Least Square Channel Estimation Research Articles

Least Square Channel Estimation for Two-Way Relay MIMO OFDM Systems

This letter considers the channel estimation for two-way relay MIMO OFDM systems. A least square (LS) channel estimation algorithm under block-based training is proposed. The mean square error (MSE) of the LS channel estimate is computed, and the optimal training sequences with respect to this MSE are derived. Some numerical examples are presented to evaluate the performance of the proposed channel estimation method.

Joint Channel Estimation and Multiuser Detection for SDMA/OFDM Based on Dual Repeated Weighted Boosting Search

A joint channel estimation and multiuser detection (JCEMUD) scheme is proposed for multiuser multiple-input-multiple-output (MIMO) space-division multiple-access/orthogonal frequency-division-multiplexing (SDMA/OFDM) systems. We design a dual repeated weighted boosting search (DRWBS) scheme for JCEMUD, which is capable of providing “soft” outputs, which are directly fed to the forward error correction (FEC) decoder. The proposed DRWBS-JCEMUD scheme iteratively estimates the channel impulse responses and detects the users' transmitted signals while exploiting the error correction capability of an FEC decoder to iteratively exchange information between the detector and the estimator. Furthermore, the proposed DRWBS-JCEMUD scheme is capable of providing the log-likelihood ratios of the coded bits at low computational complexity (comparable with the single-user scenario), which can directly be fed to the FEC decoder. The simulation results demonstrate that the proposed DRWBS-JCEMUD scheme is capable of attaining a mean square error performance close to that of the ideal scenario of the least-square channel estimator associated with 100% pilot overhead and narrows the discrepancy with respect to the optimal maximum-likelihood (ML) MUD associated with perfect channel knowledge. As an example, at E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> /N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> = 10 dB, a factor-of-0.756 complexity reduction was achieved at the cost of a 1-dB performance penalty, in comparison with the ML-MUD.

An Efficient Pilot Design Method for OFDM-Based Cognitive Radio Systems

In orthogonal frequency-division multiplexing (OFDM)-based cognitive radio (CR) systems, the subcarriers already occupied by the primary users cannot be used by the secondary users. This leads to possibly non-contiguous positions of the available subcarriers for the secondary users. The conventional pilot design methods are no longer effective for such systems. In this paper, we propose a new practical pilot design method for OFDM-based CR systems. We first formulate the pilot design as a new optimization problem. Instead of minimizing the mean-square error (MSE) of the least-squares (LS) channel estimator, we minimize an upper bound which is related to this MSE. We then propose an efficient scheme to solve the optimization problem. Specifically, the pilot indices are obtained sequentially by solving a series of one-dimensional optimization problems of significantly lower complexity. The computational complexity of the proposed scheme is low since it only involves real additions. Simulation results show that the pilot index sequences obtained by the proposed method exhibit significantly better performance than those obtained by existing pilot design methods.

Zero padded suffix aided subspace-based narrowband interference detected adaptive channel estimation for MB-OFDM UWB systems

The ECMA-368 standard specifies multiband orthogonal frequency division multiplexing (MB-OFDM) as the definitive technology for high rate ultra-wideband (UWB) communications. Like other wireless systems, the performance of a correct data signals detection and decoding in MB-OFDM UWB is reduced by narrowband interference (NBI). A more specific problem of severity arises when interferences are present during the channel estimation process, since this eventually results to severe degradation in the performance of signal reconstruction in the whole packet layer convergence protocol (PLCP) and service data unit (PSDU). In this article, we propose an improved channel estimation technique for OFDM-based UWB systems in presence of NBI. Several steps have been carried out to achieve this purpose. First, the location of center frequency of NBI is found out through zero padded suffix (ZPS) aided subspace-based method. Secondly, we propose an adaptive band select and replace (ABSR) scheme to eliminate NBI based on frequency-domain redundancy (FR) property we introduce into preamble symbols during transmission. Thirdly, we perform least-square (LS) channel estimation on NBI-free received preamble symbols to get the estimated channel at each subcarrier. Fourthly, low rank least square minimum mean squared error (LMMSE) channel estimation is performed using this LS channel estimation. Lastly, Blackman windowing is applied on low rank LMMSE channel to reduce the spectral leakage and thus to increase the channel estimation accuracy. Link level simulation (LLS) urges that our proposed technique has improved performances. Key words: Ultra-wideband (UWB), channel estimation, multiband orthogonal frequency division multiplexing (MB-OFDM), narrowband interference (NBI), ECMA-368, wireless personal area network (WPAN).

