avenues: linear equalization with finite impulse response (FIR) beamforming filters; channel estimation and spatially correlation; optimal combining; and partial cancellation. We investigate the GR with simple linear equalization and FIR beamforming filters. Numerical results and simulation show that the GR with FIR beamforming filters surpasses in performance the optimum infinite impulse response beamforming filters with conventional receivers, and can closely approach the performance of GR with infinite impulse response beamforming filters. Channel estimation errors are taken into consideration so that DS-CDMA wireless communication system performance will not be degraded under practical channel estimation. GR takes an estimation error of a maximum likelihood (ML) multiple-input multiple-output (MIMO) channel estimation and GR spatially correlation into account in computation of minimum mean square error (MMSE) and log-likelihood ratio (LLR) of each coded bit. The symbol error rate (SER) performance of DS-CDMA employing GR with a quadrature sub-branch hybrid selection/maximal-ratio combining (HS/MRC) scheme for 1-D modulations in Rayleigh fading is obtained and compared with that of conventional HS/MRC receivers. Procedure of selecting a partial cancelation factor (PCF) for the first stage of a hard-decision partial parallel interference cancellation (PPIC) of the GR employed in DS-CDMA wireless communication system is proposed. A range of optimal PCFs is derived based on the Price’s theorem. Computer simulation results show superiority in bit error rate (BER) performance that is very close to that potentially achieved and surpasses the BER performance of the real PCF for DS-CDMA systems discussed in literature.     

Optimal design and placement of pilot symbols for channel estimation

The problem of designing and placing pilot symbols for the estimation of frequency-selective random channels is considered. The channel is assumed to be a block-fading model with finite impulse response (FIR). For both single-input single-output (SISO) and multiple-input multiple-output (MIMO) channels, under the assumption of independent and identical distributed channel taps, the Cramer-Rao bound (CRB) on the mean square error (MSE) of semi-blind channel estimators is derived and minimized with respect to pilot symbols and their placement. It is shown that the optimal strategy is to place pilot symbols satisfying certain orthogonality condition in such a way that data and pilot symbols with higher power are in the middle of the packet. The results also indicate that the optimal pilot placements are independent of channel probability distribution. For constant modulus symbols, we show that the quasi-periodic placement and its generalization in the multiuser case turn out to be optimal. We further consider estimating channels with correlated taps and show that the previous placement strategy is also optimal among orthogonal pilot sequences.     

Performance limit of finite wordlength FIR digital filters

In many practical situations, it is necessary to represent the coefficients of a finite impulse response (FIR) digital filter by a finite number of bits. This not only degrades the filter frequency response but also introduces a theoretical limit on the performance of the filter. Derivation of a lower bound on filter degradation is the purpose of this paper. We consider a general case of a length N filter with a discrete set of allowable coefficients. A theorem that gives the lower bound on the increase in minimax approximation error that is caused by the finite wordlength restriction is presented. Its extension and application to filter design cases is demonstrated. The importance of this bound is not only theoretical. Its practical effectiveness is shown in the algorithm for optimal finite wordlength FIR filter design where it significantly reduces the amount of computation.     

B-spline design of maximally flat and prolate spheroidal-type FIRfilters

A digital FIR filter is described that offers excellent passband and stopband characteristics for general applications. Design formulae include parameters that adjust the magnitude response from one having characteristics like the maximally flat designs of Hermann (1971) and Kaiser (1975, 1979) to one having characteristics like the minimum-sidelobe energy approximations of Kaiser and Saramaki (1989). The impulse response coefficients are more straightforward to obtain than these filter designs while offering preferable response characteristics in many instances. Unlike FIR filters designed by window- or frequency-sampling methods, the filter coefficients are determined from the inverse Fourier transform in closed form once B-splines have been used to replace sharp transition edges of the magnitude response. Although the filters are developed in the frequency domain, a convergence window is identified in the convolution series and compared with windows of popular FIR filters. By means of example, adjustment of the transitional parameter is shown to produce a filter response that rivals the stopband attenuation and transition width of prolate spheroidal designs. The design technique is extended to create additional transitional filters from prototype window functions, such as the transitional Hann window filter. The filters are particularly suitable for precision filtering and reconstruction of sampled physiologic and acoustic signals common to the health sciences but will also be useful in other applications requiring low passband and stopband errors