Length Of Channel Impulse Response Research Articles

Adaptive threshold for discrete fourier transform‐based channel estimation in generalized frequency division multiplexing system

AbstractEven though generalized frequency division multiplexing is an alternative waveform method expected to replace the orthogonal frequency division multiplexing in the future, its implementation must alleviate channel effects. Least‐squares (LS), a low‐complexity channel estimation technique, could be improved by using the discrete Fourier transform (DFT) without increasing complexity. Unlike the usage of the LS method, the DFT‐based method requires the receiver to know the channel impulse response (CIR) length, which is unknown. This study introduces a simple, yet effective, CIR length estimator by utilizing LS estimation. As the cyclic prefix (CP) length is commonly set to be longer than the CIR length, it is possible to search through the first samples if CP is larger than a threshold set using the remaining samples. An adaptive scale is also designed to lower the error probability of the estimation, and a simple signal‐to‐interference‐noise ratio estimation is also proposed by utilizing a sparse preamble to support the use of the scale. A software simulation is used to show the ability of the proposed system to estimate the CIR length. Due to shorter CIR length of rural area, the performance is slightly poorer compared to urban environment. Nevertheless, satisfactory performance is shown for both environments.

Adaptive Channel Estimation for OFDM Systems Using CIR Length Estimate

This letter addresses adaptive channel estimation for OFDM systems to reduce computational complexity. There are numerous methods suggested for low-complexity channel estimation, but some of them still suffer from a considerable complexity or performance degradation due to the channel energy leakage. We present an adaptive channel estimator based on the channel impulse response (CIR) length estimate to reduce the complexity without any performance degradation. We first introduce a simple and efficient method based on the sequential hypothesis test (SHT) to estimate the CIR length and then apply it to the adaptive implementation of the SVD-based LMMSE estimator. Simulation results demonstrate that the SHT method performs well with very low complexity and that the adaptive estimator not only reduces the complexity significantly but also provides better performance than the fixed estimators.

MIMO Time Domain Equalizer Design for Long Reach xDSL MIMO Channel Shortening

In discrete multi-tone (DMT) transmission based digital subscriber line (DSL) systems, a cyclic prefix (CP) is added to each symbol before transmission, where the length of the CP is larger than the estimated channel impulse response (CIR) length. This ensures the elimination of inter-symbol interference (ISI) and inter-carrier interference (ICI) between the carriers of the same symbol, and allows for single tap frequency domain equalizers and crosstalk cancellation at the receiver. Recently, long reach xDSL (LR-xDSL) has been proposed to extend the reach of conventional DSL systems. With the extended loop lengths, the required CP length increases, in order to match the larger CIR length. The longer CP adds a large overhead and results in overall throughput loss. A more efficient way to deal with extended loop lengths is to use a channel shortening filter - commonly referred as a time domain equalizer (TEQ), to reduce the length of the CIR to the length of CP. This paper focuses on minimum mean square error (MMSE) based multiple input multiple output (MIMO) TEQ design for LR-xDSL MIMO channel shortening. Constraints are applied to the minimization problem to eliminate the trivial solution. This paper proposes two new constraints for the MMSE based MIMO TEQ design for upstream scenarios, which result in a lower complexity and provide better (or similar) performance compared to existing MMSE based MIMO TEQ design methods. Furthermore, a diagonal MIMO TEQ with lower memory requirement and lower computational complexity is presented based on the proposed constraints, which can be applied in upstream as well as downstream scenarios.

A Conditional <inline-formula> <tex-math notation="LaTeX">${\ell}1$ </tex-math> </inline-formula> Regularized MMSE Channel Estimation Technique for IBI Channels

Inter-block-interference (IBI) caused in the pursuit of spectral efficiency can deteriorate channel estimation performance. For this problem, previously-proposed chained turbo estimation performs IBI cancelation by using the soft replica of the transmitted signal. The IBI cancelation technique can, however, suffer from a mean squared error (MSE) floor problem, since the soft replica is unavailable at the first turbo iteration. The IBI problem can be avoided by using channel impulse response length constraint. Nevertheless, as shown in this paper, the IBI avoidance approach is difficult to perform independently since it requires unbiased second-order statistics. This paper proposes, therefore, a new conditional $\ell 1$ regularized minimum mean square error channel estimation algorithm by jointly utilizing the IBI avoidance/cancelation and subspace techniques. Simulation results verify that the proposed algorithm solves the MSE floor problem, and, hence, improves the bit error rate convergence performance in realistic IBI channels including the effect of pulse shaping filters.