Semi-Blind Joint Channel Estimation and Data Detection for Space-Time Shift Keying Systems

A low-complexity semi-blind joint channel estimation and data detection scheme is proposed for space-time shift keying (STSK) based multiple-input multiple-output systems. The minimum number of STSK training blocks, which is related to the number of transmitter antennas, is first utilized to provide a rough initial least square channel estimate (LSCE). Then low-complexity single-stream maximum likelihood (ML) data detection is carried out based on the initial LSCE and the detected data are employed to refine the decision-directed LSCE. It is demonstrated that a few iterations are sufficient to approach the optimal ML detection performance obtained with the perfect channel state information.

On the Robustness of MIMO LMMSE Channel Estimation

The robustness of the linear minimum mean square error (LMMSE) channel estimator is studied with respect to the reliability of the estimated channel correlation matrix used for its implementation. The analysis is of interest in practical applications of multiple-input multiple-output (MIMO) systems, where a perfect estimate of the channel correlation matrix is not available. The channel estimation mean square error (MSE) is analytically analyzed assuming a general structure for the estimated channel correlation matrix used to implement the LMMSE channel estimator. The obtained results are successively detailed to the case of channel correlation matrices derived by sample correlation estimation methods. It is observed that the use of a coarse estimate of the channel correlation matrix can lead to a severe degradation on the LMMSE channel estimator performance, whereas the simpler least-square (LS) channel estimator may provide comparatively better results. Nevertheless, it is shown that a robust approach, although suboptimal, relies on implementing the LMMSE channel estimator by assuming transmissions over uncorrelated channels, since, with such an assumption, the resulting estimation MSE is certainly smaller than for the LS channel estimator.

Power Allocation for Channel Estimation and Performance of Mismatched Decoding in Wireless Relay Networks

This paper is concerned with power allocation (PA) among the source and the relays of wireless relay networks to minimize the mean-square error (MSE) of the channel estimation when distributed space-time coding (DSTC) is applied. The optimal PA scheme is numerically obtained by means of geometric programming for the least-squares (LS) estimator, and a closed-form near-optimal PA scheme is also suggested. The impact of imperfect channel estimation on the error performance of DSTC is analyzed for both the LS and linear minimum MSE (LMMSE) channel estimators. It is proved that mismatched decoding of DSTC is able to achieve the same diversity order as coherent decoding of DSTC. Furthermore, when the closed-form PA obtained in the training phase is applied to the transmission phase, mismatched decoding is able to achieve a significant coding gain over the equal-PA scheme (which assigns half of the total power to the source and equally shares the other half to all the relays).

LDPC 복호와 MAP 등화기를 결합한 DVB-T2 터보 등화기법의 성능분석

In this paper, a turbo equalizer is proposed for the digital video broadcasting for terrestrial - 2nd generation (DVB-T2) system. The proposed turbo equalizer is consisted with the maximum a posteriori (MAP) and low density parity check (LDPC) decoder. The channel information for the soft-input-soft-output (SISO) MAP equalizer is based on the least square (LS) channel estimator. The performance is analyzed through computer simulations in terms of the iteration number. Keyword : DVB-T2, Map Detector, LDPC Decoder, LS channel estimator

Sparse Channel Estimation for Multicarrier Underwater Acoustic Communication: From Subspace Methods to Compressed Sensing

In this paper, we investigate various channel estimators that exploit channel sparsity in the time and/or Doppler domain for a multicarrier underwater acoustic system. We use a path-based channel model, where the channel is described by a limited number of paths, each characterized by a delay, Doppler scale, and attenuation factor, and derive the exact inter-carrier-interference (ICI) pattern. For channels that have limited Doppler spread we show that subspace algorithms from the array processing literature, namely Root-MUSIC and ESPRIT, can be applied for channel estimation. For channels with Doppler spread, we adopt a compressed sensing approach, in form of Orthogonal Matching Pursuit (OMP) and Basis Pursuit (BP) algorithms, and utilize overcomplete dictionaries with an increased path delay resolution. Numerical simulation and experimental data of an OFDM block-by-block receiver are used to evaluate the proposed algorithms in comparison to the conventional least-squares (LS) channel estimator. We observe that subspace methods can tolerate small to moderate Doppler effects, and outperform the LS approach when the channel is indeed sparse. On the other hand, compressed sensing algorithms uniformly outperform the LS and subspace methods. Coupled with a channel equalizer mitigating ICI, the compressed sensing algorithms can effectively handle channels with significant Doppler spread.

Optimal training design and placement for MIMO orthogonal frequency division multiplexing channel estimation

This paper deals with optimal training design and placement over multiple orthogonal frequency division multiplexing (OFDM) symbols for the least squares (LS) channel estimation in multiple-input multipleoutput (MIMO) OFDM systems. First, the optimal pilot sequences over multiple OFDM symbols are derived by co-cyclic Jacket matrices based on the minimum mean square error (MSE) of the LS channel estimation. Then, an enhanced channel estimation method using sliding window is proposed to improve further the performance for the optimal pilot sequences in fast-varying channels. Simulation results show that the enhanced method can efficiently improve the performances for the optimal pilot sequences over two and four OFDM symbols, especially in fast-varying channels.

Fast channel estimation using maximum-length shift-register sequences

Least-square channel estimation techniques usually involve the large-dimensional matrix inversion, whose heavy computational complexity cannot be extendable for long channel filters. Maximum-Length Shift-Register (MLSR) sequences, or m-sequences, possess the well controlled second order cyclic statistics and have been used as the training sequences for least-square channel estimators. In this paper, we analyse the statistical characteristics of m-sequences and design a corresponding highly computationally-efficient channel estimation algorithm. Two crucial measures, namely mean-square error and computational complexity, are evaluated thereupon. It can be justified that our proposed algorithm can achieve both efficiency and satisfactory performance for communication channel estimation.

Blind turbo receivers with fast least-squares channel estimation and soft-feedback equalisation

Low-complexity blind turbo receivers composed of a soft-feedback equaliser (SFE) and fast least-squares (FLS) channel estimators are proposed. To reduce the complexity of the SFE computation, a function approximation is proposed instead of numerical algorithms in a specific step of the equaliser's computation. Concerning FLS channel estimators, a specific filter parameters initialisation procedure is proposed in each turbo iteration to avoid possible numerical instabilities. Estimation of noise variance is also considered. The proposed scheme can perform as the turbo equaliser with perfect channel knowledge from a certain signal-to-noise ratio.

퍼지 추론법을 적용한 OFDM 시스템의 LS(Least Square) 채널추정 기법

본 논문에서는 최근 여러 분야에서 불확실성에 대한 예측을 위해 사용되는 Fuzzy 추론법을 OFDM(Othgonal Frequency Division Multiplexing)의 채널추정 방식에 적용함으로써 향상된 성능과 낮은 복잡도를 갖는 새로운 채널추정 방식을 제안하였다. 제안된 방식은 LS(Least Square) 채널추정 이전에 Pilot을 이용하여 Fuzzy추론법에 의하여 채널의 통계적 특성을 계산하고 이에 대한 보간을 해 줌으로써 채널추정 성능을 향상시키는 방식이다. QPSK(Quadrature Phase Shift Keying)를 적용한 시뮬레이션 결과 제안된 채널추정 방식은 MSE(Mean Square Error)가 <TEX>$10^{-3}$</TEX>인 지점에서 MMSE(Mimimum Mean Square Error) 채널추정 방식보다는 약 1.3 dB 정도 성능이 열화되는 것으로 나타났지만 LS 채널 추정 방식과 비교하면 약 5.5 dB 정도의 성능 이득이 있는 것으로 분석되었으며, SER(Symbol Error Rate)은 SNR(Signal to Noise Ratio)이 20 dB인 지점에서 MMSE 채널추정 방식과 제안된 채널추정방식이 각각 <TEX>$10^{-1.96}$</TEX>, <TEX>$10^{-1.93}$</TEX> 정도로 유사한 성능을 보이는 것으로 분석되었고, LS 채널추정 방식 보다 약 <TEX>$10^{-0.35}$</TEX> 정도 제안된 방식의 성능이 향상된 것으로 분석되었다. In this paper, the new channel estimation was proposed that have the low complexity and high performance using Fuzzy inference method uses recently from various field for estimation about uncertainty in channel estimation of OFDM. Proposed method is channel estimation performance improve, calculation and interpolation for statistics character of channel using the pilot before LS channel estimation by Fuzzy inference method. Simulation result in QPSK proposed channel estimation method shows the enhancement of 5.5dB compared to the LS channel estimation and the deterioration of 1.3dB compared to the MMSE channel estimation in mean square error point <TEX>$10^{-3}$</TEX>. symbol error rate shows similarity performance the MMSE <TEX>$10^{-1.96}$</TEX>, proposed channel estimation <TEX>$10^{-1.93}$</TEX> and enhancement of <TEX>$10^{-0.35}$</TEX> compared to the LS channel estimation in signal to noise ratio point 20dB.