On the use of EMD based adaptive filtering for OFDM channel estimation

Hilbert Huang transform (HHT) based data driven empirical mode decomposition (EMD) in conjunction with adaptive filter (AF) is proposed for estimation of communication channel in OFDM system. EMD can be viewed as alike of wavelet decomposition which decomposes the signal of interest to intrinsic mode functions (IMF), whose basis function is derived from signal itself. In this method, the length of channel impulse response (CIR), is approximated using Akaike information criterion (AIC). Then the estimation of CIR is performed using adaptive filter with EMD decomposed IMF of the received OFDM symbol. Conventional AF uses random initial weight vector. The novelty of the proposed method lies in the fact that it uses decimated version of one of the decomposed IMFs of received OFDM symbol as initial weight vector. The selection of useful IMF component is done based on correlation and kurtosis measures. This makes the proposed EMD based AF method converge to minimum mean square error (MMSE) in less number of iterations resulting in almost 50% saving of computations. Bit error rate (BER), mean square error (MSE) and normalized root mean square error (NRMSE) are computed. The simulation studies established the efficacy of proposed method; and comparative studies under different modulation schemes and fading conditions revealed improved performance. Simulations have shown an average improvement of 3 dB in BER performance for proposed EMD based AF as compared to conventional AF.

Empirical Mode Decomposition based Adaptive Filtering for Orthogonal Frequency Division Multiplexing Channel Estimation

This paper presents an empirical mode decomposition (EMD) based adaptive filter (AF) for channel estimation in OFDM system. In this method, length of channel impulse response (CIR) is first approximated using Akaike information criterion (AIC). Then, CIR is estimated using adaptive filter with EMD decomposed IMF of the received OFDM symbol. The correlation and kurtosis measures are used to select the useful IMF component from among available IMFs. Conventional AF uses random initial weight vector. The novelty of the proposed method is that it uses decimated version of one of the decomposed IMFs of received OFDM symbol as initial weight vector. This makes the proposed EMD based AF method converge to minimum mean square error (MMSE) in less number of iterations resulting in almost 50% saving of computations. The simulation studies in terms of bit error rate (BER) and mean square error (MSE) calculations established the efficacy of proposed method; and comparative studies under different modulation schemes and fading conditions revealed improved performance.

Frequency-domain equalizers with zero restoration for zero-padded block transmission with high SNR

This paper focuses on the equalization of block transmissions with zero pad (ZP). If the channel impulse response length does not exceed the ZP length, it is possible to construct zero-forcing equalizers (ZFEs). Improved performance may be achieved using a minimum mean squared error (MMSE) equalizer. However, these equalizers are computationally intensive when a time-domain implementation is used. While the frequency-domain implementation of a ZFE has a lower complexity, it is prone to—potentially infinite—noise enhancement in the presence of spectral zeros. The MMSE equalizer in the frequency domain performs better by limiting the noise enhancement but still loses all information stored at the spectral zeros. This paper presents a method to exploit the redundancy of the padding to recover this lost information, leading to two new frequency-domain equalizers, a ZFE and an MMSE-like equalizer. These two equalizers are evaluated through simulations. They have a performance close to the time-domain equalizers, while maintaining the low complexity of the original frequency-domain equalizers. The equalizers are especially useful for scenarios with a high signal-to-noise ratio (SNR), where the performance is not limited by the presence of noise, but by the absence of the information stored in the spectral zeros. In practice, this means an SNR >30 dB. With minor modifications, the equalizers can also be applied if the ZP is replaced by a unique word (UW).