Least-squares channel estimation assisted by self-interference cancellation for mobile pseudo-random-postfix orthogonal-frequency-division multiplexing applications

A least-squares (LS) channel estimation (CE) technique is investigated to apply pseudo-random-postfix orthogonal-frequency-division multiplexing (PRP-OFDM) communications onto mobile applications, which often operate on a rapidly time-varying frequency-selective fading channel. Since conventional techniques exploiting a moving averager cannot function on a rapidly time-varying channel, the proposed technique takes advantage of several self-interference cancellation (SIC) methods to effectively and timely reduce inter-path interference, inter-symbol interference (ISI) and inter-block interference (IBI). The proposed technique can therefore overcome frequency selectivity caused by multipath fading and time selectivity caused by mobility; in particular, OFDM communication is often anticipated to operate in environments where both wide Doppler spread and long delay spread exist. Meanwhile, lower mean-square estimation errors, lower error probabilities and lower error floors can also be achieved using the proposed technique. Since conventional techniques based on minimum-mean-square-error (MMSE) CE usually highly require a priori channel information or many training preambles, a generic estimator assisted from LS CE is exploited as it can be performed serially, block by block, to reduce computational complexity. Extensive computer simulations in conjunction with strict statistical analysis are carried out to verify the improvements provided by the proposed technique.

Channel estimation assisted by postfixed pseudo-noise sequences padded with zero samples for mobile orthogonal-frequency-division-multiplexing communications

A channel estimation (CE) technique that uses a postfixed pseudo-random sequence padded with zero samples is investigated to extend pseudo-random-postfix orthogonal-frequency-division-multiplexing (PRP-OFDM) communications onto mobile applications. The proposed technique takes advantage of pseudo-noise sequences periodically inserted after each OFDM block within the original guard interval (GI) in conventional zero-padded OFDM (ZP-OFDM) or within the original cyclic prefix (CP) in conventional CP-OFDM. This allows accurate estimation of the channel impulse response. In addition, the proposed technique takes advantage of the null samples padded after the PN sequences for reducing inter-symbol interference occurring with the CEs and with the overlap-add information detection in the conventional PRP-OFDM. The proposed technique successfully applies either (1) a least-squares (LS) CE with assistance from decision-directed data or (2) an approximate LS CE method onto PRP-OFDM-like communications for the purpose of improving CE performance on rapid time-varying channels. Computer simulations in conjunction with statistical analysis assess the performance evaluation of the proposed technique and show that it can achieve lower mean-square estimation errors and lower error probabilities in mobile environments.

PERFORMANCE AND COMPLEXITY IMPROVEMENT OF TRAINING BASED CHANNEL ESTIMATION IN MIMO SYSTEMS

Multiple-input multiple-output (MIMO) systems play a vital role in fourth generation wireless systems to provide advanced data rate. In this paper, a better performance and reduced complexity channel estimation method is proposed for MIMO systems based on matrix factorization. This technique is applied on training based least squares (LS) channel estimation for performance improvement. Experimentation results indicate that the proposed method not only alleviates the performance of MIMO channel estimation but also signiflcantly reduces the complexity caused by matrix inversion. The performance evaluations are validated through computer simulations using MATLAB R ∞ 7.0 in terms of bit error rate (BER). Simulation results show that the BER performance and complexity of the proposed method clearly outperforms the conventional LS channel estimation method.