Performance of an ℓ1 Regularized Subspace-Based MIMO Channel Estimation With Random Sequences

The conventional $\ell2$ multiburst (MB) channel estimation can achieve the Cramer-Rao bound asymptotically by using the subspace projection. However, the $\ell2\;\text{MB}$ technique suffers from the noise enhancement problem if the training sequences (TSs) are not ideally uncorrelated. We clarify that the problem is caused by an inaccurate noise whitening process. The $\ell1$ regularized MB channel estimation can, however, improve the problem by a channel impulse response length constraint. Asymptotic performance analysis shows that the $\ell1\;\text{MB}$ can improve channel estimation performance significantly over the $\ell2\;\text{MB}$ technique in a massive multiple-input multiple-output system when the TSs are not long enough and not ideally uncorrelated.

Pilot Design Schemes for Sparse Channel Estimation in OFDM Systems

In this paper, we consider the pilot design based on the mutual incoherence property (MIP) for sparse channel estimation in orthogonal frequency-division multiplexing (OFDM) systems. With respect to the length of channel impulse response (CIR), we first derive a sufficient condition for the optimal pilot pattern generated from the cyclic different set (CDS). Since the CDS does not exist for most practical OFDM systems, we propose three pilot design schemes to obtain a near-optimal pilot pattern. The first two schemes, including stochastic sequential search (SSS) and stochastic parallel search (SPS), are based on the stochastic search. The third scheme called iterative group shrinkage (IGS) employs a tree-based searching structure and removes rows in a group instead of removing a single row at each step. We later extend our work to multiple-input-multiple-output (MIMO) systems and propose two schemes, i.e., sequential design scheme and joint design scheme. We also combine them to design the multiple orthogonal pilot patterns, i.e., using the sequential scheme for the first several transmit antennas and using the joint scheme to design the pilot pattern for the remaining transmit antennas. Simulation results show that the proposed SSS, SPS, and IGS converge much faster than the cross-entropy optimization and the exhaustive search and are thus more efficient. Moreover, SSS and SPS outperform IGS in terms of channel estimation performance.

A Simplified Time-Domain Channel Estimation Approach for OFDM System

OFDM usually incorporates pilot tones in the frequency domain (FD) or training symbols in the time-domain (TD) to facilitate channel estimation algorithms. TD channel estimation becomes more attractive in quasi-static channels because channel estimation scheme will optimize the spectral efficiency by re-using the training symbols designated for FD channel estimation. A channel estimation method based on time domain averaging algorithm is proposed. Due to the principle of centralized energy in time domain, the effective channel impulse response length can be detected by setting of threshold for the estimated channel impulse response length. Computer simulation demonstrates the performance of the proposed algorithms in terms of bit error rate performance.

Analysis and Design of Channel Estimation in Multicell Multiuser MIMO OFDM Systems

This paper investigates the uplink transmission in multicell multiuser multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems. The system model considers imperfect channel estimation, pilot contamination (PC), and multicarrier and multipath channels. Analytical expressions are first presented on the mean square error (MSE) of two classical channel estimation algorithms [i.e., least squares (LS) and minimum mean square error (MMSE)] in the presence of PC. Then, a simple H-infinity (H-inf) channel estimation approach is proposed to have good suppression to PC. This approach exploits the space-alternating generalized expectation-maximization (SAGE) iterative process to decompose the multicell multiuser MIMO (MU-MIMO) problem into a series of single-cell single-user single-input single-output (SISO) problems, which reduces the complexity significantly. According to the analytic results given herein, increasing the number of pilot subcarriers cannot mitigate PC, and a clue for suppressing PC is obtained. It is shown from the results that the H-inf has better suppression capability to PC than classical estimation algorithms. Its performance is close to that of the optimal MMSE as the length of channel impulse response (CIR) is increased. By using the SAGE process, the performance of the H-inf does not degrade when the number of antennas is large at the base station (BS).

LMMSE Channel Estimation Algorithm Based on Channel Autocorrelation Minimization for LTE-Advanced with Adaptive Guard Interval

In this paper, we propose an adaptive guard interval (GI) for LTE-advanced using channel impulse response (CIR) length estimation. The CIR length is estimated from the channel autocorrelation function. This estimate can be used to generate linear minimum mean square error filter coefficients for data subcarriers channel estimation and to adjust the GI length adaptively. The simulation results show that the improvement of mean square error for signal to noise ratio of 30 dB with CIR length estimation is about 10 dB when compared to conventional methods. Also, due to adaptive GI, the relative spectral efficiency can be increased by 0.11 compared to the conventional system with constant GI.

Comprehensive Impairment and Performance Description of Directly Modulated/Detected OOFDM Systems

In this paper, we obtain an analytical formulation to describe the penalty of the main important sources of impairment into the final performance in directly modulated/detected OOFDM systems. These equations aim to give a comprehensive description of deliberate clipping process at the OFDM transmitter, laser direct modulation, the impact of the channel impulse response length and the nonlinearity introduced by the laser, and the interplay between laser chirp and chromatic dispersion. Jointly, the provided expressions allow us, firstly, to analyze and understand the performance obtained in an OOFDM system in short-medium optical haul links, and, second, to optimize important transceiver parameters such as the clipping level, length of the cyclic pre/postfix, and laser modulation index.

Time-Domain Compression Based Analog Feedback for MIMO-OFDM Systems

We investigate the analog feedback of channel state information (CSI) in multiple-input-multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) based wideband wireless communication systems. In MIMO-OFDM systems, the amount of CSI to be fed back grows prohibitively with the number of subcarriers. A straightforward way of reducing the overhead is to feed back a sampled version of the CSI. But sampling based feedback suffers from the aliasing effect in some scenarios. We proved that the aliasing effect can not be eliminated unless the system feeds back more subcarrier channel matrices than the length of the time-domain channel impulse response. To improve the feedback quality and cope with the aliasing problem, we make use of the sparsity of the time-domain channel impulse response and propose a time-domain compression based analog feedback scheme. The proposed scheme overcomes the the aliasing problem, and achieves good performance.

Spectrally Efficient Frame-Format-Aided Turbo Equalization With Channel Estimation

Chained turbo equalization (CHATUE) has been recently recognized as a low-complexity frequency-domain turbo equalization technique that eliminates the necessity of transmitting the cyclic prefix (CP), and hence allows for spectrally efficient signaling in wireless communications. However, two issues arise from the original version of CHATUE (referred to as CHATUE1) as a consequence of eliminating the CP, which are the noise enhancement and the latency due to the time-concatenated structure. This paper proposes a new version of CHATUE (referred to as CHATUE2) to solve the noise enhancement problem. CHATUE2 retrieves the circulant structure of the channel matrix, originally inherent within the CP transmission, by utilizing composite replica signals that combine the received signals and the soft reference signals replicated from the log-likelihood ratio (LLR) fed back from the decoder. For this purpose, this paper determines the optimal combining ratio based on the minimum-mean-square-error (MMSE) criterion. CHATUE2 is hence able to achieve an improvement in bit-error-rate (BER) performance over CHATUE1. In addition, this paper provides a solution to solving the latency problem by making a practical assumption on the training sequence (TR) transmission, which is required to perform channel estimation generally, in practical systems. Furthermore, this paper proposes a new channel estimation technique, i.e., chained turbo estimation (CHATES), which improves the spectrum efficiency and asymptotically achieves the Cramer–Rao bound (CRB). CHATES assumes that the TR length is exactly equal to the channel impulse response (CIR) length, although the conventional technique requires twice as long or even longer TR lengths. Numerical results show that CHATUE2 with CHATES achieves a gain of 1 dB over conventional turbo equalization with a CP at a BER of $\hbox{10}^{-5}$ in realistic propagation scenarios represented by channel sounding measurement data and in model-based frequency-selective fading channels.

Blind Channel Shortening for Space-Time-Frequency Block Coded MIMO-OFDM Systems

This paper deals with multiple-input multiple-output (MIMO) broadband wireless communication systems, employing orthogonal frequency-division multiplexing (OFDM) with cyclic prefix (CP) in combination with space-time-frequency block coding (STFBC). In order to exploit the benefits of OFDM and STFBC in highly frequency-selective channels, without incurring in a significant increase of receiver complexity, a channel shortening prefilter is inserted at the receiver, aimed at reducing the length of the MIMO channel impulse response before CP removal. Two MIMO channel shorteners are proposed, both relying on linearly-constrained minimization of the mean-output-energy of the signal at the output of the channel shortener, where the linear constraints are optimally chosen so as to maximize the signal-to-noise ratio either at the output of the channel shortener or at the input of the STFBC maximum-likelihood decoder. Unlike other solutions proposed in the literature, these shortening designs are blind ones, i.e., a priori knowledge of the MIMO channel impulse response to be shortened is not required, and can be carried out in closed-form, i.e., iterative computation of the prefilter weights is not necessary. Numerical simulations show that, without a substantial increase in computational complexity, receivers equipped with the proposed blind channel shorteners pay only a negligible performance penalty with respect to non-blind channel shorteners, while being significantly more robust to finite sample-size effects.