Turbo channel estimation and equalisation for a superposition-based cooperative system

This study investigates the superposition-based cooperative transmission system. In this system, a key point is for the relay node to detect data transmitted from the source node. This issued was less considered in the existing literature as the channel is usually assumed to be flat fading and a priori known. In practice, however, the channel is not only a priori unknown but subject to frequency selective fading. Channel estimation is thus necessary. Of particular interest is the channel estimation at the relay node which imposes extra requirement for the system resources. The authors propose a novel turbo least-square channel estimator by exploring the superposition structure of the transmission data. The proposed channel estimator not only requires no pilot symbols but also has significantly better performance than the classic approach. The soft-in-soft-out minimum mean square error (MMSE) equaliser is also re-derived to match the superimposed data structure. Finally computer simulation results are shown to verify the proposed algorithm.

Least-Squares Channel Estimation for Mobile OFDM Communication on Time-Varying Frequency-Selective Fading Channels

A least-squares (LS) channel estimation (CE) technique for mobile orthogonal frequency-division multiplexing (OFDM) communications over a rapidly time-varying frequency-selective fading channel is investigated in this paper. The proposed technique keeping the comb-type pilot arrangement can achieve a low error probability by accurately estimating channel impulse response (CIR) and effectively tracking rapid CIR time variations. The LS CE technique proposed here is conducted in the time domain (TD). Meanwhile, a generic estimator is serially performed block by block without assistance from a priori channel information and without increasing computational complexity. By taking advantage of linearly frequency-modulated (LFM) or pseudorandom signals transceived for jointly sounding pilot subchannels, the proposed LS CE can inherently perform pseudonoise (PN) matched filtering (MF) to suppress multipath interference (MPI) caused by frequency-selective fading and intercarrier interference (ICI) resulting from data subchannels. The optimality of the proposed technique is verified by taking Cramer-Rao lower bounds (CRLBs) into comparison both on noise- and interference-dominant signal-to-noise ratio (SNR) conditions. In addition, the dual optimality of the LFM and PN pilot symbols is verified for both TD and frequency-domain (FD) CEs. Furthermore, the proposed technique also exhibits good resistance against residual timing errors occurring with the discrete Fourier transform (DFT) demodulation. Extensive computer simulations in conjunction with statistical derivations show the superiority of the proposed technique.

Soft Decision Directed Channel Estimation with Interference Cancellation for a MIMO System Using Iterative Equalization and Decoding

This paper proposes a novel channel estimation method for iterative equalization in MIMO systems. The proposed method incorporates co-channel interference (CCI) cancellation in the channel estimator and the channel estimation is successively performed with respect to each stream. Accuracy of channel estimation holds the key to be successfully converged the iterative equalization and decoding process. Although the channel estimates can be re-estimated by means of LS (Least Square) channel estimation using tentative decisions obtained in the iterative process, its performance is severely limited in a MIMO system because of erroneous decisions and ill-conditioned channel estimation matrix. The proposed method can suppress the above effects by means of CCI cancellation and successive channel estimation. Computer simulation confirms that the proposed channel estimation method can accurately estimate the channel, and the receiver with iterative equalization and the proposed method achieves excellent decoding performance in a MIMO-SM system.

Optimal diversity combining based on linear estimation of rician fading channels

Optimal receiver diversity combining employing linear channel estimation is examined. Based on the statistical properties of least-squares (LS) and minimum mean square error (MMSE) channel estimation, an optimal diversity receiver for wireless systems employing practical linear channel estimation on Rician fading channels is proposed. The new receiver structure includes the conventional maximal ratio combining receiver as a special case. Exact analytical expressions for the symbol error rates (SERs) of LS and MMSE channel estimation aided optimal diversity combining are derived. It is shown that, if an optimal detector is used, an MPSK wireless system with MMSE channel estimation has the same SER when the MMSE channel estimation is replaced by LS estimation. This is an interesting counterexample to the common perception that channel estimation with smaller mean square error leads to smaller SER. Extensive simulation results validate the theoretical results.