Channel Estimation and Interference Cancellation for OFDM Systems Based on Total Least Squares Solution

In this paper, we study the effects of interference to channel estimation and present an iterative total least-squares algorithm for channel estimation by using the conjugate gradient method in time-varying multipath fading channels. The Doppler shift of fast-fading channels will generate inter-carrier interference (ICI), hence, degrade the performance of orthogonal frequency-division multiplexing (OFDM) systems. Furthermore, when the length of channel impulse response (CIR) overstep the duration of cyclic prefix (CP), which will cause inter-symbol interference (ISI) and degrade system performance severely. Conventional channel estimation and equalization schemes, if applied to this case of insufficient CP, suffer significant performance degradation. By ISI and ICI analysis, an Interference elimination technique is proposed for channel estimation. After analyzing perturbation of least squares problems, we present total least-squares (TLS) scheme to eliminate the ICI, ISI and noise. We present a short theoretical overview of the TLS problem. In our estimation, residual ISI and ICI are not being handled as a noise. Since the introduction of interference, the operation of matrix becomes perplexed. We implement the Conjugate gradient total least-squares method. Simulation results confirm the performance of Conjugate gradient total least-squares method and our theoretical analysis.

The impact of impulse postfix length on the BER performance of IP-OFDM systems

The impulse postfix OFDM (IP-OFDM) system exploits the IP, which consists of a high power impulse sample and several zero samples at the end of a zero padded-OFDM symbol block, to estimate channel impulse response (CIR) in time domain. In this paper, the impact of IP length on the BER performance of the IP-OFDM system is analyzed. According to the analytic results, the BER performance can be significantly degraded with both a shorter length of IP as well as a longer length of IP than that of the CIR. Thus, an adaptive IP scheme, which adjusts the length of IP adaptively depending on the length of CIR, is proposed to enhance the BER performance of IP-OFDM systems and its effectiveness is demonstrated by computer simulations. The BER performance of the IP-OFDM systems with the proposed adaptive scheme is compared with that of the conventional IP-OFDM system over various modulation schemes. Simulation results show that the IP-OFDM with the proposed scheme can achieve about 2 dB performance enhancement compared with that of conventional systems at BER=10−2. Copyright © 2010 John Wiley & Sons, Ltd.

Joint Blind Estimation of Channel Length and Noise Variance in OFDM Systems

The information of channel impulse response (CIR) length and noise variance play an important role in blind identification and equalization of wireless multipath channels. In orthogonal frequency division multiplexing (OFDM) systems, multipath fading channels introduce interference between adjacent symbols which can be prevented by inserting a cyclic prefix (CP) before each symbol. In this letter, we find that the interference power in the cyclic prefix (CP) interval and its variation can be used to estimate the CIR length and noise variance jointly and blindly.

Low complexity channel estimation method for TDS-OFDM based Chinese DTTB system

The Chinese digital television terrestrial broadcasting (DTTB) standard uses pseudo-noise (PN) sequence as guard interval (GI) and the training sequence. This PN sequence is used to do channel estimation and synchronization in the system. The existing channel estimation methods often have to adopt iterative scheme when the length of channel impulse response (CIR) is long, which will increase the receiver complexity dramatically. In this paper, a channel estimation scheme for time domain synchronous OFDM (TDS-OFDM) systems is proposed. Interference free CIR information can be obtained by constructing special correlation windows, rather than removing interference from the time domain sequences through iteration. Moreover, the estimation can be achieved by using correlation process. Comparing to conventional schemes, the proposed algorithm greatly reduces the computational complexity. Simulation results show that the proposed method can meet the requirement of the Chinese DTTB systems. And the scheme is also suitable for other communication OFDM systems with time domain sequence headers.